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Copyright © 1996-2001 jsd

16   Flight Maneuvers


A small correction early is better than a large correction late.
— Aviation proverb

16.1   Fundamentals

During flight, you have quite a number of tasks and responsibilities: The first three items on this list are what I call the ``fundamentals'' of maneuvering.2 Simple maneuvers (including plain old straight and level flight) and even some quite complex maneuvers can be broken down into combinations of these three fundamental tasks. Of course, while you are maneuvering you still remain responsible for all the other items on the list.

Some of the maneuvers in this chapter are important parts of everyday flying. For instance, final approach requires lining up on a ``front window'' ground reference. Flying the downwind leg of the airport traffic pattern requires paralleling a ``side window'' ground reference. Oftentimes you or your passengers want to get a good view of some landmark, which requires turning around a point. If there is some wind (as there almost always is) you will need to correct for it.

The other maneuvers in this chapter, even though they are not directly practical, serve important pedagogical purposes. Chandelles and lazy eights are good illustrations of several of the points made in this book, including (a) the importance of angle of attack, (b) the relationship between angle of attack and pitch attitude, and (c) the behavior of the plane when its airspeed doesn't equal its trim speed. Some of these maneuvers may seem daunting at first, because they require doing several things at once. Fortunately, though, the ingredients are not particularly hard and can be learned separately.

16.2   Accelerating and Decelerating

This is a very important maneuver which has not always been sufficiently stressed during pilot training. The idea is to change speed while maintaining constant altitude, constant heading, et cetera.

Start from, say, cruise speed. Decelerate to VY. When you reach the new speed, set the engine controls and trim so that the plane will maintain that speed. After you have flown in this configuration long enough to convince yourself that everything is stable, decelerate to a speed well below VY (but with a reasonable margin above the stall). Again, stabilize the plane at the new speed. Then accelerate back to VY and stabilize. Then accelerate to cruise and stabilize. Iterate this a few times until you are sure you've got the hang of it.

You will have an easier time understanding how to use the throttle (especially at speeds below VY) if you keep in mind the concepts of kinetic energy and power curve. These are discussed at length in section 7.2.

You will also want to keep in mind the relationship between trim and airspeed, as discussed in section 2.6.

An interesting variation of this maneuver is to practice accelerating and decelerating with the flaps extended. (Make sure you observe the speed limit for flaps-extended operations, which is typically quite a bit lower than for flaps-retracted operations.) This is interesting because on some planes, adding power with flaps extended causes a huge nose-up trim change; you will need to roll in some nose-down trim to compensate.

16.3   Phugoids

In flight it is fairly common for the airplane to find itself at an airspeed rather different from its trim speed. This situation will result in a phugoid oscillation, as discussed in section 6.1.12. It is definitely worth seeing this behavior for yourself.

Start with an airspeed, say, halfway between VY and cruise. Pull back on the yoke until the airplane slows down about ten knots, and then let go. As discussed in section 6.1.12, the airplane tries ``too hard'' to return to its original airspeed, altitude, and attitude; it will overshoot and oscillate for several cycles.

From time to time during this maneuver, look at the airspeed indicator and altimeter. This will provide a good illustration of the law of the roller coaster (9 feet per knots, per hundred knots). See section 1.2.1. This maneuver is also a good illustration of the principle of angle of attack stability, as discussed in chapter 6.

Practice ``catching'' the phugoid at various points in the cycle. That is, by pushing or pulling on the yoke, maintain constant altitude until the airspeed returns to normal. It is particularly interesting to catch it right when the airspeed equals the trim speed. By returning it to normal attitude at that moment, you can instantly end the oscillations.

If you use the wrong procedure (pushing on the yoke when the altitude is highest and pulling on the yoke when the altitude is lowest) you will just make the situation worse. This an example of a pilot-induced oscillation (PIO). It is more common than you might think, and can cause serious trouble if it happens near the ground, as discussed in connection with evil zooms in section 12.11.8 and section 16.17.6.

16.4   Crabbing Along a Road

One of the most basic maneuvers involves choosing a ground reference such as a long, straight road and flying along it. The point of the maneuver is to practice perceiving and correcting for crosswinds, so choose the road so that there is a significant crosswind component.

Actually, correcting for the crosswind is the easy part. If the plane starts getting blown off to the left of the road, you will instinctively turn the plane a little to the right to compensate. The tricky part is to notice that you have done so. The situation shown in figure 16.1 (crosswind from the left) seems quite normal. Similarly, the situation shown in figure 16.2 (crosswind from the right) also seems quite normal. It is important to be able to perceive the difference. The outside world looks the same in both cases; the difference is that the alignment of the airplane has changed relative to the outside world.

Figure 16.3 and figure 16.4 show bird's eye views of the same situations.

You should always make a point of noting your direction of flight (which is aligned with the road in this case) relative to bolts on the cowling, marks on the windshield,3 and other parts of the airplane.

You should be especially alert to these perceptions during final approach, since you need information about the wind in order to prepare for a proper crosswind landing.

It also pays to notice the crosswind during the base leg. If the crosswind is trying to blow you toward the airport then you will have a tailwind on final and (most likely)4 a tailwind during landing. You might want to break off the approach and take a good look at the windsock before trying again.

These perceptions can give you rather precise information about the wind. The magnitude of the crosswind is proportional to the wind-correction angle and to your airspeed:
wind-left
Figure 16.1: Crosswind from the Left

wind-right
Figure 16.2: Crosswind from the Right

wind-left-bird
Figure 16.3: Crosswind from the Left — Bird's Eye View

wind-right-bird
Figure 16.4: Crosswind from the Right — Bird's Eye View

16.5   Slipping Along a Road

Another useful maneuver is the following: Make sure you are at a safe airspeed. Line up on a road with a nice crosswind, as before. Now lower the upwind wing using the ailerons, and apply opposite rudder (i.e. push the rudder pedal on the downwind side). The idea is to establish a slip so that the airplane's axis and its direction of motion are both aligned with the road.

The slip will cause lots of drag. You will have to add power to maintain altitude. For goodness sake don't pull back on the yoke; you will be at a fairly low altitude (since this is a ground-reference maneuver) and you really don't want to stall in such a situation.

Make a note of how much bank angle and how much rudder pressure are needed for a given amount of crosswind. This varies considerably from one type of airplane to another. This knowledge comes in handy during crosswind landings; you don't want to wait until you are in the midst of a landing to figure it out.

16.6   Turns

The previous section discussed how to roll into and roll out of turns. Flying around in an established turn is relatively simple. You might need to deflect the rudder toward the inside of the turn (to compensate for the long-tail slip effect) and deflect the ailerons toward the outside of the turn (to compensate for the overbanking tendency).

If you are turning to intercept a landmark, you need to think a little about how steep a turn to make and when/where to start the turn. It so happens that for any particular bankbank attitude angle, the turning radius depends on the square of your speed. A turn that consumes a tenth of a mile at 60 knots will consume nearly a mile at 180 knots.

speed rate radius bank load
(knots) (°/sec) (nm) (degrees) factor
 60 10.5 0.09 30 1.15
 75  8.4 0.14 30 1.15
 90  7.0 0.20 30 1.15
105  6.0 0.28 30 1.15
120  5.3 0.36 30 1.15
135  4.7 0.46 30 1.15
150  4.2 0.57 30 1.15
165  3.8 0.69 30 1.15
180  3.5 0.82 30 1.15
Table 16.1: Constant-Bank Turn
A standard rate turn is defined to be three degrees per second. This is what ATC expects when you're on an instrument clearance. It is also called a two-minute turn, because at that rate it takes two minutes to make a complete 360° turn. You can see from the following table that the bank angle required grows in proportion to the airspeed. Because of the changing bank, the radius of turn grows in proportion to the airspeed (not the square thereof).

You should figure out the bank angle that corresponds to a standard-rate turn for the airspeed(s) you normally use.

speed rate radius bank load
(knots) (°/sec) (nm) (degrees) factor
 60 3 0.32  9.4 1.01
 75 3 0.40 11.6 1.02
 90 3 0.48 13.9 1.03
105 3 0.56 16.1 1.04
120 3 0.64 18.2 1.05
135 3 0.72 20.3 1.07
150 3 0.80 22.4 1.08
165 3 0.88 24.4 1.10
180 3 0.95 26.3 1.12
Table 16.2: Standard-Rate Turn

16.7   Coordination Exercises

Here is a good maneuver for learning about your plane's roll-axis inertia and adverse yaw, called ``coordinated wing rocking''. The procedure is: roll rather rapidly into a 45 degree bank to the left. Pause for a moment, then roll to wings level. Pause again, then roll 45 degrees to the right. Pause again, roll wings level, and repeat.

Refer to chapter 11 for a discussion of various techniques for perceiving whether or not your maneuvers are accurately coordinated.

The rolls should be done sufficiently rapidly that significant aileron deflection is required. Do the maneuver at cruise airspeed, and then do it at approach speed and even slower speeds, so you can see how the amount of rudder required increases as the speed decreases. Do the maneuver while looking out the side (wings should go up and down like a flyswatter, with no slicing) and while looking out the front (rate of turn proportional to amount of bank, no backtracking on roll-in, no overshoot on roll-out). Pay attention to the seat of your pants.

You should do the maneuver two ways: once with large aileron deflection applied gradually, and once with large aileron deflection applied suddenly. The difference between the two demonstrates adverse yaw.

Here is another exercise. Unlike the previous one (which involved coordinated wing rocking) this one involves intentionally uncoordinated wing rocking. You bank the airplane but apply top rudder to keep it from turning. This is grossly uncoordinated, but it is amusing and educational because it lets you learn the feel of the controls and the response of the airplane. (Do not get in habit of starting turns in such a way.)

This uncoordinated wing-rocking exercise is related to (but not quite the same as) the Dutch roll oscillations discussed in section 10.6.1. Both involve slipping to one side and then the other, like a Dutch kid on skates, making a series of slips (left, right, left, right) without much change in heading. The difference is that genuine Dutch roll oscillations involve a lot of yawing, while in the coordination exercise, you use the rudder to prevent any yaw. Let's call this the ``3/8ths hesitation roll'' since it resembles three eighths of an aerobatic 8-point roll.

Another uncoordinated exercise that is somewhat amusing and educational is as follows: keeping the wings level at all times, yaw the nose to the left with the rudder. Then raise the nose with the flippers. Then yaw the nose to the right with the rudder. Then lower the nose with the flippers, and repeat. Imagine you are drawing a rectangle on the sky in front of you, using the axis of the airplane as your pencil. Because of the slip-roll coupling described in section 9.2, while pressing right rudder you will need to apply left aileron to keep the wings level. The purpose of this exercise is to illustrate yaw-axis inertia, yaw-axis stability, and yaw-axis damping. That is, you will notice that if you make a sudden change in rudder deflection, the nose will overshoot before settling on it steady-stage heading. (Once again, the combination of controls used here is very different from proper turning procedure.)

16.8   Familiarization Exercises; Configuration Changes

Imagine you are not completely familiar with the aircraft you are flying. You are have just flown an instrument approach, and have broken out of the clouds about 150 feet above the runway. You are flying at 100 knots. Within the next 15 seconds or so, you need to slow down to 71 knots in preparation for landing. Therefore you take the following actions:
  1. Pull the throttle to idle
  2. Extend the flaps the rest of the way
  3. Deploy the speed brakes5
Now imagine that those actions do not cause the airplane to slow down! You discover that on this airplane, each of those actions causes a nose-down trim change. The airplane pitches over and dives toward the ground at high speed. This is not good.

Therefore, in this airplane, a much better procedure would be to take the following actions:
  1. Pull the throttle to idle and apply some nose-up trim to compensate.
  2. Extend the flaps the rest of the way and apply some more nose-up trim to compensate.
  3. Deploy the speed brakes and apply even more nose-up trim to compensate.
  4. As you decelerate, apply yet more nose-up trim.
For any given airplane, you need to know how much trim it takes to compensate for each configuration change. This information is typically not provided by the Pilot's Operating Handbook. You need to obtain it empirically. Go to the practice area and do some experiments at a safe altitude.

First, just fly around for a while at normal cruise airspeed. This lets you see what the cruise angle of attack looks like; this information comes in handy on final approach, as discussed in section 12.11.3.

You should also take this opportunity to learn how the airplane responds. Practice the basic maneuvers as described in previous sections of this chapter. Acceleration/deceleration is worth practicing; some airplanes are much harder to slow down than others. Coordinated turns are worth practicing; different airplanes require different patterns of rudder usage. Nonturning slips are important for landings; you need to know how much yaw and how much drag is produced by a given amount of rudder pressure. Phugoids are definitely worth investigating; different airplanes respond differently.

Next, investigate the effect of the trim wheel. The wheel has bumps on it, which we can use as our unit of measurement. Move the wheel one bump, and see what effect that has on the airspeed. If you have electric trim, figure out how fast it moves (how many bumps per second).

Next, slow down to the airspeed you normally use in the traffic pattern. Again, get the airplane nicely trimmed and just fly around a while. Make a note of the angle of attack.

After the airplane is once again flying along, nicely trimmed at pattern speed, extend one notch of flaps. Maintain the same speed. Make careful note of how many bumps of trim it takes to maintain constant speed, compensating for the flap extension. Do not bother to maintain level flight. Leave the power setting along, and make a note of how much rate of descent is caused by the drag of the flaps. Also note how the pitch attitude changes; remember that extending the flaps changes the angle of incidence, as discussed in section 2.4.

Do the same for each successive notch of flaps. In each case, make careful note of how much you have to move the trim wheel to maintain constant speed. Also observe the resulting rate of descent, and observe the change in incidence.

Do the same for other possible configuration changes (landing gear, speed brakes, et cetera).

After you have done that, investigate the effect of power changes. Determine how many RPM (or how many inches of manifold pressure) you need to remove in order to change from level flight to a 500 fpm descent. Also observe the effect that such a power change has on the trim speed.

Now, during the descent, check the effects of configuration changes again. You need two sets of observations: one using a power setting appropriate for level flight in the traffic pattern, and one using a power setting appropriate for final descent. In an ideal airplane, configuration changes would not affect the trim, but in a real airplane they do, by an amount that depends on the power setting.

At this point, you should be able to construct a crib card along the following lines: where each of the blanks gets filled in with some positive number (for nose-up trim application) or negative number (for nose-down trim application). The exact values aren't important; the idea is to have enough information to prevent nasty surprises like the situation described at the beginning of this section.

Finally, fly around for a while slightly above minimum controllable airspeed, with flaps extended. See section 16.16 for more discussion of slow flight procedures. Practice rocking the wings. Make sure you can bank the plane left or right, with reflexively correct use of ailerons and rudder.

Additional familiarization exercises are discussed in connection with landings in section 12.11.4.

Familiarizing yourself with a new type of airplane can take a goodly amount of time, especially if you have modest total pilot experience. On the other hand, if you are just re-familiarizing yourself with the plane after a period of inactivity, you can run through the maneuvers fairly quickly.

16.9   Turns around a Point

Turns are more challenging if you are trying to turn around a specific ground reference, maintaining a constant distance from it. If there is any significant wind (which there almost always is), this requires constantly changing bank angles.

The best way to analyze this situation is to begin by considering what happen if you do not make any correction for the wind. Figure 16.5 shows three complete turns made using a constant bank angle.

cycloid
Figure 16.5: Turns Not Quite Around a Point

In the absence of wind, you would have performed three perfect circles around the southeasternmost tree in the orchard. However, since there is some wind, we can use the principle of relativity. Relative to the air, you have still made three perfect circles. However, the air itself has moved during the maneuver, carrying the whole pattern downwind. Therefore relative to the ground, we see the cycloid pattern shown in the figure.

To transform this pattern into one that is circular relative to the ground, you need a steeper bank at the points where you are headed downwind (e.g. point A and neighboring points), and a shallower bank at the points where you are headed upwind (e.g. point C and neighboring points). As you can see from table 16.3, the effect can be fairly large.

speed rate radius bank load
(knots) (°/sec) (nm) (degrees) factor
 60 2.9 0.33  9 1.0
 75 3.6 0.33 14 1.0
 90 4.3 0.33 19 1.1
105 5.0 0.33 26 1.1
120 5.7 0.33 32 1.2
135 6.4 0.33 39 1.3
150 7.2 0.33 45 1.4
165 7.9 0.33 50 1.6
180 8.6 0.33 55 1.7
Table 16.3: Constant-Radius Turn
If you fly the maneuver at 90 KIAS, your groundspeed will vary from 105 (downwind) to 75 (upwind). That's a ratio of 1.4 to 1. Let's assume you remain 1/3rd of a mile from the landmark, since that is the distance to which the table applies. The speed in the left-hand column of the table should be taken as a ground speed, since we want the radius to remain constant as seen from the ground. The table tells us the required bank angle will vary from 26 degrees at point A to 14 degrees at point C.

At points B and D in the figure, the bank angle will be the same as in the no-wind case — but you will need apply wind corrections to your heading, as discussed in section 16.4.

16.10   Eights Around Pylons

Eights around pylons are performed by flying turns around a point clockwise around one pylon, and counterclockwise around another pylon, as shown in figure 16.6.

eight-around-pylon
Figure 16.6: Eights Around Pylons

You need to choose the right place to roll out of the turn and begin the straightaway section, so that the two circles will be the same size. It may help to visualize the desired figure-eight shaped ground track on the ground, and then just follow that track.

This maneuver is not to be confused with eights on pylons (which are discussed in section 16.13.2).

16.11   Chandelles

A chandelle is a stylized climbing turn. The key elements are: Normally the maneuver is entered from level flight. If your airplane's manufacturer has specified a recommended entry speed, use that. Otherwise, cruise airspeed should do nicely.

The higher the entry speed, the greater the altitude gained during the maneuver. You can dive if necessary to achieve the chosen entry speed, but be careful not to overspeed the engine. A high entry speed is absolutely not required.

A chandelle is in some senses a ``maximum performance'' maneuver, but altitude gain is not one of the things that you are expected to maximize. (If people wanted absolute maximum altitude gain, they would use a rather different sequence of bank and pitch attitudes.) The maneuver is judged primarily on the accuracy and smoothness of the pitch and bank maneuvers.

The maneuver emphasizes headings and attitudes. You should use ground references to judge the correct headings, but you shouldn't bother to remain over a particular point or to correct headings for wind drift.

You have some discretion when selecting the initial bank angle. Usually 30 degrees works fine. If the bank is too shallow, during the second half of the maneuver you will find that the airplane has decelerated to its final speed before the turn is completed; ideally the final speed and the final heading should be reached simultaneously. Happily, since the airspeed is changing only rather slowly at the end, this is relatively easy to arrange.

The end of the maneuver depends on airplane performance. If your airplane has more than enough power to sustain level flight at stalling angle of attack, you are in luck. At the end of the maneuver you should lower the nose and accelerate at constant altitude.

If your airplane cannot sustain level flight at stalling angle of attack, you should arrange the timing so that at the end of the maneuver you are momentarily in level flight, at the top of the climb. Then you should lower the nose and dive gently to obtain an airspeed that will permit acceleration in level flight. Then level off and accelerate to a normal speed. You will need more skill and judgment than you would in a more powerful plane.

If you want to learn to do chandelles, it may help to divide the maneuver into separate ``climb'' and the ``turn'' components. It is sometimes useful to analyze and practice these components separately.

The second half of the climb contains an interesting lesson. The pitch attitude and power setting are constant, but the result is very far from being constant performance. The angle of attack is increasing, the airspeed is decreasing, and the rate of climb is decreasing.

This second part of the maneuver begins with the airplane climbing rapidly. The climb angle is, intentionally, unsustainable. The airplane will nevertheless climb in the short run. For a while, it can climb by cashing in airspeed, according to the law of the roller coaster.

As the airspeed decreases, the airplane must fly at an ever-higher angle of attack in order to support its weight. Since the pitch attitude is being held constant, this means that the direction of flight must be bending over. This is illustrated in figure 2.11 in section 2.10.

This should drive home the lesson that pitch attitude is not the same as angle of attack, and that angle of attack (not pitch attitude) is what directly determines performance.

You should not attempt to micro-manage the altitude during a chandelle. You should maintain the chosen pitch attitude and let the airplane's intrinsic vertical damping (and energy budget) take care of the vertical motion.

The choice of pitch attitude with which you begin the second half of the chandelle is obviously critical, since you will be stuck with it for the rest of the maneuver. If it is too nose-high, the airplane will decelerate too quickly and you will run out of airspeed before the turning part of the maneuver is completed. Conversely, if the pitch attitude is too low, you will have airspeed left over at the end of the turn. The right answer depends on the performance of the airplane (and on the timing of the turning part of the chandelle). The answer can be determined by trial and error. About 15 degrees is a good initial guess for typical training airplanes.

Now let's examine the turning component of the chandelle. Again, the second half is the interesting part. The second half, if properly performed, will take a certain amount of time. You have to roll the wings level, using a uniform roll rate over that time. If you roll too slowly, the airplane will turn through 90 degrees before the rollout is completed. Conversely, if you roll too quickly you will run out of bank before the 90 degree turn is completed. At each instant, you should estimate the amount of turn remaining and the amount of bank remaining, and fudge the roll-rate accordingly. As always, a small correction early is better than a large correction late. It is useful to practice this a couple of times in level flight, before combining it with the climbing component.

When performing the complete maneuver (climbing and turning together) there is one more wrinkle: Remember that rate of turn depends not only on bank angle but also (inversely) on airspeed. Since the airspeed is decreasing during the maneuver, you must take this into account when planning the roll rate for the complete maneuver.

Also, as the airspeed decreases you will need progressively more right rudder to compensate for the helical propwash, and progressively more right aileron to compensate for the rotational drag on the propeller blades. Furthermore, remember that adverse yaw and the effects of yaw-axis inertia become more pronounced at low airspeeds (as always). Maintain proper coordination (zero slip) at all times.

16.12   Lazy Eights

The lazy eight derives its name from the motion of the airplane's axis during the maneuver. In particular, imagine that the airplane is at a very high altitude, so we don't need to worry about the ground getting in the way. Further imagine that the airplane is centered in a cylinder of paper, 10 miles in diameter and 5 miles high. Also imagine that the airplane carries a very long pencil sticking out the front, aligned with airplane's axis. During the course of a lazy eight, the pencil will draw a giant figure eight, sideways, on the paper.

lazy-eight
Figure 16.7: Lazy Eight

Figure 16.7 shows some of the details. Start at point A, in level flight. Pull the nose up. Gradually start banking to the right. At point B, stop pulling the nose up; let it start going down. Keep the bank; keep turning to the right. At point C, the pencil slices through the horizon. The body of the pencil is horizontal, while its tip is moving down and to the right. Start rolling out the bank. Point D is the lowest pitch attitude. The bank is about half gone; keep rolling it out. At point E the pitch attitude and the bank attitude should be level. Pull the pencil straight up through the horizon. Start rolling to the left. At point F, start letting the pitch attitude back down again. At point G, the pencil-point slices through the horizon again, this time moving down and to the left. Start rolling out the bank. Point H is the lowest point in the leftward stroke. By the time you return to point A, the pitch and bank attitudes should be level again. Pull the pencil straight up through the horizon again, and repeat the maneuver.

For the next level of refinement, arrange the timing and the bank angles so that point B is 45 degrees of heading away from point A; point C is at 90 degrees, point D is at 135 degrees, and point E is at 180 degrees.

For the next level of refinement, arrange the push/pull forces so that points B and F are about 20 degrees above the horizon, and points H and D are about 20 degrees below the horizon.

Note that up to this point we have not mentioned anything about altitude or airspeed. This is primarily an attitude maneuver, and you should learn it in terms of attitudes.

When learning the maneuver, it helps to separate the ``up/down'' part from the ``left/right'' part.

The left/right part of the maneuver is quite simple. You just very gradually roll into a turn to the right, then very gradually roll out. You continue the roll so it becomes a turn to the left, and then gradually roll out.

The up/down part of the maneuver is almost as simple. You just pull the nose above the horizon for a while, then lower it to the horizon; let it go below the horizon, then pull it back to the horizon and repeat.

One tricky part about combining the left/right part with the up/down part: the vertical motion goes through two cycles (ascending, descending, ascending, descending) while the horizontal motion is going through only one (rightward, leftward).

To get a deeper understanding of the maneuver, we must think a little about the altitudes and airspeeds.

During the whole quadrant from A to C, the nose is above the horizon. The airplane is climbing and decelerating. Therefore C is the point with the highest altitude and the lowest airspeed. Point C has a high altitude even though we (correctly) drew it in the figure on the same line as point A. That is because the maneuver is defined in terms of attitude, not altitude, and we imagine that the paper on which the lazy eight is drawn is so far away that the pencil has lots of leverage — the angle matters a lot, and the altitude matters hardly at all.

To you, the low airspeed at C is more immediately noticeable than anything else. The airplane is below its trim speed, so the nose wants to drop all by itself. At this point you will not need to push on the yoke; you just need to reduce the back pressure to let the nose go down at the desired rate.

During the whole quadrant from C to E, the nose is below the horizon. The airplane is descending and accelerating. Therefore point E is has a much lower altitude than point C, and indeed should be level with point A.

The second ascending/descending cycle (from E back to A) should be pretty similar to the first.

The commercial-pilot Practical Test Standard requires that you return to your initial altitude and airspeed every time you pass point A and point E. You might hope that this would happen automatically if you leave the throttle setting alone, relying on the law of the roller coaster. But that hope is in vain, for the following reason.

Normally you start the maneuver at a speed well above VY, with a power setting appropriate for level flight at this speed. Now suppose you fly a nice smooth symmetric maneuver that returns to the original airspeed. The maneuver starts with a pull, and at all times you will have an airspeed at or below the initial airspeed. You will be flying the maneuver at more-efficient airspeeds, closer to VY.6 You will gain energy. You will gain altitude. If you try to fix the altitude by diving, you will end up with excess airspeed. The only way to make things come out even is to fly the maneuver using a slightly-reduced power setting. This is most noticeable in airplanes with big engines and long wings, where the normal operating speeds are large compared to VY.

This maneuver contains a very nice lesson about the principles of flight. Much of the vertical part of the maneuver can be considered a ``controlled phugoid''. In particular, during the phase from B to D the nose is dropping but you are not pushing it down — indeed you are maintaining back pressure as you gently lower the nose. The feeling is sort of like the feeling you get when lowering a heavy object on a rope, and is quite striking.

This should drive home the message that the airplane is definitely not trimmed for a definite pitch attitude — it is trimmed for a definite angle of attack (or, approximately, a definite airspeed). At point C, among others, the airplane is well below its trim speed, so it wants to dive and rebuild its airspeed.

As the final level of refinement, you should make the altitudes at points A and E come out equal. You can do this by fudging the attitudes and/or power settings at strategic points in each half-cycle.

You have considerable discretion as to the steepness of the banks. Increasing it just speeds up the whole maneuver. A typical choice is to have 30 degrees of bank at points C and G (the points of maximum bank).

A lesser bank is also fine, but then you will want to choose a lesser nose-high attitude at points B and F. This is because you will be spending more time ascending, and you don't want to run out of airspeed. Make sure the airspeed at points C and G is 5 or 10 percent above the stall.

As with the chandelle, you will have to work a bit to maintain proper coordination. There is nothing surprising — just a wide range of roll rates and a wide range of airspeeds.

16.13   Eights on Pylons

The ``eights on pylons'' maneuver is required on the commercial and flight instructor practical tests. Being able to do this maneuver well, especially if there is a wind, definitely demonstrates that you can control the airplane around all axes at once.

This maneuver is not to be confused with eights ``around'' pylons (which are discussed in section 16.10). The ambiguous term ``pylon eights'' should be avoided.

16.13.1   Turns on a Pylon

Before we cover the ``eights on pylons'' maneuver (section 16.13.2, we need to discuss a little theory. We begin by considering turns on a (single) pylon.

The idea is simple: Imagine a pointer that pokes through the plane from wingtip to wingtip, parallel to the pitch axis; you want this pointer to remain pointed directly at the base of the pylon. This is quite a restriction; it means that at each point in the maneuver your bank and heading are completely determined by your altitude and position relative to the pylon. The only thing that makes the maneuver possible at all is that you are free to adjust your altitude.

*   No-Wind Case

In the absence of wind, the maneuver will work at a particular altitude — the so-called pivotal altitude — and not otherwise. Interestingly, the pivotal altitude does not depend on what you choose as your distance from the pylon. As shown in figure 16.8, if you start close to the pylon, you will have a large bank angle and therefore a lot of Gs. But since you are close to the pylon, the circle will be small, and you will need a lot of Gs in order to change the airplane's velocity (from northbound to southbound and back) in the small time available. In contrast, if you start out far from the pylon, the bank will be shallow, and you will pull a smaller number of Gs for a longer time.

pivotal
Figure 16.8: Turns on a Pylon — Pivotal Altitude

The pivotal altitude is proportional to the square of the airspeed: 0.0885 feet per knot squared, or 885 feet per (hundred knots) squared.

If you happen to be above the pivotal altitude, the airplane will be banked too steeply and will turn too quickly. Your sight-line past your wingtip, which is supposed to be pointed at the pylon, will be swept backward and will appear to fall behind the pylon. Or to say it the other way, the pylon will appear to be moving ahead of where you want it to be. The solution is to descend. At the lower altitude your bank will be less, and the problem will correct itself. Any airspeed you gain during the descent can only help you by further reducing the rate of turn.

Conversely, if you are too low, the bank will be too shallow and the pylon will appear to fall behind where you want it to be.

The rule is simple: go down to speed up and ``catch'' the pylon; go up to slow down and ``wait for'' the pylon.

You may be tempted to use the rudder to swing one wingtip a little bit forward or backward, but this defeats the purpose of the maneuver and is not the correct procedure.

*   Windy Case

In the presence of wind, the pattern is no longer a perfect circle. In fact, the ground track is an ellipse with the pylon at one focus. You are nearest the pylon when the airplane is headed directly downwind. This gives max bank when flying downwind, which makes a certain amount of sense — you want to bank more steeply when the groundspeed is highest. This is shown in figure 16.9.

turn-on-pylon
Figure 16.9: Turn On Pylon — Headings

The wind also prevents you from flying the pattern at constant altitude (for reasons that will be discussed below). The altitude is highest when the airplane is headed directly downwind. This is shown in figure 16.10. Once again, this contributes to creating max bank when flying downwind, which makes sense.

altitude-on-pylon
Figure 16.10: Turn On Pylon — Altitudes

There are two strategies, depending on how much the plane speeds up when it descends.
a
If you fly the pattern at high speed (i.e., well above VY), then tiny changes in airspeed will give you plenty of up-and-down action. I call this the constant-airspeed case.
b
If you fly the pattern at a speed near VY, then changing the airspeed has only a small effect on the long-term power required — all you are doing is making a one-time exchange of potential energy for kinetic energy according to the law of the roller-coaster. I call this the constant energy case.
The typical case will lie somewhere in between; fortunately the answers in the two cases are not very different.
a
In the constant-airspeed case, the ground track is a mathematically perfect ellipse. The altitude turns out to be inversely proportional to your distance from the pylon, which can be a surprisingly large excursion even in moderate winds.
b
In the constant-energy case, the ground track deviates only imperceptibly from an ellipse (the distance deviation is less than 1%, even when the wind is 30% of your airspeed). The altitude variation (as a percentage) is about one-third as large as the variation in distance from the pylon.
When going upwind, you need to turn a lot slower. There are three factors at work:
  1. you are farther away, so the bank angle is less (by geometry);
  2. you are lower, so the bank angle is less (also by geometry); and
  3. in the constant-energy case, you are going faster (making more forward progress per unit turn).
The first two factors are diagrammed in figure 16.11. In the constant-airspeed case factor 1 does half the job and factor 2 does the other half. In the constant-energy case they all three divide the job, roughly in the ratio 50% : 20% : 30%.

angle-on-pylon
Figure 16.11: Turn On Pylon — Bank Geometry

By geometry, the angle of bank is inversely proportional to the distance r from the pylon. It is also proportional to height. In the constant-airspeed case, the height is itself inversely proportional to r. Combining these, you get that the airplane is ``attracted'' toward the pylon with an acceleration that goes like 1/r2.

You may recognize this situation from astronomy: an inverse-square central force. So it's not surprising you get a Keplerian ellipse. The airplane will sweep out equal areas in equal time, and its angular momentum about the pylon will be constant.

In the zero-wind case, the pivotal altitude is simply proportional to groundspeed squared. Several well-known books try to argue that on the upwind leg of the turn on pylon, the groundspeed is lower, so the altitude should be lower. That is a false explanation (even though the altitude is indeed lower there). The actual altitude change is much less than you would predict by the groundspeed argument (by a factor of 2 in the constant-airspeed case and by a factor of 4 or so in the constant-energy case).

You may wonder how this can be — how can the airplane keep the wing on the pylon if it is not at the pivotal altitude? The answer is simple: we are not trying to fly a circular pattern. Recall that if you are above the pivotal altitude, the airplane will spiral toward the pylon. This is exactly what is happening in half of the elliptical pattern — the airplane is above the pivotal altitude and flying gradually closer to the pylon.

Why is the center of the pattern shifted crosswind rather than downwind of the pylon? For sake of discussion, let's divide the pattern in half along the long axis (which includes the pylon). If the airplane is positioned to windward of this line, it is subject to a crosswind from outside the pattern, which tends to drift the plane sideways closer to the pylon, making the bank steeper. This effect occurs throughout the windward half, so the plane is closest and steepest when it crosses from the windward to the leeward half (at which point it is headed directly downwind).

For these turns on pylons (unlike turns around pylons), there is nothing you can do to prevent the plane from being blown sideways. Consider the point where the plane is directly upwind of the pylon. The heading is constrained to be directly across the wind. The pilot cannot crab into the wind. Therefore the plane will be blown toward the pylon.

By the same token, whenever the airplane is on the leeward side of dividing line, it is subject to a crosswind from inside the pattern, which tends to drift the plane sideways farther from the pylon and hence make the bank shallower. The effect is cumulative, so the plane is farthest and shallowest when it crosses from the leeward to windward half (at which point it is headed directly upwind).

Also, draw a line from the pylon to a generic point on the ellipse. The wings of the plane, at that point, will lie on that line; the heading of the plane will be perpendicular to that line. Except for the two special points at the ends of the ellipse, the heading will not be tangent to the ellipse; the angle between the heading and the tangent is precisely the crosswind correction angle. You will note that the plane is always crabbed into the wind. This can be seen in figure 16.9.

16.13.2   Eights on Pylons

The eights-on-pylon maneuver consists of a turn on one pylon followed by an opposite-direction turn on another pylon, as shown in figure 16.12. The two-pylon maneuver adds the complexity of planning when to shift from one pylon to the other, but is actually easier to perform because you can use the straightaway between turns to recover from any small errors.

eight-on-pylon
Figure 16.12: Eights On Pylons

You don't want to pick pylons that are too close together. You do want pylons that are crosswind from each other, so that the pattern will be symmetric. It is good to enter on a downwind heading, as shown in the figure, so that your first turn will be your steepest turn. Maintain coordination; don't fudge things with the rudder.

In flight, you can follow these simple rules:
  1. If the pointer is above or below the base of the pylon, it's easy to fix; just change your bank angle.
  2. If the pointer is behind the pylon, go down to accelerate and ``catch'' the pylon.
  3. If the pointer is ahead of the pylon, go up to decelerate and ``wait for'' the pylon.
In principle, these rules are all you need to know. However, the other information in this section makes your job 1000% easier. It allows you to anticipate the required altitude changes and the elliptical ground track. Anticipating the required actions is easier than waiting until there is an error and then making corrections.

16.14   Changing Headwinds and Tailwinds

In some ways, an airplane performs differently when going downwind as opposed to upwind — and in other ways it doesn't. There are a lot of misconceptions about both halves of this statement.

16.14.1   Steady Wind

Let us first consider the situation where there is a steady wind; that is, a wind that does not vary with time or with altitude.

Maneuvers relative to a ground reference will be different when headed downwind as opposed to upwind.   Maneuvers that do not involve a ground reference will be unaffected by the wind.

For instance, the airplane will climb and descend at a steeper angle (in terms of altitude per mile over the ground) when headed upwind.   For instance, the airplane will climb and descend at a rate (in terms of altitude per minute) that is independent of the wind.

Similarly, a constant-radius turn relative to a ground reference will require a steeper bank on downwind and a shallower bank on upwind.   Similarly, a constant-radius turn relative to a cloud will require the same angle of bank throughout the maneuver.

The point is that the airplane, the cloud, and the airmass are one big uniform moving system. By Galileo's principle of relativity, the overall uniform motion doesn't matter.

Note that obstacle clearance is an important ground-reference maneuver. Your rate of climb is unaffected by the wind, but your angle of climb is affected. You can climb at a steeper angle on an upwind heading.

Finally, consider ground observers' perceptions. There are some maneuvers, such as an aerobatic loop, that should not be corrected for the wind. Imagine you are using a smoke generator. You want the smoke to form a nice round loop. Like the cloud mentioned above, the smoke is comoving with the air, so the overall wind speed shouldn't matter. However, especially if the smoke generator is turned off, the maneuver will appear different to an observer on the ground. This appearance does not (and should not) matter to the pilot in the cockpit, but it does matter if you are on the ground piloting a radio-controlled model, or judging an aerobatic contest.

There are several good reasons for being aware of your groundspeed, including: On the other hand, during turns and other maneuvers, it would make absolutely no sense to try to maintain constant groundspeed.

16.14.2   Albatross Effect: Winds that Vary with Altitude

In the real world, the wind almost always changes with altitude. In particular, it is very common to find that the wind at ground level is blowing in the same general direction as the wind at 3000 feet AGL, but at a much lower speed. This is because of friction between the air and the surface.

Most of this frictional windshear is concentrated at the lowest altitudes. At low altitudes, it is common to see a windshear of several knots per hundred feet, while at enroute altitudes (several thousand feet AGL) it is more typical to see a windshear of a few knots per thousand feet.

Wooded areas, tall buildings, and/or steep hills upwind of your position can create particularly sharp shear layers.

On top of this, frontal activity (especially warm fronts) can cause very large windshears that are more complicated and less predictable than the normal, every-day frictional wind shear. I once was making an approach to a rather short, obstructed field. The windsock indicated that I had five or ten knots of headwind on the chosen runway, but the airplane acted as if I had at least 20 knots of tailwind on final. Even with zero engine power and full flaps I could not get the airplane to descend steeply enough to stay on the glide slope. Three approaches in a row ended in go-arounds (which allowed me to carefully check the windsock three times). On the fourth approach, by anticipating the windshear, I was able to make a reasonable landing. About half an hour later the surface wind shifted 180 degrees. This was consistent with the forecast warm front.

The situation in this anecdote (increasing headwind on final approach) is very atypical. The other 99.9% of the time there is a decreasing headwind as you descend on final. For the same reason, you expect to see an increasing headwind as you climb upwind on initial departure.

Let's analyze the effect of windshear. Suppose you start out at point A, and fly to point B where because of a windshear there is more headwind (or less tailwind). If the windshear is sudden, you will notice a sudden increase in airspeed. The windshear has added something to your energy7 budget. If the shear is more gradual, the airplane (because it is trimmed for a definite angle of attack) will probably convert the extra airspeed into extra altitude, but you will still wind up at point B with more energy than you would have without the windshear. During climb, this is great. It makes it look like you have a more powerful engine. (On short-field approach, as in the atypical anecdote above, this is not so good; the airplane behaves as if your engine were producing a fair amount of power even with the throttle at idle.)

We can apply the same line of reasoning to the opposite case: suppose you start out at point C and fly to a point D where (again because of a windshear) you have less headwind or more tailwind. This means you will arrive at point D with less energy than you would have without the windshear. This commonly happens on approach, where you are descending into a decreasing headwind. This might be a good thing, allowing you to fly a steeper approach. On the other hand, a sudden decrease in headwind could rob you of energy at a critical time.

The energy that comes from an increasing headwind can be put to good use. I call it the albatross effect. The albatross is a huge bird that spends its life flying over the oceans of the world. It rarely needs to flap its wings, but it doesn't soar in updrafts the way hawks do. Instead, the albatross flies a figure-eight pattern in the shear zone near the surface, climbing into an increasing headwind on the upwind legs and descending into a decreasing tailwind on the downwind legs — gaining energy both ways.

Note that on a typical approach, the wind makes the angle of descent steeper in two ways:
  1. the groundspeed is lower, due to the average overall headwind (as discussed in the previous section), and
  2. the rate of descent is faster, due to the decreasing headwind (albatross effect).

16.14.3   Turning Downwind; Energy Budget

The previous section discussed how you could gain or lose energy due to a windshear. In this section, we return to considering only a steady wind, and discuss what happens if you convert a headwind into a tailwind simply by turning the airplane.

Let's consider the scenario described in table 16.4.

true airspeed 100 knots
initial heading north
final heading south
time spent turning 1.2 min = .02 hour
mass of airplane 1 ton
wind speed 20 knots
wind direction from the north
Table 16.4: Downwind Turn Scenario
Let's calculate the energy and momentum twice, as shown in table 16.5. In the ``balloon'' column everything is measured relative to an observer in a balloon (comoving with the air mass), and in the ``ground'' column everything is measured relative to an observer on the ground.
balloon ground
initial momentum 100 80
final momentum -100 -120
change in momentum -200 -200
average N-S force 10000 10000
initial energy 5000 3200
final energy 5000 7200
change in energy required 0 4000
N-S distance during turn 0 .4
energy provided by wind 0 4000
Table 16.5: Downwind Turn Analysis
Here's what the first four rows mean: The momentum is calculated using the usual formula: mass times velocity. (The units here are rather strange, tons time knots, but it's OK as long as consistent units are used throughout the calculation.) The North-South component of the average force is just the change in momentum divided by the time. We see that although the initial and final momenta appear different in the two columns, the change in momentum is the same. This upholds Galileo's principle of relativity: the force required to turn the airplane is independent of the frame of reference.

Here's what the last five rows mean: The energy is calculated using the usual formula: one half of the mass times velocity squared. According to the ground observer, the airplane needs to gain quite a lot of energy during the turn. You may be wondering where this energy comes from. Obviously it does not come from the airplane's engine. Actually it gains energy the same way a baseball gains energy when it is struck by a bat. You know that although a ball does not gain any energy when it bounces off a stationary wall, it does gain energy when it bounces off a fast-moving bat. The energy gain is force times distance (counting only distance in the same direction as the force). According to the observer in the balloon, the force of the turn is (at every instant) perpendicular to the direction of the force, so there is no energy gain. Meanwhile, according to the observer on the ground, the wind moves the airplane 0.4 miles in the North-South direction during the turn, and turning the airplane requires a huge force in this direction. This effect — the airplane being batted by the wind — supplies exactly the needed energy. Again, we see that the principle of relativity is upheld: the energy budget works out OK no matter what frame of reference is used.

Note that if you overlooked the bat effect you would fool yourself into thinking that turning downwind caused a huge energy deficit. It doesn't. Don't worry about it.

16.14.4   Summary: Changing Headwinds and Tailwinds

16.15   Remarks: Ground Reference Maneuvers

16.15.1   Accounting for the Wind

Throughout each flight — and certainly before starting any ground reference maneuvers — you should have in mind a good estimate of the speed and direction of the wind. There are various ways you can figure this out It is a good idea to know the wind before starting a maneuver (rather than trying to figure it out ``on the fly''). It really helps to be able to plan the maneuver and anticipate the necessary wind corrections.

16.15.2   Entry Strategy

It is a good idea to begin ground-reference maneuvers such (as turns around a point) a downwind heading, as shown in figure 16.5, so that your first bank will be your steepest bank. You don't want to be a position where (late in the maneuver) you must choose between abandoning the effort or using an excessive bank angle.

16.15.3   Visual Reference

It really helps to have a precise visual reference for pitch and yaw, as discussed in section 11.5.2.

You can use your finger and/or a mark on the windshield, as illustrated in figure 11.3. If you can't find a suitable mark on the windshield, you can make one.

The reference should be directly in front of your dominant eye. It is a common mistake to choose a mark on the cowling. Such a mark is below where it should be, and tempts you to use too much rudder when rolling into right turns, and too little rudder when rolling into left turns. It is another common mistake to choose a reference point that is on the centerline of the airplane. Assuming your eye is quite a bit to the left of the centerline, your sight line through this point is very far from being parallel to the axis of the airplane. This tempts you to make diving left turns and climbing right turns.

As you become more experienced, you won't need to use your finger or an explicit mark on the windshield; you can just imagine where the reference point must be. Just make sure you use a point directly in front of your dominant eye.

16.15.4   Checklist

You want to take a systematic approach to all maneuvers. John Beck teaches a ``mental checklist'' for ground reference maneuvers: Repeat this list to yourself over and over again as you do the maneuver. Chant it aloud if you wish. Doing each thing as you say it not only keeps you from overlooking something, but also gives a nice rhythm to the work.

16.16   Slow Flight

If you are not proficient in handling the plane at low speeds, you have no business trying to land the plane.

To begin a practice session, go up to a safe altitude and make sure there are no other aircraft nearby. Decelerate to a speed, say, 15 knots above the stall speed. Once you are comfortable with this, reduce the speed another 5 knots. Again, once you are comfortable, reduce the speed another 5 knots.

During the maneuver, you should

16.16.1   Airspeed and Altitude

As discussed in section 7.3 and elsewhere, it would be OK to use the yoke to control altitude if you were on the front side of the power curve and you were willing to accept an airspeed excursion. However, during this slow flight maneuver, you definitely are not on the front side of the power curve and you definitely cannot tolerate airspeed excursions. Therefore you will need to use the yoke (and trim) to control airspeed, and once you've got the desired airspeed, you will need to use the throttle to control altitude. (To adjust airspeed at constant altitude, you will need to use the throttle and yoke together, as discussed in section 16.2.)

16.16.2   Yaw and Roll

Remember that the airplane is optimized for cruise flight. During cruise, you can fly straight and level with little or no control force, and you can make gentle turns with little or no use of the rudders, using ailerons alone.

In contrast, during slow flight Because (as discussed in section 5) there will be very little roll damping, you will need to apply lots of little aileron deflections to maintain wings-level flight, especially in the presence of turbulence.

16.16.3   Procedures and Perceptions

Make a note of the pitch attitude that corresponds to level flight at minimum controllable airspeed (with and without flaps). Note the pitch attitude of the nose against the forward horizon, and the wingtip against the lateral horizon. This information will come in very handy during landing, as discussed in section 12.11.3.

Practice rocking the wings. Make sure you can bank the plane left or right, with reflexively correct use of ailerons and rudder. Practice making turns to a precise heading.

Practice diving 50 feet. That is, push the nose down a few degrees (not so much that you experience negative G loads), dive for a few seconds, and then pull back and level out. Make a note of how much airspeed you gain by diving 50 feet. This information will come in handy during stall recoveries, as discussed in the next section.

16.17   Stall Practice

16.17.1   Preliminaries

There are many variations on the stall maneuver. You can stall the airplane with or without flaps extended, with or without power, during straight or turning flight, while pulling one or multiple Gs, and during level, climbing, or descending flight.

To keep the discussion simple, let's first go through one specific scenario, and discuss the possible variations later.

Scenario #1: Start out in level flight at a typical traffic-pattern speed, in the landing configuration (full flaps extended,8 landing gear extended, carb heat on, et cetera). Then reduce the power to idle. As the airplane decelerates, pull back on the yoke at a steady rate, cashing in airspeed to pay for drag, maintaining altitude. Maintain constant heading. Maintain coordination. When the airspeed gets low enough, you may observe a sudden, distinct stall. The nose will drop, even though you are pulling back on the yoke. Obviously it is time to begin your stall recovery, as discussed below.

16.17.2   Provoking a Distinct Stall

However, it is quite possible you will not always observe a sudden, distinct stall. In particular, if your airplane is loaded so that its center of mass is right at the forward edge of the weight and balance envelope, you may be unable to deflect the elevator enough to cause a stall using the procedure described above.9 At this point you are at a very low airspeed, unable to stall the airplane, and unable maintain altitude by pulling back on the yoke. At this point you should declare an end to the attempted stall and begin your stall recovery procedure. The ability to recognize the low-speed limit of performance in this situation is valuable, and should be practiced, but you should practice full-blown stalls also.

The most elegant way to improve your chances of observing a full-blown stall is to move the center of mass farther aft, using ballast. As described in section 6.1.9, 100 pounds of water stowed securely in the back of the airplane10 should make it a whole lot easier to raise the nose.

Another trick that might increase your control authority is to use a little bit of engine power, perhaps 1500 RPM. On many airplanes the propwash flowing over the elevator increases the control authority by just enough to permit a quite distinct stall. On other airplanes (including those with high T-tails, and others) this trick doesn't work at all — the propwash over the wings lowers the stalling speed more than the propwash over the tail improves the control authority.

A third way to provoke a distinct stall is to zoom a little bit. That is, you maintain constant altitude while you decelerate most of the way. Keep track of how far back you have pulled back on the yoke. When you have used up most of the available backward motion, use the last inch or so to pull back faster than would be needed to maintain 100% level flight. The airplane will rotate to a more nose-high attitude, climb a few feet, then stall.

16.17.3   Stall Recovery

Stall recovery, especially for poorly-trained pilots, poses psychological problems. In particular, if you are laboring under the dangerous misconception that the yoke is the up/down control, your instincts will be all wrong: the nose is dropping and the airplane is losing altitude, so you will be tempted to pull back on the yoke. This makes a bad situation much worse.

The correct way to think about the stall is to realize that the shortage of airspeed is your biggest problem. You need to push on the yoke and dive to regain airspeed.

In addition to the airspeed problem, you also have an energy problem. Therefore, while you are pushing on the yoke with one hand, you should be pushing on the throttle with the other hand.

As a further step to improve the energy situation, remove unnecessary drag. On most airplanes with N notches of flaps, the first several notches are somewhat helpful, because they allow you to fly slowly without stalling. The Nth notch, however, typically doesn't contribute much to lowering the stall speed, and just adds a lot of drag. This would be useful if you were trying to descend, but since we are trying to climb at the moment, you should retract the Nth notch of flaps as early as possible during the stall recovery. If the maneuver began with less than full flaps extended, leave the flaps alone, dive to regain airspeed, and then gradually retract the flaps.

While all this is going on, you should use the rudder and ailerons to keep the wings level and maintain a more-or-less constant heading.

You don't need to dive very far to regain a reasonable flying speed. According to the law of the roller coaster (as discussed in section 1.2.1), if you start out at 45 knots and dive 45 feet, you will wind up at 55 knots. If you start out at 50 knots and dive 80 feet, you will wind up at 65 knots.11

At the bottom of the dive, perform a nice gentle pull-out. If you pull too rapidly, you put a big G load on the wings, which will cause them to stall at a speed that would otherwise have been just fine.

After you have leveled out at the bottom of the dive, accelerate horizontally to best-climb airspeed. Retract any remaining flaps as you accelerate. Then climb at VY to a safe altitude.

To summarize: the key elements of stall recovery include

16.17.4   Power-On Stalls

A non-pilot might have thought that it would be hard to stall an airplane with the engine at full power, but in fact it is quite possible, and the accident statistics show that it happens fairly frequently. Therefore let's consider another scenario:

At a safe altitude in the practice area, set up for a power-off descent in the landing configuration. In particular, let this be a short-field approach, with the airplane trimmed to fly at the lowest practical airspeed. Then apply full power, as if for a go-around. In some airplanes (including the widely-used C-152, C-172, and C-182), and depending on where the center of mass is, this combination of trim, flaps, and power will cause the nose to pitch up quite dramatically. The airplane will climb very steeply and then stall. You don't need to pull back at all. Indeed, you may want to push a little bit so that the stall won't be too extreme.

In airplanes with better go-around characteristics (including a C-172 with the flaps retracted) you will need to work a little harder to perform a power-on stall. A possible — but not very stylish — way to perform this maneuver would be to start from cruising flight, add full power, and pull back until you get a stall. This is perhaps worth doing once, but it is not the recommended way of demonstrating a power-on stall, because results in climbing an unnecessarily long way. That is, it just isn't logical to apply full power while you are trying to decelerate. Therefore the conventional procedure is this: At a safe altitude, reduce power and decelerate in level flight to a speed a few knots above the stall. Then add power. (Use partial power the first time, and then use progressively more power as you learn how the airplane behaves.) Then gradually pull back some more.

As the airspeed bleeds off, you will need to apply more and more right12 rudder to maintain coordination (i.e. to compensate for the helical propwash). Coordination is very important, because even a slight slip angle will cause one wing to stall before the other. This could easily result in a spin, and even if you don't get a full-blown spin, the sudden change in bank angle is pretty unpleasant.

Also, in this high-power low-airspeed situation, you will need to apply steady right aileron (to compensate for the rotational drag of the propeller). Note that (as discussed in section 5.4.2) the roll damping goes to zero at about the same point where the stall occurs, so you will need to intervene rather actively to keep the wings level. The standard advice applies: make sure you use the ailerons and rudder together. Because the airspeed is low, you will need a whole lot of rudder deflection to coordinate with a small amount of aileron deflection, and indeed right near the stall you can quite nicely control the bank angle using the rudder alone. Imagine that the left wing is about to stall. By stepping on the right rudder pedal, you can swing the nose to the right, causing the left wing to speed up and become unstalled. During this maneuver, you might want to lower the nose a tiny bit, so the right wing, which is swinging backwards, doesn't stall.

If you manage to maintain perfect coordination and perfectly level wings right up to the point of the power-on stall, you can still expect that the airplane will want to yaw and roll to the left just after the stall. There are several factors at work:
  1. As discussed above, you are holding steady right aileron. This increases the effective angle of attack of the left wing, so it will stall first. The airplane will roll to the left.
  2. The helical propwash causes the airflow to hit the left wing root area at a higher angle, and the right wing root area at a lower angle. This also causes the left wing to stall first. The airplane will roll to the left.
  3. There is gyroscopic precession. That is, when the lift of the wings is suddenly reduced (while the lift at the tail is unchanged), it produces a torque — a nose-down pitching moment. In the absence of gyroscopic effects, this would cause the nose to drop, but as discussed in section 19.9.2, the rule for gyroscopes is that the force is 90 degrees ahead of the motion. This means that the torque around the pitch axis will cause a motion around the yaw axis — in this case, a yaw to the left. See figure 19.15. The resulting yaw will swing the left wing backwards, making it more stalled. The airplane will yaw to the left and roll to the left.
Of course, you can anticipate this, and apply additional right rudder as the nose drops. With a little experience, you can arrange that the wings stay level and the nose drops straight ahead.

The recovery from a power-on stall is basically the same: dive to regain airspeed, add power (if you were not already at full power), maintain wings level, reduce drag, and climb back to a safe altitude.

The practical test standard calls for performing power-on stalls with the flaps in the takeoff configuration and gear down (the takeoff configuration) or gear retracted (departure configuration) which simulates a stall happening shortly after takeoff. It is well worth practicing other configurations, too — particularly the approach configuration, which simulates what might happen if you mishandle a go-around.

16.17.5   Accelerated Stalls

The stall occurs at a definite angle of attack. This is not quite the same as a definite airspeed, for reasons discussed in section 2.12.5. As an example: if you are in a 45 degree bank, the load factor is 1.4, and the stalling speed will be 20% higher than it would be in ordinary one-G flight. Therefore, if you are relying on the airspeed indicator to warn you of an impending stall, you will be fooled.

Ironically, in some ways recovery from an accelerated stall is easier, because of the extra airspeed. You may not have to dive any significant distance. Otherwise, the procedure is the same: reduce the back pressure (and dive if necessary to regain airspeed), roll the wings level, add power, reduce drag, and climb back to a safe altitude.

It is the bank itself that makes a turning stall exciting. If you start out banked 45 degrees to the left, and then (due to a lapse in coordination, and/or any of the other factors discussed in section 16.17.4) the left wing drops another 45 degrees, you could wind up in a knife-edge attitude. If this happens, push forward on the yoke to the position that corresponds to zero angle of attack, so there is no load on the wings. Then just sit there for a second or two. The rudder will cause a rotation around the now-horizontal yaw axis, so that the airplane is soon pointing somewhat nose-down. After the airplane has dived a couple dozen feet, you will have enough airspeed that the ailerons are effective. Use the ailerons to roll the wings level, then pull out of the dive in the usual way.

Another thing that makes accelerated stalls a bit more challenging has to do with perception of the stall. Imagine an airplane where (due to a lack of nose-up elevator authority or whatever) the stall doesn't "break" suddenly. Then as you approach an ordinary, straight-ahead stall, you have a constant heading and everything looks fairly normal. You can devote a lot of attention to looking for subtle signs of the stall. Now contrast that with a stall during a 60-degree bank. The pitch axis is not horizontal, so any pitch change will move the nose mostly along the horizon, not perpendicular to the horizon. Also, no single outside reference stays in front of the nose for very long, so subtle pitch changes are quite a bit harder to notice. A student once complained ``I can't get this thing to stall''. I replied ``We're going down more than 2000 feet per minute. This is stalled enough for me''.

Finally, steep turns are not the only way that an accelerated stall can arise. A sharp pull-up with wings level will do it. In an aerobatic loop, for instance, you are pulling about 4 Gs at the bottom, so the stalling speed is about twice what it would be in ordinary unaccelerated flight. Especially since you might be rapidly approaching the ground at this point, there is a strong temptation to pull back, but be careful, because this would be a really inopportune time to stall. Make sure you have plenty of altitude and plenty of airspeed before attempting any high-G maneuvers.

16.17.6   Evil Zooms

As discussed in section 12.11.8, it is fairly easy to get into a situation where you have a nose-high pitch attitude, very little airspeed, and very little altitude. In this situation, the usual stall-recognition and stall-recovery techniques will do you no good whatsoever. You need to recover before the airplane stalls, and you need to recover with zero loss of altitude.

Therefore it is a good idea to practice recovering from this situation. The procedure is:
  1. Go up to a safe altitude.
  2. Set up for a power-off glide in the landing configuration.
  3. Gradually pull back on the yoke until you are a few knots above the stall speed.
  4. Then pull back on the yoke quite a bit more. Observe that the airplane rotates to a very high nose-up attitude and begins to climb.
  5. Before the airplane has climbed more than a few feet, and before it stalls, push the nose back down to the attitude that corresponds to level flight at a very low airspeed.
  6. At the same time, apply full power.
  7. Fly level until you regain airspeed, using the usual go-around procedures.
Practice this over and over, until you are confident that you can recover from a pitch excursion with zero loss of altitude.

1
... unless you are inside a cloud, in which case you hope everybody in that cloud is on an IFR clearance so that ATC can provide separation.
2
You may have seen some books that refer to the ``four fundamentals''. Here's how they get from three to four:
3
If you can't find a suitable scratch or bug corpse on the windshield, it may be instructive to make a mark, as discussed in section 11.5.2.
4
The other possibility is a windshear from tailwind to headwind, which is the opposite of what you normally encounter. This will give you excess energy, which could be a problem, especially if the field is short.
5
These are flat plates the pop up from the top of each wing. The air hits them broadside. They approximately double the airplane's coefficient of parasite drag.
6
...unless you spend a lot of time on the back side of the power curve, which is usually not practical.
7
The physics works like this: Your kinetic energy relative to the new air is greater than your kinetic energy relative to the old air. Your airspeed relative to the ground has not changed, or may even have decreased slightly, but that is irrelevant. The airplane doesn't care about the ground. The local air is the only thing that matters.
8
It is a little hard to explain why, in everyday flying, you would be flying level with full flaps extended, but don't worry about that. This maneuver (a) is a good training exercise, and (b) is an important part of the FAA practical test.
9
There is, after all, a physical limit to the amount of force any finite-sized elevator can produce, and this typically explains why the forward edge of the envelope is where it is.
10
This works fine in a four-seat aircraft with two people aboard, or a two-seater with one person aboard, but it may not be possible in a two-seater with two people aboard, because of limits on the total weight.
11
You can practice most elements of the stall-recovery maneuver without actually stalling the plane. That is, starting from level flight a few knots above the stalling speed, push the nose over, dive 50 feet or so to gain airspeed, and then level off. Don't forget to apply power, reduce drag, and maintain wings level. This sort of practice often helps students overcome their fear of stalls, by building up their confidence in their recovery procedures.
12
Assuming a standard American engine that rotates clockwise as seen from behind.

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