Precise Levelling – IGA Recommendation for Probable Systematic Error According to the International Geodetic Association (IGA) guidance for precise levelling, the probable systematic error in a levelling line of length k kilometers should not exceed which limit (units in millimetres)?

Introduction:
Levelling specifications set quantitative limits for errors to ensure reliable height transfer over long lines. This question focuses on the IGA-style recommendation for controlling probable systematic error as a function of line length k (in km). Memorizing these limits helps you validate field results and plan re-observations if needed.

Given Data / Assumptions:

• k is the length of the levelling line in kilometers.
• We are concerned with the probable systematic error component, expressed in millimetres.
• Standards assume good practice: equal backsight/foresight lengths, balanced sights, proper instrument checks.

Concept / Approach:

Systematic errors tend to accumulate with distance. Many geodetic specifications provide linear or root-length expressions. The IGA recommendation commonly cited for precise levelling caps the probable systematic error at a linear limit proportional to k, namely ± 0.1 k mm, keeping systematic trends tightly constrained for high-precision networks.

Step-by-Step Solution:

Verification / Alternative check:

Cross-check with other standards: some agencies specify additional random error limits such as C √k mm for allowable misclosure, but those pertain to random closure, not the probable systematic component asked here.

Why Other Options Are Wrong:

± 0.2 k mm is a looser limit; entries without units or with missing ± are improper; √k-based forms apply to random closure tolerance, not this systematic limit.

Common Pitfalls:

Confusing systematic error limits with allowable closing error specifications; mixing units or forgetting that k is in kilometres.

Final Answer:

± 0.1 k mm