How to Calculate Power Output on a Treadmill
Running on the tread mill delivers a force to the tread that is transmitted to the wheel, making it rotate some distance. If this wheel was connected to the shaft of a generator, it would spin, creating electricity. You are performing mechanical work on the wheel that is measured in joules. Mechanical work divided by the time over which the work is done equals power in watts. The work done is related to the distance you ran and the the time it took, as well as the mass and radius of the wheel.
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Instructions
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Run on the treadmill, then record the distance in miles and the time it took in minutes. For example, say you ran 1.2 miles in 17 minutes.
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Convert the distance ran and the time it took to meters and seconds, respectively, by multiplying the distance by 1,609.3 and the time by 60. 1,609.3 meters equals 1 mile, and 60 seconds are in a minute. This leads to a distance of 1,931.1 meters ran in 1020 seconds.
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A common wrench Utilizing a wrench, remove the wheel from the treadmill and place it on a scale to measure its weight in pounds. Then convert the weight to a mass in kilograms by multiplying it by 0.454, since 0.454 kilograms are equivalent to a single pound. Assume the mass is 3 lb. The mass in kilograms is 3 times 0.454, or 1.36 kilograms.
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A simple tape measure Measure the radius of the wheel in centimeters and then change the length to meters by dividing by 100. The radius is measured from the exact center of the wheel to its edge in a straight line. Say the radius is 10 cm, for sake of example; then you have a length of 0.10 meters.
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Calculate the circumference of the wheel in meters by multiplying the radius by 2 times the number pi. Use 3.14 for the number pi. The distance around a circular object is its circumference. Performing this calculation leads you to 0.10 meters times 2 times 3.14, which equals 0.628 meters.
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Divide the distance ran by the circumference of the wheel to obtain the total number of times the wheel has turned. In the example, the wheel has turned a total of 3,075 times, since 1,931.1 meters divided by 0.628 meters equals 3,075.
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Compute the total work done on the wheel in joules by the formula:
( 4 x pi x m x r x d x N ) / t^2,
where pi is 3.14, m is the mass, r is the radius, d is the distance ran, N is the number of turns the wheel made, and t is the time. The symbol "^" signifies an exponent. Calculating the work form the example data yields:
( 4 x 3.14 x 1.36 kilogram x 0.10 meter x 1,931.1 meter x 3,075 ) / ( 1020 second )^2,
which is 9.74 kilogram x meter^2 / second^2 or 9.74 joules, since a kilogram x meter^2 / second^2 is a joule.
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Divide the work done by the time ran to obtain the power in watts. Completing the example, you have 9.74 joules divided by 1020 seconds or a power of 0.0096 watts.
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References
- Photo Credit man assembling a treadmill image by Leticia Wilson from Fotolia.com wrench image by Edsweb from Fotolia.com tape measure image by Alison Bowden from Fotolia.com
