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

Low Cost HLV, page 3: Lightweighting the S-IC Stage.

Copyright 2012 Robert Clark

                                                    SASSTO 
                                                    SASSTO - Saturn-derived SSTO Launch Vehicle 
                                                    Credit: © Mark Wade


 I showed in the post Low Cost HLV, page 2: Comparison to the S-IC Stage that the S-IC first stage of the Saturn V could give a nearly 20-to-1 mass ratio using a lighter thrust structure and using four RD-171 engines instead of five F-1 engines. But in fact we can do better than this. The S-IC of the 1960's did not have available the aluminum-lithium alloy used for example on the Falcon 9 and shuttle ET. Here I calculate a lighter structure using this lighter alloy and some mass reducing structural changes.

 The tank mass of the S-IC stage and of some other rocket stages is discussed in this key report:

Single Stage To Orbit Mass Budgets Derived From Propellant Density and Specific Impulse.
John C. Whitehead
32nd AIAA/ASME/SAE/ASEE Joint Propulsion ConferenceLake Buena Vista, FLJuly 1-3, 1996
http://www.osti.gov/bridge/servlets/purl/379977-2LwFyZ/webviewable/379977.pdf

 On page 8 in Fig. 6 is given a comparison of the tank weights of the Saturn S-IC, Atlas II, and shuttle ET:

 We've already reduced the mass of the stage down to 113,000 kg by using a lighter thrust structure in the prior post. Fins are not really needed for large rockets with computer guidance and control, so remove these to reduce the mass again to 112,000 kg. The  four 4 meter diameter RD-171 engines can fit under the 10 meter diameter S-IC tank, so remove the engine fairings to bring the mass down to 108,000 kg.
 Now use common bulkhead design to reduce the tank mass further. The question of using common bulkhead design for the S-IC arose during the Apollo design period:

SP-4206 Stages to Saturn.
7. The Lower Stages: S-IC and S-II.
THE S-IC AND THE HUNTSVILLE CONNECTION.

The main configuration of the S-IC had already been established by MSFC, including the decision to use RP-1, as opposed to the LH2 fuel used in the upper stages. Although LH2 promised greater power, some quick figuring indicated that it would not work for the first stage booster.Liquid hydrogen was only one half as dense as kerosene. This density ratio indicated that, for the necessary propellant, an LH2 tank design would require a far larger tank volume than required for RP-1. The size would create unacceptable penalties in tank weight and aerodynamic design. So, RP-1 became the fuel. In addition, because both the fuel and oxidant were relatively dense, engineers chose a separate, rather than integral, container configuration with a common bulkhead. The leading issue prior to the contract awards related to the number of engines the first stage would mount.

http://history.nasa.gov/SP-4206/ch7.htm#197

   This could be interpreted to mean the density of the propellant made it unfeasible, but I think the relatively smaller tankage mass using the dense propellants made the more difficult common bulkhead design unnecessary. For instance as you see in that Fig. 6 from Whitehead's report, in the shuttle ET tank the intertank weighs more than the entire oxygen tank. The relative weight of the intertank is not as bad for the kerosene S-IC. Still, common bulkhead design is used for the large kerosene first stage on the Falcon 9 to help save weight.

 So to minimize stage weight we will remove the interstage and one of the bulkheads. Assuming top and bottom bulkheads weigh the same for each of the LOX and kerosene tanks on the S-IC, then from the information in Fig. 6, the LOX bulkheads weigh 4 mT each and the kerosene, 3.3 mT. Conservatively, let's say we remove one of the kerosene bulkheads instead of a LOX bulkhead since we may need the larger LOX bulkhead for strength. Then also removing the 6 mT intertank, we bring the dry mass down to 99 mT.

 Now estimate the weight saving using the lighter aluminum-lithium alloy. From the Wikipedia page on the shuttle ET, the tank weight reduced from 35,000 kg using aluminum alloy 2219, the same alloy used for the S-IC tanks, to 26,500 kg using aluminum-lithium alloy, a reduction of 24%.

 After the structural changes, the tanks now weigh 25.5 mT. Subtracting off 24% from this is a reduction in mass by 6 mT. This brings the stage mass down to 93 mT.

 Keep in mind though, the plan is to use a shuttle ET size tank to save cost on tooling. The ca. 720 mT hydrolox of the shuttle ET becomes ca. 2,100 mT with the 3 times denser kerolox. This turns out to be about the same kerolox carried by the S-IC. So the purpose here was just to get an idea of a lightweight stage you can get using modern materials.

 Now notice you get significant payload as a SSTO using the RD-171 engines at 338 s vacuum Isp. Taking the required delta-v to orbit as 9,150 m/s for kerolox, you can get 48 mT to orbit:

338*9.81ln(1 + 2,100/(93 + 48)) = 9,170 m/s.

 Note though that if we are to use the shuttle ET as a stage then the pointed end of the LOX tank would need to be removed. We could take the equivalent cylindrical LOX tank of the same volume. It would have the same dry weight, so the stage dry mass stays the same.

 However, if you take the full length of a cylindrical tank now as 46.9 m and the diameter as 8.4 m, per the specifications of the SLWT version of the ET, and the density of kerolox as about 1,030 kg/m^3, then we get about 2,600 mT kerolox. The tank weight would increase somewhat without the pointed end, but not by much compared to the entire stage weight. Then you could loft 82 mT to orbit:

338*9.81ln(1 + 2,600/(93 + 82)) = 9,160 m/s.

 A propellant load of 2,600 mT at dry mass of 93 mT corresponds to a mass ratio close to 29 to 1, rather high. But SpaceX has said with their side boosters on the Falcon Heavy they expect to achieve a mass ratio of 30 to 1, and mass ratio does get better as you scale up a stage,with this shuttle ET size stage being much larger.

 This payload of 82 mT is better than the 70 mT to be carried by the interim SLS. Remember our HLV is to be developed using the SpaceX-style commercial approach. Then based on a $2,000/kg price of the Falcon Heavy, the full two stage version of our HLV as comparably priced might only cost ca. $200 million per launch at a 100 mT payload to orbit.

 So the SSTO version would even cost less than this, perhaps only ca. $100 million per launch for the 82 mT payload to orbit.

 The dry weight could be lightened further by using composites. Estimates put the weight savings in the structural mass in the 40% range for a fully composite structure. In that case the payload could exceed 100 mT for this SSTO.

 An increase of the Isp could be possible by using an aerospike or plug nozzle, up to the range of 360 s. The multi-nozzle format of the RD-171 engines makes this feasible. The four nozzles of each engine would be shortened and arranged around a central aerospike. This was the idea behind the aerospikes planned for the X-33 and VentureStar. It was also used earlier in the planned Beta SSTO of Dietrich Koelle and the SASSTO SSTO of Phillip Bono.

 An argument against this was that the aerospike nozzle would make the propulsion system too heavy. For instance for the aerospike on the X-33 the thrust/weight ratio was only 40 to 1, compared to a 70 to 1 ratio for the SSME's for example. However, the lightweight, high temperature ceramics and composites available now should make the T/W comparable to bell nozzle engines:

Ceramic Materials for Reusable Liquid Fueled Rocket Engine Combustion Devices.
http://ammtiac.alionscience.com/pdf/AMPQ8_1ART06.pdf


  Bob Clark

Note: The SASSTO SSTO shown at the top and discussed near the end was derived from the Saturn S-IVB stage, not the S-IC, and was hydrogen fueled. The Beta SSTO discussed was also hydrogen fueled. However, a key result of the cited report of John C. Whitehead is that it is actually easier to make a kerosene-fueled SSTO. This is because the large and heavy hydrogen fuel tanks swamps out the advantage of its higher Isp.  - B.C., 6/22/2012.

Low Cost HLV, page 2: Comparison to the S-IC Stage.

Copyright 2012 Robert Clark 

The dry mass of the first stage of the vehicle described in the Low Cost HLV post was 1/20th the gross mass of the stage at 110,000 kg. Interestingly the propellant mass of the S-IC first stage of the Saturn V was about the same as in this HLV proposal, about 2,100,000 kg. Then it will be interesting to make a comparison to the dry mass of the S-IC stage. This page gives it as 130,000 kg:

Ground Ignition Weights.
http://history.nasa.gov/SP-4029/Apollo_18-19_Ground_Ignition_Weights.htm

 However, the Saturn V had a quite heavy first stage thrust structure:

SP-4206 Stages to Saturn.
7. The Lower Stages: S-IC and S-II.

Rosen apparently took the lead in pressing for the fifth engine, consistent with his obstinate push for a "big rocket." The MSFC contingent during the meetings included William Mrazek, Hans Maus, and James Bramlet. Rosen argued long and hard with Mrazek, until Mrazek bought the idea, carried the argument to his colleagues, and together they ultimately swayed von Braun. Adding the extra power plant really did not call for extensive design changes; this was Rosen's most convincing argument. Marshall engineers had drawn up the first stage to mount the original four engines at the ends of two heavy crossbeams at the base of the rocket. The innate conservatism of the von Braun design team was fortunate here, because the crossbeams were much heavier than required. Their inherent strength meant no real problems in mounting the fifth powerplant at the junction of the crossbeams, and the Saturn thus gained the added thrust to handle the increasingly heavy payloads of the later Apollo missions. "Conservative design," Rosen declared, "saved Apollo."²

http://history.nasa.gov/SP-4206/ch7.htm

Indeed it was heaviest single component of the S-IC stage, and so of the Saturn V:

S-IC.
2. Components.
http://en.wikipedia.org/wiki/S-IC#Components

 This online lecture of Dr. David Akin of the University of Maryland gives mass estimating relationships for various rocket components, taken from the reports NASA uses in designing rockets:


Mass Estimating Relations.
• Review of iterative design approach
• Mass Estimating Relations (MERs)
• Sample vehicle design analysis
http://spacecraft.ssl.umd.edu/academics/483F09/483F09L13.mass_est/483F09L13.MER.pdf

 On page 17 is given a relation between the thrust of the stage in Newtons and the mass of the thrust structure in kilograms:

M_{Thrust structure}(kg) = 2.55×10⁻⁴T(N)

 For 4 RD-171's at 7,900 kN each, this would be 8,000 kg. So we can subtract off 13,000 kg from that S-IC dry mass to get 117,000 kg. We're also using one less engine, so subtract off 8,350 kg for the one less engine. However, the RD-171 weighs about 1,000 kg more than the F-1, so add on 4,000 kg to get about 113,000 kg for the stage, quite close to the 20 to 1 mass ratio estimate. Note this is even without the weight saving alloys and composites now used.




  Bob Clark

Low Cost HLV.

Copyright 2012 Robert Clark

Credit: Modified from:
NASA's Space Launch System - Winners and Losers
by Ed Kyle, 06/17/2011
http://www.spacelaunchreport.com/sls4.html

 The announcement by two separate teams backed by highly regarded scientists and entrepreneurs for asteroidal or lunar mining means that quite likely there will be a significant market for super heavy lift. Note too that there were separate shuttle privatization plans with business models that involved privately investing perhaps $2 billion to produce a "shuttle 2.0". Quite key here though is a vehicle this size could serve as a super HLV without the ca. 80 mT shuttle orbiter. 

  I think at this point it is abundantly clear NASA can not be expected to make a cost effective launcher. An internal NASA estimate put the total development and launch cost of just four of the interim 70 mT SLS vehicles as $41 billion, which amounts to over $10 billion per launch.

 SpaceX has shown by using good cost-saving business practices to be able to produce a launcher at greatly reduced costs. They estimate their upcoming Falcon Heavy will break the $1,000 per pound barrier, or $2,000 per kg. Keep in mind then that increasing the size of your launcher is supposed to reduce your per kg costs. So likewise using good business practices, a super heavy lift launcher privately developed should be able to at least match this or exceed it. This would be in the range of $200 million per launch for a ca. 100 mT launcher, a radically reduced cost over that of the SLS. 

  I think consideration should also be given to an all liquid system. You would use the DIRECT team's Jupiter HLV hydrogen-fueled upper stage but instead of using the shuttle ET for the first stage to hold hydrolox, use the same sized tank for kerolox. This would give a super heavy lift vehicle without the SRB's.

 The DIRECT team wanted to use the same size tank to save on costs since you can use the same existing tooling in this case. However, a key fact is this will still be the case even if you switch to kerolox propellant. You would have to change the location of the divider between the fuel and oxidizer of course, but this is comparatively low cost compared to producing whole new tooling for a different size tank.

Now kerolox is a denser propellant so you are going to get a higher propellant load in this case. The density is about 3 times that of hydrolox, so lets say the propellant load of the first stage is now 2,100 mT. What about the dry mass? 

 At this point I think we should take note of the lightweight characteristics of the Falcon 9 that SpaceX was able to achieve. SpaceX has said the first stage of the Falcon 9 has a mass ratio better than 20 to 1. SpaceX did this by using well known techniques such as a common bulkhead design for the tanks. So we could follow this also to minimize first stage dry mass.

 Also, note that by scaling our propellant tanks up, we actually improve our mass ratio. So likely we can get an even better mass ratio than this for our large first stage. But using the 20 to 1 figure, or 19 to 1 for propellant to dry mass ratio, we get a dry mass of 110 mT.

 We need heavy thrust kerosene engines. I'll use the RD-171, with a sea level thrust of about 1,700,000 lbs, and vacuum Isp of 337 s. This will require 4 of the engines. This could be replaced later with the F-1 but using the RD-171 would allow you to start now on the vehicle development with better performance.

 For the specifications of the upper stage, the DIRECT team went through several versions of their Jupiter super heavy lift vehicle. I'll use the one they referred to as Jupiter-246 Heavy, LV 41.5004.08001. For whatever reason, the DIRECT team no longer has the specifications for their vehicles up on their web site. This version's specifications are within this post to the SpaceFellowship.com forum:


Re: An SSTO as "God and Robert Heinlein intended".
Posted on: Sat Mar 12, 2011 9:49 pm
http://spacefellowship.com/Forum/viewtopic.php?p=44979&sid=3d11bfaff22840cdcd239a4c452c48d6#p44979

though you'll have to register on that forum to view it.

 This version used a propellant mass of 190,849 kg, a dry mass of 11,825 kg and 6 of the RL-10B2 engines, with an Isp of 459 s. Other versions have used the new J-2X engine, but just 6 RL-10's are likely to be cheaper. 

 This version's interstage and payload fairing were at about 4,000 kg each. We'll round off the upper stage propellant mass to 190 mT and dry mass to 11 mT. Then using a 9,150 m/s delta-V to orbit we can estimate the payload to orbit as 145 mT:

337*9.81ln(1+2100/(110+201+4+4+145)) + 459*9.81ln(1+190/(11+4+145))=9,176 m/s

 Admittedly, this payload estimate seems high so I plugged some numbers into John Schilling's "Launch Vehicle Performance Calculator" and got:

Mission Performance:Launch Vehicle: User-Defined Launch Vehicle
Launch Site: Cape Canaveral / KSC
Destination Orbit: 185 x 185 km, 28 deg
Estimated Payload: 102573 kg
95% Confidence Interval: 86317 - 121993 kg

 So it's still, likely, ca. 100 mT.

 There are several variations on this theme. For example to save on development costs we could use the Ariane 5 core stage as the upper stage. Since the ESA was amenable to using it for an upper stage for a re-booted Ares I, i.e., ATK's "Liberty" rocket, they would likely be amenable to this as well. You could also make this be parallel staging with cross feed fueling to improve performance.

 Another possibility would be to make the upper stage also be kerosene-fueled. Say you used the same light-weight tooling and tank diameter for the hydrogen fueled upper stage but using now kerolox propellant. Again, you could improve performance by making it parallel staged with cross-feed fueling. But this has an additional advantage in that you could take one of the engines off the first stage to use it for the upper stage. This would result in a lower dry weight for the first stage. The upper stage though would then be somewhat overpowered using a RD-171, so it may suffice instead to use a RD-180 just for the upper stage.

 



   Bob Clark