How High is That?

At work we seldom need to measure elevation, so we can’t justify the cost of a clinometer, an instrument for measuring vertical angles. However, sometimes we do need a way to calculate heights. The solution: A do-it-yourself clinometer, I cobbled together out of a cheap protractor. Unfortunately the picture didn’t turn out, but it’s an embarrasingly simple thing cobbled together from items on-hand. Basically it works by using a string weighted with a gem clip and sighting across it, You carefully turn the protractor on it’s side and read the angle of the elevation. From there, it’s just a matter of taking the tangent of the angle and multiplying it by the distance to the object, adding the height from the ground to your eye.

It’s impossible to get an  accurate measurement with this rig, but over short distances it’s close enough for our purposes.

clinometerHere’s a type of clinometer that works nicely for pole heights. It simply consists of a sight tube, a bubble level, and an internal mirror where you can see the float and the object at the same time. To use, you move until the bubble is level and the object is at a sight wire strung across the end of the tube. Then, when you measure the distance to the object, that’s about the same as the height.

In a right triangle, where one angle is 90º, and the other two are 45º, the adjacent side is the same length as the opposite side. Notice that the distance from the person to the pole is shorter than the height of the pole due to the height of the person.

The secret is that the bubble level is mounted at a 45º angle to the tube. This means that when the bubble is level, you are looking up at a 45º angle. Since both the opposite and adjacent side are exactly the same in a 45º right triangle, measuring the distance will give you the height.

Of course, it doesn’t take into account the height of the user. Either the user would have to do an about-face, flip the sight tube so that the bubble float is toward the ground, and measure from the point he sees to the pole, or the user has to add the height to his eye to the distance.

Both clinometers need level ground for this to work. Engineers and surveyors can take into account ground slope, but you need more sophisticated instruments than my DIY clinometer or the one above.

You can do something similar in estimating distances. The story goes that one of Napoleon’s engineers once needed to know how far it was across a river. It’s said he carefully fixed the brim of his hat so that the edge of the brim marked the opposite bank, then, keeping his head and neck rigid, turned and noted where the brim marked a point on the ground. He measured the distance to that point and had an estimate of the width of the river. A nice story, but I’ve not had good results with the method.