Although the Red Bull Stratos jump is over, the physics goes on. In case you missed it (I don't know how), let me recap:
- Felix Baumgartner rides a balloon up to 128,000 feet altitude - of course he has to wear a space suit.
- He jumps (falls) out.
- During the fall, he goes faster than the speed of sound.
- Lands safely.
Although he made it, there was a tense part of the jump. While still high in the atmosphere, Felix began to spin. Why did he spin? Well, although the density of air is low, there is an interaction between Felix and the air. If he is not completely symmetrical during his fall, the air can exert a torque on him and induce a spin. If air makes him spin, can't air make him stop spinning? Yes. Of course Felix could change his body position to compensate for the spin. However, this is easier said than done. The problem is that with the density of air so low, corrections to his body position don't always have the effects you would assume.
In this case, Felix was able to control the spin. As I understand it, if the spin had gotten much worse a drogue shoot would be deployed to help him become stabilized.
G Forces in a Spin
Here is the real question. How bad was this spin? Can we even get an estimate? Well, I don't know, but I am sure going to try. Using the video above and my favorite video analysis program - Tracker, I can get some data. For this case, I will mark the position of his head and a separate point for his feet. Here is a plot of the horizontal position of his head with respect to his feet.
From this part of the data, it looks like he made 4 complete revolutions in 3.44 seconds. A quick note about the units - there are no distance units. I didn't scale the video because it would be difficult and not even necessary since I just want the number of revolutions. Well, I guess the distance units would be "pixels". Back to the data, from it I would get an angular speed of:
What kind of G-force would this produce? First, let me assume that he spins about his center of mass. Here is a diagram.
I have a value for ω but what about r? Let me just estimate that the center of his head to the center of mass is about 0.75 meters. With that, I can get an estimate for the acceleration of his head due to the spinning motion (not due to gravity - since you don't really feel that force). Remember that if an object (his head) is moving in a circle, it does accelerate even if moving at a constant speed. This is because the direction of motion for the head has to change in order to move in a circle.
In terms of angular velocity, the acceleration would be:
With an angular acceleration of 7.31 rad/s2 and a radius of 0.75 meters this gives an acceleration of 40.1 m/s2 or about 4 g's. From what I can guess, that wouldn't be much fun. Also, this since his head is accelerating towards his center of mass there would be a fake centrifugal force pushing blood towards his head. According to Wikipedia's page on G-force tolerance, a person can only take about -3 g's before a red out. This is where excess blood pressure in the capillaries causes vision problems.
Like I said before, it is fortunate that he controlled his spin before it went on for too long or perhaps even spun faster.
Bonus Data
Just for fun, let's look at the trajectory of the image. So, as Felix falls the camera tracks him. Of course, the camera doesn't do a perfect job - if it did, the x-y coordinate of Felix in the frame wouldn't change. Here is the plot.
What does this graph tell us? I guess it's not fake camera shake that I have seen before.
