In light of challenges facing NASA's Space Shuttle program, BoingBoing recently asked the question, "what would Burt Rutan do?" Many wrote in with possible answers, but the golden jackhammer prize goes to reader Brady Hauth, who says:
Pungent greetings, indefatigable Xeni, Midas of vivacity!
The specific energy required to reach the altitude SpaceShipOne (SS1) reached is this, corresponding to this speed. Orbits are only stable above around 180 km. A 200 km orbit requires a speed of 7.78 km/s, so getting into a 200 km high orbit requires a specific energy of this, corresponding to this speed. That's 7.54159384 times faster! The formula for the speed of a rocket tells us that to go that much faster requires 693.390852 times as much rocket.
The exact cost of SS1 isn't public, but was probably between $20 and $50 million – I'll say $30 million here. Scaling this up to a low earth orbit capable rocket, we get $20.8 billion. I'm estimating the payload of SpaceShipOne at 400 kg from the rules. The shuttle launches 24,400 kg – 61 times as much. Scaling costs up to something that size, we get $1.2688 trillion The costs of the shuttle program over its entire life? About $145 billion.
Add in the costs of protecting the craft from re-entry from actual orbit, and things start to look expensive.
Now, one can get higher specific impulses than Rutan did, which reduces that number above the e. It makes for more expensive engines, but it doesn't have to cost nearly as much as it costs NASA. (Maybe they're paying people to make presentations like this one from the military?) One can argue that Rutan could make a design that could make orbit cheaply. However, his building SS1 is not good evidence of that. That is a completely different requirement requiring entirely different engineering. A much harder and much more expensive requirement.
Previously on Boing Boing: WWBRD?