Friday, January 22, 2021

How Tall Is That Tree?

I've been pondering how I might be able to measure the height of tall trees. Taking a walk yesterday, I was thinking about the geometry and trigonometry of the problem. I wondered if there was an app for my smartphone that calculated dimensions of an object using the camera on the phone. It would be simple enough, all you'd need would be the distance from the camera to the object and you could use the properties of triangles to figure out the height.

Then it dawned on me that all I needed to do was fit an object of known height into the camera viewer in portrait orientation and then pace off my distance to it. I would then have the ratio of distance to the tree to its height. The Law of Similar Triangles tells us that the ratio won't change no matter how large or how distant the object might be.

I found a topped Mexican Fan Palm that was about 8' tall. Pacing off the distance and knowing the length of my stride, I figured out that if I multiplied my strides by 4, I would get the height of the object in feet.

You're welcome.

This palm tree is 52' tall.


tim eisele said...

Yeah, that should work. The principle is definitely sound. You might want to double-check the calibration on your stride, though. I've got a pretty good feel for how tall 50 feet looks, because that's how tall the silo was on our farm when I was a kid, and that tree doesn't look 52 feet tall to me. Comparing it with the height of the vehicle in the picture, and assuming the vehicle is about typical for an SUV (about 6 feet tall), I'm getting a tree height closer to 30-35 feet. Although, I suppose the vehicle could be a lot closer to the camera than I think it is.

I prefer to measure distance by heel-to-toeing with my feet instead of pacing. Which is pretty convenient because my feet are almost exactly a foot long. My wife is trained as a forester, and she says that they had to be taught how to pace to keep it a consistent length. Otherwise, it varies pretty dramatically.

Tom said...

iOS has a built in app called “measure.”

And I agree the tree is closer to 30’ than 50’ tall.

K T Cat said...

My idea for calibration is to fit a ruler into the screen and measure the distance from the camera. As for my stride, heel to toe would work well.

Ohioan@Heart said...

You need to be careful that the triangles are really similar. Generally you will frame the photo from a height of about 6’. That would mean that when you did the 8’ tree you would have been looking pretty parallel to the ground. On the picture shown you are clearly looking up. That would make the triangles not similar. I have taken pictures of Sequoias, the fact that I am looking up is clear, and the distortion it causes is also clear (and I’m pretty sure I see it, greatly reduced, in the photo you posted).

K T Cat said...


K T Cat said...

If we assume that the base of the tree and I are on the same level and that we both form a 90 degree angle with the ground and we know the height of the camera off the ground, we ought to be able to easily calculate the height of the tree if we know my distance from its base.

Diagram and calculations tomorrow.

IlĂ­on said...

I frequently wonder about the height of a white pine alongside my drive (*). Using the house as perspective, and with the difference in ground elevation, and the fact that I am looking up, I totally guess it to be 60-80 feet tall. However tall it is, if it ever fell, and fell the wrong way, it could take out a room or two.

During a fierce storm a couple of months ago, (yet another) high branch was ripped from the tree. This one was big enough to be a tree in its own right.

(*) which I can see from blocks away when I have an unobstructed view.