To throw this out there, why this scaling difference matters is primarily
insulation. If you are using cryogenic propellants, larger tanks are indeed
better than small ones - small liquid hydrogen would be very hard!
Thanks!
-David Summers
On Thu, May 30, 2019 at 6:35 AM William Claybaugh <wclaybaugh2@xxxxxxxxx>
wrote:
Henry:
Thank you, that is exactly where I was confused It is wall volume to tank
volume that scales linearly.
Bill
On Wed, 29 May 2019 at 23:19, Henry Spencer <hspencer@xxxxxxxxxxxxx>
wrote:
On Wed, 29 May 2019, William Claybaugh wrote:
Consider two cylinders of diameter 1 and 2, respectively and w/ a L/Dratio
of 5. I get a surface area of 15.7 and 62.8 respectively and volumes of1
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
(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
