[Spaceships] Homebrew: Alternate Chemical Rocket Fuel

[DaltonS]

The only propellant for chemical rockets listed on SS1 p.21 is hydrogen-oxygen. While this combination may be the most efficient one in terms of mass, it is much less so in terms of volume. As a result, many rocket designers have chosen to use denser (if less efficient) propellants, sacrificing ΔV for reduced tankage requirements. (For more information on propellants, see the Rocket Propellants page(†) of the Rocket and Space Technology website.)

The ΔV and thrust provided by different propellants can be found by comparing their specify impulses (Isp). From the classic rocket equation ΔV = Isp × g × ln(Mp/Me), we can find the ΔV in miles/second of a single tank by multiplying the Isp by a constant equal to 21.8 × ln(20/19) / 3600 = 0.00031. Reversing this equation, the Isp of standard hydrogen-oxygen propellant is 0.15/0.00031= approx. 484 seconds. I've noticed that changes in ΔV vary inversely with those of thrust; therefore, the acceleration provided by a chemical rocket using a different propellant would be 3×484/Isp = 1,452/Isp Gs. The endurance of the tank would be Isp squared times 0.00031×3600/(1452×21.8) = 0.000035 seconds.

Example: According to page 13 of "Mars Direct: A Simple, Robust, and Cost Effective Architecture for the Space Exploration Initiative" by Robert M. Zubrin (Copyright © 1991 by Martin Marietta Corp.)"the optimum oxygen to methane combustion mixture ratio is about 3.5:1, as this provides for a specific impulse of 373 s" Thus, ΔV/tank for an O2/CH4 rocket would be 373×0.00031=0.11563 mps, with its thrust being 1,452/373=3.893 Gs. A tank of propellant is consumed every 4.9 seconds. A Mars Ascent Vehicle would require at least 13.5 tanks of propellant just to reach LMO (low Mars orbit, ΔV=2.48 mps).(Note that the mixture ratio is by volume, not mass. This will be important later.)

Calculating the cost of the propellant is a little trickier. Oxidizer/fuel mixture ratios are usually stated in terms of volume, not mass. The price per ton of propellant is (R×Mo×Po+Mf×Pf)/(R×Mo+Mf) with R being the volume mixture ratio and Mo/Mf and Po/Pf being the molecular weights and price/ton of oxidizer/fuel respectively.

Example: The price of liquid methane is $500 per ton (SS7 p.21). I tried in vain to locate a 4E price for liquid oxygen, so I had to calculate it from 3E sources. I got $18.99/ton from GURPS Transhuman Space and $20.83/ton from GURPS Vehicles 2nd Edition, so I'm splitting the difference and pegging it a $20/ton. Thus the price O2/CH4 propellent is (3.5×32×20+16×500)/(3.5×32+16)=$80/ton.

† NOTE: Isp on this page are for sea level, not vacuum. This can make a significant difference.

Dalton “thinking about O2 for internal combustion” Spence

EDIT: I realized that I could deduce the 4E price of LOX from LH2/LOX rocket fuel. With Rocket fuel at $800, Hydrogen at $2,000 (SS1 p.46) and the ratio of oxygen to hydrogen by weight in water being 8:1, the 4E price of LOX would be ($800×9-$2,000)/8=$650/ton. Thus the price O2/CH4 propellant would be (3.5×32×650+16×500)/(3.5×32+16)=$631.25/ton.