This is an explanation of how I get BOTE numbers for such things as the comparison between LH2 and CH4 propellants as in Jons’ last post.
The focus Jon had was how much H2 do you need to carry to Mars or Venus to get a return stage if you do a straight LH2/LO2 as opposed to using in situ resources to create CH4 with the hydrogen you carried from Earth. If it was just as effective to use the hydrogen directly as using the intermediate step of converting it to methane with local carbon, then why bother with the conversion and the equipment required to carry it out. Also, if using a hydrogen stage for Earth departure, commonality of equipment is a plus for using a hydrogen stage for Mars or Venus departure. In effect, it is possible that the use of local carbon to convert the on board carbon to methane might not be a worthwhile step.
I is not a rokit sceintest so I tend to look for simplifications that I can do with a scratch pad and TI 30 calculator. A real rocket engineer calculating real missions will go far more in depth than I am capable of, but he tends toward getting paid for his efforts. So this method is worth almost what you are paying for it.
I picked Mars as the launch site for this BOTE because it is easy. I figured 6,000 m/s total V for the rocket because it seemed like a good start for a vehicle that has to reach Mars orbit and do other things once it gets there. Other things range from rendezvous with Earth departure vehicles to a surface return for more flights. If there were a good reason to figure a different V, you can do it during lunch and still have time to eat.
6,000 m/s stage with hydrogen figured as 4,500 m/s exhaust velocity and Methane as 3,700 m/s. Rocket equation gives mass ratios. propellant type hydrogen methane mass ratio 3.79 5.06
Then I translate mass ratio to percentage of propellant at lift off. percent propellant 74% 80% propellant density 0.31 0.94 tank volume per ton 3.26 meters 1.05 meters tank mass per ton at 20 kg/cu m 65.2 kg 21 kg tank mass as percent of GLOW 4.8% 1.68% engine T/W est 80 110 engine mass at 6 m/s at GLOW 0.75% 0.5% percent of propellant, tank and engine 79.55% 82.18% percent payload to GLOW 20.45% 17.82% Glow per ton of payload 4.89 tons 5.61 tons propellant mass per ton of payload 3.6 tons 4.5 tons hydrogen percent of prop load 14.28% 6.25% hydrogen per ton of payload 0.514 tons 0.28 tons
This is all just a fast way of getting a BOTE for a concept. Anyone could change a variable and have an answer for a different scenario in a few minutes. To me, the question that Jon posed is an interesting one. Is it worth doing all the conversions in favor of somewhat more hydrogen tankage? I had assumed it was. Now I don’t know. It will take a detailed trade study for a specific mission set up to see which is better, or neither. Comments on Jons’ post brought up CO for a first stage. Another mentioned perchclorate in the Martian regolith at ~1% concentrations.
I think it is fair to say that there are far more possibilities than we normally consider, and that good answers are not always the most obvious ones.
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