Tuesday, September 22, 2009

Three Stages to Orbit?

Mini Orbiter Separation
Mini Orbiter Release

Back in the rocketpunk era, we all knew that reaching orbit called for a three stage rocket. Willy Ley, with an assist from Chesley Bonestall, showed us what it would look like. (Though thanks to Walt Disney I mostly remember a later version without the huge wings. It looked like a wine bottle with a little delta winged shuttle in place of the cork.)

As it turned out, we went into orbit on rockets that weren't even two stage, but 'one and a half' stages; the Vostok with strap on boosters, and the Atlas, even closer to one stage, dropping only booster engines, no tankage. This allowed all main engines to be started on the pad, a big consideration in the 1950s. Later orbital boosters have typically been two stage, sometimes with additional strap on solids.

The popular dream of orbital access is (reusable) single stage to orbit, SSTO, though no single-stage vehicle has gone into orbit. The required mass ratio is just too extreme for our fabrication technology - and building big rocket stages is a mature tech, over 50 year old. Maybe new material science, such as Super Nano Carbon Stuff, will change that equation, but not for sure and not yet.

Perhaps we should look back in the other direction, at some form of three stage orbit lift. With three stages to orbit, launch mass relative to payload typically grows, making it less efficient in hardware and fuel. The compensation is that stage mass ratios are less extreme, permitting more conservative, robust construction.

What got me thinking about this was commenter Jean's mention, last post, of Virgin Galactic's plans for an orbital SpaceShipThree. How would you go to orbit if you want to do it cheap, both development and subsequent missions? (I'm not trying to guess how Burt Rutan would do it, though I obviously had SpaceShipOne in mind.)

First I stole the idea of a subsonic air launch. The 'zeroth stage,' the release plane, can be any big transport type. According to this paper and a Bad Astronomy forum thread, air launch does not really save much delta v, but it means the vehicle doesn't need to take off itself either vertically or horizontally, adds operational flexibility, and permits a lighter vehicle. As it is I ended up with a release mass of 100 tons. (The Shuttle's dry mass is about 70 tons, and this was probably about what the Shuttle Enterprise weighed for its release-glide tests.)

The vehicle itself is a booster-orbiter combination rather than pure two stage. After release at high subsonic speed at about 10 km altitude (32,800 ft), the vehicle enters a steep supersonic climb, passing Mach 5 at about 30 km (~100,000 ft). It has left effective atmosphere behind at booster separation, at about 3 km/s and 50 km altitude. The orbiter continues to orbit; the booster glides back about 1500 km to its landing point.

The booster has a twin-body configuration, each body structure mostly fuel tankage. The orbiter has a similar body structure with shorter tankage and a payload bay. Propellants are good old kerosine and LOX, good for an Isp of 300-325 seconds. Combined thrust of all three engines is equal to launch mass, about 1 megaNewton.

The mass breakdown I came up with is:

100 tons release mass

66 tons boost stage propellant (mass ratio 3.0)
7 tons booster dry mass

21 tons orbiter propellant (mass ratio 4.5)
6 tons on orbit mass

0.5 tons OMS, etc.
4.5 tons orbiter dry mass (heat shield, 0.5 tons)

1 ton payload

Optimistically this is good for a total 8.3 km/s of delta v, before losses to drag and climbing against gravity; add the speed of the release plane for about 8.55 km/s. Low orbit speed is 7.8 km/s, so ascent losses have to be kept to about 0.75 km/s.

The vehicle dry mass is also optimistic. As a couple of comparison points, the Thor first stage of the Delta space launcher carries 95 tons of propellants and has thrust of 890 kN. Stage dry mass (plus some unused propellant) is 5.7 tons, so our twin booster can be about 80 percent heavier and sturdier than a Thor, relative to tank capacity. Like the Thor, a Cessna Citation III biz jet has a fuselage similar in diameter to our basic fuselage-tank and wing structure, is about 50 percent longer, and has a dry mass of 5.3 tons. So our vehicle can be about as solidly built as a corporate jet.

All of which is optimistic, but perhaps not grossly so - and most paper orbiters I've tried to come up with were grossly optimistic.

By my general rule of thumb, production versions 'should' cost $11.5 million each, but transatmospheric craft require a lot of specialized materials and equipment, so let us say an ideal production cost of $25 million. The handbuilt prototype will cost a good $250 million, the whole development program $1-2 billion. A small production run of 10 orbiters and boosters might be $750 million, plus conversion of a couple of jumbo jets; call it another $1 billion, so the whole front end is perhaps $3 billion.

Recouping this at 8 percent over a 25 year service life requires an annual charge of $280 million. If we fly 280 flights per year the development cost per flight is thus $1 million. Reportedly it costs about $1 million to fly the Shuttle back from Edwards AFB to Cape Canaveral. Let's - quite optimistically - say $2 million operating cost per mission, so total cost is $3 million per mission and per ton of payload, a third of typical present day cost. If the manned version can carry a pilot and two passengers, a passenger trip to orbit costs $1.5 million a pop.

But is there enough demand for the service? Are there enough multimillionaires willing to pay $1.5 million for a trip to orbit? Enough who will do it a second time?

A modified version of our vehicle, however, might find a commercial terrestrial use. If you replace a ton of fuel and the OMS system with another ton and a half of payload, the orbiter does not reach orbit, but has a ballistic trajectory of some 10,000 km, plus maybe 2000 km of glide. I don't know whether you'd get many passengers at $750,000 per ticket, but you can deliver 2-3 hour global express for $1200/kg, about $35 per ounce - and there is probably a market for it.

If there was ever a case of selling the sizzle, not the steak, this is it. Space access disguised as faster-than-overnight express.

Related links: I talked about orbit cost at my old website.


Carla said...

I think I vaguely remember a sort of 'spaceplane' that followed a ballistic trajectory being mentioned as a super-high-speed aircraft concept back in the 80s. Have no idea if anyone even got it to prototype, though.

Does an air-breathing engine like the one designed for Hotol help your calculations? If you can get some of the oxygen for free on the way up you might not have to carry as much liquid oxygen. Or are you too high up when the booster stage comes on for that to be any use?

Anonymous said...

As I understand it - And this is just based off press reports, so someone with a better understanding of the tech may want to jump in here - the idea of scooping up air and seperating out the oxygen was dropped for two reasons. One was that the extra mass from the scoops and oxygen tanks at launch just pushed the launch weight up too high: There wasn't enough return from the system to make up for the extra lift needed. The other problem was that a ramscoop/filtration system was just one more complex part feeding into an already volatile rocket set-up: And it was a complex part operating during lift-off, already the riskiest part of any rocket operation.

Those are the problems mentioned in the popular science/technology press. Off the top of my head I can think of one other potential problem with the system: It was very closely linked to the US Air Force's dreams of a hypersonic space plane, and the USAF lost the political battle over what direction launch technologies would take. No one else wanted to pick up that particular technology, which may mean it wouldn't work or may mean they all had their own projects to sell.


Anonymous said...

Rick, make the first stage a linear accelerator, the middle stage an onboard ramjet, and the last stage an ordinary rocket...I read about this system recently, but I can't remember where. Three stages to orbit, but no one said they had to all be rockets or multiple vehicle stacks.


Jean-Remy said...

As much as I hate to do it, I'm going to be stuck playing devil's advocate here.

Ferrell: I was thinking along the same lines, but the problem with a linear accelerator catapult to launch the craft makes it useless to transport passengers, unfortunately. If the catapult is to short, it will need to impart a comparatively higher acceleration to the vehicle. Those very high accelerations are fine for cargo that is not known to withstand high g forces for too long (ie: squishy squishy humans.) To compensate for a lower acceleration, you would need a far far longer catapult, so long in fact as to become completely impractical, if it is even possible to engineer. So while catapult systems are very seductive, their very nature basically makes them suitable only for mechanical payloads.

Carla: as Ian pointed out, unfortunately, multi-phase engines, that gained some popularity in the 80's, were deemed too complex to be practical. In Rick's example, the release speed is to slow for a statoreactor, ie an air breathing engine with no turbine necessary to compress the air. To achieve the speed necessary to make the turbine unnecessary would basically mean reaching Mach 1. At this point the natural compression of moving an object at this speed is sufficient to maintain combustion. The multi-phase engines considered had to combine a normal turbofan, with the turbines blades necessary for compression, then a system to fold away the bladesto let the craft's speed achieve compression, and then a system to close the entire thing and reroute the oxygen feed supply through a LOX tank, and now the problem is you have a fluidic oxygen supply trying to function with an engine meant for use with compressed gaseous air. Whew. That would involve so many engineering breakthroughs for a LOX mass gain that would just get lost due to this very complex and most certainly massive engine.

Rick: I am thinking that rather than conversion of existing jets, this system will need a brand new delivery vehicle, ala Burt Rutan. If you look at the B-52 that delivered the X-15 and Pegasus, you can quickly see why. Those vehicles were strapped to the wing, and there's really not much room on the wings between the fuselage and engines. The orbital vehicle cannot be attached anywhere but the root of the wing because even then the aircraft was rather imbalanced. Modifying existing vehicles to carry the orbiter in its belly would mean cutting into the structure (you do want to use that landing gear.) Since aircraft are designed so that the structure as it is is integral to, well, structural integrity, I doubt that any amount of reinforcement would be sufficient, especially with 100 ton of vehicle that not only does not contribute to the structure, but actually stresses it more. A LOT more. Not only will its mass put stress on the anchor points and the structure it is linked to, but the aerodynamic stresses of flying with it will be huge. Carrying the orbiter on the roof so as to not cut into the body of the airplane is also out: the orbiter has to be dropped smoothly away so that it can light its engine at a safe distance from its carrier plane. See Moonraker for a hilariously bad but rather illustrative example as to why you lighting up a rocket engine while on top of you carrier vehicle may be considered a less-than-salutary idea. My point being: if such modifications/conversions are even possible, the design will be so significantly altered that starting from scratch would be cheaper and more efficient. Burt Rutan' solution was a twin boom aircraft, with the central wing pylon the one designed to carry his ship. It feels like a good, stable design, and since it was designed solely for the purpose of launching SpaceShipTwo, it is efficient at that task from start. I don't think it will actually add that much to the cost calculations to design the launching aircraft from scratch, so to speak, but I think it is going to be an integral part of designing the orbiter.

Rick said...

Carla - The release plane has airbreathing engines. :-)

The broader aspect of what Ian said is that for various reasons airbreathing engines operating above Mach 3 have not been developed much. Rocket engines are inefficient fuel hogs, but well developed. For a relatively cheap (!) program I wouldn't want to mixed up with developing new types of engines.

Ian - I actually wonder if producing LOX aboard a subsonic release plane might work out better, to reduce initial takeoff weight and alleviate the safety issue of taking off with 60 tons of LOX on board.

Ferrell - For a later development, yes. Above the size you can haul up aboard a transport plane, you'll need a sled to deliver the high airspeed either a ramjet or rocket vehicle requires.

But a problem for Really Fast Ramjets is the heat bath you are subjected to by prolonged atmospheric flight at those speeds.

Jean-Remy said...

Hrm can you tow it? I just thought about WWII gliders, but on second thought, trying to tow anything in the jet wash seems like a non starter.

Citizen Joe said...

From what I understand, the heat from ultrasonic transit comes from the compression of the air rather than friction. As the air ahead gets compressed, it heats up, that gets transferred into the ship. If there was some way to either divert the compressed (hot) air or to travel through without compressing it, then the heat problem would disappear.

Jean-Remy said...

CJ: Without going too far into the vastly complex realm of fluid dynamics: you can't travel through any medium without displacing it. Water being incompressible limits the ship's speed to the rate at which water will flow around the ship. Think of it as emptying a bucket of water in front and pouring it behind you, so your ship can go in the empty bucket. Air's compressibility, however, forces the air in front into a smaller area of the bucket so you can move into it before it has time to flow into the next bucket. So, compressibility is the reason it is possible to travel at high speed in the first place, and compressing air is the absolute consequence of moving through it.

Diverting the heat means transferring it to the vehicle (since to manipulate it you have to be in control of it) and then spreading it along the hull, or radiating it out. This is exactly what the materials on the space shuttle, the X-15 and the SR-71 do. Short of magical forcefields, the best we can do is improve on Inconel-X and carbon-carbon.

Anonymous said...

Jean: How about dirigible carrier-craft? Before the Second World War the US and a handful of other countries developed dirigible aircraft carriers. I don't believe they were ever used, but they did work. The fighter craft launched from hooks carried in the (gondola?)'s launch-bay, and 'landed' by rehooking themselves. As aircraft carriers dirigibles failed largely because they operated in the same medium as the fighters. Would a dirigible-carrier serve as a viable first stage for an orbiter?


Jean-Remy said...

Ian: Actually this might be a pretty good idea. Since the speed of the aircraft matters little to the overall delta-v (after all what's 800 km/h (.2 km/s) compared to the 7.8 to 8.5 km/s Rick mentioned? As he said, it's not really about the delta-v, it's about the altitude. The problem might be the altitude, ironically. As the air density becomes lower, it takes a commensurate amount of helium to remain buoyant. I'd suggest hydrogen instead. After all we're going to have to find ways to use it and store it and handle it, so a hydrogen dirigible would be better. I don't know what the volume of hydrogen would be necessary to carry 100 tons at an equivalent altitude for a jet (say 10,000 m?) plus mass of the blimp itself, but it should be easy to find out. Now, where did my calculator go...

Anonymous said...

From Wikipedia: "The US Navy developed the idea of using airships as airborne aircraft carriers.[clarification needed] There were two airships, the world's largest at the time, to test the principle—the USS Akron and Macon. Each carried four F9C Sparrowhawk fighters in its hangar, and could carry a fifth on the trapeze. The idea had mixed results. By the time the Navy started to develop a sound doctrine for using the ZRS-type airships, the last of the two built, USS Macon, was lost. The seaplane had become more mature, and was considered a better investment."

Wikipedia lists an F9C Sparrowhawk's loaded weight as 1.259 tons, and the ZRS airships carried 4-5 of them (There's some dispute over the exact number. So a 239-meter 100-ton airship carried a payload of 5+ tons. Presumably modern lighter materials will let airships carry more mass, and scaling the dimensions up a bit would greatly increase airship volume and lift... But that's still a big ship for not a lot of launch vehicle.

Can we build a viable orbital for ~10 tons?


Jean-Remy said...

"Can we build a viable orbital for ~10 tons?"

The Pegasus launch system masses at roughly 20 tonnes (19 tonnes for the basic one, almost 25 tonnes for the XL) with a payload of 400 to 500 kg. They are launched from a B-52 bomber. So we already have a cheap launch vehicle with those capabilities.

Rick said...

A purpose built jet release plane would be much better, but it means a (literally) bigger program, designing and building a new aircraft in the large transport class.

A middle ground might be yoking two jumbo jets together in a twin body configuration. It is still a major design project, but you only have to hand build the yoke wing section, not the entire prototype airframe(s).

If there's global demand for uber fast aerospace express, you'll need a fleet of carrier-release planes, and the case for purpose building gets stronger.

Dirigible launched orbiters max the coolness/charm scale! But you don't really need a dirigible; a skyhook type balloon might do better.

Hydrogen and helium have nearly the same lifting power; they displace about 1.2 kg of air per m3, and are both much lighter. In round numbers you'll get about a kg of lift per m3 volume - at sea level; less with altitude.

One advantage of a fixed wing launch is that the vehicle can fly, and may be able to climb aerodynamically more efficiently than just blasting itself upward.

Air launch of some sort is helpful for relatively small orbiters. For really big ones, like 100 ton payload, you probably want a big vertical launch TSTO.

Tim said...

Oh Lordie, sorry for the link dump.
Pegasus s actually launched from a Lockheed TriStar in sevice, but testing and early flights were done with a B-52


Jonathon Goff gives a good overview of launch concepts here


part 1 is particularly useful.

It is actually possible to launch a rocket from an existing military aircraft


You lose pretty much all the Delta-V, but the advatage is operational flexibility, which is discussed here


Interestingly, the "extended landing gear" is supposed to be fixed.


(read the first link)

someone has tried towed launch, using (I think) an F-106 and a C-141 for a proof of concept, but for the moment nothing has come of it.

Citizen Joe said...

RE: compressed air heating.

At the leading edge, air gets compressed and thus heated, but at the trailing edge, that same air is allowed to expand and thus cool off again. If the compression could be done incrementally, the heating could be managed and passed to the rear expansion/cooling processors.

Or perhaps the cool expanding air at the rear could be forced forward to create an ablative air sheath.

Or you scoop up that compressed air and use the heat (scramjet).

It just seems like there is a huge potential to use that pressure/temperature differential.

Jean-Remy said...

Issues, in reverse order

You ramjet still has edges. You can't just suck in the air before it reaches the edge of the scramjet. You still need wings on the scramjet, and the wings are a leading (pun intended) cause of the compression since they work *on* pressure differentials. That's the job of the wing. One of the X-15 flights was meant as a test bed for a scramjet engine. The aerodynamic heating at Mach 6.7 made the scramjet explode, causing critical damage to the X-15 and only the talents of the pilot even brought the craft home.

You can't push cold air out: you'd at BEST break the very compression that makes the plane fly in the first place. The wings depend on a smooth pressure differential above and below the wing to create lift. That's if you could force cold air to flow faster than the hot air flowing backward which means building an engine working *against* your direction of motion. That's even if you could vacuum efficiently from an area of low pressure (and chaotic airflow) to the front which is a high pressure system.

Incremental compression. No. The leading edge compression is a mathematically-defined function of basic physics. You can't modify it anymore than you can "find a crack in the Event Horizon" of a Black Hole.

Aerothermodynamics is a pretty advanced field that deals with that. Check out "Basics of Aerothermodynamics" by E.H Hirschel. The book is online at Google Books:


The book is specifically about the thermodynamic issues of orbital vehicles. Of note, he mentions that Ascent and Re-entry Vehicles (ARV) ie: SSTO vehicles, present a LOT of design issues because by the very nature of the various tasks it must perform, the design requirements are in opposition (Table 1.1) He also states that the heat issue is not with compression but viscosity (friction) during cruise/acceleration phase. It is compression during re-entry.

Jean-Remy said...

I'm not sure how to link things on here, just copy-paste the URL, the select the first book on the list. Enjoy

Rick said...

Tim - Thanks for the links!

The Selenian Boondocks blog is especially interesting. They seem to be tech experts active in the industry - the guy who developed Pegasus has an interesting comment on how the basic performance limits for Isp and structures were reached in the 1950s-60s, short of radical new materials.

But the guys there seem to be very aggressive about mass, talking about air launched vehicles down to 20 tons or so load mass carrying 450 kg to orbit, versus 100 tons and 1000 kg for my sketch design.

Citizen Joe & Jean - ACcelerating in atmosphere makes for much more heat load than decelerating, because you can't just use a blunt form that keeps the shock wave away from the structure.

Jean-Remy said...

Hence the design issue I mentioned. Reentry calls for a blunt design whereas acceleration demands a far sleeker form. Compare the profiles of the X-15 and the Space Shuttle.

The blunt design makes the airflow optimal for breaking, by compressing the air. The sleeker fuselage is of course better to avoid as much compression as possible and better air flow, however the air flow itself creates friction as well, and there's still some compression to deal with.

My original point (or rather counterpoint) is that there's just no magical way to prevent the craft from heating at the nose and leading edges, it's part and parcel of the physical laws that go with hypersonic speeds. You simply can't alter the very air flow that makes flying possible in the first place, you can only deal with the heat through advanced materials science.

Citizen Joe said...

So, ideally, you would accelerate straight up to minimize the time in atmosphere. Then, once atmospheric heating is gone, you switch to orbital vector and accelerate to appropriate speeds outside the atmosphere.

At what altitude does air breathing stop working? What altitude does atmospheric drag cease to be a problem. I suspect that there is a multi kilometer range band gap which is what makes things so expensive.

Rick said...

Citizen Joe - The problem with accelerating vertically until you are out of the atmosphere is that vertical speed does nothing for your orbital delta v. Any chosen trajectory is a balance and compromise between different requirements.

The altitude at which drag and airbreathing propulsion fade depend on speed, but so does heat, and so long as you stay in effective atmosphere at higher than Mach 5 or so the heat bath will continue.

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