[AR] Re: Volumetric ratio
- From: Henry Spencer <hspencer@xxxxxxxxxxxxx>
- To: Arocket List <arocket@xxxxxxxxxxxxx>
- Date: Thu, 30 May 2019 01:19:09 -0400 (EDT)
On Wed, 29 May 2019, William Claybaugh wrote:
Consider two cylinders of diameter 1 and 2, respectively and w/ a L/D ratio
of 5. I get a surface area of 15.7 and 62.8 respectively and volumes of
3.92 and 31.4; the resulting surface to volume ratios are 4.0 and 2.0...
If I assume a wall thickness of 1 and 2, respectively, and a density of 1
(for convenience) then they “weigh” 15.7 and 125.6, a factor of eight...
It looks to me like doubling the diameter and the wall thickness is
producing a square / cube outcome for constant L/D.
Bill, apologies if this was explained earlier -- I wasn't following the
early part of this discussion closely -- but exactly which ratio are you
computing that's following a square-cube law? The ratio of what to what,
precisely? I think that is where the confusion lies.
To me, the ratio of most interest here is wall mass per unit propellant
mass (i.e. per unit tank volume). Your example shows both tank volume and
wall mass growing by a factor of 8: 31.4/3.92 = 8 and 125.6/15.7 = 8.
So the wall-mass/propellant-mass ratio is constant -- a function only of
pressure and material strength and densities, *not* scaling with size,
which makes big tanks no more mass-efficient as pressurized propellant
containers than small ones. That's the ratio one usually sees mentioned
as *not* following a square-cube law, in contrast to surface-area/volume.
Henry
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