A SpaceX Heavy Lift Methane Rocket, Page 2.

Copyright 2014 Robert Clark

 In the blog post A SpaceX Heavy Lift Methane Rocket I discussed some possibilities for a heavy lift rocket using SpaceX's planned methane engine, the Raptor. Those calculations were based on the initial released values for its thrust of 660,000 lbs, 300,000 kilograms-force. However, recently SpaceX has said the Raptor may have a thrust of 1,800,000 lbs in vacuum, 1,600,000 lbs at sea level. So I'll give some revised estimates for its payload. 

 As before I suggest using the same tooling for the core stage as that used for the SLS core to save on development costs. Corresponding to the new higher thrust of the Raptor I'll use the full tank size of the SLS core, which would hold 1,000 metric tons (MT) of hydrogen-lox propellant. Since methane-lox is 2.4 times as dense as hydrogen-lox, the SpaceX methane-lox core will hold 2,400 mT of propellant. The relative densities of methane-lox compared to hydrogen-lox are given in Table 1 of this report:

Alternate Propellants for SSTO Launchers.

Dr. Bruce Dunn
Adapted from a Presentation at:
Space Access 96
Phoenix Arizona
April 25 - 27, 1996

https://web.archive.org/web/20140215015634/http://www.dunnspace.com/alternate_ssto_propellants.htm

 In regards to the specifications of the methane rocket engine it should be noted the high vacuum Isp of 380 s  cited really would only be expected of a vacuum optimized nozzle. Such engines can not be operated at sea level. However, in an upcoming blog post I'll discuss some altitude compensation methods that will allow the engine to have this vacuum optimized Isp while still being able to operate at sea level. So I'll assume both the first stage and upper stage engines have the vacuum Isp of 380 s.

 As before I'll take the number of engines for the core as five and the propellant-to-dry mass ratio as 20 to 1. For the upper stage I'll take the propellant size as approx. 1/5th that of the core stage, at 500,000 kg with the same mass ratio, and use a single Raptor for the upper stage.

SSTO Case.

 We'll use again Dr. John Schilling's Launch Vehicle Performance Calculator. Input the thrust as the value of the vacuum thrust in kilonewtons of 5 Raptors as 5*8200 kN = 41,000 kN, and the Isp as the vacuum Isp of 380 s. Input the propellant mass as 2,400,000 kg and the dry mass as 1/20th of this at 120,000 kg. For the "Default Propellant Residuals?" option select "Yes", and for the "Restartable Upper Stage?" option select "No". Selecting "Yes" for this last option would reduce the calculated payload.

 Use the default altitude of 185 km. Select Cape Canaveral as the launch site with an orbital inclination of 28.5 degrees to match the latitude of the launch site. Then the Calculator gives the result:

Mission Performance:

Launch Vehicle:	User-Defined Launch Vehicle
Launch Site:	Cape Canaveral / KSC
Destination Orbit:	185 x 185 km, 28 deg
Estimated Payload:	110395 kg
95% Confidence Interval:	75079 - 152433 kg

 So this larger version could give 110,000 kg payload as an SSTO.

Two Stage Case

For the two stage case, in the column for the 2nd stage, input the propellant mass as 500,000 kg and the dry mass as 25,000 kg. Input the thrust as the vacuum thrust of 8,200 kN, and the Isp as the vacuum Isp of 380 s. Then the calculator gives the result:

Mission Performance:

Launch Vehicle:	User-Defined Launch Vehicle
Launch Site:	Cape Canaveral / KSC
Destination Orbit:	185 x 185 km, 28 deg
Estimated Payload:	196089 kg
95% Confidence Interval:	162727 - 236334 kg

  Close to 200 metric tons payload to LEO. Actually since the mass ratio of stages improve as you scale them up, quite likely the mass ratio will be better than just ca. 20 to 1, perhaps in the range of 25 to 30 to 1. This would then improve our payload to above 200 metric tons.

Cross-Feed Fueling for Multiple Cores.

 We'll just look at the 3 core case here. As described in the A SpaceX Heavy Lift Methane Rocket post, we emulate cross-feed fueling in the Schilling calculator by inputting for the two side boosters 2/3rds the actual  propellant mass, and also increase the first stage propellant mass by an additional 2/3rds. The rest of the specifications, dry mass, thrust, Isp remain the same. 

 So enter 2 as the number of side boosters. Then in the column for the boosters, input 1,600,000 kg for the propellant mass and 120,000 kg for the dry mass of the boosters. Enter the actual vacuum thrust of 41,000 kN and Isp as 380 s. Then the calculator gives the result:

Mission Performance:

Launch Vehicle:	User-Defined Launch Vehicle
Launch Site:	Cape Canaveral / KSC
Destination Orbit:	185 x 185 km, 28 deg
Estimated Payload:	536113 kg
95% Confidence Interval:	449806 - 639526 kg

 Over 500 metric tons of payload! This rocket however would be truly massive at 3 times the mass of the Saturn V. This would likely require a new,expensive launch pad to handle a rocket this size.

  Bob Clark

UPDATE, October 25, 2014:

 Some methods of accomplishing the altitude compensation mentioned are discussed here:

Altitude compensation attachments for standard rocket engines, and applications.
http://exoscientist.blogspot.com/2014/10/altitude-compensation-attachments-for.html

A SpaceX Heavy Lift Methane Rocket.

Copyright 2013 Robert Clark

 SpaceX has announced development of a new 300 metric ton (mT), 660,000 lb, thrust engine, the Raptor:

SpaceX Could Begin Testing Methane-fueled Engine at Stennis Next Year.
By Dan Leone | Oct. 25, 2013

http://www.spacenews.com/article/launch-report/37859spacex-could-begin-testing-methane-fueled-engine-at-stennis-next-year

 This is supposed to be used for a proposed heavy lift rocket to be used for manned Mars missions. However, I'm not a fan of the 9 engine arrangement used on the Falcon 9, and even less so of the 27 engines proposed for the Falcon Heavy. I would hope that SpaceX would transition to the larger engines for these rockets as well.

 We can do an estimate of the size and payload capacity of the methane-fueled heavy lift rocket. Previous statements from SpaceX have suggested the core of the rocket might be 7 meters wide. However, I wanted to use an 8 meter wide core to make use of the tooling used for the shuttle external tank to save on costs. If we used the same size tank as the shuttle ET then we can calculate the mass of propellant could be carried as methane-lox instead of hydrogen-lox by comparing their densities.

SSTO Case.

 This report by Dr. Bruce Dunn gives densities and performance data on several propellant combinations:

Alternate Propellants for SSTO Launchers.
Dr. Bruce Dunn
Adapted from a Presentation at:
Space Access 96
Phoenix Arizona
April 25 - 27, 1996
https://web.archive.org/web/20140215015634/http://www.dunnspace.com/alternate_ssto_propellants.htm

 In Table 1 the density of methane-lox is 828 kg/m^3 and for hydrogen-lox, 358 kg/m^3. So the same volume would hold 2.4 times more methane-lox. This would put it in the range of 1,700 mT for the methane-lox. Actually it would probably be a little more than this because likely SpaceX would use common bulkhead design for the tank which would mean it could hold more propellant.

 There have been some estimates proposed for this launcher that use 7 copies of Raptor engine on the core. This many probably would be needed when you take into account the reduction in thrust at sea level if using a 1,700 mT sized tank. However, I wanted to keep the maximum number of engines on a core to be at most what was used on the Saturn V at 5 engines. Therefore I'll reduce the propellant load to 1,000 mT.

 For the dry mass, note that Elon has said that the Falcon 9 v1.1 first stage has a propellant fraction in the range of 96%, for a mass ratio of 25 to 1. As you can see in Dunn's Table 1 the density of methane-lox is about 80% that of kerosene-lox. So I'll estimate the mass ratio for the core as 20 to 1. This will put the dry mass of the core at 52,630 kg, which I'll round off to 50,000 kg.

 The vacuum thrust in kilonewtons for 5 Raptors will be 5*300*9.81 = 14,715 kN. We'll calculate the payload for this core stage first as an SSTO. Input these numbers into Dr. John Schillings Launch Performance Calculator. Select "No" for the "Restartable Upper Stage" option, otherwise the payload will be reduced. Use the default altitude of 185 km. Select Cape Canaveral as the launch site with an orbital inclination of  28.5 degrees to match the latitude of the launch site. Then the Calculator gives the result:

Mission Performance:

Launch Vehicle:	User-Defined Launch Vehicle
Launch Site:	Cape Canaveral / KSC
Destination Orbit:	185 x 185 km, 28 deg
Estimated Payload:	42487 kg
95% Confidence Interval:	28319 - 59338 kg

 Two stage case.  

 For the two stage case, I'll take the the upper stage as using a single Raptor and at 1/5th the size of the first stage, so at 200 mT propellant mass and 10 mT dry mass. Enter in 2,943 kN for the thrust of a single Raptor in the column for the second stage and select "Optimal" for the trajectory. Then the Calculator gives:

Mission Performance:

Launch Vehicle:	User-Defined Launch Vehicle
Launch Site:	Cape Canaveral / KSC
Destination Orbit:	185 x 185 km, 28 deg
Estimated Payload:	77569 kg
95% Confidence Interval:	64244 - 93424 kg

  However, for this upper stage likely you won't be able to get as good a mass ratio as the first stage since it would undergo a higher acceleration as the propellant is burned off. This would require a stronger and therefore heavier structure. Then the payload would be reduced below this, though likely still above ca. 70 mT.

Cross-Feed Fueling for Multiple Cores.

 For higher payloads we'll use a combination of 2 or 3 cores. For both of these we'll use cross-feed fueling. To emulate cross-feed fueling with the Schilling Calculator, note that during the parallel burn portion of the flight the propellant for the center core engines is coming from the side booster stage(s). This ensures that the center core will have a full propellant load during its solo burn portion of the flight, after the side booster(s) are jettisoned. 

 So the total amount of propellant burned during the parallel burn portion, is that of the side booster(s) only. But the Schilling Calculator assumes the amount of propellant burned in the center core during the parallel burn is the same as the amount burned in each side booster. So enter in the Calculator for the booster propellant load a fraction of the actual propellant load of a core equal to the number of side boosters divided by the number of cores. So if you're using 2 cores with one used as a side booster enter in the Calculator booster column 1/2 the amount of the actual core propellant load. And if using 3 cores with 2 used as side boosters, enter in 2/3rds the actual core propellant load in the booster section. This will ensure the Calculator interprets the total propellant burned during the parallel burn portion is that of the actual side booster(s) only.

 But you also want the Calculator to take the amount of propellant burned during the center core's solo burn portion of the flight as that of a full propellant load. Since it is already taking it to have burned the same amount as what the side boosters have burned during the parallel burn portion, add this amount onto the actual propellant load of a core and enter this into a first stage column of the Calculator. For the other specifications for both booster(s) and center core such as Isp, dry mass, and thrust enter in the actual values.

2 Core Version.

 Here one core will be used as a side booster. As described above, to emulate cross-feed fueling enter in the Calculator only 500,000 for the propellant load of the booster. Enter in though the actual dry mass of 50,000 kg, actual thrust of 14,715 kN, and actual Isp of 380 s. And for the center core, enter in the first stage column for the propellant 1,500,000 kg, but the real dry mass, thrust, and Isp values. Also use all the actual values for the second stage. Then the Calculator gives the result:

Mission Performance:

Launch Vehicle:	User-Defined Launch Vehicle
Launch Site:	Cape Canaveral / KSC
Destination Orbit:	185 x 185 km, 28 deg
Estimated Payload:	145339 kg
95% Confidence Interval:	121566 - 173707 kg

 This is surprisingly high. However, another consideration besides the fact that the second stage mass ratio likely won't be as good as used here, is that as propellant is burned off during the parallel burn portion, the engines will have to be gimbaled because the propellant is only coming from the side booster stage. This will reduce the payload somewhat.

3 Core Version.

 Here two cores will be used as side boosters. As discussed, to emulate cross-feed we'll enter in the booster column for the propellant load, 2/3rds the actual amount, so only 660,000 kg. And for the center core's propellant load, enter into the first stage column 1,660,000 kg. All the other specifications are given their actual values. Then the Calculator gives:

Mission Performance:

Launch Vehicle:	User-Defined Launch Vehicle
Launch Site:	Cape Canaveral / KSC
Destination Orbit:	185 x 185 km, 28 deg
Estimated Payload:	211268 kg
95% Confidence Interval:	177052 - 251940 kg

  Remarkably high. Twice the payload of the SLS at about the same gross mass.

   Bob Clark

UPDATE, May 1, 2015:

 To get such high performance you would need the lower stage engines to have the high vacuum Isp of 380 s. But lower stage engines usually compromise their performance to use a single nozzle that can work both at low altitudes and high altitudes. Ideal then would be a nozzle that could adapt to the altitude, an altitude compensating engine.
 Some possibilities for this are discussed here:

Altitude compensation attachments for standard rocket engines, and applications.
http://exoscientist.blogspot.com/2014/10/altitude-compensation-attachments-for.html