Alexander Mikhailov wrote:
> 
> Gentlemen,
> 
> there is a somewhat theoretical question. It is often
> assumed that for bigger (liquid) rockets it's easier
> to get the good mass ratio than for smaller one.
> Usually one says that the mass of, say, tanks - a
> major contributor to the rocket dry weight - is
> proportional to the second power of their size, while
> the weight of propellant, carried in them, is
> proportional to the third power.
> 
> At the same time, if the tanks are pressurized (and
> this reasoning should hold for all pressurized
> volumes), the thickness of the wall should be
> proportional to the tank size, because the same
> pressure over a bigger diameter produces the bigger
> force.
> 
> So, where do the savings come from? Is it the case
> only for tanks with small inner pressure, so their
> wall thickness is determined by other considerations?

Basically, yes... for a high-pressure tank, if you make
it twice as big (linear dimension) you will also need 
twice the wall thickness to contain the same pressure,
so tank dry mass scales with volume.

For small tanks at lower pressure, it may not be practical 
to use a wall as thin as would be calculated for the pressure 
requirement, due to such issues as fabrication and handling, 
attaching fittings and mounting points, etc., so the tank must 
weigh more than would be indicated by the scaling relationship 
in pure form.

Similarly, other hardware, such as valves, transducers, etc., 
is typically less weight-efficient in smaller sizes, either 
by being available in sizes no smaller than a certain minimum, 
or by being less amenable to reduced-weight designs. Compare, 
for example, one of the Shuttle main engine oxygen valves (as 
illustrated in the Sutton book) with a standard off-the-shelf 
industrial valve for, say, a 1/4 in. line... the Shuttle valve, 
if scaled down to the same line size, would be a tiny thing 
compared to the industrial valve, but would be a much more 
difficult item to manufacture at that size.

-dave w
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