Copyright 2013 Robert Clark
SpaceX has announced development of a new 300 metric ton (mT), 660,000 lb, thrust engine, the Raptor:
By Dan Leone | Oct. 25, 2013
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:
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:
| 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:| 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:
| 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:
| 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
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
