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Question about Power and Gravity

  1. Oct 18, 2014 #1
    I'm not a math wiz by any means, so I was hoping someone smarter than I am could help me figure something out.

    I'm trying to document the total "work capacity" of an individual across a wide variety of tasks in order to transfer the information to a graph to compare the amount of power generated for a set of task.

    On the X axis I want to document the time of effort, and on the Y axis the amount of power output. This is where I'm having issues:

    If Work = Force x Distance and Power = Work / Time

    If a person A can squat 160kgs and the total distance traveled is 1 meter (.5m on the way down and .5 on the way up) and it took them 3 seconds.
    Person B weighs 80kgs walks 2 meters in 3 seconds.

    By the simple equations above both person A and B did the same amount of work and had the same power output. We know that the person squatting expended more energy and generated more power however.

    What am I missing on this equation? Do I need to document gravity since one is working against it and the other perpendicular to it?

    If a person climbs up a 3m rope in 10 seconds and walks 3m in 10 seconds they would be generating the same amount of power during both movement with these definitions.

    I have seen another work equation that may be helpful but I don't understand how to factor or apply gravity to it.

    Work = Force x Distance x Cos(theta)

    Where Theta is the angle between the force and distance vectors.

    Thanks for the help!
  2. jcsd
  3. Oct 18, 2014 #2


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    Work is done only when a force acts, across a distance, against other force, such as gravity (in the case of squatting or rope-climbing) or against friction of the body joints and the elastic forces of the body that have to be overcome by walking.

    No work is done by moving a mass on a level surface without friction, however large that mass may be...

    I am not sure, but I believe that human (and animal, in general) physical work is measured by indirect means, metering the oxygen consumption or something like that...
  4. Oct 18, 2014 #3
    Yikes, I wonder how I could possibly document that for sprinting and such. The goal is for it to be variable by inputting the weight/height of the individual and being able to track power output throughout long distance runs, sprints, and lifts and graph them all. I still can't figure out how to correlate them all to be apples to apples on the graph.
  5. Oct 18, 2014 #4


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    All that has been extensively researched, not only for athletes, but even for birds... Try to find the data in books or magazines on the physiology of sport...
  6. Oct 18, 2014 #5
    Yes, but most of the articles I am coming across dives pretty deep into heat dissipation, muscle volume and such. I'm wondering if there is anything that would document the power of a runner at a certain weight running a set distance against the time it takes them to do that? Should I be looking for an average friction equation for running applications? I want to be able to plug and play the weight, distance, and time and compare against others and appropriately document it against, say a 1 rep max dead lift or squat.
  7. Oct 18, 2014 #6
    For Power = (Force x Distance x Cos (theta)) / Time

    The lifting portion is easy enough for that

    I think I need to find a way to get a vector in-between the force of gravity and the force applied toward propelling a human body a said distance in a said time.

    Anyone know a formula I can use?
  8. Oct 19, 2014 #7


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    For a human, and for most animals, the energy invested in walking or running doesn't come only from overcoming internal or external friction, but from keeping on all two (or four) legs. Besides, the muscle elasticity used when running is not perfect, and some energy is lost to heat by those 'springs' that must be replaced. Simple physics equations are not going to solve your problem for the case of simple walking. However, the energy spent in some tasks may be approximated. For example, if you climb up ten stories in one minute, most of the muscular energy delivered by your body will be invested in increasing your body's potential gravitational energy. But moving onself's body with muscular power along a level surface is different...

    I'm adding below a diagram published in 'Scientific American', in the 70s I believe, in an article titled 'Bicycle Power'. Please note how a man on bicycle needs far less energy that a man walking...

    Last edited: Oct 19, 2014
  9. Oct 23, 2014 #8


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    That implies your calculation for the power output by person A was something like

    160 x g x 1 / 3

    Which suggests you included the power on the way down as well as the way up? In theory the man expends no energy on the way down because gravity moves the weights. It only feels like hard work for the man on the way down because he isn't an "ideal" man. (Aside: I'm assuming he lowers the weights slowly so we can ignore the energy he uses decelerating the weights).

    As others have said, you can't calculate the power required when walking the way you have. Walking involves falling forward (which also lowers the centre of mass) then raising that mass back up again. So the centre of mass goes up and down as you go along. Someone has attempted to model and quantify the power expended here. I've no idea how accurate it is..

  10. Oct 23, 2014 #9


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    PS: I believe sports scientists measure how much oxygen you consume to calculate your power output. Presumably they first calibrate you by putting you on an exercise bike that logs your power output and oxygen consumption rate. Then when running or walking all (?) they have to so is measure your oxygen rate and look up the corresponding power output figure from the exercise bike data. There is a table here..


    Interestingly they say you burn more energy shivering than walking.
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