## Scale Determination

A common task in Aerial Photogrammetry is to determine the scale of an image. This method can be applied to aerial photographs or photocopies maps that may have changed scale from the original.

Scale is a function of two factors first is the focal length f of the camera and the second is the distance to the object being imaged.

The scale formula is usually expressed as:

$$S= \frac{f}{H-h}$$

Where f is the focal length of the camera, H is the height above mean sea level and h is the height of the ground above mean sea level. To calculate scale this way you need information from the camera margins between the images on a standard aerial camera.

This information is not always available. An alternative using similar triangles is to use:

$$S = \frac{photo distance}{ground distance}$$

Where photodistance is a distance measured between two points on your unknown scale image and grounddistance is the distance between the same two points on the ground using the same units.

Scale is usually expressed as a fraction such as 1:24,000 the scale of a USGS 7.5 minute topographic map. If you applied the above formula to the USGS 7.5 minute topographic map you would get 0.000042 which is the decimal equivalent of 1:24,000. to make it easier to produce the fraction we usually calculate the Photo Scale Reciprocal (PSR).

$$PSR = \frac{ground distance}{photo distance}$$

Created by David R. Larsen July 2, 2004
Last Updated: August 6, 2012