Level 2 is hard
A lot of people have advised me to ignore the 180 until the 90 is in the bag. Its probably good advice, but I’d like to start doing some 180 second development tests when we go out to the site to test the 90 second vehicle. The trip to the test site is a significant portion of the time involved with a test and so I’d like to use that time for testing both if possible. I did a very detailed model last night. I started with the following assumptions:
- It needs to stay as an amateur vehicle IE total impulse < 200K lb/sec
- I’ll use an off the shelf LR-101 as the motor
- I’ll use the same AMS industries Spun 5086 aluminum hemispheres for tankage that we used for the 90 second vehicle.
- I’ll assume that the LR-101 ISP starts at 200 at design Cp and degrades along the same slope as Cpropep down to the minimum Cp (Cpropep says LR-101 should give 230 Isp at design pressure) This discrepancy is probably because the LR101 is significantly over-expanded at sea level.
I included in the model:
- Pressure Drops in the LR-101 Jackets, and Injectors
- Isentropic Gas expansion in blow down mode.
Given these assumptions I could not build a 180 second vehicle. so I modified the assumptions:
- Add one Carbon fiber SCI 602 presurization bottle and Regulator to use on the LOX side. Allowing us to fill the Lox sphere past the point where blow down mode would run out of pressure.
Given these assumptions the model says we can hover for 200 seconds.
This probably won’t work for the following reasons:
- The motor is WAAAY over-expanded for the entire flight. We could use all the LR101 dimensions and injector and build a motor that has the same internal dimensions and lower expansion ratio. this would likely give us back some ISP, but we are no longer off the shelf.
- The motor needs to throttle 4:1 and as the pressure drop in the injectors goes down that low then we probably don’t get good mixing.
- The outcome is really sensitive to the initial loading conditions over/under filling the Lox tank by 5% causes a 10 second change in the hover period.
- We need to get the same hydro test performance out the tanks as Armadillo is getting and our first tank was 25% low, we have not yet been brave enough to test the 2nd tank to the level we need.
- It would be really hard to keep the mixture ratio matched exactly over a 4:1 throttling ratio without really good closed loop controls.
- The LR 101 is hard to get lit.See the SDSU rocket at 1:42 into http://www.youtube.com/watch?v=Wzl_IaSJx28
Some additional thoughts on the 180 second problem:
If I use different sphere sizes and thicknesses and put on lots of pressurant bottles I can get my detailed model to say we hover for 230 seconds, but the same issues identified above apply.
The 180 second level 2 is all about getting good mass ratio and ISP. For non-pumped systems the density of the propellants really matters. I’m using 1.1 as my Lox density 0.8 as my RP-1 density. I really think Peroxide would be better, 90% peroxide has a higher density than Lox 1.36, and it also makes up a higher percentage of the total propellant load so the portion of your propellant at 0.8 is lower. I’ve seen Density * Isp ^2 as a figure of merit (FOM) in SSTO studies.
- Peroxide RP1 at 200 PSI running at best ISP has ISP 215.6 and Density 1.246 FOM: 58K
- Lox RP1 running at LR-101 mixture ratios and 200 PSI has ISP 219 and Density 0.993 FOM: 48K
- Lox RP1 running at best ISP and 200 psi has ISP 230 and density 1 FOM: 53K
You are much more likely to get the peroxide motor running at peak ISP to cool in regen mode as there is much more cooling fluid available with a much higher heat capacity. Its clear the LR-101 designers with an infinite budget did not choose to give up 10 points of ISP with out trying.
One LLC competitor that had a static display at the 2006 xprize cup, had a system with electrically driven positive displacement pumps using peroxide, liquid catalyst and a fuel. this insures constant mixture ratios across the entire throttling range and makes your FAA safety system really easy as you just have a power relay that drops power to the pump and all propellant flow stops. Your tank thicknesses are set by minimum gage issues not pressure requirements. If one developed this it would also be easily transfered to vehicles with more aerodynamic tankage than the big spheres. (Space here we come….)