Well the faster you fly the more drag there is so mach 10 would have a very large drag at the altitude normal planes fly (about 10km). It just gets more and more difficult to fly fast low. Speed wouldn't make a man pass out, its the force acting on him to cause g-loc!
Dan
Well: There's no highest speed that a man can survive following an inertial path, but if you are traveling at any speed other than orbital velocity and are maintaining altitude, your path is not inertial, and thus you will feel a g loading. For speeds lower than orbital velocity, the highest g loading you will experience is 1 g at zero speed. For speeds higher than orbital velocity, the g loading you experience will increase as your speed increases. You can calculate this by taking the equation for centripital force:
F=mv^2/r
Dividing by mass (because F=ma) to get acceleration:
F/m = a = v^2/r
Subtracting the Earth's gravity from the right side (because at v = orbital velocity a = 0. Here I am using the acceleration relative to an inertial, or freefall path, ie, an orbit.):
a = (v^2/r) - 9.8 m/s ^2
or with acceleration measured in g's
a = (v^2/r) - 1g
Now we have our equation, and can start plugging in variables.
A healthy, trained fighter pilot in a G-suit can withstand about 9 g's for short periods without blacking out (although much depends various factors, such as position). So we'll plug that in for a:
9g = 88 m/s^2 = (v^2/r) - 9.8 m/s^2
Our aircraft will be maintaining a constant altitude within the atmosphere, and thus will be tracing out a circle with a radius approximately equal to that of the Earth, so we plug the radius of the Earth in for r:
88m/s^2 = (v^2/6400 km)-9.8 m/s^2
Solve for v:
add 9.81 m/s^2 to both sides:
88m/s^2 + 9.8 m/s^2 = 98 m/s^2 = (v^2/6400 km)
multiply both sides by 6400km:
98 m/s^2 * 6400km = v^2
Take the square root of both sides:
sqrt(98 m/s^2 * 6400 km) = v
v = 25 km/s
So if you want to remain on Earth, the fastest you can go without blacking out is 25 km/s. But if leaving the planet is fine with you, then you won't black out at any speed.
oh yeah, we don't feel anything from that, so it's not very exciting..
