Sometimes I wonder why I'm in the humanities. Like for example, while we were watching the last minutes of regular play during the world cup final my friend Colin absent-mindedly wondered if there was any way you could humanly make it to Europe by the time overtime concluded. About 30 minutes.
Those of you who have known me for awhile probably see where this is going.
Folks suggested the Concorde, or various fighter jets, but it quickly became apparent that those were way too slow. Even the fastest Air-breathing aircraft (the SR-71 and the XB-70, both retired, both with a top speed of about Mach 3) would take 2 hours to cover the 4000 miles between here and Europe. I suggested the Space Shuttle, since I knew orbital velocity took you around the world in 90 minutes. There were questions about acceleration and deceleration times. The issue was dropped.
Well, dropped by everyone else. Something in my tortured nerdy brain had to know... could you get to Europe in half an hour with exisiting technology? Could it be done?
So I continued to think about it. After some reflection I remembered reading somewhere that Intercontinental Ballistic Missles could do that sort of distance in about half an hour... and sure enough this sez a Minuteman could do 8000 miles (more than we need) in about 2060 seconds (30 minutes, give or take). Of course it also tells us the re-entry vehicle hits the ground at 7,000 miles an hour. Owie. (What the fact that the fastest way of getting between two points on the earth's surface ever built is a delivery system for thermonuclear weapons says about the human race is left as an exercise for the reader.)
But nonetheless, clearly this points the way to go, the fastest way between two points on the earth's surface is to launch yourself 50km up, past the atmosphere, and then boost yourself onto a parabolic, sub-orbital path that will land you where you need to go. The only question is, could you survive re-entry?
So I cracked open the old physics textbooks, looked up the section on parabolic motion, and tried my best to figure it out. According to my (very rough) calculations, launching yourself at a 54.6 degree angle at a velocity 5407.44 meters per second ought to put you on a parabolic path that will cover about 3500 miles in 30 minutes. (I allowed 500 miles for boost and re-entry) Since you will re-enter the atmosphere 50 km at this same 54.6 degree angle, trig sez you have about 200km of Atmosphere to bleed off you re-entry velocity in. That works out to an average deceleration load of about 7.5 gs for a little over a minute. Which this says is human survivable. Of course, that's not really how it would happen, but since that's the average load, I'm going to assume you could work out some way to manage the load so that it doesn't squish you, since people can survive stronger loads for short periods.
All this computed, I downloaded Orbiter a free (as in beer) space simulator, and ran my computed trajectory in an unobtanium fueled imaginary ship they have for beginners. Sure enough, my parabolic path took me from florida to western europe in about half an hour. But when I re-entered the atmosphere, my glider shaped ship skipped off! I went flying on another parabola that took me well out over russia... and quit the simulator.
That only supports my intuition that you probably wouldn't want a winged vessel to fly this flight path with. The shuttle, after all, makes huge S-shaped turns in the upper atmosphere to bleed off speed so it can use its wings to land. That takes too much time. No, if anything could fly the Ohio-France express mission, it's a Soyuz capsule.
So, if you had a Soyuz fueled and ready, you might be able to do it IF (and this is a big if) a Soyuz booster could actually generate enough thrust to put the Capsule onto the parabolic trajectory I described. Since the booster is designed to boost the capsule into orbit, this seems likely to me, but my rocket fantasy kick is wearing off and I need to get back to reading about the cultural implications of the information society (as is my actual vocation) so I can't take the time to look up the info on the booster and find out for sure.
But hey, if any of you want to... break a leg.
This was my geek of the week moment.