Sears–Haack body

The Sears–Haack body is the shape with the lowest theoretical wave drag in supersonic flow, for a slender solid body of revolution with a given body length and 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 Kármán–Moore 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.