Calculate the height of an object by its shadow length on the map
This calculator allows you to calculate the height of an object based on the length of its shadow, which is often necessary when designing antenna systems. The length of the shadow can be measured directly with a tape measure or other measuring instrument. In addition, if the object has a significant height, you can use the Google Earth program. The idea of calculating and creating such a calculator belongs to Ochir Bashendzhiev - UA6IGI. It is known from the school course that the height of an object can be calculated by simultaneously measuring the shadow of an object with a known height and applying the theorem on the similarity of triangles. However, you can simplify the task by simply determining the position of the Sun on the celestial sphere. If you use the Google Earth program, you can get the result without even leaving your computer, simply by measuring the length of the shadow on a satellite imagery! The source code for calculating the position of the Sun at a given time is ©Senol Gulgonul.
As a result, the calculator is divided into two separate ones.
- The first one is for those who used direct measurement of the shadow length. In addition, you will need to know the exact coordinates of the observation point and the exact time of measurement. The geographic coordinates of your location can be easily found out from the Google Maps services. Usually, they can be obtained as a string of two digits separated by a comma: latitude and longitude. They can be copied and pasted into our calculator. The time zone in this case is the difference in hours with world time, taking into account the transition to daylight saving time.
- The second one is for those who used the Google Earth program. Incidentally, I will note that it will not be possible to use the online service Google Maps, since we will not be able to determine the time of imagery using them. Using Google Earth, we can at least find out the date when the satellite imagery was taken, and then, using simple calculations, determine the photo time using the azimuth angle of the shadow. More details are under the second calculator.
Get object height by measuring its shadow length
±GMT – Time different from Greenwich (UTC)
Calculator of the object height by measuring its shadow length in the Google Earth
The source data for the second calculator are all available from the Google Earth program. The date of the satellite photo (Imagery Date) and the exact coordinates of the object are available in the program status bar. Then we find the shadow and measure it using the
Tools->Ruler->Line tool. The tool shows us the length of the shadow (Ground length) and its azimuth (Heading). The concept of “azimuth” is used here in common use, as on a compass. Zero direction to the north and then counting clockwise. In order to correctly determine the azimuth to the sun in the Google Earth program, you need to remember one simple rule: the shadow must be measured from its end towards the object, in other words, in the direction of the sun. Then the azimuth value is correct. Knowing the value of the azimuth of the sun, the calculator determines the time of imagery and finds the height of the object.
The method of determining the height of an object by its shadow has the following limitations that reduce its accuracy:
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- Error in measuring the length of the shadow. For small lengths (objects less than 10 m high): direct measurement is better. For high objects: measurement in the Google Earth program is better.
- The slope of the surface (not horizontal) on which the shadow falls.
- The fall of the end of the shadow on objects having the own height (garage, neighboring building, etc.).
- The imageries in the Google Earth do not always show clear shadows from the desired object, especially if the picture was taken when the sun is high (in summer in the Northern Hemisphere).
- To get the correct imagery, the 3D Buildings layer must be turned off.
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