# Pipes, solar heating, and temperature...

There is a pedestrian footbridge over the river in our town that has railings made up of horizontal pipes welded to uprights. The pipes at the bottom are about 1" in diameter (they may be solid rods rather than tubes). As you go up, the pipes get bigger in diameter; there are 2", 3", and 4" pipes, and the top rail is probably 5" in diameter. I cannot say whether the pipes all have the same wall thickness, as the ends are not exposed. They appear to be all the same type of sandblasted steel, and they’re pretty solid; knocking on them produces just a dull thunk.

While leaning on the railing the other day, in direct sunlight, I noticed that the top pipe was uncomfortably warm, to the point that I couldn’t leave my hand on it for more than ten or fifteen seconds. However, the smaller pipe below it was not quite as hot. In fact, the smaller the diameter of the pipe, the lower its temperature: the 1" pipes at the bottom of the railing were barely warm at all. None of the pipes were shadowing each other; they were all in full sun. As I walked along the 400’ bridge, I checked at several spots, and the temperature thing held true on both sides of the bridge all along its length.

I’m assuming that the same number of watts/m[sup]2[/sup] fall on all the pipes, so why is there such a significant temperature difference between them? I would imagine that this effect could only go so far - I would not expect a pipe with a diameter of a meter to glow cherry red. Now that I think about it, I should stop by the bridge later tonight to see whether the temperature effect is reversed at night, due to differences in radiative surface area.

I’d be willing to bet that it’s an effect of the different surface to volume ratios of the tubes.
There’s a calculator here for radiative cooling of a sphere. You don’t have spheres, your pipes probably aren’t solid, and you’ve also got air cooling to contend with; however smaller spheres cool faster than big spheres. Pipes are just a similar case with a nastier set of equations to solve.

The amount of solar energy is dependent on its angle of incidence. If you think about the large diameter pipes, they present a larger area normal (at right angles) to the solar radiation. As a pipe’s diameter increases, it becomes flatter.