Work & Power Calculator
In issue 31 of the CrossFit Journal, Coach Greg Glassman calculated the work completed and power generated by an athlete (Greg Amundson) performing the classic diagnostic CrossFit workout “Fran” (21-15-9 reps of 95 lb thrusters and pull-ups).This got us thinking: Wouldn’t it be righteous to create a resource that would allow an individual to quickly and easily approximate the work and power output of a workout?
In other words, let’s provide a simple tool for the individual without the requisite time, energy and/or knowledge to generate quantitative measurements of training beyond simply the volume of vomit discharged. Even for someone capable of performing the necessary calculations independently, it would be a useful tool to generate the figures with far less time and effort and without significantly compromising accuracy.
Speaking of Accuracy
With the aforementioned goal in mind and no planning, we spent some time at NorCal Strength & Conditioning's facility measuring distances of travel of some staple movements in order to provide the initial data that would allow the creation of the necessary power output calculator. We then erased all of our numbers after recognizing a litany of flaws and decided that developing a more deliberate and rational approach would likely generate more accurate figures. With this new approach, we returned to NorCal Strength & Conditioning and harvested our data.
It’s important to remember that regardless of the precision of our measurements and calculations, the figures that will be produced by the resulting tool are approximate for a number of reasons.
Probably the largest single contributor is the calculations' imperfection is their lack of consideration of the energy expenditure of the eccentric portion of the movements. One study measuring the respective energy demands of ascending and descending a given grade found that the descent demanded as much as 30% of the energy expended during the ascent. Unfortunately, the number of variables involved in calculating the eccentric energy precludes its inclusion in this particular project. All calculations therefore assign no value to eccentric energy output; the numbers generated will be consistently lower than the actual output, although to varying degrees depending on the movements and the manner of their execution.
Another significant contributor to the figures’ imperfection worth mentioning is the inherent imprecision of extrapolation. There are variations in body structure from individual to individual. Despite the ratios pictured in da Vinci’s Vitruvian Man, two men of equal height and weight may have different body segment lengths, translating into disparity in both segment masses as well as distances of travel of their bodies and/or external weights in various movements, ultimately resulting in differing amounts of work.
Remaining factors of imperfection are numerous but relatively minor. The height of an individual's shoes will affect the distance of travel of an external weight being lifted from the floor; the width of the grip on movements will affect the distance of travel of an external weight, or, in the case of pull-ups, the body; the width of the feet during movements with a squatting component will affect the distance of travel of the body. Fortunately the effects of these things are minute enough to be in this case inconsequential. If, however, you intend to use the calculator to compare series of your own efforts, consistency in the movements will improve your figures' accuracy.
Assumptions and Standards
Our measurements are based on a number of necessary assumptions and standards. One important assumption is that the movements in question are being performed with what we would consider proper form through a full range of motion.
Squat depth for all movements is the 12 inches regardless of the individual’s standing height. To address two particularly complex movements, the clean and the snatch, we assume that the receiving position is a full-depth squat as described previously. We also assume that the movements are being performed with exemplary skill, i.e. the individual is not engaging in superfluous movement such as pulling the bar significantly higher than the ultimate receiving height. Finally, it is assumed that the starting positions for the clean and snatch, as well as the deadlift, have the hips somewhat higher than in the squat, but not excessively elevated; these movements started with higher hips will result in somewhat less work because less of the body’s mass is being displaced vertically.
The actual body mass moved has been calculated based on typical body segment mass percentages. For example, we assume that during a squat, none of the foot or lower leg and half of the thigh are lifted; this amounts to 74.44% of total body mass being moved in the squat. A pull-up, on the other hand, amounts to 91.5% of total body mass due to the arms’ far lesser mass in comparison to their lower body counterparts.
Our foundational data were obtained by measuring two individuals, one male and one female, with a six-inch height differential. Using those numbers, we calculated a constant for each movement (two constants if the movement involves travel of both the individual's body and an external weight), which, when multiplied by an individual's height, will approximate the distance of travel of the movement for that individual.
The calculator process is fairly simple: Bodyweight is adjusted for segment percentages and then multiplied by its distance of travel, and the external weight is multiplied by its distance of travel; these figures are then multiplied by the total reps performed to calculate the work performed. The combined work is then divided by the duration of the workout to determine power.
The Results
The output of the calculator will be figures representing the work and power of the athlete during the workout in question. Work will be calculated in joules, kilogram-meters, and foot-pounds. Power will be calculated in watts, horsepower, kilogram-meters/second, and foot-pounds/second.
Check out the calculator here on Catalyst Athletics
In other words, let’s provide a simple tool for the individual without the requisite time, energy and/or knowledge to generate quantitative measurements of training beyond simply the volume of vomit discharged. Even for someone capable of performing the necessary calculations independently, it would be a useful tool to generate the figures with far less time and effort and without significantly compromising accuracy.
Speaking of Accuracy
With the aforementioned goal in mind and no planning, we spent some time at NorCal Strength & Conditioning's facility measuring distances of travel of some staple movements in order to provide the initial data that would allow the creation of the necessary power output calculator. We then erased all of our numbers after recognizing a litany of flaws and decided that developing a more deliberate and rational approach would likely generate more accurate figures. With this new approach, we returned to NorCal Strength & Conditioning and harvested our data.
It’s important to remember that regardless of the precision of our measurements and calculations, the figures that will be produced by the resulting tool are approximate for a number of reasons.
Probably the largest single contributor is the calculations' imperfection is their lack of consideration of the energy expenditure of the eccentric portion of the movements. One study measuring the respective energy demands of ascending and descending a given grade found that the descent demanded as much as 30% of the energy expended during the ascent. Unfortunately, the number of variables involved in calculating the eccentric energy precludes its inclusion in this particular project. All calculations therefore assign no value to eccentric energy output; the numbers generated will be consistently lower than the actual output, although to varying degrees depending on the movements and the manner of their execution.
Another significant contributor to the figures’ imperfection worth mentioning is the inherent imprecision of extrapolation. There are variations in body structure from individual to individual. Despite the ratios pictured in da Vinci’s Vitruvian Man, two men of equal height and weight may have different body segment lengths, translating into disparity in both segment masses as well as distances of travel of their bodies and/or external weights in various movements, ultimately resulting in differing amounts of work.
Remaining factors of imperfection are numerous but relatively minor. The height of an individual's shoes will affect the distance of travel of an external weight being lifted from the floor; the width of the grip on movements will affect the distance of travel of an external weight, or, in the case of pull-ups, the body; the width of the feet during movements with a squatting component will affect the distance of travel of the body. Fortunately the effects of these things are minute enough to be in this case inconsequential. If, however, you intend to use the calculator to compare series of your own efforts, consistency in the movements will improve your figures' accuracy.
Assumptions and Standards
Our measurements are based on a number of necessary assumptions and standards. One important assumption is that the movements in question are being performed with what we would consider proper form through a full range of motion.
Squat depth for all movements is the 12 inches regardless of the individual’s standing height. To address two particularly complex movements, the clean and the snatch, we assume that the receiving position is a full-depth squat as described previously. We also assume that the movements are being performed with exemplary skill, i.e. the individual is not engaging in superfluous movement such as pulling the bar significantly higher than the ultimate receiving height. Finally, it is assumed that the starting positions for the clean and snatch, as well as the deadlift, have the hips somewhat higher than in the squat, but not excessively elevated; these movements started with higher hips will result in somewhat less work because less of the body’s mass is being displaced vertically.
The actual body mass moved has been calculated based on typical body segment mass percentages. For example, we assume that during a squat, none of the foot or lower leg and half of the thigh are lifted; this amounts to 74.44% of total body mass being moved in the squat. A pull-up, on the other hand, amounts to 91.5% of total body mass due to the arms’ far lesser mass in comparison to their lower body counterparts.
Our foundational data were obtained by measuring two individuals, one male and one female, with a six-inch height differential. Using those numbers, we calculated a constant for each movement (two constants if the movement involves travel of both the individual's body and an external weight), which, when multiplied by an individual's height, will approximate the distance of travel of the movement for that individual.
The calculator process is fairly simple: Bodyweight is adjusted for segment percentages and then multiplied by its distance of travel, and the external weight is multiplied by its distance of travel; these figures are then multiplied by the total reps performed to calculate the work performed. The combined work is then divided by the duration of the workout to determine power.
The Results
The output of the calculator will be figures representing the work and power of the athlete during the workout in question. Work will be calculated in joules, kilogram-meters, and foot-pounds. Power will be calculated in watts, horsepower, kilogram-meters/second, and foot-pounds/second.
Check out the calculator here on Catalyst Athletics
| Greg Everett is the owner of Catalyst Athletics, publisher of The Performance Menu Journal and author of Olympic Weightlifting: A Complete Guide for Athletes & Coaches, Olympic Weightlifting for Sports, and The Portable Greg Everett, and is the writer, director, producer, editor, etc of the independent documentary American Weightlifting. Follow him on Facebook here. |
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