Find height of clouds with a stop watch.

Finding the height of clouds requires a set of complex optics, electronic and computing accessories. But you can also find the height of cloud using simple laws of math and physics. Here is a way to find the height of cloud just by using a stop watch.

Image source: wikimedia.org

You might have noticed that even after sun set if we can see sun light in clouds. It is so because the clouds are at a height and they receive sunlight even after sun sets in horizon.

Even if this method cannot be reliable it is fun to find and educative to find height of clouds by this method.

To find the height of cloud first of all wait till sun set.
Make your stop watch ready and start the stop watch the moment sun the sun disappears in the horizon.
Now see at the clouds. You can see sun light is still there. Wait till the sun light disappears in cloud and stop the watch the moment sun light disappears from cloud.

The following two picture describes the measurement we did.

The condition when the sun sets at horizon.

The condition when sun sets at the clouds.
Where r = radius of earth i.e. 6.37 × 10^6 h = height of cloud , d = angle made earth to its mean position due to its rotation in time period measured by stop watch.

If we suppose the time measured by the stop watch is ”t” seconds then,
the earth rotated by angle “d” in the time period of “t” seconds and it rotates by angle 360 º in 24 × 60 × 60 seconds = 86400 seconds.

Then,

d º / t seconds = 360 º / 86400 seconds

From this equation we can find value of angle rotated by earth(d) in the mean time “t” seconds.
so now we have value of d , t and r

And from the second figure above we clearly see that ,

Cos d = r/(r+h)

As we know the value of “d” and “r” we can easily find the value of “h” which is height of cloud easily from above equation.