Handbook of Civil Engineering Calculations

DETERMINING SCALE OF

OBLIQUE PHOTOGRAPH

In a high-oblique aerial photograph, the distance between the apparent horizon and the
principal point as measured along the principal line is 86.85 mm. The flying height is
2925 m above sea level, and the focal length is 152.7 mm. What is the scale of this photo-
graph along a line that is normal to the principal line and at a distance of 20 mm above the
principal point as measured along the principal line?

Calculation Procedure:

1. Locate the true horizon in the photograph
   Refer to Fig. 33. An oblique aerial photograph is one that is taken with the optical axis in-
   tentionally displaced from the vertical, and a high-oblique photograph is one in which this
   displacement is sufficiently large to bring the earth's surface into view. By definition, the
   principal plane is the vertical plane that contains the optical axis, and the principal line is
   the line of intersection of this vertical plane and the plane of the photograph.
   Assume that the terrain is truly level. The apparent horizon is the slightly curved
   boundary line in the photograph between earth and sky. Consider a conical surface that
   has its vertex at the front nodal point L and that is tangent to the spherical surface of the
   earth. If atmospheric refraction were absent, the apparent horizon would be the arc along
   which this conical surface intersected the plane of the photograph. The true horizon is the
   straight line along which the horizontal plane through L intersects the plane of the photo-
   graph; it is normal to the principal line. In Fig. 33, M 1 and M 2 are lines in the principal
   plane that pass through L\ line M 1 is horizontal, and M 2 is tangent to the earth's surface.
   Points K 1 and K 2 are the points at which M 1 and M 2 , respectively, intersect the plane of
   the photograph; these points lie on the principal line. Point K 1 lies on the true horizon; if
   atmospheric refraction is tentatively disregarded, K 2 lies on the apparent horizon.
   Refer to Fig. 34a. The principal plane contains the angle of dip d, which is angle
   K 2 LK 1 the apparent depression angle a, which is angle oLK 2 the (true) depression angle

Optical axis

Plane of

photograph

Surface

of earth

FIGURE 33. Elevation normal to principal plane.