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Difficulty: HardElementary Surveying Instruments and Fieldwork

During a chain survey along a baseline, a surveyor uses a 20 m20\text{ m} chain that is later discovered to be 0.10 m0.10\text{ m} too short due to bent links. If the recorded length of the baseline is 400 m400\text{ m}, what is the true ground distance of the baseline, and what category of error is produced by this tape defect?

  1. 398.00 m398.00\text{ m}; cumulative errorAnswer
  2. B
    402.00 m402.00\text{ m}; cumulative error
  3. C
    398.00 m398.00\text{ m}; compensating error
  4. D
    402.00 m402.00\text{ m}; compensating error

Answer

398.00 m398.00\text{ m}; cumulative error
The true ground distance is calculated using the formula True Distance=Recorded Distance×(L′/L)\text{True Distance} = \text{Recorded Distance} \times (L'/L), where L′L' is the actual chain length (19.90 m19.90\text{ m}) and LL is the nominal length (20.00 m20.00\text{ m}). Applying this yields 400×(19.90/20)=398.00 m400 \times (19.90 / 20) = 398.00\text{ m}. Furthermore, because the flaw in the instrument is constant and acts in one direction throughout the survey, the resulting error accumulates continuously, making it a cumulative error.

Step-by-Step Solution

1
Determine the actual length of the chain
Nominal length L=20.00 mL = 20.00\text{ m}; actual length L′=20.00−0.10=19.90 mL' = 20.00 - 0.10 = 19.90\text{ m}.
The chain is 0.10 m0.10\text{ m} too short, so each full chain layout measures only 19.90 m19.90\text{ m} of ground distance.
2
Calculate the true ground distance using the proportion formula
True Distance = Recorded Distance ×L′L=400×19.9020.00=398.00 m\times \frac{L'}{L} = 400 \times \frac{19.90}{20.00} = 398.00\text{ m}.
When an instrument is too short, the measured distance is over-reported, so the true distance must be less than the recorded distance.
3
Classify the nature of the surveying error
Cumulative (systematic) error.
Errors arising from constant instrumental flaws (like an incorrect chain length) always act in the same direction and accumulate in magnitude as more chain lengths are measured.

Key Concept

Chain Surveying Distance Correction and Error Classification
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Topics

Elementary Surveying Instruments and Fieldwork

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