Shubedobedubopbopbedo wrote:Well, for one thing, the use of a massive pusher plate is just plain dumb. The impact of the blast would require shock absorbers, which in turn would require a cooling system and huge radiators. Not only would a large fraction of the energy of the blast be wasted by not impinging on the pusher plate, a large fraction of the energy impinging on the plate would be wasted as well, damped and converted into heat.
A few points:
1) The "shock absorbers" are not spring-dashpot units like in a car. They're undamped. Most of the excess mechanical energy in the shock absorption system just stays there during operation; the system is essentially a harmonic oscillator, and a pulse just reverses the direction of travel of the plate, rectifying the oscillation (or not, in the case of a dud/misfire, but the system is designed to handle this situation; it just waits another cycle of the oscillation and tries another bomb).
2) The collimation factor for a properly-designed Orion using properly-designed pulse units can get quite high. These are not spherically-symmetric explosions.
3) Your energy accounting is missing some numbers.
The base design was a 4000-ton vehicle with (according to Wikipedia) 0.15 kt bombs. That's 628 GJ per blast. Apparently each blast adds 30 mph to the fully-loaded vehicle (perhaps the pulse units are not all identical, or perhaps Wiki is wrong about the yield... if that were vacuum performance with all-identical 0.15 kt pulse units, you'd have trouble fitting even a single 900-unit charge into a vehicle with a 4000-ton GLOW, never mind a half a dozen spare magazines of 900 units each). Anyway, that's 326 MJ of vehicle kinetic energy added per 628 GJ blast, in the vehicle inertial reference frame immediately prior to the pulse.
Now, this sort of thing is unavoidable considering the vast difference in mass between the spacecraft and the pulse unit. Conservation of momentum alone dictates the amount of energy 'lost'; the amount of damping loss in the shock absorber system does not affect it at all (well, except for an infinitesimal advantage obtained from a higher downward velocity of the pusher plate during the blast, but that's negligible; it increases Isp by maybe a few parts per thousand even at this low performance level). Barring improvements in the collimation factor (which is already pretty good), you cannot improve on the energy ratio without reducing the Isp. It's no different from chemical rocketry, in which most of the energy of combustion leaves with the high-velocity propellant.
Most of the heating on the pusher plate is handled by the ablative oil sprayed on between blasts, so it can be ignored. What about the shock absorber system?
The blast rate is about one per second. Based on the diagram in the Nuclear Pulse Space Vehicle Study, part III, the pusher plate (86' across, 3.75" thick at the edge, at least 8" in the centre) is probably in the vicinity of 600 tons or more. Thus the initial velocity of the plate is 200 mph, with an energy of 2.18 GJ. So the live energy in the shock absorber oscillation is about 1.85 GJ. How much of that does it bleed off in half a cycle (about one second)?
Well, it's complicated, since the system is designed for the obviously unachievable target of zero damping, but let's pick a number out of the air and say 5%. If that number is somehow accurate, the shock absorber system dissipates 92.5 MJ per pulse, or 92.5 MW.
[Just FYI, I calculate that ionizing radiation from the blast puts about twice that amount of energy (give or take an order of magnitude or two) into the pusher plate. It would be more, but the heavy tungsten/beryllium oxide reaction mass absorbs a bunch of it. In any case, the thing is sprayed with oil every time, which helps a lot with cooling...]
Please note that a typical "burn" for the baseline Orion was about 800 pulses, and it actually could not exceed 900 pulses in one go without pausing to swap in a fresh magazine. A thousand tons of carbon steel, initially at room temperature before absorbing 800 doses of 92.5 MJ each, will heat up by about 168 K, assuming
no cooling, radiative or otherwise. That leaves the assembly at 466 K, or just barely hot enough to melt solder.
With the use of higher-Isp (=lower-thrust, leading to reduced pusher energy) pulse units in space, and the potential for lower shock absorber system losses than the 5% per half-cycle I used above, I'd hazard a guess that an Orion of this class with a surface emissivity of zero could expend its entire bomb load without getting the steel anywhere near hot enough to fail...
What would it take to dissipate 92.5 MW in steady-state? Keeping in mind that you don't have to...
Well, based on the drawings in the study, the second-stage shock absorbers have a surface area in the range of 1000 m², and the first-stage shock absorbers have a surface area in the range of 900 m² (counting the intermediate platform but not the pusher). Taking intercept fractions into account (eyeballed values), and accounting for surface availability during a pulse cycle, let's say 400+400+200 = 1000 m². Assume an emissivity of 0.55 for steel.
1312 K equilibrium temperature. That's 1039ºC, or 1902ºF. Coat the steel with something with an emissivity of 0.9, and the temperature drops to 1160 K, or 887ºC, or 1629ºF.
Steel should be able to handle that, right?
Sure, there might be hot spots and issues with internal conductive heat transfer. But these are preliminary design studies - detailed designs could easily include provisions for efficient waste heat radiation. It doesn't take much, as you can see. Nothing particularly "huge" - the outer surface of the upper section of the propulsion module would do nicely all by itself...
Or you could simply design it to have lower damping losses. At 1% loss per half-cycle, 776 K is adequate. That's 503°C, or 937ºF. Even aluminium could survive
that...
