CNES ESA Prometheus / Callisto proposal

[envy887]

Methalox just doesn't work well without staged combustion and densification.

Precisely. Boiling methane is a much worse than subcooled kerosene in terms of density and thrust. A vehicle with a worse fuel and worse engines and much worse mass fractions simply isn't going to be able to beat F9 on payload by 40% without being gigantic.

The authors of this study seem tot think that they can take none of the risks that SpaceX took and still get a similar vehicle, which is just absurd.

They are also ignoring the dial-a-landing feature of Falcon: RTLS for small payloads, land downrange on large payloads, and expend the booster for very large payloads. Very large payloads are rare and you can charge a premium to launch them.

[ZachF]

That's for 1D, 1D Full Thrust opened the throat a little to increase thrust. That lowered the ER, which slightly increased SL ISP while slightly decreasing vac ISP. Chamber pressure also increased slightly.

http://www.b14643.de/Spacerockets/Specials/U.S._Rocket_engines/engines.htm

1D FT is 289/312. Average ISP for both didn't really change much though.

Methalox just doesn't work well without staged combustion and densification.

Interesting, thanks. In that case ~303s/334s would make more sense, especially since they assume a chamber pressure of 12MPa, which is more than Merlin. Weird.

A GG methalox engine that gets 289/320 is probably around 70 MPa in chamber pressure.

You mean 70 bar, or 7 MPa? That is what I get in RPA lite for a 70 bar methalox engine at 3.25 O/F, assuming 0.966 engine efficiency and 3% mass flow through the GG.

Using the same assumptions with 12 MPa,  I get 301 SL / 332 vacuum.

To get 320 seconds in vacuum requires using 6.7% of the mass flow in the GG, which seems really high.

Yeah, meant bar not mpa 

Study also seems to use MR of 2.5:1

[ZachF]

Methalox just doesn't work well without staged combustion and densification.

Precisely. Boiling methane is a much worse than subcooled kerosene in terms of density and thrust. A vehicle with a worse fuel and worse engines and much worse mass fractions simply isn't going to be able to beat F9 on payload by 40% without being gigantic.

The authors of this study seem tot think that they can take none of the risks that SpaceX took and still get a similar vehicle, which is just absurd.

They are also ignoring the dial-a-landing feature of Falcon: RTLS for small payloads, land downrange on large payloads, and expend the booster for very large payloads. Very large payloads are rare and you can charge a premium to launch them.

Here is a comparison I made in the Raptor thread.

https://forum.nasaspaceflight.com/index.php?topic=47506.40

Prometheus with those stats is actually pretty awful as a reusable platform. It's much worse than Merlin, and the stage would actually have a physical volume almost as large as a theoretical SSME powered stage.

Look at how steep the improvement is though from Prometheus (GG, avg ISP of 304) to BE-4 (ORSC, avg ISP of 325) to Raptor (FFSC, avg ISP of 344, densified propellants).

[ncb1397]

Something odd is going on in these studies. They are designing vehicles larger than New Glenn, doing the same downrange landing, but getting less than half the expected payload (even compared to the 2-stage methalox NG). And they are nearly 3 times the GLOM of F9 with only 30% more payload.

Where did you get 3 times the GLOM of F9? Anyways, New Glenn has a gigantic expendable upper stage. And the diameter and length are smaller than New Glenn (5.5-5.2 m diameter, similar length).

edit: It appears that you were looking at the model based on structural indices that over-estimates 2nd stage mass(and therefore 1st stage mass).

edit 2: And propane?

Figure 7 of the study posted below. F9 has a GLOM of about 550 t. The methalox and propalox vehicles have a GLOM of ~1400-1750 t.

Even New Glenn is going to be in the 1400 t range for GLOM, since it will only have ~1700 t of thrust at liftoff. It does have the advantage of staged combustion, but it is using a first-iteration engine from a private company that never developed a staged combustion engine before. Surely ESA and DLR with all of Europe's resources could develop something similar.

I wouldn't get too worked up about specific graphs that were generated when ruling out configurations and when using pessimistic assumptions. The results section gives what they distilled down to...

2 Results The results of the analysis of the LOx/LH2 and the LOx/LCH4 launcher with more detailed mass model are presented in Table 5. Both launchers show a great decrease in GLOM of about 45% compared to the results of the first iteration modelled with pre-assumed structural index. This decrease can mainly be explained by the overestimation of the second stage dry mass by using the structural index method. The problem with the extrapolation method of the structural index is the fact that the second stages are relatively large and in a tankage domain corresponding to existing first stages. However, the structural indices of first stages tend to be higher than the respective indices of upper stages as they have to carry an upper stage on top and withstand higher bending loads. This leads to an overestimation of the second stage dry mass which in the further course leads to a higher first stage mass and thus a heavier launcher.

The LOx/LH2 launcher is about half the mass of the LOx/LCH4 launcher. This relation could also be observed in the first iteration, which is an indication that the relative results of the first iteration are up to a certain extent still valid even if the pre-assumed structural index were too pessimistic. The LOx/LH2 launcher has a GLOM that is less than that of the Falcon 9 (550 tons), while delivering about two tons additional payload into GTO (7500 kg vs 5500 kg of Falcon 9). However, due to the fact that hydrogen has a much lower density than RP-1 the LOx/LH2 launcher is larger, see Fig. 12. The LOx/LH2 launcher and Falcon 9 both have 9 engines. 

The LOx/LCH4 launcher has a mass at lift-off of 884 tons and has 11 engines. Due to the difficult accommodation of the engines, the diameter of the launcher had to be set to 5.5 m, the minimum possible to fit all 11 engines within the rear skirt. Furthermore, the second stage engine barely fits in the interstage, so in future studies the interstage length should be increased. Due to the higher density of methane, the C648C142 launcher is almost of the same volume as the LOx/LH2 launcher. The payload capability is about 7500 kg which is less than the announced 13 tons to GTO of the LOx/LCH4 launcher “New Glenn” that is currently under development at Blue Origin [22]. However, the New Glenn is about 76% bigger (regarding total volume) than the VTOL methane launcher, presented here.
 

Anyways, ~3x Falcon 9 mass with a bit more payload to GTO (8 t vs 5.5 t or a 45% increase) is exactly what Falcon Heavy is. So having a configuration of many configurations listed here with similar specs isn't really that suprising.

Anyways, it isn't entirely illegitimate to build a big VTOL first stage and the smallest expendable upper stage that you can get away with. Presumeably, the bigger the lower stage is, the smaller you can make the upper stage. Eventually for upper stage size X varying and a fixed large lower stage, you will match payloads of various significantly smaller launchers.  We haven't really seen that approach so far with Falcon and New Glenn (their upper stages are quite large), but it is an approach that has some merit and hasn't been tested in the market. Could that lead to high GLOMS and low payload numbers? Yes, you can see that with Falcon Heavy. The Reusable portion sizes and masses went up by a lot while the payload didn't go up proportionally.

[ZachF]

Anyways, ~3x Falcon 9 mass with a bit more payload to GTO (8 t vs 5.5 t or a 45% increase) is exactly what Falcon Heavy is. So having a configuration of many configurations listed here with similar specs isn't really that suprising.

The major difference is that this is an after-the-fact addition to an existing reusable architecture. Now they can increase payload by over 45% without expending a first stage/core, and the payload for when a core is expended has massively increased.

Anyways, it isn't entirely illegitimate to build a big VTOL first stage and the smallest expendable upper stage that you can get away with. Presumeably, the bigger the lower stage is, the smaller you can make the upper stage. We haven't really seen that approach so far with Falcon and New Glenn (their upper stages are quite large), but it is an approach that has some merit and hasn't been tested in the market.

If you want to transfer more of the impulse to the lower stage, simple GG engines with poor mass fractions and TWRs aren't going to cut it. Look at the comparison chart I made above... If your mass fraction is poor, you need more of your fuel to land. If your ISP is poor, you need more fuel to land. If your rocket has a middling TWR you need more fuel to land. If you need more fuel to land, you need a much larger stage overall to get the required dV. This huge negative feedback loop is why Raptor as a system works so well, and all of these Arianespace proposals work so poorly.

[ncb1397]

If you want to transfer more of the impulse to the lower stage, simple GG engines with poor mass fractions and TWRs aren't going to cut it. Look at the comparison chart I made above... If your mass fraction is poor, you need more of your fuel to land. If your ISP is poor, you need more fuel to land. If your rocket has a middling TWR you need more fuel to land. If you need more fuel to land, you need a much larger stage overall to get the required dV. This huge negative feedback loop is why Raptor as a system works so well, and all of these Arianespace proposals work so poorly.

You seem to be under the impression this study is assuming 289/320 s ISP for the methalox GG engine.

That's for 1D, 1D Full Thrust opened the throat a little to increase thrust. That lowered the ER, which slightly increased SL ISP while slightly decreasing vac ISP. Chamber pressure also increased slightly.

http://www.b14643.de/Spacerockets/Specials/U.S._Rocket_engines/engines.htm

1D FT is 289/312. Average ISP for both didn't really change much though.

Methalox just doesn't work well without staged combustion and densification.

Interesting, thanks. In that case ~303s/334s would make more sense, especially since they assume a chamber pressure of 12MPa, which is more than Merlin. Weird.

A GG methalox engine that gets 289/320 is probably around 70 MPa bar in chamber pressure.

EDIT: fixed unit mistake

Reading table 3 that was posted by Salo and matches the source PDF lists sea level ISP of 302.5 and vacuum ISP of sea level engines as 334.1 under the LCH4 GG column. This is in comparison to Raptor at 330 s/356 s. DLR is probably more pessimistic than Musk. DLR is capping chamber pressure at 160 bar to lightly stress the engine while Musk is trying to maximize it.

[envy887]

Something odd is going on in these studies. They are designing vehicles larger than New Glenn, doing the same downrange landing, but getting less than half the expected payload (even compared to the 2-stage methalox NG). And they are nearly 3 times the GLOM of F9 with only 30% more payload.

Where did you get 3 times the GLOM of F9? Anyways, New Glenn has a gigantic expendable upper stage. And the diameter and length are smaller than New Glenn (5.5-5.2 m diameter, similar length).

edit: It appears that you were looking at the model based on structural indices that over-estimates 2nd stage mass(and therefore 1st stage mass).

edit 2: And propane?

Figure 7 of the study posted below. F9 has a GLOM of about 550 t. The methalox and propalox vehicles have a GLOM of ~1400-1750 t.

Even New Glenn is going to be in the 1400 t range for GLOM, since it will only have ~1700 t of thrust at liftoff. It does have the advantage of staged combustion, but it is using a first-iteration engine from a private company that never developed a staged combustion engine before. Surely ESA and DLR with all of Europe's resources could develop something similar.

I wouldn't get too worked up about specific graphs that were generated when ruling out configurations and when using pessimistic assumptions. The results section gives what they distilled down to...

2 Results The results of the analysis of the LOx/LH2 and the LOx/LCH4 launcher with more detailed mass model are presented in Table 5. Both launchers show a great decrease in GLOM of about 45% compared to the results of the first iteration modelled with pre-assumed structural index. This decrease can mainly be explained by the overestimation of the second stage dry mass by using the structural index method. The problem with the extrapolation method of the structural index is the fact that the second stages are relatively large and in a tankage domain corresponding to existing first stages. However, the structural indices of first stages tend to be higher than the respective indices of upper stages as they have to carry an upper stage on top and withstand higher bending loads. This leads to an overestimation of the second stage dry mass which in the further course leads to a higher first stage mass and thus a heavier launcher.

The LOx/LH2 launcher is about half the mass of the LOx/LCH4 launcher. This relation could also be observed in the first iteration, which is an indication that the relative results of the first iteration are up to a certain extent still valid even if the pre-assumed structural index were too pessimistic. The LOx/LH2 launcher has a GLOM that is less than that of the Falcon 9 (550 tons), while delivering about two tons additional payload into GTO (7500 kg vs 5500 kg of Falcon 9). However, due to the fact that hydrogen has a much lower density than RP-1 the LOx/LH2 launcher is larger, see Fig. 12. The LOx/LH2 launcher and Falcon 9 both have 9 engines. 

The LOx/LCH4 launcher has a mass at lift-off of 884 tons and has 11 engines. Due to the difficult accommodation of the engines, the diameter of the launcher had to be set to 5.5 m, the minimum possible to fit all 11 engines within the rear skirt. Furthermore, the second stage engine barely fits in the interstage, so in future studies the interstage length should be increased. Due to the higher density of methane, the C648C142 launcher is almost of the same volume as the LOx/LH2 launcher. The payload capability is about 7500 kg which is less than the announced 13 tons to GTO of the LOx/LCH4 launcher “New Glenn” that is currently under development at Blue Origin [22]. However, the New Glenn is about 76% bigger (regarding total volume) than the VTOL methane launcher, presented here.
 

Anyways, ~3x Falcon 9 mass with a bit more payload to GTO (8 t vs 5.5 t or a 45% increase) is exactly what Falcon Heavy is. So having a configuration of many configurations listed here with similar specs isn't really that suprising.

Anyways, it isn't entirely illegitimate to build a big VTOL first stage and the smallest expendable upper stage that you can get away with. Presumeably, the bigger the lower stage is, the smaller you can make the upper stage. Eventually for upper stage size X varying and a fixed large lower stage, you will match payloads of various significantly smaller launchers.  We haven't really seen that approach so far with Falcon and New Glenn (their upper stages are quite large), but it is an approach that has some merit and hasn't been tested in the market. Could that lead to high GLOMS and low payload numbers? Yes, you can see that with Falcon Heavy. The Reusable portion sizes and masses went up by a lot while the payload didn't go up proportionally.

FH does 10,000 kg to GTO with all ASDS, per Hans at IAC 2018:

https://forum.nasaspaceflight.com/index.php?topic=46493.msg1862987#msg1862987

So 2.6x the liftoff mass (because the upper stage is the same) gets 1.8x the payload. Of course, it does have the advantage of an additional half-stage.

These models have more GLOM than FH but only 70% of its payload. Their upper stages do seem to be overly heavy, which is definitely part of the problem. FH does have more booster engines, which helps because it reduces the relative dry mass of the upper stage. These proposed vehicles are using a gigantic upper stage engine.

I think a better approach to estimating upper stage dry mass would be to assume a structural fraction, then add in propulsion mass. Especially since they don't seem to have a good model for large upper stage mass fractions.

Also, they can't fit a 180:1 nozzle in the interstage? Why not? Are they limited to 5.5 meter core diameter for some reason? Coaxing all the ISP you can get out of the upper stage is critically important to a 2-stage hydrocarbon to GTO architecture.

[Salo]

That's for 1D, 1D Full Thrust opened the throat a little to increase thrust. That lowered the ER, which slightly increased SL ISP while slightly decreasing vac ISP. Chamber pressure also increased slightly.

http://www.b14643.de/Spacerockets/Specials/U.S._Rocket_engines/engines.htm

1D FT is 289/312. Average ISP for both didn't really change much though.

Methalox just doesn't work well without staged combustion and densification.

Interesting, thanks. In that case ~303s/334s would make more sense, especially since they assume a chamber pressure of 12MPa, which is more than Merlin. Weird.

A GG methalox engine that gets 289/320 is probably around 70 MPa in chamber pressure.

You mean 70 bar, or 7 MPa? That is what I get in RPA lite for a 70 bar methalox engine at 3.25 O/F, assuming 0.966 engine efficiency and 3% mass flow through the GG.

Using the same assumptions with 12 MPa,  I get 301 SL / 332 vacuum.

To get 320 seconds in vacuum requires using 6.7% of the mass flow in the GG, which seems really high.

Yeah, meant bar not mpa 

Study also seems to use MR of 2.5:1

https://www.eucass.eu/doi/EUCASS2017-537.pdf

The engine delivers 100tons of thrust. A single shaft turbo-pump is used to feed the combustion chamber, cooled via a methane regenerative circuit. Four main valves feed the chamber and the gas generator. Three of them are fully regulated valves and allow a throttling level from 30% up to 110%.
The nominal combustion chamber pressure is set to 100 bar, on the basis of engine mass correlation, engine feedback and performance target. The combustion chamber mixture ratio is set to 3.5 which is near the optimum for the combustion chamber, as it is illustrated in Figure 5.
The ejection pressure was selected to 400 mbar. This value was chosen because the Prometheus engine is a 1st stage engine and needs a good sea level thrust.

[envy887]

Study also seems to use MR of 2.5:1

2.5:1 is the O/F ratio of the GG only. Overall O/F is 3.25:1 in that paper. As Salo noted, Prometheus seems to be targeting 3.5:1, which is probably closer to optimal for impulse.

[Salo]

Nominal chamber pressure 100 bar. Maximal chamber pressure 110 bar.

[Oggust]

The Wikipedia page for Prometheus: https://en.wikipedia.org/wiki/Prometheus_(rocket_engine)
...says it will have an Isp of 360s...

(I added the "citation needed" for that last weekend.)

[ZachF]

That's for 1D, 1D Full Thrust opened the throat a little to increase thrust. That lowered the ER, which slightly increased SL ISP while slightly decreasing vac ISP. Chamber pressure also increased slightly.

http://www.b14643.de/Spacerockets/Specials/U.S._Rocket_engines/engines.htm

1D FT is 289/312. Average ISP for both didn't really change much though.

Methalox just doesn't work well without staged combustion and densification.

Interesting, thanks. In that case ~303s/334s would make more sense, especially since they assume a chamber pressure of 12MPa, which is more than Merlin. Weird.

A GG methalox engine that gets 289/320 is probably around 70 MPa in chamber pressure.

You mean 70 bar, or 7 MPa? That is what I get in RPA lite for a 70 bar methalox engine at 3.25 O/F, assuming 0.966 engine efficiency and 3% mass flow through the GG.

Using the same assumptions with 12 MPa,  I get 301 SL / 332 vacuum.

To get 320 seconds in vacuum requires using 6.7% of the mass flow in the GG, which seems really high.

Yeah, meant bar not mpa 

Study also seems to use MR of 2.5:1

https://www.eucass.eu/doi/EUCASS2017-537.pdf

The engine delivers 100tons of thrust. A single shaft turbo-pump is used to feed the combustion chamber, cooled via a methane regenerative circuit. Four main valves feed the chamber and the gas generator. Three of them are fully regulated valves and allow a throttling level from 30% up to 110%.
The nominal combustion chamber pressure is set to 100 bar, on the basis of engine mass correlation, engine feedback and performance target. The combustion chamber mixture ratio is set to 3.5 which is near the optimum for the combustion chamber, as it is illustrated in Figure 5.
The ejection pressure was selected to 400 mbar. This value was chosen because the Prometheus engine is a 1st stage engine and needs a good sea level thrust.

Thanks for correction.

Updated table with corrected numbers, Merlin 1DFT stage still beats it:

[Salo]

The Wikipedia page for Prometheus: https://en.wikipedia.org/wiki/Prometheus_(rocket_engine)
...says it will have an Isp of 360s...

(I added the "citation needed" for that last weekend.)

For second stage with expansion ratio 120-180 may be.

[Salo]

Topology Optimization of Turbine Manifold in the Rocket Engine Demonstrator Prometheus:
https://ltu.diva-portal.org/smash/get/diva2:1228857/FULLTEXT01.pdf

[Salo]

https://iafastro.directory/iac/paper/id/44345/summary/
https://iafastro.directory/iac/paper/id/44345/abstract-pdf/IAC-18,C4,1,2,x44345.brief.pdf?2018-07-04.11:29:37

Paper ID: 44345
oral

69th International Astronautical Congress 2018
IAF SPACE PROPULSION SYMPOSIUM (C4)
Propulsion System (1) (1)

Author: Ms. Pamela SIMONTACCHI
ArianeGroup SAS, France, [email protected]
Mr. Roland Blasi
ArianeGroup, Germany, [email protected]

PROMETHEUS: PRECURSOR OF NEW LOW-COST ROCKET ENGINE FAMILY

Abstract
Prometheus is the Precursor of a new liquid rocket Engine family designed for low-cost, flexibility and reusability.
This Project, undertaken through cooperation between CNES and Ariane Group, entered in the ESA Future Launcher Preparatory Programme after the ESA Ministerial Conference in December 2016, with Germany, Italy, Belgium, Sweden and Switzerland joining France in the support of this Programme. The aim of Prometheus project is to design, produce, and test an advanced low-cost 100-tons class LOX/LCH4 reusable Engine. This Engine, designed for 1M recurrent cost, targets also flexibility in operation through variable thrust, multiple ignitions, compatibility to main and upper stage operation, and minimized ground operations before and after flight. To reach those ambitious objectives, an extreme design-to-cost approach is mandatory, as well as innovative technologies and advanced industrial capabilities; among the major levers, there are the extensive recourse to Additive Manufacturing for the production of engine components, the introduction of a full electric command system and the on-board Rocket Engine Computer (REEC) for Engine management and monitoring.
In addition, Prometheus programme promotes the application of Agile and Frugal methodologies to get maximum profit in product innovation and value creation in operation.
This paper presents the global status of Prometheus development and gives a specific insight regarding additive manufacturing production of low-cost components.
Prometheus is part of the effort to prepare long terms Ariane6 evolution, called Ariane6Next.

[Alpha_Centauri]

The Wikipedia page for Prometheus: https://en.wikipedia.org/wiki/Prometheus_(rocket_engine)
...says it will have an Isp of 360s...

(I added the "citation needed" for that last weekend.)

I have no idea where 360 has come from but this document refers to the Prometheus Isp as ~350;

https://academieairespace.com/wp-content/uploads/2018/06/Conf_rence-palais-de-la-d_couverte-31-mai-2018.pdf

Note however the Isp it gives for Merlin is vacuum, so 350 is probably the vacuum Isp of Prometheus.

[envy887]

That's for 1D, 1D Full Thrust opened the throat a little to increase thrust. That lowered the ER, which slightly increased SL ISP while slightly decreasing vac ISP. Chamber pressure also increased slightly.

http://www.b14643.de/Spacerockets/Specials/U.S._Rocket_engines/engines.htm

1D FT is 289/312. Average ISP for both didn't really change much though.

Methalox just doesn't work well without staged combustion and densification.

Interesting, thanks. In that case ~303s/334s would make more sense, especially since they assume a chamber pressure of 12MPa, which is more than Merlin. Weird.

A GG methalox engine that gets 289/320 is probably around 70 MPa in chamber pressure.

You mean 70 bar, or 7 MPa? That is what I get in RPA lite for a 70 bar methalox engine at 3.25 O/F, assuming 0.966 engine efficiency and 3% mass flow through the GG.

Using the same assumptions with 12 MPa,  I get 301 SL / 332 vacuum.

To get 320 seconds in vacuum requires using 6.7% of the mass flow in the GG, which seems really high.

Yeah, meant bar not mpa 

Study also seems to use MR of 2.5:1

https://www.eucass.eu/doi/EUCASS2017-537.pdf

The engine delivers 100tons of thrust. A single shaft turbo-pump is used to feed the combustion chamber, cooled via a methane regenerative circuit. Four main valves feed the chamber and the gas generator. Three of them are fully regulated valves and allow a throttling level from 30% up to 110%.
The nominal combustion chamber pressure is set to 100 bar, on the basis of engine mass correlation, engine feedback and performance target. The combustion chamber mixture ratio is set to 3.5 which is near the optimum for the combustion chamber, as it is illustrated in Figure 5.
The ejection pressure was selected to 400 mbar. This value was chosen because the Prometheus engine is a 1st stage engine and needs a good sea level thrust.

Thanks for correction.

Updated table with corrected numbers, Merlin 1DFT stage still beats it:

I did a full model calculating the GLOM of a 2-stage to GTO LV based on average and vac ISP, mass fractions, payload, booster entry velocity, and EDL delta-v. Iterating over upper stage delta-v as these authors did, and plugging in Falcon 9 numbers, it looks like a good model... getting GLOM and booster mass values consistent with what we know about F9.

But when I plug in the payload, ISP and structural fractions from this paper, I get much, much smaller GLOM and dry mass values, in the 800 tonne and 45 tonne range.

[ZachF]

I did a full model calculating the GLOM of a 2-stage to GTO LV based on average and vac ISP, mass fractions, payload, booster entry velocity, and EDL delta-v. Iterating over upper stage delta-v as these authors did, and plugging in Falcon 9 numbers, it looks like a good model... getting GLOM and booster mass values consistent with what we know about F9.

But when I plug in the payload, ISP and structural fractions from this paper, I get much, much smaller GLOM and dry mass values, in the 800 tonne and 45 tonne range.

The numbers made more sense when I thought the Prometheus was an 289/320 ISP engine...

With my admittedly simplistic first stage model the 304/332 ISP version shouldn't be that much worse than the Falcon 9/M1DFT first stage.

I kinda think they've purposely sandbagged it... For various reasons they wanted a result showing reusability to be harder than it actually is.

[envy887]

I kinda think they've purposely sandbagged it...

Purposely or not, it's definitely sandbagged. I'm just trying to figure out where.

One thing I noticed was that they run the booster up to higher altitudes and velocities than F9. I think that combined with low upper stage delta-v is leading to them using far more fuel for reentry compared to F9, which exponentially increases the size of the vehicle.

I've worked around this in my model by setting an entry velocity of 2300 m/s, which is what a hot F9 enters at, then adding a "boostback" burn (which is really just extra fuel for deceleration prior to entry, not a boostback). I'm optimizing for minimum boostback fuel (i.e. staging velocity=entry velocity), and it's coming out a higher upper stage delta-v of around 7400 to 7500 m/s, similar to what F9 does. This is also near the optimum for booster dry mass.

The 7000 and 6600 m/s delta v upper stages yield much higher booster staging velocities, requiring it to carry more fuel for braking. For upper stage delta-v less than 6400 m/s, there is actually no solution with the given methalox ISP and stage mass fractions, and for 6500-6600 m/s the vehicles are enormous - hundreds of tonnes larger than the optimal stack with a 7500 m/s upper stage.

I'm going to look into running sensitivity analyses of both S2 ISP and S2 mass fraction with this model. I think the high upper stage mass fractions and decision to use a 120:1 nozzle are also unnecessarily increasing the size of the proposed vehicles.

[Oli]

But when I plug in the payload, ISP and structural fractions from this paper, I get much, much smaller GLOM and dry mass values, in the 800 tonne and 45 tonne range.

If you're referring to Figure 2, those are the results of the 2017 paper with overestimated second stage dry mass. As they admit themselves in that paper and therefore also present results with a more detailed mass model (though only for the 7km/s version, not for 7.6km/s. For the 7km/s version the reduction in 2nd stage GLOW is substantial, from ~270t to 157t). It's a mystery to me why they point to those faulty results (according to them) to exclude 7.6km/s in the 2018 paper.