If I run a fixed number of miles, is there any solid scientific evidence on whether running at a faster speed makes me more likely to get injured? I'm a physicist, so my tendency is to try to make models based on mechanics. Presumably injuries like plantar fasciitis are caused by strain that exceeds the elastic limit of the tissue, and strain should be proportional to the square of the speed at which I run. This suggests to me that injury should depend critically on speed: if my speed is below a certain threshold, then my tissues never go past their elastic limit, but once I get past that threshold, I suddenly start doing damage.
So speed kills -- true or false? Is there any good evidence-based medicine on this topic? The following is the only thing I've come across that seems possibly relevant: http://articles.latimes.com/2013/jun/27/news/la-sn-ultra-marathon-20130627 This is a newspaper article describing research that seems to show that running very long distances may be, counterintuitively, less likely to cause injury, possibly because the greater distance forces the runners to go more slowly.
On the other hand, people often do get plantar fasciitis even when all they do is stand or walk around.