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.