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What are the drag coefficients for a cylinder, a wedge, etc?

I know there are other reasons for a rocket to be cylindrical that aren't related to aerodynamics such as efficiency when mixing the propellants etc… or is that the exclusive reason why they are cylindrical?

Or is it more related to the logistics or both? If it is due to both things being true, then with 3D printing etc bringing costs of building other shapes down, is it likely we will see a wedge shaped rocket anytime soon?

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  • $\begingroup$ Related question $\endgroup$ – neelsg Jun 1 '15 at 12:14
  • $\begingroup$ Also space.stackexchange.com/questions/7992/… $\endgroup$ – Hobbes Jun 1 '15 at 14:34
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    $\begingroup$ Empty an undamaged soda can and then step on it. Unless you are very heavy it will support your weight. Not bad for something that's all of 15 grams! Rockets use the same characteristics of a cylinder to make their bodies as light as possible. $\endgroup$ – GdD Jun 2 '15 at 11:36
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Rockets are cylindrical for the same reason maize silos are cylindrical: A circle has the largest area vs perimeter of any shape and also provides maximum strength from internal pressure. This means you can save on weight for the walls of a rocket when it is cylindrical.

A cylinder is not the absolute best aerodynamic shape as the Drag Coefficient section of this document shows (Also see the Sears-Haack Body), but aerodynamics are most certainly not the only consideration. On the other hand, the nose of a rocket is usually a cone purely for aerodynamic reasons.

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    $\begingroup$ @Joze: What do you mean by that? The drag coefficient is a shape factor that explains the difference in drag force for objects of the same cross section. The drag coefficient is for the entire shape, both the "upstream" (front) and "downstream" (back) part. $\endgroup$ – MSalters Jun 1 '15 at 12:34
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    $\begingroup$ What's interesting is to think about why rockets are rather longer than they need to be if they were optimizing on weight/material of the rocket itself, sans fuel. I think (without doing the math) that the minimum material will be used when it's about the shape of a beer can. Which says there must be a tradeoff between weight and aerodynamic drag, no? $\endgroup$ – jamesqf Jun 1 '15 at 17:24
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    $\begingroup$ I can't see how that document relates to the question or the answer. The cross section of the objects is not given thus you can't infer cylinders are somewhat worse or better of any other shape. $\endgroup$ – Vladimir Cravero Jun 1 '15 at 21:18
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    $\begingroup$ Doesn't it matter which direction the drag is? The prism (wedge shape) has the broad side going first. Would there be a difference if the narrow side (pointy end) went first? $\endgroup$ – CJ Dennis Jun 2 '15 at 1:58
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    $\begingroup$ It's worth noting that a Saturn V launch loses just half a percent of its total impulse to atmospheric drag. There's not that much drag optimization left to be done. $\endgroup$ – Russell Borogove Jun 2 '15 at 16:35
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It's a combination of factors. Basically, cylinders are easy to make at large sizes, have low drag, and overall work well. The bulk of the drag is going to come from the top or bottom ends. The bottom end contains the engines, which have particular shape requirements. The top contains the payload typically, which also has particular requirements. The tank needs to have a shape that works with both. A cylinder is nearly optimal, and vastly easier to make than the air foil shape that would be optimal.

As for 3-d printing, rockets are large enough where it would be very difficult to make such a thing.

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  • $\begingroup$ I wonder what sort of material could be used with a 3D printer that will also support moving through the atmosphere (even if we only consider ascent) at something like a kilometer per second. That's Mach 3, give or take, and spacecraft reach that after on the order of seconds... never mind the point of max Q. $\endgroup$ – a CVn Jun 1 '15 at 14:52
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    $\begingroup$ Titanium can be 3D printed these days. And I suspect during ascent the time spent at low altitudes is too short for significant heating to occur, hence no elaborate heat shields on nose cones. $\endgroup$ – Hobbes Jun 1 '15 at 18:27
  • $\begingroup$ It's not the shape that is difficult, it's the size. Very few 3-d printers could print a rocket sized shape at all, and it would take a long time. $\endgroup$ – PearsonArtPhoto Jun 1 '15 at 22:00
  • $\begingroup$ I suppose you'd built a custom 3D printer for your rockets anyway, even if the commercially available ones were big enough. The quality control for rockets is far above average, so you'd want to have a feedback from your printer whether the printing went smoothly, and if not which locations should be inspected. $\endgroup$ – MSalters Jun 3 '15 at 11:08
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Rockets fly mostly at supersonic speeds. Under those conditions, the Area Rule (constant cross-section area, or at least smoothly varying) is the most important determinant of drag. A cylinder trivially has a constant cross section, and the nose cone serves as a smooth transition.

Of course, a long rectangular box could also have a constant cross-section, but at that point neelsg's answer already explains why a cylinder is ideal.

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  • $\begingroup$ Another issue is that mass distribution is an incredibly critical factor in space flight because any thrust that isn't as straight through the center of mass as humanly possible is going to cause rotation. You don't get much more symmetrical than a cylinder unless you've got the option of making a perfect sphere... $\endgroup$ – Shadur Jun 3 '15 at 7:17
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    $\begingroup$ @Shadur: That matters less than you think - the thrust has to be along the z axis regardless, and if it is then a rectangular shape also works. $\endgroup$ – MSalters Jun 3 '15 at 11:05
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The question has probably been pretty well answered, but I want to emphasize a few things.

One is that pressure vessels want to be round. Think of what happens when you leave out the orange juice carton with the cap on--it warms and bulges out. That's more of a thing for solid-fuel rockets where basically the whole thing is a pressure chamber.

The other is that wind resistance matters. There is a thing called Max Q, which is the maximum dynamic pressure (wind drag) on the rocket, which occurs somewhere between resting on the launch pad and flying in an airless orbit. It's a point where structural failure can occur, and rockets are often throttled down during that time, for safety. So it's not just a fuel efficiency thing.

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