While an individual may or may not have a net cooling effect, the ambient temperature in a room full of twitching kids is sure to rise if there is no other cooling method. This effect may be observed in certain ice cream shops, like my local Baskin-Robbins. The ice cream is kept nice and cold in the freezers, but the freezers dump all the waste heat into the rest of the shop, where there is no air conditioning to counter it. The result is that the inside of the shop is sometimes hotter than the outside. Come to think of it, that could be a cheap tactic to get people to buy more ice cream.
sturmhauke, your point is well-taken, but I have something totally irrelevant to say:
I wish that, at the end of a really long Straight Dope column, they’d put a very simple answer for those of us whose eyes glaze over when we see a lot of stuff like this:
At the end of the column, preferably in big letters, it should say either “Yes, fanning makes you cooler,” “No, fanning makes you hotter,” or “The world’s greatest scientists differ.” That way I could go spout about it to my friends and get to act all superior without having to risk a headache.
Una did you take into account the drop in air velocity as the moving air from the fan spreads out?
It seems to me that with a small hand fan, the air speed right next to the fan is comparatively high, but that the air is going to move out in a cone-like shape (like light from a diffuse lamp) and get slower at a geometric rate, such that by the time it spreads out and affects half your upper body (as you assume in some examples) it is going to be moving much slower than its initial speed.
Of course you may already have allowed for all this, I appreciate that you said you have made a large number of unstated assumptions.
It also occurs to me that air from a hand fan is not steady but pulsed, did you allow for that? You probably have done, I’m just throwing out suggestions here.
My original article was very lengthy and took into account an enormous amount of variables. It was about 9 single-spaced Arial 10-point pages.
Ed said “Umm…needs trimming.”
So it went through at least 6 re-writes, over the course of about a year (I actually wrote this some time ago), getting shorter each time, until it arrived at its current form. I tried to make it as readable as possible to a general science-interested audience, which meant I didn’t lay out all my assumptions.
Now, Princhester, I think your points are valid - the spread of air from the fan, as well as the pulsation are important points. However, modeling those effects may take something on the level of a CFD analysis (which I was thinking of doing, having a few friends who could do it for me as a favour…) but that seemed really out of scope for the article.
The truth is, there are a large number of variables, and several different ways to model the impacts. I looked at a variety of heat transfer equations, from technical conferences and military studies for heat resistance of soldiers, and decided to choose the simplified ones I combined for the report. That is, I found many ways to model the effects of convective and evaporative heat transfer, and chose the ones that were most standardized.
From my initial report, I wrote this:
In fact, I was hoping people would ask some questions, so I could provide some additional information. For example, if you want to do some different calculations and want to know some skin surface areas, I have the following list for you, from the Reference “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.”
In addition, a major point made by hibernicus, who reviewed this prior to posting, was that most people would primarily fan their face and neck, and thus relations developed for an average clothed body might be off by a bit. I agree with this point, but decided to, for the purpose of example and lacking a “nude skin” equation, go with the relations I was able to find. I was able to find a reference giving equations of forced convective heat transfer for a clothed and a “stripped to waist” person. From “Fang, Koh Look. Thermal Environment - Identification, Evaluation, & Controls, Institution of Singapore Engineers”, we have
Clothed: C = 8.1 * Va^0.6 * (35C - Ta),
where C is convective cooling in Watts,
Va is air velocity in meters/second, and
Ta is the ambient temperature, in degrees Centigrade.
Stripped to the Waist: C = 13.6 * Va^0.6 * (35C - Ta),
where C is convective cooling in Watts,
Va is air velocity in meters/second, and
Ta is the ambient temperature, in degrees Centigrade
Note that the only difference between these two equations is the factors “8.1” and “13.6”, so in effect the author is claiming that the difference in cooling between being clothed and stripped to the waist is about a factor of 1.68 : 1. From this, we might extrapolate, were we to be so bold and risk being flamed back into the Stone Age, to say that nude skin might warrant a factor of double that, or 3.36 : 1. Thus, we might multiply our convective heat transfer factor by 3.36 to account for the nude skin of the face and neck.
In addition, the author also claims a factor which varies the evaporation heat transfer between “fully clothed” and “stripped to the waist” of effectively 21 : 12.5, or 1.68 : 1 as well. Thus, we could (were we wearing asbestos knickers) assume that our evaporative heat transfer factor for the nude skin of the face and neck also should be multiplied by the same 3.36 : 1 as we saw above.
Now, in “Wenger, C. Bruce. Medical Aspects of Harsh Environments, Volume 1, pp 52-64”, the author replaces the numeric terms and velocity terms with a single factor for convection heat transfer, and one for evaporative heat transfer. These are termed “hc” and “he”, and are presented graphically only, as a function of the air velocity and vapour pressure.
People even argue a bit over the use of the saturation pressure in the evaporation equation. According to the Wenger Reference and others, the water on the surface of the skin should only be assumed to be at saturation pressure if the skin is completely coated with water, or a film of water. Skin which contains only a lesser covering or very light beading might only see evaporative heat transfer dependent upon the vapour pressure at the skin temperature, not the saturation pressure at the skin temperature. This assumption could change the heat loss predictions considerably.
And all this is just to try to figure out the area fanned, how to model sweatm and the guiding heat transfer equation to use taking into account area and clothing. So you can see how complicated this might be.
Ah, the other side of the coin. Well…I’ll sum it up into one sentence: “The process seems simple but is complicated because of the large number of variables - what I’ve shown is one method to try to model it, which shows that under normal conditions one might get hotter, cooler, or stay roughly the same temperature.”
I mean, some things in life just don’t have an easy answer unless you define the problem well enough and with rigid enough constraints. What is the best car? How long is a piece of string? Which is the least sexually threatening Teletubby? In the absence of data, you have to use equations to define the behaviour of the process.
One thing that missed the snips was the offhand Kaczynski ref. He didn’t write a manifesto against math, but only against technology. He was a mathematician (and a student of a good family friend, to boot).
The reference actually wasn’t a direct Kaczynski reference, but it was a deliberate parody. Inserted as a humourous aside. It’s most unfortunate that it seems to have upset you that much that you think it should be snipped.
Yes, your facts are right. But, we still got the reference, and I, at least, got a chuckle out of it. A sense of humour is a terrible thing to waste.
Now, personally, I would just have assumed that the area of skin affected by the fan is equal to the area of the fan. After all, if the fan is close to the skin, then you’re (probably) not going to see significant effects far away from the edges of the fan. If it’s further away, then you will see effects there, but your airspeed will also be diminished, and it’s reasonable to suppose that those two effects will (approximately) cancel out.
I can tell that the person who defined the ‘standard worker’ never worked in my office …
Ah, but now we have another variable (what is the area of a typical “fan” or object used for fanning?) as well as the factor of angle of attack of the airflow. If the airflow hits the skin at an angle, it is going to flow along the surface, picking up some heat as it goes, and flowing over a larger area than just the surface area of the fan. Consider the lady in the example I gave fanning to hit her right breast at a 45 degree angle, and envision the air flowing along her chest, across her left breast, the cool air caressing and teasing and and hardening her ni - never mind, just imagine it from a fluid flow standpoint. Even a direct perpendicular hit fans the air out after impinging - my graduate fluid dynamics text has a nice example of it, but I made it a firm New Year’s Resolution not to do another Staff Report containing partial differential equations, so here we are.
I’m not sure how one can provide an easy answer for the heat and mass transfer aspects of that, except from a general sense. I suspect I know a guy who can model it with a CFD package in my office, but he’s a bitter, angry man who yells at people and plays way too much Hank Williams Jr. on his speakers, so maybe I’ll leave him be…
Very interesting. As an EMT, I learned the “rule of 9’s” for estimating proportion of the body’s surface that was burned. My wife was taught the same rule in med school. No-one could ever remember those numbers, but it’s interesting that the percentaes for the same portions do hover within a percent or two of 9.
One, the least sexually threatening Teletubby is Po, obviously.
Two, I would guess that fanning yourself with your hand cools your HAND much more than your face and neck. After all, the hand itself is getting much more convection, right? If we add in cooling of the hand we’re probably going to get much better numbers.
Three, to paraphrase Claude Raines, Una is the kind of woman that… well, if I were a woman, I should be in love with Una.
Well, maybe not snipped. I’m just afraid that this will inspire people to write such manifestoes (manifesti?).
We cannot have that happening - Math is queen and servant of what I do. In addition to being fun as long as you’re in the zone…
Excellent article, here’s a few more points to ponder:
If you wanted to MAXIMIZE the amount of cooling, look at the exponents involved:
(1) Cooling seems to go as the 0.6 power of the air velocity, so doubling the air speed isnt a good strategy-- any increase in air speed pays of less and less as the speed increases, while :
(2) The amount of energy it takes to move air goes up as some high power, something like the third or fourth power IIRC. So if you try to souble the air speed, you have to worksomething like 8 times harder, to get less than a doubling of cooling effect.
So ideally for best overall cooling efficiency you’d like a relatively LOW airspeed, covering as much of you as possible.
Perhaps one of those huge “Arabian” fans that look like a hinged awning would be good. You might expect the folks in really hot countries to have empirically worked out the best fan designs over the centuries.
Yeah, but if Catherine Cornelius is alive in this universe, you wouldn’t have a chance.
I think that more than the quanititive analysis given, we could give brief consideration to the desire to fan. This was a very unscientific analysis conducted at a local park with temp and RH taken at 30 minute intervals over the course of 1 day (9a - 4p) here are my measurements:
[Time], [Temp], [RH], [# Present], [# Fanning], [% Fanning]
9:00a, 72 F, 30%, 25, 0, 0
9:30a, 72 F, 32%, 22, 1, 5
10:00a, 75 F, 33%, 20, 3, 15
10:30a, 81 F, 45%, 40, 10, 25
11:00a, 86 F, 46%, 42, 11, 26
11:30a, 89 F, 50%, 60, 18, 30
12:00a, 92 F, 58%, 71, 25, 35
12:30a, 92 F, 63%, 77, 33, 43
1:00p, 95 F, 65%, 68, 22, 32
1:30p, 96 F, 70%, 57, 12, 21
2:00p, 94 F, 77%, 40, 6, 15
2:30p, 91 F, 83%, 20, 2, 10
3:00p, 90 F, 82%, 12, 0, 0
3:30p, 92 F, 79%, 15, 1, 7
4:00p, 88 F, 80%, 18, 0, 0
As you can see, the percentage of park-goers who fanned themselves increased with the temperature until the environmental temp came close to the body’s skin temperature.
More significantly I believe is my observation that it was the more closely dressed people who did the most/more vigorous fanning. For example at Noon of the 25 people fanning 12 were in suits or button down shirts, 7 were in close-fitting blouses, and only six were in tee shirts, no fanners were in bathing suits or shirtless though 16 people overall fit this last category.
My current hypothesis is that fanning has a greater effect on the warm moist layer of air trapped between the skin and clothing especially around the neck and upper torso, than it has on overall body temperature.
Comments / suggestions on testing this hypothesis are welcome.