Friday, April 01, 2011

Stephanie Powell's super footwear

kw: super powers, observations

I am too much of a skeptic to get much enjoyment out of shows about super powers. I know too much physics. Before getting over-educated I enjoyed Superman comics and the TV episodes with George Reeves, and I even had a good time watching the more recent Fantastic Four film, even though it is wildly implausible. Anyway, I happened to watch part of an episode of No Ordinary Family, mostly a fight between Mr. Powell and a chemically-induced werewolf. Just at the end, Mrs. Powell (Stephanie) ran off into the future. I guess this is like Superman flying twice the speed of light to go into the past. I don't recall how he was supposed to return.

I remembered the show's trailer, where she zips around the track and her friend says she was going a mile every six seconds. That comes to 600 miles per hour, and it got me thinking. An ordinary racing track has two 100 meter straight segments and two curved segments at the ends, each a 100 meter arc. The diameter of the arcs is about 64 meters, or a radius of just under 32 m. How much centripetal force is required to keep Stephanie on the curve when she is going 600 mph? It works out like this:
  • F = Mv2/r, where
  • M = 50 kg (110 pounds, assumed)
  • v = 600 mph = 880 feet/sec = 268 m/s
  • r = 31.83 m
  • v2 = 71,900, so
  • F = 113,000 Nt / 9.8 = 11,500 kg force
Thus, if Stephanie weighs 50 kg, it requires 11.5 metric tons of force (almost 13 short tons) to hold her along the arcs at the ends of the track. Now, she is doing this by running, so she must have special shoes with super-friction or she'd simply slide right off even at speeds much less than 600 mph. Not only that, when a person runs, a foot is in contact with the ground half the time or less, so the actual force of each of Stephanie's footsteps may be of the order of 25-30 tons, perhaps more. Not only does she have super-strong bones, but her shoes have to be much stronger than steel. Plus, after a single circuit of the track, it would be torn up by meter-wide divots. She'd have to be careful where she stepped on the next circuit.

But this is possibly rather slow, held back by those nasty laws of physics of a body following a circular arc. No wonder she said, "I thought I was faster than that." It is noted elsewhere that when running in a straight line, she covers ten miles in five seconds. That is 3,000 mph, or mach 4, substantially faster than the old Supersonic Transport. She'd carry along a shock wave that broke out all the windows within a few miles on either side! It must be that her super power includes a super-slippery way of getting the air to separate and close in behind without creating a shock wave.

Magic reality doesn't have to make sense, I suppose. Neither do I, considering what day it is…

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