In the TV show, The Flash, Barry Allen (Grant Gustin) utilizes the "speed force" to attain superhuman speeds. Unfortunately, Barry does not have a full grasp of his powers when he first gets them and is susceptible to some of the laws of physics. In Season 1's episode Going Rogue, Barry runs so fast his shoes catch fire. Many fans will tell you how hot Barry (or Grant) is, but what about the real science behind how much Flash's feet could create?
How much heat can Barry make?
This may seem like a silly problem for a sci-fi superhero show but it can be analyzed using physics. (If you can't turn your serious science degree into solving pointless problems in popular culture, you should forfeit your degree.) The IMDB website indicates that Grant is 6' 2" tall, so we'll assume the same for Barry. This means Barry should have an average Men's US size 11 sole. The surface area of the sole is approximately 0.02 square meters.
As Barry runs, his shoes rub against the concrete and produce heat. We can figure out the "heat flux", or how much heat goes through the soles. Barry's feet must slip or no heat will be generated. This is very different from when you run or walk; your feet do not move, but stay planted instead. In Barry's case, we will be looking at the kinetic friction between his rubber soles and concrete, which has a value of 0.8.
The first equation is the heat flux equation. The term P is the pressure (Barry's weight over his soles) and V is his speed. The second equation tells us how the rubber's temperature rises for a given quantity of heat. If we assume that Barry was running for five seconds, we can calculate the amount of heat generated by multiplying the first equation by 5 seconds. This will be equal to the second equation. This will let us solve V, which is the speed Barry must run for his shoes to start burning. Doing our little algebra magic, here's what we get!
The term ÃÂT is the change in temperature. Rubber begins to burn at about 260Ã¢ÂÂ or 500Ã¢ÂÂ. At this point, we just plug in what we know and discover that Barry has to run 138 meters per second for his shoes to catch fire. This is about 497 kilometers per hour (or 309 miles per hour). You may be thinking that is pretty fast, but don't forget Barry is the fastest man alive (or haven't you been paying attention?).
Catch Fire or Wear out?
As you walk, your shoes rub against the concrete and "wear out" due to friction. We can calculate how much of Barry's soles will wear out as he runs using the "Archard equation."
The constant H is the hardness of the rubber. Substituting the values we know, we get
We see from equation (3) that Barry will generate enough heat to burn rubber before he reaches the speed in equation (4) to wear away the rubber in his soles. It turns out that Barry really is a hottie, but not for the reasons fans may think! Looks like Cisco (Carlos Valdes) will have to use a special heat resistant material in that Flash suit.
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