## Wednesday, May 5, 2010

### height vs mass for sub-27 minute 10 km times

Chris Solinsky

In comments to the Science of Sports blog post on Chris Solinsky's remarkable sub-27 minute 10 km time, data on the height and mass of those who've managed to break that barrier were listed. It's interesting to see how the numbers scale:

height vs mass for sub-27 min 10 km running times

While constant BMI certainly describes the upper bound of these data, at the lower margin, the trend is closer to a constant ratio of mass to height. It was proposed a factor may be the ability to dissipate heat, which becomes more difficult for larger runners than smaller runners at a fixed BMI.

For fun, I also plotted my numbers, and while I'll never run close to a 27 minute 10 km (40 minutes would make me happy), my dimensions certainly fit in nicely with this super-elite crowd:

I added myself to the plot

#### 4 comments:

NadiaMac said...

what do you mean by constant ratio? help out the math illiterate

NadiaMac said...

also, I am assuming chris is the outlier on the upper right of your graph-- is this correct (sorry, can't convert from english to metric at this early hour)?

djconnel said...

Chris is the outlier, yes. Although on a BMI basis, he's not the highest.

Constant BMI implies mass is proportional to the square of height, while constant ratio implies the mass is simply proportional to height. Across typical populations, mass scales somewhat stronger with height than the square (modeling a human as a sphere of sea water, as we did in undergraduate physics, it would be the cube of height, but reality is taller people aren't as wide for their height as short people: organs need only so much room).

So the result is taller runners tend to be extremely thin to go the same speed as shorter runners. Chris is an obvious exception.

djconnel said...

In the weightweenies blog, someone pointed out an alternative explanation for the relative lack of tall big guys in the data is that tall, big, fast guys are snatched up by football and basketball, for example, and therefore never train specifically for the 10 km. I like it.