Low Technology Institute

How Tall Is That Tree?

We’ve got a pine tree that is dying. It may be too shaded behind the Black Locust and Larch trees to the south. It isn’t an unusual variety or specimen and we need timbers to build a chicken coop so, the tree will be coming down. But we need to do it in a way that we don’t destroy other plants, animals, or buildings in the fall radius. To figure out this potential zone of destruction, we need a height estimate and I remember back to a Mr. Wizard’s World segment I watched as a kid (yes, I was a bit of a nerd then, too). I couldn’t find the video clip, but here’s the process.

  1. Get a pan with a black interior and enough water to cover an inch of the bottom.
  2. Get a long measuring tape.
  3. Walk a fair distance from the tree (it doesn’t really matter, but between 1/2 and 3/4 of the tree height is fine).
  4. Put the pan on the ground and add the water.
  5. Stand back with the pan between you and the tree. Look in the pan and walk backwards or forwards until you see the top of the tree in the center of the reflective water.
  6. Measure the distance between your toes and the center of the pan (variable b). Measure the distance from the ground to your eyes (variable a). Measure the distance from the tree to the center of the pan (variable y).
  7. Plug the distances into the following formula: (a/b)×y=x, where x is tree height.

This works because you’re making two similar triangles. I mean “similar” in the geometric sense: as all the angles are the same, the lengths of the sides are proportional to one another. The length to the pan and height of the tree are proportional to the length to the pan and the height of your eye.

In my case, the pan was 43′ from the tree and 3′ from my toes. My eyes were 5.5′ high, meaning the tree should be about 79′ tall. I’ll report back on the height once it is down and I can measure it directly.

 

You can also estimate the tree height with a yardstick, as outlined in the following video.

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