Somebody on another board proposed a question after the jump yesterday - if they had jumped at the same moment, would Baumgartner have passed Kittinger in freefall? If so, at what altitude?
I apologize in advance for the imperial units.
The official numbers (so far) for Baumgartner are a 128,100 foot altitude and a maximum freefall velocity of 834 mph (!). The Stratos Wikipedia article says it took 42 seconds to reach terminal velocity. So, 834 mph is 1223 fps. To arrive at 1223 fps in 42 seconds, one must have an average acceleration of 29.11 fps^2. That seems reasonable (not quite right, but close enough for our purposes), and it puts him at max V around 102,500’.
Coincidentally, Kittinger jumped from almost exactly that altitude - 102,800 feet. However, he deployed a 6’ drogue chute which stabilized his descent to prevent the spin that Baumgartner experienced yesterday, but also limited his maximum velocity to 614 mph, or 900 fps. Assuming the same average acceleration (just lower terminal velocity), it would have taken Kittinger 31 seconds and 14,000 feet to reach his max V, so that would be at 88,800’. Right about that same time, Baumgartner would have been accelerating through 614 mph and 114,000’. Eleven seconds later, ‘ol Joe is passing 78,100’ as Felix finally hits 834 mph at 102,500. So 42 seconds into the jump Baumgartner is 24,400 feet above Kittinger, and he’s closing the gap at 320 fps. Assuming no change in velocity, the two pass at 9500’.
Now obviously, neither one of them was anywhere near their max V at 9500’. This is where it goes way over my head. Baumgartner’s terminal velocity is 36% faster thanks to Kittinger’s 6’ drogue, and that ratio shouldn’t necessarily change as they descend into denser air. My understanding is that air density follows an exponential curve as you descend through the atmosphere, but I don’t have the slightest idea of how to apply that information to this problem. If it helps, Kittinger’s freefall time from 102,800 to 17,500 was 4:36, while Baumgartner’s freefall time from 128,100 to 4900 was 4:19.
My guess is that our Austrian friend would have passed Kittinger somewhere in the high 20’s, but that’s really nothing more than a complete WAG.
