Sunday, September 12, 2010
Pressure Fed Upper Stage.
I've been doing some calculations on what an upper stage for the 1Kg Nanosat launcher would look like. One of the interesting twists is that if the motor only has to run in vacuum then it's ISP is almost independent of chamber pressure. So for any small launcher you are going to have minimum gauge problems long before you hit the minimum optimum tank wall thickness. This opens the possibility for tanks with things like 3L soda bottles and PVC valves. It makes me wonder why Space X went with the turbo pump 2nd stage for the F9. a lot of complexity for very little gain? Maybe just because they had one that was approximately the right size.
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Low pressure upper stage engines lead to large exit diameters. This becomes a limit on expansion ratio. Also for RP, higher chamber pressures lead to more complete burning. Delta 2 uses a pressure fed upper stage with storable propellants.
Higher chamber pressures mean smaller motor size and likely less mass. There is some benefit in that.
Yeah, your nozzle potentially won't fit the interstage... or the rocket will have to be wide and thus draggy.
Remember drag loss in m/s is inversely proportional to the rocket length - it's bad for small rockets!
That is - unless your upper stage is very very small so even a low thrust density doesn't result in a large nozzle exit diameter.
No rocket with a liquid pressure fed first stage has yet reached orbit, am I right? You'd always need an extra stage to put the pressure fed higher delta vee stage above most of the atmosphere, and that lifter stage then gets really big because of the low thrust density.
Air launch was on to something.
I second the PVC plumbing for low pressure peroxide idea.
How about large diameter PVC pipe for tankage? I'm not sure if it would be lighter than the fiber wrapped polyethylene tanks, but it's worth a comparison.
I know you love shaving grams, but you could sure put together a cheap OTRAG with off the shelf PVC fittings.
Hmm, I might have said something that wasn't correct... Investigating.
I believe the french launched a pressure fed orbital vehicle.
http://cs.astrium.eads.net/sp/LauncherPropulsion/Aestus-Rocket-Engine.html
http://www.spl.ch/news/SEPR/AIAA-90-1835.pdf
The French Launched Diamant-A and Diamant-B with pressure fed first stages.
Here's the best information I've been able to get on the performance characteristics of the Diamant A launcher:
Diamant A
Ed L
If I did my math right that got to orbit with 8784 m/sec DV.
Yeah, 8784 m/s looks right. Don't forget the earth's rotation which can add up to about 304 m/s due east at the equator (the French launched from Algeria). Still, this seems like a low margin to me.
Nonetheless, larger rockets have lower aerodynamic losses. I've done the same analysis for a number of other large rockets and it seems that they often target about 9144 m/s total delta V.
My simulations on small vehicles show they can make orbit with about 9144 m/s total delta V. The key is the higher acceleration rate (lowering gravity losses) and small frontal surface area (reducing aerodynamic losses). Obviously, you _want_ to optimize the design to have have the largest diameter and lowest acceleration, so there's an optimization point which usually results in 1.33 G's acceleration (2.33 thrust/weight) in a full-throttle burn of the first stage. This keeps the first-stage end-of-flight acceleration below 10 G's. You may also back off throttle at max Q to keep stresses on the vehicle lower.
Although there's an old adage (from Von Braun) that you shouldn't design rockets with a "fineness ratio" greater than 10, in smaller orbital rockets, you usually have to go higher than that to keep aerodynamic losses down. Most of my designs have a "fineness ratio" upwards of about 20. This is not unheard of in orbital rockets. The Iranian Safir 2 rocket had a "fineness ratio" of 17 and it made orbit last year (est. total dV of 9.6 km/s).
Safir 2 Image
Paul, I had the same thought about a year or two ago (pressure-fed upper stage isn't that bad Isp-wise because of vacuum outside, using 3L bottles for a cheap nanosat upperstage). Probably isn't terribly feasible, but would be cheap!
Why wouldn't it be feasible? For dense fuels a pressure-fed upper stage isn't such a bad idea. At low delta-v saving the mass of a turbopump may outweigh the higher tankage mass and gravity losses. Ariane EPS and the Delta 2 upper stage are pressure-fed for example.
Pressure fed to orbit - its possible. Look at huge solutions from Beal Aerospace HTP/PR-1 engine Launchers. Cheap and promising but closed due to the NASA.
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