Chain surveying – correcting a measured distance when the chain length is erroneous In practical chaining, if the chain/tape has an actual length different from its nominal (standard) length, how do you obtain the correct horizontal distance from the measured distance?

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:

  • The chain/tape has nominal (standard) length L_nom but actual verified length L_act.
  • A line on ground is measured and recorded as D_meas using that chain.
  • Temperatures, pull, and sag are assumed already accounted for; only standard-length error remains.


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:

Let n = number of chain applications; D_meas = n * L_nom (by record).True distance D_true = n * L_act.Hence D_true = (n * L_nom) * (L_act / L_nom) = D_meas * (L_act / L_nom).Thus, Correct distance = Measured distance * (Actual / Nominal).


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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