Difficulty: Easy
Correct Answer: Correct distance = Measured distance * (Actual chain length / Nominal chain length)
Explanation:
Introduction / Context:
In chain and tape surveying, the measured distance is proportional to the physical length of the measuring device. If the chain is worn long or short, every application introduces a systematic scale error. Converting a field-measured distance to the correct value requires applying a length correction factor. This question tests the fundamental relationship between measured distance and the ratio of actual-to-nominal chain length.
Given Data / Assumptions:
Concept / Approach:
The measurement process counts how many “chain lengths” fit into the line. If each physical chain length is L_act instead of L_nom, the true distance must scale in the same ratio. Therefore the correction is a pure multiplicative factor equal to L_act / L_nom. If the chain is too long (L_act > L_nom), the measured number of chains understates the true distance; multiplying by L_act / L_nom increases it appropriately. If the chain is too short, the factor reduces the result.
Step-by-Step Solution:
Verification / Alternative check:
On a standardized base line, determine L_act; apply the same factor to several trial measurements. The proportional misclosure disappears after scaling by L_act / L_nom, confirming the formula’s validity for cumulative length errors.
Why Other Options Are Wrong:
Option B inverts the factor; it would make a long chain shorten the computed distance incorrectly.
Option C adds a constant difference in lengths, which is dimensionally and conceptually wrong for a scale error.
Option D is incorrect because the correct multiplicative relation is known and standard.
Common Pitfalls:
Forgetting to distinguish between standard-length error (scale) and sag/pull/temperature (variable) effects; mixing up numerator and denominator in the ratio; neglecting to re-check L_act periodically as chains wear.
Final Answer:
Correct distance = Measured distance * (Actual chain length / Nominal chain length)
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