How do we calculate 'Power'?
How we calculate power, and other kinematic variables:
I recently received an email from a person wanting to know more about how we calculate power in the Power Tool. This person is clearly doing his homework in selecting the right technology. He asks some very good questions which I think will be on the minds of many practitioners. I've included the whole email conversation here with names removed to protect the innocent!
Fri, Sep 9, 2011 at 9:17 AM
I have a question regarding the power calculations that are included in the GymAware unit. In the document title ‘Sports Physics - What is POWER and how can it be measured’ available on your website you discuss the use of formula Power = Work/Time, which is of course mechanically valid. However, you cite the Cronin et al. (2004) paper as empirical evidence in support of the use of your power calculations from linear position transducers. After reading this article it appears that there were no measures of power made at all in this paper. Indeed the linear position transducer described in the paper clearly functions in the way that you describe in the document ‘GymAware Sampling Method’ as less valid that your own. Therefore I was wondering if you could shed some more light on the validity of the power measurements reported by your unit so I can interpret the data obtained from a more informed position?
Fri, Sep 9, 2011 at 10:24AM
Thanks for your email and your question. The Cronin paper does indeed study the validity of force measurements taken by a Linear Position Transducer (such as the GymAware PowerTool) compared to a force plate. Since Power = Force x Distance/Time and we have first principle measurement of distance(optical encoder) and very accurate time measurement(crystal
Having said that, there are limitations with this approach. The power measure and the work done are unlikely to be valid for calorific studies (where absolute work and power are desired) as assumptions are made as to the contribution of body weight to the lift mass. This is especially so when measuring jumps as the body weight is a major component of the lift mass.
The power measurement is valid from a sports performance perspective however. In this setting we are looking for
the amount of power the athlete can deliver, in a tackle, sprint or jump. Typically our users are interested in
trends over time within the athlete, and comparisons between athletes. In this setting the measurements are very
useful and are a valid measure of the performance of the athlete.
In regard to the sampling method the VRS method is different (and superior) to the one in the paper as it requires no further filtering. In this fact sheet where we compare the GymAware unit to another LPT that uses the method in the Cronin paper and overlay the two traces for the same lift. You can see that the signal of interest closely match but the traditionally sampled signal is noisy and requires filtering.
I hope this answers your questions, there is a lot more that can be said on this and a lot of research of mixed quality is out there. If you tell me a bit more about your interest in this perhaps we can write up a story for our newsletter.
Mon, Sep 12, 2011 at 10:09 PM
Thanks for your email, the article you forwarded looked like good evidence for the velocity values reported. However, I could do with a bit more clarification on the power issue. Your document on the website on the power calculations suggests that you don’t use force for measuring power (rather using P = mgh/v or P = 0.5mv^2/t), indeed it discounts the force method but in your email you say that you do use force data combined with distance and time data. As I understand it the Cronin paper validates the calculation of force variables from LPTs (using a constant sampling rate, but with unreported methods of calculation to obtain force) but your unit does not use force in calculation of power (ref here). Therefore I cannot see the link between the GymAware power values and the validation provided by Cronin, could you shed further light on this and/or specify the exact data calculation procedures that are used in determining power?
Apologies for the examination I am just trying to make sure that I have a full understanding of the issues at play with the various systems. Indeed I am also looking at the validity of the BMS unit you compare the GymAware signal to, as well as some force plate data.
Any thoughts would be great on any of the issues above.
Thanks for getting back to me, I appreciate these questions. We are constantly trying to improve the way we communicate these concepts to our users and its great to get feedback on how well we are doing this. First, regarding force being used in the power calculation. All LPT systems measure just two things - displacement and time, (actually GymAware measures three things when you include angle of lift).