This brings to mind an interesting analogy: turning an aircraft by means of a skidding flat turn, rather than by banking and relying on the wing's lift vector, makes about as much sense as does flying along a horizontal path in a knife-edge fashion, rather than flying the aircraft along the same horizontal path by keeping the wings level and relying on the wing's lift vector!)
It's worth noting that the change in turn rate caused by a slip or skid is not really the fundamental reason that the slip-skid ball displaces to one side. When the nose of the aircraft is yawed out of alignment with the actual direction of the flight path and airflow, the fundamental driving force that displaces the slip-skid ball to one side is the real, tangible force created by the impact of a sideways (slipping or skidding) airflow component against the side of the aircraft. In a bit more detail: as the sideways airflow exerts a real, tangible aerodynamic "push" against the side of the aircraft, the slip-skid ball (and the pilot's body) responds by deflecting in the opposite direction as the aircraft as being "pushed". This real, tangible aerodynamic "push" is also what causes the change in the turn rate.
If the aircraft is meeting the airflow head-on and there is no sideways airflow or aerodynamic sideforce, then slip-skid ball will stay centered, regardless of the G-loading (lift force) or bank angle or airspeed or turn rate, and regardless of whether there is any upward or downward curvature in the flight path or gain or loss of airspeed. (Of course, all these variables are inter-related in some way.)
What a slip-skid ball or bubble really measures is the ratio of the aerodynamic sideforce (which is primarily generated by the impact of a sideways airflow against fuselage and other components of the aircraft) to the wing's lift vector (which always acts in the "upward" direction). And here, we're using the words "sideways" and "upwards" strictly in relation to the aircraft's own reference frame--the orientation of the aircraft with respect to the outside world is irrelevant. Contrary to popular belief, things like "gravity" and "the centrifugal force generated by the curving flight path" do not enter into the picture. If the fuselage is properly aligned with the airflow, no aerodynamic sideforce is created, and the ball and bubble are centered, plain and simple. (But see the next section of this article for one rather esoteric exception!)
Caveat: in certain situations where a rudder is strongly deflected to cancel some sort of external yaw torque, but the nose of the aircraft is pointing straight into the airflow or relative wind, the aerodynamic sideforce created by the rudder itself can cause the slip-skid ball to be deflected even though the yaw string is centered. In this case it is more efficient to leave the slip-skid ball slightly off-center, than it would be to increase the rudder deflection, center the ball, and displace the yaw string to the side. For more, click here.
9) More on yaw strings and slip-skid balls and bubbles
Elsewhere on this website, we'll refer to slip-skid bubbles. A slip-skid bubble simply moves in the opposite direction as a slip-skid ball. Slip-skid bubbles were employed in many of the experiments described on this website, because they are lightweight and can be acquired cheaply in hardware stores. In this photo, the multiple curved tubes are mounted in a way that duplicates the function of a single, longer tube with the same radius of curvature. The red tuft of yarn is a yaw string, and the wires are visual bank-angle gauges (for comparison with the horizon).
One advantage of a yaw string over a slip-skid ball or bubble is that a yaw string continues to work during negative-G (e.g. sustained inverted) flight. During negative-G flight, the tube of a ball or bubble is curved in the "wrong" direction, so the ball or bubble tends to "slam" all the way to one of the ends of the tube and stay there.
In the particular case where an aircraft is flying on a constant heading, i.e. when there is no curvature in the flight path, then a slip-skid ball or bubble also serves as a bank angle gauge. Fundamentally, the slip-skid ball or bubble measures aerodynamic sideforce, not bank, so using the slip-skid ball as a bank-angle gauge imposes some peculiar constraints. For example, we're not free to change the bank angle without also making other some other adjustments to keep the plane moving along a linear path. Generally speaking, the only way that an aircraft can be banked and flying in a straight line if it is sideslipping through the air. After all, some sort of aerodynamic sideforce must be present to create an additional horizontal force component to cancel out the horizontal force component from the banked wing and prevent a turn, and this "something" is usually the aerodynamic sideforce generated by a sideways airflow impacting against the fuselage and other components of the aircraft (but see the above "Caveat" for one other alternative source of aerodynamic sideforce.)
10) Fallacies in the flight training guides
In many flight training guides, one can read that slips and skids are produced by an "inadequate amount of lift in relation to the bank angle", or by an "excess of centrifugal force", or by the "downward pull of gravity on the contents of the aircraft", etc. These explanations are extremely misleading and often contain errors. "Centrifugal" force--as least as it is usually invoked--does not actually exist. Gravity has the remarkable quality of "working from within" and exerting an equal acceleration on every molecule of the aircraft and pilot, so it cannot exert stresses and strains on the aircraft or pilot or be "felt" by the pilot in any way. It's a misconception that whenever the G-load is "too low" for the bank angle, the force of gravity will "pull" the pilot and the slip-skid ball toward the low side of the cockpit or control frame, as anyone who has experienced low-G or 0-G (weightless) maneuvers can attest. Slips and skids are yaw-axis phenomena--they are caused by nothing more complicated than the nose of the aircraft being out of alignment (in the yaw axis) with the actual direction of the relative wind, i.e. with the actual direction of the aircraft's flight path through the airmass. For more on the errors in the descriptions of slips and skids in the flight training literature, see the following related articles on this website (links are given at the bottom of this page): "Notes for new hang glider and trike pilots--on sideslips", "Looking for the "slipping" turn while hang gliding--overview", "You can't
'feel' gravity!", "Complete analysis of forces: fully balanced turn, turn with inadequate lift or G-load, slipping turn, non-turning slip, and skidding turn", and "The myth of the slipping turn in hang gliding and 'conventional' aviation".
11) Causes of adverse yaw: the "twist" in the relative wind as an aircraft rolls to a different bank angle
Let's shift our focus to the actual causes of adverse yaw. The term "adverse yaw" actually encompasses several different physical effects. In most aircraft, one of the most important causes of adverse yaw is the fact that the descending wing and the ascending wing each experience a twist in the local direction of the relative wind, compared to the direction of the relative wind experienced by the aircraft as a whole. This change in the direction of the local relative wind is caused by the rolling motion of the aircraft--because the descending wing is descending, its relative wind vector has more of an upward component than does the overall relative wind experienced by the whole aircraft. This change in the local direction of relative wind twists the descending wing's lift vector forward, creating a thrust component in relation to the reference frame of the whole aircraft. Conversely, because the ascending wing is rising, its relative wind has more of a downward component (or less of an upward component) than does the overall relative wind experienced by the whole aircraft. This change in the local direction of the relative wind twists the ascending wing's lift vector aftwards, creating a drag component in the relation to the reference frame of the whole aircraft. Naturally, these thrust and drag components create a yaw torque. The higher the roll rate, and the lower the airspeed, the more pronounced this phenomenon will be.
For an excellent illustration of this twist in the lift vectors, see this diagram from John S. Denker's superb "See how it flies" website.
12) Causes of adverse yaw: change in airfoil shapes
Another significant cause of adverse yaw in most aircraft is the physical difference between the shape of the descending and ascending wings that arises (due to the deflection of the ailerons, or in a flex-wing aircraft, due to billow shift) when the pilot makes a roll control input. The basic phenomena at work here is that lowering an aileron (and increasing the wing's lift coefficient) generally creates more drag than does raising an aileron by the same amount (and decreasing the wing's lift coefficient). Many aircraft employ differential travel (the rising aileron moves much more than the descending aileron) which will minimize adverse yaw from this source, or in some cases might even generate a helpful "proverse" yaw torque. In aircraft that use spoilerons rather than ailerons for roll control, deploying a spoileron will certainly create drag and generate a "proverse" yaw torque, as well as reducing the wing's lift and creating a roll torque. If this "proverse" yaw torque is large enough, it may even overcome the adverse yaw from other sources (the "twist in the relative wind" that we described above, and the adverse-yaw-like effect of the aircraft's yaw rotational inertia that we'll describe below), resulting in the complete elimination of slip while rolling into turns and the complete elimination of skid while rolling back to wings-level.
13) Causes of adverse yaw in weight-shift controlled aircraft: change in lengths of wings
In a weight-shift controlled hang glider or trike, we also have an additional cause of adverse yaw: whenever the pilot is making a weight-shift roll control input, we can visualize that not only does a difference arise in the cambered airfoil shape of the two wings, but one wing also becomes physically longer than the other wing, in relation to the CG of the whole system (including the pilot's body). The longer wing will tend to experience more drag than the shorter wing.
14) Rotational inertia in the yaw axis
Another effect that is not negligible is an aircraft's rotational inertia in the yaw axis. If an aircraft had a control system that was designed to create zero yaw torque (no adverse or "proverse" yaw) when the pilot made a roll input, the pilot would still see some slip while rolling into a turn and some skid while rolling out a turn, due to the aircraft's rotational inertia in the yaw axis. (Actually, this is only true for bank angles up to 45 degrees--as the bank angle is increased beyond 45 degrees, the turn begins to involve more rotation about the aircraft's pitch axis and less rotation about the aircraft's yaw axis. Because the aircraft's yaw rotation rate needs to decrease rather than to increase, with further increases in bank angle the aircraft's yaw rotational inertia will tend to create a skid rather than a slip.) The basic mechanism at work is that as the wing banks and the flight path starts the curve, the nose of the aircraft will initially tend to stay on its original heading until some corrective yaw torque is applied to initiate a rotation about the aircraft's yaw axis. The aircraft's inherent yaw stability (the "weathervane effect") will apply this yaw torque, but only after the flight path has diverged from the actual direction of the aircraft's heading by a noticeable amount, creating a temporary sideways airflow over the aircraft. Of course, once the aircraft's yaw stability mechanism has fully "kicked into gear" and created a sufficient increase in the aircraft's yaw rotation rate so that the aircraft's yaw rotation rate is "in synch" with the rate of curvature of the flight path, yaw rotational inertia is no longer a factor.
Rotational inertia in the yaw axis is important even on a light-weight aircraft like a flex-wing hang glider or trike--for example it plays a key role in the yaw oscillations that may be a seen when a hang glider pilot makes an abrupt, forceful roll input. In this case the average deflection of the yaw string is as described above--away from the direction that the pilot is shifting his body, indicating an adverse yaw effect--but this overall average movement is actually comprised of a series of oscillations, where the yaw string shifts first strongly away from the pilots body, and then shifts slightly toward the other side of the aircraft centerline, and the shifts back away from the pilot's body by a lesser amount than was seen during the initial deflection, and so on in a series of damping oscillations that after several seconds and two or three visible cycles brings the yaw string to its "final" position several degrees to the side of the aircraft centerline, away from the pilot's body. (Only the initial one or two of these oscillation cycles actually cause the yaw string to move all the way to the "proverse" side of the aircraft centerline; the subsequent cycles just involve a rising and falling in the amount of adverse yaw that is present). If the aircraft's yaw rotational inertia were trivial, this yaw oscillation would not occur. Similar yaw oscillations--which again are evidence of the importance of yaw rotational inertia-can be created by alternately pumping the left and right rudder pedals of a "conventional" aircraft until a very large yaw oscillation is taking place, and then removing one's feet from the rudder pedals and noting the several cycles of yaw oscillation that take place before the nose of the aircraft and the yaw string and/or slip-skid ball settle down in a constant, centered position. (Use some caution; "pumping" the pedals in this manner creates much higher sideslip angles and produces much higher loads on the rudder and vertical fin than occur in any other flight regime). Again, if the aircraft's yaw rotational inertia were trivial, then these yaw oscillations would not occur: alternately "pumping" the left and right rudder pedals would create no more of yaw deflection (sideslip angle) than would a single hard rudder input, and once the pilot ceased making rudder inputs, the aircraft's nose would immediately align itself with the relative wind rather than "overshooting" and going through several visible oscillation cycles before settling down.
The relationship between adverse yaw driven by real, adverse, aerodynamic torques, and yaw rotational inertia, is complex. In most cases where a pilot is making an intentional control input with ailerons, the adverse aerodynamic torques are probably the main factor that makes the nose point in a different direction from the actual direction of the flight path and relative wind, and yaw rotational inertia probably works in the pilot's favor, minimizing this "wrong-way" swing of the nose. But in situations where a vertical gust tips an aircraft into a bank, the aircraft's yaw rotational inertia may play an important role in keeping the nose pointing on its original heading, creating a sideways airflow over the aircraft as the flight path starts to curve but the aircraft's heading remains nearly constant. Similar dynamics may take place in some spoileron-controlled aircraft. In aircraft controlled by weight-shift, the adverse aerodynamic torques may be the dominant factor--certainly when I make a strong roll input on my hang glider and the yaw string swings to the side, indicating a sideways component in the airflow, I've often noticed that the nose of the glider swings visibly in the "wrong" direction in relation to the horizon, rather than simply remaining on its original heading as the flight path starts to curve.
15) Adverse yaw in constant-banked turns: yaw torque created by the difference in airspeed between the low (inside) and high (outside) wingtips
The sources of adverse yaw that we've been discussing up till now operate mainly as an aircraft rolls from wings-level into a turn, or rolls from a banked attitude back to wings-level. We'll examine adverse yaw during rolling motions a bit more near the end of this article when we look at the "layman's explanation" for adverse yaw, which holds that as an aircraft rolls into a turn, the rising wing creates more drag "because it is creating more lift". But first we'll shift our focus a bit:
Another source of adverse yaw operates whenever an aircraft is banked and turning, even when the bank angle and turn rate are constant. As an aircraft turns, the outboard wingtip moves at a higher airspeed, and therefore experiences more drag, than the inside wingtip. This tends to yaw the nose of the aircraft toward the high side or outside of the turn. This is most pronounced in long-spanned aircraft flying at low airspeeds. Sailplane pilots are well acquainted with the need to hold a touch of inside rudder during constant-banked, constant-speed, thermalling turns, if the yaw string and slip-skid ball are to remain centered. Without this rudder input, the nose of the aircraft will point slightly toward the high side or outside of the turn, in relation to the actual direction of the flight path and relative wind at any given moment.
A related effect can occur in an aircraft with a long fuselage. We'll call it the "long tail arm" effect. More on this in just a bit, after we set the stage by talking about the "airflow curvature" effect.
16) The "airflow curvature" effect
Remember that the relative wind is just the apparent wind created by an aircraft's movement through the airmass. We can speak of the local relative wind experienced by a particular point on the aircraft as well as the overall relative wind experienced by the aircraft as a whole. If different parts of the aircraft are moving in different directions and/or at different speeds, they will experience differences in the direction or speed of their local relative winds. The difference in wingtip airspeeds that we discussed immediately above is a reflection of this idea. So is the "twist" in the relative wind direction that takes place when a wing rises or falls as the aircraft rolls, as we discussed earlier. Now here's another example of the way that different parts of an aircraft can experience differences in the direction of their local relative winds: in a steady, constant-bank turn, the airflow or relative wind actually curves to follow the circumference of the turn. We'll refer to this as the "airflow curvature" effect. We're not trying to claim that any individual air molecule follows a curving trajectory through space as it passes over the aircraft. Rather, the curvature in the relative wind is due to the fact that each point on the aircraft structure is engaged in both a linear motion, and a rotational motion about the aircraft's yaw axis, so different parts of the aircraft structure are moving in slightly different linear directions at any given moment. (Actually the pitch axis is also involved, especially at steep bank angles, and the roll axis also becomes involved if the aircraft is climbing or descending as it turns. We'll explore these ideas in more detail elsewhere on the Aeroexperiments website; for now it's sufficient to focus on the aircraft's rotational motion about the yaw axis, or if we want to be more precise, we can focus on the curvature in the flight path and relative wind as viewed by an observer looking down on the aircraft from above, which actually ends up describing the complete curvature in the flight path and relative wind, including the curvature components about each of the three axes of the aircraft.) This is really all much less complicated than we're making it sound: for an illustration of this curving airflow, see figure 8.9 in John S. Denker's "See how it flies" website. For an extreme example of the "airflow curvature effect", imagine an aircraft with no forward velocity, pinwheeling about its CG. It's obvious that a yaw string on the nose and a yaw string on the tail would blow in opposite directions. In an actual turn in an aircraft, the slight difference in that we would see in the orientation of a yaw string at the nose and a yaw string at the tail reflects the fact that the aircraft is makes one complete "pinwheeling" rotation during the course of each full circle of the flight path.
17) Difference between "relative wind" and airflow?
This might be a good time to interject that for the purposes of the Aeroexperiments website, any time our discussion is centered the around the idea of a "relative wind", we're ignoring the actual displacement of the air by the aircraft, and we're treating the air molecules as pristine, undisturbed elements whose velocity with respect to any part of the aircraft is determined solely by the trajectory that that part of the aircraft is following with respect to the airmass as a whole. When we use the word "airflow" instead of the phrase "relative wind", things get a bit murkier, and it would probably be clearer if we religiously used the phrase "relative wind curvature" rather than "airflow curvature". However, "relative wind curvature" seems a bit too clunky, so we'll stick with "airflow curvature" for the most part.
18) Adverse yaw in constant-banked turns: the "long tail arm" effect
Once we understand the "airflow curvature" idea, it's not hard to guess what the "long tail arm" effect might be: as the vertical tail tries to "weathervane" into alignment with the curving airflow, the nose and most of the rest of the fuselage end up pointing toward the outside of the actual direction of the flight path of the aircraft as a whole, so that the fuselage as a whole experiences a sideways airflow component. Let's revisit figure 8.9 in John S. Denker's "See how it flies" website to see how this 'airflow curvature" effect tends to create a slipping airflow over the main part of the aircraft, as the tail finds a position that is approximately aligned with the direction of the airflow or relative wind at the tail. Clearly, to center the slip-skid ball, some inside rudder is needed to align the main part of the fuselage with the overall direction of the airflow. To center the yaw string, a touch more inside rudder would be needed, because the yaw string only reflects the direction of the airflow at the extreme nose of the aircraft. There's no good reason to align the extreme nose of the aircraft with the relative wind, and some sailplane pilots intentionally allow the yaw string to show a bit of slip in a thermalling turn for this reason. Some sailplane pilots feel that drag, including drag from the fin and rudder, will be reduced if the pilot keeps his rudder inputs small enough to allow some slipping airflow over the central part of the fuselage, and over the wings. In this case the slip-skid ball would be slightly off-center. The slipping airflow also interacts with the dihedral geometry of the sailplane's wings to create a rolling-out torque, reducing the need for the pilot to apply inside aileron to counteract the rolling-in torque created by the difference in airspeed between the two wingtips. Naturally, the wings are more efficient when the ailerons are near neutral than when they are not, though the sideslipping airflow imposes its own penalties. Note that a thorough analysis of the drag of the fin and rudder would reach somewhat different conclusions in a case where the aircraft had an all-moving vertical tail, than in a case where the fin and rudder were separate.
For more on the "long tail arm" effect or "long-tailed slip" effect, see the related article on this website entitled "Analyzing the "long-tailed slip" effect, with notes on how "airflow curvature" affects a swept- or delta-winged aircraft".
19) Adverse yaw in constant-banked turns: combining the yaw torque created by the difference in airspeed between the low (inside) and high (outside) wingtips with the "long tail arm" effect
Now we need to admit that we haven't told the full story yet, especially in relation to a long-spanned aircraft like a sailplane. The reality is that we can't consider the "long tail arm" effect independently from the yaw torque created by the difference in airspeed between the two wingtips, which we discussed earlier. Because the outside wingtip experiences more airspeed and more drag than the inside wingtip, the outside wing will tend to "lag" and the inside wing will tend to "lead". This will make the nose of the aircraft point even further toward the outside or high side of the turn, and will increase the amount of inside rudder that the pilot must apply to avoid an extreme slip angle. For more on this topic, see the related article on this website entitled "Analyzing the "long-tailed slip" effect, with notes on how "airflow curvature" affects a swept- or delta-winged aircraft".
20) Adverse yaw in constant-banked turns: hang gliders and trikes
In a swept-wing all-wing aircraft like a hang glider or trike, the distance along the longitudinal axis (parallel to the keel) from the CG back to the wingtips is very roughly equivalent to the distance from the CG back to the tail in a "conventional" aircraft. If the wing as a whole--including the rearmost parts--are experiencing a strong slipping airflow component, it's clear how this would create a yawing-in torque that would counteract the yawing-torque generated by the increased airspeed experienced by the outboard wingtip. However, the swept leading edges will create a significant yawing-in torque even if aircraft is flying in a yaw attitude such that the very rearmost parts of the aircraft are experiencing little or no sideways airflow, i.e. even if the "tangent point" between the curving airflow and the line of the keel lies somewhere between the trailing edge of the wing and the center of area of the wing. For more on this topic, see the related article on this website entitled "Analyzing the "long-tailed slip" effect, with notes on how "airflow curvature" affects a swept- or delta-winged aircraft". If the aircraft does in fact adopt such a yaw attitude, then a vertical tip fins or a vertical keel fin will experience little sideways airflow, and will have little impact on the aircraft's yaw attitude and on the balance of roll torques in a steady constant-banked turn.
21) Adverse yaw in constant-banked turns: summarizing...and focussing on the idea of the "tangent point"
If we've lost you somewhere in the last three sections, the take-home message is that in a sustained, constant-bank turn, the yaw torque created by the difference in airspeed between the inside and outside wingtips, plus the curvature in the airflow along the length of the fuselage or keel of the aircraft, will cause the aircraft to adopt a yaw orientation where the nose is yawed slightly to the outside or high side of the turn, and we can consider this to be a form of "adverse yaw". A key point is that the slower the airspeed, the more pronounced this effect will be, because the turn will have a smaller radius, i.e. the flight path and relative wind will have more curvature. If the aircraft has a rudder, the pilot can use it to reduce or eliminate this sideslip as viewed by the aircraft as a whole, although strictly speaking, because of the curvature in the airflow, the airflow can never be exactly "straight" over the entire planform of the turning aircraft. Only one point along the length of the fuselage or keel can be tangent to the curving flight path. If this point falls at the C.G. of the aircraft--or perhaps we should say if this point falls at the center of lateral area of the aircraft, which is nearly always located aft of the C.G. (the center of lateral moment must always be located aft of the C.G.)--then we might say that the aircraft as a whole is aligned with the overall direction of the flight path and relative wind at that particular moment. In this case, the net aerodynamic sideforce generated by the net action of the airflow over the entire aircraft should be zero
22) Adverse yaw in constant-banked turns: effect of pilot's roll inputs on aircraft's yaw orientation in "conventional" 3-axis aircraft
Of course, in a steady constant-bank turn the pilot's roll input will also affect the balance of yaw torques. In a long-spanned aircraft like a sailplane, the pilot must exert a significant rolling-out torque to balance the over-banking tendency created by the fact that the outside or high wingtip is moving much faster than the inside or low wingtip. This roll input will tend to increase the drag of the inside or low wing, unless the aircraft achieves roll control through spoilerons, or through ailerons with a high degree of differential. An increase in drag of the inside or low wing will reduce the aircraft's tendency to orient itself in a slipping attitude, i.e. in attitude where the nose is yawed toward the outside or high side of the turn. Obviously we're dealing with a "loop" of closely interconnected variables here--as we've mentioned above, in an aircraft with dihedral the pilot could also (inefficiently?) combat the overbanking tendency by allowing or even forcing the aircraft to yaw toward the outside or high side of the turn, reducing the need to make a rolling-out roll input with the ailerons. In a sailplane that uses the rudder as the sole means of roll control--as do many RC model sailplanes--this is what must happen.
23) Yaw and roll in constant-banked turns: more on the effect of pilot's yaw inputs on the aircraft's yaw orientation, and on the balance of roll torques, in "conventional" 2-axis or 3-axis aircraft
Let's make a little detour to take a more detailed look at a rudder-controlled RC model sailplane or any other aircraft that has good hands-off stability characteristics and uses a rudder for roll control. If the aircraft is left to its own devices, the yawing-out torque created by the high drag experienced by the faster-moving outboard wingtip will make the aircraft will yaw toward the outside of the turn (slip) so much that the sideways airflow will interact with the ample dihedral to roll the aircraft back to wings-level. To keep the bank angle constant the pilot must apply some inside rudder which reduces--but does not eliminate--the sideslip. The bank angle will stay constant when the mild remaining sideslip interacts with the dihedral to create just enough rolling-out torque to counterbalance the increased lift created by the faster airflow around the outboard wingtip. Any more inside rudder would reduce the slip angle (or even create a skid) and create a net rolling-in torque, and any less inside rudder would increase the slip angle and create a net rolling-out torque. In a somewhat similar vein, as we've already mentioned, the pilot of a full-scale 3-axis sailplane who has decided to allow some sideslip would still almost certainly be holding some inside rudder so that the sideslip angle did not get too extreme, even though this would decrease the amount of rolling-out torque that was created by the interaction between the slipping airflow and the dihedral wing, which would likely mean that the pilot would in fact have to hold a touch of outside aileron to cancel the over-banking tendency created by the faster-moving outside wingtip.
24) Adverse yaw in constant-banked turns: effect of pilot's roll inputs on aircraft's yaw orientation in flex-wing hang gliders and other weight-shift controlled aircraft, and the myth of the efficient, skidding, "flat" turn
In a flex-wing hang glider, in a steady-constant bank turn the pilot may have to exert either a rolling-in torque or a rolling-out turn, depending on many complex factors including pilot weight and VG setting. (We'll explore the balance of roll torques in a circling flex-wing hang glider in more detail elsewhere on this website.) In general, we'd expect the pilot's roll input to affect the glider's yaw orientation in much the same way as we described in section 22, at least to some degree. A rolling-out input lengthens the low wing (relative to the CG of the entire system) which should increase the drag of the low wing and reduce the glider's tendency to orient itself in a position that is yawed toward the outside or high side of the turn. A rolling-in input lengthens the high wing (relative to the CG of the entire system) which should increase the drag of the high wing and increase the glider's tendency to orient itself in a position that is yawed toward the outside or high side of the turn. However these effects may or may not be very important in light of all the other yaw torques acting on the glider, as discussed above.
Some hang glider pilots believe that when they need to make a strong rolling-out ("high-siding") control input, the nose of the glider is actually pointing toward the inside or low side of the turn (this would be a skid), which they believe allows the glider to turn "flatter" and more efficiently. I'm skeptical of all of the links in this chain of logic.
Because the fact that the outboard wing tip is in a faster airflow than the slower wingtip tends to create a yaw torque toward the outside or high side of the turn as described above, I'd be rather surprised if any tailless aircraft oriented itself with its nose pointing to the low side or inside of constant-banked turn. Considering all the other yaw torques that are present, and considering the complex nature of the main cause of adverse yaw as discussed above, it seems a leap of faith to assume that a pilot's high-siding roll torque will create enough adverse yaw to cause the glider to skid. We're dealing with a closed-loop system here and the variables are all inter-related in some rather interesting ways. Most flex-wing hang gliders have enough anhedral that they exhibit a negative coupling between slip (yaw) and roll throughout most of the flight envelope, especially with the VG loose. (This is explored in more detail elsewhere on the Aeroexperiments website.) This means that in the absence of other factors (such as the fact that the outside wingtip is moving faster than the inside wingtip), when a glider slips the pilot will have to high-side the bar to counteract the rolling-in torque created by the anhedral, and when a glider skids the pilot will actually have to low-side the bar to counteract the rolling-out torque created by the anhedral. Again these roll torques may or may not be very important in light of all the other roll torques are present--if the slip or skid angle is small, the roll torque created by anhedral will be small, and at angles-of-attack near min. sink the anhedral effect may be quite mild, especially with the VG tight where in some gliders the coupling between slip (yaw) and roll actually becomes positive rather than negative at high angles-of-attack.
Regardless of the complete balance of yaw and roll torques acting on a circling flex-wing hang glider, a key point is this: even if the glider were in fact oriented with the nose pointing toward the low side or inside of the turn, in a skidding attitude, this skidding airflow would not help to minimize the glider's sink rate for a given turn radius. Skidding turns are inefficient in all aircraft (as we discussed earlier in this article), and most of all in flying-wing aircraft such hang gliders and trikes, where the drag penalties arising from a sideways airflow may be relatively low, but the helpful centripetal aerodynamic sideforces generated by a sideways airflow will be almost non-existent. This means that for a given bank angle, skidding the aircraft will create virtually no increase in the turn rate, i.e. in the rate of curvature of the flight path. In other words, for a given turn rate or circling radius, skidding the aircraft will allow virtually no reduction in the bank angle, and there will be a net increase in drag and sink rate.
I suspect that if there are any detectable efficiency advantages associated with high-siding a turn in a hang glider, these might be related to the glider orienting itself in a position that is well relatively well aligned with the overall direction of the flight path and relative wind, with less yaw (slip) toward the outside or high side of the turn than would otherwise exist. (Even this idea is somewhat problematic--as we noted above, in many cases the less a glider slips, the less we would expect it to require high-siding, because most flex-wing hang gliders have enough anhedral that they exhibit a negative coupling between slip (yaw) and roll throughout most of the flight envelope, especially with the VG loose.) Another way that high-siding a turn might increase the glider's efficiency is that it might distribute the pilot's weight slightly more optimally over the wing, allowing the faster-moving outer or high wing to "work harder" than the slower-moving inside or low wing. Since we'll be asserting later that the sail doesn't really "feel" the pilot's weight, we should point out that another way of expressing the same idea is to say that the same 3-dimensional sail shape that offers the most efficient lift distribution across the entire span might also happen to require a high-siding control input to hold the bank angle constant. I should emphasize that this last paragraph has taken us well into the realm of conjecture--it's not obvious to me that there are any theoretical or practical performance benefits from configuring a hang glider to require high-siding during a constant-banked turn.
25) Adverse yaw in constant-banked turns: effect of the rolling motion inherent in a constant-banked turn
Although it seems counterintuitive, a constant-banked turn involves a rolling motion unless the flight path is completely horizontal with respect to the surrounding airmass. In a descending turn, the rolling motion is toward the inside of the turn. Aerodynamic damping in roll tends to stop this rolling motion, causing the bank angle to decrease. We've already seen how rolling motions create adverse yaw torques. In a descending turn, the rolling motion toward the inside of the turn creates an adverse yaw torque toward the outside of the turn, encouraging the aircraft to slip. These effects may or may not be significant in light of all the other roll and yaw torques that are present. In a constant-banked turn that is ascending with respect to the surrounding airmass, the effect is reversed: the inherent rolling is toward the outside of the turn, aerodynamic damping in roll tends to oppose the rolling motion and cause the bank angle to increase, and the rolling motion toward the outside of the turn creates an adverse yaw torque toward the inside of the turn, encouraging the aircraft to skid. For more on the rolling motion inherent in a constant-banked descending or ascending turn, see the related article on this website entitled "Constant-bank turns involve a rolling motion".
Again, a full discussion of the balance of roll torques on a circling flex-wing hang glider is beyond the scope of this article, but it appears to me that the effect described immediately above--particularly the way that aerodynamic damping in roll tends to decrease the bank angle in the case of a turn that is descending with respect to the surrounding airmass--is the primary reason that some gliders require low-siding in a constant-banked turn, particularly when those same gliders exhibit a slight slip during a constant-banked turn, and have enough anhedral to create at least a mild amount of negative coupling between yaw (slip) and roll throughout the flight envelope, so that a slipping airflow would interact with the anhedral to create a rolling-in torque. (This describes the observed characteristics of my Spectrum hang glider and many other beginning or intermediate level hang gliders--this will be discussed in more detail elsewhere on the Aeroexperiments website.)
26) Returning to the dynamics of rolling motions
Now let's move away from our discussion of the way that an aircraft orients itself in the yaw axis in relation to the flight path and relative wind in a steady, constant-speed turn, and bring our focus back to dynamics that place as an aircraft is actually rolling to a different bank angle.
27) The "layman's" explanation of adverse yaw, and a look at aerodynamic damping in the roll axis
We'll ease our way into a discussion of "aerodynamic damping in the roll axis" by giving some attention to the "layman's explanation" of adverse yaw, which holds that as an aircraft rolls into a turn, the rising wing creates more drag "because it is creating more lift". This explanation cannot be accurate. In the case of a "conventional" aircraft, once the roll rate becomes constant (no more acceleration in the roll axis), Newton's laws tell us that the net roll torque must be zero, which means that both wings must be creating an equal amount of lift. In this article we've examined many other sources of adverse yaw that do not involve the idea that the rising wing is "creating more lift".
The reason that the roll rate is constant, and the lift created by each wing is equal, even though the ailerons are deflected, is that the increase in lift coefficient created by the lowered aileron on the rising wing is cancelled out by the decrease in lift coefficient created by the decrease in angle-of-attack experienced by the rising wing. This decrease in angle-of-attack is caused by the change in the direction of the relative wind that is caused by the rising wing's upward motion through the airmass, as we described at the beginning of our discussion of the causes of adverse yaw. Likewise, the decrease in lift coefficient created by the raised aileron on the descending wing is cancelled out by the increase in lift coefficient created by the increase in angle-of-attack experienced by the descending wing. In other words, the angles-of-attacks of the rising and falling wings are altered by virtue of their own relative motions through the airmass, which eventually equalizes the magnitude of their lift vectors and brings the net roll torque to zero, preventing any further increase in the roll rate. This phenomenon is called "aerodynamic damping" in the roll axis: a crude visualization would skip over the nuances of angle-of-attack and simply think of the rising wing as meeting "resistance" as it rises upward through the airmass in a paddle-like fashion, and similarly for the descending wing.
28) Details of aerodynamic damping in the roll axis in weight-shift aircraft
In the case of a weight-shift controlled flex-wing hang glider or trike, the same phenomena are taking place but we have to modify our description slightly. For convenience--it will simplify our description--let's define the "center" of our system in relation to the CG of the whole system (including the pilot's body), rather than in relation to the keel of the hang glider or trike. When the pilot shifts his body to one side--say to the left--the left wing becomes shorter and the right wing becomes longer. (Remember, we are defining the center of the system, which divides the "left" wing from the "right" wing, based on the CG of the whole system, not based on the keel of the aircraft). Since the right wing is longer than the left wing, the aircraft begins to roll toward the left. As the aircraft begins to roll, the descending left wing experiences an increase in angle-of-attack and an increase in lift coefficient and lift-per-unit area, due to the change in the direction of the relative wind caused by the fact that the left wing is descending through the airmass. (This is the "aerodynamic damping" effect that we explored above.) Similarly, the ascending right wing experiences a decrease in angle-of-attack and a decrease in lift coefficient and lift-per-unit-area, due to the change in the direction of the relative wind caused by the fact that the right wing is rising through the airmass. (This is another component of the "aerodynamic damping" effect that we explored above.) When the difference in lift-per-unit area has risen enough to exactly counteract the fact that right wing is bigger than the left wing, then both wings will be creating the same amount of lift and the net roll torque will become zero and the roll rate will stop increasing and become constant. (Astute readers will note that to keep the length of this article manageable, we're making one slight oversimplification--we're ignoring the fact that because the left and right wings have slightly different spans and therefore act at slightly different moment-arms from the CG, in order for the roll torques to be in balance, the longer, rising right wing must in fact be creating slightly less total lift than the shorter, descending left wing. If we were to take this into account, it would further reinforce our conclusion that when the pilot's body is shifted to the left and the roll rate is constant, the left wing is creating more lift-per-unit-area than the right wing.)
29) Notes on the causes and consequences of sail billow shift
Here's another key point in relation to flex-wing hang gliders and trikes: the "aerodynamic damping" effect that we've been discussing will be greatly reduced by the fact that the wing will undergo a "billow shift"--a physical change in the shape of the wing--that will partially offset the increase in lift coefficient and lift-per-unit-area experienced by the descending wing, and will also partially offset the decrease in lift coefficient and lift-per-unit-area experienced by the ascending wing. This will allow a much higher roll rate to be achieved by the limited roll torque available from the pilot's meager weight-shift input than if the wing were of a fixed, rigid shape. But it remains true that when the roll rate becomes constant, both wings must be generating the same amount of lift, which means that the smaller, descending left wing must be generating more lift-per-unit area than the larger, rising right wing. So clearly, although the billow-shift effect partially relieves the aerodynamic damping effect that we've been discussing, it cannot actually reverse the situation to the point where the rising right wing is actually experiencing more lift-per-unit-area than the descending lift wing.
Let's consider the cause-and-effect relationships surrounding the billow-shift effect in more detail. A wing "feels" the wind. It does not "feel" gravity. The billow-shift phenomenon is not actually driven by the fact that the pilot's weight is shifted to one side. (To take an extreme case, in a vacuum, the pilot's weight-shift inputs would have no influence on the shape of the sail!) The billow-shift phenomenon is actually driven by the damping effect that we've been discussing--i.e. by the fact that the relative wind has more of an upward velocity and creates more lift-per-unit-area on the descending wing, and has more of a downward velocity (or less of an upward velocity) and creates less lift-per-unit-area on the rising wing. This disparity in lift, acting on the surface of the sail, is the actual physical force that makes the shape of the wing change. The billow shift is the glider's way of "venting" or "relieving" a large part--but not all--of the asymmetrical lift-per-unit-area load that the asymmetrical relative wind--not the asymmetrical distribution of the pilot's body weight--is imposing on the glider. Because of this fundamental relationship--i.e. because of the fact that the "twist" in the direction of the relative wind across the length of the wingspan, and the resulting asymmetry in lift-per-unit-area between the left and right wings, is the fundamental driving force behind the billow-shift effect--it can never be the case that the billow-shift effect is so pronounced that it causes the descending wing to actually experience less lift-per-unit-area than does the rising wing. In other words, the "passive" billow-shift effect is not really completely analogous to the action of ailerons or to "active", hard-wired, wing-warping controls such as were used by the Wright brothers. Instead, the "passive" shifting of the billowed surface of the wing is actually tangible evidence that the descending, smaller wing is experiencing more lift-per-unit-area than is the ascending, larger wing.
In other words, when the pilot shifts his body to the left, and the left wing starts to drop, the change in the direction of the relative wind increases the left wing's lift-per-unit-area and lift coefficient. (These two terms are equivalent, for our purposes here.) Despite the fact that the sail billows in a way that decreases the efficiency of the left wing, the lift coefficient of the left wing remains higher than the lift coefficient of the right wing as long as the glider is rolling. (The sail billow will also remain shifted to the left as long as the glider is rolling.) These points would need to be kept in mind if we were to take this analysis of the adverse yaw to the next level and try to assess the changes in the drag coefficients in the left and right halves of the sail as the glider rolls and as the sail billows.
In an aircraft controlled by an "active", hard-wired wing-warping system or by ailerons or spoilerons, we have the power to do something that we can't do in a standard weight-shift flex-wing hang glider: as we've already noted, we can actually cause the descending wing to initially experience less lift-per-unit-area than the ascending wing. Then as the roll rate increases and the "aerodynamic damping" effect became stronger and the roll rate stabilizes at a maximum value, the lift-per-unit-area generated by each wing again become equal, at least if the pilot's body is located on the aircraft centerline. If the spoilerons or ailerons are connected to a weight-shift system as per modern rigid-wing hang gliders, then when the roll rate stabilizes at a maximum value, the slightly shorter descending wing is once again generating more slightly more lift-per-unit-area than is the slightly longer ascending wing.
We'll close this article with just a few more thoughts on sail billow. (Admittedly we've now strayed rather far from the subject of adverse yaw!) We've made the point that when a flex-wing hang glider pilot makes a roll input (let's say to the left) to initiate a rolling motion during wings-level flight, the sail won't change its shape until after the glider starts rolling, which creates a difference in the relative wind as experienced by the left and right wings, which forces the change in the sail shape. Once the roll rate stops increasing and becomes constant, we can think of the glider as having reached sort of a "steady state" where the pilot's uneven weight distribution, in combination with the lack of further increase in roll rate, is serving as evidence that the airflow is forcing the left wing to "work harder" than the right wing. This same airflow is also responsible the shifted sail billow. It might therefore be reasonable to expect to see very roughly the same amount of billow shift in a case where the pilot's weight is shifted the same amount to the left in a constant-banked turn. (Depending on the high-siding or low-siding characteristics of the glider, this turn might be toward the right or toward the left.) In either case, the pilot's uneven weight distribution, in combination with the lack of change in roll rate (which in this case is fixed at zero, at least if we overlook the slight rolling-in rotation about the glider's roll axis that accompanies a constant-banked descending turn), is once again serving as evidence that the airflow is forcing the left wing to "work harder" than the right wing. As noted previously, we'll explore the balance of roll torques for a circling flex-wing hang glider in more detail elsewhere on the Aeroexperiments website in the future.
For more on adverse yaw and slips and skids, see these related articles on the Aeroexperiments website:
Questions of interest part 1: Relationship between pitch inputs and sideslips in hang gliders and other aircraft
Questions of interest part 2: Aerodynamic sideforce created by the sideways airflow as a hang glider sideslips
Questions of interest part 3: Roll torque created by the sideways airflow component as a hang glider sideslips
"What makes an aircraft turn?"
Notes for new hang glider and trike pilots--on sideslips