Still want an SSTO? Your move.

[Exoscientist]

21 hours ago, sevenperforce said:

Unfortunately the higher-ISP kerolox engines are ORSC, which makes them much heavier for their thrust than the Merlin engines.

The RD-180 boasts a SL specific impulse of 311 seconds, and kerolox has a maximum theoretical vacuum isp of 353 seconds. Using these numbers decreases fuel fraction to 93.7%, which is not a huge improvement but it's something. Note that this doesn't account for increased gravity drag resulting from slower fuel consumption.

So we have the Merlin 1D with a TWR of 183:1 and a fuel fraction of 94.3%, and the RD-180 with a TWR of 78.44 and a fuel fraction of 93.7%. Fuel fraction calculations were made with the assumption of a LV TWR of 1.3:1, so with the Merlin 1D this requires 0.77% of GLOW to be engine mass, leaving 5.53% of GLOW for payload, tankage+structure, and margins. For the less powerful but more efficient RD-180, we have 1.66% of GLOW as engine mass, leaving 4.64% of GLOW for payload, tankage+structure, and margins. So switching from the Merlin 1D to the RD-180 is a worse tradeoff, even before you factor in the increased gravity drag of the lower fuel consumption. It's possible that the RD-180 could have improved TWR/isp tradeoff using a variable mixture ratio as used in the F1 engines on the Saturn V first stage, but it would still have some difficulty.

...

 

 As Elon has now famously said, the F9 first stage can be SSTO though with smaller payload than the full F9. The first stage Merlins though don't have a very good ISP at only ca. 312 s. So I wondered what would be the payload with the Merlins switched out with the RD-180 engine, at ca. 330 s ISP. Note this is just the straight engine without altitude compensation. You do though have to consider the greater weight of the RD-180. 

I used the launch performance estimator here:

http://www.silverbirdastronautics.com/LVperform.html

 I found the RD-180 case did give increased payload even when you take into account the greater stage weight using the RD-180. 

 You have to be aware of some quirks of this program though. First the option "Restartable upper stage" should be checked "No", otherwise the payload will be reduced. This is true even for the SSTO case. I believe this is because the program keeps some propellant on reserve for the last stage that reaches orbit.

 Secondly, make sure you match the launch inclination to the launch site latitude, otherwise the payload will be reduced. This is a known fact in orbital rocketry. It is related to the fact performance i.e. payload is reduced if you have to make a plane change. So for Cape Canaveral input 28.5 as the launch inclination to match the launch site latitude.

 Finally, for the thrust and ISP values always enter the vacuum values. This is because the program takes into account their diminution at sea level.

 BTW, also try using just one RD-171, rather than two RD-180's to see what the result is.

  Bob Clark

[sevenperforce]

1 hour ago, Exoscientist said:

 As Elon has now famously said, the F9 first stage can be SSTO though with smaller payload than the full F9. The first stage Merlins though don't have a very good ISP at only ca. 312 s. So I wondered what would be the payload with the Merlins switched out with the RD-180 engine, at ca. 330 s ISP. Note this is just the straight engine without altitude compensation. You do though have to consider the greater weight of the RD-180. 

I used the launch performance estimator here:

http://www.silverbirdastronautics.com/LVperform.html

 I found the RD-180 case did give increased payload even when you take into account the greater stage weight using the RD-180. 

 BTW, also try using just one RD-171, rather than two RD-180's to see what the result is.

The RD-171 has a lower isp AND a lower TWR than the RD-180, so that doesn't seem like it would be very useful. The RD-191 has better thrust than the RD-180, though, so I can consider it.

Using SL-expanded isp values for the Merlin 1D, RD-180, and RD-191 (282/311, 311/338, and 310.7/337) in my calculations provides fuel fractions of 95.6%, 94.28%, and 94.32%, respectively. As noted in part earlier, engine mass fractions are 0.71% for the Merlin 1D, 1.66% for the RD-180, and now 1.46% for the RD-191. Structural fractions are 4.17%, 4.12%, and 4.12%, respectively, so the resulting payload fractions are:

• SL Merlin: -0.48%
• SL RD-180: -0.06%
• SL RD-171: -0.10%

So you were right; going to a more efficient engine does increase payload when you are dealing only with sea-level-optimized engines rather than altitude-compensating engines. Unfortunately, payload fraction ends up negative in all cases.

This was with the base assumption of 1.5 km/s in combined gravity drag and aerodynamic drag, split down the middle, and distributed over what seemed to be the approximately correct range. If gravity drag and aerodynamic drag are significantly lower, or should be distributed differently, then positive payload fractions can be obtained, though they are still miniscule. In particular, the lone Falcon 9 first stage would have such ridiculously high TWR that its gravity drag would be minimal, which is probably what would allow it to reach orbit on its own. For example, if I cut gravity drag in the simulation from 750 m/s down to 375 m/s, payload fraction goes up to 0.18% of GLOW. Of course, that's still just 781.2 kg of payload for the cost of a whole Falcon 9 first stage, flown expendable.

The linked simulator provides 1,472 kg for the Falcon 9 first stage, which seems generous...though its 95% confidence interval goes from 0 to 6751 kg, so that's within the range of my estimate. If you provide the same vehicle TWR for an RD-180-based or RD-191-based SSTO, payload fraction does definitely increase.

[Exoscientist]

3 hours ago, sevenperforce said:

The RD-171 has a lower isp AND a lower TWR than the RD-180, so that doesn't seem like it would be very useful. The RD-191 has better thrust than the RD-180, though, so I can consider it.

Using SL-expanded isp values for the Merlin 1D, RD-180, and RD-191 (282/311, 311/338, and 310.7/337) in my calculations provides fuel fractions of 95.6%, 94.28%, and 94.32%, respectively. As noted in part earlier, engine mass fractions are 0.71% for the Merlin 1D, 1.66% for the RD-180, and now 1.46% for the RD-191. Structural fractions are 4.17%, 4.12%, and 4.12%, respectively, so the resulting payload fractions are:

 

 The specs for the RD-171 that are cited here:

http://www.astronautix.com/r/rd-171.html

give it a mass of 9,500 kg. This is 1,500 kg less than using two copies of the RD-180. So it is possible the payload could be more using a single RD-171 rather than two copies of the RD-180, eventhough the RD-180 does have a slightly better Isp.

 BTW, about the RD-191 you could use either three copies or four to provide sufficient liftoff thrust. Using three would give a lower stage mass, but using four would reduce the gravity drag. So it would be interesting to see which provided the better payload.

  Bob Clark

Edited April 19, 2017 by Exoscientist

[Exoscientist]

 In regards to simulating a flight to orbit, there is this:

 

 However, not being a Kerbal-guy, I don't know if this can be used for Earth-launch rather than Kerbal-launch.

 

  Bob Clark

Edited April 19, 2017 by Exoscientist

[sevenperforce]

55 minutes ago, Exoscientist said:

The specs for the RD-171 that are cited here:

http://www.astronautix.com/r/rd-171.html

give it a mass of 9,500 kg. This is 1,500 kg less than using two copies of the RD-180. So it is possible the payload could be more using a single RD-171 rather than two copies of the RD-180, eventhough the RD-180 does have a slightly better Isp.

My table uses fuel fraction and fixed vehicle TWR to estimate component dry masses as a percentage of GLOW, so the actual mass of a given engine is not really factored into the equation.

There's a discrepancy between what is listed on astronautix and what is listed on Wikipedia; I was going by the latter.