Aerial photogrammetry scale: for a truly vertical photograph with camera focal length f taken from flying height H above mean sea level (MSL), at a ground point of reduced level h, what is the local photo scale at that point?

Introduction / Context:
Photo scale varies with terrain elevation. Converting image distances to ground distances requires the correct scale at each ground point, especially over undulating terrain.

Given Data / Assumptions:

• Vertical photograph (tilt ≈ 0).
• Camera focal length = f.
• Flying height above MSL = H.
• Ground point reduced level = h above MSL.

Concept / Approach:
Local scale S equals focal length divided by flying height above ground at that point. Flying height above ground is H − h (since both are referenced to MSL for a vertical photo). Thus: S = f / (H − h)

Step-by-Step Solution:
Compute height above ground: H_g = H − h.Apply vertical photo scale formula: S = f / H_g.Therefore S = f / (H − h).

Verification / Alternative check:
Derivation from similar triangles between camera center, image point, and ground point yields the same relation.

Why Other Options Are Wrong:

• f/H ignores ground elevation (valid only if h ≈ 0).
• (H − h)/f is the inverse (not the scale).
• f/(H + h) uses the wrong sign; ground elevation reduces flying height above ground.

Common Pitfalls:

• Using a single average scale over significant relief, causing planimetric and height errors.

Final Answer:
f / (H - h)