vehicles on Mars: lifting capacity

[whswhs]

One of the vehicle written up in GURPS Mars is a Martian blimp. However, it statistics are for Mars as it is now, and the future Mars of my campaign has undergone early terraforming, increasing its atmospheric mass of carbon dioxide and thus raising its air pressure. I wanted to figure out what its lift would be under those conditions, so I took a look at data on Mars—and found that, whereas Mars's atmospheric pressure in about 0.6% of Earth's, GURPS Mars says that one cubic foot of hydrogen at Earth pressure would occupy 30 cf at Martian pressure. That doesn't seem right: PV = P'V', and the inverse of 0.006 is 167, not 30!

After some thrashing around, I decided I needed to work out the lift factor from first principles, as the differences in weights between a volume of hydrogen and a volume of Martian atmosphere.

So, to begin with, since PV = P'V', and since P' for my fictional Mars is twice that of real Mars, or 0.012 atmospheres, V' must be 83.3. That is, any given number of molecules must occupy 83.3x as much volume on Mars as on Earth. One cubic foot of Earth air turns into 83.3 cf of Earth air on Mars.

What's the mass of that volume of air? Dry air on Earth has a mass of 1.29 kg per cubic meter. The mean molecular weight of dry air is 28.97. That of hydrogen is 2.016, which gives a mass of 0.09 kg. I don't have a figure for Mars's atmosphere, but it's 95% carbon dioxide, and (by assumption) all the extra gas that goes into doubling the pressure is also carbon dioxide, raising that to 97.5%; treating it as pure carbon dioxide will come fairly close to the correct figure. Carbon dioxide has a molecular weight of 44.09, so its mass is 1.96 kg. That takes up one cubic meter on Earth, but 83.3 cubic meters on Mars. A cubic meter is 35.3 cubic feet, so 83.3 cubic meters is ~2942 cubic feet. To avoid working with ridiculously small figures, I'm going to figure masses per million cf: 30.6 kg for hydrogen and 666.2 kg for carbon dioxide.

How much do those masses weigh? On Earth, a kilogram mass weighs 2.205 pounds. Mars's gravity is 0.3794g. Taking 30.6 x 2.205 x 0.3794 gives 25.6 pounds for hydrogen; taking 666.2 x 2.205 x 0.3794 gives 557.3 pounds for carbon dioxide. The difference is 531.7 pounds (of Martian weight, of course). Dividing this into a million, I find that it takes 1880 cubic feet of hydrogen to lift one pound against Martian gravity. (For cost purposes, that's the equivalent of 22.6 cubic feet on Earth.)

The 9.5M cf lifting gas in GURPS Mars will lift a bit over 5000 pounds on Mars—if I've done the calculation right. Anyone want to check me?

If I'm right, then since the Mars blimp has a loaded weight of 1.85 tons, or 3700 pounds, it ought to need 7M cf of lifting gas.