Why are so many sci-fi's set set close to now, when the technology clearly won't exist?

POSTED BY: chrisisall
UPDATED: Tuesday, December 4, 2007 22:12
VIEWED: 12199
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RALLEM

Monday, December 3, 2007 10:53 PM

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Nuclear vs Chemical
Directly comparing the performance of a nuclear engine and a chemical one is not easy; the design of any rocket is a study in compromises and different ideas of what constitutes "better". In the outline below we will consider the NERVA-derived engine that was considered by NASA in the 1960s, comparing it with the S-IVB stage from the Saturn it was intended to replace.

For any given thrust, the amount of power that needs to be generated is defined by P = T * Ve / 2, where T is the thrust, and Ve is the exhaust velocity. Ve can be calculated from the specific impulse, Isp, where Ve = Isp * g, Using the J-2 on the S-IVB as a baseline design, we have P = 414 s * (1014 kN * 9.81) / 2 = 2,060 MW. This is about the amount of power generated in a large nuclear reactor.

However, as outlined above, even the simple solid-core design provided a large increase in Isp to about 850 seconds. Using the formula above, we can calculate the amount of power that needs to be generated, at least given extremely efficient heat transfer: P = 1014kN * (850 * 9.81) / 2 = 4,227 MW. Note that it is the Isp improvement that demands the higher energy. Given inefficiencies in the heat transfer, the actual NERVA designs were planned to produce about 5 GW, which would make them the largest nuclear reactors in the world.

The fuel flow for any given thrust level can be found from m = T / Ve. For the J-2, this is m = 1014 kN / (414 * 9.81), or about 250 kg/s. For the NERVA replacement considered above, this would be 121 kg/s. Remember that the mass of hydrogen is much lower than the hydrogen/oxygen mix in the J-2, where only about 1/6th of the mass is hydrogen. Since liquid hydrogen has a density of about 70 kg/m³, this represents a flow of about 1,725 litres per second, about three times that of the J-2. This requires additional plumbing but is by no means a serious problem; the famed F-1 had flow rates on the order of 25,000 l/s.

Finally, one must consider the design of the stage as a whole. The S-IVB carried just over 300,000 litres of fuel, 229,000 litres of liquid hydrogen (17300 kg), and 72,700 litres of liquid oxygen (86 600 kg). The S-IVB uses a common bulkhead between the tanks, so removing it to produce a single larger tank would increase the total load only slightly, for argument's sake, perhaps 2,000 litres. Assuming this for the moment, this means the new hydrogen-only nuclear stage would carry about 231,000 litres in total (231 m³), or about 16,500 kg (36,350 lb). At 1,725 litres per second, this is a burn time of only 135 seconds, compared to about 500 in the original S-IBV (although some of this is at a lower power setting).

The total change in velocity, the so-called delta-V, can be found from the rocket equation, which is based on the starting and ending masses of the stage:


Where m0 is the initial mass with fuel, m1 the final mass without it, and Ve is as above. The total empty mass of the J-2 powered S-IVB was 13,311 kg, of which about 1,600 kg was the J-2 engine. Removing the inter-tank bulkhead to improve hydrogen storage would likely lighten this somewhat, perhaps to 10,500 kg for the tankage alone. The baseline NERVA designs were about 15,000 lb, or 6,803 kg, making the total unfueled mass (m1) of a "drop-in" S-IVB replacement around 17,300 kg. The lighter weight of the fuel more than makes up for the increase in engine weight; whereas the fueled mass (m0) of the original S-IVB was 119,900 kg, for the nuclear-powered version this drops to only 33,800 kg.

Following the formula above, this means the J-2 powered version generates a of (414sec * 9.81) ln (119,900 / 13,311), or 8,925 m/s. The nuclear-powered version assumed above would be (850 * 9.81) ln (33,800 / 17,300), or 5,585 m/s. This drop in overall performance is due largely to the much higher "burnout" weight of the engine, and to smaller burn time due to the less-dense fuel. As a drop-in replacement, then, the nuclear engine does not seem to offer any advantages.

However, this simple examination ignores several importa

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