# Some People Running

This video seems like it is getting popular, but maybe that is because it is so awesome.

Maybe it is just me, but I find this video very visually satisfying. I love the way they compare the different runners.

Anyway, there is some physics here. Commenter Ben sent me the link to this video (thanks!) with some great questions. Which of the runners has a greater kinetic energy? What about the power? These aren't too difficult to answer, but the first thing is to get the data. There are several options (including just using a stop watch). But no, that is not good enough for me. Instead, I used my favorite free, multi-platform video analysis tool Tracker Video.

It turns out that there were a couple of problems analyzing this video. First, it was tedious. Second, there is some perspective error as the camera pans along the motion. To fix this, I broke the video into three segments with different coordinate systems and then kind of "stitched" them together. The video above shows several people running, I only plotted the "normal" guy, Jacoby Ford, and Terrance Cody. Here is what I get using LoggerPro.

I went ahead and fit a linear function for these three runners for the portion that they were at a constantish speed. If you can't read the image, I have:

• Normal dude: 7.3 m/s (16.3 mph)
• Jacoby Ford: 11.5 m/s (25.7 mph) (damn that is fast)
• Terrance Cody: 8.4 m/s (18.8 mph)

To calculate the kinetic energy, I will need the masses. Let me use 75 kg for the normal dude. Cody has a wikipedia page that lists his mass at 161 kg. Jacoby's wikipedia page gives a mass of 84 kg. So, here is a plot of kinetic energy as a function of time.

Note: since I used Logger Pro to take the derivative of the position to get the speed, I also used the "smoothAve" function to smooth the data out. Looking at the graph, it is interesting that Jacboy and Cody have similar kinetic energies. I am not sure why (or really if) Jacoby is slowing down. When you look at the position time graph for Jacoby, it doesn't look like he is slowing down that much. Either way, these two athletes have some serious energy compared to the normal guy.

What about power? Power is difficult with running people. The problem is that there are two things going on. First, there is some air resistance. Second, when you are running at a constant speed, it is not the same as moving a particle at a constant speed. You have to keep accelerating your legs in order to maintain this motion. So, when running and speeding up, you have to do three things: increase your kinetic energy, have a greater rate at which you change the kinetic energy of your legs, and last fight against air resistance.

I am going to have to come back to running in a future post because it is quite interesting. However, for now I will calculate the power just due to change in kinetic energy. In a short time interval, think of power as:

So, this would be the slope of the above KE plot. I know I already "smoothed" it once, but this will give an idea of the power of these people.

First, negative power. That is not negative power. That means the rate of energy going into KE is going down. There is still energy going into moving the legs and air resistance. Second, are these ok for power of a human? Well, it is not 56,000 watts (ESPN Sport Science) - and that is a good, right? This wikipedia page lists the sprinting output of a cycler at about 2000 watts. So, I don't see anything crazy in this graph.

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In terms of power, there are a couple of ways to look at it. Many years ago I wondered why I could ride a bicycle at 10 m.p.h. for hours on end but running at 10 m.p.h for more than a very short time would be nearly impossible (for me). After all, bike + me weighs more and presents at least as much area to the wind as me alone. But clearly, it's the fact that I'm continuously lifting myself up and then coming back down when I run. So if you look at power required to accomplish it (i.e., food energy burned*efficiency of turning that into muscular activity) running at a given speed uses much more power. Whereas if you look at energy used to do "useful" work (i.e., moving forward), not so much.

@Rob,

I think you hit it - that is the key. So, it couldn't just be air resistance or change in KE of the whole body (or bike). It must be the change in motion of the legs and the change in center of mass of the body (you don't move up and down while riding a bike).

This is a topic I will certainly be coming back to.

I think the biggest factors in bike vs. run are a) that if you stop expending energy while biking, you decelerate slowly due to bearing/ground friction and air resistance, whereas if you stop expending energy while running you stop; b) the limit on the speed of legs when running vs. the ability to match optimum speed of the legs to the ground speed through the gearing and drive wheel.