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Answering "what" is the easy part. "Why" takes actual thought.
I hope today's anonymous editor will tell why a google search for "two stage to orbit" produces 950 results, while "three stage to orbit" generates only 18. What accounts for the 50 fold difference? Why is TSTO so special? Mackerm 08:03, 11 Mar 2004 (UTC)
Hmmm, well I finally saw this talk function, only a month later. :)
I think there are three main reasons why TSTO is more commonly thought about than thre stage to orbit.
Firstly, the logistical problems which are annoying with two stages are horrible with three. If you have a 2:1 ratio of first stage to second stage, then the first stage comes down less than 500KM downrange of the launch site; that's managable. It also never reaches very high velocities. With three stages, you're mostly done fighting gravity and atmosphere when the second stage ignites, so it will come down far further away, and you have to put real thought into handling the heat of re-entry. It especially makes alternating polar and equatorial orbits extremely hard, given the same launch site.
Secondly, TSTO is 'good enough.' Assume we can build an SSTO with current technology - which isn't settled, but I'm prepared to believe it. It would need to be around 10% structural mass, and would have structural tolerance margins of between 10% and 25%. Given the same technology, it's fairly trivial to handwave that you can build a TSTO which is 20% sstructural mass and has 100% margins. 100% margins are the norm in commercial aviation; you just stopped talking about a cutting edge research project and started talking about a relatively routine aviation project (well, not quite because the difference between nominal and maximum loading is different between spacecraft and aircraft, but it's roughly correct.)
Thirdly, three stage to orbit would also have to be called TSTO, and since aerospace engineers are only capable of thinking in anacronyms... :)
I'm not too sure how to put any of this onto a page, though. Jamougha