::Aero-Experiments::

See for yourself--simple in-flight demonstrations that you can do to the explore the physics of flight--in a "conventional" airplane

February 10, 2006 edition
Steve Seibel
steve at aeroexperiments.org
www.aeroexperiments.org

1) Noting the control yoke position at the stall angle-of-attack

2) Flying without using the control yoke or control stick -- creating a pitch "phugoid" oscillation

3) Flying without using the control yoke or control stick -- exploring relationships between yaw and roll, and between roll and pitch

4) Flying with a fixed elevator position� -- creating a pitch "phugoid" oscillation

5) Flying with a fixed elevator position -- exploring relationships between roll and pitch

6) Flying without using the rudder -- looking at adverse yaw (sideslip)

7) Exploring yaw oscillations

8) Direction of tail's lift

9) "Feeling" the wind direction in flight?

1) Noting the control yoke position at the stall angle-of-attack

Note February 2006: This section will soon be modified. I now believe that the "curvature in the relative wind" is not the primary driving force behind the relationships described in this section. Stay tuned for an alternative explanation, plus quantitative data.

Note: central to this discussion are the assumptions that the stall warning horn always sounds at one particular angle-of-attack, and that the stall always occurs at one particular angle-of-attack.

Pilots are usually aware of control pressures rather than control positions. From an engineering point of view, control position is more closely related to fundamental aerodynamic processes than control force or pressure is. To a first approximation, the elevator will always be in one specific position when a particular aircraft reaches the stall angle-of-attack, at least for a given CG condition. However a closer look reveals many reasons why the elevator position will vary when the stall angle-of-attack is reached. In this section we'll look at variations of the elevator position when the wing reaches the stall angle-of-attack, under various flight conditions.

The experiments described in this section can be carried in any aircraft that has a control yoke with a torque tube that enters the control panel at a defined point that is within the pilot's reach.

It's interesting to note the variations in control yoke position that occur at the stall angle-of-attack, or any other angle-of-attack, during various flight conditions. One way to explore this is to make a mark on the control yoke torque tube at the point where it enters the instrument panel at the moment that the stall break occurs. On an aircraft with a stall warning horn, more precise and repeatable results can be obtained by marking the angle-of-attack where the stall warning horn sounds, rather than the angle-of-attack of the actual stall break. In this case, both left and right banks should be explored, in case the stall warning horn has some asymmetry in its function.

For making a mark on a dark-colored torque tube, I've had good results with a white "Mean Streak" permanent marking stick from "Sharpie", or a white "Painty" marker from "Zig" (both available in arts and crafts supply stores).

For repeatable results, it's very important to use a constant throttle setting, and a very slow rate of deceleration to the stall (less than 1 mph per second), rather than trying to hold the aircraft in a constant pitch attitude as the airspeed slows.

In the wings-level unaccelerated condition, in a high-winged Cessna you'll find that the yoke will be further forward at the stall at a high power setting than at a low power setting--the action of the propwash over the tail tends to drive the nose up, placing the wing at a higher angle-of-attack for any given position of the control yoke. This effect will be more pronounced with the flaps down than with the flaps up. In a high-winged Cessna, you'll also find that the yoke will be further forward at the stall when the flaps are down than when the flaps are up. This effect will be more pronounced at high power settings than at low power settings.

The practical ramifications of this are a bit sobering--while holding the control yoke in a fixed position, in many aircraft it is possible to create a stall simply by opening the throttle to increase the engine power setting.

After marking the control yoke position at the wings-level idle power unaccelerated stall for various flap positions, perform a full-stall landing. Have a passenger note how much further aft the yoke is when the stall horn first sounds in ground affect, than was the case out of ground effect. This happens because the wing's downwash over the tail is reduced by ground effect, which tends to reduce the downward lift (or increase the upward lift) created by the tail at any given position of the control yoke. Therefore the yoke must be further aft to place the wing at any given angle-of-attack in ground effect, than out of ground effect. This effect will probably be most pronounced at low power settings, when the propwash over the tail is least significant.

The control yoke will be further aft at the stall in a steep bank than in wings-level flight. This happens because a turn involves a curvature in the flight path in the pitch dimension, especially at steep bank angles. As the flight path curves during the turn, so does the relative wind. (The concept of the curvature of the relative wind will be explored in more detail in the theory section of this website in the future.) When the aircraft is banked, the curving relative wind tends to have more of an upward component at the tail of the aircraft. This increases the tail's upward lift or decreases the tail's downward lift, which tends to kick the nose down, decreasing the wing's angle-of-attack. To maintain any given angle-of-attack, the yoke must be held further aft in a steep turn than in wings-level flight.

60 degrees is a good bank angle to use for steep turns while exploring this phenomenon.

In actual practice this last effect may be difficult to detect in flight in many aircraft. The longer the fuselage (tail arm), the easier this effect will be to detect at any given bank angle. Also, the lower the wings-level stall speed, the easier this effect will be to detect at any given bank angle, because a low airspeed correlates to a higher radius of curvature, for any given bank angle.

(In sailplanes this effect is quite pronounced--in a steep thermalling turn the control stick is positioned much further aft than it would be in wings-level flight at the same minimum-sink angle-of-attack. At least one well-known author advocates moderately steep turns in the pattern partly to reduce the risk of a stall. Other reasons for this recommendation: in unpowered flight the loss of altitude per degree of turn is least with bank angles around 45 degrees. Also, turning steeply minimizes the temptation for a pilot to apply excessive bottom rudder, coupled with excessive back stick to "hold the nose up" despite the excessive bottom rudder, all of which is an invitation to a stall/spin accident.)

In a high-winged Cessna, I've found that the variation in control yoke position with bank angle, at the stall angle-of-attack, is more pronounced at high power settings than at low power settings.

Actual measured data relating to this section will be posted on this website in the future.

2) Flying without using the control yoke or control stick -- creating a pitch "phugoid" oscillation

Note: the specific numbers and techniques and flight characteristics given here are for a Cessna 152.� "Your mileage may vary"--the specific numbers and techniques and flight characteristics given here may or may not apply to your aircraft.� If your aircraft's pitch attitude starts to become too extreme at any point, be vigilant against the possibilities of tailsliding, stalling, overspeeding the engine, exceeding the airspeed limitations, or overstressing the aircraft.� Be familiar with stall recovery and spin recovery procedures before trying these experiments.� Give yourself plenty of altitude.

Note: central to this discussion are the assumptions that the stall warning horn always sounds at one particular angle-of-attack, and that the stall always occurs at one particular angle-of-attack.

Before we start, here is a nice illustration of a "phugoidal oscillation" in the pitch axis from John S. Denker's excellent "See How It Flies" website.

Trim the aircraft for hands-off flight at 55 KIAS at roughly 2250 RPM's.� Don't worry about whether or not the altitude is remaining constant.� Practice keeping the aircraft wings-level with the rudder only till you get the hang of it.� Then bring your hand back to the yoke and slowly lower the nose, without adjusting the trim or power, until you see 85 KIAS.� Find the pitch attitude where the airspeed holds steady at 85 KIAS.� Then abruptly let of the control yoke and enjoy the pitch "phugoid" oscillation that ensues.� If your aircraft is "dynamically stable" as well as "dynamically stable" in its current configuration, the pitch oscillation will slowly damp out.� Before that happens, you'll see some rather interesting nose-high pitch attitudes.� Bear in mind however that as the aircraft floats over the top of the each pitch oscillation, the airspeed can safely drop significantly below the normal 1-G stall speed, since when the flight path is curving downward, the wing is generating less than 1 "G" of lift.� However there is still a real possibility of stalling at the top of a severe pitch oscillation--more on this in a bit.

(Note that the "top" of each pitch oscillation occurs not when the aircraft's nose is high above the horizon, but later, when the aircraft is in an approximately level pitch attitude.� Note also that the "bottom" of each pitch oscillation occurs not when the aircraft's nose is well below the horizon, but later, when the aircraft is in an approximately level pitch attitude.)�

To a very loose approximation, after the control yoke is abruptly released, the ensuing dynamics all take place at a constant angle-of-attack.� The fundamental reason that the nose rises well above a level pitch attitude when the control yoke is abruptly released is that the flight path curves rapidly upward.� The fundamental reason that the flight path curves rapidly upward is that the lift vector is larger than it "should" be.� The fundamental reason that the lift vector is larger than it "should" be is that the wing has been abruptly returned to the original trim angle-of-attack without allowing time for the excess airspeed (e.g. 85 KIAS minus 55 KIAS equals 30 KIAS excess airspeed) to bleed away--the aircraft is not in an equilibrium state.� Likewise, throughout the rest of the pitch "phugoid" oscillation that follows, the airspeed is constantly undershooting and then overshooting its "appropriate" value in relation to the trim angle-of-attack, before eventually settling down to the "appropriate" value.

If we limit ourselves to slow, gradual changes in the fore-and-aft position of the control yoke, then the airspeed will have plenty of time to bleed away or increase as necessary, and the aircraft will remain very nearly in an equilibrium state. The nose will always be in very nearly the "right" pitch attitude for the control yoke position, and the airspeed will also always be very nearly the "right" airspeed for the control yoke position. We'll still see a significant drop of the nose (and an increase in airspeed) whenever we move the control stick forward, and we'll still see a significant rise of the nose (and a decrease in airspeed) whenever we move the control stick aft, but whenever we freeze the control yoke position the aircraft's pitch attitude and airspeed will stay nearly constant. We won't see the "excessive" changes in pitch attitude and airspeed, plus the subsequent pitch phugoid oscillations which continue even after the control yoke position has been frozen, that we see when make more rapid changes in control yoke position.

These are actually the same principles that make aerobatic flight possible. For example, by moving the control stick or yoke aft at a brisk or moderate rate rather than more slowly, the aircraft retains "excessive" airspeed and therefore the lift force becomes "excessive", i.e. greater than 1 G. This causes the flight path to curve upward into the beginning of a loop. If we made the identical motion of the control stick or yoke, but much more slowly, the airspeed would have to time to bleed away as the angle-of-attack increased, and the aircraft would remain in nearly 1-G condition. Rather than the start of a loop, we would just see a slow transition to high-angle-of-attack, low-airspeed condition.

Let's return to the experiments described in this section, where the wing's angle-of-attack is kept nearly constant, but the airspeed rises and falls, which also causes the wing's lift vector to increase and decrease in magnitude.� If you are flying with a G-meter (such as this home-made version) you can see the variations in the lift vector--the G-load (which is just the mirror image of the wing's lift vector) will be greatest at the bottom of each pitch oscillation and lightest at the top of each pitch oscillation.� Since the angle-of-attack is nearly constant, the G-load (lift vector) will rise and fall in synch with the increases and decreases in the airspeed. The time lag in the rise or fall of the airspeed (and the lift vector) is the main factor that is driving the pitch oscillations.

But it's not quite exactly true that all these dynamics are taking place at a constant angle-of-attack.� For example, as the aircraft flies through the series of "phugoid" pitch oscillations, you may hear the stall horn sound near the top of the each pitch oscillation.� In severe cases, the aircraft may actually stall at the top of a pitch oscillation.

Also, as you allow the elevator to float freely in the airflow, you'll notice that its position changes slightly.� For example, the control yoke will be slightly further aft at the "bottom" of each pitch oscillation (as defined above) than at the "top" of each pitch oscillation (as defined above).� This is because as the flight path curves (as seen in a side view) during the phugoid pitch oscillation, so does the relative wind.� (The concept of the curvature of the relative wind will be explored in more detail in the theory section of this website in the future.)� Assuming for the moment that the elevator is well enough balanced that it floats freely in the airflow (which is not exactly true), the free-floating elevator serves as a crude indicator of the angle of the airflow at the tail.� The reason that the elevator rides higher (and the yoke rides further aft) at the bottom of each pitch oscillation is that at the bottom of each pitch oscillation, the curving relative wind tends to have more of an upward component at the tail of the aircraft, which raises the elevator.� The upward component in the relative wind at the tail of the aircraft also interacts with the fixed portion of the horizontal tail in a way that tends to kick the nose down a few degrees, decreasing the wing's angle-of-attack. The reason that the elevator rides lower (and the yoke rides further forward) at the top of each pitch oscillation is that at the top of each pitch oscillation, the curving relative wind tends to have more of a downward component at the tail of the aircraft, which lowers the elevator.� The downward component in the relative wind at the tail of the aircraft also interacts with the fixed portion of the horizontal tail in a way that tends to kick the nose up a few degrees, increasing the wing's angle-of-attack (and hence the stall horn may sound at the top of each pitch oscillation).

Don't confuse yourself by thinking that for a given trim setting, if the control yoke floats further aft, this should increase the wing's angle-of-attack.� In hands-off flight with a given trim setting, the elevator serves more as an indicator of the direction of the airflow than as an active control surface. When the yoke moves aft, this shows that the elevator is riding higher, which shows that the tail is experiencing more of an upward relative wind, which will kick the nose down and decrease the wing's angle-of-attack.

As you explore the pitch "phugoid" oscillations using the techniques described in this article, the difference that you'll see between the position of the control yoke near the top of each pitch oscillation and the position of the control yoke near the bottom of each pitch oscillation will be on the order of 1 to 1.5 centimeters in a Cessna 152.� Wiggle the control yoke forward and aft by 1 to 1.5 centimeters while looking over your shoulder at the movement of the elevator, to get a feeling for the small magnitude of the change in the angle of the airflow over the tail created by the curvature of the relative wind in the pitch axis during the pitch "phugoid" oscillation.

3) Flying without using the control yoke or control stick -- exploring relationships between yaw and roll, and between roll and pitch

Note: central to this discussion are the assumptions that the stall warning horn always sounds at one particular angle-of-attack, and that the stall always occurs at one particular angle-of-attack.

Trim the aircraft for flight at a given airspeed and RPM.� Don't worry about whether or not the altitude is remaining constant.� 70 KIAS and 2200 to 2400 rpm works well in a Cessna 152.� Fly for half an hour or so without touching the control yoke.� Steer the aircraft with the rudder.� Practicing rolling from a 30-degree bank in one direction through wings-level to a 30-degree bank in the other direction.�

You'll quickly get a feel for the way that the rudder creates a roll torque: this is the "positive coupling between slip (yaw) and roll" that is created by the slight dihedral in the wing, and by the high-wing configuration.�

You'll also see that rate of change of the aircraft's pitch attitude is strongly related to the rate of change of the bank angle--whenever you roll the aircraft too quickly from a bank toward wings-level, the nose will rise abruptly (which in the most extreme cases will create the risk of a tailslide or a stall).� And then the rest of the "phugoid oscillation" will follow--the nose will then fall steeply and then the aircraft will go through several more pitch oscillations before coming into equilibrium.� And whenever you roll the aircraft too quickly from wings-level into a bank, the nose will fall abruptly.� And then the rest of the "phugoid oscillation" will follow--the nose will rise again, and then the aircraft will go through several more pitch oscillations before coming into equilibrium.� Whenever the aircraft's nose is starting to rise too high, you can bring it back down by increasing the bank angle, and whenever the aircraft's nose is starting to fall too low, you can bring it back up by decreasing the bank angle.

Here is a nice illustration of a "phugoidal oscillation" in the pitch axis from John S. Denker's excellent "See How It Flies" website.

To avoid extreme pitch attitudes while rolling from a 30-degree bank in one direction to a 30-degree bank in the other direction, you'll find that it works much better to use a very gentle rudder input, producing a very slow roll rate, than to use an aggressive rudder input, producing a high roll rate.

To a very loose approximation all these dynamics are happening at a constant angle-of-attack--the fundamental reason that the nose rises quickly as the aircraft is briskly rolled toward a shallower bank angle is that the flight path curves rapidly upward.� The fundamental reason that the flight path curves rapidly upward is that the lift vector is larger than it "should" be for the actual bank angle at any given moment.� The fundamental reason that the lift vector is larger than it "should" be for the bank angle at any given moment is that the bank angle has changed rapidly enough the that excess airspeed retained from the earlier, higher bank angle has not yet had time to bleed away--the aircraft is not in an equilibrium state.� Likewise, the fundamental reason that the nose drops quickly as the aircraft is briskly rolled toward a steeper bank angle is that the flight path curves rapidly downward.� The fundamental reason that the flight path curves rapidly downward is that the lift vector is smaller than it "should" be for the actual bank angle at any given moment.� The fundamental reason that the lift vector is smaller than it "should" be for the bank angle at any given moment is that the bank angle has changed rapidly enough the that airspeed retained from the earlier, shallower bank angle has not yet had time to increase--the aircraft is not in an equilibrium state.� If we were using the control yoke in a normal way, we would avoid these dynamics by constantly adjusting the angle-of-attack to keep the aircraft in equilibrium or near equilibrium.� (Hang glider pilots, who have somewhat limited pitch control in comparison to "conventional" aircraft, are well aware that increasing the bank angle helps to bring the nose down, and that a rapid roll from a steeply-banked high-speed turn to wings-level flight will cause the nose to rise dramatically.)

If we limit ourselves to slow, gradual changes in bank angle, then the airspeed will have plenty of time to bleed away or increase as necessary, and the aircraft will remain very nearly in an equilibrium state. The nose will always be in very nearly the "right" pitch attitude for the bank angle. We'll still see a significant drop of the nose (and an increase in airspeed) whenever we increase the bank angle, and we'll still see a significant rise of the nose (and a decrease in airspeed) whenever we decrease the angle, but whenever we freeze the bank angle the aircraft's pitch attitude and airspeed will stay nearly constant. We won't see the "excessive" changes in pitch attitude and airspeed, plus the subsequent pitch phugoid oscillations which continue even after the bank angle has been frozen, that we see when make more rapid changes in bank angle without any compensating pitch inputs.

Let's return to the experiments described in this section, where the wing's angle-of-attack is kept nearly constant, but the airspeed rises and falls, which also causes the wing's lift vector to increase and decrease in magnitude.� If you are flying with a G-meter (such as this home-made version) you can see these "anomalies" in the lift vector.� The G-load is just the mirror image of the wing's lift vector.� As you roll quickly from a bank to wings-level, the G-load will initially remain raised significantly above 1 G.� As you roll quickly from wings-level to a bank, the G-load will initially remain near 1 G.� Since the angle-of-attack is nearly constant, the G-load (lift vector) will rise and fall in synch with the increases and decreases in the airspeed. The time lag in the rise or fall of the airspeed (and the lift vector) is the main factor that is driving the pitch oscillations.

But it's not quite exactly true that all these dynamics are taking place at a constant angle-of-attack.� For example, as the aircraft flies through a series of "phugoid" pitch oscillations, you may hear the stall horn sound near the top of the each oscillation.�

As you allow the elevator to float freely in the airflow, you'll notice that its position changes slightly.� For example, the control yoke will be slightly further aft at the "bottom" of each pitch oscillation than at the "top" of each pitch oscillation.� This is because as the flight path curves (as seen in a side view) during the phugoid pitch oscillation, so does the relative wind.� (The concept of the curvature of the relative wind will be explored in more detail in the theory section of this website in the future.)� Assuming for the moment that the elevator is well enough balanced that it floats freely in the airflow (which is not exactly true), the free-floating elevator serves as a crude indicator of the angle of the airflow at the tail.� The reason that the elevator rides higher (and the yoke rides further aft) at the bottom of each pitch oscillation is that at the bottom of each pitch oscillation, the curving relative wind tends to have more of an upward component at the tail of the aircraft, which raises the elevator.� The upward component in the relative wind at the tail of the aircraft also interacts with the fixed portion of the horizontal tail in a way that tends to kick the nose down a few degrees, decreasing the wing's angle-of-attack. The reason that the elevator rides lower (and the yoke rides further forward) at the top of each pitch oscillation is that at the top of each pitch oscillation, the curving relative wind tends to have more of a downward component at the tail of the aircraft, which lowers the elevator.� The downward component in the relative wind at the tail of the aircraft also interacts with the fixed portion of the horizontal tail in a way that tends to kick the nose up a few degrees, increasing the wing's angle-of-attack (and hence the stall horn may sound at the top of each pitch oscillation).

When the aircraft's pitch attitude is stable, you'll notice that the elevator rides slightly higher (and the yoke rides further aft) when the aircraft is banked than when the aircraft is wings-level.� This is because a turn involves a curvature in the flight path in the pitch dimension, especially at steep bank angles.� As the flight path curves during the turn, so does the relative wind.� (Again, the concept of the curvature of the relative wind will be explored in more detail in the theory section of this website in the future.)� Again, assuming for the moment that the elevator is well enough balanced that it floats freely in the airflow (which is not exactly true), the free-floating elevator serves as a crude indicator of the angle of the airflow at the tail.� The reason that the elevator rides higher (and the yoke rides further aft) when the aircraft is banked than when the aircraft is wings-level is that when the aircraft is banked, the curving relative wind tends to have more of an upward component at the tail of the aircraft.� This kicks the nose down, decreasing the wing's angle-of-attack.

The difference in the position where the control yoke tends to "float" during rudder-only flight when the aircraft is banked at 30 degrees, and when the aircraft is wings-level, is only on the order of 1 centimeter in a Cessna 152.� At a 45-degree bank angle the aft position of the control yoke becomes slightly more noticeable. Wiggle the control yoke forward and aft by 1 to 1.5 centimeters while looking over your shoulder at the movement of the elevator, to get a feeling for the small magnitude of the change in the angle of the airflow over the tail created by the curvature of the relative wind in the pitch axis during a turn.� In an aircraft that flies at lower airspeeds, such as an ultralight airplane or hang glider, the curvature in the relative wind during a turn is much more pronounced, meaning that a strong nose-up pitch input would be required to produce a given angle-of-attack (including the stall angle-of-attack) in turn.� In a slow, efficient turn in a sailplane, the control stick is usually quite far aft, and in a slow efficient turn in a hang glider, the control bar is usually quite far forward (which is equivalent to the control stick or yoke being quite far aft).

Now, while continuing to fly with the rudders only, change the trim of the aircraft.� In wings-level flight, slowly apply a nose-up trim input until the stall warning sounds.�� When you are confident that the aircraft has stabilized at an airspeed where the stall horn is sounding steadily, gently use the rudder to very slowly increase the bank angle, without touching the control yoke.� The stall horn will stop.� Again, in a turn, the curvature in the relative wind tends to kick the tail up and the nose down, decreasing the wing's angle-of-attack.� Now hold the aircraft in a 30-degree bank angle, and trim the aircraft so that the stall horn is just barely not sounding.� Use the rudder to very slowly roll the aircraft to wings-level flight, and the stall warning horn will sound again, and you may even get a full-fledged stall.� Do these experiments using both left and right banks, to guard against any asymmetries caused by the position of the stall horn inlet on the right wing.

In wings-level flight, while continuing to fly with the rudders only, slowly increase the power setting and notice how the nose rises.� This is largely due to the change in the direction of the flight path, but also (in the case of most aircraft) reflects an increase in the wing's angle-of-attack.� (This may only be true in cases where the tail is trimmed to produce a downforce--as the power setting is increased, the increased propwash over the tail increases the downforce. �Most aircraft are usually trimmed in such a way that the tail produces a downforce).� Now reduce the power to idle.� Trim the aircraft to an airspeed where the stall horn is just barely not sounding.� Open the throttle very slowly and listen as the stall horn begins to sound.� By the time you get to full power, the aircraft may have entered a full stall.� Recover!�

As you gain experience in flying with the rudder only, do you think that you could land the aircraft without using the control yoke, in an emergency?� PS bear in mind that in a situation where the elevator is jammed rather than freely floating, the elevator trim wheel acts in the reverse direction as usual, because the trim tab acts as a miniature elevator rather than a trim tab.

4) Flying with a fixed elevator position� -- creating a pitch "phugoid" oscillation

This experiment replicates experiment 2 ("Flying without using the control yoke or control stick -- creating a pitch "phugoid" oscillation") but in a way that allows you to use the ailerons an addition to the rudder for roll inputs, while holding the elevator in a fixed position.

Note: central to this discussion are the assumptions that the stall warning horn always sounds at one particular angle-of-attack, and that the stall always occurs at one particular angle-of-attack.

The best way to carry out these experiments is to use the same special tool that we described in the previous section--a padded, modified vise grip that will allow you to hold the control yoke in a completely fixed position in the pitch axis. (Click here for photos and a detailed description of this tool.) You'll gently clamp this tool to the control yoke torque tube at the point where the control yoke torque tube enters the control panel, placing the vice grips on the aft (tail-ward or pilot-facing) side of the control panel. Apply light pressure on the control yoke to hold the vise grips in contact with the control panel, and voila--you've frozen the control yoke in a fixed position in the pitch axis, while still allowing yourself normal roll control with the ailerons. (With some aircraft, some care may be needed to find an orientation of the vise grips tool where there is no interference with protruding knobs or other items on the control panel.) Of course you'll only use a light clamping pressure on the vise grip tool so that there is no risk of stressing or distorting the control yoke torque tube. This light clamping pressure will also allow you to release the vice grip very easily.

However, you can also carry out these experiments simply by reaching forward with your free hand and "pinching" the control yoke where it enters the panel, so that you do not allow the control yoke to slide forward. Again, light forward pressure on the control yoke with the other hand will hold the control yoke in a fixed position in the pitch axis, while affording full freedom of motion in the roll axis. One problem with this method is that it may be difficult to hold the control yoke torque tube firmly enough to prevent it from sliding when pitch pressures get heavy.

Before we start, here is a nice illustration of a "phugoidal oscillation" in the pitch axis from John S. Denker's excellent "See How It Flies" website.

Trim the aircraft for hands-off flight at 55 KIAS at roughly 2250 RPM's.� Don't worry about whether or not the altitude is remaining constant. .� Freeze the control yoke in a fixed position in the pitch axis as described above.� Then very slowly increase the bank angle, until you see 85 KIAS.� When you get the airspeed completely stabilized, roll quickly back to wings-level flight using the ailerons and rudder together in an aggressive, coordinated fashion while continuing to hold the elevator in a fixed position.� Enjoy the pitch "phugoid" oscillation that ensues.� If your aircraft is "dynamically stable" as well as "dynamically stable" in its current configuration, the pitch oscillation will slowly damp out.� Before that happens, you'll see some rather interesting nose-high pitch attitudes.� Bear in mind however that as the aircraft floats over the top of the each pitch oscillation, the airspeed can safely drop significantly below the normal 1-G stall speed, since when the flight path is curving downward, the wing is generating less than 1 "G" of lift.� However there is still a real possibility of stalling at the top of a severe pitch oscillation--more on this in a bit.

Now repeat the above procedure using the original trim and power settings, but increasing the starting airspeed from 85 KIAS to 90 KIAS, and then repeat at 95 KIAS, etc.� Again, be sure that the aircraft is in stabilized flight at a constant airspeed before you roll quickly back to wings-level.� At some point the nose-up part of the ensuing pitch "phugoid" oscillation will become too severe and you'll have to intervene to prevent a stall or tailslide.� You can do this either by freeing the control yoke and pushing the control yoke forward, or simply by increasing the bank angle, using the ailerons and rudder together in a "coordinated" fashion..

To a very loose approximation, after the aircraft is quickly rolled back to wings-level, the ensuing dynamics all take place at a constant angle-of-attack.� The fundamental reason that the nose rises well above a level pitch attitude when the aircraft is quickly rolled back to wings-level is that the flight path curves rapidly upward.� The fundamental reason that the flight path curves rapidly upward is that the lift vector is larger than it "should" be.� The fundamental reason that the lift vector is larger than it "should" be is that the aircraft has been quickly returned to wings-level without allowing time for the excess airspeed (e.g. 85 KIAS minus 55 KIAS equals 30 KIAS excess airspeed) to bleed away--the aircraft is not in an equilibrium state.� Likewise, throughout the rest of the pitch "phugoid" oscillation that follows, the airspeed is constantly undershooting and then overshooting its "appropriate" value in relation to the trim angle-of-attack, before eventually settling down to the "appropriate" value.

Here's why the angle-of-attack is higher at the top of each of the pitch oscillations than at the bottom of each of the pitch oscillations, even when the elevator is held in a fixed position: as the flight path curves (as seen in a side view) during the phugoid pitch oscillation, so does the relative wind.� (The concept of the curvature of the relative wind will be explored in more detail in the theory section of this website in the future.)� At the bottom of each pitch oscillation, the curving relative wind tends to have more of an upward component at the tail of the aircraft, which interacts with the horizontal tail in a way that tends to kick the nose down a few degrees, decreasing the wing's angle-of-attack.� At the top of each pitch oscillation, the curving relative wind tends to have more of a downward component at the tail of the aircraft, which interacts with the horizontal tail in a way that tends to kick the nose up a few degrees, increasing the wing's angle-of-attack (and hence the stall horn may sound at the top of each pitch oscillation).

5) Flying with a fixed elevator position -- exploring relationships between roll and pitch

This experiment replicates much of experiment 3 ("Flying without using the control yoke or control stick -- exploring relationships between yaw and roll, and between roll and pitch") but in a way that allows you to use the ailerons an addition to the rudder for roll inputs, while holding the elevator in a fixed position.

Note: central to this discussion are the assumptions that the stall warning horn always sounds at one particular angle-of-attack, and that the stall always occurs at one particular angle-of-attack.

The best way to carry out these experiments is to use a special tool--a padded, modified vise grip that will allow you to hold the control yoke in a completely fixed position in the pitch axis. (Click here for photos and a detailed description of this tool.) You'll gently clamp this tool to the control yoke torque tube at the point where the control yoke torque tube enters the control panel, placing the vice grips on the aft (tail-ward or pilot-facing) side of the control panel. Apply light pressure on the control yoke to hold the vise grips in contact with the control panel, and voila--you've frozen the control yoke in a fixed position in the pitch axis, while still allowing yourself normal roll control with the ailerons. (With some aircraft, some care may be needed to find an orientation of the vise grips tool where there is no interference with protruding knobs or other items on the control panel.) Of course you'll only use a light clamping pressure on the vise grip tool so that there is no risk of stressing or distorting the control yoke torque tube. This light clamping pressure will also allow you to release the vice grip very easily.

Trim the aircraft for flight at a given airspeed and RPM.� Don't worry about whether or not the altitude is remaining constant.� 70 KIAS and 2200 to 2400 rpm may work well in a Cessna 152.� Freeze the control yoke in a fixed position in the pitch axis as described above.� Practicing rolling from a 45-degree bank in one direction through wings-level to a 45-degree bank in the other direction, using the ailerons and rudder in a "coordinated" manner.

You'll quickly see that the rate of change of the aircraft's pitch attitude is strongly related to the rate of change of the bank angle--whenever you roll the aircraft too quickly from a bank toward wings-level, the nose will rise abruptly (which in the most extreme cases will create the risk of a tailslide or a stall).� And then the rest of the "phugoid oscillation" will follow--the nose will then fall steeply and then the aircraft will go through several more pitch oscillations before coming into equilibrium.� And whenever you roll the aircraft too quickly from wings-level into a bank, the nose will fall abruptly.� And then the rest of the "phugoid oscillation" will follow--the nose will rise again, and then the aircraft will go through several more pitch oscillations before coming into equilibrium.� Whenever the aircraft's nose is starting to rise too high, you can bring it back down by increasing the bank angle, and whenever the aircraft's nose is starting to fall too low, you can bring it back up by decreasing the bank angle.

Here is a nice illustration of a "phugoidal oscillation" in the pitch axis from John S. Denker's excellent "See How It Flies" website.

To avoid extreme pitch attitudes while rolling from a 45-degree bank in one direction to a 45-degree bank in the other direction, you'll find that it works much better to use a very gentle roll rate rather than a rapid roll rate.

To a very loose approximation all these dynamics are happening at a constant angle-of-attack--the fundamental reason that the nose rises quickly as the aircraft is briskly rolled toward a shallower bank angle is that the flight path curves rapidly upward.� The fundamental reason that the flight path curves rapidly upward is that the lift vector is larger than it "should" be for the actual bank angle at any given moment.� The fundamental reason that the lift vector is larger than it "should" be for the bank angle at any given moment is that the bank angle has changed rapidly enough the that excess airspeed retained from the earlier, higher bank angle has not yet had time to bleed away--the aircraft is not in an equilibrium state.� Likewise, the fundamental reason that the nose drops quickly as the aircraft is briskly rolled toward a steeper bank angle is that the flight path curves rapidly downward.� The fundamental reason that the flight path curves rapidly downward is that the lift vector is smaller than it "should" be for the actual bank angle at any given moment.� The fundamental reason that the lift vector is smaller than it "should" be for the bank angle at any given moment is that the bank angle has changed rapidly enough the that airspeed retained from the earlier, shallower bank angle has not yet had time to increase--the aircraft is not in an equilibrium state.� If we were using the control yoke to make pitch inputs in the normal fashion, we would avoid these dynamics by constantly adjusting the angle-of-attack to keep the aircraft in equilibrium or near equilibrium.� (Hang glider pilots, who have somewhat limited pitch control in comparison to "conventional" aircraft, are well aware that increasing the bank angle helps to bring the nose down, and that a rapid roll from a steeply-banked high-speed turn to wings-level flight will cause the nose to rise dramatically.)

If you are flying with a G-meter (such as this home-made version) you can see these "anomalies" in the lift vector.� The G-load is just the mirror image of the wing's lift vector.� As you roll quickly from a bank to wings-level, the G-load will initially remain raised significantly above 1 G.� As you roll quickly from wings-level into a bank, the G-load will initially remain near 1 G.� Since the angle-of-attack is nearly constant, the G-load (lift vector) will rise and fall in synch with the increases and decreases in the airspeed. The time lag in the rise or fall of the airspeed (and the lift vector) is the main factor that is driving the pitch oscillations.

Now free the control yoke and change the trim of the aircraft.� In wings-level flight, slowly apply a nose-up trim input until the stall warning sounds.� When you are confident that the aircraft has stabilized at an airspeed where the stall horn is sounding steadily, again freeze the control yoke in a fixed position in the pitch axis as described above.�� Now gently initiate a very slow roll to a steeper bank angle, using the ailerons and rudder in a coordinated manner.� As the bank angle increases, the stall warning horn will stop. Now free the control yoke again and hold the aircraft in a 30-degree bank angle, and trim the aircraft so that the stall horn is just barely not sounding.� Again, freeze the control yoke in a fixed position in the pitch axis as described above.� Very slowly, roll the aircraft back to wings-level flight, and the stall warning horn will sound again, and you may even get a full-fledged stall.� Do these experiments using both left and right banks, to guard against any asymmetries caused by the position of the stall horn inlet on the right wing.

Here's why the angle-of-attack is lower in a bank (turn) than in wings-level flight, for a given position of the elevator: a turn involves a curvature in the flight path in the pitch dimension, especially at steep bank angles.� As the flight path curves during the turn, so does the relative wind.� (Again, the concept of the curvature of the relative wind will be explored in more detail in the theory section of this website in the future.)� When the aircraft is banked, the curving relative wind tends to have more of an upward component at the tail of the aircraft.� This kicks the nose down, decreasing the wing's angle-of-attack.

And here's why the angle-of-attack is higher at the top of each of the pitch oscillations than at the bottom of each of the pitch oscillations, even when the elevator is held in a fixed position: as the flight path curves (as seen in a side view) during the phugoid pitch oscillation, so does the relative wind.� (The concept of the curvature of the relative wind will be explored in more detail in the theory section of this website in the future.)� At the bottom of each pitch oscillation, the curving relative wind tends to have more of an upward component at the tail of the aircraft, which interacts with the horizontal tail in a way that tends to kick the nose down a few degrees, decreasing the wing's angle-of-attack.� At the top of each pitch oscillation, the curving relative wind tends to have more of a downward component at the tail of the aircraft, which interacts with the horizontal tail in a way that tends to kick the nose up a few degrees, increasing the wing's angle-of-attack (and hence the stall horn may sound at the top of each pitch oscillation).

To quantify the curvature in the relative wind in a turn, you can trim the aircraft for wings-level flight with the stall horn just barely sounding, and then freeze the control yoke in a fixed position in the pitch axis as described above.� (Note that you still have the freedom to move the control yoke further aft if needed.)� Then very slowly roll into a 45-degree or 60-degree-banked turn, continuing to hold the control yoke in a fixed position in the pitch axis.� The stall horn will stop.� After the airspeed has stabilized, very slowly ease the control yoke aft until the stall horn begins to sound again.� When you are confident that the airspeed has stabilized and the stall horn is just barely sounding, note the distance by which you've moved the control yoke aft from the original, "fixed" position.� You'll see a centimeter or two of torque tube exposed between the vice grips (or your fingers) and the panel.

Once you've noted this distance, look over your shoulder at the elevator as you wiggle the control yoke fore and aft by this distance (e.g. a few centimeters).� The slight visible change in the elevator's position will give you a sense of the small change in the angle of the relative wind at the tail created by the curving flight path.� In an aircraft that flies at lower airspeeds, such as an ultralight airplane or hang glider, the curvature in the relative wind during a turn is much more pronounced, meaning that a strong nose-up pitch input would be required to produce a given angle-of-attack (including the stall angle-of-attack) in turn.� In a slow, efficient turn in a sailplane, the control stick is usually quite far aft, and in a slow efficient turn in a hang glider, the control bar is usually quite far forward (which is equivalent to the control stick or yoke being quite far aft).

As you gain experience in flying without pitch inputs, do you think that you could land the aircraft without using the elevator in an emergency?� PS bear in mind that in a situation where the elevator is jammed rather than freely floating, the elevator trim wheel acts in the reverse direction as usual, because the trim tab acts as a miniature elevator rather than a trim tab.

6) Flying without using the rudder -- looking at adverse yaw (sideslip)

Note: this experiment can be carried out in nearly any type of aileron-controlled aircraft

Fly the aircraft with your feet off the rudder pedals. Note that abrupt roll inputs create a lot of adverse yaw (sideslip)--the slip-skid ball moves to the side as the nose yaws in the "wrong" direction. Note that for a given starting airspeed and a given roll rate, you see about the same amount of sideslip regardless of whether you make a normal nose-up pitch "coordination" to keep the airspeed or pitch attitude or altitude roughly constant as you roll from wings-level into a turn, or you make your roll input with a single finger pushing down on the control yoke (or sideways on the control stick) in a way that does not exert any pitch force on the yoke (or stick), or if you make your roll input in concert with a nose-down pitch input that makes the airspeed rise rapidly. In other words, the sideslip that we see as we roll briskly into a turn without using the rudder, is caused by adverse yaw and has nothing to do with a "lack of lift" due to failure to make the correct pitch "coordination" inputs.

To explore this further in an airplane with a control yoke, use the special tool described above to limit the forward travel of the control yoke, or simply limit the forward travel of the control yoke by using your free hand to pinch the control yoke torque tube at the point where it enters the instrument panel. Apply gentle forward pressure on the yoke to hold it firmly against this artificial stop. While keeping the yoke "frozen" in the fore-and-aft direction in this manner, and keeping your feet off the rudder pedals, make an abrupt roll input, and note how much adverse yaw (sideslip) is indicated by the slip-skid ball. Then, starting in wings-level-flight with the control yoke held firmly against the artificial stop, make the same abrupt roll input but bring the control yoke aft to hold the airspeed or pitch attitude or altitude approximately constant as the bank angle increases. Watch the slip-skid ball and note how the amount of adverse yaw (sideslip) is approximately the same as was seen when the yoke was kept "frozen" in the fore-and-aft direction as the bank angle changed. Again, this shows that the sideslip we see as we roll briskly into a turn without using the rudder, is caused by adverse yaw and has nothing to do with a "lack of lift" due to failure to make the correct pitch "coordination" inputs..

7) Exploring yaw oscillations

Note: this experiment can be carried out in any aircraft with rudder pedals

Slowly apply full deflection with one rudder pedal, then abruptly release the pedal and keep both feet off the rudder pedals.� Watch the yaw (sideslip) oscillations that ensue--the nose will go through several small swings from side to side before coming to rest.� These yaw oscillations show that the aircraft's yaw rotational inertia is significant--if it were not, then when you released the rudder pedal, the nose would instantly yaw to a fixed position and then stay there.�

For a more dramatic demonstration of the importance of yaw rotational inertia, "walk" the rudder back and forth to "pump up" a strong left-and-right yawing motion.� (You'll be creating a larger yaw (slip) angle than the aircraft experiences in almost any other situation, so use some caution not to put too much of a load on the vertical tail -- keep the airspeed fairly low, and don't make the yawing motion get too extreme.)� The fact that you can "pump up" the oscillation to a much large yaw (slip) angle than you could obtain simply by maintaining steady pressure on one rudder pedal demonstrates the importance of yaw rotational inertia.� Then, as the yaw (slip) angle is peaking during one of the oscillations, take both feet off the rudder pedals and notice how the nose will swing back and forth through several more yaw oscillation cycles before coming to rest.

Note how the yaw oscillation cycles take place on a much shorter time scale than do the pitch "phugoidal" oscillations that we explored earlier. If you trim the aircraft for hands-off flight and use the rudder to aggressively roll the aircraft from wings-level to a 30 or 45 degree bank, any yaw oscillations triggered by the aggressive rudder input will have damped out long before the aircraft reaches the bottom of the first of the pitch "phugoidal" oscillation cycles that will be triggered by the rapid change in bank angle. Likewise when you take your feet off the rudder and use the yoke to aggressively roll the aircraft from wings-level to a 45 degree bank, the adverse yaw from the rolling motion, plus any subsequent yaw oscillations, will all have disappeared long before the aircraft reaches the bottom of the first of the pitch "phugoidal" oscillation cycles that will be triggered by the rapid change in bank angle.

8) Direction of tail's lift

Here is an interesting excerpt from section 6.14 of John S. Denker's superb "See How It Flies" website:

I took a Cessna 172 Skyhawk and put a couple of large pilots in the front seats, with no luggage and no other passengers. That meant the center of mass was right at the front of the envelope, so the tail had to produce considerable negative lift in order to maintain equilibrium. There was lots and lots of angle of attack stability.

I took the same Skyhawk and put a small pilot in the front seat, a moderately large mad scientist in the back seat, and 120 pounds of luggage in the rear cargo area. That put the center of mass right at the rear of the envelope, so the tail had to produce considerable positive lift in order to maintain equilibrium. The airplane still had plenty of stability. (As far as the pilot could tell, it was just as stable as it ever was.)

The easiest way to determine whether the tail lift is positive or negative is to observe the direction of motion of the tip vortices, as discussed in section 3.12. To observe the vortices, I attached a streamer of yarn, about half a yard long, to each tip of the horizontal tail, at the trailing edge.

By the way, in the discussion of the curvature of the flight path and relative wind in sections 1 through 6, I didn't mean to imply that the horizontal tail always experiences a positive angle-of-attack when the flight path is curving in the "upward" direction in the pitch axis (for example in a turn, or at the bottom of a pitch "phugoid" oscillation cycle). The upward curvature in the flight path and relative wind could cause the angle-of-attack experienced by the tail to be more positive than it would be if the flight path and relative wind were linear, or could cause the angle-of-attack experienced by the tail to be less negative than it would be if the flight path and relative wind were linear. In either case, the wing will fly at a slightly lower angle-of-attack than it would if the flight path and relative wind were linear. And in either case, a free-floating elevator will ride slightly higher, and a free-floating control yoke or stick will ride slightly further aft, than if the flight path and relative wind were linear.

9) "Feeling" the wind direction in flight?

Note: this experiment can be carried out in any aircraft with suitable instrumentation

If you ever meet a pilot who is convinced that an aircraft can somehow "feel" the direction of a smooth steady wind in flight, even high above the surface of the ground, subject to them to this test. Take them flying under an overcast, so there will be no shadows in the cockpit. Cover up the compass and turn off the navigation radio and GPS. Have them don a blind flying hood. Have them shut their eyes while you perform several steep turns and then change the setting of the heading gyro by 90 degrees or so. Don't tell them that you are re-setting the heading gyro! At this point they should have no way to guess which way the external, meteorological wind is blowing, in relation to the heading gyro. Now have them open their eyes, give them controls, and as they fly "under the hood" with reference to the instruments, tell them to use the "feel" of the controls, and the way the aircraft tends to climb or dive or gain airspeed or lose airspeed during a series of slow 360-degree turns or any other maneuver, to figure out which way the wind is blowing, without benefit of navigation instruments or outside references. They will fail, of course. Repeat the test several times. At the end of the experiments, use a GPS to find the true direction of the wind (i.e. find the heading that yields the lowest groundspeed, as you fly at a constant airspeed.)

To further reduce the possibility of accidental "cheating", carry out the test above an undercast (between layers), and/or at night!

Along the same lines, although the edges of thermal updrafts can be easily "felt" by any pilot, widespread smooth lift cannot be "felt" in any way and has no effect on the way that an aircraft handles. Unfortunately, conditions that allow an actual in-flight test of these principles are very rare. Of course, if a pilot is flying a powered airplane by reference to the altimeter, he'll notice that he can sustain a higher airspeed when there is an updraft than when there is not, because the updraft allows the pilot to place the wing at a lower angle-of-attack and still maintain altitude. However, in areas of patchy lift and sink, if it is not essential that the aircraft maintain a constant altitude, the most efficient practice is to apply aft pressure on the control yoke to slow down slightly in the lift, and to apply forward pressure on the control yoke to speed up slightly in the sink. Over the long run, this will allow a powered aircraft to complete a cross-country flight in a given amount of time with the least fuel burn, or with a given fuel burn in the least amount of time. (If it is essential that the aircraft maintain a constant altitude, some theoretical benefits along these same lines could be obtained by decreasing power and airspeed in the lift, and increasing power and airspeed in the sink, but few pilots would want to bother with these power changes.)