To The Moon
One of the really fascinating things about listening to the streaming audio of the first moon landing is how much time was spent debugging the spacecraft, resetting this and that.
As the memory fades away, Charlie Stross wrote about the difficulties in going back to the moon:
Not only does the cost of putting a payload into orbit increase with the cube of the payload weight — this rule holds true in the opposite direction, too. Stick a LEM on the moon and bring the contents back? Easy. Increase the mass that the LEM brings back? Very expensive — the price goes up as the sixth power of the weight you’re returning from the lunar surface (because you have to loft the heavier LEM into Earth orbit to begin with).
I don’t follow the cube law. Charles definitely knows his rockets so I don’t think he’s wrong. I’ll explain out loud and maybe figure it out myself in the meantime.
One form of the rocket equation is:
(M + P) / M = e ^ (?V / C)
The left side of the equation is the mass ratio; M is the mass you want to move, and P is the mass of the propellant. A sample mission might have the weight of the fuel being 10 times the weight of the mission mass.
The right side is propellant. ?V for a one-way trip to the moon or Mars is (very roughly) 10 km/s. C is exhaust velocity, and for the best chemical rockets with a Specific Impulse of 450, it’s about 4.4 km/s.
That makes the right-hand side e^(10/4.4), or something like 7.4. That’s a linear increase of propellant in terms of mission mass.
There are some issues of scale that I haven’t accounted for, like the mass of the rocket boosters, and they’ll definitely pile up if you try to push too much into a single flight. Although the Space Shuttle is around 2000 tons.
Assembling stuff in space is very very hard. Assembling stuff on the surface of a planet, while nothing I’ve done myself, is much easier by comparison. We can drop things onto the moon or onto Mars and put them together later.
(And with Mars we have the real possibility of reacting imported hydrogen with atmospheric carbon dioxide to manufacture rocket fuel at a huge mass advantage.)
I think what you’re missing is that when you add fuel, you now have to lift the mass of that additional fuel, as well. And when you’re talking about an out-and-return mission, the fuel for the return trip has to be lifted twice.
In its pure form, the rocket equation makes there be a linear relation between mass and propellant. If your mass-ratio is 9.7, you need your M+P to be 9.7 times P.
Now if you want to go farther (like a return trip), those fuel costs scale dramatically. A mission with a ?V/C of 20 will have a mass-ratio 22,000 times worse than one with a ?V/C of 10. (The 22,000 number is the mass ratio on each leg of the trip; they multiply together.)
A return-human(s)-from-the-surface-of-Mars mission is pretty much impossible if you don’t manufacture fuel on the planet’s surface.
I think the cube-law comes from the infrastructure, like needing more and bigger fuel tanks, which count as “mission mass” in the rocket equation but really don’t fit any goal.
How big a thing can you launch from an air-breathing plane?
I have been reading your posts lately, just want to say thanks for all informative stuff i have found here, helped me learn alot lately.
Much Regards, Mark