# Influence of Relief on Geometry of the Conventional Aerial Photograph: Relief Distance Formula & Scale (Especially for GATE-Geospatial 2022)

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So far, our discussion of tilting has ignored the effects of relief. It is important to note that the map is essentially an orthogonal projection as shown in below Figure, which is in contrast to the central projection of the aerial photograph.

Assuming the case of a truly vertical aerial photograph, the introduction of the relief causes scale change and relief displacements as shown in below figure.

The position of the hilltop at A ′ should be represented on the map as the orthogonal projection of A ′ at A on the datum level; but on the negative plane of the aerial photograph, it is imaged as a ′ as a result of the central projection through o. The correct position for the hilltop A on the negative plane should be a. The distance aa ′ on the negative plane is called relief ′ displacement (Δr) .

## Scale in Presence of Relief at Single Elevation

When the relief is introduced, the scale of the photograph is defined by the ratio a ‘p-A’ P ‘. which by similar triangles a’ op and A ‘P’ o, is A Pr equal to

## Scale in Presence of Relief at Several Elevations

This only gives the scale at one elevation. For a large area with changes in elevation, the average scale is required, which can be found by averaging the heights of the various terrain points, i.e..

where is the average scale, f is the focal length, H is the flying height above the datum lane and h is the mean height of the terrain.

## Relief Displacement Formula

The relief displacement can be employed to determine the height of an object because, with reference to the above Figure, it can be mathematically related to the height of point A thus:

where hA is the height of the object A above the datum, Δr is the amount of relief displacement, r is the distance on the photograph from the principal point to the image of the top of the object (i.e.. the radial distance) , and H is the flying height from the datum.

This is the relief displacement formula which is particularly useful to the geographer who wants to determine the heights of a few prominent objects such as buildings, tree. 2, etc, whose base is clearly visible on the photograph. Obviously, objects near the edge of

the photograph or at the furthest distance from the principal point give rise to larger relief displacements and hence their heights are much easier to determine. In practice, to obtain an accurate measurement of relief displacement of an object, a scale magnifier is required.

The foregoing discussion on relief displacement assumes that the aerial photograph is perfectly vertical. When tilting is introduced, the relief displacement can be seen to be radial from the nadir point (n) .