Using Shadows to Measure Height

on Aerial Images


The length of a shadow can be used to measure the height of an object if:

1.      the shadow is being cast on level ground

2.      the feature is straight and vertical

3.      you know or can calculate the scale of the photo

4.      you know or can calculate the date and time of the photo


5.      you can compare the length of the shadow to the shadow of an object of known height


To use the sun angle to calculate the height


1.      Measure the length of the shadow on the photo from the base of the object.  Note that if the object is three dimensional such as a building or tank, as opposed to a pole or tree, you will need to be careful to measure the length of the shadow of the part of the object you want to measure, for example from the corner of a building to the point on the shadow where that side joins the roof.

2.      Use the scale to calculate the length of the shadow in the real world, s, and convert the number to useful units such as feet, yards or meters

3.      If you do not know the time but can find north on the photo, measure the angle to the sun from north. This is called the sun’s azimuth.

4.      Use the time or the azimuth to find the sun’s altitude angle, α.  This can be found most easily on the web using a site such as the US Naval observatory 

5.      Apply the formula to calculate the height of the object, h.  h = s  tan(α) Make sure that if α is in degrees that your calculator is set for angles in deg, not radians (to check, tan(45deg)=1)


Example:   photo in Amherst MA on March 27, 1965. 


scale = 90 ft between bases = 0.39 in [ 1:2800


shadow length = 7/16” x 2800”/1” x 1’/12” = 102’


sun azimuth = 145 deg   [ sun altitude = 28 deg


tan 20 deg = .0.53


so the light poles are .53*102’ = 54’ tall