[FoRK] dQ/dt

Stephen Williams sdw at lig.net
Thu Mar 4 11:14:11 PST 2010

Dave Long wrote:
>> Though those adaptations make humans and our immediate ancestors 
>> better runners, it is our ability to run in the heat that Lieberman 
>> said may have made the real difference in our ability to procure game.
>> Humans, he said, have several adaptations that help us dump the 
>> enormous amounts of heat generated by running. These adaptations 
>> include our hairlessness, our ability to sweat, and the fact that we 
>> breathe through our mouths when we run, which not only allows us to 
>> take bigger breaths, but also helps dump heat.
> Men perspire, but horses sweat.
> Rather than lose their hair, equids adapted a salivary protein to 
> produce latherin, which is currently believed to act as a wetting 
> agent, promoting evaporative cooling even through fur...
> -Dave
> (horses can move 1'800L/min of air when working at 6,5kW.  What's the 
> equivalent for human heat exchange?)

We only weakly use our lungs for heat exchange, but for comparison, an 
estimate of the absolute maximum air exchange would be:

6L [2] of lung capacity max
2 full breaths per second max (empirical testing)
60 seconds
720L / minute - This is highly inflated, probably 1.5-3x, because you 
can't fully exhaust air in your lungs during a breath.

Weight of a healthy athletic man: 150-200lbs
Weight of a typical horse: 1354lbs [1], or 7x the weight for 2x the air 
movement.  Possibly shows a worse ratio.

For humans, there is evaporation, radiation, and convection which are 
detailed well here: [3]
The max effects in high heat are for sweating / lung evaporation at -95 
W/m^2 at 39C.  Total dissipation max seems to be at 16C: -99+-12, plus 
-40 of storage for -111W/m^2 long term and -154W/m^2 for short term 
periods (until the body overheats).

[3] doesn't have running in their metabolic table.  It would range up to 
and past their highest sport: tennis at 8.7 "met".  A met == 58.2 
W/m^2.  A human male has a surface area of about 1.8m^2 [4].
So a human can produce at least 9*58.2*1.8 = 942.84 ~= 1KW of heat and 
can bleed it off at 0.10 KW or handle 0.15 KW for a short time.

Most numbers published are for average people, not trained athletic 
ones.  Few doctors care about those, since they don't give as much 
business perhaps.

[1] http://www.cowboyway.com/HowTo/HorseWeight.htm
[2] http://en.wikipedia.org/wiki/Human_lung
[3] http://personal.cityu.edu.hk/~bsapplec/heat.htm
[4] http://hypertextbook.com/facts/2001/IgorFridman.shtml


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