Longitudinal Derivatives

The normal force is given by Z = 1/2 pU[1] [2]SCz. Here, the area S is the maximum body cross-section reference area. Cz is the normal force coefficient and is a function of AOA (called incidence in pitch) for a given altitude and Mach number.

Za is defined as

— pU2SCZ, 2m Za

or

Zw = 2m pUSCza

The actual values of the normal force coefficient depend on the shape of the missile and the reference area S. The normal force coefficient for a missile is expressed in the literature as [5]

CN = CN0 + CNaa + CN, 2V + CNa( 2V ) + (4.38)

Here, V is the resultant velocity or the cruising speed of the missile. The parameter c is the total body length of the missile. In the case of the missile N denotes the normal force unlike for aircraft where Z denotes the vertical force. We use Z for the normal force uniformly. The meanings of the derivatives do not change.

Mw and Mq have the same significance as in the case of aircraft aerodynamics. Md will have an opposite sign for a missile with canard control surface (in the front). Mw will also change sign in case of an unstable missile configuration. Zd is related to Md in the usual manner and both are elevator control surface effectiveness derivatives. The derivative Zq is of no practical significance and hence neglected in missile aerodynamics.

1.4.1 Lateral-Directional Derivatives