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 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 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.) I PART ONE: PRACTICAL TURN "COORDINATION"
AND PITCH AXIS DYNAMICS II PART TWO: A BRIEF OVERVIEW OF SIDESLIP DYNAMICS
IV.A.1 FRAME OF REFERENCE IN TURNING FLIGHT
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. 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. 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. 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 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. 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. 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! 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. 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. ***** 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. ***** 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. ***** 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. ***** 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: Airspeed (mph): Turn Radius (ft): Total Airflow Curvature (degrees) over
keel length (352 cm): Airflow Curvature in Yaw Axis (degrees)
over keel length (352 cm): Airflow Curvature in Yaw Axis (degrees)
from extreme rear of keel to: "Center" of Wing (dist. 139
cm): Yaw String in Front of Basebar (dist. 290 cm): Apex of Glider (dist. 352 cm): "Bowsprit" Yaw String (dist.
539 cm): 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 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
I PART ONE: PRACTICAL TURN "COORDINATION"
AND PITCH AXIS DYNAMICS II PART TWO: A BRIEF OVERVIEW OF SIDESLIP DYNAMICS
IV.A.1 FRAME OF REFERENCE IN TURNING FLIGHT
steve at aeroexperiments.org
July 6, 2000 edition
seibel999@hotmail.com
July 6, 2000 edition
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.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.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.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
ANHEDRAL EFFECTS AND POSSIBLE LINKS TO PITCH INPUTS
10
20
30
45
60
22.7
23.2
24.2
26.8
31.8
194
99
68
48
39
3.4
6.7
9.7
13.6
16.5
3.3
6.3
8.4
9.6
8.2
1.3
2.5
3.3
3.8
3.3
2.8
5.1
6.9
7.9
6.8
3.3
6.3
8.4
9.6
8.2
5.1
9.5
12.7
14.3
12.2
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.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.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.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