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Metabolic Equations ACSM Formulas

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**Conversion Factors used in Metabolic Calculations**

1 KG= 2.2 lb 160 lb/2.2=72.7 kg kgX 2.2=132 lb 1 mph= 26.8 meters per minute 6.0 mph x 26.8 = m.min

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**Conversions, cont. Min/mile pace= 60 min/mph 1 L = 1000 ml**

60 min/7mph= 8.6 min/mile or 8:36 min:sec/mile 60 sec x 0.6 min= 36 sec 1 L = 1000 ml 1 L of O2= 5 kcal 1 MET = 3.5 ml . Kg . Min 1 MET = 1 kcal . Kg . Hr 1 Watt= 6 kgm.min 540 kgm/6 = 90 Watts kgm.min= kg x 6 x rpm (monark cycle)

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**Metabolic terms: Absolute VO2= rate of O2 uptake in Liters/min.**

Relative VO2= rate of O2 uptake in ml/kg/min. Used to compare VO2 between individuals of different body size. Gross VO2= total consumption of O2 under any circumstances Net VO2= O2 consumption rate above resting O2 consumption rate. Used to describe the caloric cost of exercise

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**ACSM Leg Ergometry Equation:**

For power outputs between kgm/min, or watts VO2= (1.8 x kgm/min)/ M (wt. in kg) + (7) Or VO2= (10.8 x watts) / M (wt. in kg) + (7)

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**ACSM Leg Ergometry Equation**

To calculate the energy expenditure of a 62 kg woman cycling at a work rate of 450 kgm.min:

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**VO2= (1.8 x 450)/ 62 + 7 VO2= 810/62 + 7 VO2= 13 + 7 VO2= 20 ml/kg/min**

To calculate the energy expenditure of a 62 kg woman cycling at a work rate of 450 kgm.min: VO2= (1.8 x 450)/ VO2= 810/62 + 7 VO2= VO2= 20 ml/kg/min

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ACSM Walking Equation For speeds of m/min. ( mph) VO2= Resting Component + Horizonal Component + Vertical Component R= 3.5 ml. kg. min. H=speed (m/min) X 0.1 V=grade (decimal) X m/min X 1.8 VO2= (0.1 x S) + (1.8 x S x G) + 3.5 (H) (V) (R)

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ACSM Walking Equation Calculate VO2 for a 70 kg subject who is walking on the treadmill at a speed of 3.5 mph and a grade of 10%:

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Calculate VO2 for a 70 kg subject who is walking on the treadmill at a speed of 3.5 mph and a grade of 10%: 1. Convert speed in mph to m.min (3.5 x 26.8= 93.8) 2. Calculate horizontal component. H = speed (m.min) x 0.1 (93.9 x 0.1 = 9.38 ml.kg.min 3. Calculate vertical component: V= grade (decimal) x speed x 1.8 (.10 x 93.8 x 1.8= ml.kg.min 4. Calculate total VO2 by adding H, V, and R (resting) components: VO2= H + V + R ( )= ml.kg.min Convert VO2 to METS by dividing by 3.5: (29.76/3.5 = 8.5 METS How many kcals burned in 20 minutes?

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**ACSM Running/Jogging Formula**

For speeds > 134 m/min (>5.0 mph), (or for speeds as low as 3mph if jogging) VO2= Resting Component + Horizontal Component + Vertical Component R= 3.5 ml.kg.min H= speed (m/min) X 0.2 V= grade (decimal) X m/min X 0.9 VO2= (0.2 x S) + (0.9 x S x G) + 3.5 (H) (V) (R)

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**ACSM Jogging/Running Formula**

Calculate VO2 for someone running a 7.5 mph. (200 meters/min) With a 5% grade?

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**For uphill running, add: grade (decimal) x m/min x 0.9 **

Calculate VO2 for someone running at 7.5 mph. (200 meters/min) With a 5% grade? VO2= 3.5+ (m/min X 0.2) 43.5= (200 x 0.2) For uphill running, add: grade (decimal) x m/min x 0.9 VO2= (200 x 0.2) + (.05 x 200 x 0.9) VO2= 52.5

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**What is the total amount of work on a cycle ergometer**

Kpm/min Joules With 2-kg resistance, 6 m•rev–1, 60 rev•min–1 for 5 min

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**With 2-kg resistance, 6 m•rev–1, 60 rev•min–1 for 5 min**

2 kg needs to go to N X 9.79 = 19.58 19.58 x 6m/rev x 60 revs/min x 5 min 35244 Joules For kpm/min – use 2 kg and do not convert to N 3600 kpm/min

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**Calculate the avg. power output during 10 min of cycle ergometer**

Exercise in which a total of 10,000 kpm of work was performed Answer in kpm/min and Watts

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**Calculate the avg. power output during 10 min of cycle ergometer**

exercise in which a total of 10,000 kpm of work was performed. Answer in kpm/min and Watts Work = Force X Distance Power = Force X Distance divided by time 10,000 kpm of work Divide by 10 min 1,000 kpm/min 1,000/6 = Watts 1 Watt = 6 kgm/min

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Calculate the work during 2-min of treadmill exercise by a 60-kg person running at 200 meters/min up a 10 % grade.

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Calculate the work during 2-min of treadmill exercise by a 60-kg person running at 200 meters/min up a 10 % grade. Vertical displacement = % grade x distance 0.1 x (200 m•min–1 x 2 min) = 40 m Work = body weight x total vertical distance 60 kg x 9.79 = N 587.4 N x 40 m = J Power = work ÷ time 23496 J ÷ 120 s = W

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