Plane Table – Displacement on Plan Due to Centering Error Across a 40 m Ray While setting a plane table, the station was mis-centered so that the plotted station is 30 cm perpendicular to a 40 m ground ray. If the mapping scale is 1 cm = 2 m, what is the displacement of the end of the ray on the plan from its true position?

Introduction / Context:
In plane table surveying, small centering errors at the plotted station produce proportional displacements at plotted detail points along rays. Quantifying this displacement helps decide whether to re-center or accept the error for the given scale and required accuracy.

Given Data / Assumptions:

• Ground ray length = 40 m.
• Centering (perpendicular) error at station = 30 cm = 0.30 m.
• Map scale = 1 cm represents 2 m.
• Error is perpendicular to the ray, producing maximum plotted shift at the ray end.

Concept / Approach:

The displacement at the end of a plotted ray caused by a perpendicular centering error e is proportional to the ratio e / ground_ray_length, applied to the plotted ray length. This is similar to similar-triangle scaling of the small lateral error along the ray.

Step-by-Step Solution:

Verification / Alternative check:

As a ratio: 0.30 m over 40 m is 1 in 133.33; 20 cm / 133.33 ≈ 0.15 cm, corroborating the result.

Why Other Options Are Wrong:

0.02 cm and 0.10 cm understate the proportional effect; 0.02 m is a ground unit, not plan; 0.50 cm overstates the error by more than 3 times.

Common Pitfalls:

Confusing ground and plan units; using linear instead of proportional scaling; not ensuring that the error is perpendicular to the ray, which gives the maximum displacement case.

Final Answer:

0.15 cm