6 - CORRECTIONS DUE TO OTHER EFFECTS

Summary

“A falling body ought by reason of the earth's diurnal motion to advance eastward and not fall to the west as the vulgar opinion is.”

Sir Isaac Newton (1642–1727)

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.