How to measure depth of water

There is a simple way that allows you to measure depth of water in river, lake or sea using only a rope (or a fishing line), a plummet and two floats. This method was invented in the USSR in 1966 year by two inventors V. Zdanovich and Y. Sharikov.

How to use it. Cut two pieces of rope, the first one short (with the length not less than the depth), and the second one, longer. Tie them up to the plummet and to the floats (see picture below). Put it in the water. There must be a current or a wind to stretch the system. Somehow you would have to find the distance between two floats (try to use your accurate eye).

Edges L1, L2 and A form an obtuse triangle. We just need to find its height H.

If you know the distance A between two floats, the length of L1 and L2, you can find the depth H using this approximate formula:

H = (4*A²*L₁² - (L₂² - L₁² + A²))/(2*A)

It's a very simple math, but the result is not so accurate as it can get by using a formula derived from Heron's formula:

H = (L₂² - ( (-L₁²+L₂²+A²) / (2*A) )² )^0.5

This formula provides precise results, but it takes more complicated math.

Here is an online obtuse triangle calculator that calculates the height of the triangle, it uses both formulas described above:

L1 = 

L2 = 

A =  

 
 

For example, if the first rope L1 is 10 meters long, the second L2 - 12 meters, and the distance between two floats A is 5 meters, by using this calculator the depth H is 9.8 meters (the exact value) or 9.9 meters (the approximate value).

The advantage of this water depth measuring method is that it requires very primitive and cheap tools, while its results are quite accurate and it can be used on the river. However the disadvantage is that there is a problem how to throw all that things into the water, it takes some skill, and how to measure the distance between that two floats.

But if there is silent waters with no current, how can we measure its depth? Here is the other way to measure the depth of water - see the picture below:

This is so called "sliding float" rig. There is a plummet, a fishing line and a float with the tiny bended pipe inside. If the fishing line has some slack, the float can freely move along it. When the line is stretched, the float can't move along it.

How to use this sliding float rig. Move the float toward the plummet, then throw the rig into the water (use your hands or a spinning). Wait for a while until the float pops up to the surface, then stretch the line and pull out the line to the shore. Now measure the distance between the float and the plummet - and you got the depth of water! That's all!