Re: Big dumb rockets vs. small dumb rockets

From: David Summers (david_at_ualmiles.com)
Date: 02/02/05 

Date: 2 Feb 2005 07:11:42 -0800

This is sort of moot, but in your case the cube-square law goes the
other way. For a simple illustration:

Let's say we have a rocket in the shape of a cube 10 m on a side (makes
math simpler - but the shape doesn't matter...).

The volume is 10*10*10=1000 m^3
The surface area is 10*10 * 6 = 600 m^2

The surface to area ratio is 600/1000, or 0.6. The mass ratio is
vaguely inversely proportional to that.

Now we shrink the rocket to 1 m on a side:

The volume is 1*1*1=1 m^3
The surface area is 1*1 * 6 = 6 m^2

Now the surface to area ratio is 6/1, or 6. The mass ratio is vaguely
inversely proportional to that. So as we shrank the rocket, the mass
ratio gets worse.

In reality, though - you must alter the second case by increasing the
wall thickness. For the math to be easier, you should use a sphere -
but the basic result is that since the wall thickness scales up exactly
as fast as the surface area scales up, a smaller rocket is exactly the
same ratio.

Of course large engines are harder to debug, small engines are harder
to cool, electronics don't scale, and you could argue that safety
factors get better or worse with different sizes. But using just the
tanks and estimates for the engines (BTW, I recommend just using a
thrust to weight ratio of 50 to estimate engine weight), there is
pretty much no difference.

-David

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