The X-prize is different. They did what was required to win the
prize, which was get someone into space and return. Well, maybe the
scramjet did what was required to set the world's speed record too,
but it fails to impress since it wasn't the jet's engine that got it
going that fast. The jet only contributed the last few pounds of
thrust required to defeat air friction to keep it going at that speed
and maybe a few more to accelerate a half Mach or so.

I did a calculation that makes some assumptions that may or may not be
completely accurate. I am neither an aeronautical engineer or a fluid
dynamics expert, but I still made a go at trying to compute how
difficult it was for the scramjet to accelerate from Mach 9.5 to Mach
10.

Newton's first law of motion tells us that a plane released from a
rocket at Mach 10 will, in the absence of air friction, continue at
that speed indefinitely (or until it encounters another object, like
the Earth), and never have to turn on its engines to do so. The
scramjet only has to have enough power to overcome what little air
friction there is at 100,000 feet to maintain its release speed. The
question is how much air friction is there at Mach 10 at 100,000 feet.

Since I don't know how to compute the actual frictional effects at
that speed and altitude, it occured to me that maybe I can at least
compute the ratio between overcoming friction at that speed and
altitude and at say, Mach 1 at 5000 feet. That would provide a way of
making a comparison that makes sense to me.

My first assumption is that for the same air density, the friction is
directly proportional to the speed of the aircraft. If that is true,
the scramjet has to exert 10 times as much thrust to overcome friction
than a jet flying at Mach 1 for the same air density.

But the scramjet is flying at 20 times the altitude of the other jet,
and the air density is much lower up there. My second assumption is
that air resistance is directly proportional to air pressure. If this
is true, I can compute the relative ease of overcoming the friction by
simply computing relative air pressures. Air pressure decreases with
the square of the distance from Earth. So the difference between the
air pressure at 5000 feet and 100,000 feet is 1/20 squared, or 1/400.
And since air pressure and air density are proportional, there is
1/400 times as much air per cubic centimeter at 100,000 feet than
there is at 5,000 feet.

So, if all my assumptions are correct, then it is about 40 (400/10)
times as easy to maintain Mach 10 at 100,000 feet as it is to maintain
Mach 1 at 5000 feet. My final assumption is that this also means that
it takes about 1/40 the thrust to accelate from Mach 9.5 to Mach 10 at
100,000 feet as it does to accelerate from Mach Mach 1.0 to Mach 1.5
at 5000 feet. And if that is true, then it is also true that it takes
exactly the same amount of thrust to go from Mach 9.5 to Mach 10 at
100,000 feet as it takes to go from Mach 1 to Mach 1 plus 1/40 of a
half Mach. 1/40 of a half Mach is about 10 miles an hour increase in
speed.

Therefore, according to my calculations, if the scramjet accelerated
from Mach 9.5 to Mach 10, it took about as much thrust as for a jet
flying at Mach 1 at 5000 feet to increase its speed by 10 miles per
hour.

Like I said, I am neither an aeronautical engineer nor a fluid
dynamics expert, so consider the source. If there is an aeronautical
engineer or a fluid dynamics expert out there who can point out the
errors in these calculations, please do. Just leave out the flames,
OK? At least I made an attempt at reasoning through the problem and
realize my limitations.


-- Don French





Regardless, it seems to me that the rocket's speed has to be
subtracted from the jet's speed to arrive at the actual jet speed when
you talk about the world's record for speed of a jet plane.

Hmm. Would you say the same for Yeager and the X-1, it having been dropped
from the belly of another aircraft, or is your particular question related
just to the rocket?

Would this same sort of criteria apply to the X-prize given that Space Ship
One was given a lift to an intermediate altitide?

Interesting.
-c