My friends and I did some math on #ForAllMankind's Pathfinder shuttle and came to the conclusion that, to be able to reach orbit from an airlaunch, have the propellant fit inside its hull, and be light enough for a C-5 Galaxy to lift it, it needs to have a Liquid Core NTR.
From an airplane launch, let us assume you need around 8.8 km/s of ΔV.
A NERVA engine has an Exhaust Velocity of about 8.25 km/s.
Using Tsiolkovsky's rearranged to find the mass ratio, we get that:
e^(8.8/8.25) ≈ 2.9
1/?
A NERVA engine has an Exhaust Velocity of about 8.25 km/s.
Using Tsiolkovsky's rearranged to find the mass ratio, we get that:
e^(8.8/8.25) ≈ 2.9
1/?
Let us assume Pathfinder weights more-or-less the same as the Shuttle Orbiter, and has a payload capacity of ~80 Tons. It thus has 80 + 20 tons = 100 Tons at launch, sans propellant.
A mass ratio of 2.9 makes it so it has a wet mass of 290 tons.
A mass ratio of 2.9 makes it so it has a wet mass of 290 tons.
Wet mass of 290 t - 100 t of payload + vehicle means it has 190 t of propellant - Liquid Hydrogen.
Liq. Hydrogen has a density of 0.072 Tons per m³, so 190 tons of Liq. Hydrogen would take up a volume of 2639 m³.
That's... a lot. For comparison:
3/?
Liq. Hydrogen has a density of 0.072 Tons per m³, so 190 tons of Liq. Hydrogen would take up a volume of 2639 m³.
That's... a lot. For comparison:
3/?
The Space Shuttle cargo bay is 18.3 meters long and has a diameter of 4.57 meters.
Assume it is a cylinder. It'd have a volume of ~300 m³.
Pathfinder's wings may be THICCC (with 3 Cs), but they most certainly do NOT total 8.79666... times the volume of the cargo bay.
4/?
Assume it is a cylinder. It'd have a volume of ~300 m³.
Pathfinder's wings may be THICCC (with 3 Cs), but they most certainly do NOT total 8.79666... times the volume of the cargo bay.
4/?
Let us assume instead that the NTR is running on water.
A solid-core NTR operating at 3200 K running on water has an Exhaust velocity of 4.042 km/s.
e^(8.8/4.042) ≈ 8.82
That translates to a total of 782 tons of water, taking up... 782 m³. That's still too much.
5/?
A solid-core NTR operating at 3200 K running on water has an Exhaust velocity of 4.042 km/s.
e^(8.8/4.042) ≈ 8.82
That translates to a total of 782 tons of water, taking up... 782 m³. That's still too much.
5/?
Woops, I mean payload capacity of ~20 tons.
80 ton orbiter, 20 tons of payload.
80 ton orbiter, 20 tons of payload.
A Liquid-Core NTR running on water has, instead, an exhaust velocity of 10.3 km/s (see the LARS engine). Let us assume 10 km/s for error margins.
e^(8.8/10) ≈ 2.41
That translates to 141 tons of water, for a total vehicle launch mass of 241 tons.
6/?
e^(8.8/10) ≈ 2.41
That translates to 141 tons of water, for a total vehicle launch mass of 241 tons.
6/?
A C-5M Comet has a maximum takeoff weight of 417.3 tons. It weighs 172.4 tons.
So it can take off with our Liquid NTR Pathfinder, but with only a measly 3.94 tons of jet fuel.
Presumably the Pathfinder carrier variant is of the C-5 is lighter.
7/8
So it can take off with our Liquid NTR Pathfinder, but with only a measly 3.94 tons of jet fuel.
Presumably the Pathfinder carrier variant is of the C-5 is lighter.
7/8
Thus we conclude that uh... some liberties were taken.
Then again, who knows? Maybe they have all the data and they'll release it to us at some point.
Maybe Pathfinder is just much lighter than the Shuttle.
8/8
Then again, who knows? Maybe they have all the data and they'll release it to us at some point.
Maybe Pathfinder is just much lighter than the Shuttle.
8/8
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