Tacheometric Distances – Which Corrections Apply to Horizontal Distance Derived from Stadia? When horizontal distances are computed tacheometrically from staff intercepts and vertical angle, which correction(s) are normally applied to the computed horizontal distance for standard engineering accuracy?

Introduction / Context:
Tacheometry yields distances from optical measurements rather than direct taping. The raw distance lies along the line of sight and must be converted to a horizontal distance for mapping and setting out. This question explores which corrections are normally relevant in routine tacheometric work.

Given Data / Assumptions:

• A standard fixed-multiplying stadia instrument is used.
• Staff intercept s and vertical angle θ are observed.
• Ordinary topographic ranges (typically under a few hundred metres) are considered.

Concept / Approach:

The tacheometric distance computed from D = k * s + C is along the line of sight. The required plan distance is its horizontal projection. Thus, a slope reduction (multiplying by cos θ or using the appropriate formula that includes sin and cos terms) is essential. Temperature correction pertains to tape length variation and does not apply to optically derived distances. Curvature and refraction mainly influence very long sights or precise levelling; for ordinary tacheometry their effect on horizontal distance is negligible and usually ignored by specification, though vertical components may warrant atmospheric considerations in precision work.

Step-by-Step Solution:

Verification / Alternative check:

Survey manuals show the horizontal component derived directly in the tacheometric equations; ancillary corrections are absent unless doing long-range geodetic-quality observations.

Why Other Options Are Wrong:

Temperature correction belongs to tapes and EDM scale factors, not optical stadia. Curvature/refraction corrections target vertical refraction in precise levelling; their contribution to short-range horizontal distance is minuscule.

Common Pitfalls:

Over-correcting tacheometric distances with tape-based formulas; forgetting to reduce the sloping line-of-sight distance to horizontal, which is the essential step.

Final Answer:

Slope correction (reduction from the line of sight to horizontal)