When working with aerial photography, particularly older sets of photography, one will invariable come across a project or set of prints in which the scale has not been defined. This of course is a problem, since no real spatial analysis such as distance, size, etc., can be done without a known scale. Without this information, the photos take on more of a historical records, since they cannot be used for real analysis. However, one needn’t despair. Calculating the scale of an aerial photograph is actually a simple process. There are actually two simple methods that can be used to find photo scale, though each will require the use of a map.
Method I: Object of know size on a map
This is generally easiest to do, if you can measure the distance of 1 mile on a map. This will be your control. Once you have settled on an object on map, find this object on your aerial photo. Since I am using 1 mile as my control, I will measure the object on the photo and record the results in inches. However, if I was using 1 kilometer as my control, I would measure the distance in centimeters. For the example, if the distance between two houses on my map was exactly one mile, I might use that as my point of reference. Now, finding these two houses on my photo, I find that the distance between them is 6.2 inches on the photo. Armed with that information, I just plug the numbers into the equation.
Equation: (6.2 in/1 mile) * ((1/6.2)/(1/6.2)) * (1 mile/63,360 in) = 1/10,220 or 1:10,220 (results are rounded)
Method II: Comparing with another map with a known scale
The second method will require you to use a little bit of algebra to calculate the distance of an object on a map with a known scale against the distance of an object on an aerial photograph of unknown scale. For example, lets say we are measuring the distance between two houses. On the aerial photography, the distance is 7.2 cm. Now on my map covering the same area at 1:24,000, the distance between the two houses is 2.4 cm. To find the scale of the photo, we create an algebraic expression to solve for the unknown variable.
Equation: 7.2 cm . (photo) * (x/1) = 2.4 cm. (map) * (24000/1)
Therefore: 7.2 * x cm. = 2.4 * 24000 cm.
Since the units are the same, we cancel them out, and get the final equation: x=(2.4 * 24000)/7.2
x=8000 or 1:8000