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  oscillator) it follows that since Cronin says we have a good force measurement, we can say that we have a good power measurement. Here is a good paper done recently by a student, where the devices are tested on a range of measures against a purpose built calibration rig.

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.
Rob Shugg

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.

Finally more of a LPT application question. How do you view the use of LPTs attached to the bar (for example in a jump squat) vs attached to a belt (as in the Cronin paper). As I have interpreted the issue attaching the LPT to the bar allows for greater range of motion in the same time frame compared to that of the system centre of mass. Therefore this results in greater velocity and higher reported power values than compared to either belt measured data or force platform data. Also it appears that attachment to the bar allows for measurement of the bar power (i.e. the power exerted on the bar by the athlete) as opposed to the system power (i.e. the external power generated by the athlete, perhaps more important in sports where acceleration of the body is more important that acceleration of external objects) that could be more accurately measured by GRF or using a belt LPT (due to its approximate measurement of system CoM)?
Any thoughts would be great on any of the issues above.
Tue, Sep 13, 2011 at 12:59 PM
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).
Differentiating once gives us velocity and differentiating twice gives us acceleration. Once we have acceleration we can enter a system mass so we can calculate force with F=Ma. As I mentioned in my last email the method for determination of system mass needs to be consistent for results to be comparable. So while we can report a value for force and power, it is always subject to the way the system mass has been determined. This is that same for all LPT systems. In practice, when monitoring athletes for changes in performance this is no problem, as a method for determining system mass is consistently used.
So it really comes down to what you want to measure, if you are particularly interested in force then you need to measure it directly with a force plate or load cell. But you need to use a real force plate. Having worked in sports technology for over 20 years I have not seen a single portable force plate that I would rely on and I am very sceptical of the claims made by those supplying the cheaper portable force plates. If you are interested in measurements other than just force then you need to consider an LPT system as you can't reliably measure displacement and velocity with a force plate, due to integration error.
Another thing that is often overlooked when selecting a system for monitoring athletes is ease and speed of use. GymAware is completely portable and takes less than a minute to set up. Then when analysing the results GymAware will automatically and consistently mark up the concentric phase of each lift jump or throw. This makes daily power monitoring so simple that we have athletes self recording on a daily basis. With system like the BMS you mentioned, you have to manually mark up each rep. This is time consuming and error prone.Regarding your questions on attachment to belt or bar. This is not my area so much, I'm more on the engineering side of things, but I can say that your measurement protocol should best reflect your performance training goals. If you are looking at moving the body weight faster, then use a belt or broom stick, if you are looking for tackle breaking power then maybe a weights bar attachment is more appropriate.