Difficulty: Easy
Correct Answer: ± 0.5 k mm
Explanation:
Introduction / Context:
Levelling specifications define acceptable random (accidental) error growth with distance to safeguard vertical control quality. The International Geodetic Association (IGA) provides widely cited limits for precise levelling. Knowing these values helps surveyors plan section lengths, balancing sight lengths and refraction to meet standards.
Given Data / Assumptions:
Concept / Approach:
Probable accidental error scales approximately with distance because many small random effects (reading scatter, target shimmer, rod handling) accumulate. IGA guidance expresses an upper limit in millimetres as a simple function of k for specification checks. The commonly quoted allowance for probable accidental error is ±0.5 k mm for precise levelling, distinguishing it from tighter limits on systematic components and from alternative national standards that may use root-mean-square formulations with square-root distance dependence for closures.
Step-by-Step Solution:
Verification / Alternative check:
Comparative specifications (e.g., national mapping agencies) provide similar magnitude limits, with some adopting closure rules based on square-root of distance; the stated IGA figure fits within that family for precise work and is a standard exam recall value.
Why Other Options Are Wrong:
±0.1 k mm is more typical of systematic-error guidance (stricter but not for accidental errors). The higher values (±1 k, ±2 k, ±5 k mm) are too permissive for precise levelling and would not meet control standards.
Common Pitfalls:
Confusing accidental error limits with misclosure limits or with systematic error allowances; forgetting to report the unit as millimetres per kilometre, not per setup.
Final Answer:
± 0.5 k mm
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