Stability Derivative Contributions
Each stability derivative is determined by the position, size, shape and orientation of the missile components. In aircraft, the directional stability determines such features as dihedral of the main planes, size of fin and area of tailplane, but the large number of important stability derivatives involved precludes a detailed discussion within this article. The missile is characterised by only three stability derivatives, and hence provides a useful introduction to the more complex aeroplane dynamics.
Consider first, a body at an angle of attack generates a lift force in the opposite direction to the motion of the body. For this reason is always negative.
At low angles of attack, the lift is generated primarily by the wings, fins and the nose region of the body. The total lift acts at a distance ahead of the centre of gravity (it has a negative value in the figure), this, in missile parlance, is the centre of pressure . If the lift acts ahead of the centre of gravity, the yawing moment will be negative, and will tend to increase the angle of attack, increasing both the lift and the moment further. It follows that the centre of pressure must lie aft of the centre of gravity for static stability. is the static margin and must be negative for longitudinal static stability. Alternatively, positive angle of attack must generate positive yawing moment on a statically stable missile, i.e. must be positive. It is common practice to design manoeuvrable missiles with near zero static margin (i.e. neutral static stability).
The need for positive explains why arrows and darts have flights and unguided rockets have fins.
The effect of angular velocity is mainly to decrease the nose lift and increase the tail lift, both of which act in a sense to oppose the rotation. is therefore always negative. There is a contribution from the wing, but since missiles tend to have small static margins (typically less than a calibre), this is usually small. Also the fin contribution is greater than that of the nose, so there is a net force, but this is usually insignificant compared with and is usually ignored.
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