does anyone know was Felix Baumgartner terminal velocity was calculated? how was
ID: 2215124 • Letter: D
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does anyone know was Felix Baumgartner terminal velocity was calculated? how was the information put into the terminal velocity equation to come out to be 373 meters per second, or 833.9 mph (1342 kph)? from this website: http://theairspace.net/science/fearless-felix-falls/Explanation / Answer
I'm pretty sure they compared Baumgartners speed to the normalized average speed of sound at sea level, not with the speed of sound up where he reached his maximum velocity. Assuming they indeed use mach 1 at sea level, there is a simple - be it timely way - to approximate a solution, discretely. First calculate the terminal velocity (let's call it V_term) of an object with a given mass and drag coefficient at a given height in - say - 100 meter intervals. Start at the top (highest point = ca. 39 km, where V_term might be something like mach 5) and keep on calculating until you reach an altitude where V_term equals mach 1. Assume G is constant because we're always relatively close to Earth. Plot the values you've just calculated for all these heights. Now you have a plot, with 100 meter intervals giving you the V_term > (or =) mach 1 at any given altitude. Now calculate the speed of this same object assuming it falls in air which has a constant pressure similar to the pressure found at the drop point (in this case 39 km up) and find out at what altitude it would reach mach 1. Do a similar calculation, but now you assume it falls in air which has a constant pressure equal to the pressure found at the spot where V_term = somewhat above mach 1. If in both cases mach 1 is reached before it has fallen down as far as the altitude where V_term = mach 1 you can be 100% sure it will break the sound barrier in free fall. Now by starting the drop from several other (probably lower) altitudes, start with -say- 35 km and performing the same two calculations you can approximate the minimum altitude from which this object has to fall in order to reach a V_term = mach 1. Guestimate wisely. Once you get close to the critical point, I guess it would be somewhere around 32 km, start using smaller intervals (you might want to revisit your V_term plot as well for added precision).
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