### Author Topic: Minimum fuel fractions for SSTOs  (Read 2304 times)

#### sevenperforce

• Full Member
• Posts: 743
• Liked: 172
• Likes Given: 220
##### Minimum fuel fractions for SSTOs
« on: 04/15/2017 01:32 PM »
There are so often discussions about various SSTO proposals. I was doing a little research on airbreathing nuclear-thermal rockets and ended up expanding it out to provide fuel fractions for a wide range of possible SSTOs. These all represent (within error) the minimum achievable fuel fraction for an SSTO rocket; if someone wants to build an SSTO, it would have to be within these margins. For each fuel/propellant type, I've shown the fuel fraction for a pure rocket, a ducted rocket, a turborocket, and (where applicable) a precooled compressor air turborocket.

If the table says a given fuel fraction is 85.5%, then you've gotta fit your engines, tanks, airframe, and payload (plus margins and recovery hardware) into the remaining 14.5% of GLOW. Note that I didn't even include the values for a "true" airbreather (e.g., turbojet/ramjet/scramjet), because the thrust losses of combusting the airstream while still trying to accelerate make net performance far, far worse than even a pure rocket design. Skylon is a possible exception, but I didn't try to model it.

Here's the table:

A visual chart:

Each SSTO ascent profile is constructed around a base assumption of 7.8 km/s to orbit, plus 750 m/s of gravity drag and 750 m/s of air drag.

The NTRs are Tantalum Halfnium Carbide pebble-bed reactors operating at slightly over 4400 K; basically the best thing we could actually build with modern tech.

Assumed specific impulses:

- NTR (H2O): 469 s at SL, 555 s in vacuum
- NTR (LH2): 820 s at SL, 971 s in vacuum
- 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

Rocket only. This is provided mostly for comparison. It is assumed that a rapid climb is used to leave the atmosphere as soon as possible, with peak specific impulse and zero drag being reached around 2 km/s. This design invariably has the worst fuel fraction but allows the highest TWR engines. As mentioned above, altitude compensation is assumed; specific impulse climbs linearly to 2 km/s before plateauing at the vacuum value.

Air-augmented. This is an optimally designed intake shroud/duct with area behind the duct for expansion. A 22% static thrust boost is assumed due to pressure entrainment. Thrust augmentation reaches 100% around Mach 1.75, then begins to drop around Mach 6, decreasing to zero at the exhaust velocity of the actual engine. Aerodynamic drag is higher, at 800 m/s, and is spread out over a larger range of airspeeds, with vacuum specific impulse being reached much later. This represents a large fuel fraction gain for a fairly modest decrease in engine TWR. Specific impulse starts at slightly higher than the vacuum isp, then rises rapidly before dropping gradually.

Turbocharged. This adds a single-stage compressor fan to the shroud inlet. The increase in static thrust is substantial, allowing a physically smaller engine, but there is only a fractional improvement in net fuel fraction, as the fan is only useful to about Mach 2. Because the fan intake is more demanding than a ram intake, the design and vehicle integration may prove to cost significantly more in dry mass than it saves. However, the turbocharger can (in principle) be used alone as a ducted fan for a hover-light landing, which is a nice and very efficient advantage if you're looking for that (e.g., with an integrated-cabin manned launch vehicle). Aerodynamic drag increases to 850 m/s.

Precooled. This is the design employed by SABRE, albeit without combustion of the airstream. Precooling the intake air allows the compressor fan to operate up to Mach 5 with hydrogen and Mach 3 with densified methane, with a corresponding improvement in fuel fraction. Water and kerosene are excluded, for obvious reasons. Dry mass penalty will be hefty, though.

For those who REALLY want to nerd out, I can also provide the specific impulse curves and drag curves I used to generate the fuel fractions.

#### kkattula

• Member
• Senior Member
• Posts: 2504
• Melbourne, Australia
• Liked: 8
• Likes Given: 3
##### Re: Minimum fuel fractions for SSTOs
« Reply #1 on: 04/15/2017 02:34 PM »
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.

#### sevenperforce

• Full Member
• Posts: 743
• Liked: 172
• Likes Given: 220
##### Re: Minimum fuel fractions for SSTOs
« Reply #2 on: 04/15/2017 04:03 PM »
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.
If you look more closely, you'll note that the fuel fraction calculations exclude considerations of tankage ratio and engine TWR. These values represent the minimum fuel fraction for the given configuration; you still have to add in your engine mass (which will be a larger percentage of GLOW with higher-isp propellants) and your tankage and airframe mass (which will also be a larger percentage of GLOW with low-density propellants) and any other margins, like added drag losses.

This table doesn't say that SSTOs are automatically possible, but it does readily exclude a given SSTO proposal if it requires a fuel fraction lower than what is provided in the table. You can also use the table to project what tankage ratio and engine TWR are required for a given payload fraction or vehicle dry weight...or, on the flip side, to quickly determine what maximum payload fraction you would have for a given engine TWR and material tankage ratio.

For example, if your goal is 10 tonnes to LEO with a dry vehicle weight of 10 tonnes, and your methalox air-augmented engine can reach a TWR of around 40 including the weight of the ducting (and assuming a vehicle takeoff TWR of 1.3), then your tankage ratio needs to be around 25:1 in order to work.

#### lkm

• Full Member
• Posts: 508
• Liked: 91
• Likes Given: 1
##### Re: Minimum fuel fractions for SSTOs
« Reply #3 on: 04/16/2017 12:07 PM »
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.

#### sevenperforce

• Full Member
• Posts: 743
• Liked: 172
• Likes Given: 220
##### Re: Minimum fuel fractions for SSTOs
« Reply #4 on: 04/16/2017 03:59 PM »
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.
Yeah, TWR is a biggie. Depending on your propellant type, you can certainly add a LANTR-style afterburner to boost takeoff thrust, though this won't work with an inert propellant like water. Then again, you can also just add nozzle injectors that flood it with water at sea level to boost thrust with greatly reduced specific impulse, albeit temporarily. This also allows you to use a vacuum-sized nozzle at sea level without flow separation.

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. There is only marginal disassociation at the 3200K operating temperature of a NERVA-style NTR, but if you use a liquid-fissile-fuel pebble-bed reactor with a sufficiently heat-resistant encapsulator (like TaHfC), you can push operating temperature up over 5000K and your disassociation fraction skyrockets, pushing specific impulse up over 500 seconds while still maintaining TWR upwards of 40-60.

Then there's always a solid-core pulsed NTR with near-torchship performance, but the neutron flux would make a manned version kind of tricky.

I didn't include true airbreathers or liquid-air-cycle/remass designs, because the intake drag goes way too high to model in a straightforward way.

#### john smith 19

• Senior Member
• Posts: 5366
• Everyplaceelse
• Liked: 660
• Likes Given: 3696
##### Re: Minimum fuel fractions for SSTOs
« Reply #5 on: 04/16/2017 08:36 PM »
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.
Provided of course you can build a flight weight PBR.
"Solids are a branch of fireworks, not rocketry. :-) :-) ", Henry Spencer 1/28/11  Averse to bold? You must be in marketing."It's all in the sequencing" K. Mattingly.  STS-Keeping most of the stakeholders happy most of the time.

#### Asteroza

• Full Member
• Posts: 422
• Liked: 42
• Likes Given: 1
##### Re: Minimum fuel fractions for SSTOs
« Reply #6 on: 04/16/2017 11:50 PM »
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?

#### Katana

• Full Member
• Posts: 233
• Liked: 22
• Likes Given: 3
##### Re: Minimum fuel fractions for SSTOs
« Reply #7 on: 04/17/2017 03:17 AM »
NH3 should be much better than H2O as it decompose to N2 and H2

• Senior Member
• Posts: 2381
• Boca Chica, Texas
• Liked: 2734
• Likes Given: 185
##### Re: Minimum fuel fractions for SSTOs
« Reply #8 on: 04/17/2017 04:11 AM »
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.

#### Asteroza

• Full Member
• Posts: 422
• Liked: 42
• Likes Given: 1
##### Re: Minimum fuel fractions for SSTOs
« Reply #9 on: 04/17/2017 04:43 AM »
NH3 should be much better than H2O as it decompose to N2 and H2

There was recent work about a plasma membrane based ammonia reformer that works at low temp/pressure that used a perforated iron tube and a thin palladium foil tube to get super high hydrogen gas production/separation, but considering the hydrogen travels through the palladium foil, not a high enough rate to support rocket propellant on the fly, but maybe suitable for a fuel cell or slow but steady hydrogen gas production.

Sadly, the announcement is in japanese

there's a sort of english translation, sadly located at one of those weird-japan-news syndicators unfortunately...

http://en.rocketnews24.com/2017/04/07/japanese-professor-develops-device-to-allow-cars-to-cleanly-run-on-hydrogen-from-ammonia/

#### hkultala

• Full Member
• Posts: 518
• Liked: 116
• Likes Given: 41
##### Re: Minimum fuel fractions for SSTOs
« Reply #10 on: 04/17/2017 07:01 AM »
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

Don'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)
« Last Edit: 04/17/2017 07:55 AM by hkultala »

#### Welsh Dragon

• Full Member
• Posts: 163
• Liked: 147
• Likes Given: 18
##### Re: Minimum fuel fractions for SSTOs
« Reply #11 on: 04/17/2017 07:49 AM »
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.
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.

#### envy887

• Full Member
• Posts: 1924
• Liked: 842
• Likes Given: 505
##### Re: Minimum fuel fractions for SSTOs
« Reply #12 on: 04/17/2017 02:20 PM »
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

Don'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)

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...

#### sevenperforce

• Full Member
• Posts: 743
• Liked: 172
• Likes Given: 220
##### Re: Minimum fuel fractions for SSTOs
« Reply #13 on: 04/17/2017 04:06 PM »
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.
Provided of course you can build a flight weight PBR.
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.

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.
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.
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.

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
Don'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)
Yeah, sorry; I just ripped isps from the SSMEs, the Merlin D, and the Raptor (projected). Is there a better list?

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...
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.

#### acsawdey

• Full Member
• Posts: 259
• Minnesota
• Liked: 130
• Likes Given: 263
##### Re: Minimum fuel fractions for SSTOs
« Reply #14 on: 04/17/2017 04:15 PM »
Yeah, 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.

#### john smith 19

• Senior Member
• Posts: 5366
• Everyplaceelse
• Liked: 660
• Likes Given: 3696
##### Re: Minimum fuel fractions for SSTOs
« Reply #15 on: 04/17/2017 04:25 PM »
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.
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.

Quote from: sevenperforce
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.
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.

You should this site for previous threads on  fission and in particular pebble bed systems. RAndyC did several posts on other threads and pointed out the flow dynamics on pebble beds are complex.

On a more general point water at high temperatures and pressures is chemically very aggressive. Inside a PWR it's 300c at 200 atmospheres. You might like to google "Supercritical Wet Oxidation" to see what it can do as the temperature and pressure rises.
"Solids are a branch of fireworks, not rocketry. :-) :-) ", Henry Spencer 1/28/11  Averse to bold? You must be in marketing."It's all in the sequencing" K. Mattingly.  STS-Keeping most of the stakeholders happy most of the time.

#### envy887

• Full Member
• Posts: 1924
• Liked: 842
• Likes Given: 505
##### Re: Minimum fuel fractions for SSTOs
« Reply #16 on: 04/17/2017 04:56 PM »
Yeah, 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.

And hydrolox can easily get up to 465 seconds when highly expanded in vacuum.

#### josespeck

• Member
• Posts: 29
• Liked: 5
• Likes Given: 5
##### Re: Minimum fuel fractions for SSTOs
« Reply #17 on: 04/17/2017 05:23 PM »
NH3 should be much better than H2O as it decompose to N2 and H2

NH3 + H2O2 or O2?
Isp?

#### acsawdey

• Full Member
• Posts: 259
• Minnesota
• Liked: 130
• Likes Given: 263
##### Re: Minimum fuel fractions for SSTOs
« Reply #18 on: 04/17/2017 05:48 PM »
NH3 should be much better than H2O as it decompose to N2 and H2

NH3 + 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 = 12
2 NH3 --> 3 H2 + N2 avg molecular weight (3*2+28)/4 = 8.5

So, 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.

#### envy887

• Full Member
• Posts: 1924
• Liked: 842
• Likes Given: 505
##### Re: Minimum fuel fractions for SSTOs
« Reply #19 on: 04/17/2017 06:04 PM »
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.

If you're looking for a limit, try using RPA to get the theoretical maximum performance values at the highest practical chamber pressures. You can also plot altitude dependence, even in the lite version.

#### sevenperforce

• Full Member
• Posts: 743
• Liked: 172
• Likes Given: 220
##### Re: Minimum fuel fractions for SSTOs
« Reply #20 on: 04/17/2017 06:05 PM »
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.
Not really surprised due to its density but I'd like to see what that does to it's Isp. NERVA was around 900secs.
Exhaust velocity is, as I note above, 5.4 km/s. So that's around 550 seconds. Obviously you can do much better at equivalent temperatures with LH2, but at greatly reduced thrust.

Quote
I'd also like to see what you're using for the Isp curve for a deeply pre cooled airbreathing hydrolox design.
I was looking at partial airbreathing: a turboramrocket rather than something as complex as SABRE. I can do SABRE, though. Note that I'm using net effective Isp, subtracting intake drag. Here's the specific impulse curve for the precooled hydrolox turboramrocket:

One issue with doing SABRE-SKYLON is that I'd have to add in lift drag, which is an entirely different beast.

Quote
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.
The design noted above was liquid-metal-fission fuel, so the TaHfC encapsulation shell encases the fuel pellets, which melt as soon as operating temperature is reached, but are contained by the shell.

Yeah, 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.
I mean, in theory I could just look at the potential energy of each propellant choice and operate from that, since what I'm really looking for is minimum fuel fraction.

NH3 should be much better than H2O as it decompose to N2 and H2
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.

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.
Let's see -- it was supposed to be a one thousand tonne GLOW with seven linear aerospike engines producing 13.4 MN of thrust. It was to be planned with thrust reserves of around 16% to allow for an engine out. Ariane 5's Vulcain hydrolox GG engine has a TWR of around 84:1, which is probably close to the maximum you can get with hydrolox. An aerospike will necessarily be heavier, though. If we give it a 5% mass penalty, which is generous, our TWR drops to 79.8:1; to get the required thrust we'd need 19.9 tonnes of engine.

By my table, minimum fuel fraction for hydrolox is 89%, so that's 890 tonnes of propellant. Claimed payload to LEO was 20.4 tonnes.

This means that to make it work, they'd have 69.7 tonnes of mass for the tanks, the airframe, the TPS, the wings, and the landing gear.

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.
Wow, that's beautiful! Of course this is all closed-cycle; the "turbine" doesn't actually interact with an airstream at all. But a very very cool design nonetheless.

Quote
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?
Beamed power has basically the same fuel fraction as an NTR. That's the nice thing about solving for fuel fraction; you can substitute in your vehicle's structural fraction and engines.

#### acsawdey

• Full Member
• Posts: 259
• Minnesota
• Liked: 130
• Likes Given: 263
##### Re: Minimum fuel fractions for SSTOs
« Reply #21 on: 04/17/2017 06:18 PM »
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.

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.

#### sevenperforce

• Full Member
• Posts: 743
• Liked: 172
• Likes Given: 220
##### Re: Minimum fuel fractions for SSTOs
« Reply #22 on: 04/17/2017 06:55 PM »
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.

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.
Oh, whoops. My mistake.

Wonder what the difference is, then. Ammonia has an isp about 13% higher than water at lower operating temperatures, but that gap would narrow at higher temperatures, where water disassociates more readily. Thrust is pretty poor, though.

#### sevenperforce

• Full Member
• Posts: 743
• Liked: 172
• Likes Given: 220
##### Re: Minimum fuel fractions for SSTOs
« Reply #23 on: 04/17/2017 07:03 PM »
Correction of the above: it's 12 MN, not 12 kN. On the water PB NTR.

#### hkultala

• Full Member
• Posts: 518
• Liked: 116
• Likes Given: 41
##### Re: Minimum fuel fractions for SSTOs
« Reply #24 on: 04/18/2017 07:26 AM »

1) 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 later

2) 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.

#### sevenperforce

• Full Member
• Posts: 743
• Liked: 172
• Likes Given: 220
##### Re: Minimum fuel fractions for SSTOs
« Reply #25 on: 04/18/2017 12:47 PM »

1) 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 later

2) 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.
Both good ideas to be sure.

To your first suggestion: Switching propellants is promising, but implementing it is challenging. Getting a deep-cryo liquid and a room temperature liquid to flow through the same piping and turbopump is virtually impossible. I suppose you could have a heat exchanger to warm the hydrogen to an appropriate temperature, but then the poor thrust of an LH2 NTR is even worse.

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.

#### acsawdey

• Full Member
• Posts: 259
• Minnesota
• Liked: 130
• Likes Given: 263
##### Re: Minimum fuel fractions for SSTOs
« Reply #26 on: 04/18/2017 01:20 PM »
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.

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.

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.

#### sevenperforce

• Full Member
• Posts: 743
• Liked: 172
• Likes Given: 220
##### Re: Minimum fuel fractions for SSTOs
« Reply #27 on: 04/18/2017 01:37 PM »
Yeah, 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.
If you use the higher SL isp of the RD-180 along with the maximum theoretical vacuum specific impulse of kerolox (353 seconds), pure-rocket fuel fraction drops to 93.7%. That's without factoring in any increase in gravity drag from the slightly lower fuel consumption.

But you're right, the TWR is less than half (78.44 to the Merlin 1D's uprated 183). So based solely on dry mass considerations, the Merlin 1D still wins (5.53% of GLOW for payload, structure, and margins vs. the RD-180's 4.64%).

I wish we had good TWR numbers for the Raptor.

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.
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.
At lower temperatures, with less disassociation, ammonia beats water by 13%; at liquid-uranium pebble-bed reactor temperatures, I'm guessing the isp would go up by about 10%. The idea mixture ratio would have to be determined analytically, but if I model it as a gradual ramp-up from SL water ISP to vacuum ammonia ISP, (running pure ammonia through at around 50% of GLOW), then fuel fraction drops from 83.1% to 80.1%, which is helpful.

Quote
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.
Ah, yes, good point. Not sure what I was thinking there. Though you're still dealing with hot LOX in the nozzle injection ports.
« Last Edit: 04/18/2017 01:46 PM by sevenperforce »

#### josespeck

• Member
• Posts: 29
• Liked: 5
• Likes Given: 5
##### Re: Minimum fuel fractions for SSTOs
« Reply #28 on: 04/18/2017 05:06 PM »
NH3 should be much better than H2O as it decompose to N2 and H2

NH3 + 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 = 12
2 NH3 --> 3 H2 + N2 avg molecular weight (3*2+28)/4 = 8.5

So, 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.

Thank you.

Tags: