Re: question on hyrdogen launchers

In article <1136581903.476471.281960@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Mike Lorrey <mlorrey@xxxxxxxxx> wrote:
>> ...The mass of pressure-vessel walls scales with the volume enclosed,
>> not with the surface area, because a bigger vessel needs thicker walls to
>> contain the same pressure... And if hydrostatic pressure is the
>> dominant pressure in the tank, then the pressure scales with depth...
>> Hence the fourth-power rule for big tanks.
>
>This seems to say that everything I've been told by experts about why
>spherical tanks are the perfect shape for tank mass to volume mass
>ratio, and that bigger launchers are easier to get good mass fractions
>on, is a lie.

Note that I didn't say anything about shape -- I was talking solely about
how tank mass scales with *size*.

If you are using metals -- more precisely, if your materials are
isotropic, equally strong in all directions, like most metals -- then
non-spherical tanks do incur a mass penalty. However, it has nothing to
do with minimizing surface area (well, not directly); it's more subtle
than that. A cylindrical pressure vessel, for example, needs twice as
much strength against hoop stresses (bulging) than it does against
longitudinal stresses (stretching), so an isotropic-material tank that's
adequately strong in the hoop direction has more longitudinal strength
than it needs, and that translates to a mass penalty. With composites,
however, it's quite possible to make a material that *is* twice as strong
in one direction as in the other; given that, spheres have no particular
mass advantage over cylinders or other reasonable shapes.

As for bigger launchers, it *is* generally easier to get good mass
fractions with big launchers, but it has nothing much to do with the tanks
being lighter. There are a number of other masses which scale with
surface area, with linear size, or not at all, and they all hurt small
launchers and benefit bigger ones. In addition, there are considerations
of "minimum gauge" (the thinnest material it's reasonably practical to
handle) and interior accessibility among other things, which typically
make it possible to build larger structures in more sophisticated ways and
come closer to theoretical limits.
--
spsystems.net is temporarily off the air; | Henry Spencer
mail to henry at zoo.utoronto.ca instead. | henry@xxxxxxxxxxxxx
.

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