Plane vs geodetic assumptions: which statements are valid? Decide which statements about plumb lines, curvature, and survey extent are correct for practical surveying.

Introduction / Context:
Survey computations rest on geometric assumptions about the Earth. Over small extents, the Earth can be approximated as a plane; over larger extents, it must be treated as a curved surface. Plumb lines (gravity directions) also vary slightly in direction across the globe. This question checks your ability to choose appropriate assumptions by survey scale.

Given Data / Assumptions:

• Plane surveying approximations apply over small areas.
• Geodetic principles are required over large areas.
• Plumb lines point toward the Earth’s center of mass direction locally; they are not parallel across distance.

Concept / Approach:

For small projects (e.g., site plans), neglecting curvature and treating level surfaces as planes yields negligible error. For long lines and large networks, curvature and convergence of meridians matter. The non-parallelism of plumb lines reflects Earth’s curvature and gravity anomalies; while the effect is tiny locally, it is fundamental conceptually.

Step-by-Step Solution:

Verification / Alternative check:

Textbooks define plane surveying limits (often within a few kilometres) and recommend geodetic treatment for state/national networks.

Why Other Options Are Wrong:

Any subset misses at least one correct statement; hence “All of the above” is the best choice.

Common Pitfalls:

Applying plane formulas across long distances; assuming plumb lines are exactly parallel everywhere.

Final Answer:

All of the above