Sears–Haack body (Drag Coefficient related to the maximum Radius)

Description

The Sears–Haack body is the shape with the lowest theoretical wave drag in supersonic flow, for a given body length and given volume. The mathematical derivation assumes small-disturbance (linearized) supersonic flow, which is governed by the Prandtl-Glauert equation.
In aeronautics, wave drag is a component of the drag on aircraft, blade tips and projectiles moving at transonic and supersonic speeds, due to the presence of shock waves. Wave drag is independent of viscous effects,and tends to present itself as a sudden and dramatic increase in drag as the vehicle increases speed. The theory indicates that the wave drag scales as the square of the second derivative of the area distribution D=.S’’(x)]^2.
So for low wave drag it’s necessary that area distribution be smooth. Thus, the Sears–Haack body is pointed at each end and grows smoothly to a maximum and then decreases smoothly toward the second point.
The drag coefficient depends on maximum radius and the length of the body.