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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.

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There is an article in the International Journal of Sports Physical Therapy by Danish researchers that concluded that:

...running volume may somehow be associated to the development of PFPS, ITBS, and PT while running pace may be associated with development of AT, GI, and PF.

So speed would be associated with plantar fasciitis, achilles tendinopathy, and gastrocnemius injuries.

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... and strain should be proportional to the square of the speed at which I run.

Almost all the load placed on your body is a function of your vertical motion, not speed (horizontal motion). There are two running styles:
(1) fewer strides, more distance per stride, significant vertical motion. more damage.
(2) more strides, less distance per stride, minimum vertical motion. less damage.

Sports scientists explain this issue in full here

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Almost all the load placed on your body is a function of your vertical motion, not speed (horizontal motion). Vertical motion also speeds up when you run faster. In general, I don't think this answer addresses the question. –  Ben Crowell Nov 30 '13 at 18:27
Speed is the wrong variable. (1) a person could not skip rope for infinity. With no speed, the ankle, knee, or hip eventually breaks. (2) Imagine a 300-pnd man on a frictionless surface, that declines 1-degree, in a vacuum. He could attain an infinite amount of speed while standing still doing no damage to himself. Damage is caused by your needing to absorb your body weight as it crashes down for the next stride. A 300-pd US football player cannot use long strides because it'd break their legs. –  kingyo Nov 30 '13 at 23:09
The question asks whether there is evidence, not whether the hypothesis seems plausible to you. –  Ben Crowell Dec 2 '13 at 21:59
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