Airplanes - Physics for Game Programmers - page 295

Figure 10-22. The pitch, roll, and yaw rotations relative to the center of gravity.

Pitch, roll, and yaw are relative to the center of gravity of the airplane. For game simulation
purposes, it is usually valuable to define the airplane orientation relative to a fixed point on the
ground in terms of climb, heading, and roll angles. The climb angle was previously introduced
in Figure 10-20. The tangent of the climb angle is equal to the vertical velocity component, v z ,
divided by the horizontal velocity component, v h .

v
v

tan f =

z

(10.31)

h

The horizontal velocity component is equal to the sum of the squares of the x- and y-velocity
components.

2 2

v =+ v v

(10.32)

h x y

As shown in Figure 10-23, the heading angle, q , of the airplane is defined as the orientation
of the velocity vector of the airplane in the x-y plane. The x-axis is assumed to point north and
is at a heading angle of zero.

x

v h

θ

y

Figure 10-23. The heading angle is the orientation of the velocity vector in the x-y plane.