# Squirrely Physics

At the time I write this sentence it’s 10:13 pm. The sun has been under the horizon for almost two hours. It’s 93 degrees Fahrenheit outside here in College Station. I believe it peaked out right at 100 during the day, and it feels hotter in the sun. Even the animals are clearly not pleased.

Some of them are the cutest thermometers I’ve ever seen:

I wish I had taken a picture so I could show you exactly how the thermometer works. Fortunately there’s nothing that’s not on the internet, and other people have documented this particular phenomenon on film. The thermometer is a binary state instrument. The above picture is in the “not so hot” state. The below picture is in the “really really hot” state.

They find a shaded area of concrete and just splat themselves right on the ground. They’re so hot they don’t even run when you walk within three feet of them.

Which is interesting from a physics standpoint, because a priori they should have a much easier time staying cool than us humans. An average human being might burn something like 100 watts of basal metabolism when going about everyday business that’s not particularly strenuous. That same person might have a total surface area of maybe 2 square meters. All total that means every square centimeter of the body will on average radiate 5 milliwatts or so.

Now all other things being equal surface area scales as the square of linear dimension. Volume scales as the cube of linear dimension. Assuming that a squirrel has the same rough shape and metabolism per volume as a human, a 6-inch squirrel ought to have a surface area of about 138 square centimeters or so. His body ought to generate about (6 inches / 6 feet)^3 times as much energy, or around 57 milliwatts. That’s about 0.5 milliwatts per square centimeter, much less than a person has to deal with.

At best these are extremely sketchy Fermi-problem estimates, but the general principle is a very firmly established one: ratios of volume to surface area are hugely important in biological processes. For heat dissipation it’s not really the summer most critters have to worry about. Assuming there’s not too many predators about, humans and squirrels can just find a patch of shade and lay around reducing their metabolic heat output. The winter is another story – the squirrels and other small animals have so much surface area per volume that their bodies would rapidly become hypothermic without a way to combat the heat loss. The normal adaptations animals use are things like high heat-generating metabolism, insulating fur, fat stores, insulating nests, that sort of thing. The disadvantage of these adaptations is that not all of them can just be switched off (though many can), leaving them just as uncomfortably hot as the rest of us despite what would otherwise be a much easier job of cooling. In particular due to their metabolic adaptations I’d be pretty surprised if the geometric 57 milliwatt was anywhere near as as high as the real figure probably is.

Here’s hoping the squirrel thermometer switches states soon. It’s mid-July in Texas though, so I don’t we can reasonably expect it to. Sigh.

(I will be mostly out of pocket this weekend. Sunday Function will probably be delayed till Monday. See you then!)

## Comments

1. #1 Russell
July 17, 2009

The other thing you’ll notice, is the grackles gape-mouthed.

2. #2 Art
July 17, 2009

As I understand it the normal body temperature of a common gray squirrel is something like 101F. Wouldn’t this increase losses?

Some time ago I set in the shade bird feeders and a pair of birdbaths with a drip emitter that helps keep the water fresh and announces the presence of water with the dripping. Took some doing to squirrel-proof my feeders but one thing I hadn’t considered is that squirrels seem quite attracted to the water. For some reason I had never considered squirrels as drinking water. Odd.

Pretty common to see two or three squirrels gleaning the ground for dropped seed and occasionally jumping up to drink from the birdbath.

Between the shade and the water, even though this is hot and humid Florida, I have never seen a squirrel in the prone position. The photo of the prostrate squirrel was something of a revelation. LOL. Thanks for posting it.

3. #3 MikeM
July 17, 2009

Isn’t the scaling factor for living organisms somewhere between square and cubic?

4. #4 Jim
July 17, 2009

At our local walmart (in Texas) the grackles will run under your car as soon as you turn off the engine. They are apparently drinking the cold water that condenses and drips off the air conditioning system.
Has anyone seen this elsewhere? I’m wondering if this is a common behavior or something the birds learned locally.

5. #5 6EQUJ5
July 17, 2009

When I was a kid, coming inside from hot weather, I would spread out on my back on the concrete floor of the basement in the dark.

It was years later (physics class) that I realized where the faint draft was coming from: I was a hot spot in the middle, and heat would rise from me, with cool floor air coming in from all sides.

I never saw squirrels doing the heat-sink spread, and I lived for 12 years in Barstow, California.

6. #6 MarkAidan
July 17, 2009

This sounds like the perfect lead in to a post about evaporative cooling!

7. #7 Russell
July 17, 2009

Of course, the other sign of summer is newcomers to the state asking, “Does it always get this hot?” I was getting asked that before we hit triple digits, and were still just in the high 90s. My response was, “It’s not hot. Yet.””

8. #8 The Chemist
July 17, 2009

Funny, Wolfram doesn’t seem to have any data on squirrels in this regard. Chicken on the other hand.

9. #9 CCPhysicist
July 18, 2009

Some of our squirrels do that quite regularly, but they would be hawk lunch if they did it where yours is! Ours sprawl in a shady bit of lawn, which is even cooler than concrete.
In winter they spend their spare time in a well-insulated nest.

Question: Do squirrels sweat?

Observation: Humans don’t have the same fur thickness to volume ratio. The “R” value for fur needs to be included in your estimate. And since they have less belly fur, the conduction is improved by sprawling out.

10. #10 Anonymous
July 19, 2009

Maybe you should shave your squirrels for the summer, like little sheep. Then you can even makes some squirrel-fur sweaters for your dolls.

11. #11 Neil B ♪
July 19, 2009

Why don’t we see more baby squirrels around? I figure more would fall out of nests etc, but I saw maybe one in my whole life around neighborhoods or parks etc.

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