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
or
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 http://aa.usno.navy.mil/data/docs/AltAz
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
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