When the airspeed is changing... some thoughts on the real meaning of pitch "coordination"
Last updated June 30, 2014
If we have any real interest in understanding flight dynamics, we need to start by thinking about what drives a change in airspeed. For example, let's think about what happens when we are flying at trim, and then we pull in the bar. We decrease the wing's angle-of-attack and lift coefficient. Lift has now become less than weight. More accurately, lift has now become less than the component of weight that acts perpendicular to the flight path. The glider is producing "inadequate lift", so it "falls". The flight path curves downward. As the flight path curves downward, the component of weight that acts parallel to the flight path becomes larger, so that is larger than the drag vector. This makes the airspeed start to rise.
Of course, by pulling in the bar, we also decreased the drag coefficient. But the dynamics wouldn't be all that different if the drag coefficient simply stayed constant.
Unless the pilot makes some corrective pitch input-- some change in bar position-- to stabilize things, the flight path will always curve downward at least a little bit "too far". The flight path will reach a point where it is aimed more steeply downward than the "correct" or steady-state glide angle or flight path for the bar position. The reason for this is that at the instant that the flight path matched the "correct" or steady-state glide angle for the bar position, the airspeed had not had enough time to increase to the "correct" or steady-state value. Lift was still less than component of the weight vector that acts perpendicular to the flight path, and the flight path was still curving downward.
At the point where the flight path is aimed most steeply downward, the airspeed has increased enough that lift is exactly equal to the component of weight that acts perpendicular to the flight path. Then the airspeed increases a bit more and the flight path starts curving upward, toward horizontal. But even as the flight path starts curving upward, the airspeed is still rising. Because the flight path has "overshot" to a steep downward trajectory, the component of weight that acts perpendicular to the flight path is larger than it would be at the "correct" or steady-state glide angle for the bar position, and this makes the airspeed keep rising till it is substantially higher than the "correct" or steady-state airspeed for the bar position. Finally, at some point the continued upward curve of the flight path brings the glider to the point where drag is exactly equal to the component of weight that acts parallel to the flight path, and the airspeed stops rising.
But now the airspeed is much larger than the "normal" or steady-state airspeed for the bar position, so the flight path keeps curving upward. It curves upward past the "normal" or steady-state glide angle or flight path for the bar position, and may even curve up above horizontal. Meanwhile the airspeed is bleeding away.
This whole process is called a pitch "phugoid". To a first approximation, if the bar position is constant (after the initial pull-in from trim), then the wing's angle-of-attack will be constant. That's not exactly true-- the angle-of-attack is actually larger whenever the flight path is curving downward, and smaller whenever the flight path is curving upward-- but it's a good enough approximation for this discussion.
Eventually this dynamic "dance" between lift, weight, flight path, and airspeed will come to an end as the glider settles down to the "correct" or steady-state glide angle for the bar position. Now lift is exactly equal to the component of weight that acts perpendicular to the glide path, and drag is exactly equal to the component of weight that acts parallel to the glide path. Or put another way, the vertical component of lift plus the vertical component of drag is exactly equal to weight. The glider is finally "in balance".
For flat glide paths-- like we normally have in a glider-- it's a close approximation to say that the flight path will curve downward whenever the vertical component of lift plus the vertical component of drag is less than weight. For steep glide paths-- like we'll see if we quickly move the bar very far aft and hold it there for many seconds-- it's more accurate to say that the flight path will curve downward whenever lift is less than the component of weight that acts perpendicular to the flight path, and the flight path will curve upward whenever lift is larger than the component of weight that acts perpendicular to the flight path.
Much of what we do as pilots is all about preventing the pitch phugoid. Can we make a glider very rapidly accelerate, and then stabilize exactly at some target speed with no "overshoot"? Sure. But it will involve more than simply yanking the bar violently in to a well pulled-in position and then simply holding it there. We can start moving the bar briskly aft and then ease it slowly aft the last inch or two so that acceleration slowly tails off to zero. Or if we pull the nose down steep enough, we may need to then make a deliberate forward motion of the bar to smoothly "round out" of the steep accelerating dive and enter stabilized, constant-speed flight, with its associated flatter glide angle.
Whenever the glider is "out of balance", with lift less than the component of weight that acts perpendicular to the flight path, the flight path will curve downward, the nose will drop, the airspeed will rise, and the airspeed will tend to "overshoot" the "correct" or steady-state value for the bar position.
In general, a pilot strives to keep all changes in airspeed smooth and gradual, especially as the airspeed approaches the desired target value. If the airspeed is only changing slowly, the aircraft is nearly "in balance", with the glide path close to the "correct" or steady-state glide angle for the bar position, and lift nearly equal to the component of weight that acts perpendicular to the glide path, and drag nearly equal to the component of weight that acts parallel to the flight path.
We'll say that again for emphasis-- if the airspeed is only changing slowly, the aircraft is nearly "in balance". If the airspeed is changing rapidly, the aircraft is "out of balance".
The situation is more complicated if we can make large changes in the drag coefficient-- or in thrust, if we have a motor-- without changing the lift coefficient. But for glider flying-- and for most cases in light airplane flying as well-- if the airspeed is only changing slowly, the aircraft is nearly "in balance", with lift nearly equal to the component of weight that acts perpendicular to the flight path.
We've framed this discussion in the context of unbanked flight. If we roll the glider briskly from wing-level into a steep turn, it's very much like pulling the bar abruptly aft and holding it there. The "upward" component of lift becomes much less than the "downward" component of weight, and the flight path curves downward. The sink rate "spikes" and the airspeed rises and tends to "overshoot" the "correct" or steady-state value for the bank angle and bar position.
A note on terminology-- by "upward" component of lift, we mean the component that acts perpendicular to the flight path when we view the glider from the side. For any given constant glide path through the sky, this "upward" component of lift must remain the same, regardless of the bank angle. In a shallow glide, this component is aimed slightly forward of true vertical. We can't think of a better word for this component than "upward", so that's what we'll call it. In a steep dive, this "upward" component of lift is aimed well forward of the true vertical direction. Similarly, we're getting tired of writing out "the component of weight that acts perpendicular to the flight path", so we'll call this the "downward" component of weight. For steep dives, this "downward" component of weight is aimed well aft of true vertical. We'll always enclose these words in quotes, in recognition that this is a somewhat quirky and unorthodox usage.
How can we prevent this "overshoot" in airspeed? By rolling the glider very slowly into the turn, rather than briskly. Or by moving the bar forward enough to arrest the rapidly rising airspeed as we approach our target airspeed. Or by slowly easing the aft to smoothly gain all the airspeed that we'll need in the turn before we even begin to roll into the turn. In the last case, no matter how briskly we roll into the turn, we can move the bar forward at whatever rate is needed to hold the airspeed constant. When we hold the airspeed constant, we are keeping the glider "in balance".
Let's look at little closer at the last case above, where we are holding the airspeed exactly constant. As the glider rolls into the turn, drag is remaining exactly equal to the component of weight that acts perpendicular to the flight path. Since we are increasing the drag coefficient by moving the control bar forward, the glide path cannot remain exactly constant-- it must become steeper, so that the component of weight that acts parallel to the glide path can become larger-- but this change is happening in a smooth controlled manner, with no tendency for an excessive dive followed by a marked "overshoot" in the airspeed. And since the flight path does curve down a bit, it must be the case that at some point in the transition, the "upward" component of lift was slightly less than the "downward" component of weight. So it's really not quite true that by keeping the airspeed constant, we are keeping the all the forces on the glider in balance. But it's almost true!
A different twist on this would be to move the bar forward more, to increase the angle-of-attack more, as we roll into the turn. This larger change in bar position and angle-of-attack would provide enough lift to keep the glide path (as seen from the side) exactly constant-- the "upward" component of lift would always equal the "downward" component of gravity, and the flight path would not curve downwards at all. Since we stated that the airspeed remained exactly constant in the original case, we know that the airspeed must decrease in the new case. Basically what we're saying in the new case is that we were flying wings-level with the bar well pulled-in, giving a rather poor glide path, and as we entered the turn we let the bar out far enough to hold the glide path exactly constant as viewed from the side. By letting the bar out, we increased our L/D ratio enough to hold the ratio of "upward" lift to drag-- which determines the glide path through the air-- exactly constant, even though a substantial part of the lift vector is now directed sideways. I can't think of any reason anyone would want to carry out this particular maneuver in a glider, except to give a demonstration of exactly what it really means to keep the "upward" component of lift exactly equal to the "downward" component of weight. On the other hand, this is exactly how powered aircraft normally turn when cruising around at a constant altitude. The concern is not with any kind of efficiency, but rather with keeping that little hand on the altimeter exactly stationary. The initial airspeed is well above the max L/D or min sink rate speed-- like having the bar well pulled-in a hang glider-- and there's lots room to increase the angle-of-attack and bleed off airsped to prevent the flight path from curving downward. With all that extra airspeed available, wouldn't the turn perhaps be completed quicker if the pilot bled off even more airspeed, trading kinetic energy for altitude in a mild wingover? Surely a 180-degree course reversal, for example, would be completed much faster this way!
What we've been working toward here is a conception of what it means to "coordinate" a turn in a hang glider. By keeping the airspeed exactly constant-- or more loosely speaking, by preventing large and abrupt changes in airspeed-- we also prevent the flight path from curving sharply downward, and the sink rate from "spiking", and the airspeed from tending to "overshoot" the "correct" or steady-state value for the bank angle and bar position. To accomplish this kind of "coordination"-- to hold the airspeed roughly constant-- we're going to have to move the bar forward to increase the angle-of-attack whenever we are increasing the bank angle. The faster we're increasing the bank angle, the faster we'll have to increase the angle-of-attack if we want to hold the airspeed constant or nearly so. Obviously, if we're going to move the bar forward in this fashion while we are briskly rolling the glider through a large change in bank angle, we'll have to pull the bar well in first, unless we have very long arms!
Actually, for any given change in bank angle, the total amount of forward motion of the bar to give a "perfect" pitch coordination-- yielding exactly zero change in airspeed-- will always be the same, regardless of roll rate. It's just that the faster the roll rate, the more important it is to make something approximating a "perfect" pitch coordination input. For a very low roll rate, we won't throw the glider significantly "out of balance" even if we don't move the bar forward at all as we roll. Sure, the airspeed will rise, but slowly and smoothly with little tendency to "overshoot" the final steady-state value, and with no sharp downward "plunge" in the flight path or "spike" in the sink rate. With a brisk roll rate, we still don't need to get it absolutely "perfect", but we had better make a substantial increase in angle-of-attack to limit the glider's acceleration as we roll, or the nose will plunge sharply downwards due to the extreme "shortage" of lift that results from the rapid increase in bank angle. When the bank angle increases slowly, any required increase in airspeed has plenty of time to happen, and doesn't throw the glider out of balance. When the bank angle increases rapidly, the airspeed lags far behind, and if we aren't "making up the difference" by increasing the angle-of-attack, the resulting "shortage" of lift makes the sink rate spike and the flight path curve sharply downward.
The time scale of the pitch "phugoid" isn't the same as the time scale of the change in bank angle. When we roll abruptly to a much steeper bank angle, it will take many seconds for the airspeed to hit its peak value. So we don't necessarily have to make our whole pitch "coordination" movement-- the entire forward motion of the bar-- as we're actually changing the bank angle. If we roll briskly to a steeper bank angle without moving the bar forward, and the airspeed starts to rise, we can then move the bar forward to stabilize the airspeed. We aren't "doomed" to experience the whole pitch "phugoid" dynamic just because we didn't move the bar forward as we rolled. Unless of course the bar was already very far forward, so the glider was "mushing", before we begin to roll toward a steeper bank angle. Now we really have no room to move the bar any further forward, so we're going to see a rapid rise in airspeed.
These dynamics are a bit complicated by the fact that a glider trims to a lower angle-of-attack in a steep turn than in wings-level flight. If we briskly roll in to a turn without moving the bar forward, as far as the glider is concerned, it's really like we're actually pulling the bar aft as we roll! In either case, we're forcing a decrease in angle-of-attack.
Nonetheless, if we start with the bar extremely pulled in, we can "coordinate" a rather brisk roll toward wings-level without ever letting the bar come all the way out to trim. We're not trying to say that to "coordinate" a turn entry, the bar must come to trim or forward of trim. We're just saying that if we're making a large change in bank angle using a high roll rate, the bar needs to move substantially forward of its starting place, or the nose will drop sharply and the airspeed will rise rapidly.
All these dynamics play out "in reverse" when we roll towards wings-level.
Backing up to the case of simple wings-level flight, if we are flying along with the bar well pulled-in and then jam the bar forward to the normal trim position and hold it there, does the glider smoothly transition to flight at the "correct" or steady-state airspeed and glide path for the new bar position? Hardly! The airspeed doesn't bleed off instantly, so we create an extreme "excess" of lift. We might perform an abrupt loop! At the very least, we'll enter a steep "zoom climb" as we exchange kinetic energy (airspeed) for altitude. We might end up in a very nose-high attitude with a very low airspeed, at risk of a whipstall, tumble, or tailslide. With a slightly milder input, the flight path will curve upward into a climbing attitude and then the airspeed will fall to a very low value as the flight path curves back down through horizontal. Again this is the start of a pitch "phugoid"-- the nose will keep falling, the airspeed will keep rising, and we'll go through several oscillations involving continual "undershoots" and "overshoots" in airspeed and glide path before everything settles down.
Likewise, if are flying along in a steep bank and then we briskly roll toward wings-level without pulling the bar aftwards, what happens? As the glider retains the high airspeed from the turn, and the lift force remains high, the "upward" component of lift quickly becomes dramatically larger than the "downward" component of weight, and the flight path curves sharply upward. The nose rises skyward like crazy as the glider exchanges kinetic energy (airspeed) for altitude. Again we'll risk a loop, whipstall, tumble, or tailslide.
We can prevent all this "excitement" by bringing the bar aft as we roll toward wings-level, to keep the nose down. Or more descriptively, to keep the "upward" component of lift roughly equal to the "downward" component of weight, even as the glider is temporarily retaining excess airspeed from the turn. Taken to extreme, the "perfect" pitch coordination input would cause the glider to retain all the excess airspeed from the turn. More typically we'll wish to slowly decelerate. But by allowing the deceleration to happen gradually, over many seconds, we aren't forcing the glider to go through wild gyrations in the vertical plane as it converts kinetic energy to altitude.
Similarly, if we want to enter a turn, if we smoothly gain some airspeed before we start to roll, then we have room to move the bar forward as we roll, so that there is no more than a modest acceleration in airspeed as the bank angle is changing. Again, by spreading the total acceleration out over many seconds of time, we aren't forcing the glider to go through abrupt maneuvers in the vertical plane (spike in sink rate, downward "plunge: in flight path, "overshoot" in airspeed) as it converts altitude to kinetic energy.
In actual practice in hang gliding, the tendency of the flight path to curve upwards above the horizontal when we roll quickly out of a steep turn is much more obvious than the tendency of the nose to drop "too far" and the sink rate to "spike" and the airspeed to "overshoot" when we roll quickly in to a steep turn. And the former is also much more dangerous. If you are in a steep turn with the airspeed high and the bar well pulled-in, never initiate a brisk roll toward wings-level! You won't have enough room to pull the bar further aft to limit the dangerous rise of the nose. And if you are in an extreme nose-high attitude, always use roll (toward the lower wing) as well as pitch to help bring the nose down.
Turn "coordination" in hang gliders is all about matching pitch inputs with roll inputs so that any changes in airspeed happen gradually rather than abruptly. When we are increasing the bank angle, we'll generally want to be moving the bar forward to control the glider's tendency to dive and gain airspeed, and when we are decreasing the bank angle, we'll generally want to be moving the bar aft to control the glider's tendency to climb and bleed off airspeed. The larger and faster the changes in bank angle, the more important these inputs are. A very abrupt change in bank angle of only ten degrees, or a very slow rate of roll into a 45 degree bank, doesn't throw the glider significantly "out of balance". The airspeed has plenty of time to increase, and the "upward" component of lift remains nearly equal to the "downward" component of weight. We won't see much tendency for the nose to drop excessively, or for the sink rate to "spike", or for the airspeed to "overshoot" the final or steady-state value for the bank angle and bar position. Not so, when we rapidly roll from wings-level into a very steep turn!
At the end of the day it's really very simple-- as far as the "balance" between lift and weight goes, increasing the bank angle is much like moving the bar aft, and decreasing the bank angle is much like moving the bar forward. Very gradual adjustments, or very small adjustments, of bank angle or fore/aft bar position don't throw the glider "out of balance", and no aerobatic maneuvers result. Large, rapid changes of bank angle or large, rapid forward or aft movements of the bar do lead to aerobatic gyrations, unless we are "coordinating" the roll inputs with opposing pitch inputs to smooth things out. When we increase the bank angle, the nose wants to fall excessively, so we hold it up, if we can do so without mushing or stalling. When we decrease the bank angle, the nose wants to fall excessively, so we pull it down, if we aren't already fully pulled-in. And all these dynamics stem from the fact that the airspeed doesn't change instantly-- the glider has inertia and kinetic energy, and rapid, large airspeed changes are always associated with "interesting" upward or downward changes in the flight path. By helping the airspeed to change gradually rather than abruptly, we smooth out the flight path, and this is what pitch "coordination" is all about.
Turn "coordination" has another benefit in addition to controlling the airspeed and preventing the flight path from curving downward. Remember, by increasing the wing's angle-of-attack, we are promptly increasing the lift vector or G-loading so that the "upward" component of lift stays nearly equal to the "downward" component of weight, without waiting around for the airspeed to increase. This means that we're also promptly increasing the horizontal, sideways component of lift-- the "centripetal" component that drives the turn-- without waiting around for the airspeed to increase. So the turn rate rises promptly as we roll, and stays at the "correct" value for the airspeed and bank angle. By promptly "loading up" the wing with the correct G-loading for the bank angle, we get the turn going sooner. If we didn't move the bar forward to increase angle-of-attack, and we simply let the glider increase the lift vector or G-loading in its own way-- by increasing the airspeed-- the turn rate will initially be lower. It will take some time for the airspeed to increase, and the lift vector or G-loading will initially be "too small" for the bank angle. When we pull in for speed and then let the bar out to promptly "load up" the wing and hold the airspeed roughly constant as we roll in to the turn, we "carve" a much quicker, nicer turn than if we let the nose drop and the airspeed rise as we roll in to the turn.
Turn "coordination" inputs would remain important even if the position of the base bar directly controlled the angle-of-attack of the wings, regardless of the bank angle. But as noted above, these dynamics are further complicated by the fact that a glider trims to a lower angle-of-attack in a steep turn than in wings-level flight. If we briskly roll in to a turn without moving the bar forward, as far as the glider is concerned, it's really like we're actually pulling the bar aft as we roll! In either case, we're forcing a decrease in angle-of-attack. And if we briskly roll from a steep turn to wings-level without moving the bar aft, it's really like we're actually moving the bar forward as we roll-- we're forcing an increase in angle-of-attack. It's as if we're making "anti-coordination" inputs.
It's important to keep in mind that there's really no absolute criteria for judging a turn entry or exit to be "coordinated". Basically we mean that the nose isn't sharply falling or rising and the airspeed isn't rapidly increasing or rapidly bleeding away. Few pilots would agree that a maneuver should only be called "coordinated" if the airspeed remains exactly constant throughout, though that would be one logical definition.
It's also important to keep in mind that the opposite of "coordinated" is not "slipping", in the hang gliding context. Our pitch "coordination" inputs have nothing to do with preventing sideslips. A diving, accelerating turn is not necessarily a slipping turn. Sideslip is yaw phenomenon, not a pitch phenomenon. Sideslip is not easy to detect in hang gliders. Most hang glider pilots--even very advanced hang glider pilots-- have no idea whether a glider is or is not sideslipping at any given instant. There's really no practical need or place for a discussion of "sideslip" in a practical hang gliding training curriculum.
What then is the opposite of "coordinated"? Rather than describing a particular maneuver as "uncoordinated", why not go ahead and say that the glider is gaining excessive speed and diving, or bleeding off speed in a "zoom" climb, if that's what we mean?
Often the whole subject in pitch "coordination" in the context that we've discussed it here-- relating to rapid changes in airspeed and "imbalances" in the forces acting on the glider-- is confused and muddled with the issue of flight at a high airspeed and a high sink rate. Some pilots tend to say that a turn is "uncoordinated" whenever the bar is well aft (or perhaps even whenever the bar is not kept forward of trim position) and the sink rate is high, even if the turn was entered smoothly (perhaps by first pulling the bar even further in and then moving the bar forward as the glider rolled) with no excessive drop of the nose and "spike" in the sink rate compared to final "steady state" condition. This makes a little bit of sense-- we've noted already that a glider tends to trim to a lower angle-of-attack in a turn than wings-level, and for some pilots the concept of turn "coordination" seems to extend to encompass the idea of compensating for this trim change by exerting forward pressure on the bar to produce a good efficient thermal turn. (Turning at this high an angle-of-attack, close to the min. sink angle-of-attack, would not be appropriate in strong turbulence!) Or we could say that if-- for example-- we roll very briskly to a steep bank angle while exerting no forward or aft pressure on the bar, the resulting maneuver will be "uncoordinated" in two distinctly different senses. One, we're not moving the bar forward as we roll, so the "upward" component of lift will temporarily become much less than the "downward" component of weight, so the flight path will curve sharply downward and the sink rate will "spike" and the airspeed will "overshoot" the "correct" or steady-state value for the bank angle and bar position. And two, even after the airspeed falls back off to the "correct" or steady-state value for the bank angle and bar position, the airspeed and sink rate will both be higher than if the pilot had moved the bar forward as needed to hold the same angle-of-attack that he had when wings-level. The first meaning of "coordination"-- keeping the glider nearly "in balance", with the airspeed nearly constant, while rolling-- requires an continual increase in angle-of-attack as the bank angle changes, in proportion to the roll rate. The second sense of "coordination"-- flying at the same angle-of-attack in the turn as we had while wings-level-- requires that the bar be kept further forward in the turn that it was in wings-level flight.
A third definition of "coordination", a little different from the second, views a "coordinated" turn as any turn where the sink rate is as low as is possible-- the glider is flying at the angle-of-attack for minimum sink rate. And yet we have at least one well-known instructor advocating that only advanced pilots should position the bar forward of trim in a turn! Presumably this instructor wouldn't advise his students to not "coordinate" their turns at all, so he must not be a proponent of this particular definition of turn "coordination".
At the end of the day, if we say a maneuver is "coordinated", perhaps we simply mean that we are making the appropriate pitch inputs to make the glider do what we want it to do! It's really not that helpful to describe a particular maneuver as "coordinated" or "uncoordinated", unless the context is crystal clear. Why not go ahead and describe the maneuver in detail-- say what the glider is doing-- whether it is accelerating or losing speed, or diving or "ballooning" upwards in a zoom climb, or flying at a constant airspeed a bit faster than the min. sink airspeed for that bank angle, etc. And we should refrain from using "coordinated" and "slipping" as opposites. For every possible meaning of "coordination" or "coordinated", it seems there's someone calling the opposite condition a "sideslip", so we end up with multiple different kinds of "sideslip"-- and not one of them has anything whatsoever to do with the glider actually slipping sideways through the air.
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