The Cost of HydroLox (mass)

[Racescort666]

Long winded introduction in spoiler:

Spoiler

A while back I had done some spreadsheet engineering of what an NTR powered Falcon upper stage might be. As it turns out, NTRs have pretty egregiously bad performance mostly because of their very poor thrust to weight. The other thing that I noticed is that their fuel tanks end up being huge, so big that getting the same dV out of an NTR powered stage on a Falcon 9 would require just the NTR stage to be taller than a regular Falcon 9 rocket. For the way I was calculating it, the stage length was also very sensitive to diameter but a 5.2 m diameter stage still ended up being 49.5 m tall.

Anyway, I started thinking about regular HydroLox powered engines recently. They (and really any engine that uses liquid hydrogen) suffer from a similar problem, they have mediocre TWR and also suffer from hydrogen's low density. So I considered the Space Shuttle ET, the hydrogen is 1/6th the mass but takes up 3X the volume. Surely all of the extra tankage dips into the performance of a rocket.

I put together a hypothetical situation to compare the Space Shuttle ET mounted with 1 SSME to a Metholox powered stage with 1 engine. For this exercise, I was interested in what the mass of a Metholox powered stage would come in at. In other words, attach 1 SSME to ET, fire, how much dV? (14.3 km/s) Use the rocket equation to figure out a Metholox stage with the same dV and compare mass.

Raptor:

• Thrust: 1900 kN
• TWR: 198.5
• Mass: 977 kg
• ISP: 380 s 
• Fuel Mix: 3.8

SSME:

• Thrust: 2279 kN
• TWR: 65.9
• Mass: 3527 kg
• ISP: 452 s
• Fuel Mix: 5.9

ET:

• Gross mass: 760 000 kg
• Dry mass: 26 500 kg

Notes:

Spoiler

 

Note 1: wiki might be wrong on the ET dry mass because if you subtract the propellant mass from the gross, you get less than the dry mass.

Note 2: Some of the performance figures for the new engines (BE-4 and Raptor) are pretty speculative but barring any other information, I took them at face value. I used the Raptor engine as my baseline because performance was easier to track down but I consider the BE-4 to be basically the same engine considering convergent evolution.

Note 3: I also ended up doing some algebra wizardry to figure out tankage mass for the hypothetical Metholox stage. Basically, I took the dry mass of the ET and divided by the area and used the kg/m2 of the ET to approximate tankage mass based on fuel mass. The assumption was that the tank would be a 8.4 m diameter cylinder just like the ET. If anyone is interested, PM me and I'll send you my spreadsheet and powerpoint with the equations.

 

Metholox stage: 119 331 kg including tank, fuel, and engine. o_O this can't be right...

Nobody shoots an empty fuel tank into space for fun so I decided to account for a payload. You can see in the plot below how the stage mass changes as payload increases.  

There are a couple of things going on behind this plot, first the dry mass of the SSME + ET doesn't change (about 30t), second the Metholox stage dry mass does change (4.4t to 13.6t). At the cross point of the blue and purple lines (20t payload) the Metholox stage is 11 385 kg close to 1/3 of the dry weight. Interesting that there is a payload range where Metholox has the advantage. I suspect that it has to do with the dry mass to payload ratio. Also, TWR for this whole deal is about 0.25 with a 20t payload. 

Interesting... what if we add...

MOAR BOOSTERS:

Changing up the plot a bit, here we have a 3 engine hypothetical situation. For the ET+SSME contraption, it's probably not too far off of Shuttle-C with no SRBs. With more engines the cross point moves up to 30t and the TWR is 0.73 at the cross point which is in the range of common upper stages.

Anyway, there was no real science here and I suppose that if we want to go someplace in a hurry, Metholox might be a decent strategy. Maybe if you wanted to send the Hubble Space Telescope on an escape trajectory...

Closing thoughts: this situation is kind of unrealistic, could I come up with a more realistic situation to better reflect a hypothetical Metholox upper stage? Yes, probably. I think the point remains that there is possibly a situation where a higher density fuel makes more sense from a mass standpoint than a hydrogen powered one though. 

[Bill Phil]

Tanks are light, so there's not much of a performance hit for using hydrogen. You get a lower mass ratio, but so long as the increase in isp overcomes it, then hydrolox would have higher performance, at least for the specific case under study.

Nuclear thermal is not very good for launch, but in space, it would fair pretty well. The only issue would be tankage mass, but if we can build the tanks in space, they can be much lighter. Although that also applies to other propellants, but doubling ISP means we can reduce the mass ratio to the square root of its previous value.

Edited March 12, 2018 by Bill Phil

[Racescort666]

1 hour ago, Bill Phil said:

Tanks are light, so there's not much of a performance hit for using hydrogen. You get a lower mass ratio, but so long as the increase in isp overcomes it, then hydrolox would have higher performance, at least for the specific case under study.

Nuclear thermal is not very good for launch, but in space, it would fair pretty well. The only issue would be tankage mass, but if we can build the tanks in space, they can be much lighter. Although that also applies to other propellants, but doubling ISP means we can reduce the mass ratio to the square root of its previous value.

That's the point though, between the engines and the tankage, it's not that light. Yes, you reach a median value where all is equal but you definitely take a mass hit where the tanks are concerned; the ET is over 3 times the mass of the Metholox in the 1 engine example. I will be the first to admit that I haven't looked at this from all angles but the increase in specific impulse isn't all it's cracked up to be. 

As for NTRs, optimally, they require a spherical tank. Practically, they need active fuel cooling to be useful beyond an Earth departure burn. In which case, chemical generally works out better (or Ion but that's another topic).

[sevenperforce]

Using the STS ET (even the SLWT variety) isn't a good comparison, because a) the ET was a transverse-load-bearing member, and b) it had simply huge square-cube advantages. So it's not representative at all.

Better to use something like Centaur. Compare to a methalox upper stage of equal mass and to one of equal volume and see how they fare.

[Bill Phil]

1 minute ago, Racescort666 said:

That's the point though, between the engines and the tankage, it's not that light. Yes, you reach a median value where all is equal but you definitely take a mass hit where the tanks are concerned; the ET is over 3 times the mass of the Metholox in the 1 engine example. I will be the first to admit that I haven't looked at this from all angles but the increase in specific impulse isn't all it's cracked up to be. 

As for NTRs, optimally, they require a spherical tank. Practically, they need active fuel cooling to be useful beyond an Earth departure burn. In which case, chemical generally works out better (or Ion but that's another topic).

Tanks are quite light. Just looking at the ET's dry mass, that thing is extremely light. But tanks are light no matter what we're talking about. What matters is mass ratio, and using hydrolox does hurt the mass ratio (kerolox can get up to 17 at least, counting engines, while hydrolox is kind of stuck at 11 as far as I know, when factoring in engines). However, if the isp increase is enough to overcome that then hydrolox outperforms the others. It depends on specific cases. Otherwise no one would ever use hydrolox. It works better than the alternatives in the cases where it is used most often. It certainly isn't optimal for a launching stage, as evidenced by the lower thrust of hydrolox engines (in general), but it works out pretty well for upper stages. Delta-V is directly proportional to ISP (benefiting hydrolox) and directly proportional to the natural log of the mass ratio (hurting hydrolox). But the natural log of ever larger numbers eventually stops increasing quickly. Basically, it depends on how much performance you lose in mass ratio vs how much you gain in ISP, or, rather, ISP is more important than mass ratio, but both are quite important. Hydrogen gets a pretty well sized edge, but there are instances where other propellants beat it.

NTRs don't require active cooling save for propellant flow, as far as I know. Not to mention the serious benefits of reducing the necessary mass ratio for a given delta-V, which could potentially overcome the losses from the cooling system, if one is required. Doubling ISP is nothing to be laughed at. If your mass ratio needs to be 9 with a certain ISP, by doubling ISP you only need a mass ratio of 3.

[Racescort666]

4 minutes ago, Bill Phil said:

Delta-V is directly proportional to ISP (benefiting hydrolox) and directly proportional to the natural log of the mass ratio (hurting hydrolox). But the natural log of ever larger numbers eventually stops increasing quickly. Basically, it depends on how much performance you lose in mass ratio vs how much you gain in ISP, or, rather, ISP is more important than mass ratio, but both are quite important. Hydrogen gets a pretty well sized edge, but there are instances where other propellants beat it.

This is what I was trying to get at. 

4 minutes ago, Bill Phil said:

NTRs don't require active cooling save for propellant flow, as far as I know. Not to mention the serious benefits of reducing the necessary mass ratio for a given delta-V, which could potentially overcome the losses from the cooling system, if one is required. Doubling ISP is nothing to be laughed at. If your mass ratio needs to be 9 with a certain ISP, by doubling ISP you only need a mass ratio of 3.

I was referring to active cooling of the propellant to prevent/manage boil off. Maybe NTRs work better for larger payloads, I only looked at them for smaller ones. The other problem with NTRs is that they don't scale like chemical rockets do, which is maybe where I was forming my opinion of them. 

[Bill Phil]

2 minutes ago, Racescort666 said:

I was referring to active cooling of the propellant to prevent/manage boil off. Maybe NTRs work better for larger payloads, I only looked at them for smaller ones. The other problem with NTRs is that they don't scale like chemical rockets do, which is maybe where I was forming my opinion of them. 

Hydrolox also needs active cooling, and to an extent methalox and kerolox as well. The only propellants that don't really need active cooling of some sort would generally be hypergolic propellants, and other types of storable propellants.

[Racescort666]

@sevenperforce Centaur is something I can look into since I have the relevant numbers at hand. There are not currently any Methelox engines in the R10 thrust range but it's probably safe to assume that the technology scales easily with the same TWR. I'll have to look into it. It's worth noting that Centaur's kg/m2 is 14.5 while the ET is 19.9. 

Just now, Bill Phil said:

Hydrolox also needs active cooling, and to an extent methalox and kerolox as well. The only propellants that don't really need active cooling of some sort would generally be hypergolic propellants, and other types of storable propellants.

Oops, my bad, I forgot to include the part that was specific to NTRs: if you're using hydrogen, they require active cooling for extended use, if you use something like water or ammonia, they don't but still retain very high ISP. 

[sevenperforce]

28 minutes ago, Racescort666 said:

@sevenperforce Centaur is something I can look into since I have the relevant numbers at hand. There are not currently any Methelox engines in the R10 thrust range but it's probably safe to assume that the technology scales easily with the same TWR. I'll have to look into it. It's worth noting that Centaur's kg/m2 is 14.5 while the ET is 19.9. 

kg/m² meaning tank dry mass divided by tank surface area?

If so, that's not surprising. Centaur is a balloon tank that cannot support its own mass under compression unless it is pressurized; the ET was very much load-bearing.

Then again, consider that the SLWT variant of the ET boasted a propellant fraction of 96.5% while Centaur only manages a propellant fraction 91.4% (subtracting engine weight). That's the square-cube law for you.

But hydrogen is so fluffy that the Falcon 9 upper stage beats both Centaur AND the much larger SLWT hands-down, with a whopping propellant fraction of 96.9%. 

28 minutes ago, Racescort666 said:

Oops, my bad, I forgot to include the part that was specific to NTRs: if you're using hydrogen, they require active cooling for extended use, if you use something like water or ammonia, they don't but still retain very high ISP. 

Or, rather, they end up with high-end hydrolox isp, but with kerolox-level density.

Doesn't necessarily compensate for the tremendously high dry mass of the engine.

[kerbiloid]

Is liquid deuterium as much unstorable as liquid protium?

Spoiler

Btw H₂O is not just dihydrogen monoxide, but also diprotium monoxide. Usually polluted with dideuterium monoxide.

Spoiler

Tetradeuterium methane and tetradeuterium hydrazine would contain more lightweight stuff per mass than usual ones.

Though the former could be too tough to break.

But N₂D₄ wouldn't be the fuel of interplanetary spaceships?

 

Edited March 13, 2018 by kerbiloid

[Hannu2]

3 hours ago, kerbiloid said:

Is liquid deuterium as much unstorable as liquid protium?

  Hide contents

Btw H₂O is not just dihydrogen monoxide, but also diprotium monoxide. Usually polluted with dideuterium monoxide.

  Hide contents

Tetradeuterium methane and tetradeuterium hydrazine would contain more lightweight stuff per mass than usual ones.

Though the former could be too tough to break.

But N₂D₄ wouldn't be the fuel of interplanetary spaceships?

 

Practically it is. Boiling point is only couple of degrees higher than for normal hydrogen and heat of vaporization is low. I think that deuterated propellants would not pay back high costs compared to little larger storage of normal propellants. Also, low weight of regular hydrogen is benefit because it gets more velocity at certain temperature.

Water ionizes spontaneously to H3O+ and OH- ions. Reaction is dynamic and happens in both directions. In other words water molecules exchange hydrogen atoms continuously as they collide into each other. Therefore most deuterium atoms is moved to DHO molecules and D2O is very rare (if D concentration is low).

 

[Racescort666]

@sevenperforce I ran the numbers for Centaur. I didn't do exactly what you asked, I was still comparing the mass difference of equal dV for a given payload. This is also assuming that a Metholox engine scales and will maintain a 198.5 TWR when scaled down to produce 99.2 kN of thrust.

Interesting finding: for the New Horizons launch on an Atlas V 551, it would have had a faster escape trajectory with the Metholox design. The payload was around 2615 kg (New Horizons + a Star 48B) which puts the upper stage at 23 228 kg vs Centaur's 25 692 kg so the stage separation speeds would be higher. Not that New Horizons needed more velocity since it had to slow down after the Star burn.

 

[Racescort666]

@Bill Phil @sevenperforceI ran the numbers for New Horizons if Centaur were replaced with a Metholox stage:

• Payload:
  • New Horizons + Star 48B: 2615 kg
• Stage Mass:
  • 25 692 kg (same for both stages)
• Engine ISP:
  • RL10: 451
  • Metholox: 380
• Engine Mass:
  • RL10: 168 kg 
  • Metholox: 51 kg
• Tank Mass:
  • Centaur: 2079 kg
  • Metholox: 739.6 kg
• Fuel Mass:
  • Centaur: 20 830 kg
  • Metholox: 22 286 kg
• Delta V:
  • Centaur: 7358 m/s
  • Metholox: 7525 m/s

So, maybe I was wrong, a 2% increase in performance isn't exactly great. 167 m/s improvement on an Earth departure stage probably doesn't gain you much but I suppose it's better than nothing. Anyway, I shall find some seasoning for my hat...

Edited March 15, 2018 by Racescort666

[Bill Phil]

17 minutes ago, Racescort666 said:

@Bill Phil @sevenperforceI ran the numbers for New Horizons if Centaur were replaced with a Metholox stage:

• Payload:
  • New Horizons + Star 48B: 2615 kg
• Stage Mass:
  • 25 692 kg (same for both stages)
• Engine ISP:
  • RL10: 451
  • Metholox: 380
• Engine Mass:
  • RL10: 168 kg 
  • Metholox: 51 kg
• Tank Mass:
  • Centaur: 2079 kg
  • Metholox: 739.6 kg
• Fuel Mass:
  • Centaur: 20 830 kg
  • Metholox: 22 286 kg
• Delta V:
  • Centaur: 7358 m/s
  • Metholox: 7525 m/s

So, maybe I was wrong, a 2% increase in performance isn't exactly great. 167 m/s improvement on an Earth departure stage probably doesn't gain you much but I suppose it's better than nothing. Anyway, I shall find some seasoning for my hat...

They get more but you have to remember that the trajectory was carefully planned to a specific delta-v.

[Racescort666]

9 minutes ago, Bill Phil said:

They get more but you have to remember that the trajectory was carefully planned to a specific delta-v.

[Bill Phil]

1 hour ago, Racescort666 said:

? 

Man, it's been a while since I've seen Futurama...