2300 AD Reaction Drives, Only Nukes Compute

bytedruid

Mongoose
Yesterday I ran a quick "back of the napkin" calculation of the specific impulse for a SparrowHawk Spaceplane form the Aerospace Engineers' Handbook using:

Isp = Δv / (g ln( mass_initial / mass_final) )

and was quite pleased to come up with a value of about 1600 seconds for the reaction drive. That's a lot more advanced then today's rockets but not insane like I expected. Nice work Colin Dunn et. al..

So now I'm looking around for some explanation of why 2300 AD reaction drives are ~4 times better then the RS-25s that powered the Space Shuttle. Of course it's just a game and this explanation isn't needed, but there's many ways to enjoy a game, including checking it's math.

Skimming Wikipedia I see the following for reaction drive Isp's.
 Engine Type Specific Impulse (s) Comments Solid Chemical Rocket about 250 Just here for comparison, not really applicable Liquid Chemical Rocket (Space shuttle main Engine) about 450 Hydrogen is bulky, 2300 AD ships don't seem to devote much space to fuel tanks. Plus Isp is too low. Nuclear Thermal Rocket (Solid Core - Nerva, Gas Core - Nuclear Lightbulb) about 800 to 2,000 Looks like the right range, but requires fissionable materials which is probably unavoidable. Electric Rocket (Hall thrusters, Vasimir, etc.) 1,300 to 21,000 Awesome fuel efficiency, but only works in vacuum, takes HUGE powerplant for any reasonable amount of thrust, a non-starter for interface operations. Combination Nuclear thermal + Nuclear Electric about 800 to 4,000 Basically a nuclear thermal rocket with a "kicker" from electric heating to get higher Isp. This feels about right.

The energy to get reactants up to speed has to come from somewhere, and the only reasonably space efficient option seems to be provided by nuclear energy. So to make the rules believable, take the reaction mass needs of the Rocket reaction drive (4% hull tonnage/burn) but apply them to the Nuclear Thruster (which is normally only 1.5% hull tonnage/burn) and we're no longer egregiously violating the rocket equation. This still makes 2300 AD ships very advanced... but reasonable.

Unfortunately the reaction mass/burn given for Rockets on page 15 of the AEH isn't believable. Chemical energy just ain't that dense. Even burning HIGHLY unstable metallic hydrogen in a rotating detonation engine (~1000 s) still doesn't get you there.

Anyway, hat's off too 2300 AD. It passes believably tests far better than the vast majority of SciFi settings. I look forward to exploring it more.

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An isp of 1600 is pretty much exactly the isp for monoatomic hydrogen, which if we could stabilize it would be a perfect rocket fuel for high thrust applications like getting into orbit.

Sounds plausible, though the AEH states that Rockets, as used on the SparowHawk spaceplane, are HydroLox (page 23). So ultradense monoatomic metallic hydrogen fuel isn't part of the rules a written, but of course there's no reason a Ref couldn't go that route for their game.

Instead of proposing something so exotic, there is another route. The Isp of a gas core nuclear rocket is greater then 2000 s, and other than the uranium hexafluoride (which isn't expended in the exhaust) the only fuel is liquid H2. Since H2 quickly dissociates at nuclear rocket chamber temperatures, you get all the benefits of monoatomic hydrogen without even having to store it in that form. So if a Referee just assumes assumes nuclear engines on interface craft, the designs mostly work with just a small increase in the fuel requirements.

In fact, nuclear rockets more then meet the needs of the setting, so a Ref could use this extra performance to make commercial interface craft cheaper to operate. Instead of liquid H2, purified water could be used as the fuel for a nuclear rocket. Granted you're going to get a drop in ISP of about 25%, but nuclear thermal rockets (especially ones with a microwave afterburners) provide such crazy high exhaust temperatures, that some of the performance could be "wasted" on sub-optimal fuels in order to significantly reduce operating costs.

Water-fed nuclear thermal rockets seem like such a neat combination low-tech and high-tech, that I think I'll make them the standard TL 10/11 interface engines of the game. They will certainly be easier for players to service in rough-field conditions then HydroLox craft.

There was nothing as sophisticated as the rocket equation used. Just a fudge.

The Sparrowhawk has 8.4 dTons of rocket fuel, or ca. 53.5 metric tons of fuel if hydrogen-oxygen.

At 30 dTons, it should be approximately 300 metric tons, giving a mass fraction of 17.8% (or 23.7% with the 225 ton figure). In round figures, it has 0.7 kps of dV, or half of one "burn."

However, it is given as 7 burns, and so exhaust velocity must be 14 times that of a H2/O2 rocket, or ca. 63 kps. Since chamber temperature varies per the square of the exhaust velocity (i.e. to double velocity and hence dV, you have to burn 4 times hotter), for 7 burns out of that fuel, the temperature 14^2 or 196 times the real temperature of H2/O2 rockets. It requires a drive a little over 1 million K.

Suffice to say, that if your drive is a million kelvin, then the ship is an expanding ball of plasma...

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