baithammer said:
There is an error in the math shown.
140 MJ/kg = 140 GJ/dt as the conversion between MJ -GJ is 1/1000 whereas kg to dt is 1,000 to 1 therefore negating the difference between units.
Yes, that is correct, thank you.
Let me start over:
Hydrogen has an energy density of ~140 MJ/kg. 1 Dt = 14 m³ contains 1 tonne LHyd, so 1 Dt contains 140 MJ/kg × 1000 kg = 140000 MJ =
140 GJ.
Petrol has an energy density of 47 MJ/kg. 1 Dt = 14 m³ contains 14 × 0.7 ≈ 9.8 tonnes of petrol, so 1 Dt contains 47 MJ/kg × 9800 kg ≈ 460000 MJ =
460 GJ.
But you also have to carry the needed oxygen to burn the fuel.
Each kg of hydrogen requires about 8 kg of oxygen. 1 Dt LHyd = 1000 kg requires ~8000 kg LOX which is 8 / 1.3 ≈ 6 m³ or
0.45 Dt LOX.
Each kg of petrol requires about 3 kg of oxygen. 1 Dt petrol = 9800 kg requires 9800 × 3 = 29.4 tonnes of LOX, which at ~1.3 tonne/m³ takes 22.6 m³ or
1.6 Dt.
So totally we get:
Hydrogen: 140 GJ for 1 + 0.45 = 1.45 Dt, or
96 GJ/Dt.
Petrol: 460 GJ for 1 + 1.6 = 2.6 Dt, or
176 GJ/Dt.
I seem to have made the same mistake for both hydrogen and petrol, so the conclusion stands:
If we use hydrogen we need about twice as much fuel as if we use hydrocarbon fuel.