Physics Today, the Flash and project Rosetta

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A random conflation of three separate items for this post:

Physics Today’s Facebook page just added a link to a Q&A session they did with me about my book.  The reviewed it in the last issue of the journal, and it got a very nice review from Edward Belbruno, a physicist I respect quite a lot.

The Flash can run on water!  At least, so says the episode last night.  According to his lab rat friends, he needs to run at 650 mph to do this – is this accurate?  I think the answer’s lower: more like 60-100 mph.  Still an impossibility, but not so impossible an impossible.  The issue is momentum transfer: every step he takes across the water transfers some fraction of his momentum to the water.  The rate of momentum transfer is the force he applies; Newton’s third law says that an equal force is pushing up on him.  A quick estimate says that the speed is about the square root of (g (the acceleration of gravity) times the stride length (maybe 2 meters?) times a fudge factor (which should be somewhere between 10 and 100, in lieu of difficult detailed models)).  Putting all this together, the needed speed is about 50 meters per second, or about 100 mph, maybe even lower.  Running up the side of a building is a different matter: if he tries to run up fast, he’ll just bounce off because of his high speed of approach.  Better he should run up a long ramp and launch himself into the air, except that landing after doing that is a problem…

Of course, the big news today is Philae, the lander for project Rosetta, landing on comet 67P/Churyumov-Gerasimenko.  It may have bounced once after harpoons failed to anchor it to the surface, which worried the scientists, for good cause. The escape velocity of a body like it depends on two things: its density and its mean radius.  Because it’s small and light (most comets are loosely-held conglomerations of dust and ice), the escape speed is going to be very low.  It’s about 4 km across, roughly 1,000 times smaller than Earth; if its density is 1/10 that of Earth, the escape speed will be about 3,000 times less than Earth’s (escape speed goes as size times square root of density.)  This might lower the escape speed to meters per second, making it very possible for it to drift away on a bad bounce.

xkcd, as usual, has an excellent comic covering the landing.

The first images look amazing.

Dieting in a Flash

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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!

Physics in a Flash

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I saw the first episode of the new CW show “The Flash” last night. Like most shows on the network, it was mindless fun. It has the CW stamp of lightweight actors, cardboard characters, bubblegum philosophy and idiotic science, but it was still enjoyable. The show, of course, centers around the eponymous superhero who can move at speeds impossible for the mundane human, and how he uses this new power to right wrongs and fight evil. It’s very formulaic; one could guess within the first few minutes who fit where into the grand scheme of things: who’s evil, who’s good, who the love interest is, who will eventually betray whom, and so on. But beyond the surface entertainment, the “science” of the show provides even more fun.

I’m a physicist, and like to think about physics in this world and in the magical world of TV land. The Flash provides a good venue for some entertaining ideas: first of all, how fast does the Flash move? It’s a bit hard to tell just by watching the show, but the writers/directors provided an indirect clue when they showed him moving against a graphic of city streets as seen from above. He seemed to move about 10 blocks in about a second. In New York, 10 city blocks is 1 mile, so 1 mile per second seems a pretty reasonable guess; in metric terms, about 1,600 meters per second. This is about 1,000 times faster than the average walking speed of an adult mundane. Hmmm… Well, if he’s going from 0 to 1600 in about a tenth of a second flat, he’s got an acceleration of nearly 1600 g’s! (I’m using the fact that acceleration is change in velocity over change in time, and that 1 g is about 10 meters per second per second in metric units.) He’s got to be made of stern stuff, as even experienced jet pilots will black out at 9 g’s, and get pretty dead if they’re exposed to accelerations of better than 20 g’s for any length of time. Another way to put it is that this acceleration is something like falling from the stratosphere and hitting the ground suddenly. Oww…

This leads to some other things: if he suddenly sped up and launched himself off of a ramp into the air, he could go a distance of about 160 mile before hitting the ground again! (I’m ignoring air resistance here, and the curvature of the Earth, and Coriolis force, and a bunch of other things as well. However, the show itself is hardly realistic, so neener, neener.) What if we don’t ignore air resistance? The force due to drag of the air as he runs around is something like 800 times his own weight; think about lying on a matress with 800 people sitting on top of you. This is what he feels whenever he runs around! The power which it takes to get him to run around like this is something like 10 million times the average metabolic rate of a normal human being, or the total power used in all of the daily activities by all of the residents of a large town!

The moral: thinking about Physics makes shows like this much more fun.

A quick note:  One thing which I had forgotten (shame on me!) is that if my estimate is correct, he’s running at several times the speed of sound.  My estimates for the forces acting on him are low.  I was assuming that he wasn’t compressing the air ahead of him to any significant extent.  Running this fast,  he’s going to generate a shock wave because the compression of the air in front of him can’t get out of the way fast enough.  Someone watching him as he runs by will see him first, then hear the noise of his passage, as he is outrunning the sound waves he generates…  It’s like watching a supersonic jet pass overhead.