I’m pretty happy with the new TV show “The Flash” – it just keeps on giving to someone like me, who likes to look for the science in fiction. In my last post I made a rough estimate of the Flash’s speed, and in last week’s episode they confirmed that it was in the right ballpark. There’s a throwaway line between Barry Allen, the Flash, and his mentor/father figure, Detective Joe West. The captain says that he’s used to runners doing a mile in 4 minutes, not in 4 seconds. Barry looks a bit sheepish and tells him, “More like three seconds.” This is about one-third of my estimate of about 1 mile every second, but mine was a pretty darn crude one so I don’t feel too bad. A mile every three seconds is 1800 feet per second, or about 540 meters per second. Because he’s going a bit slower than I estimated, all of my calculations in the last entry are off by factors of about 5-10, but the general conclusions still stand. In particular, he’s traveling at Mach 1.5, so as people watch him go by, he should generate a sonic boom.
The episode gave me a new topic to consider: his diet. In the episode, he kept on having dizzy spells, nearly fainting at one point. His science support team ultimately realized that moving that fast took a lot of energy – he needs to eat a lot to support his running habit. There’s some banter on the show about redoing the calculations based on eating cheeseburgers instead of pizza, or some such (I think the line was “It’s a whole new set of equations!”, but I can’t swear to it.) So: how much more should he be eating?
The energy expenditure rate by the average adult male is about 2,000 Cal per day, which is the same as 100 Watts – we’re all relatively bright light bulbs, energetically speaking. Now, people move around with an average speed of some 3 miles per hour, give or take, which is about the same as 1.3 meters per second. The Flash moves 400 times faster than this, so he’s expending energy at a much higher rate.
Accodring to biophysics textbooks, the energy expenditure for running generally scales proportionally to the speed. (This has to be taken with a big grain of salt, because there is, of course, no data for running 1.5 times the speed of sound.) So when he is running, if we believe this model, he is expending at least 400 times more energy than normal. The issue is complicated, because the energy needs could be much higher: running costs for these sorts of models are based on the energy expenditures of moving the body itself, ignoring external factors like air drag. It could be tens of millions of times higher, if one believes a simplistic model based on air resistance.
To give him the benefit of the doubt, let’s say it’s only a thousand times higher. Well, he doesn’t run all of the time: he’s a sprinter rather than a marathon runner. If he’s only moving at such high speeds for 1% of the time, his total metabolic rate will only be some ten times higher than the average human being, meaning he needs to eat some 20,000 Cal per day to do this.
Getting rid of this excess heat won’t be easy. The human body is only about 20% efficient in turning food energy into useful work. The other 80% goes out as heat. He’s got to get rid of some 800 Watts of heat! (This isn’t only when he’s running – remember, his top energy expenditure rates will be a thousand times higher than normal.) Instead of being a bright light bulb, he’s an iron. This is equivalent to doing very heavy exercise on a stationary bike, all of the time. Sweat should continually be pouring off his skin, making his attempts to impress Iris problematic, at best. He’s also going to dehydrate pretty quickly.
This is the conservative estimate for his metabolic rate; another way to look at it is to think about the power consumption rate of a supersonic transport like the late, great Concorde SST, which flew at about the same speed he runs at. The Concorde’s engines had an amazing 200 megawatt power consumption rate. (It flew higher than subsonic passenger aircraft to reduce drag.) It carried about 100 passengers, so maybe we should estimate the energy requirements for the Flash as perhaps 1% of the energy requirements for the SST, meaning 2 megawatts whenever he’s running. If this estimate is the correct one, even if he only runs around for about 1% of the time, he’s still going to run through food at a rate about 200 times that of the average human, and have to dispose of excess heat at about the same rate as a small car’s engine. Hot stuff!