Accurate diagram of forces in a “fully coordinated” turn with no sideslip and adequate lift (G-loading), a turn with inadequat

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).

(This page last updated August 8 2004)

 

 

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 "L" vector is meant to be drawn "square" to the wingspan and the "S" vector is meant to be drawn parallel to the wingspan.

Though the aircraft in these illustrations are hang gliders, the diagrams and text also apply to 'conventional' sailplanes and airplanes.

We’re ignoring drag for now; the drag vector is difficult to draw in this head-on view of the aircraft, so we’ll confine ourselves to a 2-dimensional representation and pretend that the flight path at this instant is exactly horizontal rather than descending.  (When the flight path is descending in relation to the airmass, the drag or (drag minus thrust) vector is needed to create a fully balanced vector diagram, and when the flight path is ascending in relation to the airmass, the (thrust minus drag) vector is needed to create a fully balanced 3-dimensional vector diagram. However when we confine ourselves to a head-on view of the aircraft, we only introduce a small error by ignoring these additional vectors.)

In all cases the horizontal component of N is the centripetal force that creates the turn. Note that we have not drawn a “centrifugal force” vector per se, other than the centrifugal component contained within vector S in the third picture.  (The concept of “centrifugal force”, as it is usually invoked, is a myth).  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" or accelerates earthward. Na is the force transmitted from the aircraft to the pilot and is really the total G-loading "felt" by the pilot. 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 aircraft, because the net aerodynamic force vector and G-loading, Na, is no longer squarely perpendicular to the aircraft's wingspan. The sideslip shown in case 3 could arise either because the aircraft has acquired a sideways motion toward the low wingtip and the nose has not yet yawed into alignment with the new direction of the flight path, or because the aircraft has yawed toward the high wingtip without changing the direction of the flight path. (Figure 3 illustrates the latter case--the flight path is pointing straight toward the reader and the nose of the aircraft is yawed toward the upper left corner of the page). In either case the aircraft will be moving sideways through the air and the there will be a spanwise airflow component over the aircraft, blowing from the low wing tip toward the high wingtip. This will generate the sideways or spanwise aerodynamic force vector S in figure 3. While the aircraft is slipping, the aerodynamic side force toward the high wing tip (vector S) is transmitted to the pilot through the seat, or in the case of a hang glider, through the pilot's arms. A freely hanging pilot who exerts no pressure with his arms, or the freely rolling slip-skid ball, will not “feel” a sideways force in the reference frame of his body, strictly speaking, but 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.

With an all-wing aircraft such as a hang glider, the sideways aerodynamic force vector S will be quite small even if the nose of the aircraft is pointing much too far toward the outside or high side of the turn, so that there is a there is a very significant sideways airflow component.  In other words when a hang glider sideslips we will see a very minimal deflection of a slip-skid ball or bubble, and of the pilot’s body, for a given angular deflection of a yaw string or telltale.

Now let's focus on the relationship between pitch inputs and sideslip. Of course if there is a rudder, the pilot can prevent the aircraft from slipping or skidding regardless of the physics at play, so we'll assume that the aircraft has no rudder, or that the pilot is not using the rudder. Also we'll ignore things like p-factor and gyroscopic effects that may strongly affect the relationship between pitch inputs and yaw coordination in an airplane with a propeller. (Readers who explore these relationships for themselves in a powered airplane will find that a low or idle power setting is best, to avoid these complications.)

What happens when a pilot is in a "coordinated" turn as in case 1, and then pulls in the bar (or pushes forward the control stick or yoke) to "unload" the wing 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 aircraft will change as it noses down into a steeper dive.  If the yaw rotation rate must decrease, there will be a tendency for the aircraft's inherent yaw rotational inertia to momentarily swing the nose too far into the direction of the turn, creating a brief skid. If the aircraft's yaw rotation must increase, there will be a tendency for the aircraft's inherent yaw rotational inertia to make the nose momentarily lag behind the actual direction of the flight path, pointing too far toward the outside of the turn, and creating a brief slip. In reality, when the aircraft eventually returns to equilibrium (case 1) at the new, pulled-in bar position (or the new, forward control stick 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: the aircraft's inherent yaw rotational inertia has swung the nose a bit too far toward the inside or low side of the turn, exposing the aircraft to spanwise airflow component blowing from the outside or high wingtip toward the inside or low wingtip, which interacts with the aircraft's inherent yaw stability or 'weathervane effect' to create the yaw torque needed to decrease the aircraft's yaw rotation rate. In actual practice I've found that pitch inputs generally don't have any noticeable affect on sideslip, when the bank angle is held constant--see below for more on the real-world in-flight observations behind this statement.

The same reasoning applies when we examine the influence of the pilot's pitch inputs as the aircraft rolls from wings-level into a turn.  If the pilot does not give a nose-up pitch input to increase the wing's angle-of-attack and lift vector (G-loading) as he rolls into the turn, the force balance will initially be as shown in figure 2, where the lift vector (G-loading) is only equal to the aircraft's weight (1 G) which is not enough to balance the vector diagram when the wing is banked. Again the aircraft will respond by nosing down and 'falling' or accelerating earthward, and eventually the rising airspeed will increase the lift vector (G-loading) to bring the forces back into balance as shown in figure 1. (In the case of a glider, or any aircraft that is descending with respect to the airmass, the drag or (drag-thrust) vector will also play a role in bringing the vector diagram into balance as the aircraft accelerates.) Will the aircraft slip sideways at any point in this process, to a greater degree than if the pilot had made the same roll input along with a nose-up pitch input to increase the lift vector so that the aircraft did not nose down and gain airspeed? Again the overall picture is quite complex, but the fact that the aircraft will eventually end up at a higher airspeed and lower turn rate when the pilot does not increase the wing's angle-of-attack as he enters the turn suggests that the aircraft's yaw rotational inertia will actually be less important in this case than when the pilot makes a normal nose-up pitch input as he enters the turn. This suggests that there will actually be slightly more sideslip with a normal, 'balanced' entry into the turn than when the pilot simply makes a roll input with no pitch input. In actual practice I’ve found that my pitch inputs have no noticeable effect on the amount of sideslip seen while rolling into a turn in a wide variety of types of aircraft, except for the fact that adverse yaw is usually much more pronounced when the whole process is initiated at a low airspeed than at a high airspeed.

The observations we've made here about what a pilot will see 'in actual practice' are based on a long series of careful experiments where I paid close attention to the behavior of a yaw string or telltale, and also a slip-skid ball or bubble, during rudderless turn entries, both with and without the usual nose-up pitch input to keep the flight path from curving downward and the airspeed from rising, in hang gliders, sailplanes, and airplanes. Other related experiments involved "loading up" the wing with extra G's or reducing the lift vector to zero (weightlessness), while holding the bank angle constant. In general these pitch inputs, or the absence of pitch inputs, did not cause the aircraft to slip or skid sideways through the air. Readers are highly encouraged to repeat these experiments for themselves. (In the case of a hang glider, some effort is needed to place a yaw string in a position where it may easily be viewed in flight and is located on the centerline of the aircraft to avoid parallax issues; see other portions of this website for pictures of the basebar-mounted 'probes' used in my experiments. And in the case of a powered aircraft with a propeller in front, the propwash will interfere with a yaw string, so the observations may need to be confined to the slip-slid ball or bubble. )  

I visualize the nose-up pitch input that usually accompanies a turn entry as serving only to prevent the aircraft from diving and accelerating, not to prevent the aircraft from slipping sideways with respect to the airmass.

I also feel that pilots--especially in the world of hang-gliding--often mistake the feeling of diving and accelerating with a reduced or inadequate lift vector and G-loading, for the feeling of slipping sideways through the air.

Additional notes:

If 'inadequate' or 'faulty' pitch inputs during turns--or deliberate nose-down pitch inputs to reduce the wing's angle-of-attack--are not a cause of sideslips, then when will a rudderless aircraft like a hang glider slip sideways through the air? By paying close attention to a yaw string (telltale) that was mounted where I could easily view it in flight, I've observed that hang gliders sideslip primarily due to adverse yaw (and yaw rotational inertia) while the pilot is giving a roll input to increase the bank angle. When the bank angle is constant (and non-zero) there is typically only a very slight amount of sideslip, regardless of any changes that might be occurring in the control bar position or airspeed or angle-of-attack; this small sideslip is due primarily to the 'airflow curvature' effect that we'll explore elsewhere on this website. A 'conventional' airplane or sailplane that is being flown without use of the rudder will show the same behavior--it will tend to sideslip due to adverse yaw and other related effects whenever the bank angle is increasing, and it will tend to show a very slight sideslip during turns when the bank angle is held constant.

We haven't illustrated a linear or non-turning sideslip, which can only be sustained in an aircraft with a rudder. Astute readers will be able to provide their own diagram for this case--basically, the forces are similar to Figure 3, except the aerodynamic sideforce vector 'S' is large enough that the net aerodynamic force vector Na ends up being purely vertical, equal to the aircraft's weight, with no horizontal component, and the net force vector N is zero. For a given bank angle, to balance out the vector diagram, the lift vector L will end up being smaller in a non-turning sideslip than in a slipping turn.

(An extreme case of a non-turning sideslip occurs when an aerobatic aircraft demonstrates sustained knife-edge flight with a bank angle of 90 degrees. In this case the wing's lift vector is reduced to zero and most of the aircraft's weight is borne by the spanwise aerodynamic force vector S, which points straight up. This spanwise or sideways aerodynamic force vector S is generated by the spanwise or sideways airflow component impacting against the fuselage and vertical tail. A flying-wing aircraft would have difficulty with this maneuver, because with no fuselage, a given amount of sideways or spanwise airflow will generate only a very small aerodynamic sideforce vector S. In addition to the spanwise aerodynamic force vector S, the engine thrust will also bear a part of the aircraft's weight during this knife-edge maneuver; this is one case where it is not adequate to assume that the engine thrust vector acts parallel to the flight path.)

We haven't illustrated a skidding turn. Sustained skidding turns normally only occur when a pilot holds too much rudder in the direction of the turn. However, when any aircraft is given a strong roll input to decrease the bank angle, adverse yaw will temporarily swing the nose toward the inside or low side of the turn, creating a skid. (This can be easily demonstrated with a yaw string or telltale on a hang glider, even though most hang glider pilots believe that their aircraft are much more prone to slipping than to skidding). Again, astute readers will be able to provide their own diagram for the skidding turn--basically, the forces are similar to Figure 3, except the direction of the aerodynamic sideforce vector S is reversed, because the nose of the aircraft is pointing too far toward the inside or the low side of the turn, creating a spanwise airflow component that blows from the high wingtip to the low wingtip. To convert Figure 3 to an illustration of a skidding turn, vector S should be reversed to start at the tip of vector L and run down and toward the right. Vector Na will end up on the right side of vector L. For any given bank angle, to balance out the vector diagram so that the net force vector N is purely horizontal, the lift vector L must be larger in a skidding turn than in a slipping turn, or in a turn with no slip or skid. The net force vector N will end up being larger in the skidding turn than in either the slipping turn or the fully 'balanced' turn with no slip or skid, so the turn rate will be higher. However the aerodynamic sideforce vector S, not the increased turn rate, is what causes the pilot to be thrown to outside or high side of the aircraft during a skidding turn. In other words the net aerodynamic force vector (or G-loading vector) Na is no longer squarely perpendicular to the aircraft's wingspan, but rather is tilted toward the inside or low side of the turn (i.e. toward the right in these diagrams). Again, with an all-wing aircraft the sideways aerodynamic force vector S will be quite small even if the nose is pointing much too far toward the inside of the turn, creating a very significant sideways or spanwise airflow component.

 

Copyright © 2004 aeroexperiments.org