Stoke Space Technologies: General Company and Development Updates and Discussions

[john smith 19]

Balooney, there’s no need for a radical design for making an upper stage of a multistage rocket reusable.

I suppose it depends what you mean by "radical." Personally I'd say switching construction material (twice), fuel, engine design (with about 2x the chamber pressure of Merlin AIUI)  and adding large drag surfaces to the US is quite radical, but maybe I'm just a bit conservative. 

If it was that simple shouldn't SX have been able to deliver what they showed in their video a decade ago? Just doing upgrades to the baseline F9 design.

[Robotbeat]

F9 upper stage reuse would have been viable if they chose that path. Fully reusable Falcon Heavy’s reuse penalty would’ve been small enough to LEO that it probably would’ve been pretty practical.

The only thing truly radical feature-wise about Starship is the chopsticks.

The other stuff is super aggressive like Raptor or the raw scale, but not what I’d call radical. It’s largely demonstrated on Shuttle, Soviet engines, Atlas, F9, and DC-X.

[HMXHMX]

Single-stage Earth-orbital Reusable Vehicle (SERV) and its Manned Upper-stage Reusable Payload (MURP) spaceplane was designed in 1969-1971 as one of the many proposed Space Shuttle designs.

BTW SERV was an unsolicited entry to the STS competition (because y'know Chrysler, what do they know about building aircraft?)

I don't think that is quite correct. The Marshall Space Flight Center (MSFC) issued Alternate Space Shuttle Concepts (ASSC) studies to Chrysler, Lockheed and Grumman/Boeing. The ASSC was initiated on 6 July 1970. Chrysler's space launch experience came building the Saturn I and Saturn IB first stages for MSFC who did the actual design. Chrysler developed SERV (Single Stage Earth Orbital Reusable Vehicle).

See Dennis R. Jenkins excellent book "Space Shuttle: The History of Developing the National Space Transportation System; The Beginning Through STS-50" pages 85 to 87.

On Dec. 7, 1972, I was standing next to the VAB at the Cape, having received a VIP invitation to the launch of Apollo 17 only the day before.  By happenstance, the fellow next to me was a VP at Chrysler, and told me about the SERV effort.  I told him about my interest in reusable VTOL SSTOs and a few days later a crate appeared on my doorstep, with the entire SERV proposal/report, on paper.  I still have it.  It was another era, where ITAR didn't exist and a 22 year old could get anything they asked for.

[Elmar Moelzer]

Yup.

Stoke is really putting these SSTO concepts to the test....
And by putting it on top of a reusable first stage, they'll be basically guaranteed to have enough performance to reach orbit...

This is why I find theme one of the most interesting space launch teams at the moment. They are not yet another SpaceX clone.

[chopsticks]

Yes, I really hope these guys will be successful. I think it's a great sign that they're starting with the upper stage (likely the most difficult part).

[Robotbeat]

Yup.

Stoke is really putting these SSTO concepts to the test....
And by putting it on top of a reusable first stage, they'll be basically guaranteed to have enough performance to reach orbit...

This is why I find theme one of the most interesting space launch teams at the moment. They are not yet another SpaceX clone.

...except for the first stage kinda.

[chopsticks]

But for a reusable first stage, are there really other good options but to do more or less do what SpaceX does? New Glenn has fins instead of grid fins for example but other than small things like that, I'm not sure what you could radically change and still have a good design.

I'd like to hear about other ideas though if there are some good ones.

[Elmar Moelzer]

Yup.

Stoke is really putting these SSTO concepts to the test....
And by putting it on top of a reusable first stage, they'll be basically guaranteed to have enough performance to reach orbit...

This is why I find theme one of the most interesting space launch teams at the moment. They are not yet another SpaceX clone.

...except for the first stage kinda.

Yeah, but the second stage is completely different and also fully reusable. Plus the engine design and fuel choice is also very different. So even the first stage has some differences, even if the exterior design is similar.

[john smith 19]

But for a reusable first stage, are there really other good options but to do more or less do what SpaceX does? New Glenn has fins instead of grid fins for example but other than small things like that, I'm not sure what you could radically change and still have a good design.

I'd like to hear about other ideas though if there are some good ones.

Not really relevant in the context of this thread but the obvious one is aspect ratio. Historically it's been several to 1 (IIR somewhere around 5-10:1). Because it's going to break the sound barrier, thansonic drag rise etc.

But that's pretty much irrelvant for a rocket. Drag peaks in the transonic range, then falls. So above about M1.1 designing for low drag is a bit pointless. Also not only is your speed but also your altitude is rising. IOW atmospheric pressure is dropping rapidly.

OTOH if you went with something squatter, like the Bono SSTO designs, you have a much stiffer vehicle, that's not so bendy (and a key part of early rocket GNC was figuring out how to compensate for that bendiness).  Higher diameter --> 2nd moment of area --> higher stiffness.

The downside is that moving anything with a very substantial diameter becomes a major logistics headache. Either build and launch on the same site or you need some sort of water or sea transport (or a very large plane like the Airbus "Baluga")

Note that SX's first goal was build a TSTO ELV that worked. F1 and F9 were very conventional LV's. To begin with. Most of the other tricks to improve performance would apply to any rocket design. Check the SSTO threads for more details if you're interested.

[Robotbeat]

it’s wrong to claim it’s pointless to design for drag.

[JEF_300]

I think people get pretty enamored by aerospikes. There’s little advantage over just a high chamber pressure, and basically no real advantage for an upper stage. At the expense of low thrust to weight ratio. The reentry method playing well with the aero spike concept is clever, but I’m not sure it’s really so much better than a conventional approach.

You seem to forget that while this is an upper stage engine, they also want to land propulsively using this engine on the stage's return to Earth. That means that the engine does have to fire both in a vacuum and at sea level (if only briefly), which means the traditional massive upper stage bell nozzle wasn't ever even an option. It was either an aerospike, a reversible extending nozzle, or something crazier like a TAN. With that in mind, and then adding in the aerospike's dual use as a heat shield, I think the aerospike was clearly the best option.

People also get too enamored with hydrogen. Besides the handling difficulties, the dry mass of the tanks and the pumps just is much worse for hydrolox than other fuels, largely negating the Isp advantage (especially if you use it fuel rich on both first and second stages).

I have no particular evidence for this, but I suspect that in this case they picked liquid hydrogen not for it's performance as a propellant, but for it's performance as a coolant.

I worry a little that it suffers from the too-clever-by-half, novelty for novelty’s sake approach to RLVs, part of what killed X-33 so completely (and which likely would’ve kept it from even achieving F9’s cost per kg even if they had managed to get VentureStar to orbit). (And Starship isn’t completely immune to this, honestly… we’ll see if the chopsticks end up working well for them or not.)

But making it two stages means they can do several things suboptimally and still achieve orbit.

There are two reasons I don't worry about this design being too clever.

The first is, well, look at their progress! If they had made a design that was more clever than needed, and that was slowing them down, I seriously doubt they would have gone from their first seed funding round to firing the complete (maybe?) upper stage engine assembly in a year and a half. Honestly at this rate, I expect starting on the first stage to be the thing which slows them up, and that's the part that's reasonably tried and tested.

The other thing is, I can't actually come up with a way to make a reusable TSTO vehicle that is simpler than this. It's like Starship, but without the need for a carefully controlled reentry, or hundreds of tiles, or aerodynamic surfaces, or aerial maneuvers, etc. In trade for not having to deal with all that, all Stoke has to do is actively cool a heatshield.

[TrevorMonty]

Can't find any info on booster but it is using methane. To speed things up could buy the engines. NB Usra are developing a 200klbs engine but don't say who its for.

For RLVs buying engines may make more sense especially if they are good for 10-20 flights. After which could be sent back to manufacturer for refurbishment.

[Robotbeat]

I think people get pretty enamored by aerospikes. There’s little advantage over just a high chamber pressure, and basically no real advantage for an upper stage. At the expense of low thrust to weight ratio. The reentry method playing well with the aero spike concept is clever, but I’m not sure it’s really so much better than a conventional approach.

You seem to forget that while this is an upper stage engine, they also want to land propulsively using this engine on the stage's return to Earth. That means that the engine does have to fire both in a vacuum and at sea level (if only briefly), which means the traditional massive upper stage bell nozzle wasn't ever even an option. It was either an aerospike, a reversible extending nozzle, or something crazier like a TAN. With that in mind, and then adding in the aerospike's dual use as a heat shield, I think the aerospike was clearly the best option.

People also get too enamored with hydrogen. Besides the handling difficulties, the dry mass of the tanks and the pumps just is much worse for hydrolox than other fuels, largely negating the Isp advantage (especially if you use it fuel rich on both first and second stages).

I have no particular evidence for this, but I suspect that in this case they picked liquid hydrogen not for it's performance as a propellant, but for it's performance as a coolant.

I worry a little that it suffers from the too-clever-by-half, novelty for novelty’s sake approach to RLVs, part of what killed X-33 so completely (and which likely would’ve kept it from even achieving F9’s cost per kg even if they had managed to get VentureStar to orbit). (And Starship isn’t completely immune to this, honestly… we’ll see if the chopsticks end up working well for them or not.)

But making it two stages means they can do several things suboptimally and still achieve orbit.

There are two reasons I don't worry about this design being too clever.

The first is, well, look at their progress! If they had made a design that was more clever than needed, and that was slowing them down, I seriously doubt they would have gone from their first seed funding round to firing the complete (maybe?) upper stage engine assembly in a year and a half. Honestly at this rate, I expect starting on the first stage to be the thing which slows them up, and that's the part that's reasonably tried and tested.

The other thing is, I can't actually come up with a way to make a reusable TSTO vehicle that is simpler than this. It's like Starship, but without the need for a carefully controlled reentry, or hundreds of tiles, or aerodynamic surfaces, or aerial maneuvers, etc. In trade for not having to deal with all that, all Stoke has to do is actively cool a heatshield.

You could do all that without really weird, heavy rocket engines.

Using hydrogen for cooling isn't ever as effective as just using water. Water has like 4 times the mass-specific heat of vaporization of hydrogen, not to mention like 20-40 times the volume-specific heat of vaporization, and this advantage isn't fully undone by the low boiling temperature of hydrogen. Plus, water doesn't burn like hydrogen does. And is cheaper and doesn't have the extreme temperature changes of hydrogen.

Water-cooled active shield would be superior in /nearly/ every way.

[chopsticks]

Can't find any info on booster but it is using methane. To speed things up could buy the engines. NB Usra are developing a 200klbs engine but don't say who its for.

For RLVs buying engines may make more sense especially if they are good for 10-20 flights. After which could be sent back to manufacturer for refurbishment.

Hopefully the engines should be fine without refurbishment longer than that if they are methane/lox = no coking.

Ideally that is. We are seeing tons of engine work done on Raptor 2 right now before even flying (yeah, I know Raptor 1 flew, but that doesn't preclude my point), but I guess it's still in it's infancy as well.

[chopsticks]

I think people get pretty enamored by aerospikes. There’s little advantage over just a high chamber pressure, and basically no real advantage for an upper stage. At the expense of low thrust to weight ratio. The reentry method playing well with the aero spike concept is clever, but I’m not sure it’s really so much better than a conventional approach.

You seem to forget that while this is an upper stage engine, they also want to land propulsively using this engine on the stage's return to Earth. That means that the engine does have to fire both in a vacuum and at sea level (if only briefly), which means the traditional massive upper stage bell nozzle wasn't ever even an option. It was either an aerospike, a reversible extending nozzle, or something crazier like a TAN. With that in mind, and then adding in the aerospike's dual use as a heat shield, I think the aerospike was clearly the best option.

People also get too enamored with hydrogen. Besides the handling difficulties, the dry mass of the tanks and the pumps just is much worse for hydrolox than other fuels, largely negating the Isp advantage (especially if you use it fuel rich on both first and second stages).

I have no particular evidence for this, but I suspect that in this case they picked liquid hydrogen not for it's performance as a propellant, but for it's performance as a coolant.

I worry a little that it suffers from the too-clever-by-half, novelty for novelty’s sake approach to RLVs, part of what killed X-33 so completely (and which likely would’ve kept it from even achieving F9’s cost per kg even if they had managed to get VentureStar to orbit). (And Starship isn’t completely immune to this, honestly… we’ll see if the chopsticks end up working well for them or not.)

But making it two stages means they can do several things suboptimally and still achieve orbit.

There are two reasons I don't worry about this design being too clever.

The first is, well, look at their progress! If they had made a design that was more clever than needed, and that was slowing them down, I seriously doubt they would have gone from their first seed funding round to firing the complete (maybe?) upper stage engine assembly in a year and a half. Honestly at this rate, I expect starting on the first stage to be the thing which slows them up, and that's the part that's reasonably tried and tested.

The other thing is, I can't actually come up with a way to make a reusable TSTO vehicle that is simpler than this. It's like Starship, but without the need for a carefully controlled reentry, or hundreds of tiles, or aerodynamic surfaces, or aerial maneuvers, etc. In trade for not having to deal with all that, all Stoke has to do is actively cool a heatshield.

You could do all that without really weird, heavy rocket engines.

Using hydrogen for cooling isn't ever as effective as just using water. Water has like 4 times the mass-specific heat of vaporization of hydrogen, not to mention like 20-40 times the volume-specific heat of vaporization, and this advantage isn't fully undone by the low boiling temperature of hydrogen. Plus, water doesn't burn like hydrogen does. And is cheaper and doesn't have the extreme temperature changes of hydrogen.

Water-cooled active shield would be superior in /nearly/ every way.

But water is just dead mass, hydrogen gets used later for propellant: dual purpose.

Unless you run the math and it actually works out that water (or something else) is actually more mass efficient even if it's dead mass.

[Robotbeat]

I think people get pretty enamored by aerospikes. There’s little advantage over just a high chamber pressure, and basically no real advantage for an upper stage. At the expense of low thrust to weight ratio. The reentry method playing well with the aero spike concept is clever, but I’m not sure it’s really so much better than a conventional approach.

You seem to forget that while this is an upper stage engine, they also want to land propulsively using this engine on the stage's return to Earth. That means that the engine does have to fire both in a vacuum and at sea level (if only briefly), which means the traditional massive upper stage bell nozzle wasn't ever even an option. It was either an aerospike, a reversible extending nozzle, or something crazier like a TAN. With that in mind, and then adding in the aerospike's dual use as a heat shield, I think the aerospike was clearly the best option.

People also get too enamored with hydrogen. Besides the handling difficulties, the dry mass of the tanks and the pumps just is much worse for hydrolox than other fuels, largely negating the Isp advantage (especially if you use it fuel rich on both first and second stages).

I have no particular evidence for this, but I suspect that in this case they picked liquid hydrogen not for it's performance as a propellant, but for it's performance as a coolant.

I worry a little that it suffers from the too-clever-by-half, novelty for novelty’s sake approach to RLVs, part of what killed X-33 so completely (and which likely would’ve kept it from even achieving F9’s cost per kg even if they had managed to get VentureStar to orbit). (And Starship isn’t completely immune to this, honestly… we’ll see if the chopsticks end up working well for them or not.)

But making it two stages means they can do several things suboptimally and still achieve orbit.

There are two reasons I don't worry about this design being too clever.

The first is, well, look at their progress! If they had made a design that was more clever than needed, and that was slowing them down, I seriously doubt they would have gone from their first seed funding round to firing the complete (maybe?) upper stage engine assembly in a year and a half. Honestly at this rate, I expect starting on the first stage to be the thing which slows them up, and that's the part that's reasonably tried and tested.

The other thing is, I can't actually come up with a way to make a reusable TSTO vehicle that is simpler than this. It's like Starship, but without the need for a carefully controlled reentry, or hundreds of tiles, or aerodynamic surfaces, or aerial maneuvers, etc. In trade for not having to deal with all that, all Stoke has to do is actively cool a heatshield.

You could do all that without really weird, heavy rocket engines.

Using hydrogen for cooling isn't ever as effective as just using water. Water has like 4 times the mass-specific heat of vaporization of hydrogen, not to mention like 20-40 times the volume-specific heat of vaporization, and this advantage isn't fully undone by the low boiling temperature of hydrogen. Plus, water doesn't burn like hydrogen does. And is cheaper and doesn't have the extreme temperature changes of hydrogen.

Water-cooled active shield would be superior in /nearly/ every way.

But water is just dead mass, hydrogen gets used later for propellant: dual purpose.

Unless you run the math and it actually works out that water (or something else) is actually more mass efficient even if it's dead mass.

Hydrogen that absorbs heat boils off and is lost, just like the water. You can't use it as propellant later on because it'll be gone.

[chopsticks]

I think people get pretty enamored by aerospikes. There’s little advantage over just a high chamber pressure, and basically no real advantage for an upper stage. At the expense of low thrust to weight ratio. The reentry method playing well with the aero spike concept is clever, but I’m not sure it’s really so much better than a conventional approach.

You seem to forget that while this is an upper stage engine, they also want to land propulsively using this engine on the stage's return to Earth. That means that the engine does have to fire both in a vacuum and at sea level (if only briefly), which means the traditional massive upper stage bell nozzle wasn't ever even an option. It was either an aerospike, a reversible extending nozzle, or something crazier like a TAN. With that in mind, and then adding in the aerospike's dual use as a heat shield, I think the aerospike was clearly the best option.

People also get too enamored with hydrogen. Besides the handling difficulties, the dry mass of the tanks and the pumps just is much worse for hydrolox than other fuels, largely negating the Isp advantage (especially if you use it fuel rich on both first and second stages).

I have no particular evidence for this, but I suspect that in this case they picked liquid hydrogen not for it's performance as a propellant, but for it's performance as a coolant.

I worry a little that it suffers from the too-clever-by-half, novelty for novelty’s sake approach to RLVs, part of what killed X-33 so completely (and which likely would’ve kept it from even achieving F9’s cost per kg even if they had managed to get VentureStar to orbit). (And Starship isn’t completely immune to this, honestly… we’ll see if the chopsticks end up working well for them or not.)

But making it two stages means they can do several things suboptimally and still achieve orbit.

There are two reasons I don't worry about this design being too clever.

The first is, well, look at their progress! If they had made a design that was more clever than needed, and that was slowing them down, I seriously doubt they would have gone from their first seed funding round to firing the complete (maybe?) upper stage engine assembly in a year and a half. Honestly at this rate, I expect starting on the first stage to be the thing which slows them up, and that's the part that's reasonably tried and tested.

The other thing is, I can't actually come up with a way to make a reusable TSTO vehicle that is simpler than this. It's like Starship, but without the need for a carefully controlled reentry, or hundreds of tiles, or aerodynamic surfaces, or aerial maneuvers, etc. In trade for not having to deal with all that, all Stoke has to do is actively cool a heatshield.

You could do all that without really weird, heavy rocket engines.

Using hydrogen for cooling isn't ever as effective as just using water. Water has like 4 times the mass-specific heat of vaporization of hydrogen, not to mention like 20-40 times the volume-specific heat of vaporization, and this advantage isn't fully undone by the low boiling temperature of hydrogen. Plus, water doesn't burn like hydrogen does. And is cheaper and doesn't have the extreme temperature changes of hydrogen.

Water-cooled active shield would be superior in /nearly/ every way.

But water is just dead mass, hydrogen gets used later for propellant: dual purpose.

Unless you run the math and it actually works out that water (or something else) is actually more mass efficient even if it's dead mass.

Hydrogen that absorbs heat boils off and is lost, just like the water. You can't use it as propellant later on because it'll be gone.

Are you referring to transpiration cooling? I was thinking of a closed loop system with cooling channels (like regenerative cooling in an engine bell) where the hydrogen would recondensed/cooled, or perhaps stored as a supercritical fluid. Whichever would be best I guess. But maybe this isn't a viable solution.

I suppose if it isn't, transpiration cooling with water might be a good alternative to ablative heat shield (better for reusability of course), but would sort of act the same way.

[Robotbeat]

I think people get pretty enamored by aerospikes. There’s little advantage over just a high chamber pressure, and basically no real advantage for an upper stage. At the expense of low thrust to weight ratio. The reentry method playing well with the aero spike concept is clever, but I’m not sure it’s really so much better than a conventional approach.

You seem to forget that while this is an upper stage engine, they also want to land propulsively using this engine on the stage's return to Earth. That means that the engine does have to fire both in a vacuum and at sea level (if only briefly), which means the traditional massive upper stage bell nozzle wasn't ever even an option. It was either an aerospike, a reversible extending nozzle, or something crazier like a TAN. With that in mind, and then adding in the aerospike's dual use as a heat shield, I think the aerospike was clearly the best option.

People also get too enamored with hydrogen. Besides the handling difficulties, the dry mass of the tanks and the pumps just is much worse for hydrolox than other fuels, largely negating the Isp advantage (especially if you use it fuel rich on both first and second stages).

I have no particular evidence for this, but I suspect that in this case they picked liquid hydrogen not for it's performance as a propellant, but for it's performance as a coolant.

I worry a little that it suffers from the too-clever-by-half, novelty for novelty’s sake approach to RLVs, part of what killed X-33 so completely (and which likely would’ve kept it from even achieving F9’s cost per kg even if they had managed to get VentureStar to orbit). (And Starship isn’t completely immune to this, honestly… we’ll see if the chopsticks end up working well for them or not.)

But making it two stages means they can do several things suboptimally and still achieve orbit.

There are two reasons I don't worry about this design being too clever.

The first is, well, look at their progress! If they had made a design that was more clever than needed, and that was slowing them down, I seriously doubt they would have gone from their first seed funding round to firing the complete (maybe?) upper stage engine assembly in a year and a half. Honestly at this rate, I expect starting on the first stage to be the thing which slows them up, and that's the part that's reasonably tried and tested.

The other thing is, I can't actually come up with a way to make a reusable TSTO vehicle that is simpler than this. It's like Starship, but without the need for a carefully controlled reentry, or hundreds of tiles, or aerodynamic surfaces, or aerial maneuvers, etc. In trade for not having to deal with all that, all Stoke has to do is actively cool a heatshield.

You could do all that without really weird, heavy rocket engines.

Using hydrogen for cooling isn't ever as effective as just using water. Water has like 4 times the mass-specific heat of vaporization of hydrogen, not to mention like 20-40 times the volume-specific heat of vaporization, and this advantage isn't fully undone by the low boiling temperature of hydrogen. Plus, water doesn't burn like hydrogen does. And is cheaper and doesn't have the extreme temperature changes of hydrogen.

Water-cooled active shield would be superior in /nearly/ every way.

But water is just dead mass, hydrogen gets used later for propellant: dual purpose.

Unless you run the math and it actually works out that water (or something else) is actually more mass efficient even if it's dead mass.

Hydrogen that absorbs heat boils off and is lost, just like the water. You can't use it as propellant later on because it'll be gone.

Are you referring to transpiration cooling? I was thinking of a closed loop system with cooling channels (like regenerative cooling in an engine bell) where the hydrogen would recondensed/cooled, or perhaps stored as a supercritical fluid. Whichever would be best I guess. But maybe this isn't a viable solution.

I suppose if it isn't, transpiration cooling with water might be a good alternative to ablative heat shield (better for reusability of course), but would sort of act the same way.

I mean, there's no real way for the hydrogen to be recondensed. What exactly is at 20 Kelvin for it to recondense to??

If you're just using it as a working fluid, there's zero to recommend hydrogen over helium in this application, and a phase change fluid using liquid metal or something would likely outcompete. Liquid metal heat pipes are one solution used for this, to spread the heat where there are hotspots on hypersonic vehicles. But it's a heavy approach, and I don't think that's the one Stoke is using.

[trimeta]

I may be misunderstanding the design, but is the actively-cooled heat shield only actively-cooled during reentry, a time when the engine isn't running? Or is that same area hot during engine burns, such that regenerative cooling (followed by that heated hydrogen being sent into the combustion chamber) could be used during that phase as well? If the latter is true, perhaps being dual-use like this means that some cooling systems which would be necessary anyway are also being used for reentry, reducing the mass of including separate systems for each (and offsetting the disadvantages of bleeding hydrogen during reentry instead of bleeding water).

[john smith 19]

You could do all that without really weird, heavy rocket engines.

Yet another piece of folklore/old-wifes-tale/line-in-Sutton that deserves to put down (along with the idea that LOX cooling is impossible). 

For the record Rocketdyne build a LH2/LO2 dual expander cycyle for the USAF in 1974. The AF specificed it must be "flight weight" IE able to be attached to a stage. Failure to make flight weight --> terminate contract.

Rocketydne delivered the flight weight engine that hit IIRC 380secs at sea level. There is an AIAA report. Unfortunately someone used the wrong grade of welding rods. GO2 and GH2 combined to form water droplets. When the engine was started up again they flash-boiled and wrecked IIRC a whole quadrant of the engine. 

BTW IIRC some of the GH2 from the turbine drive was exhausted though the baseplate, which was a diffusion bonded Titanium with lots of holes drilled in the bottom plate, creating the "Aero-plug" effect.  It was somewhere between 10-20% the full length of an equivalent engine with a nozzle of that expansion ratio.

Using hydrogen for cooling isn't ever as effective as just using water. Water has like 4 times the mass-specific heat of vaporization of hydrogen, not to mention like 20-40 times the volume-specific heat of vaporization, and this advantage isn't fully undone by the low boiling temperature of hydrogen. Plus, water doesn't burn like hydrogen does. And is cheaper and doesn't have the extreme temperature changes of hydrogen.

Water-cooled active shield would be superior in /nearly/ every way.

You might like to check that first statement. Alan Bond of Reaction Engines said that it's LH2 that has 4x the heat  of vaporization per unit mass of water, although H2 has other handling issues.

What using H2 for the cooling gives you is flexibility.

 You can't burn water as fuel with LOX (and just to quell the pedantic yes I know water can burn with the right oxidizers, as can concrete and asbestos, but no sane developer would consider using those oxidizers).  You can monitor the shield temp and if it runs hot run a bit more H2 through it. You have less margin but you can still land in one piece and hence live to launch another day.