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

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


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