Handbook of Civil Engineering Calculations

FIGURE 34
AERIAL PHOTOGRAMMETRY
which is angle oLK1. Then d a. Let H flying height above sea level in meters,
and dangle of dip in minutes. Then d1.775 2 H,
Eq. a. This relationship is based
on the mean radius of the earth, and it includes allowance for atmospheric refraction.
From Fig. 34a, tan oK2/f, Eq. b. Then d 1.775 2 2925 96.0, or d 1°36.
Also, tan 86.85/152.7 0.5688, giving 29°38. Thus, 1°36 29°38
31°14. From Fig. 34a, oK1 f tan , or oK1 152.7(0.6064) 92.60 mm. This dimension
serves to establish the true horizon.
2. Write the equation for the scale of a constant-scale line
Since the optical axis is inclined, the scale S of the photograph is constant only along a
line that is normal to the principal line, and so such a line is called a constant-scale line.
As we shall find, every constant-scale line has a unique value of S.
Refer to Fig. 35, where A is a point on the ground and a is its image. Line AQ is normal
to the principal plane, Q lies in that plane, and q is the image of Q. Line Rq is a horizontal
line in the principal plane. If the terrain is truly level and curvature of the earth may
be disregarded, the vertical projection of the distance from A to L is H. Let e distance in
photograph from true horizon to line qa. Along this line, S qa/QA Lq/LQ LR/LN.
But LR e cos and LN H. Thus, S (e cos )/H, Eq. c.
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