### Author Topic: Minimum fuel fractions for SSTOs  (Read 4559 times)

#### sevenperforce

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##### 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

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##### 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

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##### 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

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##### 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

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##### 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

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##### 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.
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#### Asteroza

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##### 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

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##### 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

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##### 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

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##### 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

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##### 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

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##### 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

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##### 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

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##### 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

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##### 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

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##### 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.
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#### envy887

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##### 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

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##### 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

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##### 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

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##### 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.

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