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Clearly, running fast is harder than running slow. If I run a 5k in 30 minutes, I will be panting harder and feel more uncomfortable by the end of it than if I jog it in 45 minutes.

Why is this? How can we quantify the difference? An obvious thing to try is to count calories - what is the energy cost of running a certain distance at a certain speed? However, it seems to be fairly well accepted that calories per kilometer is constant, independently of your speed. See e.g. Margaria et al. 1963, Energy cost of running. The claim is also stated very clearly in Carrier et al. 1984, which cites the first paper:

...the cost of transport for a running human does not depend on speed. Consequently, a man running a marathon will consume the same amount of energy for transport whether he runs at a slow jog or at a world-class pace.

If not calories, what is an appropriate way to measure "perceived effort" of running a given distance at a given speed?

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  • I don't have the time to write a complete answer but I would assume it has to do with a combination of how much energy can be converted by the body at any given moment, how much oxygen is required for a more intense workload and the increase in build up of lactic acid in the muscles when the workload is higher.
    – MJB
    Sep 15 at 11:55
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If we assume that energy used by an individual athlete during a run (without elevation changes or wind) is dependent only the distance of the run, then the difference between a fast 5k run and a slow 5k jog, and the explanation for why the former will leave you more out of breath, is the rate of energy expenditure. A 30 minute 5k run requires you to burn energy at a 50% higher rate than a 45 minute 5k run, hence during the run you need 50% more oxygen, and will breathe faster in order to provide that.

If you want a quantification of this intensity, then METs (Metabolic Equivalent of Task) or simply calories burned per hour could be used.

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  • Is there some law saying that the rate (w.r.t. time) at which you burn oxygen is proportional to the rate (w.r.t. time) at which you burn calories?
    – Jack M
    Sep 15 at 14:06
  • @JackM I don't know about a "law", but oxygen usage is how they measure energy expenditure in some studies. There is a correlation. Another method is measuring carbon dioxide production in breath which is also related to oxygen burn.
    – DeeV
    Sep 15 at 21:01
  • To be clear, if O2 usage is directly proportional to running speed, then total O2 usage over the course of a given distance is independent of speed, just like energy. But you're saying the instantaneous O2/time ratio at any given moment will be higher, and this is (part of) what produces a feeling of greater exertion?
    – Jack M
    Sep 15 at 21:40
  • @JackM yes, aerobic respiration requires oxygen consumption proportional to calories burned. (Anaerobic energy production is more complex, but basically also requires oxygen proportional to calorie burn, it's just that the oxygen comes after the energy is produced, as a debt.) So O2 consumption and CO2 production rates at an instant can be said to be proportional to running speed and also responsible for the feeling of greater exertion, and total O2 consumption and CO2 production over a run can be said to be determined by the distance of the run but not its speed. Sep 16 at 2:10

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