Continuing with our story from last time…
The next day, your boss pokes his head in your office and asks:
“How’s those forty trans-Mars injection stages going?”
He notices that you’re checking out scuba-dive sites in the Caribbean for your upcoming vacation with your feet up on the desk, and comes into the room with the blood rising to your face. In your defense, you blurt out that you’ve already done the analysis!
He, somewhat increduously, demands to see the results, so you show him the spreadsheet. He’s less than impressed.
“I thought you were going to design each stage! I need pictures and layouts of these things, with lists of mass and volumes and so forth…you’re showing me a little number. Furthermore, I’ve got the Ohio and Nevada congressional delegations breathing down my neck to send billions of dollars to Stan Borowski to develop an NTR that he promises will get us to Mars faster. You’ve got to show me more detail for this. And how do you even know that your equations are correct?”
Now on the defensive, you offer to try to quickly verify two of the comparison cases for your boss. He looks through your results and decides to pick a comparison point in the middle of the trade space: 4000 m/s delta-V and 0.5 initial thrust-to-weight. Your spreadsheet quickly predicts that the NTR stage will have a payload fraction of 0.3828 and that the chemical stage will have a payload fraction of 0.3955, with a ratio of the two of 1.033, but your boss wants to see proof that your equations are correct.
So how do you go about turning these expressions into masses and volume and graphics?
This time, it took considerably longer than ten minutes, but you showed that your equations match up with reality (at least to the resolution of your initial assumptions). You can see, physically, that the NTR stage is much larger than the chemical stage, even though both carry roughly the same payload. The NTR stage needs almost 6 engines to meet the T/W requirements, while the chemical stage only needs 4. The real difference between the two stages, from a mass perspective, is in the engine weight. You can see that the total engine weight on the chem stage is 1480 lb, while on the NTR stage it is 29,333 lb. This is a staggering difference, due almost entirely to the wretched thrust-to-weight ratio of the NTR engines. This could also lead to another problem. There will be every incentive to try to remove weight from the NTR engines, and with six engines in close proximity, it is almost certain that there will be a lot of neutronic leakage from one engine to another. This means that the engines won’t be able to be controlled individually, but will have to be controlled as a group. It may not be possible to shut one of them down in flight. It also means that they might have to be tested as a group which will drive costs up like crazy.
From the propellant side of the house, the NTR LH2 tank is much larger than the chem tanks, and the mass devoted to tankage on the chem side is 1554 kg, whereas the NTR tank is 4426 kg. Those big NTR LH2 tanks might cause you to hit the volume constraint on your launch vehicle before the mass constraint is reached.
Your boss is happy, for now. He’s got the numbers to show that for 4000 m/s and 0.5 T/W, the NTR stage only has a few more percent payload, and that’s not worth paying the billions to develop it.
But unfortunately for you, now he knows you can get this kind of preliminary analysis work done much faster, so he’s loaded you down with all kinds of new analyses. And that beach vacation is looking further and further away…
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