Thursday, October 31, 2013

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

 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

 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.

Saturday, October 5, 2013

DARPA's Spaceplane: an X-33 version.

Copyright 2013 Robert Clark

 DARPA has announced that it will be funding research into a reusable first stage booster to carry an orbital upper stage. But looking at the specifications of the cancelled programs the DC-X's suborbital follow-on, the DC-X2, and on the X-33 you'll note that they each could have performed this role. This would have led to greatly reduced orbital costs. Then both programs were cancelled prematurely.

 Part of the problem is that they were viewed as purely demonstration or experimental programs, without any potential profitability of their own. The profitability would have come with the full, and expensive, SSTO programs to follow. However, if it had been noted these could have been used as fully reusuable first stages, then their value would have been seen on their own. So that they would have been understood as deserving of funding whether or not the SSTO's were to follow.

 The story of the X-33 is well-known now among space advocates:

X-33/VentureStar – What really happened.
January 4, 2006 by Chris Bergin

 It was to be a suborbital experimental test vehicle for a larger SSTO called the VentureStar. For the VentureStar to have been SSTO with significant payload would have required aggressive weight saving techniques such as composite tanks. Such composite tanks were to be tested on the X-33 before committing to the full VentureStar.

 However, the composite tanks failed on the X-33. Since it was felt the SSTO version could not succeed with regular metal tanks, the program was cancelled. However, in point of fact even if you replaced the failed composite tanks with aluminum-lithium ones the X-33 could still be used as a reusable first stage.

 The problem with the tanks is that their unusual conformal shape required them to use greater tank mass compared to the mass of propellant carried than by usual cylindrically shaped tanks:

Space Access Update #91 2/7/00.
The Last Five Years: NASA Gets Handed The Ball, And Drops It.
...part of L-M X-33's weight growth was the "multi-
lobed" propellant tanks growing considerably heavier than promised.
Neither Rockwell nor McDonnell-Douglas bid these; both used proven
circular-section tanks. X-33's graphite-epoxy "multi-lobed" liquid
hydrogen tanks have ended up over twice as heavy relative to the
weight of propellant carried as the Shuttle's 70's vintage aluminum
circular-section tanks - yet an X-33 tank still split open in test
last fall. Going over to aluminum will make the problem worse; X-
33's aluminum multi-lobed liquid oxygen tank is nearly four times as
heavy relative to the weight of propellant carried as Shuttle's
aluminum circular-section equivalent.

  However, ironically it turned out that the hydrogen tank weight for the X-33 actually went down when replaced by aluminum:

From "X-33/VentureStar – What really happened" :
Faced with a project failure, Lockheed Martin and X-33 NASA managers gave the green light to proceed with the fabrication of the new tank. Ironically this new tank weighed in less than the composite tank – disproving one of the reasons for going with a composite tank in the first place.
While the aluminium LH2 tank was much heavier than the composite tank in the skins, the joints were much lighter, which was where all the weight in the composite tank was, due to the multi-lobed shape of the tank requiring a large amount of surrounding structure, such as the joints. Ironically, the original design of the X-33 on the drawing board had the tanks made out of aluminium for this reason – but the cost played a factor for the potential customer base.
Then on replacing the composite hydrogen tanks with Al-Li the dry mass should be less. So I'll use the same numbers for the dry mass and gross mass, 75,000 lbs for the dry mass and 285,000 lbs for the gross.

 The X-33 was to use two aerospike XRS-2200 engines. According to Wikipedia, the XRS-2200 produces 204,420 lbf (909,300 N) thrust with an Isp of 339 seconds at sea level, and 266,230 lbf (1,184,300 N) thrust with an Isp of 436.5 seconds in a vacuum. So two will have a vacuum thrust of 2,368,600 N.

 Now choose for the upper stage an efficient cryogenic stage such as the Centaur or the Ariane H10. We'll use Dr. John Schilling's Launch Performance Calculator to estimate the payload possible. Take the specifications for the Centaur rounded off as 2,000 kg dry mass, 21,000 kg propellant mass, 100 kN vacuum thrust and 451 s vacuum Isp. Then the Calculator gives a payload of 5,275 kg to orbit:

Mission Performance:
Launch Vehicle:  User-Defined Launch Vehicle
Launch Site:  Cape Canaveral / KSC
Destination Orbit:  185 x 185 km, 28 deg
Estimated Payload:  5275 kg
95% Confidence Interval:  4252 - 6507 kg

 The cost of a Centaur upper stage is in the range of $30 million. But how much for a reusable X-33? This article gives the cost to build a X-33 as $360 million in 1998 dollars:

Adventure star  
12:00 18 Nov 1998  Source:  Flight.
By:  Graham Warwick/WASHINGTON DC

 Even taking into account inflation the cost should not be terribly much more than that when you also take into account the decrease in price for composites because of their more common use. 

 The launch preparation costs should also be low since the X-33 was expected to be operated by only a 50 man ground crew compared to the 18,000 required for the shuttle system:

Lockheed Secret Projects: Inside the Skunk Works.

 Say the builder expected a 25% profit over cost of the vehicle over 100 flights. That would be a charge of $4.5 million per flight. With the Centaur upper stage that would be $34.5 million per flight for 5,275 kg to orbit, about $6,500 per kilo. This is a significant saving over the ca. $10,000 per kilo for launchers in the West. It is still well above DARPA's desired price point of $5 million per flight, but it is for a larger payload than the DARPA required 3,000 to 5,000 pounds.

 A lower cost launcher could be obtained using a cheaper upper stage, such as the Ariane H10 stage. This is about 12 mT in propellant load and 1.2 mT in dry mass at 445 s vacuum  Isp and 63 kN vacuum thrust. The Calculator gives a payload mass of 3,762 kg.

 The cost for the H10 stage according to Astronautix is $12 million. Then the total would be $16.5 million. At a payload of 3,672 kg, this is $4,500 per kilo. This would be a great cut in cost for small size payloads, but the total cost is still too high for the DARPA price requirements.

 Another possibility for a cheaper upper stage would be the Falcon 1's first stage. This has a dry mass of 1,450 kg and propellant mass of 27,100. We'll use for it though the upgraded Merlin 1D Vacuum at 800 kN vacuum thrust and 340 s Isp. Then the Calculator gives a payload mass of 5,238 kg. 

 The latest listed price for the Falcon 1 in 2008 was about $8 million. But we only need the first stage. Elon Musk has said for the Falcon 9 the cost of the first stage is 3/4ths the cost. If also true for the Falcon 1, that would put the cost at $6 million for the first stage. Then the total cost would be $10.5 million, $2,000 per kilo. This is a quite low cost per kilo and it would be a significant advance to have payload this size launched at such low cost, whether or not it would qualify under the DARPA program.
 We can get closer though to the DARPA total cost requirement by taking instead the Falcon 1's upper stage. This has a 360 kg dry mass and 3,385 kg propellant mass. The vacuum thrust is 31 kN and vacuum Isp, 330 s. Then the Calculator gives a payload of 959 kg. Taking the cost of the Falcon 1 upper stage as 1/4th that of the $8 million cost of the Falcon 1, this puts the total cost as $6.5 million

 This is a little below the DARPA requirement to LEO of at least 3,000 lbs and at a cost a bit above the $5 million limit, but likely tweaking the sizes of the lower and upper stages can get them within the required range.

 In regards to changing the size, an ideal solution would be to get an upper stage from a scaled down X-33. This would in fact allow us to get a fully reusable two-stage system. Say we scaled down the size of the X-33 by a half in the linear dimensions. This would give us a vehicle 1/8th as large in mass. Then the dry mass would be 4,000 kg with 12,000 kg propellant mass. Take the thrust as 1/8th as large as well at 300 kN, while using the same Isp 436.5 s. Then the Calculator gives us a payload of 1,902 kg.

 Given its 1/8th as large mass, we may estimate the cost to build this half-scale X-33 as $45 million. Using again a 25% price markup over 100 flights, that would be $560,000 per flight. This then would be quite close to the total cost range requirement for the DARPA program.

   Bob Clark