Scott K. Powers • Edward T. Howley
Theory and Application to Fitness and Performance
SEVENTH EDITION
Chapter
Measurement of Work, Power,
and Energy Expenditure
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.
Chapter 6
Objectives
1. 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.
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Chapter 6
Objectives
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.
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Chapter 6
Outline
 Measurement of
Energy Expenditure
 Units of Measure
Metric System
SI Units
Direct Calorimetry
Indirect Calorimetry
 Work and Power
Defined
 Estimation of Energy
Expenditure
Work
Power
 Calculation of
Exercise Efficiency
Factors That Influence
Exercise Efficiency
 Running Economy
 Measurement of Work
and Power
Bench Step
Cycle Ergometer
Treadmill
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Units of Measure
Chapter 6
Units 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
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Units of Measure
Chapter 6
Common Metric System Prefixes
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Units of Measure
Chapter 6
Important SI Units
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Units of Measure
Chapter 6
In 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.
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Work and Power Defined
Chapter 6
Work
• 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
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Chapter 6
Work and Power Defined
Common Units Used to Express Work
Performed or Energy Expenditure
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Work and Power Defined
Chapter 6
Power
• 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
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Chapter 6
Work and Power Defined
Common Units Used to Express Power
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Measurement of Work and Power
Chapter 6
Measurement of Work and Power
• Ergometry
– Measurement of work output
• Ergometer
– Device used to measure work




Bench step ergometer
Cycle ergometer
Arm ergometer
Treadmill
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Chapter 6
Measurement of Work and Power
Ergometers used in the Measurement of
Human Work Output and Power
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Figure 6.1
Measurement of Work and Power
Chapter 6
Bench 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
685 N x 150 m = 102,795 J (or 102.8 kJ)
• Power = work ÷ time
102,795 J ÷ 600 s = 171.3 W
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Measurement of Work and Power
Chapter 6
Cycle 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
14.7 N x 6 m•rev–1 x 60 rev•min–1 x 10 min = 52,920 J
• Power
52, 290 J ÷ 600 s = 88.2 W
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Measurement of Work and Power
Chapter 6
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
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Chapter 6
Measurement of Work and Power
Determination of Percent Grade on a
Treadmill
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Figure 6.2
Chapter 6
Measurement of Work and Power
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
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Chapter 6
Measurement of Work and Power
In 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
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Measurement of Work and Power
Chapter 6
Measurement of Energy Expenditure
• Direct calorimetry
– Measurement of heat production as an indication of
metabolic rate
Foodstuffs + O2  ATP + heat
cell work
Heat
– Commonly measured in calories
 1 kilocalorie (kcal) = 1,000 calories
 1 kcal = 4,186 J or 4.186 kJ
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Chapter 6
Measurement of Work and Power
Diagram of a Simple Calorimeter
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Figure 6.3
Measurement of Work and Power
Chapter 6
Measurement of Energy Expenditure
• Indirect calorimetry
– Measurement of oxygen consumption as an
estimate of resting metabolic rate
Foodstuffs + O2  Heat + CO2 + H2O
 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
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Measurement of Work and Power
Chapter 6
Open-Circuit Spirometry
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Figure 6.4
Chapter 6
Measurement of Work and Power
In 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.
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Chapter 6
Estimation of Energy Expenditure
Estimation 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
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Chapter 6
Estimation of Energy Expenditure
The Relationship Between Walking or
Running Speed and VO2
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Figure 6.5
Estimation of Energy Expenditure
Chapter 6
A Closer Look 6.1
Estimation of the O2 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:
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
– Vertical VO2:
1.8 ml•kg–1•min–1 x 80 m•min–1 x 0.05 = 7.2 ml•kg–1•min–1
– Total VO2:
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)
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Estimation of Energy Expenditure
Chapter 6
A Closer Look 6.2
Estimation of the O2 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:
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
– Vertical VO2:
0.9 ml•kg–1•min–1 x 160 m•min–1 x 0.05 = 7.2 ml•kg–1•min–1
– Total VO2:
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)
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Chapter 6
Estimation of Energy Expenditure
Relationship Between Work Rate and
VO2 for Cycling
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Figure 6.6
Estimation of Energy Expenditure
Chapter 6
A Closer Look 6.3
Estimation of the O2 Requirement of
Cycling
• 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:
VO2 (ml•kg–1•min–1) = 1.8 x work rate x M–1 + 7
 Work rate in kpm•min–1
 M = body mass in kg
 7 = sum of resting VO2 and VO2 of unloaded cycling
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Chapter 6
Estimation of Energy Expenditure
In 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).
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Chapter 6
Calculation of Exercise Efficiency
Calculation of Exercise Efficiency
• Net efficiency
– Ratio of work output divided by energy expended
above rest
Work output
% net efficiency =
x 100
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
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Chapter 6
Calculation of Exercise Efficiency
Factors 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
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Chapter 6
Calculation of Exercise Efficiency
Net Efficiency During Arm Crank
Ergometery
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Figure 6.7
Chapter 6
Calculation of Exercise Efficiency
Relationship Between Energy
Expenditure and Work Rate
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Figure 6.8
Chapter 6
Calculation of Exercise Efficiency
Effect of Speed of Movement of Net
Efficiency
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Figure 6.9
Chapter 6
Calculation of Exercise Efficiency
In 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.
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Running Economy
Chapter 6
Running 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
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Running Economy
Chapter 6
Comparison of Running Economy
Between Males and Females
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Figure 6.10
Running Economy
Chapter 6
In 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.
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Chapter 6
Study Questions
1.
Define the following terms:
a. work
b. power
c. percent grade
d. relative VO2
e. net efficiency
f. metric system
g. SI units
2.
Calculate the total amount of work performed in five minutes
of exercise on the cycle ergometer, given the following:
Resistance on the flywheel = 25 N
Cranking speed = 60 rpm
Distance traveled per revolution = 6 m
3.
Compute total work and power output per minute for ten
minutes of treadmill exercise, given the following:
Treadmill grade = 15%
Horizontal speed = 200 m•min–1
Subject’s weight = 70 kg
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Chapter 6
Study Questions
4.
Briefly, describe the procedure used to estimate energy
expenditure using (a) direct calorimetry and (b) indirect
calorimetry.
5.
Compute the estimated energy expenditure during
horizontal treadmill walking for the following examples:
a. Treadmill speed = 50 m•min–1
Subject’s weight = 62 kg
b. Treadmill speed = 100 m•min–1
Subject’s weight = 75 kg
c. Treadmill speed = 80 m•min–1
Subject’s weight = 60 kg
6.
Calculate the estimated O2 cost of horizontal treadmill
running for a 70-kg subject at 150, 200, and 235 m•min–1.
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Chapter 6
Study Questions
7.
8.
9.
Calculate net efficiency, given the following:
Exercise VO2 = 3.0 L•min–1
Resting VO2 = 0.3 L•min–1
Work rate = 200 W
Calculate the power output during one minute of cycle
ergometer exercise, given the following:
Resistance on the flywheel = 50 N
Cranking speed = 50 rpm
Distance traveled per revolution = 6 m
Calculate the total work performed during ten minutes of
cycle ergometer exercise, given the following:
Resistance on the flywheel = 20 N
Cranking speed = 70 rpm
Distance traveled per revolution = 6 m
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.
Chapter 6
Study Questions
10. Calculate net efficiency, given the following:
Resting VO2 = 0.3 L•min–1
Exercise VO2 = 2.1 L•min–1
Work rate = 150 W
11. Compute power output for three minutes of treadmill
exercise, given the following:
Treadmill grade = 10%
Horizontal speed = 100 m•min–1
Subject’s weight = 60 kg
12. Calculate the power output (expressed in watts) for a
subject who performed ten minutes of cycle ergometer
exercise, given the following:
Resistance on the flywheel = 20 N
Cranking speed = 60 rpm
Distance traveled per revolution = 6 m
13. Compute the oxygen cost of cycling at work rates of 50, 75,
100, and 125 W for a 60-kg person.
Copyright ©2009 The McGraw-Hill Companies, Inc. All Rights Reserved.