TEACHER'S GUIDE

HUMAN HORSEPOWER


A STUDY OF THE POWER OUTPUT IN A PUSHUP

INTRODUCTION:

Power is the rate at which work is done. In order to estimate the horsepower output during an exercise, we must know how much work is done during a time interval. The work done is the product of the force exerted and the distance the force is exerted over.

POWER = WORK/TIME = FORCE X DISTANCE/TIME

There are usually two components to the total force exerted during an exercise motion. The first component is the force needed to overcome gravity. This component is calculated as the product of the mass being moved and the acceleration due to gravity. If there is any acceleration in the motion, then there is a second component to the total force. This component is calculated as the product of the mass being moved and its acceleration.

FORCE #1(N) = MASS(kg) X 9.8 (m/s/s)

FORCE #2(N) = MASS(kg) X ACCELERATION(m/s/s)

NET FORCE = F#1 + F#2 = MASS X 9.8 + MASS X ACCELERATION

Fnet = Mass X ( 9.8 + Acceleration)

Determining the mass being accelerated during an exercise requires ingenuity. Careful analysis of the motion of the body and any equipment (ie. barbells or weight machine parts) will allow you to estimate this mass. Your analysis of this mass estimate must be carefully presented to convince others of the accuracy of your power estimation. For example, in a pushup the hands and arms are supporting some portion of the total body mass. Ask the subjects to assume the pushup position with their hands placed on an accurate scale. Compare the readout of the scale at the upper and lower positions of the pushup. Describe why you decided to use a particular mass and address the significance of any error introduced by this estimate in the error analysis of your conclusions section.

The acceleration of the mass can be measured accurately using a sonic motion detector. Be sure that the detector tracks the best linearapproximation of the movement of the mass. For a pushup we can position the detector above the shoulders of the subject to track their vertical motion. In other exercises the best tracking may require other orientations. Your choice of tracking position should be discussed in the error analysis section of your conclusions

Since the force exerted at any point during an exercise can vary, we should look at the total work done as the sum of many individual increments of work, each the product of a forces operating over a small increment of distance.

WORK = F1 X d1 + F2 X d2 + F3 X d3........

or

WORK = Si=1->n(Fnet X Dd)i

or

WORK = Si=1->n(mass X (9.8 + acceleration) X Dd)i

Since power is work divided by time, the power over any small increment of distance is the work done in that increment divided by the increment of time to complete that work:

POWER in that increment = Work in that increment / DTime

POWER = mass X (9.8 + acceleration in that increment) X Dd / Dt

If we consider the increment of distance that the mass moves during that increment of time, then we are really looking at its velocity during that time. Then substituting Dd/Dt=v, the equation for power becomes:

POWER = mass X (9.8 + acceleration) X velocity

The motion detector allows us to track both the velocity and acceleration at any time during the exercise. Since each subject will have a different mass being accelerated, this should be measured and recorded for each exercise. The power formula can be input into a new column using the subject's accelerated mass and referencing it to the acceleration and velocity as shown above. This will allow real time tracking of the power output during all phases of the exercise.

We can convert the power output in watts to horsepower units using the equality : 1Hp = 746 watts. We will set up a new column with the formula:

Horsepower = Power(watts) / 746

We will be estimating the horsepower of several subjects in the project. In order to compare the power output of different subjects we will be calculating their power vs mass ratio. Set up a new column with the formula:

POWER to MASS ratio = POWER(watts) / TOTAL MASS (kg)

PROCEDURE:

Set up the motion detector in a secure stand about 1.5 meters above the shoulders of the subject.

Using a floor scale determine the mass of the subject supported by the hands and arms while in the pushup position. Also determine the total mass of the subject. Record both of these masses for the subject.

Plug the motion detector into port#2 of the ULI and connect the ULI to the modem port of the Macintosh computer.

Open the Macmotion program from the Vernier software folder. Set up new columns for Power , Horsepower , Power to mass ratio as described in the introduction. Be sure that the subject's masses are entered into the appropriate formulae. Save the file with the name of the subject and date.

Open the Collect menu and pull down to set up "configure distance probe" selection. Click on the choice " distance away is negative" . This will make motion toward the detector positive and the upward portion of the pushup will be positive power output. We will however have to make a new column to view the distance as a positive quantity. More on that later.

Position the subject under the motion detector. Remind them that their job is to do pushups as fast as possible. Set the time axis to 45 seconds and start collecting data as you tell the subject to start exercising.

The distance data recorded by the motion detector will show distances with a negative sign. Select analyze data from the analyze menu and determine the average value of the most negative(down) positions in the cycles of pushups. Record that value and set up a new column for corrected distance by subtracting that value from the distance measurements. This does not affect the other columns in the program, it merely moves the distance graph up above the x-axis so that it corresponds to the subjects movements relative to the floor. We can now see the performance characteristics at different parts of the pushup more easily.

Save the data under the subject's name and date. To get ready for the next subject's data, you can use the previous person's data as a template. Just modify the Power, and power to mass ratio columns using the data menu to account for the different accelerated mass and total mass of the new subject. Then choose "save as" from the file menu and rename the file with the new subject's name and date.

Select any data before or after the subject did the exercise and clear it out using the "clear selected data" selection from the edit menu.

Open Excel, or other spread sheet, and enter the peak power and the time of the peak for each cycle of the exercise. Name the columns "Powerdate" and "timedate". Plot peak power vs time. This curve will give us an estimate of the endurance and fatigue rate of the subject. Save this spread sheet under the subject's name.

STUDENT'S DATA:

In this section of your report include the following graphs for each subject:

1) Power vs time for the whole exercise

2) A two graph display of distance corrected vs time and power vs time for a selected series of pushups.

3) Power vs distance corrected ( the performance envelope)

4) Peak power per cycle vs time ( the endurance curve)

STUDENT'S ANALYSIS:

Performance analysis:

In this section of your report you should select the data from a series of four or five pushups the have similar power curves. Compare the power vs time curve to the distance corrected vs time curve using the "two graphs" selection from the display menu. Describe how the changes in the power curve relate to the distance curve through one cycle of a typical pushup. Focus on the shape, maximum, minimum, and slopes of the power curve. Set up a single graph of power vs distance(corrected). This graph produces what we could call a performance envelope for the subject for that exercise. Use what you learned from the previous analysis to interpret the information from this graph. Discuss the shape, maximum, minimum, and slopes of the peak power vs time curve from the spread sheet. Discuss the physical significance of these graphs.

Biomechanical Analysis:

Identify the major muscle groups and bones involved in the pushup. Draw a diagram of the basic positions involved in the movement. Determine when each muscle is at full extension and at full contraction. Describe how the leverage and mechanical advantage changes for each joint. Relate this analysis to the performance analysis above.


STUDENT'S ASSIGNMENT:

1) Over the next 12 weeks of the football season we will perform weekly tests on the selected players. Your assignment as a class is to track the performance of the players for the pushup exercise. It would be great if this report was in the form of a set of hyperstudio stacks.

2) Your individual assignment is to design an experiment to analyze the power output and performance characteristics of subjects doing another different exercise. Identify the major muscle groups and bones involved and do a biomechanical analysis of that exercise.

3) Your individual assignment is to prepare an individual report analyzing the performance tests for your exercise on the selected players. You can get extra credit if you agree to track the players' performance on this exercise over the training season.






TEACHERS NOTES:

1) This lab is presented with much of the analysis done in detail in the introduction. Much of this might be better developed by the students with your guidance in a discovery mode.

2) My classes work with their football team as subject in a long term training study. this begins before school a continues through the season. We get great cooperation from the coaches and players when we share the analysis with them and they see some value in the ongoing study.

3) This lab could also be done by collecting the data with a motion detector attached to a CBL, or any interface, and then copying the data into a spreadsheet. Once in the spreadsheet the calculated columns of Power, Horsepower, Power to mass ratio, and Peak Power per cycle vs time can be set up.

SAMPLE GRAPHS:


SAMPLE GRAPHS FROM EXCEL SPREADSHEET