Energy Units

Biologists are concerned with energy flows over a wide range of scales, from a single bacterium to the whole earth. Here are some useful conversion factors and some tables of data illustrating biological energy problems.

Units of Force

• newton = kilogram-meter/sec^2
• dyne = gram-centimeter/sec^2
• newton = 100,000 dynes = 0.225 lb
• It is appropriate that 1 newton is approximately the force needed to hold up an apple against gravity (Keith Frayn. Metabolic Regulation. London: Portland Press, 1996).

Units of Pressure

• Pressure at sea level is referred to as an atmosphere. This pressure will push up the column of mercury in a barometer 760 millimeters
• pascal = newton/meter^2
• atmosphere = 760 mm Hg = 14.7 lbs/sq inch = 101,300 pascals
• 1 bar = 100,000 pascals (used in meteorology)

Units of Energy & Work

• joule = kilogram-meter^2/sec^2 = 10 million ergs
• erg = gram-centimeter^2/sec^2
• A calorie will raise the temperature of 1 gm water by 1 degree C
• A Calorie (used by nutritionists) = 1000 calories = 1 kilocalorie
• 1 calorie = 4.186 joules
• 1 BTU (British thermal unit) will raise the temperature of 1 lb water 1 degree F
• 1 BTU = 252 calories
• 1 foot-pound = 1.356 joules
• 1 barrel of oil is equivalent to 1.46 million kilocalories or 6.1 billion joules
• therm = 100,000 BTUs (this unit is used in the insulation and power businesses. Your gas bill uses the therm unit)
• 1 kilowatt-hour = 3414 BTUs (your electric bill uses the kilowatt hour unit)

Units of Power

• watt = joule/sec
• kcal/min = 1440 kcal/day = 69.8 watts
• 1 kilowatt = 20,630 kcal/day
• horsepower = 550 ft-lb/sec = 746 watts
• Exercise physiologists use a unit called the MET. A MET is the oxygen uptake of 3.5 ml per kilogram per minute. For a 60 kg person it is 210 ml O2/min. Energy production in animals is related to oxygen consumption. The amount of energy depends upon the type of fuel being oxidized (carbohydrate, fat, protein), but a good average figure is 4.82 kcal per liter of oxygen consumed. Using this figure, the 60 kg person has a power output of:

Power output (1 MET) = (0.21 L O2/min)(4.82 kcal/L O2) = 1.01 kcal/min

Energy for Bacterial Growth

 % Dry Weight Approx. MW Molecules per Cell Molecules Synthesized per Second ATPs used per Second %Total Energy for Synthesis DNA 5 2 billion 1 .00083 60,000 2.5 RNA 10 1,000,000 15,000 12.5 75,000 3.1 Protein 70 60,000 1,700,000 1,400 2,120,000 88.0 Lipid 10 1,000 15,000,000 12,500 87,500 3.7 Sugars 5 200,000 39,000 32.5 65,000 2.7

These figures were calculated by Albert L. Lehninger for the E. coli bacterium, which has a division time of 20 minutes. Every 20 minutes during growth the cell must make all of the components needed for a new cell.The biosynthesis requires 2,400,000 molecules of ATP and 400,000 molecules of oxygen every second. Note that almost 90% of the ATP energy goes into making new proteins. From: Albert Lehninger. Biochemistry: the Molecular Basis of Cell Structure and Function. NY: Worth Publishing, 1975.

Energy for Hummingbird Migration

Some ruby-throated hummingbirds do non-stop migration flight across the Gulf of Mexico for 800 kilometers (about 500 miles). The flight takes 10 hours, a speed of 80 km/hr (50 mph). It is amazing because the bird weighs only 3 to 4 grams (a little more than a penny). This weight must include both the flying machine and the fuel.

During flight the birds use about 250 ml of O2 per hour. The energy required can be calculated from the oxygen consumption:

Power = (0.25 liters O2/hr)(4.82 kcal/liter O2) = 1.2 kcal/hr

Total energy required = (1.2 kcal/hr)(10 hrs) = 12 kcal

The amount of fuel required can be calculated by assuming that the hummingbird stores the energy as fat at 9 kcal/gm:

Fat required = (12 kcal)/(9 kcal/gm) = 1.3 gm

If the energy were stored as carbohydrates (glycogen) 3.0 gm would be needed, plus some extra water that glycogen carries with it. About 3 times more fuel weight would be required. This is why migrating animals store energy as fat instead of carbohydrates. Hummingbird data is from: Oliver Pearson. The metabolism of hummingbirds. Scientific American, January, 1953, p. 69-72.

Energy Stores of the Human Body

 Storage Form Amount kg Energy Stored kcal Time of Use min at 3 mph Miles at 3 mph ATP & Creatine Phosphate ATP = 0.1 CP = 0.15 10 3 0.15 Glycogen 0.425 1700 510 25 Fat (triglycerides) 15 135,000 40300 2015

In addition to these molecules the body can burn protein for energy. There is 10-15 kg of protein in the body, giving a potential of another 40,000 to 60,000 calories. Much of the protein is required for cell structure and function, however, so it is not clear how much protein is available for energy. Data from:

Peter Hochachka & George Somero. Biochemical Adaptation. Princeton University Press, 1984, chapter 4.
George Brooks & Thomas Fahey. Fundamentals of Human Performance. NY: Macmillan, 1987, chapter 1.

Power Output for Human Walking and Running

 Velocity mph Velocity meters/min Oxygen Consumption mL/min Power kcal/min Power watts 0 0 210 1.01 70 2 54 530 2.57 179 3 81 700 3.35 233 4 107 850 4.11 286 5 134 1820 8.76 610 6 161 2140 10.3 719 7.5 201 2630 12.7 883 10 268 3430 16.5 1150 15 403 5050 24.3 1690

Values from 0 to 4 mph are for walking. For 5 mph and above figures are for running. Calculations are for a 60 kg person.This person will use 1440 kcal each day at rest. If she walks 2 miles/day this will add 94 kcal to her energy use. If she were to run the 2 miles she would add 188 kcal (running costs twice as much as walking in energy). Figures are calculated from equations in: American College of Sports Medicine. Guidelines for Exercise Testing and Prescription, 4th edition. Philadelphia: Lea & Febiger, 1991, p. 285-300.

Power Costs of Human Activities

This table gives a picture of relative energy costs of common activities. A MET is 0.0169 kcal per min per kilogram. To calculate your energy output multiply the MET figures by 0.169 and your weight in kilograms. Suppose y
 Activity Energy Cost METs Sleep, watching TV while lying 0.9 Reclining or sitting while talking, writing, reading, kissing 1 to 2 Standing quietly 1.2 Light home activities: cooking, dish washing, watering lawn 1.5 to 2.5 Office work 1.5 to 2.5 Driving car 2 Playing music 2 to 3 Light carpentry, plumbing, electrical work 3.5 Walking 3 mph 3.5 Bicycling, leisurely 4 to 6 Painting, remodeling 4.5 to 5 Playing baseball 5 Dancing 5 to7 Carrying groceries, boxes, furniture 6 to 8 Backpacking, cross country skiing 7 to 9 Playing basketball, football 8 to 9 Digging ditches, carrying bricks 8 to 9 Running 6 mph 10 Fast rope jumping 12 Running, 8 mph 13.5 Running, 10 mph 16
ou are backpacking (8 METs) and weight 70 kg:

Power = (0.0169 kcal/min-kg)(8)(70 kg) = 9.46 kcal/min = 660 watts

These figures are from: Barbara Ainsworth, William Haskell, Arthur Leon, David Jacobs, Jr., Henry Montoye, James Sallis & Ralph Paffenbarger, Jr. Compendium of physical activities: classification of energy costs of human physical activities. Medicine and Science in Sports and Exercise 25: 71-80, 1993.

I question 2 of the figures from the Ainsworth table. Sexual activity ("active, vigorous effort") is given only a 1.5 MET rating, while showering is given a value of 4.0 METs! I wonder if they mixed up the 2 values.

Human Power Limits

 Activity Duration Power watts Power kcal/min Energy Used Power X Time kcal Single vigorous jump or lift < 1 sec 4500 64 1 Sprint 20 sec 2200 32 10 Mile run 5 min 1100 16 80 Marathon 2 hr 400 5 600 Manual labor 10 hr 150 2 1200 Rest 24 hr 75 1 1440

The maximum power the body can produce is seen in jumping or in rapidly lifting heavy weights. We can sustain this level of activity for a second or less ("the harder one works the sooner one must stop" Bent). If we cut down the power output we can go for a longer period of time. Power output of the body is determined by the amounts of different energy stores and by the enzymes that release the energy. ATP and creatine phosphate can be broken down very rapidly (high power), but the total amount is small. Burning of fats for energy is very slow (low power), but there are huge amounts.

The table comes from: Henry A. Bent. Energy and exercise. I: How much work can a person do? Journal of Chemical Education 55: 456-458, 1978.

Use of Energy in Human Society

In addition to metabolism of food we use energy, mostly in the form of fossil fuels derived from living creatures, for industry and transportation. Use of energy varies widely from country to country. In the US we use about 42 barrels of oil equivalent per capita every year, while in India, Nigeria and the Phillipines the amount is 2 to 3 barrels per capita per year.

Using the conversion factors from above (a barrel of oil is equivalent to 6.1 million joules) it is easy to convert the 42 barrels/year into watts or calories/day:

(42 barrels/yr)(6.1 billion joules/barrel)/(365 days/yr) = 702 million joules/day

(702 million j/day)/(4.18 j/cal)(1000 cal/kcal) = 168,000 kcal/day = 8140 watts

A fairly good estimate for the average power output of a human is 100 watts. Comparing this with the figure for industrial energy use we see that industrial user is about 80 X the metabolic energy use. In a sense each of us has 80 energy servants working for him continuously. For further information on this subject see the September 1990 special issue of Scientific American (Energy for Planet Earth).

Energy Budget of the Earth