Re: question on hyrdogen launchers
- From: John Schilling <schillin@xxxxxxxxxxxxx>
- Date: 6 Jan 2006 12:53:46 -0800
In article <1136471022.754785.292100@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>, Mike Lorrey
says...
>
>
>John Schilling wrote:
>>In article <1136389491.845595.51490@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>, Mike Lorrey
>> says...
>>
>> >No. Tank mass scales by square rule, while contents mass scales by cube
>> >rule. Ideally you could build a very large LH2/LOX launcher the size of
>> >an aircraft carrier or larger, with tanks that are essentially blimp
>> >skins of metal wire and kevlar woven impregnated with a silicone.
>> No, you could not. Only very small tanks, with minimum-gauge walls, scale
>> by the square rule. Larger tanks, including most rocket fuel tanks, scale
>> by the cube rule - or more precisely, as tank volume times tank pressure.
>> Very large tanks, like your LH2 aircraft carrier, scale by a fourth-power
>> rule, as the internal pressure starts to be dominated by the weight of
>> the propellant.
>What, you are counting the mass and pressure twice each?
I'm not. Math below.
>If the volume is so large that the propellant weight is the prime
>determinant of internal pressure, then you don't need to pressurise
>it other than to keep the empty volume taut, and the rocket is
>automatically a pressure fed system.
Right. A very heavy pressure-fed system, whose tank mass scales as
the fourth power of its linear dimension.
The mass of the tank is proportional to the tank pressure times the
tank volume, each counted once only. Volume is proportional to cube
of linear dimension, so tank mass is proportional to tank pressure
times cube of linear dimension.
Tank pressure is the higher of A: the inlet pressure required by the
engines or B: the hydrostatic pressure associated with the weight of
the propellant. The hydrostatic pressure is proportional to the
density of the propellant times the acceleration of the rocket times
the height (linear dimension) of the tank.
So, if the height of the tank is large enough that hydrostatic pressure
is greater than required engine inlet pressure, the tank mass becomes
proportional to propellant density times vehicle acceleration times
the fourth power of the linear dimension. With nothing double-counted.
>It doesn't take much tank size for that to happen, the STS ET sees
>that effect.
Only in the LOX tank, AFIK, and that only to a limited extent. I'm
pretty sure cube-law scaling works for the ET.
I don't know of any vehicles offhand that have hydrostatically-dominated,
fourth-law tanks. But I'd want to look closely at the Titan IV. Smaller
tanks than the shuttle, but tall and skinny ones, loaded with rather dense
propellants, and the SRB-only boost phase means those tanks will see hefty
accelerations while still fully loaded.
Hmm, Isakowitz indicates the Titan IV tank walls are twice as thick as
those of the II, despite similar volume, geometry, and engine requirements.
So I'm thinking maybe it is the hydrostatic pressure associated with that
boost profile, pushing the TIV into fourth-power tank scaling where the II
could get away with third-power tanks.
Shuttle, not so much.
--
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- question on hyrdogen launchers
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