What is the ideal shape for a rocket?

Question

Obviously there are many factors that go into the design of a rocket. However, to me, many rockets seem very tall and skinny.

What I mean is that an ideal rocket would have as little mass used for the tank structure, and hold the maximum amount of fuel. Which, if it operated in a vacuum, would call for a spherical tank. I.e., Surface area (dry mass) to volume (fuel mass) ratios would be worse in a tall skinny rocket.

However:

• Launching a rocket requires passing through the atmosphere.
• An airfoil shape has less drag than a sphere.
• Fabricating a sphere is much harder than fabricating a cylinder

So, for a single stage rocket, I would assume a bullet shaped rocket with something like a 3:1 length to diameter ratio would be ideal for an Earth launched rocket.

And for a multistage rocket, the top stage would have something like a 3:1, and the lower stages something like 1:1 - 2:1 length to diameter ratios.

Now, rocket designers are reasonably smart folks, and have probably thought of this;

So what am I missing? Where in my broad estimations / calculations have I made naïve assumptions?

Answer 1

For supersonic flow, the Sears-Haack body offers less drag than the shorter teardrop that's optimal in the subsonic regime. Sears-Haack is pretty similar to the German V-2 rocket body.

(Note that the proportions of this particular example aren't part the definition of the Sears-Haack shape; for minimal drag you'd have to have an impractical body of infinite length and infinitesimal cross section.)

The tapered "boat-tail" at the back of the Sears-Haack shape, though, moves the center of aerodynamic pressure forward. For stability, you want to keep the center of pressure behind the center of gravity -- this is why darts, arrows, and many rockets have fins at the back; the fins add drag at the base, moving the center of pressure back and keeping the projectile stable.

Keeping the bottom end of the Sears-Haack shape cylindrical, or even flaring it out slightly, rather than boat-tailing, improves stability dramatically. Also, you need to put the engines there. So that's where the basic familiar rocket shape comes from.

Once you're making a really big rocket, other constraints, like how high your factory roof is or how wide your train tunnels are, start to come into play, and you may have to get longer and skinnier than the aerodynamically optimal shape as well.

Answer 2

I think you answered your question in the first sentence. I am reminded of this image:

Aerodynamics is but one (albeit a large one) of many concerns in the systems engineering of a rocket. Others include manufacturability, propulsion, changing flight regimes, safety, structures, economics, etc... All of these seem to have converged on a simple, more-or-less cylindrical design.

For the sake of innovation however, I encourage you to try something new!