Relation between air base and photographic base: for successive vertical photographs with flying height H and focal length f, how are the ground air base B and the image photographic base b related?

Introduction / Context:
In aerial photogrammetry, the air base B is the ground distance between successive exposure stations, while the photographic base b is the distance between corresponding principal points on the overlapping photographs. Their relation under vertical photography links image geometry to ground geometry.

Given Data / Assumptions:

• Vertical photographs with negligible tilt.
• Flying height above datum = H; camera focal length = f.
• Scale approximately uniform: scale ≈ f / H at the principal point.

Concept / Approach:
Linear distances on the photo are related to ground distances by the scale factor f / H. Thus, a ground distance equals the corresponding photo distance multiplied by H / f. Applying this to the inter-exposure distance yields B = (H / f) * b.

Step-by-Step Solution:
Scale at principal point: photo length / ground length = f / H.Rearrange: ground length = (H / f) * photo length.Let photo length = b → ground length (air base) B = (H / f) * b.

Verification / Alternative check:
Dimensional reasonableness: larger H increases B for a fixed b, matching intuition; larger f reduces scale and thus reduces computed B for fixed b.

Why Other Options Are Wrong:

• B = (f / H) * b or b = (H / f) * B invert the scale mapping.
• B = (H * f) / b is dimensionally inconsistent.
• b = (f / H) * B restates the inverse but fails to answer the form asked.

Common Pitfalls:
Confusing scale f/H with its reciprocal H/f; ignoring minor variations in scale away from the principal point.

Final Answer:
B = (H / f) * b