Airplanes - Physics for Game Programmers - page 307

If you want to try for a more gentle landing experience, decrease the angle of attack and/or
throttle and try to set the plane down with a vertical velocity smaller than -5.0 m/s .

Trim and Stability
The final topics that will be discussed in this chapter are the trim and stability of an airplane.
As you have learned in the previous sections, airplanes are subject to various forces that act
through different locations on the airplane. These forces create moments that can cause unde-
sirable rotational motion of the airplane. If left unchecked, the moments can cause the airplane
to spin out of control. The study of trim and stability is an effort to predict, minimize, and
control the moments experienced by an airplane in flight

Moments
Earlier in the chapter, you learned that lift acts through the center of pressure of the airfoil.
The force of gravity acts through the center of gravity (or c.g.). As shown in Figure 10-25, if the
center of gravity and center of pressure are in different locations, then the opposing forces of
lift and gravity will create a moment that will pitch the airfoil up or down. The “+” symbol in
Figure 10-25 indicates the center of rotation for the moment.

F L

c.g.

+

c.p.

mg

Figure 10-25. Gravitational and lift forces can generate a moment.

The moment generated by an airfoil is characterized by an equation very similar to the
standard lift and drag expressions. The moment, M , is a function of a moment coefficient, C M ;
the air density, r ; the square of the air velocity, v ; the wing wetted area, A ; and the chord length, c .

If you recall, the chord is the distance from the leading edge of the wing to the trailing edge.

1
2

2

MCv = r c

(10.38)

M

Moments are always defined with respect to a center of rotation, the point at which the
moment is applied. A given force will result in a different moment, for example, if the moment
is evaluated at the leading edge than it will be if it is evaluated at the center of gravity. It was
found both experimentally and analytically that if the moment is evaluated at a point approxi-
mately ¼ of the distance from the leading edge to the trailing edge (called the quarter chord
point ) that the moment value is relatively independent of the angle of attack. The point at
which moment is independent of the angle of attack is also known as the aerodynamic center
(or a.c.) of the airfoil.