How to Find the Height of a Tall Building … using a radio!

I always knew that one day I would find a way to combine my Bachelor’s degree in Physics with my passion for radio. So I gave some thought to the idea of how to find the height of a tall building using a radio. I came up with four different ways of doing it ranging from the complex and expensive to the (literally) stupid, cheap and simple. Here are my four methods in decreasing order of complexity:

1. From the ground at the base of the building set up your radio with a multi-element Yagi antenna. It would be best to perform this measurement using a frequency in the 70cm band, or higher, to avoid having to employ a physically large antenna. Point the antenna directly at the eavestrough at the top of the building. You will need some means of keying the radio so that it transmits a very short pulse of RF, a few microseconds will be quite long enough; shorter would be better. You will also need an oscilloscope with an RF detector circuit connected to one of its inputs to measure the reflected radio signal from the eavestrough. The other input of the scope will be connected to an RF sniffer to measure the transmitted pulse. I should add that the oscilloscope must be a very high speed instrument because the interval between the transmitted and reflected pulses will be vanishingly brief. The rest is simple physics. Knowing the velocity (c) of an electromagnetic wave, and the interval (t) between the transmitted and reflected pulses you can calculate the height (h) of the building using the formula h=c/t.
2. My second method is very dangerous and carries a safety warning; please see the note at the end of this article. This method also employs the laws of physics at an elementary level plus a little simple mathematics. You will need your radio and an accurate chronometer, stopwatch or similar. For really accurate measurement you may wish to devise some electronic timing equipment with automatic transducers. We will describe the basic method and let you improve on it as you wish. First, weigh your radio using an accurate scale, then take the radio and stopwatch to the roof of the building. With your finger primed and ready on the stopwatch button, hold the radio over the roof edge. As you release the radio, press the button to start the stopwatch. When you see the radio hit the ground, press the button again to stop the timing. From the time of fall (t), the weight of the radio (m) and the universal gravitational constant (g) you will be able to calculate the height of the building.
3. The third method also involves going up onto the roof of the tall building (not for the faint of heart) but does not involve any expensive equipment, any knowledge or physics or mathematics. You will need only your radio and a long piece of string or paracord. Absolutely any kind of radio may be employed. Your ground preparation, before going up onto the roof is critical. You must accurately tie a knot every twelve inches along your piece of string and attach one end to your radio. Once out on the roof you will then lower the radio to the ground, steadily and carefully, counting the knots as they pass through your hand. When the radio reaches the ground you will instantly know the building’s height in feet (N.B. metric measurements may be substituted if desired).
4. My final method is stupidly simple (or possibly simply stupid). It does, however, carry the potential to yield a highly accurate result without any knowledge of physics or mathematics. But first, please read the safety warning below. You will not need any expensive measurement equipment, nor any calculations, only your radio. This final method is also most suitable for those who suffer from vertigo since you will not need to venture out onto the roof of the building. Simply take your radio and knock on the door of the building superintendent. When he answers tell him: “If I give you this fine radio would you please tell me the height of your building”.

Note: Safety Warning! This method should only be done using any Icom radios that have accidentally come into your possession. Most sensible radio amateurs avoid such equipment. On no account should any Yaesu radio equipment be subjected to this treatment.