If we build a 1000 ton fusion-powered spaceship loaded with 10,000 tons of deuterium fuel?

Question

what maximum speed could such spaceship achieve, assuming D+D->He4 reaction and 100% efficient rocket motor?

Note:
usually D+D fusion produces either or He3+n or T+p, but lets not worry about this. Consider that engineers solved all problems and D is on input, and He4 on output.

Answer 1

Since there is no D-D fusion, we have to assume that the T or He3 produced will then react with another D to finalize the reaction and get an energy estimate; on average, starting with deuterium and ending with He4 (+protons + neutrons) will give an energy release of about 10 MeV per pair of D, or 5 MeV for each individual deuterium atom. We can thus assume that the reaction products have an energy of 1.6E-12 J on average, with a mass of 4 g per mole, or 241E9 J per gram. This, in turn, allows a reaction mass ejection velocity of 22000 km/sec (e =1/2 m v^2).

Tsiolkovsky's rocket equation is:

delta V = (ejection speed) ln ( m0/m1)

where m0 is the initial mass, and m1 the final mass. Here m0 is 11000 and m1 is 1000.

This allows the rocket to ultimately reach a speed variation that is 2.4 times the speed of its reaction mass, or 52667 km/sec ultimately (that is 17.6% the speed of light).

Note that my calculations are not adjusted for relativistic effet, mind you, at 17% of the speed of light, those are minimal and can be neglected.

You may want to read the BIS report on Project Deadalus (if you can find it); but the broad lines can be found on the attached link. The reaction is not supposed to be as efficient as your hypothetical perfect DD fusion, and the reaction mass fraction has to be greater, and in the end the target delta V is still only 7% of the speed of light, but that give a good idea how stuck we are with too long distances and not enough energy to make it on time.

The universe is just too big and life is just too short, it seems, for the type of technology we can currently extrapolate.
We'll have to figure out something else...


(To dansigner61 above: you eject the resulting helium as reaction mass. The mass reduction due to fusion is in the order of 0.7% in the case of proton-proton reaction, too small to impact the evaluation of the reaction mass bulk)

Answer 2

I'm not sure how you would use fusion to power a space ship. A spaceship needs to eject mass at high velocity in order to accelerate by the conservation of linear momentum. (Equal and opposite reaction and all that.) A fusion reaction consumes mass to produce energy, usually in the form of heat and radiation. However, the energy can't be used to do anything useful to cause mass to be ejected out of the nozzle, so what's the point?

Answer 3

What is the thrust, what is the total mass? These questions will decide acceleration and thus the final velocity, which in any case cannot exceed c the velocity of light in vacuum or even become a sizable fraction of it.

Answer 4

your never going to have a 100% effecient rocket motor.