Q22. If the plane table is not horizontal in a direction at right angles to the alidade, the line of sight is parallel to the fiducial edge only for:
📚 Detailed Explanation: Effect of Table Tilt on Line of Sight vs Fiducial Edge
This question tests understanding of the geometric relationship between the plane table’s alignment and the accuracy of ray drawing when the table is unlevel in a specific direction.
The alidade lies along the drawing sheet. Its fiducial edge defines one horizontal axis of the sheet plane. The line of sight (through the vane sights or telescope) must be in the same vertical plane as the fiducial edge for the drawn ray to correctly represent the direction to the target.
When the table is tilted in the direction perpendicular to the alidade’s length (i.e., the table tilts sideways relative to the alidade), the fiducial edge remains horizontal (it lies along the non-tilted axis), but the sheet plane is now tilted sideways.
For a horizontal line of sight, the sight remains in the same vertical plane as the fiducial edge regardless of the table’s side tilt, because both the fiducial edge and the horizontal sight are in the same horizontal plane. The ray drawn on the sheet still correctly represents the horizontal direction to the target.
For an inclined sight (upward or downward), the line of sight tilts into a different vertical plane than the fiducial edge due to the table’s side tilt. The drawn ray diverges from the true direction to the target — introducing a systematic error in the plotted position.
Why Inclined Sights Are Affected
When the table tilts sideways and the alidade is inclined to sight up or down a slope, the tilted table causes the telescope’s optical axis to swing slightly out of the vertical plane containing the fiducial edge. The ray drawn on the tilted sheet is then displaced from the correct direction by an angle proportional to both the table tilt and the sight inclination. Horizontal sights have zero vertical angle, so no such displacement occurs.
Key Concepts for Students
- Horizontal sights are immune to side tilt: A horizontal line of sight lies in the horizontal plane, which coincides with the plane of the correctly-placed fiducial edge. Side tilt of the table does not move the horizontal sight out of the fiducial edge’s plane, so no error is introduced.
- Inclined sights need a level table: Whenever the alidade is elevated or depressed to sight a target at a different elevation (as in tachometric surveys or hilly terrain), the table must be level to avoid a lateral divergence between the sight and the fiducial edge.
- This is why levelling is the first setup step: Levelling must be done before sighting because inclined rays (which are very common in undulating terrain) require a perfectly horizontal table for accurate directional plotting. Horizontal sights alone cannot justify skipping the levelling step.