Relief displacement calculation – height of a tower (minar) from aerial photo data A camera flies at 1,000 m above mean ground. On the vertical photo, the top of a minar is 10 cm from the nadir point, and the measured relief displacement of the top is 7.2 mm. Estimate the height of the minar (assume base at mean ground).

Introduction / Context:Relief displacement on vertical aerial photographs provides a direct way to estimate object height when the flying height and radial distance are known. This principle is widely applied in single-photo heighting and for quick checks in mapping projects.

Given Data / Assumptions:

• Flying height above mean ground (datum), H = 1,000 m.
• Radial distance to the top from nadir on photo, r = 10 cm.
• Measured relief displacement of the top, d = 7.2 mm = 0.72 cm.
• Base of the minar is at the datum (mean ground).
• Photo considered vertical; scale variations across the object are negligible.

Concept / Approach:For vertical photos and objects standing on the datum, the relief displacement formula is:d = (r * h) / Hwhere h is object height. By rearranging, we obtain:h = (d / r) * H

Step-by-Step Solution:Convert units consistently: r = 10 cm; d = 0.72 cm.Compute ratio d / r = 0.72 / 10 = 0.072.Multiply by flying height: h = 0.072 * 1,000 m = 72 m.Therefore, the minar height is 72 m.

Verification / Alternative check:A quick sense-check: a 7.2% displacement relative to r (since 0.72/10 = 0.072) implies h is about 7.2% of H → 0.072 * 1,000 ≈ 72 m, consistent with the detailed computation.

Why Other Options Are Wrong:

• 52 m and 62 m underestimate the height relative to the measured displacement.
• 82 m overestimates; the computed ratio does not support this value.

Common Pitfalls:Mixing millimetres and centimetres or using the principal point instead of nadir for r; ensure consistent units and correct reference for radial distance.

Final Answer:72 m