Figure 1. Falcon Heavy Space Shuttle (FHSS). A Shuttle concept for the 2020s based largely on the X-37B and X-37C, but also drawing ideas from STS and SpaceShip One. Top and side views. (C) F. Harris

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Steps toward building the first orbital passenger liner

A New Shuttle Concept: Boosted to orbit by Falcon Heavy

By F. E. Harris

March 12, 2016.

1. Introduction

In response to several requests, I am putting down on paper a concept for a new orbital shuttle, launched atop a Falcon Heavy triple core. This replaces the second stage, payload, and payload fairing of the Falcon Heavy with a fully reusable second stage and external tank. The resulting vehicle suffers a more than 50% payload penalty compared to the Falcon Heavy, but is fully reusable, and may reduce the cost of delivering passengers to Low Earth Orbit (LEO) by more than a factor of ten.

Contents:

  1. Introduction
  2. Design Overview - Interface with Falcon Heavy
  3. Heat Shields - Thermal Protection Systems
  4. Main engine
  5. Orbital Maneuvering Systems (OMS)
  6. Aerodynamics / Aerothermodynamics
  7. Power Systems
  8. Landing and Mechanical Systems
  9. Environmental Control Systems (ECLS)
  10. Guidance, Navigation and Control
  11. Docking Systems
  12. Cargo Compartment
  13. Passenger Module
  14. Typical Missions
  15. Test Program
  16. Mission Control
  17. Ground Servicing Operations
  18. Development Team
  19. Conclusions
  20. Appendix A: Calculations
  21. References

Design Overview - Interface with Falcon Heavy

The present Falcon Heavy second stage is 3.66 m diameter by 13.8 m length. The present Falcon Heavy fairing is 5.2 m diameter by 13.1 m length.^1 Since the Falcon Heavy Space Shuttle (FHSS) is intended to replace the existing second stage and fairing, we will take these combined numbers as the length and diameter of the FHSS.
  1. Length: 26.9 m
  2. Diameter: 5.2 m
  3. Wing span: 14 - 15 m
  4. Orbiter empty dry mass: 24,000 kg
  5. Maximum payload: 20,000 kg
  6. External tank dry mass: 8,000 kg
  7. External tank fuel and LOX: 80,000 kg
  8. Orbiter internal fuel and LOX: 15,000 kg
  9. Total mass, orbiter, tank, fuel, LOX, and payload: 147,000 kg
This compares to the Falcon Heavy.
  1. 2nd stage length: 13.8 m
  2. Fairing length: 13.1 m
  3. Total length, 2nd stage and fairing: 26.9 m
  4. Fairing diameter: 5.2 m
  5. 2nd stage empty dry mass: 4,000 kg
  6. Maximum payload: 53,000 kg
  7. 2nd stage fuel and LOX: 93,000 kg
  8. Total mass, 2nd stage, fairing, fuel, LOX, and payload: 147,000 kg

Front and side views of tank and orbiter
Figure 2. a. "Top" view of booster, tank and orbiter. b. Side view of booster, tank and orbiter. c. Tank and orbiter flying under power of second stage engine, using fuel from tank. d. Orbiter flying under power of internal fuel, after separation from external tank. Tank will glide to landing at Cape Verde Islands, while orbiter continues to orbit.

Thus it may be expected that the performance of FHSS is about the same as FH on a low orbit mission, but with less than half the payload. It should be pointed out that this is worthwhile, if the entire stack is ~100% recoverable and reusable, including the external tank.

The mass of the external tank might seem high to a careful reader. This is because the external tank has wings, control systems and landing gear. Its shape is nearly identical to the orbiter. It is designed to detach from the orbiter at suborbital velocity, reenter, and glide to a landing at the Cape Verde Islands in the South Atlantic. The orbiter carries sufficient fuel to continue to orbit, maneuver, and perform the reentry burn, in internal tanks.

The need to recover the external tank places limits on the orbital inclinations FHSS can reach. By landing at the Cape Verde Islands, the Canary islands, or the Azores, inclinations from about 10° to 35° can be reached, but it is not possible to reach the ISS, in its 51° orbit, except by landing the external tank at St. John's Airport, Newfoundland, carrying a reduced payload to orbit.

The wings and control surfaces of the external tank are ~identical to the orbiter, however, because the tank's reentry velocity and dry weight is much less, lighter heat shields and landing gear are required. The tank and the orbiter ride belly to belly on top of the Falcon Heavy's center first stage.

FHSS is designed to fly manned or unmanned. There is a cargo area with a single hinged door, much like the shuttle, but more like the X-37B. On the inside of the door there is a fold out solar cell panel and a cooling radiator, to extend the time FHSS can stay on orbit. From the cargo area a satellite can be released, with a solid rocket motor to raise its orbit if necessary. The cargo area can also carry a small passenger compartment with an IDA docking adapter, or a large passenger compartment with IDA and additional life support, that fills the entire cargo area.

Heat Shields - Thermal Protection Systems

Both the orbiter and external tank have a bottom heat shield made of tiles of PICA-X. This material is denser, but considerably more resistant to damage than the glass tiles of the shuttle. It can be formed into tiles that are about 20 times the area of shuttle tiles. Fewer that 100 tiles will be needed for the orbiter, and fewer than that needed for the external tank. The sides and top of the orbiter and the tank will be covered in Nomex cloth, or ablative paint.

Main engine

I started this project, assuming that FHSS would use the 'mini Raptor' engine that the Air Force is paying SpaceX to develop. Tank sizes were worked out assuming methane fuel and un-desified liquid oxygen (LOX). However, because of the lack of available data on mini Raptor, I used Merlin 1D-Vac for dimensions of the engine and bell. I had originally hoped there would be room for 2 engines, to provide redundancy in an engine out situation, but there is not enough room with the large bell of M1D-Vac. Thus, FHSS has a single main engine, and relies on thrusters as a redundant means to initiate reentry, the same as the shuttle.

The main engine draws fuel from the external tank for 85%-90% of the burn required to reach orbit. The engine then throttles back to a very low setting, while the external tank is ejected. The engine then throttles back up for the remainder of the trip to orbit.

In abort situations, the main engine fires at full throttle, drawing fuel from internal tanks and leaving the external tank behind. This permits sufficient acceleration for the orbiter to escape.

Orbital Maneuvering Systems (OMS)

The same main engine that takes the second stage to orbit is used for maneuvering while in orbit. There is no separate hypergolic fuel system and dedicated OMS engines. Similarly, the thrusters operate using methane and oxygen for fuel and oxidizer. Methane/oxygen is much easier to ignite than kerosine/oxygen, so this fuel/oxidizer combination is reliable enough to use for main engine and thrusters, with spark ignition.

Avoiding the use of hydrazine NTO, the hypergolic fuel mixture used for the shuttle OMS and thrusters, avoids the high toxicity of those chemicals, and the many expenses, delays, and risks to passengers that go along with hypergolic fuels.

In the event of main engine failure, the maneuvering thrusters can fire for several minutes to slow he orbiter to suborbital speeds, to initiate reentry.

Aerodynamics / Aerothermodynamics

Aerothermodynamics:

FHSS uses tiles of PICA-X, like that used on Dragon and Dragon 2. These tiles can be made ~10 to 20 times the area of Space Shuttle glass tiles, and FHSS is smaller, so far fewer tiles are needed. PICA-X tiles are tougher, though more dense, so they do not require as frequent inspection and replacement as shuttle tiles. PICA-X tiles are ablative, so the tile set will require complete replacement, every tenth flight. A lighter heat shield will be required on the external tank, which is designed to reenter at suborbital velocity, and glide to a landing at the Canary Islands.

Pica-X tile placement
Figure 3. Trial PICA-X tile placement on the first Dragon capsule. (C) SpaceX/Roger Gilbertson

Upper parts of the orbiter will be protected either by Nomex blankets, or by ablative paint, depending on the severity of heating at that part. There will be two small, double-paned windows for the pilot and copilot, but windows in the passenger compartment will be on the pressurized passenger module when it is installed, and protected by the cargo bay door during reentry.

Like the Shuttle and the X-37B, the design of FHSS is a flat bottomed, low wing monoplane, and like the X-37B, there are 2 V-tail control surfaces that serve both as rudders and horizontal stabilizers. The flat bottom helps to create a continuous sheet of plasma under the vehicle during reentry, which reflects the majority of heat, without focusing heat in areas like the wing roots, creating hot spots. All outer surfaces are rounded, also to prevent the formation of hot spots. The wing plan of FHSS is a tapered monoplane wing with more taper near the wing root, again like the X-37B and not like the delta wing of the Shuttle. The FHSS wing is a design that provides good control at hypersonic speeds and much better glide slope and control at subsonic speeds, especially on final approach and during landings.

Aerodynamics:

Use of the V-tail permits these control surfaces to be effective during hypersonic reentry, unlike the Shuttle's rudder. Like Scaled Compostes' SpaceShip One, a substantial portion of the trailing edge of the wing folds upward during reentry, to increase stability and to permit a much wider range of CG locations during reentry than was possible with the Shuttle. There is also a movable flap of heat shield protecting the main engine bell during reentry. This is an important control surface at hypersonic speeds, but unimportant at subsonic speeds and during landing.

X-37B 3-View
Figure 4. X-37B 3-View. The X-37B is the aerodynamic model for Falcon Heavy Space Shuttle (FHSS). FHSS will be much larger, with more wing area in proportion to the plan form, and with the capability to carry 20,000 kg to Low Earth Orbit (LEO) in unmanned mode, or up to 16 passengers and 2 pilots, in manned mode. (C) NASA/USAF/Boeing

FHSS comes in at a high angle of attack during the hypersonic portion of reentry. The V-tails and the back portion of the wing are turned to present minimal resistance to the air stream at this time. While not creating the 'carefree reentry mode' of SpaceShip One, this does reduce the need for active control during this phase, compared to the Shuttle.

At about 100,000 feet, the transition to supersonic flight occurs. Heating during reentry drops dramatically. The plasma sheath in front of and around the orbiter collapses, and radio communications can resume. Transition to nose-forward flight can occur at supersonic speeds, or it can be made at subsonic speeds, with a loss of cross range capability. In Hypersonic flight the L/D of FHSS is about 0.6, much lower than the shuttle, but higher than capsules like Dragon 2. In subsonic flight the L/D of FHSS is about 8, or roughly twice as good as the shuttle. This makes landing a much safer event.

Power Systems

There are 3 power systems on FHSS, any of which can serve as backups for the others.

1. Batteries. These can provide enough power for 6-12 hours of operation, since the power demands during ascent and reentry are high. Batteries can be recharged by the other systems. If charging is not possible due to system failures, then reentry should be initiated as soon as it is safe to do so.

2. Solar cells. Within the payload bay door, there are fold out solar cells and a radiative cooling panel. These are necessary for long term operation of FHSS, and obviously, the Solar panels should be positioned to shade the cooling radiator.

3. Internal combustion engine/generator APU, run from gasses bled from the main methane and oxygen tanks. This will be a small engine, in the 1 - 10 Kilowatt range, barely more than a model airplane engine in size and weight. Cooling loops from the LOX and methane tanks will be used to cool the engine and to heat the tanks, and exhaust gas from the engine will provide a small amount of thrust, to keep the tanks settled. This engine will run during liftoff and reentry, to provide additional power for the aerodynamic controls discussed in the previous section. It will also run as necessary to recharge batteries, but it will definitely be off during docking maneuvers, since the exhaust provides a small continuous thrust that is undesirable during docking.

Landing and Mechanical Systems

Landing gear is spring loaded, and folds back when opened, so that the air stream provides a backup means of locking the gear down. Rear landing gear is small wheels with disk brakes, for slowing the craft on the ground and for steering. Front landing gear is a skid shoe, with an outer layer of PICA-X, and an inner layer of steel or some plastic that is more suitable to the task. The skid shoe will be worn out and discarded after every landing, but this is a small, cheap part, lighter and more reliable than a wheel with a brake and a steering mechanism.

Mechanical systems consist of the aerodynamic flight controls, which are electrically operated by either battery power, or the ICE/generator APU. There can be high horsepower demands on these controls at times during flight, and overheating in zero-G may be a problem, unless the motors are in air and equipped with cooling fans, or some liquid cooling system.

The final mechanical system is the payload bay doors, and their opening and closing mechanisms. These are very important because on opening they reveal the solar cells and the cooling radiator, both essential systems for long flights. On closing, the door must have secure enough closure to be an effective part of the thermal protection system.

Oddly enough, research during shuttle design revealed that the best mechanism to ensure high strength and good alignment when closing a large, lightweight, flexible door like this is some form of zipper. When the door is closed, the mechanism aligns one corner, and travels from that corner to the other corner of the door, making one closure at a time along the way. The result is lightweight and very reiable.

Environmental Control Systems (ECLS)

Environmental control systems must deal with heat, pressure, oxygen, carbon dioxide removal, humidity removal, toxic and noxious trace gas removal, human waste disposal or recycling, and providing water and food. Much of the research performed aboard the ISS in the last 10 years has been aimed at improvng these systems. Modern ECLS systems do more recycling, take up less mass and bulk, and consume less scrubbing chemicals than previous systems.

The approach used depends on mission duration and size of crew. For short missions one can carry larger tanks of oxygen and water, and dump wastes overboard, since recycling systems take weight and power. The shuttle generally used this approach. The ISS has more systems that remove undesirable chemicals from the environment, and then convert them back into usable form. Urine and humidity from sweat can be removed from the air using a cold trap, and then by the process of electrolysis, turned into oxygen and hydrogen. The hydrogen can be dumped overboard, or combined with carbon from the carbon dioxide scrubber to make methane, which can be pumped into the fuel tank. The oxygen from electrolysed water can be put back into the air supply. All of this requires power. It is not clear if FHSS will have the power available to do electrolysis, since it can only carry a limited number of solar cells to orbit. Using the internal combustion engine APU to generate power for electrolysis is just silly, since using it involves burning oxygen and making H2O and CO2 to get the energy to convert H2O and CO2 into oxygen. Better to dump the waste overboard and siphon some oxygen out of the main tank.

No matter what approach to ECLS is used, carbon dioxide must be scrubbed from the air. CO2 builds up to toxic levels faster than oxygen is depleted. To simply replace contaminated air would waste a lot of oxygen. LiOH scrubbers have been used to remove CO2 since project Mercury, and they do the job well. I believe that on the ISS, silver oxide scrubbers have been developed that can be cleaned and recycled by heat and exposure to vacuum, dumping the CO2 into space. This may be the best method to use on FHSS.

Cold traps are the best method for removing water vapor, and carbon filters are still used to remove toxic and noxious trace gasses. If there is not enough solar power available to turn urine into oxygen, then the best approach to all human waste is to store it and return it to Earth, or to dump it overboard as was done in Apollo.

Guidance, Navigation and Control

This is a far easier subject than it once was. We now have GPS, and GPS works well in orbital space. For short term backup, optical gyroscopes and accelerometers are thousands of times smaller, and more accurate than they were in the 1960s.

Redundant computers and controls have been a requirement for manned spacecraft for some time. Commercial off the shelf components are faster, more powerful, and cheaper than older, space-rated equipment. This is a problem that SpaceX has solved in a superior way for Dragon and Dragon 2. No change in approach is required.

Docking Systems

Not all missions for FHSS will require docking. To prevent carrying useless weight to orbit, the docking adapters will be parts of modules that can be installed in the payload bay/cargo compartment as needed. Standard IDA (International Docking Adapter) or CBM (Common Berthing Module) adapters should be used, since common standards are essential to safety in this area.

Space Shuttle Atlantis
Figure 5. Space Shuttle Atlantis preparing to dock with the International Space Station. In this picture the docking ring/adapter can be seen in the payload bay, immediately behind the crew compartment. FHSS will use a similar placement of its IDA docking adapter. (C) NASA

The IDA or CBM, when installed, rides just aft of the pilot's compartment, leaving the aft part of the cargo compartment for satellites or other vacuum cargo. The IDA and CBM modules will have a window and manual docking controls, to back up the automatic systems.

Cargo Compartment

The cargo compartment has been mentioned several times above, as have the cargo bay doors. The cargo compartment is considerably smaller than the payload fairing of Falcon 9/Falcon Heavy. It is much smaller than the cargo bay of the shuttle, but it is larger than the cargo bay of the X-37B. Dimensions are a half-cylinder, 5.2 meters diameter by 12 meters. The height of the cargo compartment is about 2.4 meters.

The Cargo compartment will have 3 sets of attachment points: A) a standard payload adapter ring, at the back of the compartment. This can accommodate satellites designed to launch on the Falcon 9, Falcon Heavy, Proton, Soyuz, Ariane 5, Atlas 5, Delta 2, Delta 4, etc., assuming the satellite fits within the size and weight parameters FHSS can accommodate. B) There will be 2 rows of mounting brackets along the edges of the floor of the cargo compartment. These were included to be compatible with certain shuttle payloads, but they are no longer standard in the launch industry, and might be omitted from the final design. C) A reinforced CBM ring at the front of the cargo compartment, leading into the pilots compartment. This is normally used to attach the IDA/CBM module, if docking/berthing to a space station or MCT is required by the mission, or for attaching the Passenger Module, if more than 4 people are being delivered to or carried away from a space station or MCT. The passenger Module's main structural attachment is the ring at the back of the cargo compartment. If no module is attached to this CBM, then a door should be emplaced to prevent air from escaping from the pilots compartment.

Passenger Module

The Passenger Module can carry 16 people, and two people can ride in the pilots compartment. Fewer people can ride in comparitively greater luxury. The front part of the passenger compartment contains an IDA, further limiting headroom for the first 2 passengers. Passengers behind the first 2 will each have a window, but will not be able to see out of it during launch or reentry, since the passenger module will be covered by the cargo compartment door.

The rear part of the passenger compartment will contain an augmented ECLS module, to permit a total of 18 people to have supplies to stay in space for up to 4 days, if necessary.


Figure 6. Shuttle concept for the 2020s. (C) F. Harris

Typical Missions

1. Cargo: All early missions will be unmanned cargo missions, until there is confidence that FHSS is safe enough to carry test pilots, and later, passengers.

Cargo missions can carry a satellite(s) to be released in Low Earth Orbit (LEO). It is also possible to carry a solid rocket motor, to deliver a smaller satellite to high Earth orbit, GTO, or beyond to the Moon or Mars.

Cargo missions can also rendezvous with a space station or MCT, where cargo can be removed from the cargo compartment by a robot arm, not included in the FHSS design.

2. Mixed missions: The short IDA module can be installed in the cargo compartment of FHSS, leaving room behind for vacuum cargo. Pressurized cargo can be carried inside the IDA module. Two pilots or passengers can ride in the pilots compartment. In this mode, FHSS would be able to fulfill the roles of Dragon 1 and Dragon 2 for space station resupply. The advantage of using FHSS for this is that FHSS is totally reusable, except for a few cheap parts.

3. Passenger missions: The long Passenger Compartment would be installed in FHSS, permitting up to 18 people to be transported to orbit, to a space station or an MCT, or to be returned. This is the main purpose of FHSS: to act as a space taxi, delivering larger numbers of people to and from orbit than has ever been done before, in a single flight.

FHSS in passenger mode will have a limited time on orbit. Probably its limit for autonomous flight with a full passenger compartment will be 4 days. By then it will either have to dock with a space station or an MCT, or to return to Earth. The limiting factor is likely to be the ECLS. Once docked to a station or to an MCT, FHSS could stay on orbit for months if necessary, drawing oxygen, power, and other life support from the station's ECLS.

Test Program

The test program will procede in 4 steps:
1. Unmanned testing of abort/escape systems.
It will be possible to test FHSS much more thoroughly than the Shuttle. Since the aerodynamics and size of the external tank and the orbiter are almost identical, it would be possible to fly both on a suborbital trajectory that ends in the Canary islands. Various other abort scenarios, including RTLS, can be tested, although I would think one suborbital abort test would be enough.
2. Unmanned orbital test.
It is possible to fly FHSS to orbit with no payload (or just a wheel of cheese) and land it back at the Cape a day later. This flight could also be used to launch cubesats or other student or charitable payloads.
3. Unmanned orbital payloads.
Prior to manned flights, FHSS can build up a hertage of unmanned missions, to test all aspects of operation. Ground control can open the cargo compartment and release satellites, or satellites with booster stages to take them to higher orbits. Cargo runs can be made to space stations, carrying all vacuum cargo, a mix of pressurized and unpressurized cargo, or all pressurized cargo. By these flights, the docking module and the passenger module can be tested.
4. Flights manned with test pilots.
There really is not much reason to fly cargo flights to a space station with test pilots aboard, other than to verify the ECLS works properly. Still, it is a necessary step before passenger lives are risked on the spacecraft.

At this point FHSS is ready to start carrying passengers. Note that it could pay its own way throughout the test program, except for the first flight or two.

Mission Control

FHSS is designed so that it can be flown from the ground, which minimizes risk for test flights, cargo flights that do not need pilots, or long duration flights, since the time limit for FHSS flights is imposed by the limitations of the ECLS. For unmanned flights, a larger ground control team may be needed. For manned flights, the pilots are in command, and mission control could be limited to 3-5 people on duty after the launch.

Ground Servicing Operations

Other than laser metrology of the heat shield after every flight, post flight processing of the orbiter should be minimal. Systems aboard the orbiter are simpler than Dragon 2, and the systems on the external tank are even simpler than that. So far as I can see, the FHSS upper stage comes close to the ideal of, "Inspect, refuel, and refly."

There are a few use-once parts to replace after every flight. These are the mini-fairing that protects the noses, heat shields, and wing leading edges of the orbiter and the external tank during ascent, the load ring that connects the orbiter and tank to the FH center core's first stage, and the PICA-X/composite front landing shoe, which is designed to wear out by friction during landing.

Development Team

This is a more complex vehicle than Dragon 2, with control and aerodynamics design problems SpaceX has never faced before. At one time I thought that the delays and added expense of working with an outside design and prototyping firm like Scaled Composites would doom this vehicle. But then I remembered that even a vehicle that flies in so many different regimes does not really require a big firm. Scaled Composites built and flew SpaceShip One with a crew of 22, in four years. The chief architects of that success, Burt Rutan, Jim Tighe, and Matt Steinmetz, have since left Scaled Composites and can be recruited to join SpaceX. The team at Scaled never had the money or the resources to do the software or the controls properly, but these are areas where SpaceX already has the expertise in house. This project can be done, and for nowhere near the cost that most people would expect.

The team that designs and builds this upper stage should be small and independant, like other SpaceX teams. They should be allowed to redesign extensively to meet requirements, if the initial assumptions of the design are shown to be wrong. If necessary, a pure test vehicle, that cannot carry the design payload to orbit should be built, as proof of concept, and then improved. As we have seen with other products from SpaceX, there should be a willingness not to freeze the product too early, but instead to keep improving it, until it meets the needs of the market.

Conclusions

Low operating costs makes FHSS an attractive proposition. I do not see a show stopper to eventually flying FHSS for under $10 million / mission.

High development costs for FHSS may be avoidable. A small, knowledgeable team using NASA data from the Shuttle and X-37B does not have to reinvent the wheel; only to improve it.

The main obstacle to FHSS development may be that FHSS is a spacecraft in search of a mission, like the shuttle. Its cargo payload to LEO is similar to the Falcon 9. Its usefulness for GTO launches is very limited. Its main strength is what it was designed to do: carry relatively large numbers of people to a LEO destination, at 0° to 35° orbital inclination. No such destination exists today.

If such a destination is built in the next 10 years, a space taxi capable of transporting more than 7 people at a time will be wanted. The destination could be an Earth orbiting space station, a shuttle designed to go from Earth orbit to Moon orbit and back, or the MCT.

Until one or more of these destinations is nearing completion, there is no economic case for FHSS. If the Air Force or NASA will fund development in a way that gives SpaceX a free hand, perhaps FHSS development can start in the next 2 years, to reach a prototype/first flight stage by 2021. More likely it will be better to wait for a firmer understanding of the destination to emerge before designing FHSS to be optimized to service that destination. If the destination is the MCT, then 2026 should be the goal for FHSS going into service

Going into this study, I was convinced that the aerodynamics and control problems would make FHSS too expensive and uncertain to develop, and the risk of bankrupting SpaceX was too great for developoment to proceed. As I continued my work, I came to a different conclusion: that this project is doable. If FHSS can see frequent service with complete reuse, then launches for under $10 million become possible, and passenger flights for under $600,000 become realistic.

Appendix A: Calculations

1. Volumes of LOX and Methane

a. External tank: What are the dimensions of 80,000 kg of liquid methane and oxygen?

CH4 + 2 O2 = CO2 + 2 H2O

CH4 = 16 gram/mole
2 O2 = 64 gram/mole

Stochiometric Mass ratio is about 4kg O2 to 1 kg CH4. Mix should be fuel rich to preserve engine and increase ISP, so a real ratio of 3.75 kg O2 to 1 kg CH4 is about right.

Densty of liquid oxygen = DLOX = 1141 kg/m3
Densty of liquid methane = DCH4 = 423 kg/m3
Total fuel and LOX mass, external tank = 80,000 kg
Fuel mass, external tank = (1/4.75) x 80,000 = 16,842 kg
16,842 kg CH4 / 423 kg/m3 = 39.82 m3
LOX mass, external tank = (3.75/4.75) x 80,000 = 63,158 kg
63,158 kg O2 / 1141 kg/m3 = 55.35 m3
Total tank volume = 39.82 m3 + 55.35 m3 = 95.17 m3

What is the volume available in the external tank? Tank is a half cylinder, 5.2 m in diameter and 2.6 m high.

Area = 1/2 π r2 = 10.618 m2
Assume we lose some of that due to insulation and tank wall thickness, so let's take Area = 10 m2. Then
Length of tank = Volume of tank / Area = 95.17 m3 / 10 m2 = 9.517 m

With an overall length of ~26 m available for the external tank, this means that the tank diameter could be much less than that of the orbiter, or the tank could be made larger, to allow larger payloads to orbit.

b. Volumes of tanks within the orbiter: What are the dimensions of 15,000 kg of liquid methane and oxygen?

We could go through the same calculations again, but let's cut to the answer:

Volume = 17.85 m3

Separately these are Volume Methane = 7.47 m3
Volume Oxygen = 10.38 m3.

Assuming two spherical tanks, we get

V = 4/3 π r3
r3 = 3V/4π
r = (3V/4π)1/3
rCH4, internal tank = 1.2127 m
rLOX, internal tank = 1.3532 m

These volumes are small enough to fit side by side in the orbiter. The orbiter tank should be made larger, though, to provide oxygen for breathing. Alternatively, a second oxygen tank for breathing could be provided, with provisions for the two tanks to serve as backups for one another, in the event of a life support problem, or a problem similar to Apollo 13, where one tank fails.

2. Size and Placement of the Cargo Compartment, and Other Systems.


Figure 7. Space devoted within FHSS to various systems. (C) F. Harris

The question of how much space would be available for the cargo compartment was settled by awarding it the space not needed by other systems.

Engine and bell, 5 meters.
This is based on the Merlin 1D-vacuum engine, and is assumed to be similar to the small upper stage Raptor engine, about which few details have been released. Several clusters of thrusters are in this area. Structural, fuel, and LOX connections to the external tank are here also.
Tanks and aft avionics, 3 meters.
Fuel, oxygen tanks, other tanks such as nitrogen and helium, and the aft avionics bay, containing batteries, the internal combustion APU, and the motors that power the rudders and flaps are contained in this section, as well as the aft landing gear. It was calculated above that the fuel and oxygen tanks can sit side by side, in 1.35 meters of space, but so many other systems need to fit here that 3 meters was allocated.
Cargo Compartment, 12 meters.
This was the linear space left over after space was allocated for all other bulky systems. Wingtip thrusters for roll control are here, as well as most of the wing. For reasons of aerodynamic stability, it is necessary that the cargo compartment be over the wing and near the notional center of gravity.
Pilots compartment, 3 meters.
This was larger than the original estimate. It includes forward ECLS systems, including the toilet. Perhaps some of these systems should be add-on modules in the cargo compartment, since they are not needed for unmanned missions.
Forward avionics bay, 3 meters.
Several thruster clusters, navigation instruments, computers and other control systems are located here, as well as a battery pack with sufficient power for an emergency reentry. The forward landing gear is here, as well as structural and control connections to the external tank.

---

References

1. "Transcript - Elon Musk: Q&A Session at University of California," Shit Elon Says, 2013-10-09
http://shitelonsays.com/transcript/elon-musk-qa-session-at-university-of-california-2011-03-08
2. "NASA + SpaceX Work Together," by Andrew Chambers and Dan Rasky, Appel, October 17, 2010
http://mars.jpl.nasa.gov/msl/multimedia/raw/?s=741&camera=MAST_
3. "Boeing X-37C Crew Vehicle," Andrea Gini, Space Safety Magazine (reprint from Spacecraft Design), October 8, 2011
http://www.spacesafetymagazine.com/aerospace-engineering/spacecraft-design/boeing-x-37c/
4. Densities of Methane and Oxygen:
http://encyclopedia.airliquide.com/Encyclopedia.asp?GasID=41#GeneralData
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