How to find out true length for survey line?

Question

Examoogle · Accepted Answer

Option A: $l' 	imes \frac{L'}{L}$

Explanation & Concepts:
The true length of a survey line is determined by applying a correction factor to the measured length based on the actual (standard) length of the chain used. If a chain is not of its designated standard length, the measured distances will be incorrect, necessitating adjustment.

Working Principle: The principle of correction is derived from the proportionality of ratios: the ratio of the true length to the measured length is equal to the ratio of the actual length of the chain to its nominal (standard) length. Mathematically, $\frac{True Length}{Measured Length} = \frac{Actual Length of Chain}{Nominal Length of Chain}$. Rearranging this gives $True Length = Measured Length 	imes \frac{Actual Length}{Nominal Length}$.

Key Formulas: $True Length = l' 	imes \frac{L'}{L}$ — where $l'$ is the measured length, $L'$ is the actual length of the chain, and $L$ is the nominal length.

Key Points: If $L' > L$, the chain is too long, and the measured distance is less than the true distance.; If $L'; Corrected area = $Measured Area 	imes (\frac{L'}{L})^2$.; Corrected volume = $Measured Volume 	imes (\frac{L'}{L})^3$.

Advantages: Ensures accuracy in large-scale mapping.; Compensates for manufacturing errors or wear in chain links.

Disadvantages: Requires precise measurement of the chain's current actual length.; Does not account for temperature or tension corrections which require separate calculations.

Applications: Chain surveying for land parcel mapping.; Highway and railway alignment surveys.; Verification of survey equipment standards.

Additional Info: In the formula, $L$ represents the standard (nominal) length of the chain/tape (e.g., 20m or 30m), and $L'$ is the actual length of the chain used in the field after accounting for wear/tear.. Option B represents the reciprocal and would result in an erroneous value if applied.

Answer: A is correct — The true length is calculated by multiplying the measured length by the ratio of the actual chain length to the nominal chain length.

Exam Tip: Always remember the mnemonic 'Actual over Nominal' for any correction factor in surveying to ensure the ratio is applied correctly.

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Option B: $l' 	imes \frac{L}{L'}$

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Option C: $L 	imes \frac{L'}{l'}$

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Option D: None of the above

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