Two weeks ago I wrote a column on the majesty of our clouds that often show a great variety of shapes and forms over a few days.

The clouds are formed by rising moist air that cools, then condensing into tiny water droplets. These water droplets are kept aloft by the upward currents of air (called thermals). For this warmer air is lighter than the surrounding air and is buoyed upward.

Most clouds are continually renewing themselves as sunlight shining on the upper layers of a cloud causes these water droplets to evaporate while on the lower part of the clouds new water droplets form.

There are two distinctive types of clouds that are easy to recognize, the wispy, high flying cirrus clouds and the cottony cumulus clouds.

Using a little bit of math and your hands as angle measurers, you can estimate the distance and size of these clouds. For both types of clouds have a typical average height above the surface or land.

One of the key rules of geometry is that for a triangle, if you know one angle and one side length, you can determine the length of the other sides. This field of math is called trigonometry and used to be taught in high school for an entire year, just as algebra and geometry currently are. Now with scientific calculators, there is less emphasis on trigonometry, but this area of math is still used heavily in physics and engineering.

Here follows a simplified approach for clouds less than half-way up in the sky (clouds closer to the horizon than to the top of the sky). According to “The Cloud Spotter’s Guide” (by Gavin Pretor-Pinney, Perigee Books, 2006), a puffy cumulus cloud (cumulus mediocris) averages about 2500 feet altitude (1/2 mile) over flat land.

This variety of cumulus is about as thick as it is wide. The less common cirrus clouds resemble a horse’s tail blown in the wind and average about 30,000 feet altitude or six miles high. At this height, the water droplets have become frozen ice crystals that are responsible for rings around the moon (night) and sundogs (usually in the late afternoon).

So the above heights can be used as the known side of a triangle, called the opposite side as it is opposite the angle you will be measuring with the your fist.

Here’s how to use your fist to measure angles in the sky (both clouds and stars). Extend both arms and make clenched fists with your hands as if you were to fight someone.

Start with one fist so its bottom is level (in line with the horizon) and then put the other fist on top. Then take the first fist and put it on top of the second fist. Continue until the top of the last fist is directly overhead.

For my hands and arms, it takes eight fists to cover an angle from the horizon to directly overhead. This is an angle of 90 degrees so each of my fists is about 11 degrees high (90/8 = 11.2) Rotate your fists by 90 degrees as you extend your arms to measure horizontal angles as well.

Key formula is: Mid Cloud Hor.Angle(deg)=C* Mid Cloud Altitude(mi)/Cloud Dist. or Cloud Dist.(mi) = C* (Mid Cloud Altitude(mi))/(Mid Cloud Hor.Angle(deg)).

Here C is 57.3 degrees or 180 degrees divided by Pi (radians in 180 degrees). To get the cloud’s vertical or horizontal dimensions, the formula to use is:

Cloud dimension (either hor./vert.)=(Dimension angle)*(Cloud Dist)/(57.3 Deg.) So once the Cloud Dist(mi) is known, we can find both the Cloud Vertical Size (from base to top of cloud) and the Cloud Horizontal Width (from side to side).

For example, consider a cumulus cloud about as wide horizontally as it is vertically and whose middle is two fists above the horizon (2 x 11 deg.= 22 deg.), the Cloud Distance = 57.3 deg.* 0.5 miles/(22 deg.) = 1.3 miles away. If this same cloud is one vertical fist by 1 horizontal fist across, then the cloud’s dimensions are both Cloud Dimension = 11 deg. * 1.3 miles/ 57.3 deg.= .25 miles.

So this cumulus cloud would be 1.3 miles distant and 0.25 miles from top to bottom and 0.25 miles wide.

The moon was new early this morning, passing South of the sun (no eclipse). By Wednesday, the moon will have moved far enough along its orbit, so it can be seen as a slender crescent low in the western dusk with its lighted bow facing the sun.

Next Sunday, the moon will appear half full in the evening sky and at its best for crater spotting with binoculars and telescopes.

Now featured at the Frostburg State Planetarium is “Bare Eye Astronomy,” a good beginner’s introduction to the night sky. This free public program is shown at 4 p.m. and 7 p.m. today and next Sunday in Tawes 302.

Visit our website at http://www.frostburg.edu/Planetarium for more information.