## Speed of clouds

Suppose I lie on my back and look vertically up. I can see a cloud passing overhead, and measure the time (t, in seconds) that it takes to change its angle from the vertical by one degree. If I knew the height (h, in metres) of the cloud I could calculate the distance moved by the cloud in the horizontal plane, and thus the speed (v) of the cloud in metres per second. Tan (1º) = 0.01745; so, if the cloud were 100m above me, the 1º would represent 1.745m in t seconds. (Multiply by 2.2369 to get the answer in mph.)  But I do not know the height of the cloud. Here is a possible method for determining both height and speed.

Object: to determine the height above ground level of the bottom of a cloud layer, and its speed across the land.
Equipment: 2 observers (A & B) at 2 different known locations some 500 - 1000 m apart, 2 mobile phones, 2 astrolabes or sextants, 2 compasses, 2 pencils and paper.
Method: Observer A identifies a cloud (C) of which the shape is sufficiently distinctive to describe uniquely (e.g. "the one shaped like a hen"). He rings B and waits till B has identified the same cloud. Each observer then determines and records the inclination above the horizontal (a) of C and its compass bearing (b).
Calculation: The data is then passed to a 15 year old with a slide rule or "scientific" calculator. He is going to assume that the two compass bearings on the cloud define two vertical planes ACD and BCD that intersect at the cloud and the point D that is the projection of the cloud on the ground. The orientation and length of the line AB between the two observers is known. The point D can be identified by drawing the lines AD and BD on the map. If the observations are repeated after 1, 2, 3, etc minutes the speed and direction of the cloud can be determined.

The angles CAD and CBD provide two series of estimates of the height of the cloud (distance CD). (Comment: If the terrain is not flat to the horizon in all directions, observers will also need a bucket of water in order to determine a "false horizon" by which to determine the inclination angles; the true inclination will be half the angle between the cloud and its reflection in the bucket.) 