The completion of any space mission requires the execution of preplanned propulsive maneuvers, each with a known velocity change, or ?V. The amount of ?V is irrespective of the propulsion system, however the type of propulsion system largely affects the size of vehicle needed to deliver the velocity change.
One measure of a propulsion system’s effectiveness is specific impulse, but this doesn’t always tell the whole story. Perhaps a better measure is the total mass that must be placed in orbit to complete the mission. For instance, suppose a mission to the Moon requires 140,000 tons to be placed in orbit using one particular type of propulsion system. If a different propulsion system allows the same mission to be completed by placing only 120,000 tons into orbit, then arguably the second system is the superior system.
I applied this same philosophy to the different NTR propellants discussed previously. Which propellant allows us to deliver a particular ?V with the least amount of total mass?
To do this I had to estimate the inert mass of the vehicle, i.e. the mass less propellant. First, what’s the mass of the propulsion system? I figure the thrust chamber and turbo-machinery should weight about the same as a chemical engine. After studying several engines, I determined an engine’s mass in kilograms is about 3*Q, where Q is the volumetric flow rate in liters/second.
The mass of the reactor is much less certain. The NERVA engines had thrust-to-weight ratios of about 3 to 4. This is pretty bad, but other designs were studied that would have improved this to 5 or perhaps much better, though they weren’t fully developed. I decided to make the reactor mass that needed to give my hydrogen system a T/W ratio of 5. I came up with the formula Mass = 3*Power+1000, where mass is in kg and power in megawatts. This is really just a wild guess, but when applied to my hydrogen NTR, the T/W ratio is 4.93 (engine + reactor). Since the reactor power and volumetric flow rates of the other propellants is much less than hydrogen, those systems have far better T/W ratios.
I also added a mass of 1,200 kg for electric and hydraulic power systems and avionics. The idea for this number comes from NASA’s Exploration Systems Architecture Study (2005). The ESAS report includes a mass breakdown for the proposed CLV and CaLV (later Ares I and Ares V). Using the CLV second stage and the CaLV EDS (Earth Departure Stage) as a guideline, I came up with the 1,200 kg figure.
For the payload I used a mass of 25,000 kg. This number was chosen because it gives my hydrogen NTR an average acceleration approximately equal to that produced by the Saturn S-IVB stage when used with the Apollo payload.
Something else I needed to do before completing this analysis was to determine how much propellant is required to drive the turbopumps. I calculated the pump power assuming a 75 atm pressure rise and 75% efficiency. A turbine efficiency of 67% was assumed for a combined turbine/pump efficiency of 50%. I figured a heat exchanger and gas generator system that delivers 1,000 K gas to the turbine with an inlet pressure of 50 atm and an exit pressure of 3 atm, for a pressure ratio of 16.67. Based on these parameters, I calculated the mass of propellant needed to deliver the power to the turbine. The energy needed to raise the propellant to 1,000 K is not more than 1% of the reactor power.
The pump power, turbine power, and turbine propellant flow rate are included in the table in Post #50, which has been updated. I also recalculated the specific impulse based on the total propellant flow to the engine, including that to both the chamber and the turbine.
Finally, I assumed a propellant residual equal to 5 seconds of burn time. All the above assumptions and calculations gives us the following masses, in kilograms. These numbers are fixed and do not change relative to the propellant load. LOX-hydrogen chemical propulsion is included as a comparison to NTR propulsion.
TABLE 1 H2 CH4 C3H8 C2H8N2 C2H5OH NH3 LOX-H2
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Engine 2,502 542 412 372 402 526 1,013
Reactor 7,837 4,879 3,896 2,945 4,414 5,487 N/A
Power/avionics 1,200 1,200 1,200 1,200 1,200 1,200 1,200
Payload 25,000 25,000 25,000 25,000 25,000 25,000 25,000
Residuals 296 382 399 490 528 598 571
Total 36,836 32,003 30,907 30,007 31,544 32,811 27,784
Next we need an equation to estimate the mass of the propellant tanks and related structure. One good example of a propellant tank we can use as a guideline is the Shuttle External Tank. A tank’s surface area is proportional to its volume raised to the 2/3 power. Applying this to the Shuttle ET we get the equation Mass=1.65*Volume^2/3, where mass is in kg and volume is in liters. This includes all primary and secondary structures and separation systems. The numbers given in the NASA ESAS Report are in the same ballpark, so we’ll go with it.
Given the masses shown in the above table and an equation to calculate the tank mass, I can calculate the propellant mass needed to achieve a specified ?V. Adding it all up and we have the total mass of the entire vehicle delivered to orbit. Below are the masses, in kilograms, for four different ?V budgets:
TABLE 2 H2 CH4 C3H8 C2H8N2 C2H5OH NH3 LOX-H2
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?V = 3,000 m/s
Tank 6,834 2,176 1,773 1,687 1,870 2,387 3,372
Propellant 18,629 19,875 20,099 25,377 29,585 36,930 30,652
Total * 62,298 54,054 52,780 57,071 63,000 72,128 61,808
?V = 6,000 m/s
Tank 13,470 4,223 3,451 3,446 3,913 5,249 7,532
Propellant 52,075 54,381 55,258 75,016 90,582 121,760 103,671
Total * 102,380 90,606 89,616 108,469 126,039 159,820 138,988
?V = 9,000 m/s
Tank 22,531 6,944 5,694 6,033 7,056 10,108 14,950
Propellant 112,994 115,113 117,581 174,376 220,099 326,395 290,899
Total * 172,361 154,061 154,183 210,416 258,698 369,314 333,633
?V = 12,000 m/s
Tank 36,050 10,852 8,926 10,169 12,357 19,391 30,339
Propellant 228,999 225,239 231,163 382,193 510,839 868,289 842,092
Total * 301,885 268,094 270,996 422,369 554,740 920,491 900,216
* - Includes total from TABLE 1.
Although hydrogen has the best specific impulse, methane and propane win the mass battle thanks to their far better densities. The huge tanks required to store the low-density hydrogen is just too much of a mass penalty to overcome. This isn’t as big a problem with chemical propulsion because hydrogen isn’t used alone; it’s used in combination with LOX, which raises the combined density to something tolerable. But in an NTR, hydrogen is used all by itself.
The winner between methane and propane is pretty much a toss up, with propane being a little better with a small delta-v, and methane being a little better with a large delta-v. Propane has a better boiling point, so boil-off may be less of an issue. However, methane can be manufactured from in situ recourses.
I’d like to close by saying there’s a lot of guesswork in these numbers, so take them with caution. Nonetheless, I think the results are interesting to ponder.
The calculation I’m most worried about is the specific heat ratio of the carbon containing propellants. I’m confident in my method when the exhaust products are all gaseous, but with carbon we have a solid in the exhaust. I think I’m going about it correctly, but I have nothing to check my results against to confirm. One of the reasons methane and propane look so good is because of their low specific heat ratios. If I’ve calculated the ratios too low, then the results could be thrown off considerably – possibly enough to swing the advantage back to hydrogen.
(Edit) Added LOX-LH
2 chemical propulsion for comparison.
