Map Scale & Curvature – When Must Earth Curvature Be Considered? For plane surveying approximations, at what approximate area extent should curvature of the Earth be taken into account to avoid significant positional error on maps?

Introduction / Context:
Small-area surveys can often neglect Earth curvature and treat the surface as a plane. As the extent grows, curvature introduces measurable discrepancies between plane and spherical geometry, affecting distance reduction, azimuth convergence, and level surfaces. Surveyors use a rule-of-thumb area threshold to decide when geodetic considerations become necessary.

Given Data / Assumptions:

• Plane surveying approximations are acceptable only for limited extents.
• Target is a practical area threshold rather than a precise formula.
• Normal topographic accuracy and common map scales are assumed.

Concept / Approach:

Many standard texts suggest that for areas on the order of a few hundred square kilometres, curvature effects begin to compromise plane assumptions. An often-cited nominal limit is around 260 square kilometres. Beyond this, curvature corrections (and sometimes refraction considerations in levelling) and map projections should be applied for accuracy and consistency, particularly when joining with adjacent control networks.

Step-by-Step Solution:

Verification / Alternative check:

Specification documents and teaching references list similar thresholds; exact need also depends on accuracy class and whether the survey ties to geodetic control and projections.

Why Other Options Are Wrong:

100–200 sq km may still be safe for plane treatment in many engineering tasks; 400 sq km is too lax and risks noticeable distortion.

Common Pitfalls:

Relying on area alone; elongated corridors may require geodetic treatment sooner; forgetting projection scale factors when moving to map coordinates.

Final Answer:

260 sq km