Math CentralQuandaries & Queries


Question from Zora, a parent:
How many feet does a shadow move per hour?


I can't tell you that, it depends on how big the shadow is and what time of day it is. Shadows of big things move faster (at the tip) than shadows of small things, and shadows grow or shrink very fast at sunset and sunrise.

The angle by which a shadow moves per hour is somewhat easier to describe. It's reasonably close to 15 degrees per hour (360 degrees per 24 hours), especially in high latitudes and at times of year when the sun does not get too high in the sky. In tropical climates, the angle changes slowly in the morning and evening, and very fast at midday.

This can be used (in the Northern Temperate zone, at least) to approximate North (or South) without a compass, if you have a watch. It's easiest with a watch with hands. Hold a matchstick upright at the center of the watch, with the shadow falling halfway between solar noon and the hour hand. (Solar noon is 12:00 unless you are on daylight savings time, in which case it's 1:00) Then the solar noon mark on your watch points north.

You can make this more precise by adjusting for latitude and time of year, but usually in Canada, the US, or Europe, the basic method will be precise enough for getting "unlost".

Good Hunting!


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