What formula defines a curve for a nose cone with the minimal possible drag?

The nose cone is attached to a cylinder (assume it goes on forever). The volume of the nose cone is not relevant. The nose cone isn't near the ground. And the object will be traveling at 20m/s max.

So far, I've been using the sears haack body but im not sure if it is actually the best possible curve.


1 Answer 1


I am no expert on aerodynamics but according to Wikipedia a Sears–Haack body has the lowest theoretical wave drag, where wave drag occurs when moving at transonic and supersonic speeds due to the presence of shock waves.
However you are saying that your object would not move faster than $20 ms^{-1}$, which is far below the speed of sound ($mach 1\approx 340 ms^{-1}$) assuming this would be in earths atmosphere near sea-level.
And according to another Wikipedia page about nose cone designs:

For aircraft and rockets, below Mach .8, the nose pressure drag is essentially zero for all shapes. The major significant factor is friction drag, which is largely dependent upon the wetted area, the surface smoothness of that area, and the presence of any discontinuities in the shape. For example, in strictly subsonic rockets a short, blunt, smooth elliptical shape is usually best.

So elliptical cone would be a good choice, however it is not given which length would give the lowest drag. I would suspect that the length would be larger than the radius, because the drag coefficient (for $F_D\propto v^2$) for a half-sphere (elliptical cone with length equal to the radius) is higher that a elliptical cone with a slightly longer length.

After a bit of searching I did found some experimental results which are in the region of your maximum speed ($39.2 mph\approx 17.4 ms^{-1}$). The results from this experiment showed that a long elliptical nose cone had the least drag, which had a length to diameter ratio of approximately 3. The experiment also contained a shorter elliptical nose cone with a ratio of approximately 1.4. I would not be able to say that a ratio of 3 would be optimal, but it should at least be bigger than 1.4.


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