Measurement of Work, Power, and Energy Expenditure

Scott K. Powers • Edward T. HowleyScott K. Powers • Edward T. Howley

Theory and Application to Fitness and PerformanceTheory and Application to Fitness and PerformanceSEVENTH EDITION

Chapter

Presentation prepared by:

Brian B. Parr, Ph.D.University of South Carolina Aiken

Copyright ©2009 The McGraw-Hill Companies, Inc. Permission required for reproduction or display outside of classroom use.

Measurement of Work, Measurement of Work, Power, and Energy Power, and Energy

ExpenditureExpenditure

Chapter 6

Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.

ObjectivesObjectives1. Define the terms work, power, energy, and net

efficiency.2. Give a brief explanation of the procedure used

to calculate work performed during: (a) cycle ergometer exercise and (b) treadmill exercise.

3. Describe the concept behind the measurement of energy expenditure using: (a) direct calorimetry and (b) indirect calorimetry.

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ObjectivesObjectives

4. Discuss the procedure used to estimate energy expenditure during horizontal treadmill walking and running.

5. Define the following terms: (a) kilogram-meter, (b) relative VO2, (c) MET, and (d) open-circuit spirometry.

6. Describe the procedure used to calculate net efficiency during steady-state exercise.

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OutlineOutline

Units of MeasureMetric SystemSI Units

Work and Power DefinedWorkPower

Measurement of Work and PowerBench StepCycle ErgometerTreadmill

Measurement of Energy ExpenditureDirect CalorimetryIndirect Calorimetry

Estimation of Energy Expenditure

Calculation of Exercise EfficiencyFactors That Influence Exercise Efficiency

Running Economy

Chapter 6


Units of MeasureUnits of Measure

• Metric system – The standard system of measurement for

scientists– Used to express mass, length, and volume

• System International (SI) units– For standardizing units of measurement

Units of Measure

Chapter 6


Common Metric System Common Metric System PrefixesPrefixes

Units of Measure

Chapter 6


Important SI UnitsImportant SI UnitsUnits of Measure

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In SummaryIn Summary The metric system is the system of

measurement used by scientists to express mass, length, and volume.

In an effort to standardize terms for the measurement of energy, force, work, and power, scientists have developed a common system of terminology called System International (SI) units.

Units of Measure

Chapter 6


WorkWork• Work = force x distance• In SI units:

– Work (J) = force (N) x distance (m)• Example:

– Lifting a 10-kg (97.9-N) weight up a distance of 2 m• 1 kg = 9.79 N, so 10 kg = 97.9 N

97.9 N x 2 m = 195.8 N-m = 195.8 J

• 1 N-m = 1 J, so 195.8 N-m = 195.8 J

Work and Power Defined

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Common Units Used to Express Work Common Units Used to Express Work Performed or Energy ExpenditurePerformed or Energy Expenditure


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PowerPower

• Power = work ÷ time• In SI units:

– Power (W) = work (J) ÷ time (s)• Example:

– Performing 20,000 J of work in 60 s

20,000 J ÷ 60 s = 333.33 J•s–1 = 333.33 W 1 W = 1 J•s–1, so 333.33 J•s–1 = 333.33 W


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Common Units Used to Express PowerCommon Units Used to Express Power


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Measurement of Work and PowerMeasurement of Work and Power

• Ergometry– Measurement of work output

• Ergometer– Device used to measure work

• Bench step ergometer• Cycle ergometer• Arm ergometer• Treadmill

Measurement of Work and Power

Chapter 6


Ergometers used in the Measurement of Ergometers used in the Measurement of Human Work Output and PowerHuman Work Output and Power

Figure 6.1


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Bench StepBench Step• Subject steps up and down at specified rate• Example:

– 70-kg subject, 0.5-m step, 30 steps•min–1 for 10 min• Total work = force x distance

– Force = 70 kg x 9.79 N•kg–1 = 685.3 N– Distance = 0.5 m•step–1 x 30 steps•min–1 x 10 min = 150

m

• Power = work ÷ time


685 N x 150 m = 102,795 J (or 102.8 kJ)

102,795 J ÷ 600 s = 171.3 W

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Cycle ErgometerCycle Ergometer

• Stationary cycle that allows accurate measurement of work performed

• Example: – 1.5-kg (14.7-N) resistance, 6 m•rev–1, 60 rev•min–1

for 10 min• Total work

• Power

14.7 N x 6 m•rev–1 x 60 rev•min–1 x 10 min = 52,920 J52, 290 J ÷ 600 s = 88.2 W


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Treadmill Treadmill • Calculation of work performed while a subject runs or

walks on a treadmill is not generally possible when the treadmill is horizontal– Even though running horizontal on a treadmill

requires energy• Quantifiable work is being performed when walking or

running up a slope• Incline of the treadmill is expressed in percent grade

– Amount of vertical rise per 100 units of belt travel• 10% grade means 10 m vertical rise for 100 m of

belt travel


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Determination of Percent Grade on a Determination of Percent Grade on a TreadmillTreadmill

Figure 6.2


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Treadmill Treadmill

• Example– 60-kg (587.4-N) subject, speed 200 m•min–1,

7.5% grade for 10 min– Vertical displacement = % grade x distance

0.075 x (200 m•min–1 x 10 min) = 150 m– Work = body weight x total vertical distance

587.4 N x 150 m = 88,110 J– Power = work ÷ time

88,110 J ÷ 600 s = 146.9 W


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In SummaryIn Summary An understanding of terms work and power

is necessary in order to compute human work output and the associated exercise efficiency.

Work is defined as the product of force times distance: Work = force x distance

Power is defined as work divided by time:Power = work ÷ time


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• Direct calorimetry– Measurement of heat production as an

indication of metabolic rate

– Commonly measured in calories• 1 kilocalorie (kcal) = 1,000 calories• 1 kcal = 4,186 J or 4.186 kJ

Measurement of Energy ExpenditureMeasurement of Energy Expenditure

Foodstuffs + O2 ATP + heatcell work

Heat


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Diagram of a Simple CalorimeterDiagram of a Simple Calorimeter


Figure 6.3

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• Indirect calorimetry– Measurement of oxygen consumption as an

estimate of resting metabolic rate

• VO2 of 2.0 L•min–1 = ~10 kcal or 42 kJ per minute

– Open-circuit spirometry• Determines VO2 by measuring amount of O2 consumed

• VO2 = volume of O2 inspired – volume of O2 expired

Measurement of Energy ExpenditureMeasurement of Energy Expenditure

Foodstuffs + O2 Heat + CO2 + H2O


Chapter 6


Open-Circuit SpirometryOpen-Circuit SpirometryMeasurement of Work and Power

Figure 6.4

Chapter 6


In SummaryIn Summary Measurement of energy expenditure at rest

or during exercise is possible using either direct or indirect calorimetry.

Direct calorimetry uses the measurement of heat production as an indication of metabolic rate.

Indirect calorimetry estimates metabolic rate via the measurement of oxygen consumption.


Chapter 6


Estimation of Energy ExpenditureEstimation of Energy Expenditure

• Energy cost of horizontal treadmill walking or running– O2 requirement increases as a linear function

of speed• Expression of energy cost in metabolic

equivalents (MET)– 1 MET = energy cost at rest– 1 MET = 3.5 ml•kg–1•min–1


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The Relationship Between Walking or The Relationship Between Walking or Running Speed and VORunning Speed and VO22

Figure 6.5


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Estimation of the OEstimation of the O22 Requirement of Treadmill Walking Requirement of Treadmill Walking

• Horizontal VO2 (ml•kg–1•min–1)– 0.1 ml•kg–1•min–1/m•min–1 x speed (m•min–1) + 3.5 ml•kg–1•min–1

• Vertical VO2 (ml•kg–1•min–1)– 1.8 ml•kg–1•min–1 x speed (m•min–1) x % grade

• Example: – Walking at 80 m•min–1 at 5% grade

– Horizontal VO2:

Vertical VO2:

– Total VO2:


0.1 ml•kg–1•min–1 x 80 m•min–1 + 3.5 ml•kg–1•min–1 = 11.5 ml•kg–1•min–1

1.8 ml•kg–1•min–1 x 80 m•min–1 x 0.05 = 7.2 ml•kg–1•min–1

11.5 ml•kg–1•min–1 + 7.2 ml•kg–1•min–1 = 18.7 ml•kg–1•min–1

(or 5.3 METs)

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Estimation of the OEstimation of the O22 Requirement of Treadmill Running Requirement of Treadmill Running

• Horizontal VO2 (ml•kg–1•min–1)– 0.2 ml•kg–1•min–1/m•min–1 x speed (m•min–1) + 3.5 ml•kg–1•min–1

• Vertical VO2 (ml•kg–1•min–1)– 0.9 ml•kg–1•min–1 x speed (m•min–1) x % grade

• Example: – Running at 160 m•min–1 at 5% grade– Horizontal VO2:

– Vertical VO2:

– Total VO2:


0.2 ml•kg–1•min–1 x 160 m•min–1 + 3.5 ml•kg–1•min–1 = 35.5 ml•kg–1•min–1

0.9 ml•kg–1•min–1 x 160 m•min–1 x 0.05 = 7.2 ml•kg–1•min–1

11.5 ml•kg–1•min–1 + 7.2 ml•kg–1•min–1 = 42.7 ml•kg–1•min–1

(or 12.2 METs)

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Relationship Between Work Rate and VORelationship Between Work Rate and VO2 2

for Cyclingfor Cycling

Figure 6.6


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• Comprised of three components:– Resting VO2

• 3.5 ml•kg–1•min–1

– VO2 for unloaded cycling • 3.5 ml•kg–1•min–1

– VO2 of cycling against external load • 1.8 ml•min–1 x work rate x body mass–1

• Equation:

• Work rate in kpm•min–1

• M = body mass in kg• 7 = sum of resting VO2 and VO2 of unloaded cycling


VO2 (ml•kg–1•min–1) = 1.8 x work rate x M–1 + 7

Estimation of the OEstimation of the O22 Requirement of Cycling Requirement of Cycling

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In SummaryIn Summary The energy cost of horizontal treadmill

walking or running can be estimated with reasonable accuracy because the O2 requirements of both walking and running increase as a linear function of speed.

The need to express the energy cost of exercise in simple terms has led to the development of the term MET. One MET is equal to the resting VO2 (3.5 ml•kg–

1•min–1).


Chapter 6


• Net efficiency– Ratio of work output divided by energy expended above

rest

• Net efficiency of cycle ergometry– 15–27%

• Efficiency decreases with increasing work rate– Curvilinear relationship between work rate and energy

expenditure

Work outputEnergy expended

above rest

% net efficiency = x 100

Calculation of Exercise EfficiencyCalculation of Exercise EfficiencyCalculation of Exercise Efficiency

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Calculation of Exercise Efficiency

Factors That Influence Exercise EfficiencyFactors That Influence Exercise Efficiency

• Exercise work rate– Efficiency decreases as work rate increases

• Speed of movement– There is an optimum speed of movement and

any deviation reduces efficiency• Muscle fiber type

– Higher efficiency in muscles with greater percentage of slow fibers

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Net Efficiency During Arm Crank Net Efficiency During Arm Crank ErgometeryErgometery


Figure 6.7

Chapter 6


Relationship Between Energy Expenditure Relationship Between Energy Expenditure and Work Rateand Work Rate


Figure 6.8

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Effect of Speed of Movement of Net Effect of Speed of Movement of Net EfficiencyEfficiency


Figure 6.9

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In SummaryIn Summary Net efficiency is defined as the mathematical ratio of

work performed divided by the energy expenditure above rest, and is expressed as a percentage.

The efficiency of exercise decreases as the exercise work rate increases. This occurs because the relationship between work rate and energy expenditure is curvilinear.

To achieve maximal efficiency at any work rate, there is an optimal speed of movement.

Exercise efficiency is greater in subjects who possess a high percentage of slow muscle fibers compared to subjects with a high percentage of fast fibers. This is due to the fact that slow muscle fibers are more efficient than fast fibers.


Chapter 6


Running EconomyRunning Economy• Not possible to calculate net efficiency of horizontal

running• Running Economy

– Oxygen cost of running at given speed– Lower VO2 (ml•kg–1•min–1) at same speed indicates

better running economy• Gender difference

– No difference at slow speeds– At “race pace” speeds, males may be more

economical that females

Running Economy

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Comparison of RunningComparison of Running Economy Between Economy Between Males and FemalesMales and Females

Running Economy

Figure 6.10

Chapter 6


In SummaryIn Summary Although is is not easy to compute efficiency

during horizontal running, the measurement of the O2 cost of running (ml•kg–1•min–1) at any given speed offers a measure of running economy.

Running economy does not differ between highly trained men and women distance runners at slow running speeds. However, at fast “race pace” speeds, male runners may be more economical than females. The reasons for this are unclear.

Running Economy

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Measurement of Work, Power, and Energy Expenditure