Aerodynamics:

Spotting Moments Acting on Airplanes

Roll Moments

The airplane to the left flies just like the space shuttle in orbit. As such there is no friction and more importantly there are no air forces on the airplane to stop its motions.

While this situation is not what we normally experience it is nevertheless an opportunity for us to see clearly when moments (in this case roll moments) exist and when they don't.

Just like the space shuttle this airplane is controlled with two "thruster jets" Use the left and right arrow keys on your keyboard to start the airplane rolling. Hold down the shift key while using the arrow keys to create a larger rolling moment.

You will find it very difficult to control the airplane. Try rolling to a new bank angle and then stopping there. (not easy is it?)

You should notice that:

If you hold down an arrow key the rate of rotation keeps increasing and increasing.
When you release the button the moment becomes ZERO, but the rotation continues at a steady rate.

Real airplanes fly in air like the one to the left. When an airplane rolls in the air the wind strikes the wings at different angles of attack. The down going wing has an increased angle of attack, and the up going wing has a reduced angle of attack. This creates a moment in the opposite direction to the roll. The faster the airplane rolls the greater that moment. The green vectors represent this counter force. The red vectors represent the force created by deflected ailerons.

Use the left and right arrow keys. Holding down the shift key is like turning in a greater amount of aileron.

In this case the roll rate increases until the moment created by the ailerons is balanced by the counter force. From then on the roll rate is constant. If you release the ailerons their moment disappears instantly but the counter force still exists. That causes the roll rate to slow and stop.

The simulation has a slider that allows you to change the amount of damping. Roll damping depends on the density of the air, speed of the airplane, and the wingspan. We will explore this in more detail in the chapter on control. For now concentrate on noting when roll moments exist.

You should notice that if you hold down an arrow key the airplane will roll at .5 degrees per second, once a steady state is reached. At that point the roll moment is zero. If you hold down the shift key the airplane rolls at 5 degrees per second. Again the roll moment becomes zero after a few seconds. In a real airplane the time to reach a steady roll rate is usually less for short wingspan airplanes and more for long wingspan, but also depends on the size of the ailerons and the moment of inertia of the airplane.

NOTE: the two possible roll rates in the movie correspond to small and large aileron inputs by the pilot. In a real airplane the pilot can input an infinite range of aileron input thus getting any roll rate s/he desires.

You will find it easier to see how the counter force builds as roll rate increases if you set the roll damping to low in the simulation. You will of course also find it much easier to control the airplane if the roll damping is high. (Does it make you glad your not a Space Shuttle pilot?)

Pitch Moments

You should now realize that when a moment exists the rate of rotation changes. During a steady rotation, such as a steady roll there is no moment.

The same is true for a steady pitch, as shown to the left.

As long as the rate of pitch change is constant there is no pitching moment.

In this simulation you can grab the airplane in the middle and swing it. When you swing it you create a moment but if you "toss it" the moment stops the second you let go.

The outer airplane shows the flight path the airplane would actually follow. It performs either a loop or an outside loop (nose up or nose down pitch direction.) It is important for you to realize that these are BOTH THE SAME AIRPLANE just viewed from a different perspective. In both cases the pitch moment is zero whenever the pitch rate is constant.

When the moment is zero that does NOT mean that the pilot is applying no force to the control column.

In the simulation to the left use the down arrow key to represent pulling back on the control column (shift key for a harder pull.) If you hold down the arrow key and wait a few moments the pitch rate becomes constant and the pitch moment returns to zero. This corresponds to the pilot holding back on the control column to do a loop. The pilot must apply a force, but the net moment on the airplane, once a steady rate of pitch is established, is ZERO. The moment is zero because the pitch force generated by the tail due to the pilot deflecting the elevator is exactly offset by a counter force (shown in green) due to the tail striking the air at a different angle of attack. One you let go of the control column the pitch force immediately disappears, but the counter force exists as long as the airplane is pitching, therefore it stops the airplane. Once again it is easy to see why people incorrectly are lead to believe that a force is needed to make the airplane change attitude.

To see the forces in the diagram hold down the shift key while pressing up or down arrow. The red vector is caused by you deflecting the elevators. The green vector forms as a result of the rotation causing the air to strike the tail. After holding a key for a few seconds release it. You will see the red vector instantly disappears. The green vector then slows the airplanes rotation, as it does the green vector itself becomes shorter (due to less rotation) and eventually there is no force once the rotation stops. To see this more easily set damping to low.

Yaw Moments

The same analysis as provided above applies to yaw. In other words once an airplane is turning (heading is changing) there is no turning moment. The tail needs to apply a force only to start a turn or to stop it. Usually when we turn an airplane we do so by placing it in a banked attitude. This allows the airplane to turn without any control surfaces needing to be deflected, consequently the pilot can almost let go of the controls and the airplane will turn. This is closer to the situation a physicist would expect of a object that obeys Newton's laws. However, you can make an airplane do a skidding turn by stepping on a rudder pedal. If you do there is still no turning moment once a steady rate of turn is achieved. The situation is just like the pitch situation shown above. The airplane turns only so long as you hold the rudder. The counter force caused by the air striking the fin makes the net force zero. As soon as you take your foot off the rudder the counter force begins to stop the yaw and within a second of two the airplane is once again flying straight.

Summary

Hopefully you now are getting good at telling when there is a moment and when there isn't. You now know that you can't go by whether or not you, the pilot, are having to apply a force to the controls. However, you do no know that when you do have to apply a force to the controls, but there is no moment there must be a counter force. You can learn quite a bit about why airplanes fly the way they do, and why they are designed the way they are, by reflecting on these counter moments. For example try imagining an airplane design that did not develop a counter pitching moment (tip: move the elevators to a different location) if you can do this you will then know why the elevators are usually at the back of an airplane, and have some insight into the consequences of putting them somewhere else. Repeat the same analysis for the other two axis.

We will return to a discussion of the above points in the chapter called stability.

Next Lesson: Conservation of Energy

Aerodynamics:

Definitions

Physics Review

Performance

Misc

Spotting Moments Acting on Airplanes

Roll Moments

Pitch Moments

Yaw Moments

Summary