The distance in the x direction between two control points on a vertical aerial photograph is 4.5". If the distance between these same two points is 3.6" on another photograph having a scale of 1:24,000, determine the scale of the first vertical aerial photograph. If the focal length of the camera is 6"and the average elevation at these points is 100 ft, determine the flying height from which each photograph was taken.
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Let the actual distance between the points MN be x feet
M'N' = 3.6 in = 0.3 ft
(M'N') / (MN) = (ON') / (ON) = Scale 1:24,000
1 / 24000 = 0.3 / x
x = 7200 feet
Now solve for the scale of the second photo.
M'N = 4.5 in = 0.375 ft
Scale = 0.375 / 7200
Scale = 1:19,200
Now determine the height from which the first photo was
taken (H1).
1 / 19,200 = (6.0/12) / (H1 – 100)
H1 = 9,700 feet
Now determine the height from which the second photo was taken (H2).
1 / 24,000 = (6.0/12) / (H2 – 100)
H2 = 12,100 feet
Therefore, the scale of the first photograph is 1:19,200, the elevation it was taken
from is 9,700 feet, and the second photograph was taken at an elevation of 12,100
feet.
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