Measure the Height of Any Tall Object Without Actually Measuring It (Clinometer)

Hi, in this instructable, we will be measuring the height of any tall object.i.e.a tree, a flagpole or even a building. We will accomplish this by making our own mathematical instrument called "clinometer".

A clinometer is basically a mathematical instrument that measures the angle of elevation of any tall object. Once we get this angle measurement accurately, we can easily calculate the height to the tall object using simple geometry.

You will need the following supplies.

1. An old protractor
2. An old pen
3. Some electrical/duct tape
4. Some transparent tape
5. Something as a weight (an old nut)
6. A blade or scissors
7. Some thread

Cut a piece of thread about 10-15 cm long. Now tie it to the rusty nut(or whatever you have taken as a weight). For this step, do not use a weight too heavy or it will be difficult to hold the clinometer and will affect the measurement. Use a weight that is comfortable for you.

Now, carefully poke a hole into the protractor in the center of the semi-circle(usually the part that is marked at the upper potion of the protractor.

At this step, be careful not to break the protractor.

Note: some protractors from standard geometry boxes come with the relevant hole marked already.

Now, take the old pen and attach it to the upper part of the protractor using some electrical tape or duct tape. This will act as our scope. Here, be careful not cover up the markings of the angles as covering them up will make it hard to make measurements.

Now pass the other end of thread tied to the weight through the hole poked in the center of the semi-circle of the protractor. Attach the thread passed to the other side of the protractor by some transparent tape as shown in the images. Now our protractor is ready.

This step completes the instrument.

Now that our clinometer is ready, we will learn to use it by measuring the height of a tree.

Note: In this step you will need the height of your own body as well so go and measure it first if you haven't already.

Stand next to the tree from some distance 'l' from the tree. Now take the clinometer and align it to the top of the tree by looking through the scope as shown in the figure. Hold the clinometer in this position and note the angle smaller angle on the clinometer. Now subtract the angle obtained from 90 to get the angle of elevation.

Now use a calculator to calculate tangent of the angle of elevation obtained. Multiply the tangent by your distance from the tree(l) and note the value obtained. Now add your own height to the value. The final value obtained is the total height of the tree.I have given a formula for illustration.

Total height of tree = (Your distance from tree) * [tangent of (90-angle measured by clinometer)] + (your height)