# What is the ideal volume distribution for minimization of transonic drag?

I am aware what the area rule states - my question is what is defined as "as smooth as possible area distribution" - Is there a formula for the curve?

Since Drag is proportional to S'', the key is to derive a shape that has a minimum S''.

The result is the 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 area is given by:

$$S(x) = \frac {16V}{3L\pi}[4x(1-x)]^{3/2} = \pi R_\text{max}^2[4x(1-x)]^{3/2}$$

And the radius is given by:

$$r(x) = R_\text{max}[4x(1-x)]^{3/4}$$