Mean scale of a vertical aerial photograph – choose the correct formula If H is the flying height above mean ground level and f is the principal distance (focal length), what is the mean scale of a true vertical photograph over plane terrain?

Introduction / Context:
Scale links image measurements to ground distances. In vertical aerial photography over level ground, the mean scale is determined by the camera focal length and the aircraft height above ground at exposure.

Given Data / Assumptions:

• True vertical photograph (zero tilt) or negligible tilt.
• Level terrain (no relief differences).
• Principal distance equals calibrated focal length f.

Concept / Approach:
The central projection of the camera implies that any ground distance projects to the image with a linear ratio equal to focal length over flying height. Therefore mean scale S can be written as S = image distance / ground distance = f / H, provided both are expressed in compatible units.

Step-by-Step Solution:
Write the basic relation for similar triangles: x / X = f / H.Recognize that scale S = x / X → S = f / H.Hence the correct expression is f / H.

Verification / Alternative check:
Planimetric mapping commonly assumes S = f / H for block adjustment pre-computations when relief and tilt are small.

Why Other Options Are Wrong:

• H / f is the reciprocal (denominator of scale).
• (H − f) / H and H + f do not arise from the projection geometry.
• “None” is invalid because a standard formula exists.

Common Pitfalls:
Mixing up scale with the representative fraction denominator; remember RF denominator = H / f, while the scale ratio itself is f / H.

Final Answer:
f / H