# Fuel Efficiency of a Human: The Energy Impact of Exercise

## Marie Maher December 18, 2011

### Submitted as coursework for PH240, Stanford University, Fall 2011

Of late, there has been a significant drive to encourage people to seek more eco-friendly ways of transportation. Advocates of this cause would point to the fact that human transport (i.e. walking/running/biking) is more energy efficient and inherently fossil-fuel free. While it is undeniably true that the activity itself consumes no fossil fuel and is carbon neutral, there are hidden sources of fossil fuel expenditure embedded within these activities.

## "Fuel Economy" of a Human

Researchers have found that a team of long-distance runners consume an average of 3.5 MJ/h while travelling at a pace of 10.1 km/h (6.25 mi/h). [1] To compare this fuel consumption to a car, we can assume that there are approximately 122 MJ/gal gasoline and convert the human fuel economy to about 220 MPG. [2] In a separate study, researchers determined that the maximal efficiency of a human riding a bicycle was 20%, in terms of energy generated on a stationary bicycle compared to calories burned. [3] They also list the peak power of their study group at 363 W. Assuming that peak power is sustainable (which it almost certainly isn't), then these numbers can then be converted into MPG equivalent by relating to the drag power equation: [4]

Pd = ½ ρ v3 A Cd

The maximal power output must equal the resistive force to maintain constant speed, so using published drag area data allows us to calculate that a peak power of 363 W corresponds to a sustained speed of 8.4 mi/h. [5] Generating 363 W at 20% efficiency requires the consumption of 1815 W, which over a one hour time period consumes the equivalent energy of 0.053 gallons of gasoline, for a fuel economy of 159 MPG. These figures for running and bicycling give the impression that human transportation is a far more fuel efficient compared to an average vehicle; however, that comparison overlooks two major issues: specific fuel consumption and energy cost of fuel production.

## Specific Fuel Consumption of a Human

The power of a runner can be estimated from the above drag power equation using data found in the literature. The average frontal area of a human is 0.55 m2 and the average drag coefficient is 1.16. [6] Assuming an air density of 1.225 kg/m3, the power produced by a runner running at an average speed of 10.1 km/h is 6.75 W. Those same runners consume an average of 967 W while running at that pace (so their efficiency is 0.7%. (Note that this calculation should underestimate power output because it doesn't take into account the energy required to move limbs relative to one another, which doesn't affect wind resistance but is energy put to "useful" work). Based on the specific gravity of gasoline, 0.74, and the above energy content, 967 W over the course of an hour consumes the equivalent of 80g of fuel. [2] Specific fuel consumption is typically cited in units of g/kW-h, so combining our power output over the course of that hour (0.00675 kW-h) with the mass of "fuel" consumed, a human running achieves a specific fuel consumption of 11852 g/kW-h. Analogously, a bicyclist producing 363 W of power consumes the equivalent of 148 g of gasoline, for a specific fuel consumption of 408 g/kW-h. As a point of comparison, the Toyota Prius (model year '04) has a relatively constant specific fuel consumption ranging from 225-250 g/kW-h and a fuel economy of 65.8 MPG. [7] Clearly, running is not an energy efficient means of getting around town, however a bicycle is not that much worse than one of the most fuel efficient vehicles available. Of course, in the Prius you can travel much faster from location to location, and in the event of a collision with another vehicle, you are certainly better protected than a bicycle.

## Fuel Production Energy Expenditure: The Loss Multiplier

A recent European study analyzed the amount of energy required to bring fuel from its crude form and deliver it to the fuel tank of an automobile. In order to determine the most efficient fuel to use, the researchers defined a concept called the "loss multiplier". The loss multiplier is the sum of the energy content of the fuel and the energy expended producing the fuel divided by the energy content of the fuel. For all fuels, the loss multiplier must be greater than 1. The magnitude of the loss multiplier indicates how wasteful the fuel is, with larger numbers being more wasteful. This allows a comparison of the energy required to obtain different fuels normalized to the energy extracted. The researchers list the loss multiplier for gasoline and diesel to be 1.14 and 1.16, respectively. [8] Therefore, in terms of energy economy, we must adjust fuel efficiency numbers to account for the hidden energy losses in the system. For example, a car that has a fuel economy rating of 100 MPG, running on gasoline, would have an adjusted economy of 100/1.14, or 87.7 MPG. Therefore the Prius above has an adjusted fuel economy of 57.7 MPG.

It is also possible to calculate the loss multiplier for human fuel - i.e. food. The Department of Agriculture recently released a report on the energy use in the US food system, claiming that 15.7% of the total annual US energy budget goes to food production, packaging, transport, preparation and disposal. [9] The total US annual energy demand is about 1x1020 J. [10] This means that feeding the US requires an astounding 1.57x1019 J. According to a 1997 study, the average American consumes about 1800 kcals per day. [11] This number reflects data from 1977 and 1987, so for the purposes of calculation, we can assume that Americans consume around the 2000 kcals per day (3.05x109 J/person-year) suggested by federally-required food labels. As of the time of writing this article, the US population is estimated to be around 312,571,000. [12] Therefore, the total annual energy consumed by the population is 9.53x1015 J. If we calculate the loss multiplier from these numbers, we find that the amount of energy tied up in food production, preparation, etc, is 16.5 times the energy contained in the food itself, for a loss multiplier of 17.5. Compared to gasoline, human fuel is extraordinarily inefficient. Therefore, if we go back and adjust the human fuel economy numbers to provide a fair comparison, we find that the runner is achieving 12.6 MPG, and the bicyclist is managing 9.1 MPG.

© Marie Maher. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.

### References

[1] J. M. Wilson et al., "Effects of Static Stretching on Energy Cost and Running Endurance Performance," J. Strength Cond. Res. 24, 2274 (2010).

[2] S. C. Davis, W. S. Diegel and R. G. Boundy, "Transportation Energy Data Book, 30th Edition," Oak Ridge National Laboratory ORNL-6986, June 2011, Appendix B.

[3] T. Korff et al., "Effect of 'Pose' Cycling on Efficiency and Pedaling Mechanics." Eur. J. Appl. Physiol. 111, 1177 (2011).

[4] H. C. Smith, The Illustrated Guide to Aerodynamics (TAB Books, 1992), pp. 65, 119.

[5] T. Defraeye et al., "Computational Fluid Dynamics Analysis of Drag and Convective Heat Transfer of Individual Body Segments for Different Cyclist Positions," J. Biomechanics 43, 2281 (2011).

[6] A. D. Penwarden, P. F. Grigg and R. Rayment, "Measurements of Wind Drag on People Standing in a Wind Tunnel," Building and Environment 13, 75 (1978).

[7] K. Muta, M. Yamazaki and J. Tokieda, "Development of New-Generation Hybrid System THS II - Drastic Improvement of Power Performance and Fuel Economy," in Hybrid Gasoline-Electric Vehicle Development, J. M German, ed. (SAE International, 2005).

[8] M. Simonsen and H. J. Walnum, "Energy Chain Analysis of Passenger Car Transport," Energies 4, 324 (2011).

[9] P. Canning et al., "Energy Use in the U.S. Food System," U.S. Department of Agriculture, ERR-94, March 2010.

[10] A. D. Cuellar and M. E. Webber, "Wasted Food, Wasted Energy: The Embedded Energy in Food Waste in the United States," Environ. Sci. Technol. 44, 6464 (2010).

[11] A. F. Heini and R. L. Weinsier, "Divergent Trends in Obesity and Fat Intake Patterns: The American Paradox," Am. J. Med. 102, 259 (1997).

[12] "Population Projections of the United States by Age, Sex, Race, and Hispanic Origin: 1995 to 2050," U.S. Bureau of the Census, P25-1130, February 1996.