1. Energy Costs of Physical Activity
chapter 4
Energy Costs of Physical Activity

2. Ways to Measure Energy Expenditure
Direct calorimetry: transfer of body heat to water
Indirect calorimetry: measure VO2 uptake
Convert VO2 to kilocalories: use caloric equivalent of O2 ( kcal . L–1) . .

3. Measuring Oxygen Uptake
Closed-circuit system: Breathe 100% O2.
Open-circuit system: Breathe room air. Measure timed volume of exhaled air. Measure O2 and CO2 content. Calculate VO2 by standard procedures. .

4. Ways to Express Energy Expenditure.
VO2: L · min–1
Kcal · min–1 VO2 (L · min–1) x kcal · L–1
VO2: ml · kg–1 · min–1
METs VO2 (ml · kg–1 · min–1)/3.5 ml · kg–1 · min–1
Kcal · kg–1 · hr–1 . . .

5. Estimating the Energy Cost of Activities
Estimates have a standard deviation of about 7% to 9%.
Estimates represent the steady-state cost of the activity.
Total O2 cost = net cost of activity ml · kg–1 · min–1.

6. Estimating the Oxygen Cost of Walking
Good for speeds from 1.9 to 3.7 mi · hr–1 (50 to 100 m · min–1)
VO2 = [horizontal component] + [vertical (grade) component] + rest. .

7. What Is the Oxygen Uptake of a 176 Lb (80 Kg) Person Walking at 3 mi · hr–1 on a 10% Grade?
Given: 1 mi · hr–1 = 26.8 m · min–1; 1 L O2 = 5 kcal; 1,000 ml = 1 L
3 mi · hr–1 = 80 m · min–1; fractional 10% grade = 0.10
(continued)

8. What Is the Oxygen Uptake of a 176 Lb (80 Kg) Person Walking at 3 mi · hr–1 on a 10% Grade? (continued) .
VO2 = [8 ml · kg–1 · min–1 ] + [14.4 ml · kg–1 · min–1 ] ml · kg–1 · min–1
VO2 = 25.9 ml · kg–1 · min–1. .

9. Estimating the Oxygen Cost of Running.
VO2 = [horizontal component] + [vertical (grade) component] + rest.

10. What Is the Oxygen Uptake for Running at 6 mi · hr–1 (161 m · min–1)?
Note that the vertical component is 0 because the grade is 0.
VO2 = [32.2 ml · kg–1 · min–1]
+ 3.5 ml · kg–1 · min–1
VO2 = 35.7 ml · kg–1 · min–1. . .
(continued)

11. What Is the Oxygen Uptake for Running at 6 mi · hr–1 (161 m · min–1)
What Is the Oxygen Uptake for Running at 6 mi · hr–1 (161 m · min–1)? (continued)
How many METs is that?
35.7 ml · kg–1 · min–1/3.5 ml · kg–1 · min–1 = METs.

12. Oxygen Cost of Cycle Ergometry.
VO2 (ml · kg–1 · min–1) = work + unloaded cycling + rest.
VO2 (ml · kg–1 · min–1) = [1.8 ml · kgm–1 x work rate (kgm · min–1)]/kg ml · kg–1 · min– ml · kg–1 · min–1.
VO2 (ml · kg–1 · min–1) = [1.8 ml · kgm–1 x work rate (kgm · min–1)]/kg + 7 ml · kg–1 · min–1.
In watts (W), where 1 W = approximately 6 kgm:
VO2 (ml · kg–1 · min–1) = [10.8 ml · W–1 x work rate (W)]/kg + 7 ml · kg–1 · min–1. . . .

13. What Is the VO2 of a 198 lb (90 kg) Person Working at 600 kgm · min–1?.
What Is the VO2 of a 198 lb (90 kg) Person Working at 600 kgm · min–1? .
VO2 (ml · kg–1 · min–1) = [1.8 ml · kgm–1 x 600 kgm · min–1]/90 kg + 7 ml · kg–1 · min–1.
VO2 (ml · kg–1 · min–1) = 12 ml · kg–1 · min– ml · kg–1 · min–1.
VO2 (ml · kg–1 · min–1) = 19 ml · kg–1 · min–1. . .

14. Does the Same Work Rate Require a Greater Relative Effort by a 132 lb (60 kg) Person?
VO2 (ml · kg–1 · min–1) = [1.8 ml · kgm–1 x 600 kgm · min–1]/60 kg + 7 ml · kg–1 · min–1.
VO2 (ml · kg–1 · min–1) = 18 ml · kg–1 · min–1 + 7 ml · kg–1 · min–1.
VO2 (ml · kg–1 · min–1) = 25 ml · kg–1 · min–1. . . .

15. Oxygen Cost of Arm Cycle Ergometry.
VO2 (ml · kg–1 · min–1) = work + rest.
VO2 (ml · kg–1 · min–1) = [3 ml · kgm–1 x work rate (kgm · min–1)]/kg ml · kg–1 · min–1.
In watts (W), where 1 W = approximately 6 kgm:
VO2 (ml · kg–1 · min–1) = [18 ml · W–1 x work rate (W)]/kg ml · kg–1 · min–1. . .

16. .
What Is the VO2 for a 110 lb (50 kg) Person Working at 25 W on an Arm Ergometer? .
VO2 (ml · kg–1 · min–1) = [18 ml · W–1 x 25 W]/50 kg ml · kg–1 · min–1.
VO2 (ml · kg–1 · min–1) = ml · kg–1 · min–1 = 12.5 ml · kg–1 · min–1. .

17. Oxygen Cost of Stepping.
VO2 = [stepping back and forth] + [stepping up and down] + rest.
VO2 = [0.2 ml · kg–1 · min–1 x step rate] + [1.8 ml · kgm–1 x 1.33 x height (m) x step rate] ml · kg–1 · min–1. .

18. What Is the Oxygen Cost for Stepping at 30 steps · min–1 on an 8 in
What Is the Oxygen Cost for Stepping at 30 steps · min–1 on an 8 in. Step?
Given: 1 in. = 2.54 cm or m, so 8 in. = 0.2 m.
VO2 = [0.2 ml · kg–1 · min–1 x step rate] + [1.8 ml · kgm–1 x 1.33 x height (m) x step rate] ml · kg–1 · min–1.
VO2 = [0.2 ml · kg–1 · min–1 x 30] + [1.8 ml · kgm–1 x 1.33 x 0.2 m x 30] ml · kg–1 · min–1.
VO2 = [6 ml · kg–1 · min–1] + [14.36 ml · kg–1 · min–1] ml · kg–1 · min–1.
VO2 = 23.9 ml · kg–1 · min–1. . . . .

19. .
What Is the Step Rate Needed to Achieve a VO2 of 30 ml · kg–1 · min–1 on an 8 in. Step?
30.0 = [0.2 x rate] + [1.8 x 1.33 x 0.2 x rate]
26.5 = 0.2 x rate x rate.
26.5 = x rate.
Rate = 26.5 / = 39 steps · min–1.

20. Is the Energy Cost of Walking and Running a Mile the Same?
First determine the costs of each activity, given the information below.
Gross cost includes resting energy expenditure.
Net cost includes the cost of the activity alone.
Resting energy expenditure = 1 kcal · kg–1 · hr–1. For a 160 lb (72.6 kg) person, resting energy expenditure is 1.2 kcal · min–1.

21. Gross Versus Net Cost of Walking
Consider a 160 lb (72.6 kg) person who walks at 3 mi · hr–1 (4.8 km · hr–1 ) for 20 min:
Gross (total) cost per mile = 79 kcal.
Net cost = gross cost – cost of rest for 20 min (24 kcal).
Net cost = 55 kcal · min–1.

22. Gross Versus Net Cost of Jogging or Running
Consider a 160 lb (72.6 kg) person who jogs at 6 mi · hr–1 (9.7 km · hr–1 ) for 10 min:
Gross (total) cost per mile = 123 kcal.
Net cost = gross cost – cost of rest for 10 min (12 kcal).
Net cost = 111 kcal · min–1.

23. Net Caloric Cost per Mile for a 160 lb (72.6 kg) Person
Walking speed
(mi · hr–1 )
Caloric cost (kcal · mi–1)
Jogging/ running speed (mi · hr–1)
Caloric cost (kcal · mi–1) 2 55 3
111
2.5 4 5
3.5 6 70 7
4.5 84 8
100 9

24. Estimated Net Energy Cost of 30 min of Exercise at 70% HRR or VO2R.
Max METs (kcal · kg–1 · hr–1)
70% HRR (kcal · kg–1 · hr–1)
110
154
198
Net energy expenditure (kcals) 18
11.9
298
417
536 14
9.1
228
314
410 10
6.3
158
221
284 6
3.5 88
123
Body weight (lb)