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The drag coefficient cD is the most important aerodynamic coefficient and generally depends on- bullet geometry (symbolic variable B),
- Mach number Ma,
- Reynolds number Re,
- the angle of yaw d
The following asssumptions and simplifications are usually made in ballistics:
1. Re neglectionIt can be shown, that with the exception of very low velocities, the Re dependency of cD can be neglected.
2. d dependencyDepending on the physical ballistic model applied, an angle of yaw is either completely neglected (d=0) or only small angles of yaw are considered. Large angles of yaw are an indication of instability.
For small angles of yaw the following approximation is usually made:
a) cD(B,Ma,d) = cDo(B,Ma) + cDd(B,Ma) * d2/2
Another theory which accounts for arbitrary angles of yaw is called the "crossflow analogy prediction method". A discussion of this method is far beyond the scope of this article, however the general type of equation for the drag coefficient is as follows:
b) cD(B,Ma,d) = cDo(B,Ma) + F(B,Ma,Re,d)
3. Determination of the zero-yaw drag coefficient
The zero-yaw drag coefficient as a function of the Mach number Ma is generally determined experimentally either by wind tunnel tests or from Doppler Radar measurements.
Fig.: Zero-yaw drag coefficient for two military bullets
There is also software available which estimates the zero-yaw drag coefficient
as a function of the Mach number from bullet geometry. The latter method
is mainly applied in the development phase of a new projectile.
cDo(B,Ma) = iD(B) * cDo standard(Ma)
If this simplification is applicable, the determination of the drag coefficient of a bullet as a function of the Mach number is reduced to the determination of a suitable form factor alone. It will be shown that the concept of the ballistic coefficient, widely used in the US for small arms projectiles follows this idea.
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