Alsadius and I have been discussing the physics of fusion power by PM and I wanted to lay it out clearly in case anyone wants to use the actual physics.

Fusion starts with Hydrogen and turns it into Helium. In theory, you could keep fusing beyond Helium to Iron, but the energy gain is only modest and anyways "mostly Helium" is the stated output.

Hydrogen-1 yields the most energy with an atomic mass of 1.007825. This is fused into

Helium-4 with an atomic mass of 4.002602. The mass lost when fusing 4 hydrogen atoms into a helium atom is therefore d=0.028698 = 4 * 1.007825 - 4.002602. Using E=d c

^{2} this yields the energy of fusion where c is the speed of light.

Using the energy to accelerate the Helium created we can solve for the velocity v using the kinetic energy equation: d c

^{2} = 0.5 mass_helium v

^{2} . Solving, we get v = (2 d c

^{2}/ mass_helium)

^{0.5} = 35.9*10

^{6} meters / second. Plugging this into the

Rocket Equationwith a 1e-3 fraction of mass for fusion + reaction mass then implies the ship moves at about 52 hexes/minute. Rounding down slightly, this suggests 50 thrust points per 1e-3 fraction of total mass used as fuel.

So, if you wanted to maintain a thrust of 1g for a day, it would require 5.8% of the vessel mass and a 1g transit form Earth to Zenith transit point would require 53% of the vessel mass. At this level of mass consumption, the

Rocket Equation starts to matter so we should look for cheaper options.

The mass use of a constant-g transit can be decreased by simply accelerating slower---at 1/10th g, it takes only a factor of 10

^{0.5}~=3.16 longer, reducing the overall fuel mass requirements by 10

^{0.5} to about 17% of the initial mass. This square root relationship holds generally.

When traveling at station-keeping drive scales, another obvious trick comes up. You can just transit with the jumpship, but when outbound, there is no need for a turnover since you can do a jump with an arbitrary velocity. Unfortunately, jumping sheds velocity so this trick cannot be used in-bound. Not turning over saves a factor of 2

^{0.5} in time and hence in fuel use.

It is also possible to increase the thrust generated from fusion by accelerating additional mass (Hydrogen/Carbon/Oxygen/Iron/whatever) other than the Helium leftovers. The general equation here is again a square root, so increasing the mass lost by a factor of 10 yields a 10

^{0.5} increase in thrust. Given this, ship designs allowing "overthrust" by burning a factor of 4 more fuel to achieve a factor of 2 more thrust seem reasonable.

Overall, it seems feasible to run the game using something consistent with the physics of fusion, but fuel use becomes a much more important part of the process at transit scales. No constraints from the physics are imposed on ASF, but even a 200 ton smallcraft burning fuel at the "strategic" rate violates the physics---at 1g it uses up a burn-day's fuel after about 9 hours. A 30 ton smallcraft using strategic fuel rules however is consistent with the physics of fusion.

Edit: fixed a factor of 2 error in the kinetic energy equation and used rocket equation to figure out thrust.