What physiologically limits sprint, medium-distance, and long-distance performance?

Here's a question about the physiological aspects of performance limits, especially with regard to running.

When one runs, there are short distance (e.g., 100 meter sprint), medium distance (e.g., mile), and long distance (e.g., half-marathon). Is it fair to make the generalization that for short-distances, a person is limited by one's fast-twitch muscle makeup, that for medium distances, one is most limited by one's heart and lung capacity, and that for long distance, one is most limited by one's slow-twitch muscle buildup and pre-event glycogen stores? (Bear in mind that I, the person asking this, am by no means in top physical condition. Perhaps this generalization might not apply to someone near the limits of human perfection. That's not me. I'm thinking more about less-than-inspiring athletes like myself.) It just would seem to me that when I sprint, it's not my heart and lungs that are holding me back, but rather my lack of explosive leg power that keep me from sprinting faster. After all, sprinting is anaerobic. And when I run a mile or so, I'm not really limited by my legs, but rather by my heart and lungs. My legs aren't really burning up, and they seem to be willing to give more if only the heart could supply more oxygenated blood to my leg and arm muscles. After running a mile as fast as I am able, I am out of breath, light-headed, and maybe a little nauseous, but my legs feel pretty good. And when I run a half-marathon (the furthest I've ever run), my lungs and heart seem to be giving my legs all the oxygenated blood they want and yet seem to be pretty relaxed, and it seems that my legs are what keep me from going faster. After crossing the finish line, my legs feel like rubber, and I feel pretty tired in my body as a whole, but my heart and lungs still feel pretty good. Does this sound in line with how everyone is? And if so, would I likely find my sprinting ability to be aided mostly by exercises to build my fast-twitch muscle, my medium distance running to be aided mostly by cardio exercises, such as rowing, and my long distance running aided mostly by exercises to build my slow-twitch muscle? (Of course, I realize one sprints to be a better sprinter, one runs medium distances to be a better miler, and one runs long distances to be a better distance runner. I'm mostly just looking at this from a theoretical point of view.)
 
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I am more familiar with cycling, but your philosphy seems reasonable to me. Depending on what distance you want to run will determine what type of training you need to improve at that distance.
 
Well firstly your right. Fast twitch for sprints slow twitch for aerobic activity.

What do you mean by your generalization sprints are limited by fast twitch fibres?

The thing is, with sprints you simply cant mainatain that intensity for very long, it is way beyond your bodies homeostasis. The ATP-PC can fuel these runs but the problem is that they only last for about 10seconds, and now aerobic metabolism is to slow to keep up, and the byproducts of glycogen limit your performance.

However with long endurance runs, technically you could run extremly far, across australia example. Your bodies in homeostasis and have an unlimited supply of fat for energy, however your glycogen levels are responsible for hindering how far you can go non stop. So obviously having more slow twitch will mean you have a greater capacity for aerobic oxidation and therefore reducing your need to use glycogen.
 
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