Chaining Errors – Situations Causing ~1 in 1000 Relative Error with a 20 m Chain Which of the following situations typically introduces an error on the order of 1 part in 1000 when using a 20 m chain for distance measurement?

Introduction:
Understanding the magnitude of common field errors helps surveyors judge when corrections are necessary. With a 20 m chain, small mishandlings can create significant relative errors near 1 in 1000, impacting layout and quantity computations if not controlled.

Given Data / Assumptions:

• Nominal chain length = 20 m.
• Small deviations in length, alignment, or slope are considered.
• Relative error is approximated as error / measured length.

Concept / Approach:

Each listed situation yields an error roughly 20 mm over 20 m, which is 1/1000. Length error is direct. Alignment and slope errors can be estimated using small-angle approximations: the excess due to using a sloping or misaligned line rather than true horizontal/straight alignment is about d^2/(2L), which with the given numbers is near 0.02 m (20 mm) over 20 m.

Step-by-Step Solution:

Verification / Alternative check:

Exact computations using Pythagoras or alignment triangles confirm each is about 20 mm over 20 m, matching the 1 in 1000 scale.

Why Other Options Are Wrong:

Each single case indeed produces the specified magnitude; hence selecting any one alone would be incomplete. The correct holistic choice is “All of the above.”

Common Pitfalls:

Ignoring small alignment errors as “negligible”; forgetting to reduce slope distances to horizontal; overlooking periodic standardization of chains.

Final Answer:

All of the above