a vertical aerial photograph was taken with camera of focal length 152 mm from a flying height of 1500 m above datum. Images a and b of ground points A and B appear on the photograph such that their photo coordinates are: xa=-50.50 mm, ya=-45.65 mm, xb=40.75 mm, yb=43.95 mm. Determine the horizontal length of the line AB if the elevations of A and B above datum are 205 m and 148 m respectively
Question
a vertical aerial photograph was taken with camera of focal length 152 mm from a flying height of 1500 m above datum. Images a and b of ground points A and B appear on the photograph such that their photo coordinates are: xa=-50.50 mm, ya=-45.65 mm, xb=40.75 mm, yb=43.95 mm. Determine the horizontal length of the line AB if the elevations of A and B above datum are 205 m and 148 m respectively
Solution
To determine the horizontal length of the line AB, we can use the principles of photogrammetry.
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First, we need to calculate the ground scale of the photograph. The ground scale is the ratio of the distance on the ground to the corresponding distance on the photograph. It can be calculated using the formula:
Ground Scale = (Focal Length / Flying Height)
Given that the focal length is 152 mm and the flying height is 1500 m, we can substitute these values into the formula:
Ground Scale = (152 mm / 1500 m)
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Next, we need to convert the photo coordinates (xa, ya) and (xb, yb) to ground coordinates (Xa, Ya) and (Xb, Yb) using the ground scale. The ground coordinates can be calculated using the formula:
X = (x * Ground Scale) Y = (y * Ground Scale)
For point A: Xa = (-50.50 mm * Ground Scale) Ya = (-45.65 mm * Ground Scale)
For point B: Xb = (40.75 mm * Ground Scale) Yb = (43.95 mm * Ground Scale)
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Now, we can calculate the horizontal distance between points A and B using the ground coordinates. The horizontal distance can be calculated using the formula:
Horizontal Distance = sqrt((Xb - Xa)^2 + (Yb - Ya)^2)
Substituting the values we calculated earlier:
Horizontal Distance = sqrt((Xb - Xa)^2 + (Yb - Ya)^2)
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Finally, we have the horizontal length of the line AB.
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