TURNING FLIGHT AND SIDESLIP IN HANG GLIDERS

Steve Seibel
steve at aeroexperiments.org

********** Note summer 2005 **********

Some sections of this article are now slightly obsolete. If you navigated directly to this article via a search engine, please visit my new intro page at www.aeroexperiments.org, and also see the associated site map at www.aeroexperiments.org/sitemap.shtml. Much of the material in this article has now been presented in a newer format--and in more managable pieces--elsewhere on the Aeroexperiments website. All the articles connected to Aeroexperiments site map, except those connected to the "Links to older content" page, represent my current thinking on these areas. I suggest that most readers will find that their time is better spent on the newer content of the Aeroexperiments website than on this article, but if you browse through the contents of this article, you may find something that particularly interests you and is not yet covered in the newer material.

The main body of this article has not been revised since July 2000. The article is based on a long series of careful experiments on the relationship between pitch inputs and slips and skids in hang gliders and sailplanes and airplanes. I still stand by all the main conclusions in this article about the relationship between pitch inputs and sideslips. The article also contains some interesting theory that has not yet been incorporated into the current main pages of the Aeroexperiments website. In particular, the subject of "airflow curvature" is explored in great detail. The article also contains some experimental observations that have not yet been incorporated into the main pages of the Aeroexperiments website.

There are some areas of this article that I would now present slightly differently. There are also some specific areas that I now know to be significantly in error. I've now tagged those areas with comments under the section headings.

The main area where my thinking has changed since this article was written concerns the aerodynamic coupling between slip (yaw) and roll. Since this article was last revised, I've carried out a long series of experiments using rudders and wing-tip-mounted drogue chutes to make yaw inputs on 4 different flex-wing hang gliders. As a result of those experiments, I now know that most modern flex-wing hang gliders have enough anhedral to create a negative coupling between slip (yaw) and roll rather than a positive coupling between slip (yaw) and roll at most airspeeds. This allows a glider to harness the sideways (slipping) airflow created by adverse yaw to create a helpful roll torque. In this article, I assumed the opposite: I assumed that most flex-wing hang gliders had enough sweep, and a small enough amount of anhedral, that they would exhibit a positive coupling between slip (yaw) and roll, so that the sideways (slipping) airflow created by adverse yaw would create an unfavorable roll torque. The comments that I made based on these particular assumptions are still relevant to modern rigid-wing hang gliders, which typically have swept wings and little or no anhedral (in fact most of these gliders have substantial dihedral). The comments that I made based on these particular assumptions are not relevant to modern flex-wing hang gliders, except in some cases, near the min. sink angle-of-attack. Interestingly, in several places in the article I do refer to a "hypothetical blade-wing hang glider" that has so much anhedral that it exhibits is a negative coupling between yaw and roll. I now realize that this is in fact a good description of nearly all modern flex-wing hang gliders, at least at angles-of-attack above the min. sink angle-of-attack. The major parts of this article that are affected by this error are the sections entitled "EFFECT OF SIDESLIP ON ROLL RESPONSE", "BALANCING YAW AND ROLL STABILITY", "EFFECT OF A FIN ON ROLL RATE", "BALANCE OF FORCES IN THE YAW AND ROLL AXES: THEORY", and "APPENDIX 2: TOWING AND LOCKOUT DYNAMICS".

One other area where I have changed my thinking--I no longer feel that the time lag that I observed between the initiation of a roll input, and the development of the maximum amount of sideslip, should be interpreted as evidence that the sideslip is being driven primarily by the glider's rotational inertia in the yaw axis, rather than by an aerodynamic adverse yaw torque.

And yet another area where I have changed my thinking--at several points in the older article I allowed for the possibility that some hang gliders might show a slight skid, rather than a slight slip, in a stabilized, constant-bank turn. I now feel that it is rather unlikely that any long-spanned, rudderless aircraft would orient itself in a skidding attitude rather than in a slipping attitude in a stabilized, constant-bank turn.

In all these areas where more recent experimental results or re-thinking have suggested that some of the original content was in error, I've now inserted explanatory tags. At some future date the article may be completely overhauled but at present all the older content still remains, except for the deletion of a few lines from the "Summary" section.

All these errors are completely peripheral to the main question addressed in the older article, which was "Does a hang glider tend to slip toward the low wing if the pilot pulls in the bar while banked, or if the pilot banks the glider without making a pitch 'coordination' input"? I still stand by the answers to this question that are presented in this article.

The most concise summary of what I've learned about the relationship between pitch inputs and sideslips may found in the related article on this website entitled "Notes for new hang glider and trike pilots--on sideslips"..

These comments and the associated notes embedded in the main text of the article were last updated August 26, 2005

********** End of note summer 2005 **********

TURNING FLIGHT AND SIDESLIP IN HANG GLIDERS (Summary)

Steve Seibel
steve at aeroexperiments.org
July 6, 2000 edition

A turning aircraft is sideslipping when the nose is angled toward the outside of the turn instead of facing directly into the direction of travel (i.e. the relative wind). This creates a sideways component in the airflow over the glider, which creates sideways aerodynamic forces that slow the turn rate. Since the aircraft is now overbanked for the turn rate, the pilot tends to fall toward the low side of the aircraft.

During experiments in my Spectrum, I found that a brief sideslip occurred whenever I rolled the glider into a turn. The major cause of this slip appeared to be rotational inertia in the yaw axis. A brief skid occurred whenever the bank angle was decreased. The amount of slip or slid depended on the roll rate, and the slip or skid largely vanished when the bank angle was stabilized. These effects can easily be seen in a yaw string (telltale) mounted in front of the pilot: whenever the bank angle steepens or shallows, the yaw string deflects away from the direction of roll.

Pitch inputs, which control the G-loading and airspeed in the turn, didn't influence the sideslip behavior (yaw coordination) of my hang glider. As I rolled the glider into a turn, I saw about the same amount of sideslip whether I coordinated the turn in the pitch axis by letting out the bar to hold the airspeed constant, or pitched the nose steeply up or down to bleed off airspeed or to put the glider into an accelerating dive. When I held the bank angle constant and pulled in the bar to pitch the nose down, I didn't see any sideslip as the glider accelerated. I also observed similar behavior in experiments in an airplane and a sailplane, but these ideas go against the conventional wisdom among hang glider pilots which holds that a turning glider will slip toward the low wing if the turn is not properly "coordinated" in the pitch axis and the G-loading (lift force) is inadequate for the bank angle. Many of the physical sensations that hang glider pilots often attribute to sideslip are really caused by dynamics in the pitch axis, involving the interplay of airspeed, angle-of-attack, G-loading, and the pitch attitude of the glider in space. When hang glider pilots talk about turn "coordination" via pitch inputs, they are actually referring mainly to these pitch dynamics rather than to yaw coordination and the prevention of sideslip. Many of our magazine articles and training handbooks show some confusion about this point.

Sideslips often coincide with changes in pitch attitude and accelerations in airspeed, because both pitch and yaw dynamics are driven by changes in bank angle.

In my Spectrum, in steady, constant-airspeed turns at a constant bank angle, including high-speed (diving) turns, a slip-skid ball or bubble indicator showed that the turn was coordinated in the yaw axis, with very little sideways airflow over the glider as a whole, and no apparent "push" upon the pilot toward either side of the aircraft. A yaw string near the front of the glider deflected slightly toward the outside of the turn, indicating a small sideways component in the airflow there. Some experiments were also made with yaw strings mounted on a "bowsprit" and on the extreme rear of the keel, to look at the curvature of the airflow (following the circumference of the turn).

For a much more condensed description of these ideas on sideslip and turns, see my articles in the February and July 2000 issues of "Hang Gliding".

 

TURNING FLIGHT AND SIDESLIP IN HANG GLIDERS

Steve Seibel
seibel999@hotmail.com
July 6, 2000 edition

 

Before we get started, here's an outline of this paper with links to each section. (This outline is also repeated at the end, in Appendix 6.)

(Summary)

(INTRODUCTION)

I PART ONE: PRACTICAL TURN "COORDINATION" AND PITCH AXIS DYNAMICS


I.A INTERPLAY OF ANGLE-OF-ATTACK, BANK ANGLE, AIRSPEED, AND G-LOADING
I.B WHAT DETERMINES ANGLE-OF-ATTACK?
I.C DO WE SEE THE SAME DYNAMICS IN POWERED AIRCRAFT ALSO?
I.D L/D RATIO AND LIFT FORCE
I.E BUT WHAT ABOUT SIDESLIP?

II PART TWO: A BRIEF OVERVIEW OF SIDESLIP DYNAMICS


II.A DEFINITION OF SIDESLIP
II.B DETECTING SIDESLIP IN HANG GLIDERS
II.C SOME COMMON IDEAS ABOUT SIDESLIP IN HANG GLIDERS
II.D SOME IDEAS ABOUT SIDESLIP IN 3-AXIS AIRCRAFT

III PART THREE: THE HEART OF THE MATTER: MAKING THE IN-FLIGHT EXPERIMENTS, INTERPRETING THE RESULTS, AND SUGGESTIONS FOR TEACHING


III.A TOOLS FOR INVESTIGATION
III.B MAKING THE TEST FLIGHTS
III.C ACTUAL DATA, AND INTERPRETATION OF RESULTS: SLIP-SKID BEHAVIOR OF MY GLIDER (Spectrum 144)
III.D DO THESE RESULTS APPLY TO OTHER HANG GLIDERS?
III.E SUGGESTIONS FOR TEACHING METHODS<
III.F SO WHY DO WE LET OUT THE BAR WHILE ROLLING INTO A TURN?
III.G ACTUAL DATA: SLIP-SKID BEHAVIOR OF SAILPLANES AND AIRPLANES
III.H ACTUAL DATA: TIMING OF PITCH AND YAW DYNAMICS IN AN AIRPLANE
III.I ACTUAL DATA: STEEP, REVERSING TURNS IN AN AIRPLANE


IV PART FOUR: EXPANDED THEORY OF TURNS AND SIDESLIP IN HANG GLIDERS

IV.A (GENERAL BACKGROUND)

IV.A.1 FRAME OF REFERENCE IN TURNING FLIGHT
IV.A.2 WHAT MAKES AN AIRCRAFT TURN?
IV.A.3 EFFECT OF SIDESLIP ON TURN RATE
IV.A.4 MORE ABOUT TORQUE
IV.A.5 REFERENCE FRAME IN A SIDESLIP, AND GENERATION OF SIDEWAYS FORCES AND DRAG
IV.A.6 HOW DOES A HANG GLIDER PRODUCE A SIDEWAYS AERODYNAMIC FORCE IN A SLIP?


IV.B DYNAMICS WHILE THE BANK ANGLE AND AIRSPEED ARE CHANGING:


IV.B.1 SIDESLIP DUE TO YAW ROTATIONAL INERTIA
IV.B.2 ADVERSE YAW
IV.B.3 CONSIDERING ADVERSE YAW AND YAW ROTATIONAL INERTIA TOGETHER
IV.B.4 EFFECT OF SIDESLIP ON ROLL RESPONSE
IV.B.5 BALANCING YAW AND ROLL STABILITY
IV.B.6 ANHEDRAL EFFECTS AND POSSIBLE LINKS TO PITCH INPUTS
IV.B.7 EFFECT OF A FIN ON ROLL RATE
IV.B.8 WHY DO AIRSPEED CHANGES AND SIDESLIPS OCCUR TOGETHER? A COMPLETE DESCRIPTION OF THE DYNAMICS IN THE PITCH AND YAW AXES AS THE GLIDER IS ROLLED INTO A TURN
IV.B.9 FUNDAMENTAL RELATIONSHIPS: DOES AN "IMBALANCED" G-LOADING CREATE A SIDEWAYS FORCE ON THE PILOT?
IV.B.10 FUNDAMENTAL RELATIONSHIPS: WHY DOESN'T THE AIRCRAFT SLIP TOWARD THE LOW WING WHEN THE G-LOADING IS INADEQUATE IN A TURN?
IV.B.11 FUNDAMENTAL RELATIONSHIPS: HOW TO DRAW YOUR OWN VECTOR DIAGRAMS FOR TURNING FLIGHT
IV.B.12 MORE VECTOR DIAGRAMS


IV.C DYNAMICS IN STEADY TURNS AT CONSTANT AIRSPEED AND BANK ANGLE:


IV.C.1 AIRFLOW CURVATURE IN TURNING FLIGHT
IV.C.2 AIRFLOW CURVATURE AND SIDESLIP: OBSERVED EFFECTS
IV.C.3 BALANCE OF FORCES IN THE YAW AND ROLL AXES: THEORY
IV.C.4 BALANCE OF FORCES IN THE YAW AND ROLL AXES: OBSERVED EFFECTS
IV.C.5 IS THERE A BENEFIT TO A SKIDDING TURN IN A HANG GLIDER?
IV.C.6 EFFECT OF A FIN ON HANDLING IN THERMAL TURNS


V. THAT'S ALL FOLKS (except appendices...)
VI. (APPENDICES)


VI.A APPENDIX 1: A NEW CLOUD FLYING "INSTRUMENT"
VI.B APPENDIX 2: TOWING AND LOCKOUT DYNAMICS
VI.C APPENDIX 3: SLIPS IN AIRCRAFT WITH RUDDERS
VI.D APPENDIX 4: ESTIMATING THE AERODYNAMIC FORCES PRODUCED BY A SIDESLIP
VI.E APPENDIX 5: COMMENTS ON "HANG GLIDER TURN PERSPECTIVES"
VI.F APPENDIX 6: AN OUTLINE OF THIS PAPER

 

INTRODUCTION

How are the pitch and yaw axes interconnected in hang gliders? What causes a sideslip? What do we mean when we talk about turn coordination in a rudderless aircraft? I hope that this discussion of turning flight and sideslip will be illuminating to anyone who has mused upon these questions. I will provide a theoretical background, and will also present some experimental data on the sideslip characteristics of my hang glider, a sailplane, and an airplane.

My thinking on this subject has always been motivated by the assumption that all forms of fixed-wing flight are closely related in their dynamics. It's not my goal to dictate terminology or to get in the way of those who prefer to fly by pure intuition. But some pilots like to explore the physics of their flight, and when the topic of discussion is turn physics and coordination in hang gliders, there are always many conflicting points of view. This is a contribution to that exploration.

We'll start by examining the pitch-axis dynamics of turning flight in quite a bit of detail in Part One, because these dynamics are often confused with sideslip and yaw coordination in hang gliders. Then in Part Two we'll move on to talk about sideslip and yaw coordination, and in Part Three we'll look at the in-flight experiments I did in my hang glider, an airplane, and a sailplane. Part Four will revisit turn and sideslip dynamics in more detail, and the Appendices at the end will include sections on blind flying, lockout dynamics, and quantifying the aerodynamic forces produced in a slip.

Those of you with better plans for the evening than curling up with this 50-page article may want to skim directly to the sections in Part Three entitled "Suggestions for teaching methods" and "So why do we let out the bar while rolling into a turn" as they contain the main take-home lessons!

 

PART ONE: PRACTICAL TURN "COORDINATION" AND PITCH AXIS DYNAMICS

INTERPLAY OF ANGLE-OF-ATTACK, BANK ANGLE, AIRSPEED, AND G-LOADING

Of course the practical aspects of hang glider turn coordination are well understood. As a glider is rolled into a turn, the pilot usually lets the bar out to boost the turn rate and prevent the nose from falling. If we think of this as a pitch coordination move, it is not difficult to explain the physics involved. Letting out the bar increases the angle-of-attack and the G-load (lifting force), which maintains an adequate vertical component of lift as the bank angle increases. If we roll into a turn without changing the angle-of-attack, pulling only one "G", the turn rate will be sluggish, and the vertical component of lift (and drag) will be less than the aircraft weight. As the nose falls and the glider accelerates downward, the flight path will curve downward in the pitch dimension. The airspeed will be rising, which also increases the G-load (lift force) produced by the wing, and eventually leads to a stabilized, constant-airspeed turn at the new, increased airspeed, with the proper G-loading for the bank angle. So as the glider is rolled into a turn either the angle-of-attack must be increased, or the airspeed will increase, until the wing is again creating the appropriate G-loading for the turn and the glider is again in equilibrium.

When the angle-of-attack is held constant as the glider is rolled into a turn, the complete sequence of events in the pitch axis is actually an initial downward curvature in the flight path as the aircraft noses down and gains airspeed, and then a smaller upward curvature and slight loss of airspeed as the aircraft pulls out again into a steady glide at the new, increased airspeed. In fact the aircraft may go through several oscillations before settling into a steady glide at the new angle-of-attack. The whole maneuver is caused by the interplay between changes in the lift and drag vectors, and the subsequent gain or bleeding off of airspeed. The net effect of all these dynamics is a steepening of the glide path and an increase in speed and G-loading, all due to the increased bank angle.

A key factor in these pitch dynamics is the delay in the build-up of airspeed and G-loading (lift) as the glider noses over into a dive. If the glider accelerated instantly as the bank angle increased, then the glider would always be in an equilibrium state, with the flight path entirely determined by the L/D ratio (and the bank angle). We would still see a steepening of the glide path as the bank angle increased, but we would avoid the more dramatic dive-and-pullout dynamics that we've described above. The "falling" sensation and marked lowering of the nose occurs when the G-loading is well below the required value (for the bank angle) and the aircraft is pitching down into an accelerating dive. As the aircraft accelerates the airspeed and G-loading may then significantly overshoot the "required" values (for the bank angle at any given moment) which will then cause the nose to rise a bit and the airspeed and G-loading to begin bleeding off again. The aircraft may go through several of these pitch oscillations before settling into a steady glide, all because of the delay in the way that the airspeed and G-loading respond to changes in the bank angle and the pitch attitude.

Up to this point, we've been looking at what happens when the glider is rolled into a turn without the usual pitch "coordination" input (i.e. with no change in the angle-of-attack). However, the same dive-and-pullout dynamics occur whenever the pilot pulls in the bar to decrease the angle-of-attack and G-loading (lift force), without also decreasing the bank angle. If the pilot "unloads" the glider (reduces the G-loading) by pulling in the bar, the flight path will first curve downward as the aircraft dives and accelerates, and then curve upward again into a more moderate, steady glide as the aircraft settles into equilibrium at the new, decreased angle-of-attack and increased airspeed, with the G-loading (lift force) again properly matched to the bank angle. Again, the aircraft may actually go through several of these pitch oscillations before reaching equilibrium. Conversely if the pilot pulls "extra" G's by pushing out the bar, the flight path will first curve upward--possibly even climbing above the horizontal--as the excess airspeed bleeds off and then will curve downward again as the glider settles into a steady glide at the new, increased angle-of-attack. After the aircraft has returned to equilibrium and the airspeed has stabilized, the net effect of a pitch control input and change in angle-of-attack is a steeper glide path if the change in angle-of-attack has degraded the Lift/Drag ratio, and a flatter glide path if the change in angle-of-attack has improved the L/D ratio. In other words the net effect of the pitch input depends on where we are on the L/D vs. airspeed curve.

Again, the delay in the change in airspeed and G-loading plays a key role here. This delay is what allows the pilot to temporarily "pull" extra G's by increasing the angle-of-attack, until the airspeed bleeds off to the appropriate value for the new angle-of-attack and the G-loading is again in synch with the bank angle (i.e. 1 G in wings-level flight). Likewise this delay is what allows the pilot to temporarily "unload" the wing by decreasing the angle-of-attack, until the airspeed rises to the appropriate value for the new angle-of-attack and the G-load is again in synch with the bank angle.

Since the delay in the airspeed response plays a key role in allowing the pilot to "pull" extra G's or partially unload the wing--in relation to the "expected" G-loading for the bank angle--these extra loading or unloading effects are most visible when the control bar (or stick) is actually being moved forward or aft, or when the bank angle is changing. After the bank angle and angle-of-attack are both stabilized, the G-loading and airspeed will soon stabilize also, though in some cases this may require quite a few seconds, especially if the aircraft is going through a strong cyclical oscillation as it moves toward equilibrium.

If we strongly pull in the bar at the same time that we are rolling from wings-level into a turn, we will nose down abruptly due to the effects described above--the G-loading will be far less than "required" by the bank angle at any given instant, and initially the G-loading may even be less then 1 "G", creating a distinct "falling" sensation. Even if we want to end up in a fast, well pulled-in turn, we will accelerate much more smoothly, with a smoother flight path, if we let the bar out a bit as we are rolling into the turn. This avoids the sudden "deficit" in G-loading and spreads the acceleration in airspeed out over a slightly longer time period. We avoid the sudden nose-down motion and we also avoid overshooting our target speed and creating a series of pitch oscillations.

In summary, for every bank angle, there is one particular G-loading that will allow the glider to fly in equilibrium at a constant airspeed. The airspeed required to produce this lift force (G-loading) will depend upon the angle-of-attack, and vice versa. If the total lift force (G-loading) is excessive then this will create an upward curvature (acceleration) in the flight path in the pitch dimension, and a loss of airspeed. If the total lift force (G-loading) is inadequate then this will create a downward curvature (acceleration) in the flight path and a gain of airspeed. For every combination of bank angle and angle-of-attack (bar position or control stick position), the aircraft will eventually settle down at one particular airspeed where the vertical component of the G-load (lift force) equals the aircraft weight. (This is a slight oversimplification--see "L/D ratio and Lift Force" below.)

 

WHAT DETERMINES ANGLE-OF-ATTACK?

To really follow the above discussion, the reader must have a clear understanding of what determines the glider's angle-of-attack, i.e. the angle at which the wing is meeting the airflow. To a first approximation the angle-of-attack of an aircraft is determined by the position of the pilot's body on the control bar (or the position of the control stick). Pilots tend to cue onto control force rather than control position; these are related but not quite the same.

Compared to many other aircraft, a hang glider is relatively limited in control authority in the pitch axis. In particular the wing cannot be easily put at a zero or negative angle-of-attack as it can in most three-axis aircraft (which yields a 0 G ballistic trajectory or negative G's). In a hang glider the nose cannot easily be shoved steeply downwards to "unload" the wing and add a lot of airspeed, so a steep bank is often used to gain airspeed quickly, for example to begin an aerobatic maneuver. Another method used by aerobatic hang glider pilots to point the nose steeply down and build speed rapidly is to stall the glider in a very nose high condition (whipstall).

Note that the pitch attitude of the aircraft in space is really the sum of the angle-of-attack and the actual flight path through the air. When the airspeed is constant, the flight path of a glider is strictly determined by the Lift/Drag ratio (i.e. the glide ratio), and the bank angle. The Lift/Drag ratio is strictly determined by the angle-of-attack, which is determined mainly by the bar position (or control stick position) and is also somewhat influenced by the bank angle. Therefore in a steady, constant airspeed turn the bank angle and bar position (or control stick position) completely determine the pitch attitude of the glider in space, as well as the glide ratio, angle-of-attack, airspeed, and G-loading. When the airspeed is rising or falling, and the flight path is curving up or down as the glider pulls "extra" G's or is partially "unloaded", the situation is much more complex and the flight path may even temporarily arc upwards above the horizontal in a climb, wingover, loop, etc. (Of course when we refer here to the flight path we mean relative to the airmass rather than the ground; when a glider is in equilibrium with a constant airspeed it is always in a descending flight path relative to the airmass even if the glider is in "lift").

An added complexity to all this is that in a turn, the airflow curves to follow the circumference of the turn (much more on this later). At steep bank angles, this means that the curving airflow tends to "push up" on the rearmost parts of the aircraft which lowers the nose and decreases the overall angle-of-attack of the wing. The practical result of this is that as the bank angle increases, the pilot must push the control bar further out--or haul the control stick further aft--to hold a constant angle-of-attack. To see this for yourself, compare the control bar or control stick position at the stall angle-of-attack in a steep turn vs. in wings-level flight. (Note: if you are doing this in a powered aircraft pull the power to idle, as the propwash will further complicate things).

This airflow curvature effect is most noticeable at the low airspeeds and tight turn radii typical of flex-wing and rigid-wing hang gliders. However in a flex-wing the ability of the wingtips to twist (wash out) under load will significantly reduce the nose-down effect of airflow curvature in a tight turn. To a hold a given angle-of-attack as the bank angle increases, we would expect to have to push out more in a rigid-wing hang glider than in a flex-wing, at similar airspeeds and turn radii.

 

DO WE SEE THE SAME DYNAMICS IN POWERED AIRCRAFT ALSO?

All the dynamics involved in the interplay between G-loading, airspeed, angle-of-attack, and flight path will occur in powered aircraft as well as gliders. After all, it is the delay in the bleeding-off of airspeed which allows an aerobatic pilot to temporarily "pull" extra G's (beyond what is "required" by the bank angle) during aerobatic maneuvering such as when pitching up into a "zoom" climb, etc. However the final value of the G-loading (lift force) when the plane reaches equilibrium and the airspeed stabilizes will vary slightly according to the power setting, as noted below.

 

L/D RATIO AND LIFT FORCE

We've been using the terms "lift force" and "G-loading" interchangeably to mean the lift produced by the aircraft's wings, and we've been assuming that the vertical component of this force must equal the aircraft weight if the aircraft is to remain in equilibrium with a constant airspeed. In truth, if the aircraft is in a descending glide then a portion of the aircraft weight is borne by the drag vector, which slightly "unloads" the wings and decreases the lift vector (G-loading). Therefore to be technically correct we do need to recognize that the required lift vector (G-loading) will in fact vary with the angle-of-attack (L/D ratio) as well as with the bank angle. From the pilot's point of view, this effect is negligible unless the glide angle is quite steep. However if the pilot pushes the control stick far forward and leaves it there, we will see the immediate, temporary reduction in G-loading that we've been discussing, and then as the airspeed increases the G-loading will build and then stabilize at a value significantly less than 1 G (in the wings-level, unbanked case) because at this low angle-of-attack the L/D ratio is quite low, the glide angle is quite steep, the airspeed is high, and the drag vector is large enough to bear a noticeable part of the aircraft's weight. In a steeply banked, steeply diving turn the G-loading will of course stabilize at a value much greater than 1 G, but less than "required" by the bank angle if the aircraft were to maintain altitude or have a much shallower glide path. (The same would be true in a hang glider when the pilot pulls the bar in all the way, except that in a hang glider we don't have enough control authority (control bar travel) to keep the wing at the very low angle-of-attack and very steep glide angle that we're talking about here, so the reduction in the G-loading is not very noticeable). The extreme example is a sustained vertical dive an aerobatic sailplane or airplane. Here the pilot moves the control stick forward until he actually reaches the zero-lift angle-of-attack where the lift vector (G-loading) and L/D ratio are zero. This is the only case where the G-loading (lift vector) will not begin to build as the airspeed begins to increase. The aircraft is initially in a ballistic trajectory (freefall) as it arcs over into the vertical dive, and will accelerate until reaching terminal velocity, at which point the entire aircraft weight (plus thrust in a powered aircraft) is borne by the drag vector. At this point the G-loading is still zero (as we have been using the term, and as measured by the G-meter in the instrument panel which only detects "up" and "down" forces in the aircraft's reference frame) and the pilot feels none of the usual force exerted by the seat bottom against his body but he does feel a one-G force pushing on his chest as the seat belts prevent him from accelerating earthwards and falling forward into the instrument panel. (All this assuming that the wings have not departed the aircraft by this point due to flutter, excessive drag forces, or the sudden application of a heavy G-load if the pilot does allow the stick to move back and increase the angle-of-attack too quickly while the airspeed is very high).

Interestingly, the way that the drag vector begins to bear a part of the aircraft weight as the airspeed rises and the glide path steepens actually prevents the lift vector from going to infinity in a very steep turn as the bank angle approaches 90 degrees. If infinite thrust were available to sustain level flight as the bank angle approached vertical, then airspeed, lift, and drag would all go to infinity, regardless of the angle-of-attack and the L/D ratio. In the real world a very steeply or vertically banked aircraft ends up in a steeply diving corkscrew or a rolling vertical dive, with the drag vector bearing much or all of the aircraft weight, so the G-loading (lift vector) will remain finite. However we should note that this load-limiting effect does not begin to play a significant role until the bank angle is very steep and the airspeed and G-loading are already very high, especially in streamlined aircraft with high L/D ratios. In many aircraft you can still pull enough G's to remove the wings if you try to keep the aircraft in a sustained, near-vertical bank, especially if you try to "hold the nose up" by keeping the control stick moving aft to further increase the G-loading as the airspeed rises. (Of course, I'm not referring to the case where the aircraft is held indefinitely in a slip with the rudder so the fuselage, rather than the wing, supports the aircraft weight--by this method high performance aircraft can indeed sustain level flight while vertically banked).

By the way, in a powered aircraft a climb has the same "unloading" effect as a dive because part of the aircraft weight is borne by the thrust vector; here the extreme example is an accelerating vertical climb on raw thrust alone, with the wings held at zero angle-of-attack and zero G-loading (lift) to avoid arcing back into a loop. Of course this accelerating vertical climb is only possible in a few high-performance jet fighters, the space shuttle, etc but even at shallow climb angles in light planes the wings are actually generating slightly less lift in the sustained, constant-airspeed climb than in level flight. (Amaze your friends with this trivia...) The lift vector (G-loading) is exactly equal to the aircraft weight only during sustained horizontal flight with no climb or descent, with the thrust vector exactly equal and opposite to the drag vector, so none of the aircraft weight is borne by either thrust or drag. (Again we are of course talking about the flight path relative to the airmass and not considering "lift" and "sink" effects so beloved (and despised) by glider pilots which may further modify the flight path relative to the ground!)

In a powered aircraft we find the glide ratio or glide angle (in still air) by looking at the L/(D-T) ratio and the climb ratio or climb angle by looking at the L/(T-D) ratio, where T= thrust. In sustained horizontal flight thrust and drag are equal.

 

BUT WHAT ABOUT SIDESLIP?

Now we've considered the interplay between pitch inputs, airspeed, bank angle, G-loading, and flight path at great length without once mentioning sideslip! This should serve as a hint to the reader that I believe that the role of sideslip in hang glider turn dynamics is greatly overestimated. Skip ahead to the section entitled "So why do let out the bar while rolling into a turn?" at the end of Part 3 for the final punch line here.

 

PART TWO: A BRIEF OVERVIEW OF SIDESLIP DYNAMICS

In three-axis aircraft, the word "coordination" generally refers to the prevention of slips and skids, which is accomplished with the rudder. In the above discussion I've loosely used the word "coordination" to refer to the pitch inputs that a pilot makes to control airspeed and G-loading in a turn, without meaning to imply that this has anything to do with sideslip or skid. However many hang glider pilots believe that "uncoordinated", accelerating turns are in fact slipping turns. In other words, if the pilot increases the bank without letting out the control bar, or actually pulls in the bar as he rolls the glider, the glider is thought to be uncoordinated in the yaw axis as well as the pitch axis, and is thought to fall or slide sideways toward the low wingtip as it pitches down into a dive and gains airspeed. Not wanting to take this for granted, I've done some in-flight experiments to look at this further. But first let's define in more detail what we mean by a sideslip.

 

DEFINITION OF SIDESLIP

A slipping turn can be described in two ways. One, the nose is angled toward the outside of the curving flight path, instead of facing directly into the direction of flight (into the relative wind). In other words, the heading of the glider is lagging behind the actual direction of travel in the turn. This creates a sideways (spanwise) component in the airflow over the glider, so a yaw string (telltale) will blow toward the outside (high side) of the turn. Two, this sideways airflow over the glider creates a centrifugal aerodynamic force (toward the outside of the turn) which slows the turn rate. The bank angle is then too steep for the turn rate and the pilot tends to fall toward the inside of the turn (toward the low wing). A slip-skid ball (as used in many "conventional" aircraft) will shift toward the inside of the turn, and a slip-skid bubble (such as a carpenter's level) will shift toward the outside of the turn.

Because a sideways (sideslipping) airflow over the aircraft is really the only possible cause of a sideways or spanwise force toward the low wingtip, the yaw string and the slip-skid ball are nearly always in agreement about the whether the aircraft is slipping, skidding, or coordinated in the yaw axis (but see Appendix Three for a slight caveat here in aircraft with rudders). This is a very important point to understand. In general the reason that sailplanes use yaw strings and power planes use a slip-skid ball is that for planes with a propeller in front the propwash over the nose would render the yaw string useless; rear-engined prop planes often use yaw strings and a few jets do too (such as the U-2 spyplane with long wings and lots of adverse yaw).

Much more on the theoretical aspects of slipping turns will follow later in this discussion!

 

DETECTING SIDESLIP IN HANG GLIDERS

Let's consider how a hang glider pilot could be certain that he is in a sideslip. Of course there is the usual list of cues for "uncoordinated" turns in hang gliders (increasing airspeed, nose pitching down, slow turn rate, sensation of falling or inadequate G-load) but by now we've seen that most of these are caused by dynamics in the pitch axis rather than by sideslip. What specifically tells the pilot that he is actually sideslipping, i.e. that the glider is uncoordinated in the yaw axis? If there are telltales on the nose wires, they will blow toward the outside of the turn, but these are usually outside of the pilot's normal vision, and they also may be hard to read clearly if the pilot is shifted to either side of the glider centerline. The pilot might feel on his face the shift in the direction of the relative wind, but this might not be noticeable unless he is concentrating on facing straight out ahead of the glider rather than looking off to one side or the other. If the slipping airflow component is producing centrifugal forces that slow the turn rate, then the pilot will tend to fall toward the low side of the glider. This will not create the obvious, uncomfortable, sideways force that is felt by a seated, upright, pilot in a "conventional" aircraft. Instead, a freely hanging pilot will simply experience a small shift in the "neutral" hang position, meaning that if the pilot took his hands off the control bar he would tend to hang a bit to the low side of the centerline. This is only observable if the pilot is using little or no control pressure. In the real world, with turbulence, and the need for high-siding or low-siding according to the particular glider design, the pilot knows the muscular forces that he is exerting at any instant but may not be aware of the precise location of the "neutral" hang position relative to the glider centerline. In short I don't think it's always that obvious to the pilot what his glider is doing in regard to sideslip. To carefully investigate the sideslip behavior of a glider, a pilot should use a slip-skid ball or bubble, or simply a yaw string that is mounted where it is easy to read in flight.

A hang-glider sideslip is often described as a marked sensation of "falling toward the low wing". Actually, a pilot would have to firmly pull in the bar if he wished to temporarily decrease the G-load to noticeably less than one. Perhaps many pilots also describe a sense of "falling" whenever the G-load is less than normal for a given bank angle, or whenever the G-load decreases regardless of the actual magnitude of the G-load. In any case, it seems to me that anytime a turning glider pitches downward, dropping the nose, with a high sink rate and an accelerating airspeed, the pilot will describe a falling sensation regardless of the actual magnitude of the G-load. And he will likely perceive that he is falling toward the ground, i.e. towards the low wing, regardless of whether or not he actually tends to fall toward the low side of the control frame, or is able to sense the airflow coming up from the low side of the glider. In short he may greatly overestimate the amount of sideslip toward the low wing as the glider pitches down into a dive.

 

SOME COMMON IDEAS ABOUT SIDESLIP IN HANG GLIDERS

Many hang glider pilots use the word "slip" to describe the falling sensation as the nose drops and the airspeed rises when the G-loading is inadequate in a turn. As we've already discussed in detail, these effects can be produced either by pulling in the bar while banked or by failing to let the bar out adequately as the glider is rolling into a turn. As noted above, many hang glider pilots believe that these pitch-axis dynamics also involve a true sideslip in the usual aviation sense of the word, with a sideways or spanwise component in the airflow as the glider falls toward the low wing, and an imbalance of forces (in the pilot's reference frame) that allows the pilot to fall toward the low side of the control bar. Proper pitch coordination, to maintain the appropriate G-loading and a constant airspeed as the glider rolls into a turn, is thought to also ensure yaw coordination and prevent this sideslip. If the pilot actually pulls in the bar while rolling into a turn the glider is thought to enter a very marked sideslip, which later disappears as the airspeed and G-loading build and then stabilize at the appropriate values for the bank angle and angle-of-attack. In all cases the slip is said to be a temporary event because of the inherent yaw and pitch stability of the glider. Clearly this view of sideslip assumes a close interconnection between pitch and yaw axis dynamics. This viewpoint is well represented in Dennis Pagen's Hang Gliding Training Manual (pp. 128-129, 141, 149-150 (relates to spanwise airflow), and 358) and Performance Flying (pp. 34, 45, 52-54).

An important detail of this model as outlined by Pagen is that a coordinated turn may be initiated at any airspeed, as long as the airspeed is kept steady in the turn entry. Pagen is careful to separate the issue of turn coordination from the issue of the optimum speed to fly for minimum sink rate (HGTM p.129).

An alternative description of slips in hang gliders holds that all turns at high airspeed are always slipping turns, and by keeping the airspeed high, the glider can be kept in the slip indefinitely. This view was communicated to me by a very experienced instructor/ aerobatic pilot.

A third view held by some pilots is that the pitch and yaw axis dynamics are largely unrelated. By this viewpoint the nose-down motions that most pilots call "slips" really involve dynamics in the pitch axis only, with little or no actual sideslip, except for effects such as adverse yaw which are not influenced by the pilot's pitch "coordination" inputs.

 

SOME IDEAS ABOUT SIDESLIP IN 3-AXIS AIRCRAFT

Until I started my hang glider training, it never occurred to me that pitch control inputs might have an effect on sideslip. While flying sailplanes and airplanes, I've always assumed that yaw coordination was controlled entirely by the rudder, while pitch inputs affected only airspeed and G-loading. I've never noticed that pulling extra "G's" in a turn had any tendency to create a skid, or that allowing the nose to fall due to inadequate back pressure as I rolled into a turn had any tendency to create a slip. Nor have I come across such suggestions in the current flight training literature for 3-axis aircraft. However about the same time that I started digging into Dennis Pagen's Hang Gliding Training Manual and Performance Flying, I also ran across the idea that that pitch inputs will have an effect on yaw coordination in a couple of older books for 3-axis aircraft (Wolfgang Langewiesche's 1944 physics-for-pilots classic Stick and Rudder pp. 203-206 and 225-226, and p.308 in the 1966 3rd edition of Modern Airmanship (Van Sickle, ed.)). I didn't find either of these sources to be very convincing on this particular subject, though Langewiesche's book is a real gem in most respects and contains a full chapter on the physics of turns.

 

PART THREE: THE HEART OF THE MATTER: MAKING THE IN-FLIGHT EXPERIMENTS, INTERPRETING THE RESULTS, AND SUGGESTIONS FOR TEACHING

TOOLS FOR INVESTIGATION

With all of these different ideas floating around about sideslip in hang gliders, I decided to take some data of my own in my Spectrum. To see what the glider was really doing in turns, I rigged three small bubble levels to simulate a single, larger tube with the desired amount of curvature. This gadget measured up to four degrees tilt to either side. This seemed to be adequate as the bubbles rarely reached full deflection in flight, and other arrangements with more curvature yielded little movement of the bubbles in flight. Deflection of the bubble to the high side of the turn indicates a slip--a standard aircraft slip-skid ball would move the opposite direction. I also put a yaw string (telltale) on a dowel projecting forward 60 cm from the center of the base tube, for easy viewing in flight. The dowel provided a centerline reference to that helped the pilot judge the deflection angle. There was also a long yaw string attached to the rear of the keel, and on some flights, a yaw string on a long "bowsprit" projecting almost 2 meters forward from the apex. A small crossbar "index" mounted near the free end of each of the two forward yaw strings helped the pilot to compare the angular deflections of these strings, which were at different viewing angles and distances from the pilot's eyes. The "bowsprit" and rear keel yaw strings were intended to explore the curvature of the airflow in the yaw axis, following the circumference of the turn.

 

MAKING THE TEST FLIGHTS

I accumulated the data slowly over several flights in ridge lift. Obviously there must be no nearby traffic, and conditions in general must be mellow enough to allow some diversion of the pilot's attention. Glass-off conditions are ideal.

I watched the yaw strings and slip-skid bubbles as I rolled the glider from wings-level into a turn while letting out the bar to "coordinate" the turn in the pitch axis, and while pulling in the bar, and while making no pitch input. To isolate the effect of pitch inputs on yaw coordination from the effect of roll inputs on yaw coordination, I also watched the yaw string and bubbles as I pulled in or let out the bar while holding the glider in a steady, constant-banked turn. Some of these pitch inputs were quite marked and produced strong changes in the glider's airspeed, pitch attitude, and flight path.

Because a hang glider has little structure out in front of the pilot, I found that I was usually much more aware of the yaw rotation rate than of the bank angle itself. I instinctively tended to make the required roll inputs to keep the glider tracking around the horizon at a steady rate. When I wanted to hold a constant bank, it took some extra effort to overcome these habits. I used various bank angles up to about 45 degrees in the experiments involving the various pitch inputs while turning. I didn't use bank angles steeper than 45 degrees because of the difficulty in flying smoothly and precisely at very steep bank angles. In maneuvers involving simultaneous and dramatic changes in bank angle, pitch attitude, and G-loading it was challenging to carefully observe the precise timing of all the dynamics involved. In some experiments in an airplane which I'll describe later, the additional visual references provided by the cowling, windscreen, etc., and also the gyro instruments, made it much easier to make precise observations of the bank angle and to carefully relate changes in the bank angle to changes in the airspeed and pitch attitude.

I also made observations of the yaw strings and slip-skid bubbles in stabilized, constant-banked, constant-airspeed turns. In these observations in particular I was looking at small displacements of the yaw strings so it was essential that the bank angle, turn rate, and airspeed all be held steady. I made these observations at bank angles of 20-30 degrees. In 180 degree turns or single 360's, there often wasn't time to settle into a steady turn rate and it was easy to draw hasty conclusions. Flying multiple revolutions produced better results. Viewing the rearmost yaw string at the extreme rear of the keel was an extra challenge. When making quick glances to the rear of the glider, I inevitably would see a skid because I had allowed the bank angle to shallow. Longer observations tended to have the opposite effect as I inadvertently tightened the bank. I tried flying with a convex mirror, but the image was too small. Finally I found that by facing steadily rearward through multiple circles, I could keep the turn rate steady for short intervals. By controlling the glider with a slight rotation of the body (moving primarily the feet and legs), I could keep a clear sightline to the rear of the keel, while adjusting the turn rate via my view of the rear horizon, and holding a constant pitch pressure on the bar. It took some practice, and lots of clear air! Viewing the "bowsprit" yaw string involved less contortion but it was above the pilot's line of normal vision so some care was needed to keep the turn rate steady as I raised my head above the normal flying posture. These observations of the yaw string deflections in steady, constant-speed, constant-bank turns were made with a bank angle of 20 to 30 degrees.

When viewing the yaw string in front of the base bar, near the pilot's eyes, allowance had to be made for a parallax effect when the pilot was shifted away from the glider centerline.

 

ACTUAL DATA, AND INTERPRETATION OF RESULTS: SLIP-SKID BEHAVIOR OF MY GLIDER (Spectrum 144)

***** Note summer 2005 -- I no longer feel that the time lag that I observed between the initiation of a roll input, and the development of the maximum amount of sideslip, should be interpreted as evidence that the sideslip is being driven primarily by the glider's rotational inertia in the yaw axis, rather than by an aerodynamic adverse yaw torque. This delay is observable in a wide variety of aircraft including sailplanes and light airplanes, and is not incompatible with the idea that the sideslip during a rolling motion is being driven primarily by aerodynamic adverse yaw torques. When thinking about these issues it is important to realize that though a difference in lift between an aircraft's left and right wings only exists when the pilot is has just initiated the roll input and the roll rate is accelerating rather than constant, there are aerodynamic effects that create a strong adverse yaw torque even when the roll rate is constant. See the main site map of the Aeroexperiments website for more. The best way to evaluate the relative importance of aerodynamic adverse yaw torques versus yaw rotational inertia in creating a sideslip during a rolling motion, is to watch and see whether or not the aircraft's nose visibly swings in the "wrong" direction in relation to the external world as the rolling motion begins and as the yaw string deflects toward the outside of the turn. If the aircraft is simply tending to remain on its original heading as the flight path starts to curve, then it is possible that aerodynamic adverse yaw torques are playing a lesser role than the aircraft's rotational inertia in the yaw axis. In hang gliders one can usually see the nose swing in the "wrong" direction in relation to the external world during a hard roll input, suggesting that aerodynamic adverse yaw torques are important. These ideas do not conflict in any way with my original observations and conclusions about the independence between a pilot's pitch inputs, and sideslip. *****

Many of the ideas introduced here will be explored in much more detail in later sections of this paper.

I found that the slip-skid bubble was centered most of the time. The slip-skid bubble was centered in all steady, constant-bank, constant-airspeed turns. However, whenever the bank angle was increasing, the yaw strings and slip-skid bubble showed a slip, and they showed a skid when the bank angle was decreasing. So a turn entry always created a brief sideslip, and a roll-out to wings level created a brief skid. The magnitude of these slips and skids depended strongly on the roll rate. All three yaw strings (on the "bowsprit" 1.9 meters forward of the apex, and on the probe projecting 60 cm forward from the base bar, and on the tail end of the keel) were basically synchronized in their motions while the glider was rolling in or out of a turn. This point, plus the time lag described below, showed that none of the yaw strings were unduly influenced by changes in the local airflow around my body as I made roll inputs.

The slip caused by a turn entry lagged behind the initial pilot roll input. As the glider began to bank, the amount of slip gradually increased along with the bank angle, and then faded away soon after I stabilized the bank angle. This was most visible when I used a large roll input.

Much can be learned from this time lag between the pilot roll input and the resulting slip. This reveals that the major cause of the slip was probably not adverse yaw from differential airfoil shapes, which should correlate closely with the position of the pilot's body on the control bar. Instead, the major cause of the sideslip in my Spectrum appeared to be rotational inertia in the yaw axis, which will be most pronounced once the glider has reached a high roll rate and a significant change in bank angle has occurred. Other hang glider designs with more span and less sweep may well show both more adverse yaw and more yaw rotational inertia than did my Spectrum.

Pitch inputs while holding the bank constant did not cause a sideslip or skid, either in the bubble or the yaw strings. Pitch inputs while the glider was rolling into a turn did not seem to either decrease or augment the slip caused by the roll input. For some of these trials, I pulled in or pushed out the bar quite strongly which resulted in large changes in airspeed and pitch attitude, but did not appear to affect sideslip and yaw coordination. All observed deflections of the slip-skid bubble and yaw string appeared to correspond entirely to roll inputs by the pilot and seemed to be unaffected by changes of the bar position in the pitch axis, whether the glider was rolling into a turn or was established in a steady turn. I saw no evidence that the usual hang glider "turn coordination" inputs had any effect on yaw coordination and the prevention of sideslip.

When I pulled in and shifted fully to the side to enter a steeply banked diving turn, there was a marked increase in airspeed and bank angle, and a lowering of the nose. There was also a sensation of falling which was due in part to the obvious visual effect of the nose dropping. The bubble showed a slip, and then became centered within one half of a revolution from the initial input. This roughly coincided with the end of my roll input, though the whole maneuver was so dynamic that it was hard to observe such details with certainty. The G-forces seemed to increase steadily along with the airspeed as the glider slipped and rolled, until after about half a revolution the G-forces were as high as I wished to experience, so I relaxed the roll input and allowed the bank angle to stabilize, and the G-forces also stabilized at a sustained, high value. The maneuver was very dramatic and it was difficult to carefully note the precise timing of all the dynamics; as we've already discussed while looking at pitch dynamics in Part Two, and will see in more detail in the airplane experiment described below, I suspect that the airspeed and G-loading actually continued to increase for several seconds after the bank angle was stabilized. A video camera to carefully record the bank angle and pitch attitude, and a tape recorder to record the pilot's perception of the airspeed and G-loading, would allow a more detailed investigation of these points.

When I performed the same full shift to one side but without pulling in the bar, the results were much the same. In this case, it was particularly noticeable that after I shifted my weight, there was a time lag before the yaw string and bubbles showed a slip and also before the airspeed started to increase. The ultimate airspeed increase was dramatic and seemed nearly as great as when I pulled in while shifting to the side. (No airspeed data were taken). The amount of sideslip seen as the glider rolled into the turn was about the same whether or not I pulled in the bar during the maneuver.

Here is my overall view of the behavior of my hang glider during a turn entry: if the glider is rolled into a turn without the usual pitch "coordination" input, this creates both a sideslip due to rotational inertia in the yaw axis and (to a lesser extent in my glider) adverse yaw, and a marked dive and an acceleration in airspeed due to an inadequate G-loading for the bank angle at any given instant. The amount of slip and the rate of airspeed acceleration both depend on the roll rate. Once the bank angle is stabilized and the roll rate is zero, then there is little or no sideslip. The pitch dynamics will occur on a slightly longer timescale than the yaw dynamics: the airspeed and G-loading will continue to build for several seconds after the bank angle is stabilized. As the airspeed and G-loading build to the appropriate values for the bank angle and angle-of-attack or bar position, the glider will pull out of the initial dive into a more moderate glide path. As noted in our discussion of pitch-axis dynamics in Part One, the slight delay in the build-up of airspeed and G-loading are the reason that the glider goes through these dive-and-pullout dynamics rather than settling immediately into a stabilized glide that is exactly matched to the angle-of-attack and bank angle (at any given instant). During these oscillations the airspeed and G-loading are continually "out of phase" with the glide path and pitch attitude, and this is why the glider noses sharply down and accelerates, then slightly overshoots the "target" airspeed and G-loading, then pulls up into a more moderate glide, and then may actually go through several more pitch oscillation cycles before settling into the final, stabilized glide path. As I've noted, in my Spectrum it was challenging to observe the precise timing of all these events but we'll see them more clearly in some experiments I did in an airplane (see below). Of course the severity of these oscillations depends upon the abruptness of the changes in bank angle (and angle-of-attack): in many cases they will be almost undetectable in ordinary flight especially as we gain experience and learn to subconsciously correct for them.

The events in the pitch and yaw axes are both driven by the change in the bank angle, but are independent. If the bar is let out to increase the angle-of-attack as the glider is rolled into the turn, the airspeed can be held constant (if the stall angle-of-attack is not reached) but the sideslip will still occur. If the glider had a rudder the sideslip could be completely eliminated, but the glider would still pitch down into an accelerating dive if the control bar were not let out as the glider rolled into the turn. In fact with gliders with a lot of adverse yaw the initial sideslip toward the high wing will actually yaw the nose up above the horizon; correcting this with a rudder will yaw the nose down toward the low wing and move the nose further "down" relative to the horizon.

If a glider suddenly dips a wing due to turbulence, the glider will be in a slipping turn until the glider's yaw rotational inertia is overcome, at which time the turn will become coordinated in the yaw axis. (Alternatively the glider's inherent roll stability may return the glider to wing's level before the turn becomes coordinated; we will talk about this more in a later section entitled "Balancing yaw and roll stability".) The initial slip due to yaw rotational inertia is what causes the pilot to swing slightly toward the low side of the control bar as the glider is tipped to one side in turbulent air.

Getting back to my experimental observations in my Spectrum: at no time did my roll inputs create a strong sensation of being forced to one side of the control bar. On the whole I would say that sideslip had very little to do with the physical sensations that I experienced during these trials. On the other hand changes in G-loading due to pitch inputs were very noticeable. For example, "unloading" the wing by pulling in the bar during a constant-banked turn produced a general falling sensation due to the visual effect of the nose dropping and also due to a noticeable reduction in G-loading. The maneuvers involving full roll inputs, when I shifted fully to one side of the control frame, were the only instances where I saw full deflection of the slip-skid bubble (about four degrees from "level"). In these maneuvers, the yaw string in front of the base tube showed a maximum deflection of about 25 degrees. Based on previous experiments with other slip-skid bubble arrangements with more curvature, I don't think that the actual amount of slip (as "felt" by the slip-skid bubble) was ever much greater than the full deflection of four degrees from "level" described above. A bit of geometry based on the dimensions of my control frame shows that four degrees of bubble deflection corresponds to a shift in the "neutral" (hands-off) pilot hang position of only about 4 inches to the low side of the turn. While the pilot is making a large roll input and is fully shifted to the low side of the control bar, he will feel this slight change in the "neutral" hang position as a slight decrease in the muscular force that he must exert to hold himself against the low side of the control frame. (We can "simulate" this on the ground by hanging in a control frame that is tilted four degrees from "level"). Amidst all the other sensations of the steep turn entry, I had no awareness of this tendency to hang slightly low on the bar.

In all turns in my glider I had to remain slightly on the low side of the control bar to prevent the bank from decreasing (the maximum bank angle tested was about 40 degrees).

The main purpose of these experiments was to look at the slip and skid behavior of my glider while the bank angle or G-load was changing. I also had some interest in looking at the behavior of the glider in a steady, constant banked, constant speed turn: would the slip-skid bubble be centered? Would a yaw string be centered? Would yaw strings at various points on the glider show the effects of "airflow curvature", i.e. the way that the airflow follows the circumference of the turn? These questions were explored by flying with three yaw strings: one on a long "bowsprit" projecting almost 2 meters forward from the apex, one on the "probe" extending 60 cm from the center of the base tube, and one attached to the rear of the keel.

All the yaw strings generally agreed with the slip-skid bubble, deflecting the toward the high side of the glider in a slip when the bank angle was increasing, and toward the low side in a skid when the wings were rolling towards level. In addition the subtle deflections of the yaw strings in a steady, constant-bank, constant-airspeed turn did show some indication of airflow curvature, but my data weren't precise enough to look at this in great detail. About 8 degrees of airflow curvature (in the yaw axis) would be expected over the length of the keel, at 30 degrees bank and 24 mph. (See the table in Part Four for more on these calculations). The yaw string mounted 60 cm in front of the base tube showed a slight deflection toward the high side of the glider in a stabilized turn, indicating a slight sideslipping component in the airflow at this location. This deflection was roughly six degrees in a turn of 20 to 30 degrees bank. The yaw string at the tail end of the keel appeared to stream straight back in steady turns. The indication of the "bowsprit" yaw string wasn't noticeably different from the yaw string in front of the base tube. As noted earlier, it was challenging to make an accurate estimate of these deflections in steady turns because of the viewing angles involved, and because the indications were greatly affected by any accidental roll inputs. At steeper bank angles it was hard to hold the turn steady, so no comparison was made of the deflections at various bank angles or airspeeds.

So I couldn't see any difference in airflow direction over the 1.5 meters between the yaw string on the "bowsprit" and the middle yaw string (60 cm in front of the base bar), but I did see a noticeable difference over the 2.9 meters between the middle yaw string and the rear yaw string (at the tail end of the keel). The rear yaw string seemed to mark the point where the keel was tangent to the curving airflow. However, the fact that the slip-skid bubble appeared to be centered in steady turns shows that little or no slipping (centrifugal) aerodynamic forces were being generated, suggesting that the "average" airflow over the glider as a whole was well aligned with the keel. These results seem to be somewhat in conflict, since the center of surface area of the wing is about half a meter aft of the control frame, not back by the rear of the keel. In any case, regardless of the exact location of the point where the keel was tangent to the airflow, it is not surprising that some slip was indicated in the forward yaw strings (much more on this in Part Four). To gather more accurate data on these airflow angles, and to better explore various bank angles and airspeeds, cameras should be used to view the yaw strings and record bank angle and turn rate information, leaving the pilot free to concentrate on flying smooth circles!

 

DO THESE RESULTS APPLY TO OTHER HANG GLIDERS?

***** Note summer 2005 -- all hang gliders I've flown to date, including my Airborne Blade with VG either loose or tight, behave essentially the same as my Spectrum, with sideslips being driven mainly by adverse yaw and other related effects during changes in bank angle. Just as was the case with my Spectrum, with these other gliders I've seen no evidence that rolling into a turn without making a proper pitch "coordination" input will create any more sideslip than would the same rolling motion when accompanied with a proper pitch "coordination" to keep the airspeed constant and prevent the flight path from curving downward. And just as was the case with my Spectrum, with these other gliders I've seen no evidence that pulling in the control bar while banked will create a sideslip. *****

Since I did all these experiments in my Spectrum, I've left myself open to the criticism that my results are biased because I did my experiments in such a docile, user-friendly glider, and that higher-performance gliders will for some reason show more of a linkage between pitch inputs and sideslip. On this point I think its worth bearing in mind that the idea that pitch inputs control sideslip has deep roots in the early beginnings of hang gliding and did not arise with the advent of high-performance "blade wings". Nonetheless I certainly can't assume that other hang gliders will show exactly the same characteristics as my Spectrum. All rudderless aircraft will show some slip in turn entries and some skid while rolling out of a turn, due to rotational inertia in the yaw axis and adverse yaw. Gliders with more span, more mass, more rotational inertia, and less sweep and yaw stability will likely show more slip in a turn entry (and skid in a roll-out) than did my Spectrum. In general I would expect that G-loading changes (pitch inputs) would not affect yaw coordination and sideslip in other gliders any more than they do in mine, particularly if we are looking at the dynamics at a constant bank angle or at a particular rate of roll. However, Part Four we will look at some dynamics involving anhedral which may create some interaction between pitch changes, roll rate, and sideslip.

The subtle slip or skid characteristics in stabilized, constant-speed, constant-bank turns will be certain to vary markedly from one glider to another, depending on an interrelated web of factors including differential airspeed across the span, airflow curvature along the length of the keel, flex wing airfoil changes which depend on airspeed and airframe flexibility, adverse yaw created by flex wing effects and by pilot roll inputs, and the way that slip or skid interacts with sweep or dihedral to create a roll torque. Gliders that require high-siding may show a skid rather than a slip in a steady, constant-bank turn--more on all this in the second half of Part Four.

 

SUGGESTIONS FOR TEACHING METHODS

***** Note summer 2005 -- for a fresher and more concise expression of an improved teaching paradigm, see the related article on the Aeroexperiments website entitled Notes for new hang glider and trike pilots--on sideslips." *****

My findings suggest that yaw coordination is generally not affected by pitch inputs. These findings are at odds with the general understanding of sideslip among hang glider pilots. As we've already mentioned, we seem to believe that aircraft show a general tendency to slip toward the low wing whenever a turn is not correctly "coordinated" in the pitch axis, i.e. whenever the G-loading is less than "required" by the bank angle, and the flight path is arcing downward, and the airspeed is rising. My experiments in my Spectrum argue against this idea; as do some experiments I performed in an airplane and a sailplane which I'll describe in the next sections. As hang pilots we often fail to distinguish between a general sensation of falling or diving due to inadequate G-loading, and a definite swing toward the low side of the bar which is the mark of a sideslip. Looking at our training manuals, I believe that these points of confusion stem in part from some confusion about the basic physics of turning flight. The key points of interest are the net force on an aircraft in a turn at various G-loadings, and whether the pilot will "feel" a tendency to swing toward either side of the control bar, and whether the net force on the aircraft will drive a change in the yaw rotation rate and so create a temporary slip or skid. In this discussion (we'll get deeper into the physics in Part Four) I believe I've accurately explained why sideslip is driven primarily by the rate of change in bank angle and is generally not affected by changes in G-loading due to pitch inputs.

I think that our current lack of clarity about these issues originally began in the early days of hang gliding when the pioneers of our sport adopted aviation terms like "sideslip" and "coordination" without thinking carefully about how these concepts related to a 2-axis control system.

In fact I believe that our training materials and USHGA exams could be made both simpler and more accurate if many of the current references to sideslip were simply omitted. In many cases we should stick to terms like "min. sink speed", "high speed", "constant speed", and "accelerating" or "diving" to describe various types of turns. These words are clear and accurate and apply across the whole spectrum of hang glider designs. When the word "coordination" is used, we should be very clear whether we mean roll control to hold a constant bank angle (this is a loose but common usage), pitch coordination which controls our G-loading in the short run and our airspeed in the long run (this is usually what we mean in the hang gliding context), or yaw coordination which is the prevention of sideslip and is largely beyond our control in a rudderless aircraft. Clearly we need to teach students about the relationship between angle-of-attack (bar position) and turn performance, and also about all the nuances of the sensations that they will feel in flight, including the way that changes in G-loading relate to airspeed control. All these ideas can be communicated effectively and accurately without any reference to sideslip. By the way, I'm not the first to have these thoughts--one hang gliding instructor has recently told me that he has been using a similar approach in his own teaching for many years. When we do discuss sideslip we need to try for greater accuracy, regardless of how deeply we choose to delve into the underlying physics.

What would be the practical impact of adopting a more accurate point of view? I can't speak for everyone but I know that some students, especially those with some 3-axis flight time, find our current ideas overly complex and somewhat baffling. (Don't tell me, I know some readers would say the same about my own ideas too!). In my own case, coming to hang gliding with some 3-axis experience, I remember that when I completed my first altitude flights and first started ridge-soaring it took me several flights before I felt that I was starting to dial into smooth, safe turns without excessive diving or mushing. The basic advice in the training manuals about letting the bar out as I rolled into a turn was helpful, but the emphasis on yaw coordination and the prevention of sideslip led me to overdo the pitch inputs in a somewhat mechanical matter because I wasn't completely clear as to what the pitch inputs were supposed to be accomplishing. If I had been advised to simply "pull in for a bit of speed before turning, and then control the turn rate with the bank angle and control the airspeed with your pitch inputs", I'm sure that I would have dialed into the turns and gained a true feel for the glider a few flights sooner.

I also believe that a more accurate viewpoint would be helpful to any hang pilots who are transitioning to any kind of 3-axis aircraft, including "rigid-wings" like the Millennium. In many 3-axis aircraft yaw coordination with the rudder is quite important both for overall efficiency and also for spin avoidance, and it will be very dangerous if a pilot believes that holding the nose up with a pitch input is in some way equivalent to centering the yaw string or slip-skid ball with the rudder. I also think that a more accurate viewpoint would help us to analyze complex dynamics like lockouts on tow (see Appendix Two). Finally, regardless of the level of detail that we choose to include in the training manuals, I believe that increased accuracy will allow a simpler and more direct presentation of our dynamics.

I'm not arguing against the possibility of a coupling between pitch inputs and sideslip in specific maneuvers in specific gliders, as long this can be demonstrated through observations of a yaw string and slip-skid bubble. Later in this discussion I'll explore how anhedral may create a feedback between roll and sideslip. If the anhedral effect is strongest at low angles-of-attack, then we might simultaneously drive both slip and roll by pulling in the bar while rolling. The real point that I'm trying to drive home is that we can't even begin a thoughtful conversation about such interactions until we set aside our prevailing idea that all gliders sideslip whenever a turn is "uncoordinated" in pitch, i.e. whenever the G-loading is not properly matched to the bank angle. Nor can we make accurate observations in flight unless we are clear on the difference between the sensations caused by G-loading changes and the sensations caused by sideslip.

 

SO WHY DO WE LET OUT THE BAR WHILE ROLLING INTO A TURN?

***** Note summer 2005 -- this section seems awkward. The third and fourth points in the paragraph below are the most important ones. Because of the way that the "airflow curvature" effect affects the airflow over the rear parts of the aircraft, to maintain a given angle-of-attack (such as the min. sink angle-of-attack) the control bar must be positioned further forward (or a control stick or yoke must be positioned further aft) in a turn than in wings-level flight. And if we're making rapid changes in the bank angle, simply maintaining a constant angle-of-attack won't be enough to yield a smooth flight path. If we rapidly change the bank angle while maintaining a constant angle-of-attack, the airspeed won't have time to smoothly increase as needed to provide the extra lift that we need in the bank, and the nose will drop abruptly and the aircraft will go through several oscillations in its glide path and pitch attitude before things come back into equilibrium. To yield a smooth flight path, rapid changes in bank angle need to be matched with accompanying pitch inputs (changes in angle-of-attack) to avoid a sudden deficit or excess in the vertical component of lift, even if in the long run we want to bring the wing back to the same angle-of-attack that we had before we changed the bank angle. This seems rather strange when explained in detail--in actual practice a pilot just makes whatever pitch inputs are needed to avoid abrupt changes in the aircraft's pitch attitude. Another way to say this is to point out that a pilot usually makes whatever pitch inputs are needed to hold the airspeed constant or allow the airspeed to rise or fall slowly and and smoothly rather than quickly and abruptly, even if this means that the wing is temporarily placed at an angle-of-attack that is different from the one that we really want to end up with. Abrupt changes in airspeed signify a large deficit or excess in the vertical component of lift, and are associated with abrupt upward or downward curvatures in the flight path, even in cases where the wing is at some "optimal" angle-of-attack such as the min. sink angle-of-attack. Of course in actual practice a pilot has no need to think through the physics in detail--he should just make whatever pitch inputs are needed to hold the airspeed constant or to bring the airspeed smoothly and gradually to the desired value, and this will avoid abrupt upward or downward excursions in the flight path, which will also avoid abrupt changes in the aircraft's pitch attitude. *****

What are the reasons behind our usual pitch "coordination" inputs? I'll list several here, most of which stem directly from our discussion of pitch dynamics in Part One, and all of which are unrelated to sideslip and yaw coordination. One, pulling in before for extra airspeed before rolling gives more control authority and a better roll rate. Then as we approach the desired bank angle, we often wish to go back to a higher angle-of-attack to minimize our sink rate. Two, a little extra G-loading as we are rolling into the turn may augment our weight-shift control input and the related flex-wing effects, and thus help the glider roll faster. Three, airflow curvature effects increase the angle-of-attack of the "tail" (i.e. the wingtips), which tends to pitch down the nose and decrease the overall angle-of-attack of the wing. This requires that we let the bar further out as the bank angle increases if we wish to maintain a constant overall angle-of-attack. (As previously noted, this effect is less pronounced in a flex-wing hang glider than in a rigid-wing, because the wing tips can flex (wash out) and shed some of their load). Four, imagine that we are rolling into a turn and want to end up at the same angle-of-attack (or the same bar position) that we had in wings-level flight. If we try to maintain a constant angle-of-attack (or bar position) as the bank angle begins to increase, we will eventually see the airspeed and G-load increase as needed but there will be some time lag in this process and the nose will initially drop sharply as the glider "falls" into an accelerating dive because the G-loading is inadequate for the bank angle at any given instant. The glider may then go through several pitch oscillations before settling into a steady glide. If we let the bar out a bit to increase the angle-of-attack as we roll into the turn, we can avoid these abrupt changes in pitch attitude, and our turn entry will be much smoother. Even if we want to end up in a fast, well pulled-in turn, we may chose to let the bar out a bit as are rolling into the turn, and then pull back in after the bank angle is stabilized. This will spread our acceleration out over a slightly longer time interval and take us more smoothly to our desired flight path, as we can avoid the marked changes and oscillations in pitch attitude, flight path, airspeed, and G-loading which would be caused by abrupt changes in bank angle with no pitch "coordination" input.

 

ACTUAL DATA: SLIP-SKID BEHAVIOR OF SAILPLANES AND AIRPLANES

***** Note summer 2005 -- as noted previously, I no longer feel that the time lag that I observed in my Spectrum hang glider between the initiation of a roll input, and the development of the maximum amount of sideslip, should be interpreted as evidence that the sideslip is being driven primarily by the glider's rotational inertia in the yaw axis, rather than by an aerodynamic adverse yaw torque. Also, the observations given below for sailplanes and light airplanes are not entirely accurate. In these aircraft, while some sideslip may begin almost instantaneously as the pilot initiates a roll input, the maximum deflection of the yaw string and slip-skid does not occur until at least a half-second after the roll input is initiated. Again, for notes on why adverse yaw torques are generated during a constant-rate rolling motion where both wings are creating the same amount of lift, and not only during the initial acceleration in the roll rate when the left and right wings are generating uneven amounts of lift, see the main site map of the Aeroexperiments website. It does however appear to be the case that flex-wing hang gliders show more of lag between the pilot's initiation of the roll input and the development of the maximum amount of sideslip, than do light airplanes and sailplanes. This appears to suggest that yaw rotational inertia may play a relatively larger part, in relation to adverse yaw, with flex-wing hang gliders than it does with light airplanes and sailplanes. *****

***** Note summer 2005 -- Of course, anyone who has spent any time at all in a sailplane is aware that these aircraft will show a rather pronounced slip in a stabilized, constant-speed, constant-banked turn unless the pilot holds a touch of inside rudder. The same is true (but to a much lesser degree) of most light airplanes as a general rule, though for any specific power setting and specific direction of turn things are a bit more complicated due to P-factor and other related effects, as noted below. *****

(I wanted to get the "punch line" sections above before relating some further experiments in 3-axis aircraft, because I know that some pilots will be skeptical that we can draw parallels between weight-shift and 3-axis dynamics. Nonetheless the 3-axis aircraft afforded much better control and measurement of the bank angle and I was able to learn some things that were not obvious during the experiments in my Spectrum.)

When I performed the same experiments in a sailplane (Slingsby Swallow) and a light airplane (Cessna 152), flying with my feet off the rudder pedals, I saw dynamics similar to what I saw in my Spectrum: slip occurred mainly while rolling into a turn, and skid occurred while mainly rolling out of a turn. In turning flight, pitch inputs didn't seem have an effect on sideslip or skid, even when the aircraft were dramatically pitched up under a high G-load or were "unloaded" all the way to weightlessness (zero G's). The only significant difference between these aircraft and my hang glider was that in the three-axis aircraft there was no delay between the roll input and the slip: the slip began as soon as the ailerons were moved, and in fact the nose initially swung away from the direction of roll. (Many higher performance hang gliders will behave the same way). These points indicate that adverse yaw was a major cause of the sideslip in the airplane and the sailplane, in contrast to my Spectrum where adverse yaw seemed minimal.

I didn't look closely at the behavior of the airplane and sailplane in a steady, constant-bank, constant-speed turn; in general sailplanes tend to slip in a steady, constant-bank turn (if the rudder is not used) for reasons I'll explain in more detail in Part Four; in airplanes the engine torque (and p-factor, etc.) is a complicating factor so a steady turn may tend to slip or skid depending on the turn direction and airspeed.

See Appendix 4 for a rough comparison of the spanwise force created by my Spectrum 144 and by a Schweizer 2-22 sailplane, flying at similar sideslip angles.

I've done just a bit of aerobatic flying in 3-axis aircraft (wingovers, aileron rolls, and spins in airplanes, and one spectacular, fully aerobatic lesson in a sailplane with loops, rolls, a cloverleaf, a hammerhead turn, etc). These experiences were not controlled experiments but it never seemed that pitch inputs were affecting sideslip and yaw coordination, even during dramatic maneuvers with marked changes in the angle-of-attack and G-loading.

 

ACTUAL DATA: TIMING OF PITCH AND YAW DYNAMICS IN AN AIRPLANE

As noted above, in my experiments with my feet off the rudders, the airplane slipped mainly while rolling. The pitch dynamics occurred on a much longer time scale. I did some experiments where I fixed the control yoke so that it was free to move in roll but not in pitch--so no pitch "coordination" inputs were possible and the angle-of-attack was nearly constant--and looked closely at the timing of the changes in pitch attitude, airspeed, and G-loading as I rolled from wings-level into a steep (60 degree) banked turn. (I used a low power setting so the plane was normally in a descending glide). Sideslip was seen mainly while the bank angle was changing but the G-loading and airspeed continued to rise for about 10 seconds after the steep bank was established. This delay in the build-up of airspeed and G-loading created an initial "deficit" in G-loading (in relation to the bank angle) which caused the nose to pitch down quite steeply. The G-loading and airspeed then remained somewhat out of phase with the pitch attitude; for example the nose then began to rise toward a more moderate glide path and was actually approaching the horizon by the time that the airspeed and G-loading peaked put at their maximum values (after significantly overshooting the equilibrium values seen when the pitch attitude and airspeed finally stabilized) and began to decrease. The nose actually rose well above the horizon into a climbing attitude and flight path before beginning to drop again. Altogether the pitch attitude and airspeed went through at least two complete oscillation cycles before stabilizing into a steady descending spiral; this whole process took about 20 seconds after the steep bank was established.

One more detail: the nose actually rose briefly during the initial roll into the steep turn, because adverse yaw from the ailerons was yawing the nose toward the high wing. (The roll from wings-level to 60 degrees bank only required about 2 seconds). When I used the rudder to prevent this initial slip and keep the slip-skid ball centered throughout the experiment, this prevented the initial yaw toward the high side of the turn but had little effect on the subsequent pitch-axis dynamics described above.

In a hang glider the time scales and the magnitudes of the oscillations will be different but we will see the same basic dive-and-pullout dynamics when we roll quickly into a turn without making the usual pitch "coordination" input. I'm sure that the airspeed and G-loading will require several seconds to build and that the glider will go through several small oscillations in pitch attitude, airspeed, and G-loading before settling into a steady glide. Of course in a hang glider it's not so easy to perform experiments where the control bar position is completely constant in the pitch axis. The airplane experiment with the yoke fixed in the pitch axis vividly pointed out that as we enter a turn or make other changes in the bank angle, many of our small, almost unconscious pitch inputs are aimed at preventing large oscillations in pitch attitude and airspeed, whether we wish to hold a steady speed or to smoothly accelerate or decelerate to a new target speed.

Interestingly, in these experiments the turn rate seemed to correspond mainly to the bank angle. For example, immediately upon establishing the steep bank, the G-loading (total lift force) and the turning force (i.e. the horizontal or centripetal component of the total lift force) were still low but this was largely compensated by the low airspeed, so the turn rate was only a little less than after the G-load and airspeed built to their normal values

 

ACTUAL DATA: STEEP, REVERSING TURNS IN AN AIRPLANE

In these experiments I looked at several techniques involving a series of reversing turns with the goal of maximizing the sink rate. Dennis Pagen has suggested that to maximize the sink rate of a hang glider, for example to escape strong lift near cloud base, the pilot should fly as series of steep reversing turns, reversing the turn direction each time the airspeed and G-loading build to their peak values, and pulling in the bar each time the glider rolls into a new steep turn. The theory given behind this recommendation is that the glider is thought to be slipping whenever the airspeed and G-loading are building. (See Pagen's Hang Gliding Training Manual p.344 and Performance Flying pp.34 and 53). Dennis notes that the airspeed and G-loading may continue to build for several turns after the steep bank is established. Note that I've described a similar lag in the build-up of airspeed and G-loading, but based on my experiments in hang gliders and 3-axis aircraft I would expect the glider to be actually sideslipping only while the bank angle is increasing. Regardless of the role that sideslip plays in increasing the total drag, we would certainly expect the initial sink rate to be will quite high as the glider arcs over into a steepening dive until the airspeed and G-loading build up to their appropriate values. However I'm skeptical of the overall benefit of a series of changes in the bank angle and the angle-of-attack. For example, in low-speed wings-level flight we could create a high initial sink rate by firmly pulling in the bar, because the glider would dive steeply until the airspeed built up to match the new angle-of-attack and the G-loading returned to the normal value of (nearly) one "G", at which point the glider would round out into a more moderate glide path. Yet we would not use a series of these pulling-in pitch motions to sustain a high sink rate, because the nose would rise dramatically each time we let the bar back out, until we bled off some of the airspeed from the previous dive. We would expect to achieve the highest average sink rate over time by holding the bar fully pulled in, to maximize our average airspeed. Likewise the glider will pitch down steeply when we roll into a steep turn without the usual pitch "coordination" input, but it will also pitch up steeply as it bleeds off excess airspeed if we roll quickly from a steep, diving turn to wings-level without also pulling in the bar. We would expect to achieve the highest sink rate over time by holding the glider in a steeply banked turn rather than by using a series of turn reversals, unless perhaps sideslip due to adverse yaw and yaw rotational inertia was creating a great deal of drag during the turn reversals. By the same logic it's not at all clear why a repeated series of combined pitch and roll inputs would be the most effective way to sustain a high average sink rate, particularly if we don't expect our pitch inputs to contribute to sideslip during the turn reversals. Nonetheless in a recent telephone conversation Dennis told me that his reversing-turn method did yield a higher average sink rate than a sustained, pulled-in, steeply banked turn in experiments he performed in a Sensor and a Classic.

I performed my reversing-turns experiments in an airplane because this allowed for repeated climbs for altitude (altogether I burned off about 50,000 feet of altitude in all the repeated trials to look at all the nuances of the dynamics!) and also allowed much more precise measurement and control of the bank angle and better conditions for the recording of data (via a tape recorder). I used a low power setting so the plane was normally in a descending glide. Since I had already observed that pitch inputs had no apparent effect on sideslip in this aircraft, I fixed the control yoke so that it was free to move in roll but not in pitch, so that I could isolate the effect of changes in the bank angle upon the sink rate. No pitch inputs were possible; all turns were "uncoordinated" in pitch. This loosely simulated a hang glider with the bar "stuffed" or at some other constant bar position and nearly constant angle-of-attack. Therefore I did not exactly replicate Dennis's experiments but did gain some valuable insights into pitch and yaw dynamics which I believe do bear the sink rate question. In particular I saw very clearly that the pitch and yaw dynamics operated on different timescales (as described in the previous section), and that sideslips produced by adverse yaw and yaw rotational inertia as the bank angle was changing had a minimal effect on the overall drag and sink rate during these radical turning maneuvers.

For "method 1" I held the plane in a 60 degree bank. This produced the highest average sink rate. For "method 2" I flew a series of reversing 60 degree banked turns, reversing the turn direction every time the airspeed and G-loading reached their peak values. This method produced a slightly lower average sink rate than "method 1", presumably because the average bank angle and average airspeed were slightly less. Sideslip and skid were seen mainly when the bank angle was actually changing, just as in our hang gliders. The non-equilibrium pitch axis dynamics at play while the G-load was changing were complex, as I've described in more detail in the preceding section. Each time the steep bank was established, the airspeed and G-loading continued to rise for about 10 more seconds until they reached, and then significantly overshot, the steady-state values seen in "method 1". During part of this interval the sink rate was quite high as the glide path became very steep as the nose pitched steeply down, and then the nose began to rise again before the G-loading and airspeed reached their peak values. Each time the aircraft was rolled through wings-level as the turn direction was reversed, the excess airspeed and G-loading retained from the steep turn caused the nose to rise dramatically. One time I stopped the roll in the wings-level position, and a truly dramatic series of pitch oscillations resulted as the excess airspeed was bled off; in general it was obvious throughout "method 2" that the dynamics were far from the steady state and involved a lot of oscillations. For "method 3" I kept the aircraft constantly rolling between left and right 60 degree banks without waiting for the airspeed and G-load to peak out, to take advantage of the slips and skids that occurred mainly while the bank angle was actually changing. This method produced the lowest average sink rate, again presumably because of the lower average bank angle and airspeed. Clearly the slips and skids produced by adverse yaw and rotational inertia as the bank angle changed did not contribute a great deal to the overall drag of the maneuver in this aircraft, even with a fuselage and vertical fin to "feel" the full force of the sideways airflow.

Despite the fact that the control yoke was fixed in the pitch axis, I saw some variation of the angle-of-attack during some of the oscillations, and in particular the angle-of-attack was slightly lower at steep bank angles and high airspeeds. (Changes in angle-of-attack were detected by comparing the predicted, and observed, change in airspeed between the wings-level case and the stabilized 60 degree bank turn). This was appeared to be due mainly to propwash effects, but airflow curvature effects would certainly also contribute to this angle-of-attack change as described earlier in Part One. I also saw that the pitch control force (as distinct from the pitch control position) increased dramatically at high speeds, which of course is a familiar effect to both hang pilots and three-axis pilots.

How do these observations relate to flex-wing dynamics? Are there flex-wing effects that are somehow used to best advantage in the reversing-turns method in some gliders? In Part One we've already described how the curvature of the airflow (following the circumference of a turn) tends to pitch the nose down and reduce the angle-of-attack for a given bar position (or control stick position). We've noted that these effects are most pronounced when the turn radius is small (i.e. at hang-glider airspeeds) though they are somewhat alleviated by flex-wing effects. Also, the Lift / Drag ratio will tend to decrease as the whole wing flexes and "sheds G's" under load. All these factors would weigh in favor of the sustained, steeply banked, well pulled-in turn as the best method to sustain a high average sink rate in a flex-wing hang glider. We do also need to consider the linkage between pitch inputs, roll rate, and sideslip in any gliders where such a linkage can in fact be shown to occur. As the reader can no doubt tell I find myself a bit skeptical of the reversing-turns idea; at the very least it seems to me an open and interesting question whether Dennis's recommendations on this subject will apply to all flex-wing gliders. At some point when I have lots of altitude to burn I'd like to further explore this question both on my Spectrum and on a higher performance wing.

By the way, I'm presenting all this primarily as a point of aerodynamic interest. Dennis Pagen's comments on the dangers of vertigo in sustained steep turns are well taken, and at any rate I'm well aware that in very strong lift a glider must be flown out of the airmass before it can descend by any method. I should also emphasize that I'm not recommending any radical turning maneuvers for a glider that actually enters cloud.

 

PART FOUR: EXPANDED THEORY OF TURNS AND SIDESLIP IN HANG GLIDERS

We began this discussion with a detailed look at pitch-axis dynamics, and then we went through an overview of sideslip and turn dynamics before describing the in-flight experiments. Now I'm going to cover in much more detail the physics of turning flight and sideslip, considering more carefully the various effects that create the overall flight characteristics of the glider. This will fill out the theory behind the conclusions given above. We will focus first on the dynamics while the bank angle is changing, and then on the dynamics in a steady, constant-banked, constant airspeed turn. I'll also briefly describe an experiment I did in my Spectrum to look at the roll rate with and without a vertical fin. We'll end with some interesting Appendices covering topics like blind flying, and lockout dynamics, and also detailing one more experiment that attempted to quantify the sideways aerodynamic force produced in a slip, both in my Spectrum hang glider and in a sailplane.

 

(GENERAL BACKGROUND:)

FRAME OF REFERENCE IN TURNING FLIGHT

Except where otherwise stated, my reference frame is the outside world, not the accelerated reference frame of the pilot. I always use "centripetal" and "centrifugal" to mean real aerodynamic forces acting horizontally toward the inside or outside of the turn, not apparent forces as perceived by the pilot. Occasionally I will make reference to apparent side forces upon the pilot, meaning the tendency of the pilot and the slip-skid ball to "fall" toward the low or high side of the aircraft during a slip or a skid. I've chosen to use the term "G-loading" to refer to the lift vector produced by the wings, which always acts perpendicular to the wingspan; this is also the G-loading measured by the G-meter in the instrument panel of an aerobatic plane, which only detects forces acting "up" or "down" in the aircraft's reference frame. I've generally chosen not to use the term "G-loading" to refer to the total aerodynamic force at play in any given instant, which would include the drag (and thrust) vector and also any spanwise aerodynamic force vector created by sideslip.

When I use the term "airflow" I mean the "relative wind" created by the motion of the glider through the airmass. This "relative wind" or "airflow" is assumed to be aligned with the glider's flight path; I'm not taking into consideration any of the countless changes in the direction of the airflow as it encounters the wing and all the other parts of the glider's structure.

However we have already mentioned "airflow curvature" and will discuss this in much more detail later. By "airflow curvature" I mean the curvature in the airflow or relative wind that is caused by the fact that different points on the surface of the glider are actually moving through space in slightly different directions at any given instant during turning flight. Yes, this may seem strange at first--see the section entitled "Airflow curvature in turning flight" for much more!

 

WHAT MAKES AN AIRCRAFT TURN?

A turn is a curve in the flight path. The sole cause of a turn is a net force that is perpendicular to the flight path. This is called a centripetal force because it points toward the center of the circular flight path. The most efficient way of creating this centripetal force is by tilting the lift vector of the wings (banking). To keep this scenario going, the aircraft must rotate in the yaw axis to keep the heading in synch with the changing direction of the flight path (relative wind). Since aircraft are directionally stable relative to the airflow, this is easily accomplished, but an initial torque is needed to overcome rotational inertia. This is provided by the rudder, or by the force of the airflow against the vertical tail, as the direction of the relative wind changes at the start of the turn. In other words the turn will begin with a bit of sideslip if the rudder is not used.

In hang gliders, the wingtips provide the same function as would a vertical tail. Because the wing is swept, the surfaces which have the greatest moment arm (i.e. the greatest distance from the Center of Mass) are well aft of the Center of Mass, and generate drag in such a way that the glider always tends to weathervane into the relative wind so that the nose of the glider is aligned with the flight path through the airmass. (Later we'll see that airflow curvature effects will slightly complicate this picture.)

Once we establish a steady rotation in the yaw axis, the net torque in the yaw axis must be zero. In a steeply banked aircraft there is also a significant rotation in the pitch axis. In this case the aircraft's inherent pitch stability, which governs the angle-of-attack, must overcome rotational inertia to begin this rotation.

It is very common to see incorrect or incomplete descriptions of turning flight in the hang gliding training literature. For example, Dennis Pagen's bobsled analogy (p.128 Hang Gliding Training Manual and p.45 Performance Flying) runs into problems translating from a 2-dimensional flat surface to 3-dimensional space, and completely misses the fundamental connection between a sideways or centripetal force vector (acting perpendicular to the flight path) and the resulting curvature of the flight path which will produce a circular path through the sky. Pagen states as a general principle of flight that a banked wing will simply produce a sideways slipping force, and that a curvature of the flight path will occur only the pilot pitches up the nose to increase the angle-of-attack. Certainly the nose will drop and the airspeed will increase if the pilot enters the turn without the usual pitch "coordination" input, but I strongly disagree with the widespread idea that a glider will not begin to turn until the pilot makes a pitch-up "coordination" input.

If the pilot fails to make the usual pitch "coordination" input, then the G-load and turn rate will initially be somewhat below normal for the bank angle until the airspeed builds (although the low airspeed will partly compensate for the low G-loading so the initial turn rate will not be as low as we might expect). If the pilot temporarily loads the aircraft with "extra" G's while rolling into the turn then the G-load and turn rate will initially be above normal (for the bank angle) until some of the excess speed and G-loading bleed off. So it's very clear that the angle-of-attack is playing an important role in the turn dynamics; yet we cannot say that the aircraft will not turn if the angle-of-attack is not increased during the turn entry. The only instances where rolling into a bank will not produce a turn at all are if the pilot is holding the wing at the zero-lift, zero-G angle-of-attack (this is only possible in 3-axis aircraft; hang gliders don't have enough pitch control authority to keep the wing at the zero-lift angle-of-attack) or if the pilot is holding enough "top" rudder to create a strong sideslip which generates enough side force to completely cancel the centripetal (turning) force from the banked wing (this is obviously not possible in a rudderless aircraft).

On a related note, as long as the wing's lift force is the only aerodynamic force at play (besides drag), and there are no sideways aerodynamic forces such as may be created if there is a slipping airflow due to adverse yaw or yaw rotational inertia, then the net aerodynamic force is acting squarely "up" in the reference frame of the aircraft and pilot, and the pilot will feel no tendency to fall toward either side of the aircraft. This is true even if the aircraft is steeply banked and the nose is falling and the aircraft is accelerating into a steeper dive because the lift force (G-loading) is inadequate for the bank angle. This is also true even during radical aerobatic maneuvers such as a roll or loop. (Much more on this in later sections).

It is also not at all uncommon to see flawed descriptions of turning flight in the training literature for "general" aviation. I've seen one soaring manual that presented a coordinated turn as some kind of a balance between a loop (due to elevator action only) and a flat skidding turn (due to rudder action only). And then there is the ubiquitous table of G-loads versus bank angles, which states that the loads go infinite at vertical bank but rarely mentions that this analysis also assumes that infinite thrust and airspeed are available to maintain level flight. One excellent resource for anyone trying to work through the physics of turning flight is Wolfgang Langewiesche's 1942 physics-for-pilots classic Stick and Rudder (but see my comment at the end of Part Two regarding some details of his treatment of pitch inputs in turns!).

 

EFFECT OF SIDESLIP ON TURN RATE

***** Note summer 2005 -- It is very important to keep in mind that the magnitude of the aerodynamic sideforce that is produced when a sideways (slipping or skidding) airflow component strikes the side of an aircraft is entirely dependent upon the shape of the aircraft. An aircraft with a large slab-sided fuselage will experience a strong aerodynamic sideforce during a slip or skid, especially if the surface area of the fuselage and other parts of the aircraft is large in relation to the mass of the aircraft. In such an aircraft, a small angle of slip or skid (as measured with a yaw string) will have a large effect on the turn rate. In contrast, an aircraft with a slender streamlined fuselage, or a flying-wing aircraft, will experience only a small aerodynamic sideforce during a slip or skid, especially if the surface area of the fuselage and other parts of the aircraft is small in relation to the mass of the aircraft. In such an aircraft, a large angle of slip or skid (as measured with a yaw string) will have only a small effect on the turn rate. *****

Any centrifugal aerodynamic forces (toward the outside of the turn) will decrease the net centripetal force and slow the turn rate. A sideslip, where the airflow strikes one side of the aircraft (and also flows crosswise over wings and other surfaces) will create such a centrifugal force in most aircraft. The bank angle is then too steep for the net centripetal force and acceleration, and the pilot tends to "fall" toward the low side of the aircraft. A slipping turn describes a circle in space, just as any other turn, but the nose of the aircraft is always pointing toward the outside of the circular flight path, and the airflow against the "slewed" fuselage and other components of the aircraft generates forces that slow the turn rate.

During a slip at a steep bank angle, the side force created by the spanwise (slipping) airflow includes a significant vertical component that will bear part of the aircraft weight, and this will reduce the lift vector generated by the wing. For this reason, a slip actually reduces the net aerodynamic load on the aircraft and the net force or net G-loading experienced by the pilot at a particular bank angle. Again, the turn rate will be reduced, even though the centrifugal component in the aerodynamic side force from the slip starts to decrease as the bank angle increases past 45 degrees. The extreme case is sustained, high-speed, vertically banked, knife-edge flight by an aerobatic airplane. Here the wing is "unloaded" to zero G's, and the entire aircraft weight is borne by fuselage and vertical fin, which are flying at an "angle-of-attack" equal to the sideslip angle. Although the side force created by the slip no longer includes a centrifugal (horizontal) component, the turn rate is zero because the wing's lift vector has disappeared. The total aerodynamic load is one "G".

In aircraft with rudders, a sideslip can easily be made to completely cancel the turn at moderate bank angles--see Appendix 3 for more.

 

MORE ABOUT TORQUE

Note that unbalanced torques persist only briefly in aircraft. The aircraft will find its own equilibrium state. For example, if tip drag is pulling the right wing backwards during a turn to the left, that will yaw the vertical tail to the left, so that the airflow against it provides a counterbalancing torque. In hang gliders, the wingtips provide the equivalent effect of a vertical tail because they are well aft of the center of mass. The turn will continue at a steady rate in this slipping condition, with the nose yawed a bit to the outside of the turn.

 

REFERENCE FRAME IN A SIDESLIP, AND GENERATION OF SIDEWAYS FORCES AND DRAG

It is important to notice that aerodynamic terms like "centripetal", "centrifugal", "lift", and "drag", are all defined relative to the flight path (relative wind), not the aircraft heading. Therefore a sideslip is best described by saying that the nose is yawed to the outside of the flight path, so that the heading and the flight path are not the same. This could happen either by changing the flight path changing without changing the heading, or by yawing the glider to change the heading without changing the direction of the flight path. When I refer to the aerodynamic side force created by a slip, I mean the force component which is aligned with the glider's wingspan in the roll axis--acting toward the high wing--and is at the same time perpendicular to the flight path. At shallow bank angles this is mainly a horizontal force acting toward the outside of the turn (i.e. it is a centrifugal force) but as the bank angle steepens this side force remains aligned with the wingspan in the roll axis and so gains an increasing vertical component, which at very steep bank angles may bear a significant portion of the aircraft weight. Also, if the bank angle is very steep and if the flight path is steeply descending rather than level, then as this sideways aerodynamic force vector remains perpendicular to the flight path, it will be tilted significantly forward of the true vertical and so will contain a horizontal component which will point "straight ahead" along the aircraft's direction of travel. (It's not easy to pin this side force vector down with terms like "vertical" and "horizontal"; its primary reference frame relates to the direction of the flight path and airflow.)

This aerodynamic side force is actually a form of lift generated as the sideways (spanwise) airflow component impinges against the flat side areas on the fuselage, vertical tail, winglets, and other suitably shaped components of the aircraft. The sideslip angle can be viewed as the "angle-of-attack" of the fuselage and other aircraft components in the yaw axis. The sideways "lift" forces will be associated with induced drag loads which will steepen the glide path; other sources of drag will also increase as the aircraft meets the airflow in a less-than-optimal manner; these drag loads will act parallel to the airflow and so are not included in the aerodynamic side force vector.

Note that the sideways aerodynamic force vector created by the sideslip is not quite parallel to the wingspan because it is not strictly aligned with the wingspan in the yaw axis. As the aircraft's nose is yawed further away from the flight path, the direction of the sideways force vector does not change relative to the flight path (though its magnitude will increase). For example, in the case of the aerobatic airplane flying at a 90 degree bank angle and held in an approximation of horizontal flight by the application of lots of top rudder to hold the nose up and to generate a "lift" force from the slipping airflow over the fuselage, vertical tail, etc, the side force vector acts basically upwards and its direction (relative to the flight path) does not change as the pilot works the rudders to yaw the nose further up or down and change the "angle of attack" of the fuselage in the yaw axis.

 

HOW DOES A HANG GLIDER PRODUCE A SIDEWAYS AERODYNAMIC FORCE IN A SLIP?

***** Note summer 2005 -- In subsequent experiments, I've added a rudder to several different hang gliders and observed the deflection of slip-skid bubbles during intentional sustained sideslips. These observations revealed that in a hang glider, a slipping airflow produces only a very small aerodynamic sideforce. *****

How can a slipping hang glider, which has very little vertical surface area, produce a sideways aerodynamic force (and the associated increase in drag)? Think carefully about how the different components of a hang glider will react to a sideways (spanwise) airflow component. Vertical, round tubing and wires will simply change the direction of their drag vectors and therefore will generate some spanwise force components but will not generate any true spanwise "lift" forces acting perpendicular to the airflow. Lengthwise units such as the keel and the pilot's body, and streamlined downtubes, will be flying at an "angle-of-attack" (in the yaw axis) equal to the sideslip angle and so will generate some sideways "lift" components. Stepping and looking at the three-dimensional shape of the glider as a whole it is really quite hard to imagine how a hang glider in a sideslip could generate strong sideways "lift" components acting perpendicular to the airflow. With no fuselage side area and no vertical tail, we might expect the hang glider to be relatively "transparent" to a sideways airflow, so that the aerodynamic side force generated by a given sideslip angle might be minimal in a hang glider compared to other aircraft. This means that we might see a great deal of slip in the yaw string, but only a little displacement of the slip-skid bubble, and only a little apparent side force upon the pilot. If the total aerodynamic side force is small than the centrifugal (horizontal) component will also be small and will not slow the turn rate very much. This kind of slip would likely generate only a small amount of additional drag and so glide angle might not steepen very much. (See Appendix Four for a rough comparison between the forces generated in a sideslip by my Spectrum 144 and by a Schweizer 2-22 sailplane).

A slip generates drag in several ways: first, by the sideways motion of various aircraft surfaces through the air as described above. Second, if a given turn rate is to be maintained in spite of the centrifugal force from the slip (or if we desire to cancel the turn entirely and hold a constant heading in a slip in a 3-axis aircraft), the bank angle must be increased, leading to an increase in the wing's lift and drag vectors. Third, regardless of whether significant centrifugal forces are being generated, the wing is simply less efficient in the slipping airflow so the wing's induced drag increases. This may be the most important source of drag in hang glider slips.

 

DYNAMICS WHILE THE BANK ANGLE AND AIRSPEED ARE CHANGING:

SIDESLIP DUE TO YAW ROTATIONAL INERTIA

In a rudderless aircraft, the first thing that happens when the wings are banked is that the aircraft accelerates sideways toward the low wing. This is a curvature in the flight path: we are starting to turn. Since the actual heading of the glider has not changed yet, the airflow over the glider gains a spanwise component and centrifugal aerodynamic forces build in opposition to our sideways (centripetal) acceleration. These centrifugal aerodynamic forces keep the turn rate low. Meanwhile the slipping airflow interacts with the yaw stability of our aircraft, generating the torque to overcome inertia and start a rotation in the yaw axis. Once we are rotating in synch with the turn rate, then the sideways component in the airflow disappears, and we settle into a steady turn driven by the centripetal force from the banked wings. The yaw rotation rate is now steady, and there is no more need for a sideslip (at least so far as rotational inertia is concerned--later we will discuss reasons that we might see sideslip in a steady, constant-bank turn).

By the same reasoning we expect a bit of skid (airflow from the outside of the turn) when the bank angle is decreased and rotational inertia continues to yaw the nose around at the original yaw rotation rate.

This initial sideslip is not unique to hang gliders. As we will see in the section entitled "Balancing yaw and roll stability", any aircraft with sweep or dihedral depends upon this principle to keep the wings level in straight-ahead flight.

In higher performance hang gliders with more mass and wingspan and less wing sweep, the sideslip due to rotational inertia will be much more pronounced, especially at low airspeeds where the turn rate is high and the profile drag forces on the airframe are low.

One important caveat: as we roll past 45 degrees, the yaw rotation rate actually begins to decrease (while the pitch rotation rate continues to increase). Therefore above 45 degrees of bank, yaw rotational inertia reverses its effects, tending to promote a skid as the bank angle steepens and a slip as the bank angle decreases.

 

ADVERSE YAW

***** Notes summer 2005 --this section actually overlooks an effect which for many aircraft is the most important source of adverse yaw. This effect is the twist in the direction of the relative wind, and the resulting twist in the lift and drag vectors, that is experienced when a wing rises or falls as the aircraft rolls to a new bank angle. For more, see this subsection in the related article on the Aeroexperiments website entitled "Causes of adverse yaw in hang gliders and "conventional" aircraft--with notes on yaw strings, slip-skid balls, rudder usage, yaw rotational inertia, "airflow curvature", aerodynamic "damping" in the roll axis, and flex-wing billow shift". A key point is that this mechanism generates an adverse yaw torque during a constant-rate rolling motion where both wings are creating the same amount of lift, and not only during the initial acceleration in the roll rate when the left and right wings are generating uneven amounts of lift. *****

Another cause of slip in turn entries in hang gliders is the adverse yaw produced by the way the wing twists as the pilot weight-shifts. Just as in an aircraft with ailerons, the left and right airfoil shapes change, and there is a lift and drag increase on the wing that is being raised. This adverse yaw torque acts as an "anti-rudder", and initially can swing the nose in the opposite direction of the turn. This inhibition or reversal of the yaw rotation is a form of sideslip. The sideslip then interacts with the yaw stability of the aircraft to create its own torque, into the direction of turn. At some angle of sideslip all torques are balanced: we would expect to see this sideslip angle in a stabilized, constant-bank turn if the pilot had to low-side the bar. Conversely if the pilot had to high-side the bar in a constant-bank turn, this would create an anti-skid or pro-skid influence. In a hang glider adverse yaw is produced whenever the pilot is exerting a muscle force on the control frame, regardless of whether or not the bank angle is changing, and regardless of whether his body is on the glider centerline or is shifted to one side. (See the lockout discussion in Appendix Two for much more on this). Adverse yaw is greater at high angles of attack (i.e. at low airspeeds, or when the glider is "pulling" extra G's in an accelerated maneuver), and is greater in higher performance gliders with less wing sweep and more span.

As adverse yaw tends to push the nose the wrong way when a turn is initiated, it will certainly appear to the pilot that the turn rate is being greatly slowed. However, the actual change in the turn rate is not the same as the yaw rotation rate, and depends on how much centrifugal force the glider produces as it flies sideways through the air.

I can't come up with any way that our usual pitch "coordination" inputs would act to decrease adverse yaw, though flex-wing aerodynamics are undoubtedly so complex that almost anything as possible in some specific maneuver in some particular glider!

As Dennis Pagen has frequently pointed out, a weight-shift roll input would create adverse yaw even if there were no physical change at all in the airfoil shape, because the more heavily loaded inner wing would tend to fly faster. The way I like to think about this is that relative to the center of gravity of the whole system, the outboard wing has become slightly longer and has gained in surface area, while the inboard wing has become slightly smaller.

 

CONSIDERING ADVERSE YAW AND YAW ROTATIONAL INERTIA TOGETHER

***** Note summer 2005 -- if we compare the analysis given below of full 360-degree rolls, with the rudder imputs that most three-axis aircraft require during full rolls, we reach the conclusion that in most cases involving "conventional" aircraft, aerodynamic adverse yaw torques are more important than yaw rotational inertia effects. The same may well be true for flex-wing hang gliders. *****

The effects of adverse yaw and yaw rotational inertia must be considered in combination, not separately. For example, when a pilot is rolling a rudderless aircraft into a steeper turn, and the bank angle is already above 45 degrees, then yaw rotational inertia promotes a skid while adverse yaw promotes a slip. What is really happening here? Let's give a hypothetical example with some (completely hypothetical) numbers thrown in. Imagine that because of adverse yaw, when some particular rudderless aircraft is given a strong roll input by the pilot, the aircraft "wants" to fly with the nose yawed 20 degrees toward the high wing, relative to the airflow and flight path: this is the attitude where are all the yaw torques are in balance as the aircraft rolls. In this attitude, the increased drag of the outboard wing is balanced by the slipping airflow over the aircraft, so the net yaw torque is zero. As the aircraft rolls from 0 to 45 degrees bank, we know that the yaw rotation rate is increasing so we might find that the nose is actually yawed 30 degrees toward the high wing, relative to the airflow. This additional slip is caused by yaw rotational inertia as the yaw rotation rate lags behind the actual turn rate, and this additional slip is what provides the yaw torque that drives the increase in yaw rotation rate. As the aircraft continues to roll from 45 to 90 degrees bank, we know that the yaw rotation rate is now decreasing, so we might find that the nose is actually yawed now only 10 degrees toward the high wing, relative to the airflow. The decrease in the slip angle is caused by yaw rotational inertia as the nose tends to keep swinging toward the low wingtip at a high rate. Now the nose is actually aimed to the inside of the "balanced" position of 20 degrees, so the aircraft is now experiencing a net torque toward the low wing, which acts to drive a decrease in the yaw rotation rate.

(I haven't analyzed this closely but these rotational inertia effects may help to explain why an aileron roll involves some rather complex changes in rudder input to keep the slip-skid ball centered, even though the aileron deflection is constant and the airspeed is smoothly decreasing so adverse yaw should generally be smoothly increasing. The changes in G-loading through the roll will have some effect on the amount of adverse yaw present, too. See fig. 22-2 in William Kershner's The Flight Instructor's Handbook 3rd ed. (1993).)

In a rigid-wing glider like the ATOS or Exxtacy where roll control is achieved with spoilers and adverse yaw is minimal, then we would see only the effects of yaw rotational inertia, and so we might actually see a skidding airflow as we roll past 45 degrees.

Clearly, adding a vertical tail or winglets to a hang glider will increase the amount of torque generated by a given degree of sideslip, so rotational inertia and adverse yaw will be overcome more easily and less sideslip will be seen as the glider rolls into a turn.

 

EFFECT OF SIDESLIP ON ROLL RESPONSE

***** Note Summer 2005 -- this section contains a significant error. It assumes that modern flex-wing hang gliders exhibit a positive coupling between slip (yaw) and roll throughout most of the flight envelope. During the course of more recent experiments, I've discovered that most modern flex-wing hang gliders actually exhibit a negative coupling between slip (yaw) and roll through most of the flight envelope. This mean that the slipping airflow created as an aircraft adverse-yaws will provide a helpful roll torque, not an unfavorable roll torque as stated below. *****

We've already described how a sideslip interacts with a glider's inherent yaw stability to create a yaw torque. Since roll creates sideslip through yaw rotational inertia and adverse yaw, this leads to a coupling between roll and yaw. A sideslip also interacts with sweep or dihedral to create a roll torque away from the side component in the airflow. Therefore the sideslip created by yaw rotational inertia and by adverse yaw will inhibit the roll response of the glider, not just the yaw rotation rate. Glider designs that show minimal sideslip while rolling into turns will also have good roll rates.

 

BALANCING YAW AND ROLL STABILITY

***** Note Summer 2005 -- this section contains a significant error. It assumes that modern flex-wing hang gliders exhibit a positive coupling between slip (yaw) and roll throughout most of the flight envelope. During the course of more recent experiments, I've discovered that most modern flex-wing hang gliders actually exhibit a negative coupling between slip (yaw) and roll through most of the flight envelope. This mean that when a flex-wing hang glider has unintentionally dipped a wing, the resulting slipping airflow will create a destablizing roll torque that will tend to increase the bank angle, not a stabilizing roll torque. Therefore, with this type of aircraft, installing a large vertical fin to increase the "weathervane" yaw stability and decrease sideslip will reduce the aircraft's spiral instability, not increase the aircraft's spiral instability. The opposite is true of many other aircraft: free-flight model aircraft are a good example. With these aircraft, as described below, plenty of dihedral will not be sufficient to allow the aircraft to remain upright in hands-off flight in turbulent air if the vertical fin is too large. If the vertical fin is too large, when the aircraft banks it will quickly "weathervane" into a normal turn with minimal sideslip before the dihedral has time to bring the aircraft back to a wings-level condition. Rigid-wing hang gliders and any other aircraft with dihedral and/or sweep, and no anhedral, will behave in this manner, unless the fuselage is quite long in relation to the wingspan, in which case the curving airflow can interact with the vertical fin to cause a sideslip rather than to dampen sideslip. At any rate, the original content of this section applies well to rigid-wing hang gliders without anhedral, but not to flex-wing hang gliders with anhedral.*****

When an aircraft dips a wing in turbulence, it begins to turn. The rotational inertia of the aircraft creates a slip as the yaw rotation rate lags behind the turn rate. While the aircraft is slipping, the airflow interacts with sweep or dihedral and tends to roll the aircraft back to wings-level. However if the aircraft has excessive yaw stability (perhaps due to a large vertical fin or excessive sweep), it will quickly "weathervane" into a steady or tightening turn before it can roll back to level flight. On the other hand, with too little yaw stability the aircraft will slip excessively when the pilot begins a deliberate turn. As the glider slips it resists the pilot's intentions in both the yaw and roll axes.


ANHEDRAL EFFECTS AND POSSIBLE LINKS TO PITCH INPUTS

***** Note Summer 2005--During the course of more recent experiments, I've discovered that most modern flex-wing hang gliders actually do exhibit a negative coupling between slip (yaw) and roll throughout most of the flight envelope, exactly as I conjectured below in relation to the "hypothetical blade-wing hang glider". Careful tests revealed that even the Wills Wing Spectrum used in the experiments described in this article exhibits this characteristic at most angles-of-attack. And I've also discovered--as suggested below--that this characteristic is much stronger at low angles-of-attack than at high angles-of-attack. This characteristic does not make the Spectrum radically spirally unstable in any part of the flight envelope, as I suggested it might in the discussion below. It does, however, allow the glider to harness adverse yaw, converting it into a helpful roll torque.

Since so much confusion about sideslips permeates the hang gliding literature, I haven't come to any conclusions as to whether the reported behavior of the CSX glider as described below really does reflect a very strong overbanking tendency at low angles-of-attack, with accompanying severe adverse yaw (slip) caused by the rapidly increasing bank angle, or relates instead to a sensitive pitch response and a tendency to enter an accelerating, steepening, but basically non-slipping, diving turn when the pilot makes certain control inputs. I'm a bit skeptical of the former theory because for a given roll rate, in most aircraft adverse yaw is much more pronounced at high angles-of-attack than at low angles-of-attack. I have not personally encountered any hang glider that showed a marked tendency to sideslip when I pulled in the control bar, regardless of whether I was holding the bank angle constant or causing or allowing the bank angle to increase.

***** End of comments summer 2005

The above comments refer to an aircraft that is stable in roll. The same principles, but acting in the reverse sense, will apply to a glider that is unstable in roll. Consider a hypothetical high performance "blade wing" glider with little sweep, little yaw stability, and much rotational inertia and adverse yaw. This glider will be designed with a lot of anhedral to increase roll response. With enough anhedral, the glider will actually be unstable in roll, by which I mean that it will tend to roll toward rather than away from a slipping airflow and will therefore show a feedback effect between sideslip and roll when the pilot makes a roll input or a wing is lifted in turbulence. A careful look at the geometry suggests that the anhedral effect might be significantly stronger at low angles-of-attack, so we might simultaneously drive both slip and roll by pulling in the bar while rolling. This might explain the strong connection between pulling in the bar while rolling into a turn, and sideslipping, that pilots report for some high-performance gliders. (See for example p.21 of Dennis Pagen's article "Hang Glider Turn Perspectives" in the April issue of Hang Gliding; in a recent telephone conversation Dennis mentioned that he noticed this on the Moyes CSX glider in particular). I need to strongly emphasize that I've reached the hypothetical stage here: I don't have experience with high performance "blade wings" and don't know whether are fundamentally unstable in roll in this way or show this linkage between pitch inputs and the effectiveness of the anhedral. I also want to emphasize that this effect would not create a coupling between pitch inputs and slip in cases where the pilot was holding a steady bank angle as he pulled in the bar.

 

EFFECT OF A FIN ON ROLL RATE

***** Note Summer 2005 -- this section contains a significant error. It assumes that modern flex-wing hang gliders exhibit a positive coupling between slip (yaw) and roll throughout most of the flight envelope. During the course of more recent experiments, I've discovered that most modern flex-wing hang gliders actually exhibit a negative coupling between slip (yaw) and roll through most of the flight envelope. This mean that the slipping airflow created as an aircraft adverse-yaws will provide a helpful roll torque, not an unfavorable roll torque as stated below. Therefore a large vertical fin to reduce effects of adverse yaw should decrease the roll rate, not increase the roll rate. In practice I haven't been able to detect this effect while flying a several different hang gliders, including my Airborne Blade with VG loose and with VG tight, with and without a large vertical fin.*****

I was thinking about the effect of a vertical fin on roll rate during a recent visit to Wallaby Ranch. It was clear that many pilots preferred to fly without the fins that new students use to learn aerotowing, saying that many gliders roll poorly and don't thermal well with fins. For gliders that are stable in roll, a fin should actually increase the roll rate by damping sideslip as described just above in "Balancing yaw and roll stability". In the case of the hypothetical blade wing with extreme anhedral and an unstable coupling between slip and roll, a fin would decrease the roll rate (but I'm a bit skeptical that any actual hang gliders behave this way!) Notice that a rigid-wing glider with positive dihedral as well as some sweep will likely benefit quite a bit from a vertical fin, in terms of roll rate. I took a couple of tows in the calm morning air in my Spectrum to look at roll rate with and without a fin, and found no measurable change. More on how a fin might affect handling in steady, constant-bank thermal turns later.

 

WHY DO AIRSPEED CHANGES AND SIDESLIPS OCCUR TOGETHER? A COMPLETE DESCRIPTION OF THE DYNAMICS IN THE PITCH AND YAW AXES AS THE GLIDER IS ROLLED INTO A TURN

This section is really a repetition of information contained in the earlier sections on the pitch-axis dynamics and the analysis of the in-flight experiments; I give it again here for the sake of completeness.

Let's review once again the sequence of events in the pitch axis as the glider is rolled to a steeper bank angle, in an artificially "telescoped" breakdown of events: first, the pilot shifts his weight to the side. Any adverse yaw due to differential airfoil shapes will come into play at this time. Second, a significant bank angle is developed, and the flight path begins to curve due to the centripetal force from the wing (the turn has started). The heading of the glider has not yet changed, so there is a sideways component in the airflow which creates centrifugal aerodynamic forces that keep the turn rate low. Third, the aircraft begins to rotate in the yaw axis due to its inherent yaw stability (the "weathervane" effect), which creates an aerodynamic torque to overcome yaw rotational inertia and swing the nose into the relative wind. This yaw rotation removes the sideslip and allows the turn rate to increase. As long as the roll rate is substantial, a significant sideslip angle can be maintained, because the bank angle and centripetal force can keep "ahead of" the yaw rotation rate of the glider. When the bank angle is stabilized, the slip will soon end except for effects such as differential wingtip drag, and adverse yaw if the pilot is low-siding the bar.

If the angle-of-attack is not increased by letting out the bar as the glider rolls, then the vertical component of lift is being diminished as the bank angle increases, and so the airspeed must also increase as we've already noted. The airspeed takes some time to build, so the airspeed and G-loading remain lower than their equilibrium values (for the bank angle and angle-of-attack) until the glider stops rolling and the airspeed can "catch up". This makes the flight path curve downwards as the glider "falls" and the airspeed builds. While the airspeed is in transition, the airspeed, lift and drag vectors, G-loading, turn rate, and glide ratio are all slightly less then their equilibrium values for the angle-of-attack and bank angle at any given instant, and there is a downward curvature in the flight path. The airspeed and G-loading will then build and then slightly overshoot their steady-state values, leading to a slight upward curvature of the flight path that brings the glider toward its final, equilibrium glide path. Over several seconds these oscillations will damp out and the glider will settle into its stabilized, constant-airspeed flight path. The slight delay in the build-up (and loss) of airspeed and G-loading (lift) is the reason that the aircraft goes through these oscillations instead of immediately settling into the appropriate glide path for the bank angle and angle-of-attack at any given instant. The airspeed will eventually stabilize at some value dependent only upon the bank angle and the position of the pilot's body on the control bar (angle-of-attack), and the wing's lift vector (G-loading) will then be stabilized at a value depending only mainly the bank angle (and to a small extent upon the L/D ratio). The glide path or glide ratio is now stabilized at some angle determined only by the bank angle and the L/D ratio (which is governed by the angle-of-attack; the angle-of-attack in turn is governed mainly by the bar position and to a small extent by the bank angle as described earlier in Part One).

The airspeed may be held constant by letting out the bar and increasing the angle-of-attack as the glider is rolled. (However, before the glider is rolled very far, the stall angle-of-attack would be reached, so for very large changes in bank angle an increase in airspeed cannot be avoided.)

All of these pitch-axis dynamics are independent of yaw coordination and sideslip. The sideslip due to rotational inertia is roughly synchronized in time with the airspeed increase (if any) created by the pitch dynamics, but the slip is not caused by the pitch dynamics or the airspeed increase. If the airspeed is held constant by letting out the bar to "coordinate" the turn, the sideslip will still occur. The degree of sideslip depends on the roll rate rather than on the pilot's pitch inputs. In an aircraft with rudders where the sideslip can be prevented altogether, the airspeed increase will still occur unless the angle-of-attack is increased. But the fact that the roll rate simultaneously drives these dynamics in the pitch and yaw axes is no doubt one reason that many hang glider pilots believe that pitch inputs must have an effect on sideslip, or that the sideslip itself is the main cause of the airspeed increase as the glider seems to "fall" off toward the low wing.

Interestingly the component of sideslip that is due to adverse yaw (and not rotational inertia) will initially actually raise the nose relative to the horizon, as the glider yaws toward the high wing. On the long run a sideslip usually does cause the nose to fall and the airspeed to increase, because the wing is less efficient in the slipping airflow. On the other hand the fact that the sideways aerodynamic force vector bears a significant part of the aircraft weight during a sideslip at a very steep bank angle means that a sideslip will actually relieve some of the pitch-down motion and acceleration in airspeed that we would otherwise see as a glider rolls to an extreme bank angle. But all these are one-way relationships: I'm maintaining that pitch dynamics and pilot pitch inputs have little effect on the sideslip angle.

If a pilot pulls in the bar in while shifting to the side, this will exaggerate the effects that we see when we roll into a turn without letting out the bar. The initial G-loading and turn rate will be decreased and more airspeed will be gained. As long as the control bar is kept moving aft, it contributes to the same "unloading" effects as are caused by the steepening bank angle: because the airspeed is in transition, the airspeed, G-loading, turn rate, and glide ratio are less than the values predicted by the bank angle and angle-of-attack at any given moment, and the flight path curves downward. Again, these effects are independent of the sideslip condition of the glider which has its own effect upon the turn rate.

These pitch-axis effects look much like the effects of an increased sideslip angle: the nose pitches down as the glide path steepens. The crucial difference is that dynamics in the pitch axis convert altitude into kinetic energy as well as into drag, while a sideslip produces an increase in the drag coefficient that need not coincide with an increase in airspeed. This is why a sideslip is such a valuable tool for controlling the final approach path in a 3-axis aircraft, where it may be sustained indefinitely (and with no change in airspeed) even in straight-ahead flight. The large sideslip angles available to 3-axis pilots allow this maneuver to be effective even at low airspeeds, whereas a hang glider sideslip might not produce a lot of drag unless performed at a high airspeed.

If a pilot pushes out excessively to strongly increase the angle-of-attack and really "load up" the glider and "carve out the turn", the G-loading and turn rate will immediately increase, but then will settle back to their equilibrium values (for the new angle-of-attack) as the excess airspeed is bled off. The final value of the G-loading will depend only upon the bank angle (with small variations according to the L/D ratio), while there will be some net increase in the turn rate due to the lower airspeed. All these dynamics will occur regardless of the sideslip condition of the glider before and after the pitch input.

In a steady turn with a stabilized G-loading, the turn rate is inversely proportional to the airspeed, regardless of the sideslip condition of the glider. The turn radius is inversely proportional to the airspeed squared. As the airspeed is decreased, the tighter turn might seem more "coordinated" to the pilot, but this really has nothing to do with yaw coordination and sideslip.

Since a sideslip in a hang glider occurs primarily while the bank angle is changing, the only way to keep the glider slipping is to fly the glider in a series of reversing turns; see the section in Part Three entitled "Actual data: steep reversing turns..." for some thoughts on the effectiveness of this technique.

 

FUNDAMENTAL RELATIONSHIPS: DOES AN "IMBALANCED" G-LOADING CREATE A SIDEWAYS FORCE ON THE PILOT?

***** Note summer 2005 -- for a fresher take on some of the material in this section, see the related article on the Aeroexperiments website entitled "You can't feel gravity! " *****

Many pilots believe that if the magnitude of the G-load produced by the wings (lift force) is not properly matched to the bank angle, then there will be some kind of force imbalance that will push the pilot (and the slip-skid ball) toward the low side of the aircraft. (For example see figure 3-1 in Pagen's Performance Flying). I've been arguing that this isn't the case as long as there is no sideways component in the airflow over the glider. The G-load produced by the wing always acts upward (or downward when pulling negative G's) in the reference frame of the pilot, and does not exert any side force on the pilot. We can easily see this by flying aerobatic maneuvers in an airplane or sailplane. As long as we use the rudder to offset effects like adverse yaw and keep the yaw string or slip-skid bubble centered, we won't experience any tendency to fall toward the low side of the aircraft even as we are passing through a vertical bank angle during an aileron roll or wingover. This is true regardless of whether we are sinking into the seat-bottom cushion under a heavy positive G-loading or have "unloaded" the wing to zero G's and are floating weightless in the cockpit as the aircraft follows a ballistic trajectory.

However, if we used the rudder to make the aircraft fly in a sideslip (or if we allow yaw rotational inertia or adverse yaw to create a sideslip), then the fuselage and other components would produce sideways aerodynamic forces that would push us toward the low side of the cockpit. The extreme example of this is sustained, knife-edge flight in an aerobatic aircraft at a 90 degree bank angle, where top rudder is applied to hold the fuselage at a high "angle-of-attack" to the airflow to keep the flight path horizontal. In this case the wing is unloaded to zero G's, and the aerodynamic side force produced by the slipping airflow over the fuselage, vertical fin, etc. is entirely vertical and supports the entire weight of the aircraft. The pilot "feels" a 1 G force toward the low side of the fuselage as the aircraft pushes up on him (through the seat belts or the cockpit sidewall) in the opposite direction (away from the earth, and towards the high side of the cockpit) with a force equal to his body weight.

A fascinating point here is that the pilot feels only the forces produced by the aircraft. These forces are transmitted to him through the seat and seatbelts (or in a hang glider, through the hang strap and through the pilot's arms on the control bar). The force of gravity itself is not apparent in the pilot's reference frame, because it accelerates the aircraft and the pilot together. (Also the force of gravity is not felt by the pilot's muscles and nervous system because it accelerates every molecule of the pilot's body equally). If the total aerodynamic (and propulsive) forces equal zero G's, then the pilot will be weightless in ballistic flight--astronauts experience weightlessness for precisely this reason since drag, thrust, and lift are all absent in space once the engines are switched off. Gravity is present but not felt. And anytime the lift vector (plus other aerodynamic and thrust vectors) happens to equal +1G in the "upward" direction, relative to the pilot and aircraft, the pilot will feel the "normal" forces of level flight, even while banked 90 degrees, or inverted at the top of a loop or aileron roll.

Clearly, any vector diagram illustrating why the pilot "falls" toward the low side of aircraft during a sideslip must include the sideways aerodynamic force (aligned with the wingspan in the roll axis) that is created by the sideways or spanwise airflow, as this is the sole reason for an apparent sideways force in the pilot's reference frame. Yet nearly all vector diagrams that attempt to illustrate slips in hang gliders omit this sideways aerodynamic force vector, and "put the cart before the horse" by implying that an imbalance between the lift vector (G-loading) and the weight or gravity vector is the direct, immediate cause of an apparent sideways force on the pilot which allows him to fall toward the low side of the control bar. This erroneous conclusion invariably stems from an inaccurate treatment of the weight (gravity) vector and also of "centrifugal force". Much more on this later when we will learn how to draw our own, accurate vector diagrams for turning and slipping flight.

 

FUNDAMENTAL RELATIONSHIPS: WHY DOESN'T THE AIRCRAFT SLIP TOWARD THE LOW WING WHEN THE G-LOADING IS INADEQUATE IN A TURN?

In the previous section we saw that the aircraft must slip sideways through the air to create an apparent sideways force upon the pilot. If the G-loading is inadequate for the bank angle, as we pitch down and fall (accelerate) earthwards will we also slide toward the low wingtip, creating a spanwise airflow component? While flying aerobatic maneuvers in an airplane or sailplane I've never noticed any tendency for the aircraft to slip sideways when the G-loading was "too low" for the bank angle, even when I unloaded the wing to all the way to zero G's and flew a weightless trajectory. Likewise in the careful experiments I performed in my Spectrum, a sailplane, and an airplane (flying with my feet off the rudders) I saw no tendency for the aircraft to slip when I pitched the nose down to reduce the angle-of-attack, temporarily "unloading" the wing to a lower G-loading. I only saw slip while the bank angle was changing, due to adverse yaw and yaw rotational inertia.

This is a bit counterintuitive. When the G-loading is "too low" for the bank angle and the aircraft is pitching down and accelerating, we might also expect to see a sideslip toward the low wingtip as we "fall". Note that this is really an issue of a change in the yaw rotation rate: we are really saying that the yaw rotation rate might need to increase in order to yaw the nose earthwards and keep aircraft pointing into the relative wind as we begin to "fall", and this would involve some sideslip until we overcome the aircraft's yaw rotational inertia. On the other hand we might point out that when we "unload" the wing with a pitch-down input while the aircraft is banked, we actually decrease the turn rate (in terms of degrees around the horizon per second) and so the yaw rotation rate may also actually need to decrease rather than increase. In this case we would tend to see skid (rather than slip) in a rudderless aircraft until we overcome the yaw rotational inertia. Since our pitch input only changed the wing's lift vector, which acts entirely perpendicular to the wingspan, perhaps these effects cancel out without forcing any slipping or spanwise airflow at all? The situation is very three dimensional and dynamic and difficult to visualize in its entirety. However we may gain some additional insight by thinking carefully about what happens when we finally return to equilibrium at the new angle-of-attack and airspeed. When the pilot pulls in the bar and "unloads" the wing in the above thought experiment, the glider eventually settles back into a steady, constant-airspeed turn at the new, decreased angle-of-attack. The airspeed has increased, and so the turn rate has decreased. In a rudderless aircraft, this means that there has in fact been a skid, rather than a slip. This is the exact opposite of the "conventional wisdom" on hang glider turns; in practice the change in yaw rotation rate is not large and the resulting skid is negligible from the pilot's point of view. As I've already described, in my experiments I found no evidence of a noticeable link between pitch inputs and sideslip in my Spectrum and in some 3-axis aircraft.

This is interesting: rolling into a 45-degree bank while "unloading" wing to zero G's will require about the same acceleration in yaw rotation (toward the low wing) as rolling into the 45-degree bank while pulling a high G-load.

Now, to be fully complete we need to bear in mind that changes in pitch attitude do actually change the bank angle too (this complex three dimensional relationship can be seen by "flying" through a chandelle maneuver with your hand--the bank angle will steepen as the aircraft pitches up higher and higher) and so we may need to introduce roll forces--and the attendant adverse yaw--just to hold the bank angle steady! Nonetheless the main point remains that pitch inputs and changing G-loads do not drive a large change in the yaw rotation rate and thus do not create a noticeable slip or skid.

 

FUNDAMENTAL RELATIONSHIPS: HOW TO DRAW YOUR OWN VECTOR DIAGRAMS FOR TURNING FLIGHT

*****Note summer 2005 -- this section is basically redundant with the one that follows, where the graphics are actually included with the text, except that graphics aren't provided for case 2 (excessive lift), case 4 (no lift), and case 6 (skidding turn). Most readers will probably benefit from skipping directly to the next section, and then returning here if they want to learn more about those three specific cases. *****

Now we're going to revisit the ideas in the preceding section with the benefit of some vector diagrams; this is the best way to understand these concepts. After undergoing some frustration while trying to get the appropriate graphics up on this website, I've decided to give readers the satisfaction of drawing their own diagrams. The following instructions will help the interested reader create a whole table of diagrams which will serve as a "Rosetta stone" to unlock all the mysteries of turns (or will plunge the reader into a similar state of frustration of their own!). (A hint for lazy readers who don't want to draw: see the next section.)

Take out a clean sheet of paper and divide it into 6 horizontal rows and 3 vertical columns. Label the 6 rows as follows: 1. Turn is "coordinated" in pitch and yaw. 2. "Excessive" lift or G-loading for bank angle. 3. "Inadequate" lift or G-loading for bank angle. 4. Zero-G aerobatic maneuver--not advised in hang gliders! 5. Slipping turn. 6. Skidding turn.

Now label the 3 columns as follows: A. Forces on glider. B. Net force on glider. C. Force "felt" by pilot, i.e. force transmitted from glider to pilot, i.e. G-loading.

Now in all 18 boxes draw a quick sketch of a banked glider, head-on view, suggested bank angle somewhere between 30 to 45 degrees. Use the same bank angle in every box. Now fill in the vector diagrams as follows: in all the boxes in column A, draw the weight or gravity vector acting vertically downward on the glider. In box 1A, add the Lift vector, perpendicular to the wingspan and of a length such that its vertical component is equal to the gravity vector. Do not add any more vectors to box 1A besides gravity and Lift. DO NOT add a centrifugal force vector! In box 2A and 3A, again add the Lift vector, perpendicular to the wingspan, but make it respectively longer, and then shorter, than in 1A. In box 4A let the gravity vector stand alone. In box 5A, add the lift vector and also add a small spanwise force vector, perpendicular to the Lift vector and pointing toward the high side of the turn. This represents the sideways aerodynamic force generated by a slip. (Make this spanwise vector fairly small; its horizontal dimension should be smaller than the horizontal component of the lift vector, so that we still have a net horizontal force toward the inside of the turn.) Notice that you'll have to draw the Lift vector slightly shorter than in 1A to make the forces balance in the vertical axis, especially if you've drawn a steep bank angle. Go ahead and do this. In box 6A add the lift vector and a small spanwise force vector pointing toward the inside of the turn, representing the aerodynamic side force from a skid. In this box you'll have to make the lift vector slightly longer than in 1A to balance out the forces in the vertical axis, especially if you've drawn a steep bank angle. Go ahead and do this. (Note that it is convenient to use the term "spanwise lift vector" in this 2-dimensional drawing because this vector is aligned with the wingspan in the roll axis, but as explored in section entitled "Reference frame in a sideslip", during a slip the glider will be yawed so that the wingspan is no longer quite perpendicular to the airflow (which goes straight into the paper in these diagrams) while the sideways or "spanwise" lift vector will remain perpendicular to the airflow.)

For column B, in each box draw a single arrow representing the sum of the vectors in the corresponding box in column A. All the boxes except 4B should reflect a horizontal component; this is the centripetal force that drives the turn. Box 2B will include an upward component, and boxes 3B and 4B will include a downward component. (In fact box 4B will simply contain the gravity vector standing alone).

For column C, again draw a single vector representing the sum of the forces in the corresponding box in column A, but this time omit the gravity vector from your calculations. In other words we are now only summing the aerodynamic forces; we can term this sum the "total aerodynamic load". This net aerodynamic force vector is really the complete "G-loading" felt by the pilot (but recall that in this paper we've usually found it convenient to reserve the term "G-loading" to represent only the wing's lift vector). In any case this net aerodynamic force vector is the complete force that the glider will exert on the pilot. Gravity is not included in this summation because it acts simultaneously upon both glider and pilot and so is not "felt" by the pilot; this is the whole key to understanding zero-G maneuvers. Boxes 1C, 2C, and 3C will simply show the Lift vector which we drew in the corresponding boxes in column A, acting squarely perpendicular to the wingspan and straight "up" in the glider's reference frame. Box 4C will be empty--this is a zero-G maneuver. In box 5C (the sideslip) the net aerodynamic load or total G-loading vector is no longer perpendicular to the wingspan but instead is tilted toward the high wing. This is the force that the glider will exert on a pilot who is tightly buckled in or is holding on tight to the base bar. In reaction, the pilot will say that he "feels" a force toward the low side of the aircraft as his body presses back against the seat belt or against the forces transmitted through his arms from the base tube. A freely hanging pilot, and the freely rolling slip-skid ball, will "fall" toward the low wing (the inside of the turn). In box 6C--the skid--the net aerodynamic load or total G-loading vector is again not perpendicular to the wingspan--in this case it is tilted toward the low wing--this is like going around an unbanked turn in a car where the tires are exerting a sideways "push" to create the centripetal turning force. The pilot will "feel" an opposing force toward the high wing, i.e. toward the outside of the turn, and a freely hanging pilot and the slip-skid ball will tend to deflect in this direction.

These diagrams explain why either a slip-skid ball or a yaw string, may be used in most situations to tell if an aircraft is "coordinated" in the yaw axis (i.e. slipping or skidding or meeting the airflow "straight on"): a sideways airflow is generally the only possible cause of an apparent side force in the pilot's reference frame.

We can debate about which of these boxes show the action of apparent "centrifugal force"--I would suggest box 6C--but in my own opinion this is not a very interesting argument as this force exists only as a byproduct of the basic aerodynamic forces at play. The take-home message of this table is that apparent side forces on the pilot are created by actual aerodynamic side forces on the aircraft, and not by a deficiency in the wing's lift vector (G-loading).

The net force upon the aircraft included an upward component in box 2B ("excessive" G-loading) and a downward component in box 3B ("inadequate" G-loading). In the first case the aircraft will be pitching upward and losing airspeed, and in the second it will be nosing downward into a dive. A relevant question is "do these vertical dynamics create a slipping or skidding airflow component, as illustrated in rows 5 and 6?" What happens when a pilot is in a "coordinated" turn as in row 1, and then pulls in the bar to "unload" glider as in row 3, without allowing the bank angle to change? Will the resulting "falling" motion create a slipping airflow as in row 5? This is really a question about how the yaw rotation rate of the glider will change as it noses down into a steeper dive. If the yaw rotation rate is essentially constant, then aircraft will continue to face squarely into the airflow and no slip or skid is expected. If the yaw rotation rate must increase to yaw the nose down into the relative wind as the glider begins to "fall", then we expect to see some slideslip until we overcome the glider's yaw rotational inertia. On the other hand the turn rate slows as we decrease the G-loading and so we might actually expect to see a decrease in the yaw rotation rate, which in a rudderless aircraft will involve a skid. When the glider eventually returns to equilibrium (case 1) at the new, pulled-in bar position it has gained airspeed and therefore the turn rate and the yaw rotation rate have decreased. In a rudderless aircraft this implies that there has in fact been a slight skid, rather than a slip. In practice I've found that pitch inputs generally don't have a noticeable affect on sideslip, when the bank angle is held constant.

These diagrams are intended to apply to both powered and unpowered flight. The alert reader will note that the drag (or thrust) vector should be included also, as it bears part of the aircraft weight in a glide (or climb). This will not affect the basic conclusions about the direction of the apparent force on the pilot in these maneuvers, except that when the dive (or climb) angle is very steep the drag or thrust vector will add a noticeable force pushing aft or forward upon the pilot, so that part of the pilot's weight will be supported by the seat belts or the seat-back cushion. In a hang glider the pilot will tend to hang further forward on the bar when the drag vector is large and the glide path is steep, and this plays into the relationship between control bar position and pilot muscle force or control "feel". These effects can be "simulated" on the ground by tilting the pitch attitude of the aircraft up or down.

 

MORE VECTOR DIAGRAMS

***** Note summer 2005 -- for a more complete discussion of the physics of slips and turns based on these three vector diagrams, see the related article on the Aeroexperiments website entitled "Accurate diagram of forces in a “fully coordinated” turn with no sideslip and adequate lift (G-loading), a turn with inadequate lift (G-loading) and no sideslip, and a slipping turn with adequate lift (G-loading)".

Now that you've done all that work, I've put my own graphics up here too! These diagrams are from my July 2000 article in Hang Gliding Magazine. They are very similar to the diagrams I described immediately above; Figures 1,2,3 correspond to rows 1,3, and 5 in the above discussion.

 

 

L=Lift, W=Weight, S=Spanwise aerodynamic force from sideways airflow in sideslip, Na=Net aerodynamic force=L+S, N=Net force on aircraft=L+S+W

In all cases the horizontal component of N is the centripetal force that creates the turn. In case 2 (inadequate G-load or lift force) N has a downward component, so the aircraft will be nosing over into a steeper dive and gaining airspeed as it "falls". Na is the force transmitted from the aircraft to the pilot and is really the total G-loading "felt" by the pilot (though we should recall that in this paper we've usually found it convenient to reserve the term "G-loading" to represent only the wing's lift vector). The weight or gravity vector is not "felt" by the pilot because gravity acts simultaneously on both aircraft and pilot--this is the key to understanding "zero-G" maneuvers (but please don't try them in a hang glider!). Only in case 3 (sideslip) does the pilot "feel" a force toward either side of the control bar. While the aircraft is slipping, the aerodynamic side force toward the high wing tip is transmitted to the pilot through the seat or through the pilot's arms on the downtube. A freely hanging pilot, or the freely rolling slip-skid ball, will swing toward the low wing tip. In case 3 (sideslip) the pilot has been drawn on the low side of the control bar to illustrate this deflection, and also to illustrate that a pilot roll input will cause sideslip because of adverse yaw and yaw rotational inertia.

What happens when a pilot is in a "coordinated" turn as in case 1, and then pulls in the bar to "unload" glider as in case 2, without allowing the bank angle to change? Will the resulting "falling" motion create a slipping airflow as in case 3? This is really a question about how the yaw rotation rate of the glider will change as it noses down into a steeper dive. When the glider eventually returns to equilibrium (case 1) at the new, pulled-in bar position it has gained airspeed and therefore the turn rate and yaw rotation rate have decreased. In a rudderless aircraft this implies that there has in fact been a slight skid, rather than a slip. In practice I've found that pitch inputs generally don't have a noticeable affect on sideslip, when the bank angle is held constant.

 

DYNAMICS IN STEADY TURNS AT CONSTANT AIRSPEED AND BANK ANGLE:

Until now we have been concerned with the flight characteristics of the glider in response to various control inputs. Now let's consider factors that might create sideslip in stabilized turns at constant speed and bank angle.

 

AIRFLOW CURVATURE IN TURNING FLIGHT

In turning flight, the direction of the airflow changes along the length of an aircraft due to a phenomenon called airflow curvature. By this we don't mean the myriad changes in the airflow direction as the airstream impinges upon the various parts of the glider, curves around the airfoil, washes down behind the wing, etc. Instead we are referring to the change in the direction of the airflow or relative wind that is caused by the fact that different points along the length and span of the glider acre actually moving through space in slightly different directions at any given instant during turning flight. The instantaneous linear velocity at any point on the glider is affected by the rotation of the glider as well as by the linear velocity of the glider as a whole. To understand this, imagine the extreme example of a glider pinwheeling around in a yaw rotation, while fixed in space with no forward motion at all of the glider as a whole. Obviously yaw strings at the nose and tail will blow in opposite directions, due to the relative wind caused by the rotation. In this extreme example, at any given instant points at the nose and keel are traveling in completely opposite directions. In an actual turn, where the yaw rotation rate is in synch with the turn rate, the yaw rotation of the aircraft causes the relative wind to follow the curvature of the flight path, i.e. the circumference of the turn. (For example see Fig. 1 in Dennis Pagen's article "Turn Perspectives" in the April 2000 issue of Hang Gliding.) Looking down at the aircraft, we can see that the radius of this circle will be slightly less at the inboard wingtip and slightly greater at the outboard wingtip.

A turning aircraft is rotating in the pitch axis as well as the yaw axis, particularly at steep bank angles. This will create a curvature of the airflow in the pitch axis, again following the circumference of the turn. As we noted in Part One, as the bank angle increases the airflow curvature in the pitch axis "pushes" up on the rearmost surfaces of the aircraft (i.e. the tail, or the wingtips of a swept wing) and so tends to lower the nose and decrease the overall angle-of-attack of the wing.

If we visualize the airflow as the aircraft flies through a complete 360 degree turn, the effects of airflow curvature in the pitch and yaw axes make the airflow resemble a horizontal slice taken out of a giant bowl. A very steeply banked aircraft would appear to be flying high up on the near-vertical side of a small bowl, while a shallow-banked aircraft would appear to be flying on the lower, flatter, surface near the bottom of a much larger bowl. The airflow curvature effect is really only significant in-slow flying aircraft with small turn radii relative to the dimensions of the aircraft. It was well described by in a series of articles called "Spiral Stability and the Bowl Effect" by Blaine Beron-Rawdon that appeared in Model Aviation in September and October 1990, and also in articles by the same author in the same magazine in August through November of 1988. These articles discuss flow curvature in relation to stability and efficiency in rudder-controlled model sailplanes, but the ideas within apply to all aircraft.

I've computed some values for the theoretical airflow curvature over various portions of the glider in hang glider turns. If the bank angle and airspeed are known, the turn radius can be derived from the formula (centripetal force = mass * velocity squared / radius). It is then straightforward to calculate the curvature over various distances along the circumference of the turn. I used a wings-level reference speed of 22.5 mph which was then increased according to the square root of the increased wing loading in the turn. A steady turn at constant airspeed and G-load was assumed. These calculations apply to any aircraft, except that slower speeds would create more airflow curvature than is calculated here, and higher speeds would create less curvature. (Also, I've made the simplifying assumption that the flight path is horizontal. This has a negligible effect on the calculations except at very high airspeeds where the aircraft is in a steep dive with a very poor L/D ratio).


 Bank Angle:

 10 20 30 45 60

 Airspeed (mph):

 22.7 23.2 24.2 26.8 31.8

 Turn Radius (ft):

 194 99 68 48 39

 Total Airflow Curvature (degrees) over keel length (352 cm):

 3.4 6.7 9.7 13.6 16.5

 Airflow Curvature in Yaw Axis (degrees) over keel length (352 cm):

 3.3 6.3 8.4 9.6 8.2

 Airflow Curvature in Yaw Axis (degrees) from extreme rear of keel to:

         

 "Center" of Wing (dist. 139 cm):

 1.3 2.5 3.3 3.8 3.3

Yaw String in Front of Basebar (dist. 290 cm): 

 2.8 5.1 6.9 7.9 6.8

 Apex of Glider (dist. 352 cm):

 3.3 6.3 8.4 9.6 8.2

 "Bowsprit" Yaw String (dist. 539 cm):

 5.1 9.5 12.7 14.3 12.2

The maximum airflow curvature in the yaw axis occurs at 45 degrees; airflow curvature in the pitch axis continually increases with bank angle.

The data I reported earlier (about 6 degrees slip on the yaw string in the base bar "probe", and 0 degrees slip on the rear yaw string, at 20 to 30 degrees bank) are generally consistent with these figures but aren't accurate enough to explore this subject in great detail. In particular, I couldn't see a difference between the yaw strings on the "bowsprit" and the base bar probe, and I didn't explore the effect of changing the bank angle or airspeed.

 

AIRFLOW CURVATURE AND SIDESLIP: OBSERVED EFFECTS

***** Note summer 2005 -- there are bound to be at least two or three degrees of error in any observation of the position of a yaw string in actual flight, so overly detailed conclusions about the exact point along the keel of the glider that is tangent to the curving airflow aren't justified. Also, subsequent experiments of slip-skid bubbles have shown that in the case of a hang glider, a slipping airflow produces only a very small aerodynamic sideforce so it's certainly not reasonable to expect to see a significant displacement of a slip-skid ball or bubble due to the slight sideslip that takes place in steady, constant-banked turn, i.e. due to the fact that the place where the keel of the glider is tangent to the curving airflow is probably aft of the glider's center of center of surface area or "geometrical center". *****

The above analysis describes the curvature of the airflow over various distances but says nothing about whether the aircraft as a whole will be in a sideslip. In other words, we haven't identified the point on the glider where the keel is tangent to the curving airflow, or alternatively stated that the entire glider is in a slip or a skid. My reading of the rear yaw string suggests that the airflow was tangent to the keel at this point, which would create a slip angle of roughly 3 degrees over the geometrical "center" of the wing as a whole (located 139 cm from the rear of the keel, by my rough calculation from the geometry of the sail as viewed from above.) I don't know exactly how the true 3-dimensional shape of the aircraft generates side-forces at various slip angles, but I might expect a noticeable displacement of the slip-skid bubble in this slipping airflow. The fact that the slip-skid bubble was centered in steady turns suggests that the "average" airflow over the wing was in fact well aligned with the keel, and that the tangent point might have been near this "center" of the wing. Simultaneous, more accurate observation of the various yaw strings might shed more light on these points.

 

BALANCE OF FORCES IN THE YAW AND ROLL AXES: THEORY

***** Note Summer 2005 -- this section contains a significant error. It assumes that modern flex-wing hang gliders exhibit a positive coupling between slip (yaw) and roll throughout most of the flight envelope. During the course of more recent experiments, I've discovered that most modern flex-wing hang gliders actually exhibit a negative coupling between slip (yaw) and roll throughout most of the flight envelope. This means that a slipping airflow will interact with the overall 3-dimensional geometry of the wing to create rolling-in torque, not a rolling-out torque. For reasons discussed in more detail elsewhere on the Aeroexperiments website (see the site map), the glider's net geometric anhedral will be most pronounced, and therefore the rolling-in torque created by a slipping airflow will also be most pronounced, at low angles-of-attack (high airspeeds), and also when the VG is loose rather than when the VG is tight. Many other important effects come into play to affect the balance of roll torques in a circling flex-wing hang glider--for example, the more washout and billow is present, the less lift the wingtips will generate and the shorter the glider's "effective span" will be, which will minimize the rolling-in torque created by the difference in airspeed between the outside and inside wingtips. Note also that in any case where a slipping airflow is creating a rolling-in torque, installing a large vertical fin to reduce the angle of sideslip should also reduce the amount of high-siding required in a constant-banked turn. These subjects will be dealt with in more detail on the Aeroexperiments website in the future. For now, take the original content of this section strictly as "food for thought" because nearly all the statements and conclusions are affected by the error described above.*****

At first glance we might expect to see some sideslip in the overall, average airflow when a rudderless, slow-flying aircraft is in a steady turn. The rearmost portions of an aircraft act at the greatest moment arm from the center of gravity, and so tend to align themselves with the airflow: this is the basic "weathervane" principle behind yaw stability. For this reason we might expect the airflow to be tangent to the keel or fuselage at some point well aft of the center of mass.

This effect is seen in sailplanes, which usually require the pilot to hold some inside rudder for a sustained, constant-bank, coordinated turn, despite the fact that the pilot must also usually hold the ailerons toward the outside of the turn to keep the bank angle constant. In fact high-performance sailplanes are sometimes deliberately allowed to slip a bit in turns, as indicated by a yaw string at the nose, because their slender, rounded fuselages generate relatively little drag and centrifugal force in the slipping airflow, but efficiency is thought to be gained by keeping the big vertical tail streamlined in the airflow, i.e. tangent to the circle of the flight path (see Blaine Beron-Rawdon's articles, and "Winning" by George Moffat and letters to the editor April 1999 Soaring magazine for more on this).

Of course we must also consider the balance of forces in the roll axis. Due to airflow curvature effects, the outboard wingtip is experiencing a significantly faster airflow than the inboard wingtip. This creates an overbanking tendency. The inboard wing therefore must be held at a higher angle-of-attack than the outboard wing if the net roll torque is to be zero. The inboard wing will therefore generate more induced drag. In most cases the total drag of the inboard wing will therefore be greater than the outboard wing (except in aircraft that use spoilers for roll control). This will tend to yaw the nose toward the inside of the turn in a skid. Especially in a tailless aircraft, this tendency may overcome the pro-slip "weathervane" effect that we described immediately above. Clearly a particular rudderless aircraft may show either a slip, or a skid, in a steady, constant-banked turn, depending on the details of its particular aerodynamic shape. Other details like bank angle and angle-of-attack will also undoubtedly play a role; for example, anything that affects turn radius will affect the degree of curvature in the airflow.

Note that the pilot may or may not need to high-side the bar (or hold the control stick toward the outside of the turn) to maintain the necessary difference in the effective angle-of-attack between the two wings. Certainly weight-shift wing flex effects, or ailerons, or spoilers will increase the effective angle-of-attack of the inboard wing when the pilot gives a roll command toward the outside of the turn. (I'm using the term "angle of attack" very loosely here particularly in reference to spoilers, I hope my meaning is clear. It might be more accurate to say that the inboard wing has a higher lift coefficient.) Also, in a flex-wing hang glider, the faster airflow over the outboard wing will tend to bow the leading edge aft, reducing the trailing-edge sail tension and allowing the angle-of-attack of the outboard wing to decrease. This will reduce the need for high-siding, especially in a lower-performance glider with a lot of flexibility in the airframe and sail. Also, if there is in fact a slipping component in the airflow, and if the glider has either dihedral or sweep, then the inboard wing will experience a higher effective angle-of-attack than the outboard wing even if the pilot is centered on the bar. (The term "angle of attack" is correct in relation to dihedral effects but is not quite the best word to use in relation to sweep effects; "lift coefficient" might be better.) This is another reason why high-performance sailplanes are sometimes allowed to slip a bit while thermalling: the slip reduces the need for the pilot to hold the control stick to toward the outside of the turn, and so by keeping the ailerons near the neutral position the total drag is thought to be reduced. By the same reasoning, in a radio-controlled model sailplane, with a rudder but no ailerons, a steady, constant-bank turn must always involve some sideslip which interacts with dihedral to achieve a balance in lift between the two wings. (This is particularly noticeable in model sailplanes because the airflow curvature effects are much more pronounced due to the low airspeeds and turn radii involved--the previously mentioned articles by Blaine Beron-Rawdon explore this in full mathematical detail). If an aircraft is experiencing a skid, rather than a slip, in a steady, constant-banked turn, then these tendencies are reversed: the more sweep or dihedral the aircraft has, the more it will tend to roll out of the turn, and the more the pilot will be required to high-side the bar.

So we've seen that the particular aerodynamic shape of a given of aircraft will determine whether there is a slipping or skidding airflow (over the wing as a whole) in a steady, constant-banked turn, and also whether the pilot will need to give a rolling-in or rolling-out control input. As a very general rule, we might conclude that hang gliders with much sweep, much airframe flexibility, and minimal anhedral will tend to experience a slipping airflow in a steady turn due to the "weathervane effect" of yaw stability (as the rearmost parts of the glider tend to align themselves with the curving airflow) and will also tend to require the pilot to low-side the bar to counter the roll torque from the slip, while hang gliders with little sweep, much anhedral, and little airframe and sail flexibility may experience either a slipping or skidding airflow in a steady, constant-banked turn and in either case will likely require the pilot to high-side the bar. Rigid-wing gliders with little sweep, positive dihedral, and spoilers for roll control will likely show some slip in steady, constant-banked turn. If the pilot needs to high-side the bar then the drag from the spoiler on the outboard wing will create this slip; if the pilot can stay centered on the bar then it is likely that a slip is being caused by the "weathervane effect" of yaw stability and is interacting with dihedral and sweep to balance the lift between the two wings. We might expect to see the latter case when a vertical fin is installed.

Earlier in this discussion, we posed the question "are there some gliders with so much anhedral and so little sweep that they are basically unstable in roll?" Such a glider would tend to roll into a slipping airflow and away from a skidding airflow. If the pilot let go of the bar in wings-level flight, then any tipping of the wing would create a feedback cycle and the glider would slip, turn, and roll further from wings-level. Interestingly, in such a glider, the pilot would need to high-side the bar if the glider experienced a slipping airflow in a steady, constant-banked turn, and the pilot would need to low-side the bar if the glider experienced a skidding airflow in a steady turn: this is a reversal of the usual situation. (I don't know whether or not such gliders exist).

 

BALANCE OF FORCES IN THE YAW AND ROLL AXES: OBSERVED EFFECTS

***** Note Summer 2005 -- this section contains a significant error. It assumes that modern flex-wing hang gliders exhibit a positive coupling between slip (yaw) and roll throughout most of the flight envelope. During the course of more recent experiments, I've discovered that most modern flex-wing hang gliders actually exhibit a negative coupling between slip (yaw) and roll throughout most of the flight envelope. This mean that a slipping airflow will interact with the overall 3-dimensional geometry of the wing to create rolling-in torque, not a rolling-out torque. See the comments at the beginning of the previous section for more on this.

In light of this, I haven't come up with a good aerodynamic explanation of why some gliders (like my Spectrum) that exhibit a slight slip in a steady, constant-banked turn also require the pilot to exert a rolling-in ("low-siding") torque, not a rolling-out ("high-siding") torque to hold the bank angle constant. (One possible factor: a descending constant-banked turn actually involves a rolling-in rotation about the aircraft's roll axis, and a climbing constant-banked turn actually involves a rolling-out rotation about the aircraft's roll axis. The extreme cases of climbing or diving turns are vertically climbing or vertically diving rolling maneuvers. Note that we're using "climbing" and "diving" in relation to the surrounding airmass, not in relation to the ground. As a result of all this, in the absence of any other factors, a constant-banked descending turn would require the pilot to exert a rolling-in torque to overcome the aircraft's aerodynamic damping about the roll axis and keep the required rolling-in motion going to hold the bank angle constant. In a climbing-out turn, a rolling-out torque would be required to overcome the aircraft's aerodynamic damping about the roll axis and keep the required rolling-out motion going to hold the bank angle constant. Note that what we're really saying is that a descending turn is inherently more stable than a climbing turn; this point is relevant to the physics of flight under power, as discussed in an interesting article about flying hang gliders with powered harnesses entitled "Thoughts on handling under power" by Richard Cobb. Note also that these rolling motions that take place during a constant-bank angle turn will create their own adverse yaw torques, by means of the mechanism described in the discussion of adverse yaw elsewhere in the Aeroexperiments website. These adverse yaw torques will act to swing the nose toward the outside of the turn during a descending turn. Of course many other factors may also create significant yaw torques during a constant-banked turn, including whatever high-siding or low-siding roll inputs the pilot must make to hold the bank angle constant.)

Re the last two sentences of the original content below: since most flex-wing hang gliders--and especially high-performance flex-wing hang gliders--have enough anhedral to create a negative coupling between yaw (slip) and roll throughout most of the flight envelope, in the absence of any other complicating factors a need for high-siding would serve as evidence that the glider was slipping, not skidding. And regardless of the precise mechanism that is making the bank angle tend to increase during a steady, constant-speed turn in a high-performance hang glider, it would be a bit of a stretch of logic to argue that the pilot's high-siding control input will necessarily create a large adverse yaw torque that will end up making the glider skid, even though many other factors such as the difference airspeed and drag between the inside and outside wingtips would tend to create a slip.

End of notes summer 2005 *****

As noted above, in a steady, constant-banked turn in my Spectrum at a moderate bank angle (about 30 degrees) I had to low-side the bar, and the keel of the glider appeared to be tangent to the curving airflow at some point near the rear of the keel, and a slip-skid bubble appeared to be centered. As previously noted these bubble and yaw string observations are not completely consistent with each other; the fact that I had to low-side the bar suggests that the wing as a whole may have experienced a slipping airflow component which interacted with sweep to create a roll torque toward the outside of the turn. However as noted above this roll torque could also have been created by flex-wing effects that reduced the angle-of-attack of the outboard wing.

On p.20 of his article "Hang Glider Turn Perspectives" in the April 2000 issue of Hang Gliding, Dennis Pagen noted that many hang gliders require the pilot to high-side the bar in a constant-banked turn, and that for this reason many of these gliders will show a slight skid rather than a slip in a steady turn. Dennis mentioned experiments with yaw strings but I don't know which gliders were included in these tests.

 

IS THERE A BENEFIT TO A SKIDDING TURN IN A HANG GLIDER?

***** Note summer 2005 -- In subsequent experiments, I've added a rudder to several different hang gliders and observed the deflection of slip-skid bubbles during intentional sustained sideslips. These observations revealed that in a hang glider, a slipping airflow produces only a very small aerodynamic sideforce. So while a slipping airflow may create only a small drag increase in an aircraft with no fuselage or vertical tail, the same slipping airflow will create almost no aerodynamic sideforce to increase the turn rate (i.e. to decrease the turn radius) for a given bank angle. I believe that skidding turns are inefficient in all aircraft, and more so in "flying-wing" aircraft than in "conventional" aircraft. *****

Some hang glider pilots actually prefer to see a bit of skid in a steady thermal turn to achieve a higher turn rate for a given bank angle. This point requires some careful thought: is the skid really doing anything to decrease the sink rate at a given turn radius? Would the glider turn more efficiently at the same radius if it performed a coordinated (non-skidding) turn at a slightly steeper bank angle? This gets back to a question I've raised often in this discussion: "how much side force, and how much drag, is created by the spanwise airflow when a hang glider slips or skids?" My own intuition says that a skidding turn offers no advantages over a coordinated turn; this is based in part upon my experience in 3-axis aircraft where a skidding turn is considered not only to be inefficient, but also to be an invitation to a spin.

 

EFFECT OF A FIN ON HANDLING IN THERMAL TURNS

As I've already mentioned, during a recent visit to Wallaby Ranch I noticed that most pilots said that their gliders thermalled better without fins. A glance at the many interdependent factors described above in the section "Balance of forces in the yaw and roll axes: theory" will make it clear why a vertical fin could either increase or decrease the roll input required of the pilot to sustain a steady, constant-bank thermal turn. The effect could vary markedly from one glider type to another, depending on the precise direction of the airflow at the rear of the keel. In my own glider I didn't notice any particular difference in the roll input needed to sustain a steady thermal turn flying with and without a fin, but I should note that I didn't do careful experiments to look at this, except for timing the roll rate from wings-level with and without a fin as described earlier (there was no noticeable change). By the way we should consider the simple possibility that a glider will naturally handle best in the same configuration (finned, or finless) for which the particular design was optimized and tuned; a fin may be most effective when it is designed into the glider from the start.

 

THAT'S ALL FOLKS (except appendices...)

Thanks for having the interest to read this far. It takes a great deal of time and thought to really absorb these points. My own viewpoint has gone through a quite a process of evolution; the earliest versions of this paper were quite different from what you are reading now! Believe it or not my interest in these questions began several years ago not as a purely academic exercise, but rather while trying to reconcile what I was reading in the training handbooks with what I had experienced in flight in other aircraft and was just beginning to experience in hang gliders. I'm a relatively new hang glider pilot and my only claim to expertise is that I have a solid understanding of basic physics, and I've given these subjects a lot of thought, and I've gone out and done some of the necessary experiments.

At this point the reader may well be wondering, "so what is the practical application of all this!" To experienced hang glider pilots the answer will likely be "very little" because such folks are thoroughly familiar with how to control their gliders in the air and are operating largely upon ingrained instincts rather than upon theory and thought. (However they may wish to browse once more through the sections entitled "Effect of a fin on roll rate", "Effect of a fin on handling in thermal turns", the thoughts on methods to escape cloud suck in "Actual data: steep reversing turns in an airplane", and the thoughts on blind flying in Appendix One.) However to new students, and to those who are instructing new students either on the training hill or through books and magazines articles, the ideas in this discussion may have considerable application. I believe that I've given a good description of our practical pitch "coordination" inputs in Part Two in the section entitled "So why do let out the bar while rolling into a turn", and that our instructional methods can be made more streamlined and more accurate by following the ideas in Part Two in the section entitled "Suggestions for teaching methods". I also believe that the ideas I've presented in this discussion will help those trying to analyze complex problems like lockouts.

I'm continually learning more about these subjects and have benefited from advice from many other people. R. David Phillips of Australia helped me to understand flex-wing dynamics, and Don Burns originally got me thinking seriously about rotational inertia during some discussions on the hang-gliding e-mail list. A remarkable thread on the e-mail list about blind flying gadgets was what really first started me going with these experiments. Steve Morris of Bright Star filled me in on some details of how airflow curvature and wing flex combine to affect angle-of-attack in a turn, and Mark Lukey got me thinking about the free-body approach to analyzing pilot control inputs (see the Lockout section). Dennis Pagen offered valuable comments about possible anhedral effects in high-performance wings, and on the slip-skid characteristics of some other gliders in steady, constant-banked turns. And of course Dennis's various training manuals--of which I own four--are packed with interesting and useful information; in particular his detailed explanations and diagrams illustrating the prevailing understanding of turns and slips in hang gliders gave me plenty of food for thought even in the days when my own feet had scarcely left the ground of the training hill.

Above all I'm interested in learning more about other experimental work already done in flex wing dynamics, and in doing more experiments of my own on other wings. All my comments are made in the spirit of inquiry, and I'm happy to discuss any of these points in more detail with anyone so feel free to get in touch with me. I'll see you all in the air.

 

APPENDIX 1: A NEW CLOUD FLYING "INSTRUMENT"

***** Note Summer 2005 -- This section is entirely obsolete. I STRONGLY caution anyone against intentionally flying a hang glider into a cloud--over-stress and structural failure may result. Also, further experiments have shown that a bubble level or slip-skid ball or large floating ball compass (used as a level device) is absolutely useless as cloud-flying aid for hang gliding even in most optimistic case where the pilot is trying to discern the direction of a stabilized, constant-banked turn of unknown direction, because the amount of sideslip that occurs in this situation is rather small, and more importantly, because the amount of aerodynamic sideforce (and therefore the amount of displacement of a slip-skid ball or bubble level or floating compass ball) for a given angle of sideslip is extremely small. A yaw string is very slightly more useful, but is by no means adequate to allow a pilot to remain control of a hang glider even in the most ideal conditions. In the most ideal conditions the heading guidance offered by GPS receiver can be a significant help. In the most ideal conditions the heading guidance offered by a standard magnetic compass can be even more helpful, provided that the situation is such that the pilot can chose a heading in the quadrant centered around due magnetic south, and provided that the pilot manages to stay on top of things well enough that the bank angle remains very shallow and that any turn that develops is halted before the glider strays too far from a south magnetic heading. It is absolutely critical that the aircraft never turns to a heading that contains even a slight northerly magnetic component. These ideas are explored in more detail in a newer article on the Aeroexperiments website entitled "Emergency tools and strategies for cloud flying without gyro instruments in "conventional" aircraft and hang gliders". *****

In the early days of aviation pilots learned the hard way about the perils of flying into clouds without gyro instruments. An aircraft generates its own G-loading and creates an artificial sense of which way is "up" and a pilot may believe that he is in level flight when he is really entering a loop, turn, or spiral dive. While the human sense of balance can provide some information about changes in turn rate and G-loading, and can detect whether an aircraft is slipping or skidding, it cannot distinguish a steady, coordinated (non-slipping), constant-rate turn from wings-level flight. To further compound the problem, the human mind tends to create strong and disorienting illusions as it attempts to puzzle out the direction of the turn and sort out where the true horizon lies from these very limited inputs from the senses. Even in hang gliders, pilots have fallen out of turbulent clouds in a wild diving turn, even as they were holding themselves all the way to the low side of the control bar because their mind was insisting that the glider was turning in the opposite direction! (This was related in a very vivid on-line posting by one of the pilots involved).

In a sailplane or airplane, an accidental entry into cloud without gyro instruments often ends with a high-speed spiral dive and structural failure because the pilot pulls too many G's or exceeds the red-line airspeed, causing excessive drag loads or flutter. Rigid-wing hang gliders have the same vulnerability. Flex-wing hang gliders have a much better shot at surviving an accidental entry into cloud than do most other aircraft, because of factors like a greater inherent roll stability, the relatively limited nature of the pilot's pitch control authority, the general dragginess of the airframe, and the ability of the wing to flex and "shed G's" in a high-airspeed situation. Some hang pilots even make a practice of intentionally flying into clouds in mild conditions using, with no instruments of any kind. Even setting aside the illegality of this, and the risk of a mid-air collision, and the inability to hold a heading in cloud, my own "take" on all this is that hang glider pilots greatly overestimate their ability keep their aircraft under control in clouds. In calm conditions most hang gliders have enough inherent roll stability to stay upright as long as the pilot stays centered on the bar and doesn't interfere with control inputs that may be based on a false perception of what is happening. This is much like a free-flight model airplane that can fly a preset flight path and even negotiate thermally mid-day conditions without any guidance at all. However at some point in turbulent air the situation will begin to deteriorate and the glider will end up out of control. Personally, I don't advise ever intentionally flying into a cloud without gyro instruments.

With this preface, I'm going to make some comments on potential emergency cloud-flying aids. The obvious one is some kind of a small turn-rate gyro and such a device (the "Cloud Devil") has in fact been advertised in Hang Gliding magazine; this is undoubtedly a better solution then the more primitive "instruments" that I'm going to examine here. Some hang glider pilots have successfully flown in clouds using bubble levels, floating spherical compasses, and other such instruments. Of course these instruments do not indicate the true horizon, but rather are slip-skid indicators, identical in function to an aircraft slip-skid ball or the slip-skid bubble used in my turn experiments. (A hang glider pilot's body will act as a slip-skid indicator too, but as we've already noted this "pendulum" effect is probably only noticeable when the pilot is flying almost "hands-off" with a very light touch on the bar and is not exerting any muscle force to make a roll input.) (Of course a compass can also provide turn direction and turn rate information via its magnetic properties, but this information is quite difficult to interpret due to errors when the aircraft is banked. As the needle aligns itself with the vertical as well as the horizontal component of the earth's magnetic field, it will lead, lag, and even briefly move opposite to the direction of the turn.) One hang glider pilot who has used a floating ball compass in clouds (in smooth Hawaiian air) emphasizes that by watching the initial tilt of the ball, he can detect when the glider starts to roll away from wings-level, but if this roll is not immediately countered with the appropriate weight-shift input then the situation will quickly deteriorate and neither the slip-skid function of the floating ball nor the compass's directional function will be of much use as the glider goes out of control. This is consistent with what I saw in my Spectrum where a slip-skid bubble showed the direction of roll but gave no indication of where the horizon lay (i.e. whether the bank angle was steepening or shallowing), and was centered in a steady, constant-bank turn. However some hang glider pilots do believe that a bubble or float gadget can provide helpful information in all phases of turning flight, including in a stabilized, constant-bank turn. Again, these characteristics may vary from one glider to another as we noted in Part Four. Note that with all of these gadgets the margin of safety may be very slim and success may be due mainly to the glider's inherent roll stability; in fact I wonder if some of these "instruments" don't seem to "work" simply because they distract the pilot from trying to follow his instincts and thus keep him near the center of the control bar, allowing the glider's inherent roll stability to take over!

(A footnote to the above: the remarkable Bohli compass, occasionally seen in sailplanes, is not weighted to float upright in the usual manner, and so functions as a fixed platform in 3-dimensional alignment with the earth's magnetic field. This compass has no tilt or acceleration errors, and provides information on pitch and bank attitude as well as turn rate.)

As I've already related in great detail, in my turn experiments in my Spectrum I found that a slip-skid bubble indicated roll direction. The bubble always shifted away from the direction of roll, showing a slip as the bank angle increased and a skid as the bank angle decreased. In practice this tells the pilot whether the glider is rolling left or right but gives no indication of where the horizon lies (i.e. whether the bank angle is steepening or shallowing). The bubble was centered in a steady, constant-bank turn. Likewise the pilot's sense of balance, or his tendency to hang to one side of the control frame when the turn is slipping or skidding, will provide no information in a steady, constant-bank turn in my glider. By contrast, due in part to the airflow curvature effects that we've already discussed in great detail, the yaw strings on the base bar "probe" and on the "bowsprit" clearly indicated the direction of a steady, constant-bank turn as well as the direction of a roll. The yaw strings showed a large deflection toward the outside of the turn whenever the bank angle was increasing, and showed a much smaller deflection toward the outside of the turn when the bank angle was constant, and showed a large deflection toward the inside of the turn while the bank angle was decreasing. Since the yaw strings provided turn direction information as well as roll information, it follows that a yaw string mounted out in front of the base bar for easy viewing in flight would be of some value as an emergency cloud flying aid in my glider. Granted this "instrument" may be of very limited value in turbulent air, yet it may give the pilot one more chance to gain control of the glider in a desperate situation. This may be especially important in a rigid-wing hang glider which has a much greater chance of exceeding the Vne airspeed or pulling very high G-loads (but see the caveat below about different slip-skid characteristics in different gliders

To use the yaw string in cloud in a glider with slip/skid characteristics similar to my Spectrum, the basic technique will be for the pilot to "follow the yaw string" with his weight-shift inputs; this will generally stabilize the glider in roll and will also slowly bring the glider toward wings-level flight. Since the turn direction information is masked by the roll information whenever the bank angle is changing, the yaw string will by no means always provide the pilot with a clear indication of where the true horizon lies or how to immediately bring the glider to wings-level flight. For example, the most confusing case will be the instance where the glider is suddenly rolling from a steep turn towards wings-level; in this case the yaw string would actually lead the pilot shift his body toward the low wing and slow down the roll toward wings-level. The cases where the yaw string will provide the clearest cues of what is happening would be a sudden roll of unknown direction away from a known wings-level condition, or a sustained, roughly constant-bank turn of unknown direction. Again, the yaw string may be of limited value in turbulent air and I'm not recommending that pilots intentionally enter clouds with this "instrument", I'm simply suggesting that in some gliders a yaw string will be an improvement over the bubble or float gadgets that at least a few pilots are currently using for cloud flying. Also, in the rare cases where the air is smooth enough that the pilot has some hope of actually flying a compass course in a cloud--such as may be the case at some of the Hawaiian sites--the yaw string would be a valuable addition to the floating ball compass commonly used at these sites, in any hang gliders with slip/skid characteristics similar to my Spectrum.

I need to strongly emphasize that these recommendations are based on observations in my Spectrum and cannot be extended to other gliders without careful thought and experimentation. The key point is that the airflow curvature effect tends to make a yaw string mounted on the forward part of the aircraft show a bit more of a sideslip in a steady, constant-banked turn than does a slip-skid bubble, so in many cases a yaw string will be better than a bubble instrument for detecting the turn direction when the bank angle is constant. In my glider in a constant-banked turn, the yaw string showed a slip while the bubble was centered. As we've already noted in Part Four (see "Balance of forces in the yaw and roll axes: theory"), other gliders may show more slip in a constant-banked turn than does my Spectrum-in which case this might be visible to some degree in a bubble instrument as well as in a yaw string. Alternatively some high-performance gliders will actually show a skid in a constant bank turn, which will greatly limit the usefulness of a bubble indicator as it will give opposite indications in a steady turn vs. while rolling into a turn! In such a glider a yaw string will probably suffer from the same limitation, although due again to airflow curvature, it is possible that the yaw string might be centered whenever the bank angle is constant and so would at least provide usable information on the direction and rate of roll (but not the direction or rate of turn). Unfortunately any gliders that show a skid in a steady turn are also likely to be the gliders with the least inherent roll stability. (Again see our earlier discussion of the balance of forces in the roll axis in Part Four). The bottom line is that a pilot should be very familiar with the indications of either a yaw string or a slip-skid bubble instruments in various turning and rolling situations in his or her particular glider before contemplating the use of such a gadget as an emergency blind flying aid.

A pilot should also know whether his glider requires high-siding or low-siding to maintain various bank angles--if the bank tends to shallow when the pilot is centered on the bar, he should certainly take advantage of this in a blind flying situation, as the glider's inherent roll stability will be far more trustworthy than any control inputs that are based solely upon the pilot's instincts and sense of balance. As a last resort a pilot can test whether a given roll input causes the airspeed and G-loading to increase (indicating an increasing bank angle) or decrease (indicating a shallowing bank angle). Once again, my advice: don't intentionally enter clouds without gyro instruments.

 

APPENDIX 2: TOWING AND LOCKOUT DYNAMICS

***** Note Summer 2005 -- this section contains a significant error. It assumes that modern flex-wing hang gliders exhibit a positive coupling between slip (yaw) and roll throughout most of the flight envelope. During the course of more recent experiments, I've discovered that most modern flex-wing hang gliders actually exhibit a negative coupling between slip (yaw) and roll through most of the flight envelope. This error affects many of the points given in the discussion below, but some of the approaches to analyzing tow dynamics taken in the discussion below should provide "food for thought" for future efforts.******

Lockout dynamics are extremely complex. Here are some general comments aimed at both aero- and ground-based towing. Nothing in this section is meant to replace practical advice from experienced tow fliers.

Let's start with a thought experiment that gets right to the core of the lockout problem. Let's consider the simplest case, where we are towing either directly from the pilot's body, or from some combination of the pilot's body and the hang point. For this thought experiment, let's assume that the pilot is flying with a very light touch or is "hands off" the bar, i.e. he is not using his muscles to make any control inputs, particularly in the roll axis. In this "hands off" situation, a free body diagram will show that all the tow force is transmitted through the pilot's hang strap to the hang point on the keel, which is very near the C.G. of the glider. This is true regardless of the glider's bank angle or the relative positions of the glider and the tow vehicle (as long as the pilot has not been pulled against a downtube). So the tow force is not exerting a torque on the glider and has no direct tendency to make the glider either roll or yaw. Yet in reality it is not possible to tow "hands off": in turbulent conditions, or if the glider gets too far out of position relative to the tow vehicle, the glider will end up in a lockout. Why?

I think that Dennis Pagen accurately identified the initial cause of a lockout in his articles in March and April 1997 Hang Gliding magazine (and see also pp.360-361 in Pagen and Bryden's book Towing Aloft): when a glider gets into a yaw oscillation, the sideways (skidding) airflow interacts with sweep or dihedral to create an aerodynamic roll torque which makes the glider roll and turn away from the flight path.

There will be some interaction between the angle-of-attack and the amount of roll torque created by dihedral and sweep effects as a glider slips or skids during a yaw oscillation. The glider's airspeed will also play a role. The higher angles-of-attack seen during winch or truck towing may make the glider more prone to this yaw-roll coupling than during aerotow where the angle-of-attack is lower.

(By the way this presents in interesting question: a hypothetical "blade wing" glider with little sweep, and a great deal of anhedral might be unstable in the roll axis, meaning that it tends to roll into, rather than away from, a slipping or skidding airflow component. Do any such gliders actually exist? Would such a glider be less likely to lock out? It would appear so on the basis of the above analysis. However a glider with just a little bit of positive roll stability--meaning that it still has some tendency to roll toward a sideways airflow component--but very little yaw stability would be a real handful on tow, and I suspect that this may describe some of the "blade wings".)

As far as I'm aware no one has really identified why, after the initial roll and turn away from the tow vehicle during the yaw oscillation as described above, the lockout continues and quickly builds to exert a strong, sustained roll torque on the glider that the pilot cannot overcome. (If you know, tell me, and I'll include your thoughts in the next edition of this paper!) It may even be that a careful analysis would show that with modern towing arrangements, a glider flown "hands off" (with no roll control inputs) would enter a series of increasing roll and yaw oscillations but would not truly "lock out" into a sustained roll and turn away from the towplane until one of the oscillations pulled the pilot against the high-side downtube. Of course it will be rather academic to the pilot whether it is a very large yaw and roll oscillation, or a truly sustained yawing and rolling motion, that pulls him against the downtube and begins the lockout.

(On a purely practical level here is the bottom line: if the pilot is shifted fully against a downtube and the glider is still rolling away from the tow vehicle at a steady or increasing rate, or if the pilot is being pulled against a downtube or the towline is contacting parts of the glider structure or wires, then there is no real hope of recovery except to RELEASE NOW!)

Considerations of yaw rotational inertia would suggest that as the glider first begins to roll and turn away from the tow vehicle, the glider's yaw rotation rate will lag behind the turn rate so the glider's nose will tend to point toward the outside of the turn, i.e. toward the tow vehicle. Unfortunately this doesn't help us to explain lockouts; this factor actually would tend to slow the development of a lockout.

Many explanations of lockout (for example, Pagen's March and April 1997 lockout articles and p.361 of Towing Aloft) suggest that after an initial yaw oscillation rolls and turns the glider away from the tow vehicle as described above, then the sideways pull of the towline on the glider will continue to drag the glider sideways through the air in a skid, which will continue to create a roll torque on the glider until a near-vertical bank angle is reached. It's not at all obvious why this should be so. Certainly the continued sideways pull of the towline will exert a sideways (centrifugal) force on the glider which will counter the sideways (centripetal) force from the banked wings and will slow the rate at which the glider turns away from the tow vehicle, for any given bank angle of the glider. Yet the glider is inherently stable in yaw and will tend to align itself with the flight path, so there is no obvious reason why we should consider the towline (if attached near the glider's C.G.) to be dragging the glider sideways through the air in a skid, except for a few seconds at a time during a yaw oscillation. This assertion may seem counterintuitive, but in the "model airplane example" below we will show how a line can pull at 90 degrees to the flight path of an aircraft and yet create no slip or skid. Also, it is not at all obvious that when the glider does reach a very steep bank angle, it will then begin to fall earthwards in a slip as is often suggested (see again Pagen's March and April '97 lockout articles and p.361 of Towing Aloft). Certainly a glider will begin to pitch and yaw downward and accelerate when it reaches a very steep bank angle, but as we've discussed in Part Four, these dynamics need not involve sideslip (apart from adverse yaw) and we should not assuming that the glider is "sliding" sideways toward the low wingtip as it accelerates. (Recall that yaw rotational inertia actually promotes a skid rather than a slip as the bank angle continues to increase beyond 45 degrees).

Here is the extreme example of an aircraft experiencing a sideways towline force yet not slipping or skidding: a control-line model airplanes flies in perpetual wings-level circles at a constant turn rate, with the entire turning force provided by the centripetal pull of the control lines which attach near the aircraft's C.G. and pull toward the inside wingtip. A yaw string on the aircraft would be centered, indicating no slip or skid (except for airflow curvature effects). Interestingly, though, a slip-skid ball would in fact be thrown toward the outside of the turn. The horizontal (spanwise) force from the control line alters the usual one-to-one relationship between the yaw string and the slip-skid ball or bubble, so that the indications of the slip-skid ball or bubble do not directly correlate with sideways airflow components in the same way that they do in free flight. (Recall that in free flight, a sideways or spanwise airflow component is the sole cause of a sideways or spanwise aerodynamic force upon the aircraft and so the ball or bubble will deflect to the side only when the yaw string reveals a sideways airflow.) A sideways component in the towline's force vector will have exactly the same effect on a hang glider on tow, so that the indication of a slip-skid ball or bubble no longer accurately shows whether there is a slipping or skidding component in the airflow. This is point is quite important when considering whether or not a given balance of forces on an aircraft on tow will in fact create a slipping or skidding airflow which in turn would create a roll torque that may contribute to a lockout. A slipping or skidding airflow component (as revealed by a yaw string) is not caused by an imbalance in the net forces on an aircraft, rather it is caused by an actual yaw torque or by the effects of yaw rotational inertia, which cause the nose of the aircraft to be misaligned with the flight path.

One point of worth noting is that it becomes difficult to define what is meant by "slip" vs. "skid" on two--are we looking at the direction of the airflow relative to the direction of the turn? Or relative to the direction of the bank? On tow these may at times not be the same as the towline may be forcing a turn towards the tow vehicle which may be opposite to the direction of bank; however during an actual lockout the glider both banks and turns away from the tow vehicle. At any rate, in general our meaning is usually clear enough if we can at least indicate whether the airflow is coordinated or is coming from one side of the aircraft.

It seems to me that the greatest obstacle to developing a theory of lockouts lies in explaining why a glider continues to roll and turn away from the tow vehicle after the initial yaw and roll oscillation first turns the glider away from the tow vehicle. The existing books and magazine articles on lockout always end up invoking an imbalance in the horizontal or vertical forces on the glider to explain why the glider slips, skids, or rolls. (See for example fig. 2 in Pagen and Bryden's Oct. 96 article, fig. 1 in Pagen's April '97 article, and fig I-7 (p. 361) in Towing Aloft.) I believe that these explanations show some confusion between a net force on the glider, and an actual yaw or roll torque. We've already argued that a steady net horizontal force acting near the C.G. and Center of Pressure of the glider-pilot system drives a turn but not a slip or skid or the resulting roll torque. An imbalance in the net vertical forces on a glider will drive the pitch-axis dynamics of a downward curvature in the flight path and an acceleration in airspeed but these need not involve slip, skid, or roll. Let's examine some other ways, such as the "paraglider effect", that towline is often said to exert a roll torque on the glider.

Remember that when the pilot is flying "hands off" the bar or is flying with a very light touch and is exerting no muscle forces on the bar, a free-body diagram will show that all the tow forces are routed directly through the hang strap to the hang point and so can exert no roll torque on the glider. Let's consider in more detail how a pilot controls a hang glider in free flight (not on tow). A roll torque is created whenever the pilot is exerting a muscle force on the base bar to shift himself to one side. This is because his G-loading vector is displaced so that it no longer passes through the keel, but instead passes through one wing at some distance away from the keel. This asymmetrical loading of the wing creates a direct roll torque, and also creates billow shift and airframe deformation which further add to the roll torque. Note that we are looking at the pilot's G-loading vector, not his weight or gravity vector--when the glider is banked, the distinction is quite important. In a slip or skid the distinction is also important--in a slip or skid the pilot's G-loading vector is no longer perpendicular to the wingspan, so the pilot may be hanging off to one side of the glider centerline yet as long as he is exerting no muscle force through his arms, his G-loading vector will still pass directly through the hang strap to the keel and will therefore create no roll torque. The pilot must exert a muscle force on the control frame to create a roll torque on the glider. The same is true on tow: a roll torque is created whenever the vector representing the pilot's G-loading plus the towline's pull passes through the sail at some point other than the centerline (keel) of the glider. This cannot happen when the pilot is flying "hands off" the bar because all the force transmitted from the pilot's body to the glider passes directly through the flexible hang strap to the keel. A roll torque is only created when the pilot is making a muscle input (or when he has been pulled into the high-side down tube by the towline).

It is often pointed out that if you inflate a paraglider on the ground, and then run sideways, the paraglider will roll away from you and collapse in a heap. This is said to demonstrate the tendency of any aircraft to roll under the influence of a sideways force, until its vertical axis becomes aligned either with the pull of the towline, or the sum of the tow force plus the weight vector. (For example, see Pagen and Bryden's book Towing Aloft pp. 138-141). This claim is based on a faulty analysis of the vectors at play: horizontal and vertical forces are being confused with roll torques. In reality the "paraglider effect" is based upon the fact that the paraglider is undergoing a structural deformation, with half the lines becoming taut and half the lines going slack. Because of the deformation of the paraglider's flexible airframe (i.e. the lines), a sideways force cannot be transmitted from the pilot to the C.G. of the wing itself without creating a roll away from the sideways pull. This also easily seen in the way that a flexible parachute stunt kite always flies "square" to its control lines rather than "square" to the horizon. In a hang glider, if we are towing from the pilot's body or from a combination of the pilot's body and the hang point, then whenever the pilot is "hands off" and is not exerting a muscle force (and has not been pulled into the high-side down tube), then all the tow force is routed directly to the hang point on the keel with no asymmetric loads on the wing and no deformation of the aircraft structure. Even if the line has a sideways (spanwise) pull component, this creates neither a direct roll torque about the C.G. of the glider, nor any differential loading of the wings, billow shift, or deformation of the airframe, so there is no tendency to roll. This is a very fundamental difference between towing a paraglider and a hang glider.

We've noted that the towline may pull the pilot to one side without creating a roll input (unless the pilot is pulled into one of the down tubes); this is true in the pitch axis too. During aerotow the pilot is pulled further forward through the control bar than in level flight. Again, a look at the "hands off" condition shows that this does not exert any net torque about the hang point, so the trim angle-of-attack of the glider is not changed by the forward pull. The glider will still "want" to fly at the same angle-of-attack as in free flight. If the towline is pulling entirely "forward" (parallel to the flight path) then the glider will also "want" to fly at the free-flight trim speed. Of course, if the towplane is flying faster than this speed, then the pilot will need to pull in, and he will have to pull harder on a pitch-stable beginner glider than on a "blade wing". If the towline's pull contains a downward component relative to the flight path (as is obviously the case in ground-based towing) then this will "load up" the glider so that the lift vector, airspeed, and drag vector will all increase even in the "hands off" case where the angle-of-attack and L/D ratio remain constant.

The general idea that the glider tends to fly at the same angle of attack even when the pilot is being pulled through control bar on tow is sometimes used to imply that the glider is "orienting" its attitude in space relative to a different reference frame on tow, i.e. relative to the towline's pull plus gravity rather than relative to gravity alone. (Personally, I prefer to simply think of the relationship between the angle-of-attack and the relative wind.) The argument is then made that we will see the same effect in the roll axis, i.e. that the glider will tend to roll away from any sideways pull in the towline so that it "orients" itself relative to the towline plus gravity rather than to gravity alone. This is presented as another manifestation of the "paraglider effect". (See Towing Aloft p.140 for an example of this argument). There are a lot of problems with this argument. The idea of a glider "orienting" itself relative to a given reference frame is misleading, particularly in the roll axis. Roll stability comes from interactions between bank angle, turn rate, sideslip, and dihedral and sweep effects, and not from any inherent tendency to "orient" relative to gravity. The G-loading that an aircraft "feels" in a turn is not aligned with gravity. Unlike the paraglider or stunt kite which tends to orient itself relative the towline, in a hang glider in the "hands off" condition any sideways pull of the towline is transmitted to the hang point without creating a roll torque on the glider, so the hang glider will not "orient" itself relative to the towline's pull.

Now let's look at another common point of contention in discussions on lockout: when the towline pulls the pilot over to one side of the control bar, does this make a roll input? Or does this actually reduce the pilot's roll control authority in some way? We've already seen that in the "hands off" case where the pilot is exerting no muscle force and hangs at the "neutral point" on the control bar under the combined influence of his G-loading vector and the towline's pull on his body, then all the tow force is transmitted to the hang point so there is no roll torque on the glider. So it's not accurate to imagine that some kind of "self-correcting" action is going on as the towline pulls the pilot over to over to one side of the bar. However it's also not accurate to imagine that the pilot's control authority is being reduced in some way by this sideways pull, as is often stated. As a glider begins to lock out, clearly the sideways pull of the line on the pilot shifts the "neutral hang point" (described above) away from the glider centerline and toward the high side of the control bar, and gives the pilot less "room" to move further toward the high side to exert a roll torque (see fig. 5 in Pagen's April '97 article on lockouts). When the "neutral hang point" reaches the high-side down tube, and the towline pulls the pilot into the high-side downtube, then the pilot is no longer able to exert any anti-lockout roll torque and the towline in fact begins to exert a pro-lockout roll torque on the glider. So why do we say that the sideways pull of the towline has not decreased the pilot's roll control authority? Consider any situation where the pilot's body contacts the high-side downtube, whether he is holding himself there to fight the threat of a lockout or has already been pulled against the downtube as the glider locks out. Given the same bank angle and the same geometry between the position of the glider and the tow vehicle, if the towline were attached to the centerline of the base bar rather than to the pilot's body, the tow force would pass much further from the C.G. of the combined glider-pilot system and would exert a much greater pro-lockout roll torque on the glider. Therefore I don't think we can possibly argue that when we tow in part or in full from the pilot's body, then the sideways pull of the towline on the pilot's body is somehow reducing his control authority, compared to towing systems that don't attach to the pilot's body. At the end of the day, when we are looking at roll torques the key point of interest is whether the towline's force is routed as close as possible to the C.G. of the entire system (or better yet is favorably displaced so that it creates an anti-lockout roll torque) in the extreme, critical case where the pilot is shifted all the way against the high side of the control frame to make the largest possible roll input in the hopes of preventing an imminent lockout. In this situation it doesn't matter how much "room" the pilot has available to move himself further toward one side of the bar relative to the position of the neutral, hands-off hang point at any given instant, or how much muscle force the pilot is exerting. These other considerations affect the control "feel" (and the suddenness with which a lockout may develop out of an apparently docile situation) but do not affect the total control authority that the pilot has to prevent a lockout.

One of the benefits of using a v-bridle to route a component of the tow force directly to the hang point rather than towing only from the pilot's body is that the towline force component that is routed directly to the hang point cannot exert a roll torque on the downtubes by pulling the pilot's body against them.

We've been assuming that the hang point on the keel is at the glider's C.G., so that in the "hands off" condition the towline force (and the pilot's G-loading vector) acting through the hang strap cannot create a torque on the glider (unless the pilot is pulled against the downtubes; then a torque is transmitted to the glider through the control frame). We should qualify this a bit. Obviously this assumption is accurate in the roll axis: there is no way that the flexible hang strap can exert a roll torque on the glider. However on some gliders such as my Spectrum (according to the owner's manual) the hang point is significantly aft of the glider's C.G. and this creates a relationship between pilot hook-in weight and trim angle-of-attack. This also contributes to a nose-up tendency (increased angle-of-attack for a given speed) if we tow from the hang point, and it also means that a sideways pull on the towline will in fact have some tendency to yaw the nose of the glider away from the tow vehicle. (For these reasons when I towed with a v-bridle at Wallaby I attached the towline to the keel about a foot ahead of the hang point, and to my harness).

We also need to look more closely at what happens to the towline attachment point when the pilot uses his muscles to make a roll control input. As a glider begins to bank away from the tow vehicle, and the pilot responds by shifting himself toward the high side of the control bar, the towline attachment point (on his harness) is also shifted toward the high side of the control bar. We've already seen that this displacement of the towline attachment point works in the pilot's favor, as far as the direct roll torques exerted by the towline on the glider are concerned. Yet this sideways displacement of the towline attachment point also allows the towline to exert a yaw torque on the glider, which will skid the nose of the glider further away from the tow vehicle. The skid will then create an aerodynamic roll torque which will act counter to the pilot's roll input. The worst-case scenario is where the pilot is cross-controlling by shifting his shoulders (and the towline attachment point) to the high side of the bar but is not effectively shifting his weight at all. In effect the pull of the towline on the pilot is giving him "leverage" to accidentally yaw the glider in the opposite direction of his intended roll input. An experienced tow flier at Wallaby Ranch pointed this out to me, commenting that when a pilot learns to avoid this cross-controlling, then he can avoid lockouts fairly consistently, even in rowdy air and without the aid of a vertical fin. Certainly control inputs which shift the pilot's body weight effectively will have the best chance of producing the desired results, but we should recognize that this displacement of the towline attachment point and the resulting yawing effect will always reduce the effectiveness of a pilot's roll control inputs to some degree. Note that we are not so much concerned with accelerations or decelerations in the glider's yaw rotation rate; rather we want to know whether the glider will tend to remain yawed off to one side of the flight path and airflow, or will face directly into the relative wind, when all the torques come into balance. Therefore the issue is not whether the towline is attached in line with the C.G. of the glider-pilot system--as it may still be when the pilot shifts his weight to one side--but rather whether the towline is attached along the glider's centerline so that the drag forces from each wing are balanced when the glider is facing directly into the airflow rather than when the glider is yawed away from the tow vehicle. (This is an interesting difference between our treatment of the yaw and roll axes. The whole question of resolving torques relative to the center of mass, or relative to the center of aerodynamic pressure, is a very complex one that is best explored with a pencil and paper rather than with words! In this case resolving the towline's torque relative to the glider's center of pressure is a shortcut to looking at the way the torques produced by the drag from the wingtips will change as the C.G. of the whole system shifts.)

At any rate I think that this coupling between pilot roll inputs and counterproductive yaw forces plays an important role in lockout dynamics. Note that this effect only comes into play when the pilot is using his muscles to make a roll control input, and not in the "hands off" condition when he is hanging freely in the control frame. One of the benefits of using a v-bridle to attach to the hang point as well as to the pilot's body is that the component of the towline's force that goes straight to the hang point will not contribute to this yawing effect when the pilot shifts his weight to the side.

Regardless of why a glider rolls and turns away from the tow vehicle during a lockout, we can see that at some point the roll dynamics will start to become less relevant and eventually the glider may end up in a vertical dive with its belly toward the tow vehicle. Clearly at this point all the dynamics are happening in the pitch axis, and the dynamics of turn and roll and slip or skid are no longer playing any part in the lockout, and there is no sideways or spanwise component in the towline tension.

Why does a glider dive as it rolls and turns away from the tow vehicle? The answer to this lies not in the dynamics of roll and sideslip but rather in the balance between thrust and drag. An aircraft climbs for any of three reasons: it is in "lift" which allows it to climb relative to the ground (but not relative to the airmass), or it is trading airspeed for altitude, or thrust exceeds drag. On tow, the thrust vector is the component of the towline tension that acts in the direction of the glider's flight path at any given instant. As a glider banks and turns away from the tow vehicle, the thrust vector decreases while the total tow force increases (up to some constant value in the case of a tension-limited payout winch). As the towline's "load" on the glider increases, so does the glider's lift vector, and the airspeed, and the drag vector. When drag exceeds thrust the glider will descend. Unfortunately the geometry of the turn away from the tow vehicle, and later the steep dive with the belly of the glider facing the tow vehicle, are such that the towline tension is not relieved as the glider dives, so the towline continues to "load up" the wing and accelerate the glider. These dynamics are largely independent of sideslip or skid, and a glider need not be slipping or skidding as it dives earthward in the later stages of a fully-developed lockout. I think that slip/skid effects have a lot to do with the glider's initial rolling tendencies in a lockout but little to do with the resulting earthward plunge.

Before I end this section I have to note that the idea of a relationship between pitch inputs and sideslips appears often in the lockout literature, the general idea being that the tow force is preventing the glider from developing the usual curvature in the flight path, especially in the pitch dimension, which would somehow coordinate the turn and prevent a slip. See for example Pagen's March and April 97 articles, and p. 141 of Towing Aloft. By now the reader will be able to guess that I disagree with this idea: we've seen that sideways or spanwise components in the towline's pull will affect the indications of a slip-skid ball or bubble but will not create a slipping or skidding airflow (as revealed by the yaw string). "Up" or "down" components in the towline's pull, in the reference frame of the glider, will neither affect the indications of a slip-skid bubble nor a yaw string: as we've discussed in detail in Part One, pitch-axis dynamics have little to do with coordination in the yaw axis and sideslip and skid. As we've already noted, very little slip or skid may be involved in the later stages of a lockout, when the glider is plunging earthwards. However it's very clear that the tow force does play a role in the pitch-axis dynamics: as we've already noted, the added load of the towline causes the wing to fly faster and to develop more lift and therefore also more drag. If the glider gets turned away from the tow vehicle, reducing the thrust component in the towline's pull, then drag will exceed thrust and the glider will begin arcing downward as described above.

That's all for now! To read more about other pilot's ideas on towing and lockouts, check your Oct '96 through April '97 back issues of "Hang Gliding" for a string of related articles and letters by Dave Broyles, Don Hewett, Dennis Pagen, and Bill Bryden, and also Pagen and Bryden's book Towing Aloft. An interesting challenge for the reader will be to critique the vector diagrams given in some of these sources in light of the ideas I've just presented.

 

APPENDIX 3: SLIPS IN AIRCRAFT WITH RUDDERS

In three-axis aircraft the rudder is normally used to prevent the slips or skids caused by adverse yaw and yaw rotational inertia as the aircraft is rolled in or out of a turn. In general the rudder is simply applied in the same direction as the ailerons, and is neutralized along with the ailerons when the desired bank angle is established (but see the section in Part Four entitled "Balance of forces in the roll and yaw axes: theory" for more subtle details regarding on the positions of the control surfaces in constant-banked turns).

The rudder may also be used to intentionally hold the fuselage at an angle to the airflow, creating a slip or skid. A skid will augment the turn rate (and can even be used to create a wings-level turn) but is much less efficient than simply increasing the bank angle, and is also an invitation to a spin entry. A slip slows the turn rate and can in fact stop the turn entirely if the slipping fuselage and the banked wing create equal and counterbalancing side forces on the aircraft. (Alternatively we can say that the wing can be banked to prevent the flat (wings-level), skidding turn that would otherwise occur when the pilot holds a sustained rudder input to keep the nose yawed out of line with the flight path). This non-turning slip can be sustained indefinitely and is useful for steepening the glide path during the landing approach. The airspeed may be held constant at whatever speed is desired; the large sideslip angles available to 3-axis pilots make a slip an effective drag-producing maneuver even at low airspeeds. Since the fuselage is skewed away from the airflow (i.e. the relative wind or direction of travel through the airmass) a slip is a handy tool in a crosswind landing because it allows the pilot to line up the fuselage (and landing gear), the runway, and the direction of travel over the ground even while the actual flight path (relative to the airmass) is still crabbed into the wind to keep the aircraft from drifting off toward the downwind side of the runway.

The airflow over the rudder itself does create a side force as well as a torque on the aircraft and this can have some interesting ramifications. Recall that the yaw string and slip-skid ball are generally in agreement (except for airflow curvature effects) because a sideways airflow over the fuselage is generally the sole possible cause of a sideways or spanwise aerodynamic force on the aircraft. However in some situations a rudder can create a sideways force without swinging the nose out of line with the airflow (relative wind). For example, in a twin engine aircraft with one engine out, the pilot must apply the rudder toward the working engine to prevent a yaw rotation. As the airstream deflects off the rudder this will create not only the needed torque, but also a net side force that will create a turn toward the dead engine. The less efficient way to fight this turn is to further increase the rudder pressure, slipping the fuselage to create a balancing force toward the working engine. In this case the slip-skid ball would be centered because the wings are level and there is no turn, but a yaw string would indicate a slip toward the dead engine. The more efficient way to prevent the turn is to bank toward the working engine. In this case a yaw string would indicate coordinated flight in the sense that the airflow is aligned with the fuselage. A slip-skid ball would indicate a slip toward the low wing, because the force generated by the rudder is preventing any turn even though we are banked. (See William Kershner's Flight Instructor's Manual 3rd ed. (1993) pp. 192 and 196). Interestingly, this analysis can be applied any time a rudder is working against a torque, including p-factor in single-engine aircraft, and even asymmetrical tip drag in sailplane turns. In the rare cases where the discrepancy between the yaw string and the slip-skid ball is actually noticeable, it will generally be most efficient to center the yaw sting rather than the slip-skid ball or bubble (but see our discussion in Part Four about allowing some slip in sailplane turns).

 

APPENDIX 4: ESTIMATING THE AERODYNAMIC FORCES PRODUCED BY A SIDESLIP

***** Note summer 2005: more recent experiments involving sustained, straight-line sideslips in flex-wing hang gliders equipped with rudders and other yaw control devices suggest that a slipping hang glider creates only an extremely small aerodynamic sideforce. Also, I am now rather skeptical of the hang-glider-related results given in this section because they were taken during dynamic rolling maneuvers, not during straight-line sideslips. During a rolling maneuver a slip-skid ball or bubble is affected by inertial forces as the aircraft rolls and adverse-yaws, so the ball or bubble may become slightly inaccurate as a measure of the aerodynamic sideforces produced by the sideways airflow over the aircraft. This is especially true if the ball or bubble is mounted on the end of a slightly-flexible rod as was the case in these experiments.*****

Since a hang glider lacks fuselage and vertical tail surfaces, how much aerodynamic force can be produced by a spanwise (slipping) airflow? Can significant sideways "lift" forces be developed? Is the drag of the aircraft significantly increased in a slip?

It's interesting to consider the relationship between the deflection of the yaw string and the deflection of the slip-skid ball. The deflection of the yaw string indicates the sideslip angle in the airflow; i.e. the degree to which the nose is yawed off to one side of the flight path. The displacement of the slip-skid bubble indicates the magnitude of the side force created by the sideslipping airflow, in comparison to the lift force generated by the wing. The lift vector produced by the wings depends primarily upon the aircraft weight and the bank angle, plus any additional loading or unloading caused by curvature of the flight path in the vertical axis, such as pulling out from a dive. At steep bank angles, the wing's lift vector will also be reduced by the vertical component of the spanwise forces produced by the slip, which bears a part of the aircraft weight. The sideways "lift" components produced by the slip depend only upon the airspeed, the sideslip angle, and the aerodynamic shape of the fuselage and other parts of the aircraft. So for a particular aircraft, the relationship between the yaw string and the slip-skid ball will vary with weight, airspeed and bank angle: faster speeds and steeper bank angles will create more deflection of the ball or bubble for a given angle of sideslip, and heavier weights will create less. For different aircraft, characteristics such as large, flat fuselage sides will create larger side forces and will increase the deflection of the ball or bubble at a given slip angle in the yaw string. These aerodynamic side loads or "lift" forces can presumably be correlated to substantial induced drag forces which will degrade the glide angle.

I've done some in-flight comparisons between my Spectrum 144 hang glider and a Schweizer 2-22 sailplane. (Warning: these calculations will become a bit convoluted and the reader may wish to skim all the way through once before following the math in great detail). While shifting fully to one side to roll my Spectrum rapidly into a turn, I observed about four degrees of displacement in the slip/skid bubble when the yaw string was deflected about 25 degrees. (These observations aren't very precise due to the dynamic nature of the maneuver). I estimate the bank angle to have been roughly 30 degrees at the time of maximum sideslip. (The calculations aren't very sensitive to bank angle). The trigonometry is complicated unless we simplify by assuming that the force from the slip did not significantly change the lift vector from the wings, which will not introduce much error at this moderate bank angle. The force from the slip can now be calculated by either (tan ball displacement angle * aircraft weight / cos bank angle) or (aircraft weight * (tan (bank angle - ball displacement angle))). Using a pilot hook-in weight of 145 pounds and a glider weight of 55 pounds, for a total weight of 195 pounds, we find that the sideways aerodynamic force produced at 25 degrees of slip in the yaw string and 30 degrees bank was roughly 16 pounds.

The calculations were easier for the sailplane, because the vectors are simplified in a non-turning slip where the heading is held constant with the rudder. It was also much easier to make accurate observations in this stabilized configuration. Here, the ball displacement angle is the same as the bank angle. The slip-skid ball in this glider reached full displacement at about 7.5 degrees, and at this bank angle the yaw string was deflected about 25 degrees. The aircraft empty weight was about 550 pounds, plus 145 pounds pilot and ballast for a total of 695 pounds. For the nonturning slip the formula is simply sideways (spanwise) aerodynamic force = sin (bank angle) * aircraft weight, giving a total side force of 91 pounds.

What if the sailplane had been flying at the same 25 degree slip angle, but at the same airspeed as the hang glider? This would have allowed a direct comparison of the aerodynamic characteristics of these two aircraft, at a given sideslip angle. Since aerodynamic forces scale to the square of airspeed, the calculations are very sensitive to this variable. Unfortunately I had no way to accurately measure the airspeed in the slip, in either the hang glider or the sailplane. We can make a few guesses: assuming that the hang glider might have been going about 30 mph during the moment of greatest sideslip while rolling into a turn (from an initial speed of about 22.5 mph), and assuming that the sailplane might have picked up about 5 mph while slipping for an airspeed of 45 mph, we have a correction factor of ((30 / 45) squared) = .44, yielding an "adjusted" spanwise aerodynamic force of 40 pounds that would be generated by the sailplane at the 25 degree sideslip angle (as indicated by the yaw string) if it were flying at the same airspeed as the hang glider. On the other hand if we guess an airspeed of 50 mph for the sailplane and 25 mph for the hang glider, then the correction factor becomes ((25/50) squared) = .25, yielding an "adjusted" aerodynamic side force of 23 pounds that would be produced by the sailplane if it were flying at the same airspeed as the hang glider. (My guess is that the first calculation is the closest to the actual speeds.) These values are only 1.4 to 2.5 times greater than the spanwise force produced by the hang glider, which is surprising considering the vastly greater fuselage side area and vertical tail area of the sailplane. (The 2-22 is an older sailplane with a fuselage side that rather resembles a barn door, with lots of flat area and no rounding of the corners of the cross-section. I would expect to have a spanwise "lift" coefficient in a sideslip at least an order of magnitude greater than would a hang glider). I commented briefly on the above calculations in my article in the February 2000 issue of Hang Gliding.

In truth at least one major correction needs to be made to these calculations (and to my comment in the February issue). I've been referring to the sideways aerodynamic "lift" force generated by the slipping component in the airflow. This vector will act perpendicular to the flight path and will be aligned with the wingspan in the roll axis. This force will be mainly horizontal (centrifugal) at shallow bank angles and mainly vertical at very steep bank angles. As we explored in more detail in Part Four in the section "Reference frame in a sideslip", this force is not strictly aligned with the wingspan in the yaw axis because as the glider changes its yaw angle (slip angle) relative to the flight path and airflow, the sideways aerodynamic "lift" vector remains perpendicular to the airflow. Unfortunately, when the nose of the glider yaws away from the direction of the airflow, a slip-skid ball or bubble instrument mounted on the aircraft also gets yawed away from the direction of the airflow. The slip-skid ball or bubble is now no longer "square" to our primary reference frame (the airflow) so it becomes slightly less sensitive to any sideways aerodynamic forces (relative to the airflow) and it also begins to detect the glider's drag vector (and also the glider's angle-of-attack). The extreme (and obviously hypothetical) case would be a glider that somehow gets yawed 90 degrees to the airflow; here (if the glider is in constant-airspeed, nonaccelerating flight) a slip-skid ball or bubble will actually be measuring the glider's pitch attitude in space, which is the sum of the L/D ratio and the angle-of-attack (however we define the latter in this weird situation). In our case of a 25 degree angle of sideslip this kind of error will be much less extreme but it will still be significant to our calculations.

For a rough correction to our calculations, we can note that when the nose of the glider is yawed 25 degrees away from the flight path and airflow, then the drag vector, which acts parallel to the airflow, has a spanwise component equal to .42 * the total value of the drag vector. We do not consider this to be a "sideways" aerodynamic force because it is entirely parallel to the airflow and flight path, yet it does have a spanwise component relative to the glider, which will be detected by the slip-skid bubble. The slip-skid bubble will "feel" this spanwise drag component as well as the true sideways "lift" force generated by the slip. Also, the bubble will actually "feel" only .91 of the full value of the sideways "lift" force generated by the slip, because the discrepancy in reference frames means that the sideways lift force is not quite parallel to the wingspan of the glider.

The drag vector produced in a coordinated turn may be closely approximated by Drag = (Weight / Bank Angle) * sin (inverse tangent (Drag / Lift)). With the data given above for the sailplane and an assumed L/D ratio of 18, this "expected" drag vector works out to 38.9 pounds, with a 16.4 pound spanwise component at 25 degrees of sideslip. Out of the original 91 pounds of observed spanwise force, this leaves about 74 pounds as "extra" force that cannot be attributed to this "expected" drag vector, and therefore reflects the sideways "lift" components generated by the sideslip, plus the spanwise components of any new drag vectors created by the slip. However with data given for the hang glider and an assumed L/D ratio of 10, and the "expected" drag vector works out to 22.4 pounds, with a 9.5 pound spanwise component at 25 degrees of sideslip. Out of the original 16 pounds of observed spanwise force, this leaves only 6.5 pounds as "extra" force that cannot be attributed to this "expected" drag vector, and therefore reflects the sideways "lift" components generated by the sideslip plus spanwise components of any new drag vectors created by the slip. This is quite a change from our previous figures and perhaps at this point the accumulated approximations and possible errors may not justify proceeding further with these calculations. Nonetheless if we go ahead and make one more leap and adjust these "extra" spanwise force values (74 pounds for the sailplane, 6.5 pounds for the hang glider) for the airspeed difference between the two aircraft, exactly as before, then we calculate that the sailplane would generate 18.5 to 32.5 pounds of "extra" spanwise force if it were flying at hang glider airspeeds, which is 2.8 to 5 times greater than the 6.5 pounds of "extra" spanwise force generated by the hang glider.

Admittedly these calculations have been convoluted and the initial observations were rather rough; I'm presenting them more as food for thought for anyone attempting a similar experiment, than as actual data. It would be more enlightening if we could truly isolate the sideways "lift" force produced by the spanwise airflow in the sideslip, and also if we could isolate the total drag increase attributable to the slip. The aerodynamic side loads could be computed from precise measurements of turn rate, bank angle, and airspeed, and the increased drag could be calculated from sink rate observations. These data would paint a more definitive picture of the extent to which a slip generates affects the turn rate of a hang glider and also of the extent to which a slip will degrade the L/D ratio and steepen the glide path. On a much more practical level, it would be very useful to make some sink rate comparisons in several different hang gliders during a series of reversing turns versus during a sustained (non-slipping), steeply banked, high-G, high-speed spiral, to learn whether the sideslip created during the turn reversals creates enough drag to significantly increase the sink rate. See the section in Part Three entitled "Actual data: steep reversing turns in an airplane" for much more on this idea and its possible relevance (or lack of relevance!) to escaping "cloud suck".

 

APPENDIX 5: COMMENTS ON "HANG GLIDER TURN PERSPECTIVES"

***** Note summer 2005 -- my views on some of these points have changed somewhat since this section was written. I no longer feel that my experimental observations should be interpreted to conclusively show that yaw rotational inertia, rather than an actual aerodynamic adverse yaw torque, was the primary driving factor in the sideslip that occurred when I made a roll input on my Spectrum, and likewise for other hang glider types. Also I find myself a bit skeptical of the idea that any long-spanned, tailless aircraft would exhibit a skid rather than a slip in a sustained, constant-banked turn. I've not seen any evidence of this in any hang glider that I've flown to date. *****

Dennis Pagen's article "Hang Glider Turn Perspectives" in April 2000 Hang Gliding was a response to my earlier article in the February 2000 issue. Actually many of Dennis's points were in complete agreement with my own point of view--for example his comments on airflow curvature, and adverse yaw. (I didn't see much evidence of adverse yaw in my Spectrum but I have no doubt that higher performance hang gliders will behave as Dennis described). Dennis's observation that many high-performance gliders will show a skid rather than a slip in a steady, constant-bank turn filled a gap in my February article, especially in relation to the blind flying comments. (The steady-turn behavior of a glider is really quite a separate issue from the behavior of the glider as it rolls into a turn or as the pilot makes various pitch inputs). Dennis's strong warnings about the whole blind flying idea were well taken--see the current version of my extended discussion on the topic in Appendix One. However Dennis and I seem to be in some disagreement about some of the basic physics of turning flight, including the role of yaw rotational inertia, and the relationship between pilot pitch "coordination" inputs and apparent sideways (centrifugal or centripetal) forces upon the pilot. My ideas on those topics are related in great detail throughout this paper so I won't say more about them here.

A few other points--see my comments in Part Three, subsection "Actual data, and interpretation of results..." as to why I believe that my yaw strings were not unduly influenced by the local airflow around my body during roll inputs. See the section in Part Three entitled "Actual data: steep, reversing turns in an airplane" for some thoughts on the reversing-turns method of escaping strong lift near cloud base. And see the sections entitled "Detecting sideslip in hang gliders" (Part Two), "Suggestions for teaching methods" (Part Three), and "Anhedral effects and possible links to pitch inputs" (Part Four) for some thoughts regarding the marked connection between pulling in the bar, and sideslip, which Dennis reported for some high-performance gliders.

 

APPENDIX 6: AN OUTLINE OF THIS PAPER

In case the font sizes of the subtitles don't transmit well over the web, and to serve as an index, here is an outline of this paper:

TURNING FLIGHT AND SIDESLIP IN HANG GLIDERS

(Summary)

(INTRODUCTION)

I PART ONE: PRACTICAL TURN "COORDINATION" AND PITCH AXIS DYNAMICS


I.A INTERPLAY OF ANGLE-OF-ATTACK, BANK ANGLE, AIRSPEED, AND G-LOADING
I.B WHAT DETERMINES ANGLE-OF-ATTACK?
I.C DO WE SEE THE SAME DYNAMICS IN POWERED AIRCRAFT ALSO?
I.D L/D RATIO AND LIFT FORCE
I.E BUT WHAT ABOUT SIDESLIP?

II PART TWO: A BRIEF OVERVIEW OF SIDESLIP DYNAMICS


II.A DEFINITION OF SIDESLIP
II.B DETECTING SIDESLIP IN HANG GLIDERS
II.C SOME COMMON IDEAS ABOUT SIDESLIP IN HANG GLIDERS
II.D SOME IDEAS ABOUT SIDESLIP IN 3-AXIS AIRCRAFT

III PART THREE: THE HEART OF THE MATTER: MAKING THE IN-FLIGHT EXPERIMENTS, INTERPRETING THE RESULTS, AND SUGGESTIONS FOR TEACHING


III.A TOOLS FOR INVESTIGATION
III.B MAKING THE TEST FLIGHTS
III.C ACTUAL DATA, AND INTERPRETATION OF RESULTS: SLIP-SKID BEHAVIOR OF MY GLIDER (Spectrum 144)
III.D DO THESE RESULTS APPLY TO OTHER HANG GLIDERS?
III.E SUGGESTIONS FOR TEACHING METHODS<
III.F SO WHY DO WE LET OUT THE BAR WHILE ROLLING INTO A TURN?
III.G ACTUAL DATA: SLIP-SKID BEHAVIOR OF SAILPLANES AND AIRPLANES
III.H ACTUAL DATA: TIMING OF PITCH AND YAW DYNAMICS IN AN AIRPLANE
III.I ACTUAL DATA: STEEP, REVERSING TURNS IN AN AIRPLANE


IV PART FOUR: EXPANDED THEORY OF TURNS AND SIDESLIP IN HANG GLIDERS

IV.A (GENERAL BACKGROUND)

IV.A.1 FRAME OF REFERENCE IN TURNING FLIGHT
IV.A.2 WHAT MAKES AN AIRCRAFT TURN?
IV.A.3 EFFECT OF SIDESLIP ON TURN RATE
IV.A.4 MORE ABOUT TORQUE
IV.A.5 REFERENCE FRAME IN A SIDESLIP, AND GENERATION OF SIDEWAYS FORCES AND DRAG
IV.A.6 HOW DOES A HANG GLIDER PRODUCE A SIDEWAYS AERODYNAMIC FORCE IN A SLIP?


IV.B DYNAMICS WHILE THE BANK ANGLE AND AIRSPEED ARE CHANGING:


IV.B.1 SIDESLIP DUE TO YAW ROTATIONAL INERTIA
IV.B.2 ADVERSE YAW
IV.B.3 CONSIDERING ADVERSE YAW AND YAW ROTATIONAL INERTIA TOGETHER
IV.B.4 EFFECT OF SIDESLIP ON ROLL RESPONSE
IV.B.5 BALANCING YAW AND ROLL STABILITY
IV.B.6 ANHEDRAL EFFECTS AND POSSIBLE LINKS TO PITCH INPUTS
IV.B.7 EFFECT OF A FIN ON ROLL RATE
IV.B.8 WHY DO AIRSPEED CHANGES AND SIDESLIPS OCCUR TOGETHER? A COMPLETE DESCRIPTION OF THE DYNAMICS IN THE PITCH AND YAW AXES AS THE GLIDER IS ROLLED INTO A TURN
IV.B.9 FUNDAMENTAL RELATIONSHIPS: DOES AN "IMBALANCED" G-LOADING CREATE A SIDEWAYS FORCE ON THE PILOT?
IV.B.10 FUNDAMENTAL RELATIONSHIPS: WHY DOESN'T THE AIRCRAFT SLIP TOWARD THE LOW WING WHEN THE G-LOADING IS INADEQUATE IN A TURN?
IV.B.11 FUNDAMENTAL RELATIONSHIPS: HOW TO DRAW YOUR OWN VECTOR DIAGRAMS FOR TURNING FLIGHT
IV.B.12 MORE VECTOR DIAGRAMS


IV.C DYNAMICS IN STEADY TURNS AT CONSTANT AIRSPEED AND BANK ANGLE:


IV.C.1 AIRFLOW CURVATURE IN TURNING FLIGHT
IV.C.2 AIRFLOW CURVATURE AND SIDESLIP: OBSERVED EFFECTS
IV.C.3 BALANCE OF FORCES IN THE YAW AND ROLL AXES: THEORY
IV.C.4 BALANCE OF FORCES IN THE YAW AND ROLL AXES: OBSERVED EFFECTS
IV.C.5 IS THERE A BENEFIT TO A SKIDDING TURN IN A HANG GLIDER?
IV.C.6 EFFECT OF A FIN ON HANDLING IN THERMAL TURNS


V. THAT'S ALL FOLKS (except appendices...)
VI. (APPENDICES)


VI.A APPENDIX 1: A NEW CLOUD FLYING "INSTRUMENT"
VI.B APPENDIX 2: TOWING AND LOCKOUT DYNAMICS
VI.C APPENDIX 3: SLIPS IN AIRCRAFT WITH RUDDERS
VI.D APPENDIX 4: ESTIMATING THE AERODYNAMIC FORCES PRODUCED BY A SIDESLIP
VI.E APPENDIX 5: COMMENTS ON "HANG GLIDER TURN PERSPECTIVES"
VI.F APPENDIX 6: AN OUTLINE OF THIS PAPER