If only it were that simple...Unfortunately, delta v to orbit increases with higher Isp as gravity losses increase (propellant mass decreases at a slower rate), and drag losses increase with lower density propellants. LH2 NTR is the worst case for these factors.Also low density propellants require much larger tankage and bigger engines, using much more of that remaining GLOW fraction than a high density, but lower Isp, would.You really need to examime each case using reasonable aindividual ssumptions for each propellant, for things like: engine T/W, tank mass, delta v to orbit.
I've played with nuclear air-breather numbers before as well and what I found was that the crucial factor is the engine T/W at the switch to full rocket mode as that sizes the core NTR which flows through the design. With that in mind there are a couple of engine designs you've missed. Adding Lox-augmentation that tapers off through the trajectory after the transition to full rocket mode allows for a smaller core as well as atmospheric compensation in the nozzle and relatedly a SABRE precooled design that also does ACES and collects air for that thrust augmentation later in flight. Also, assuming this is technically possible, a NH3/H2 slush fuel is possibly slightly more efficient. The key design question is however, manned or unmanned. Unmanned requires very little shielding and would seem very build-able while manned requires a lot and is potentially more marginal depending on core and shielding technology.
I was surprised to find just how ridiculously well a simple water NTR performs once you move from a solid-core to an optimized pebble-bed.
NH3 should be much better than H2O as it decompose to N2 and H2
Assumed specific impulses:- Hydrolox: 366 s at SL, 452 s in vacuum- Methalox: 334 s at SL, 382 s in vacuum- Kerolox: 282 s at SL, 348 s in vacuum
Quote from: sevenperforce on 04/16/2017 03:59 pmI was surprised to find just how ridiculously well a simple water NTR performs once you move from a solid-core to an optimized pebble-bed. Provided of course you can build a flight weight PBR.
Quote from: sevenperforce on 04/15/2017 01:32 pmAssumed specific impulses:- Hydrolox: 366 s at SL, 452 s in vacuum- Methalox: 334 s at SL, 382 s in vacuum- Kerolox: 282 s at SL, 348 s in vacuumDon't look like a fair comparison. Using FRSC for hydrolox,FFSC for methalox and GG for kerolox (without mentioning it).Difference between kerolox and methalox is MUCH SMALLER when using an equivalent engine cycle and equal pressure, and still considerably smaller when using optimal cycle for each. (if FFSC is impossible for kerolox, then use ORSC for that, instead of GG)
Quote from: john smith 19 on 04/16/2017 08:36 pmQuote from: sevenperforce on 04/16/2017 03:59 pmI was surprised to find just how ridiculously well a simple water NTR performs once you move from a solid-core to an optimized pebble-bed. Provided of course you can build a flight weight PBR.And also provided it doesn't melt down. Both Earthbound pebble beds and propulsion prototypes were.... problematic at best.
To pile on this a bit: only the hydrolox numbers have been demonstrated in a single engine - RS-25. The others are probably not feasible with a single engine since they require expansion ratios of 150 or better. A double-expansion nozzle might get close. I'm not sure what aerospikes get in practice, but they might be close also.I suppose that's the least of the technical concerns when talking about nuclear SSTOs, though...
Yeah, sorry; I just ripped isps from the SSMEs, the Merlin D, and the Raptor (projected). Is there a better list?
You might be surprised. The liquid-metal TaHfC pebble-bed reactor with a water-based exhaust of 5.4 km/s has a bare-bones TWR of 260:1, including the weight of the reactor, the turbopump, the nozzle, and the gimbal system, at a 12 kN vacuum thrust rating. Of course, that's without safety margins or shielding. But it's not outside the realm of possibility.Using liquid water makes it very thrusty.
The primary problem with the NERVA prototype was, if I recall, hydrogen corrosion. Not a problem (or not as much of a problem) with water. Meltdown isn't a problem for TaHfC encapsulation; the fuel is supposed to melt. Casting the fuel pebbles might be rough, though.
Quote from: sevenperforce on 04/17/2017 04:06 pmYeah, sorry; I just ripped isps from the SSMEs, the Merlin D, and the Raptor (projected). Is there a better list?Well I suppose people might be arguing for using the RD-180 instead of the Merlin 1D. However the trade is that the TWR of M1D is more than 2x better than that of RD-180. It would be reasonable to look at both, I think.
Quote from: Katana on 04/17/2017 03:17 amNH3 should be much better than H2O as it decompose to N2 and H2NH3 + H2O2 or O2?Isp?
The idea was to create a restriction on SSTO designs. E.g., even if you had an altitude-compensating engine with full SL and vac performance to work with, you'd STILL have to beat this particular fuel fraction to make SSTO.To that end, though, I should probably use the max isp of each engine type.
Quote from: sevenperforce on 04/17/2017 04:06 pmYou might be surprised. The liquid-metal TaHfC pebble-bed reactor with a water-based exhaust of 5.4 km/s has a bare-bones TWR of 260:1, including the weight of the reactor, the turbopump, the nozzle, and the gimbal system, at a 12 kN vacuum thrust rating. Of course, that's without safety margins or shielding. But it's not outside the realm of possibility.Using liquid water makes it very thrusty.Not really surprised due to its density but I'd like to see what that does to it's Isp. NERVA was around 900secs.
I'd also like to see what you're using for the Isp curve for a deeply pre cooled airbreathing hydrolox design.
I'd be very surprised if any TaHfC design expected the pebbles to melt. Their purpose in the original designs were increase the surface area and ensure fission product containment.
By any chance, has anyone ever put together the hoped for vehicle and engine mass and performance figures for Venture Star compared to how various X-33 systems were headed before cancellation? I know engine weight was coming in high.
Might want to look over the ESA NTER work using an NTR with an inductive heater augmentation. Helium gas power cycle direct drives a turbine with rotor mounted magnets, creating what they call a turbo-inductor which skips power conversion steps and gets up to tungsten melting temps. Would this nominally be a supercharged cycle, or parallel mixed cycle concept? The kicker is this turbo-inductor is before the nozzle, so in theory that leaves room for something crazy like backending it with a VASIMR-esque accelerator/nozzle since you are near plasma conditions.
As a filler, how do beamed propulsion (laser/microwave) LH2 SSTO stacks compare for fuel fractions? If the engine is effectively offboard, doesn't that put an limit bounds on the fuel fraction graph?
NH3 is actually not that great. It disassociates readily, but since N2 is heavier than O2 and water already has a pretty solid disassociation fraction at these operating temperatures, there isn't much of an improvement. Ammonia is much, much less dense than water, too, so that's a big issue for SSTO designs.
Quote from: sevenperforce on 04/17/2017 06:05 pmNH3 is actually not that great. It disassociates readily, but since N2 is heavier than O2 and water already has a pretty solid disassociation fraction at these operating temperatures, there isn't much of an improvement. Ammonia is much, much less dense than water, too, so that's a big issue for SSTO designs.How is N2 (atomic weight ~14, molecular weight 28) heavier than O2 (atomic weight ~16, molecular weight 32)?The density is 68% of that of water which is less but not to the extreme of LH2 which is 10x worse.
What about using either1) water-hydrogen variable mixture ratio NTR. Liftoff with just water to get better T/W, and then gradually switching to pure hydrogen to get better isp later2) hydrolox-chemical-NTR-serial-hybrid rocket. Use NTR as "preburners" for chemical; First NTR warming up separately both hydrogen and oxygen into as high temperature as it can sustain, and then putting them up together in the final combustion chamber to ignite the chemical reaction which further increases the temperature and exhaust speed. And if pure hydrogen-NTR still allows better isp, then use this hybrid more only early in the flight where this might allow much better T/W than pure hydrogen-NTR.
More likely would be a transmix of water and ammonia. Water is already often used as a carrier for ammonia; in fact, pure ammonia is referred to as "anhydrous ammonia". Using a blend of water and ammonia that changes mixture ratio during flight would be a great way to get high thrust off the pad and high(er) specific impulse for the terminal part of the burn.To your second suggestion: something very similar to this has already been proposed; it's called LANTR, or LOX-Afterburning Nuclear Thermal Rocket. Basically, it's a normal liquid hydrogen NTR (although any reducing propellant would work), but the nozzle has injectors which allow LOX to be pumped into the hot exhaust stream after the nozzle throat. The LOX ignites with the nuclear-heated hydrogen, boosting thrust by a factor of about 3 but only cutting specific impulse by about half. If the LOX was "preburned" by vaporizing it in a less energetic external coolant loop, I bet the performance could be even higher...though then your pump system is dealing with Very Hot LOX, which is not a nice thing to deal with at all.
Quote from: sevenperforce on 04/18/2017 12:47 pmMore likely would be a transmix of water and ammonia. Water is already often used as a carrier for ammonia; in fact, pure ammonia is referred to as "anhydrous ammonia". Using a blend of water and ammonia that changes mixture ratio during flight would be a great way to get high thrust off the pad and high(er) specific impulse for the terminal part of the burn.The water/ammonia system is a nice idea. There is this: http://www.astronautix.com/o/okb-670.html which gives isp 430 (sl) / 470 (vac?) for mixed alcohol/ammonia fuel. Since this is from ~1958 the reactor operating temperature is probably a lot lower than you are assuming for your PBR. Still, hydrolox isp from a propellant that's a lot easier to deal with than LH2. Oh, I just found a reference to this in Rockets and People that says the propellant is heated to 3000K.
More likely would be a transmix of water and ammonia. Water is already often used as a carrier for ammonia; in fact, pure ammonia is referred to as "anhydrous ammonia". Using a blend of water and ammonia that changes mixture ratio during flight would be a great way to get high thrust off the pad and high(er) specific impulse for the terminal part of the burn.
For LANTR, why would you put a turbopump after the cooling loop? Ideally you pump LOX into the cooling circuit and it partially/completely vaporizes on the way to the nozzle injection ports.
Quote from: josespeck on 04/17/2017 05:23 pmQuote from: Katana on 04/17/2017 03:17 amNH3 should be much better than H2O as it decompose to N2 and H2NH3 + H2O2 or O2?Isp?Katana is talking about reaction mass for the high temperature pebble bed NTR, there is no oxidizer.2 H20 --> 2 H2 + O2 avg molecular weight (2*2+32)/3 = 122 NH3 --> 3 H2 + N2 avg molecular weight (3*2+28)/4 = 8.5So, for the same NTR power level seems like NH3 would give you lower thrust and higher ISP. Could have 2 tanks, use the higher thrust with water to lower gravity losses.