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## Measurement of Work, Power, and Energy Expenditure

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**Objectives**• Define the terms work, power, energy, and net efficiency. • Give a brief explanation of the procedure used to calculate work performed during: (a) cycle ergometer exercise and (b) treadmill exercise. • Describe the concept behind the measurement of energy expenditure using: (a) direct calorimetry and (b) indirect calorimetry.**Objectives**• Discuss the procedure used to estimate energy expenditure during horizontal treadmill walking and running. • Define the following terms: (a) kilogram-meter, (b) relative VO2, (c) MET, and (d) open-circuit spirometry. • Describe the procedure used to calculate net efficiency during steady-state exercise.**Units of Measure**Metric System SI Units Work and Power Defined Work Power Measurement of Work and Power Bench Step Cycle Ergometer Treadmill Outline • Calculation of Exercise Efficiency Factors That Influence Exercise Efficiency • Running Economy • Measurement of Energy Expenditure Direct Calorimetry Indirect Calorimetry • Estimation of Energy Expenditure**Units of Measure**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**Units of Measure**Common Metric System Prefixes**Units of Measure**Important SI Units**Units of Measure**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.**Work and Power Defined**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**Work and Power Defined**Common Units Used to Express Work Performed or Energy Expenditure**Work and Power Defined**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**Work and Power Defined**Common Units Used to Express Power**Measurement of Work and Power**Measurement 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**Ergometers used in the Measurement of Human Work Output and Power Figure 6.1**Measurement of Work and Power**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 • Power = work ÷ time • 685 N x 150 m = 102,795 J (or 102.8 kJ) • 102,795 J ÷ 600 s = 171.3 W**Measurement of Work and Power**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 • Power 14.7 N x 6 m•rev–1 x 60 rev•min–1 x 10 min = 52,920 J 52, 290 J ÷ 600 s = 88.2 W**Measurement of Work and Power**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**Measurement of Work and Power**Determination of Percent Grade on a Treadmill Figure 6.2**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**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**Measurement of Work and Power**Foodstuffs + O2 ATP + heat cell work Heat Measurement of Energy Expenditure • 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 Work and Power**Diagram of a Simple Calorimeter Figure 6.3**Measurement of Work and Power**Measurement of Energy Expenditure • 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 Foodstuffs + O2 Heat + CO2 + H2O**Measurement of Work and Power**Open-Circuit Spirometry Figure 6.4**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.**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**Estimation of Energy Expenditure**The Relationship Between Walking or Running Speed and VO2 Figure 6.5**Estimation of Energy Expenditure**A Closer Look 6.1Estimation 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: • 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)**Estimation of Energy Expenditure**A Closer Look 6.2Estimation 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: • 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)**Estimation of Energy Expenditure**Relationship Between Work Rate and VO2 for Cycling Figure 6.6**Estimation of Energy Expenditure**A Closer Look 6.3Estimation 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: • 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 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).**Calculation of Exercise Efficiency**Work output % net efficiency = x 100 Energy expended above rest Calculation of Exercise Efficiency • 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**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**Calculation of Exercise Efficiency**Net Efficiency During Arm Crank Ergometery Figure 6.7**Calculation of Exercise Efficiency**Relationship Between Energy Expenditure and Work Rate Figure 6.8**Calculation of Exercise Efficiency**Effect of Speed of Movement of Net Efficiency Figure 6.9**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.**Running Economy**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**Running Economy**Comparison of Running Economy Between Males and Females Figure 6.10**Running Economy**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.**Study Questions**• Define the following terms: a. work e. net efficiency b. power f. metric system c. percent grade g. SI units d. relative VO2 • 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 • 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**Study Questions**• Briefly, describe the procedure used to estimate energy expenditure using (a) direct calorimetry and (b) indirect calorimetry. • 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 • Calculate the estimated O2 cost of horizontal treadmill running for a 70-kg subject at 150, 200, and 235 m•min–1.**Study Questions**• 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 rpmDistance 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 rpmDistance traveled per revolution = 6 m**Study Questions**• Calculate net efficiency, given the following: Resting VO2 = 0.3 L•min–1 Exercise VO2 = 2.1 L•min–1Work rate = 150 W • 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 • 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 rpmDistance traveled per revolution = 6 m • Compute the oxygen cost of cycling at work rates of 50, 75, 100, and 125 W for a 60-kg person.