Forces and Moments

The equations of motion have reduced the solution of aircraft motion from determining the time derivatives of the state variables to determining the resultant forces and moments on the aircraft. The external forces and moments on the aircraft come from four general sources: aerodynamic force, propulsive force, force on the landing gear, and body forces (mostly gravity). The simulator calculates these separately and then adds them together. For example, the force in the x-direction is given by:

X = X_A + X_P + X_G + X_B (39)

There are other minor sources of forces and moments, such as internal damping, but this paper does not consider them.

Of the different types of force, calculation of body forces is the most straightforward. The most important body force in flight simulation is gravity. Gravity acts parallel to the local z-axis. Thus, the components of gravity force along body axes is the component in the local z-direction are:

$$mgC_{31}\ =\ -mg\sin\Theta$$ X_B = (40)

$$mgC_{32}\ =\ mg\cos\Theta\sin\Phi$$ Y_B = (41)

$$mgC_{33}\ =\ mg\cos\Theta\cos\Phi$$ Z_B = (42)

There are no body moments.

Another body force on the airplane is the Coriolis force due to the Earth's rotation. This force is important for high-speed, high-altitude flight, but is not that important for low-altitude, low-speed flight.

Calculation of the other types of force is difficult. The following two sections describe in detail the calculation of these forces.