Is fanning yourself energy-efficient?

Una replies:

Isn’t it sad how some of the simplest-sounding questions in life are the most difficult to answer? Such as “Why do we die?” “What is time?” and “If it’s a ‘2-minute warning,’ why is there still half an hour left in the game?” Well, this question falls into that category.

What makes things difficult is the large number of variables and assumptions in what is otherwise a basic energy balance problem. In theory, all we need to do is find two things:

1. The rate of heat removed by the fanning process.
2. The rate of heat created in the body by the fanning process.

If the heat created in the body by fanning is greater than the heat removed by the fanning, then you’ll experience a net heat gain – and if the reverse is true, a net heat loss. As we’ll see, you can arrive at many different results depending upon your starting assumptions. There’s also a difference between being physically cooler and having the perception of being cooler, but in this article I’ll focus only on the physical heat transfer aspects of the fanning process. Since this is the Straight Dope rather than Highlights for Children, we’ll assume you have enough on the ball not to freak when you see an equation or two.

The most significant modes of heat transfer between you and your environment when subjected to moving air (we call this forced convection, as opposed to free convection) are:

1. Conduction by direct contact with the environment (Cond)
2. Forced convection by air moving over your skin (Conv)
3. Evaporation of sweat from your skin (Esweat)
4. Evaporation of moisture in your exhaled breath (Ebreath)
5. Radiation of heat to or away from you (Radiation).

The heat you generate when fanning depends on:

1. Your base metabolic rate (Met)
2. The heat produced by fanning above the base metabolic rate (Fanning Work)

So the heat balance between you and your environment can be expressed as:

Heat Storage = Met + Fanning Work − Cond − Conv − Esweat − Ebreath − Radiation (Ref. 3)

Heat Storage simply tells us whether you’re getting hotter or colder. If Heat Storage is positive, then the body is producing more heat than is being removed, so your body temperature should increase. If Heat Storage is negative, then your body temperature should decrease. In order for fanning to cool you, the following must be true:

Met + Fanning Work < Conduction + Convection + Esweat + Ebreath + Radiation

Now for some simplifications. We’ll only consider convection and evaporation, because fanning doesn’t have a significant effect on the rate at which your body radiates or conducts heat. You might breathe faster when fanning, but it’s hard to determine how much, so we’ll assume heat loss due to respiration remains constant. We’ll also make a (big) assumption that your base metabolic rate stays constant during the brief time you’re fanning, and focus only on the additional metabolic heat produced by the work of fanning. Thus, the heat balance relationship above reduces to the following:

Fanning Work < Convection + Esweat

Even when reduced to these three terms the problem is still difficult due to the many variables and assumptions involved. My original write-up for this problem took so many of these factors into account that it was nearly six times as long, causing Little Ed, who edits these articles, to choke and splutter in an embarrassing manner. So as not to tax him or you unnecessarily, I’ve made some additional simplifications and assumptions, not all of which are spelled out here. If you have questions or doubts, pop on over to the Straight Dope Message Board and I’ll dump so much detail on you you’ll wish you’d never been born.

We’ll use two heat transfer equations to approximate the effects of low-speed airflow on human heat transfer:

Forced Convection. For the entire body of a standard worker wearing the customary single layer of work clothing, this is given by:

C = 0.65*Va0.6*(Tsk − Ta)*(0.0042 kcal/min / Btu/hour) (Ref. 6)

where:

C = convective heat transfer, kcal/min

Va = air velocity, feet/minute

Tsk = Mean weighted skin temperature (assumed to be 95 F)

Ta = Ambient air temperature in degrees F.

Sweat Evaporation. This is given by:

E = 2.4*Va0.6*(psk − pa)*(0.0042 kcal/min / Btu/hour) (Ref. 6)

where:

E = evaporative heat loss, kcal/min

Va = air velocity, feet/min

psk = water vapor pressure on the skin (assumed to be 42 mmHg at 95 F skin temperature)

pa = water vapor pressure of ambient air, mmHg

Now it’s time for the Math. Thankfully, if you hate Math, fear Math, or have even retired to a shack in Montana to write a Manifesto Against Math, I’ll do it all for you. Combining and simplifying the two equations above, and including a factor for the percent of the body affected by the fanning process, we come up with:

Q = Va0.6*[0.65*(95F − Ta) + 2.4*(42mmHg − pa)]*(% area of the body affected/100)*(0.0042 kcal/min / Btu/hour)

…where Q is expressed in kcal/min.

To solve this equation we need the ambient temperature, relative humidity, air velocity, and the body area affected. We can make assumptions about temperature and humidity, but how do we determine the air velocity from a hand fan? I could find no good reference at first, and crude experiments at home yielded unsatisfactory results. In some notes for a thermal sciences laboratory I helped teach, I found a cite indicating that a hand fan generates an average air velocity of 600 feet/minute (6.82 mph), which I was able to confirm from another source, so I used that as a first guess.

Next we need to find the body area affected by the fan air flow, as it has a large impact on the predicted cooling rate. Reference 7 gives typical body surface areas for an adult female, which other sources confirmed. All we need now is to plug in a temperature and relative humidity and we can calculate the cooling effect.

To determine how much heat is produced, I looked at industrial tables of metabolic rates for similar physical activities. I assumed one-handed fanning was equivalent to “Work, one arm, light,” which Reference 6 gives as 1.0 kcal/min. A range of 0.7 to 2.5 kcal/min is indicated for this activity, so there’s a sizable margin of error.

Now let’s assume that a young woman is sitting in 85F heat and 40% relative humidity, fanning herself continuously at 6.82 mph with one arm, producing 1 kcal/min of additional heat. Let’s say she’s wearing a strapless summer dress and is able to fan half of her face, neck, upper arms, and chest. This gives us a net cooling rate of 2.85 kcal/min. Since this is more than our heat production of 1.0 kcal/min, fanning makes the woman cooler.

But changes in assumptions can greatly affect the results. For example, a worst-case assumption (low air speed, only the head and neck cooled, 90 F and 50% relative humidity) yields a net cooling rate of only 0.377 kcal/min, which means that fanning would produce more heat than it removes. A best-case assumption (high air speed, half of the front half of the body cooled, 70 F and 10% relative humidity) yields a net cooling rate of 6.91 kcal/min, which is a large amount of cooling relative to the heat produced by fanning.

To show how the cooling rate is affected by three important variables (fan-produced air speed, ambient temperature, and relative humidity), I generated some graphs, assuming that all other variables were held constant at the values indicated above. I also drew lines noting the heat level produced by different assumed efforts.

You may quibble with the assumptions I made and calculate some heat transfer effects differently, but overall I think I’ve shown what’s involved in trying to answer this question. Because it’s a real-life effect that’s affected strongly by many variables, it’s impossible to say conclusively that fanning makes a person hotter or cooler. You have to treat each situation differently if you want the Straight Dope.

References

1. American Society of Mechanical Engineers, ASME Steam Tables, 6th edition, United Engineering Center, New York, NY, 1997.
2. American Society of Heating, Refrigerating, and Air Conditioning Engineers, Inc., ANSI/ASHRAE 55-1992, “Thermal Environmental Conditions for Human Occupancy,” 1992.
3. —, ASHRAE Handbook of Fundamentals, 1972 edition, George Banta Co. Publishers, Menasha, Wisconsin, 1972.
4. Huang, Francis F., Engineering Thermodynamics – Fundamentals and Applications, 2nd Edition, Macmillan Publishing Co., New York, NY, 1988.
5. Incropera, Frank P. and De Witt, David P. Fundamentals of Heat and Mass Transfer, 3rd edition, John Wiley and Sons, New York, NY, 1990.
6. American Conference of Governmental Industrial Hygienists, Industrial Ventilation – A Manual of Recommended Practice, 24th edition, Cincinnati, Ohio, 2001.
7. Tanabe, S., Arens, E.A., Bauman, F.S., Zhang, H. and Madsen, T.L., “Evaluating thermal environments by using a thermal manikin with controlled skin surface temperature,” ASHRAE Transactions: 100(1) (1994), 39-48.
8. Fang, Koh Look, Thermal Environment – Identification, Evaluation, & Controls, Institution of Singapore Engineers.
9. Wenger, C. Bruce, Medical Aspects of Harsh Environments, Volume 1, pp 52-64.

Una

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