You don’t see many of these anymore; with the sprawl of urbanization, city lights illuminate our once black night skies so that we can barely see even the brightest stars anymore. But up until the 1960s, and today only in the most rural of areas, ceiling lights were the best way for an observer to determine the height of cloud bases. In fact, these are so uncommon these days that if you try to search for the term “ceiling light” on the World Wide Web, you’ll get pages and pages of links to websites selling lights meant to mount on the ceiling of your home!
Here’s how our ceiling light works:
A high intensity halogen bulb is used to direct a beam of light, which projects a “spot” on the base of any cloud overhead at night. The observer can triangulate his or her position relative to the spot of light on the cloud’s base in order to determine the cloud-base height.
The angle created between the vertical light beam and the relatively horizontal ground is 90 degrees’ the distance the observer stands from the light can be determined easily enough with a tape measure or a measuring wheel available at most hardware stores; finally, the angle from the observer to the spot on the cloud base is determined by using a theodolite (shown in photo at the bottom of this page). Subtract from the cloud base height the height of the observer’s eyes above ground level, and an accurate measurement can be achieved.
Simple trigonometry is used to triangulate the cloud base height, or the length of the beam of light (one leg of the imaginary triangle formed between the observer, the ceiling light itself and the spot on the base of the cloud above.
Triangulation is the process of determining the location of a point by measuring angles to it from known points at either end of a fixed baseline, rather than measuring distances to the point directly (trilateration). The point can then be fixed as the third point of a triangle with one known side and two known angles. It is commonly used in simple trigonometry and Euclidian geometry, and is the brainchild of Gemma Frisius, a 16th century mathematician.
Check out my awesome drawing below illustrating the angles created between the observer, ceiling light and the cloud base “spot” created by the beam of light. Notice that the angle created between the ceiling light and ground is a right angle (90 degrees). The leg between the observer and ceiling light is known, the angle at the light is known, and the angle (with use of a theodolite; explained below) between the observer and the ground is known. Now all one needs to do is plug these known values (two angles and a leg) into an equation that seeks the tangent of the angle made between the observer and the ground.
The photo above shows the ceiling light (or ceilometer) in use. You can see the beam of light penetrating the night sky towards the clouds above (clouds not visible). Next to the ceiling light is a timer switch which can be turned clockwise to activate the light. The observer goes a measured distance from the light and uses the theodolite (pictured to the left) to get an angle measurement.
The angle at between the ceiling light and the ground is 90° (more or less.) The distance from the ceiling light is known, and the angle measured by the theodolite is recorded. With simple trigonometry, the observer is able to get the distance between the cloud base and the ceilometer (cloud-base height).
A simple example of calculation would be if the observer measures an angle of 45-degrees from his position to the illuminated spot on the cloud’s base. A right triangle with an angle of 45-degrees has, by definition, two 45-degree angles, therefore two of its legs will be the exact same length. If the observer is standing 1,000 feet from the ceiling light and his angle to the cloud base “spot” is 45-degrees, then the “leg” of light to the cloud base is also 1,000 feet. The result: the cloud height is exactly the same as the observer’s distance from the ceiling light.
~ Steve Woodruff and Devin Lussier