Sears–Haack body

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. The derivation and shape were published independently by two separate researchers: Wolfgang Haack in 1941 and later by William Sears in 1947.

The theory indicates that the wave drag scales as the square of the second derivative of the area distribution, ${\displaystyle D_{\text{wave}}\sim [S''(x)]^{2}}$ (see full expression below), so for low wave drag it is necessary that ${\displaystyle S(x)}$ 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.