# Airphoto Scale: Variation with Height and Factors Affecting Airphoto Scale (Especially for GATE-Geospatial 2022)

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On a large-scale map, the effect of the curvature of the Earth՚s surface is negligible and the map is planimetrically correct.

Map scale can, therefore, be defined as the ratio of map distance to ground distance, usually expressed as a representative fraction.

On an airphoto, the scale can be thought of as the ratio of photo distance to ground distance. We can estimate the scale as the ratio of the photo distance between the principal point and the conjugate principal point to the air base (ground distance between exposure stations) .

However, because the airphoto is a perspective view, this ratio is only approximately correct. Airphoto scale varies from the centre towards the edges of the image.

Airphoto scale can also be determined based on the camera focal length and the altitude of the front nodal point of the camera lens at the instant of exposure. However, an implication of this is that the airphoto scale varies with terrain elevation. Higher elevations are closer to the camera lens and are therefore shown on the image at a larger scale than areas of lower elevation that are further from the lens.

The scale at point A can be determined as the ratio of the image distance ao in the positive image plane to the ground distance AOA. Since the triangles Loa and LOAA are similar triangles (same shape but different sizes) . oa/OAA = Lo/LOA = f/H ‘A. , where f is the camera focal length and H’ A is the height of the front nodal point of the lens above the ground at point A. This relationship proves that airphoto scale is equal to the focal length divided by the height of the lens above the terrain.

The airphoto metadata provide values for the focal length (f) and the height of the lens above sea level (H) . To determine the scale at points A and B, we need to know their elevations above mean sea level. This information can be obtained by inspecting a topographic map of the area. Once we know the elevations of the two, we, we can calculate the scale at these locations using scale = (H-hA) . Assume that the ground elevation at A is 3000 m, the ground elevation at B is 1500, and the height of the lens above mean sea level is 4500m. Then

• scale at A = f (H-hA) = 150 mm / (4500 m - 3000 m) = 1/10,000
• scale at A = f (H-hA) = 150 mm / (4500 m - 1500 m) = 1/20,000

## Factors Affecting Airphoto Scale

Airphoto scale is thus a function of several factors including:

• camera focal length,
• the flying height of the aircraft
• ground elevation above sea level

A camera with a wide-angle lens (shorter focal length) has a wider field of view and thus produces a smaller scale image for a given file format. Conversely, a telephoto lens, with its longer focal length, views a smaller area and produces a larger scale image. Flying height also affects photo scale. The higher the altitude of the aircraft (or satellite) , the smaller the scale of the resulting image. Variations in ground elevation are the main reason for scale distortion in airphotos. Higher elevations are closer to the camera and thus appear at a larger scale in the image. It is general practice to try to minimize scale distortion by ensuring that the maximum relief of the area represented in the airphoto is less than 10 % of the flying height. This implies that in Ganga floodplain where the maximum relief is unlikely to exceed 100 m, a flying height of 2000 m is adequate to minimize scale distortion. However, in the Aravali Mountains where maximum relief might be 3,000 m, a flying height of 30,000 m would be required.