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The dynamic stability condition

Dynamic stability condition formula

Abbreviations

cD
Drag coefficient
cLa
Lift coefficient derivative
cMpa
Magnus moment coefficient derivative
cmq+cma
Pitch damping moment derivative
sg
Gyroscopic (static) stability factor
sd
Dynamic stability factor

More Abbreviations

Explanation

A projectile is said to be dynamically stable, if its yawing motion of nutation and precession is damped out with time, which means that an angle of yaw induced at the muzzle (the initial yaw) decreases.

A dynamic stability factor sd can be defined from the linearized theory of gyroscopes (assuming only a small angle of yaw) and the above dynamic stability condition can be formulated. An alternate formulation of this conditionGo to formula leads to the illustrative stability triangle.

sd however depends on five aerodynamic coefficients. Because these coefficients are hard to determine, it can become very complicated to calculate the dynamic stability factor, which varies as a function of the momentary bullet velocity.

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