Effects Other Than Constant Gravity and Variable Drag

The basic equations (4.1) or (4.3) for a projectile are essentially restricted to two dimensions. If an OZ axis is introduced orthogonal to the OX and OY axes then the absence of forces in the z-direction combined with the initial conditions z = dz/dt = 0 when t = 0 ensures that z ≡ 0 for all t. However, any non-symmetrical variation (such as spin or yaw) in the z-direction will produce a drift effect on the projectile in this lateral direction.

As soon as spin is imparted to a projectile to reduce yaw and impose stability of flight there are many effects such as cross-forces and cross-torques which have to be included in the equations of motion (see Chapter 7). Even in the absence of spin the non-symmetrical shape of some projectiles or the yawing of a symmetrical projectile will give rise to a cross-force known as lift.

The spinning of the earth also requires the inclusion of pseudo-forces (Coriolis and centrifugal) in the governing equation, particularly when the projectile has a very long flight path. For these problems gravity variations due to altitude and the non-spherical shape of the earth may also be important.