Physics, Crossfit, and Beyond the Whiteboard

We’ve noticed a few posts on our user feedback regarding work done and thought it would be a good idea to post a bit about how we calculate work and power, and what these figures mean for the layman.

What do you mean by work and power?

In physics, mechanical work is defined as the product of the force acting on an object and the distance it moved. For example, if you do a shoulder press, the work done is the weight of the barbell multiplied by the distance from the barbell’s resting position above your shoulders to its position above your head — roughly the length of your arms. So, if you did a 150-pound shoulder press, and your arms are about 2 feet long, you can find the work done in foot-pounds by just multiplying the weight by the length of your arms; in this case one rep of the shoulder press is 2 ft * 150 lb = 300 foot-pounds of work done. If you did that 50 times, you would have done 15,000 foot-pounds of work.

If you prefer metric units, as most people outside of the US generally do: if your arms are about 0.6 meters long, and you pressed 70 kg (which weighs 9.8 m/s² * 70 kg = 686 newtons on Earth), the work done for one rep is 686 newtons * 0.6 meters = 411.6 joules (or newton-meters).

Power is defined as the rate at which work is performed. This is just work done divided by the time you took to do it; we find your average power output by simply dividing your work done by the number of seconds you took to do the work, assuming we know how long you took. In a max effort lifting workout, we can’t tell you your power output since you’re not posting your total time. For example, if you did a workout which was just 50 of the above shoulder presses, no other exercises, and took 30 minutes to do so, your power output would be 15,000 foot-pounds / 1,800 seconds = 8.3 foot-pounds per second. (You can do the same thing for metric, only you end up with joules per second, also known as watts)

So, how do you find work and power for a Crossfit workout?

This is our “11 herbs and spices”. Secret ingredients. Ok, so the real 11 herbs and spices are probably salt, pepper, flour, MSG, and 7 kinds of grease, but ours are a lot more complicated. For each and every exercise for which we have sufficient information to do so, we have a work formula which tells us how much work a person did in one rep of that exercise. In some cases, we can get this information from a weigh in, so make sure to weigh in regularly! In other cases, this means we need more information than a simple weigh in, so be sure to set your work formula measurements at least once! If we don’t have your measurements we can fudge it a little, basing your deadlift height, squat height, etc. on some averages based on your total height from your last weigh in, but it will be much more accurate with real measurements. Once we have your information we can plug it in to each formula and calculate the work done over an entire workout.

Why is any of this important to a Crossfitter?

Many Crossfit workouts are relatively short, high-intensity workouts that even I can finish in under about 20 minutes, assuming you are scaling it properly. Your objective in any workout, if you’ve done that particular one before, is to beat your old time, which, assuming you’re lifting the same weight and your own weight hasn’t changed, means you’ll be doing the same amount of work but with a higher power output. However, not everyone can do every workout as Rx’d. I, for example, started Crossfit in September of last year, and weighed in at 265 pounds at 5’5″. I was in horrible shape; I nearly passed out halfway through Helen on my first day. Since then I’ve lost about 30 pounds overall, gained some lean mass, and generally have a lot more energy. If I was just looking at my times/rounds/reps I might see points where I took a lot longer to complete a workout, or did fewer reps or rounds, but since I lifted heavier weights, used a lighter band on pullups, and so forth, my work done and/or power output is much higher than my previous attempt. What is important in a case like mine is to look at your power output and make sure it’s heading upwards every time. And once again, make sure you weigh in often if you’re trying to lose or gain weight so that those power calculations are accurate.

Hey, your site says I didn’t do any work this entire workout! Tell that to my aching arms/legs/back!

There are still a good number of exercises that we don’t have formulæ for (mostly custom exercises added by gym owners which we don’t know anything about), and some exercises where you actually don’t do any work, such as running. That’s right; when you run, although you expend energy, produce a force, and move through a distance, you don’t do any mechanical work!

Huh?

This part’s going to get a little heavy, so bear with me. Work is also defined as “energy transferred by a force acting through a distance” (Thanks to wikipedia for this and a lot of the equations below, it’s been about 8 years since physics 2A). This means that unless the energy in a body changes, including kinetic energy and potential energy, no work is performed. For example, I’m writing this on a laptop weighing 5.5 pounds, which is sitting on a table. Since the laptop isn’t crashing to the ground, the table is exerting a force of 5.5 pounds upward on the laptop. However, since it’s not moving, there is no change in its potential or kinetic energy, and no work is being done. This is also why you do no work when performing an L-sit or static hang.

I think we’re going to have to dive a little deeper here and define kinetic energy and potential energy to really understand what is (or in this case, isn’t) happening.

Kinetic energy is the energy a body possesses due to its motion. In other words, an object has kinetic energy if it is moving relative to the observer. In general you can find this with the formula E = ½ * m * v², where m is the mass of the object and v is its velocity relative to the observer. In other words the faster something is moving relative to you, the more energy it has.

Potential energy is energy stored by a body. In the case of a weight that has been lifted from the ground, the weight has potential energy because if you let go of it, gravity will take over and cause the weight to move, towards your foot, and unless you move out of the way all of that newly acquired kinetic energy on the weight will transfer itself right into your toes. A simple equation for potential energy due to gravity, adequate for our purpose, is E = m * g * h, where m is the mass of the object, g is standard gravity (9.8 m/s² on Earth) and h is the height above the ground at which the object is at rest.

Knowing these two facts, can you see why running does no work? There is no change in potential energy unless you are running uphill, and we assume you are running on a fairly level surface such as a track, or a flat sidewalk. There is also no change in kinetic energy. You are both the observer and the body in question; your kinetic energy (motion) relative to yourself is always zero.

This doesn’t mean you should stop running! Despite the fact that no measurable net work is being done, you are still burning calories, strengthening your legs and your cardiovascular system, and boosting your metabolism.

Regarding exercises where work is done, but we still say zero: If you want your custom exercises given a proper work formula, give us a full, proper description of the movement (maybe a video as well, gym admins will be able to tag videos to exercises in the near future) and when we get the chance, we can come up with a formula and add it to the site. This will affect workout sessions posted in the past as well as the future, so go ahead and use any exercises you want in your workouts; when we know how to calculate the work done, your older sessions will show every ft-lb of work you did.

If you want to find out more about physics and Crossfit listen or read anything Coach Glassman has authored, and browse through the other great Crossfit Journal Articles. It’s where we started and continue to go for inspiration. Below are some CFJ articles to get you going.

2 comments

  1. MikeD · July 21, 2009

    Great article, but I have a few nitpicks (sorry, I can’t help it, I’m a physicist and a big nerd so these things just come out):

    – Your formula for work is very simplified, and works only when you’re applying a force in the same direction that the weight is moving. The real formula for work is the path integral of the dot product of force and distance (likewise the formula for power is the path integral of the dot product of force and velocity). Most of the time `this doesn’t matter, but for things like KB swings and KB snatch you have motion along an arc and the force applied isn’t parallel to the direction of motion. This make the formula for the KB work and power much harder to work out (I even simplified it for my workouts, I didn’t want to do the full path integral).

    – You certainly are doing work when running. Every step you take lifts your center of mass up (then you fall down in between steps). If I use your argument that there is no net work in running, then you’d have to say that doing a snatch also doesn’t result in any work done because you pick up the barbell and then drop it. You’re doing work on the way up, and gravity is doing the work on the way down. The net work is 0, but you certainly are working.

    – There’s also the acceleration you needed to go from stop to moving (F=ma), so there is work being done during your acceleration (and negative work being done while slowing down which usually cancels out F*d + -F*d = 0, but it’s still work your body has to do – it’s probably best to take the absolute value of work when summing in this case).

    – Also remember that the F=W*d formula is only accurate for conservative forces. Friction and turbulence caused by the wind you’re running through require a force over a distance which is work (I guess technically it’s energy expended that does no useful work).

    – Depending on your point of reference, you are also doing work for an L-sit. Granted, your COM is not moving, so there’s no useful work, but you need to remember that your muscles can only contract and release, so during an L-sit, your muscles are constantly contracting (lifting your legs up a small amount) and releasing (letting them drop a small amount), so they are doing work. Of course, if someone asked me how much work is being done, I’d still say none since you’re not moving, but from the point of view of your muscles, they are doing work.

    Like

  2. Alex · July 21, 2009

    Thanks for this info.

    Like

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