“The convertible cooling effect”

from: Jearl Walker in “The flying circus of physics”

Q: “On a hot day, you’re in luck if you’ve got a friend with a convertible. Driving down the road with a good breeze always does the trick against the heat.  You feel cooler but a thermometer should read the same, with or without a breeze, shouldn’t it?

Try it. With a thermometer in the back seat, measure the temperature when the car is parked and when it is moving. You’ll probably find that the thermometer reads about ½ °C lower when the car is moving. Why?”

A (by Walker): The reference (R.C.Plumb, below) suggests that the air current over the top of the convertible reduces the air pressure in the passenger area, implying that the air there had expanded and therefore cooled slightly. This effect would be similar to the cooling of air in the rapidly flowing air stream above an airplane wing, an effect sometimes made apparent by the fog formed above the wing.

Reference: R.C.Plumb,”The convertible effect” in “Chemical principles exemplified” J.Chem,Ed. 49 (1972) 285

Let’s do the numbers. Since, unfortunately, I don’t have access to a convertible…

 DP = (1/2)(rv²)

 

If the car moves at 15 m/s (54 kph) and density of air is r = 1.2 kg/m³ 

DP = 135 Pa

is the pressure drop.

The ideal gas equation is:

p = nRT

where R is the universal gas constant. Assuming that the number density n does not change, the drop in temperature DT is:

DT/T = Dp/p

If atmospheric pressure 1.013x10⁵ Pa corresponds to 300 K, then this pressure drop gives:

DT = 0.4 °C.

Walker mentions a value of ‘about ½ °C‘.  So that’s about OK.

Since the volume does not come into the picture, this should mean an equal magnitude of cooling if you ride a scooter at the same speed. 

However, this logic does not apply to an ordinary car with the windows down, because the pressure drop is not the same as calculated above - it's much less.

What about the plane moving at, say, 100 m/s?

The temperature drop above the wing should be about 17.8°C (by the same logic as above).

Is that enough of a temperature drop to cause fog to form? Let’s see:

https://en.wikipedia.org/wiki/Vapour_pressure_of_water

At 30 °C, the saturated vapor pressure(SVP) is 4.25 kPa. Assume the temperature drops to 15 °C, at which point the SVP is 1.70 kPa.

So if the atmosphere starts at 40% relative humidity at 30 °C, it will be at 100% RH at 15 °C.

In fact Walker states somewhere else that fog can form even at RH as low as 60% under some conditions!

What conditions? He don’t say and I dunno (but I would guess a really polluted atmosphere with lots of small particles floating around).