Q14. Which of the following is used for determining the location of station occupied by the plane table?
Correct Answer: D. Two-point problem
📚 Detailed Explanation: The Two-Point Problem for Locating the Occupied Station
This question asks which technique specifically determines the location of the station where the plane table is currently set up. This is the task of resection, and the two-point problem is one of the standard field methods for solving resection.
Two-point problem: A resection technique that locates the instrument station using exactly two visible, previously plotted control points. The procedure involves:
1. An auxiliary ray drawn to a third point on the sheet
2. Setting up an auxiliary table at a nearby plotted station
3. Back-sighting to fix the correct orientation
4. Drawing the second ray, whose intersection fixes the unknown station on the sheet.
The two-point problem simultaneously performs orientation and resection at the unknown station.
1. An auxiliary ray drawn to a third point on the sheet
2. Setting up an auxiliary table at a nearby plotted station
3. Back-sighting to fix the correct orientation
4. Drawing the second ray, whose intersection fixes the unknown station on the sheet.
The two-point problem simultaneously performs orientation and resection at the unknown station.
Why the Other Options Are Wrong
| Option | What it actually does |
|---|---|
| A — Intersection & radiation | These two methods locate external field features (not the instrument station itself). Radiation plots detail points from a known station; intersection plots inaccessible points from two known stations. |
| B — Intersection method | Intersection locates an unknown target point by sighting from two known instrument stations. The instrument station itself is known in intersection — only the target is unknown. |
| C — Radiation method | Radiation plots surrounding field details from one known station. The instrument station must already be known; radiation cannot determine an unknown station position. |
Two-Point vs Three-Point Problem
| Feature | Two-point problem | Three-point problem (Lehmann) |
|---|---|---|
| Known points used | 2 | 3 |
| Method | Auxiliary ray + back-sight at auxiliary station | Trial-and-error using triangle of error |
| Accuracy | Lower (fewer references) | Higher (additional constraint) |
| Field effort | Requires moving to an auxiliary station | All work from one instrument station |
Key Concepts for Students
- Two-point problem is a resection method: Both the two-point and three-point problems are methods for solving resection — fixing the occupied but unknown instrument station. Do not confuse them with intersection, which fixes a remote target, not the instrument.
- Three-point problem is more accurate: Because it uses three known reference points (vs two), the three-point problem provides an additional constraint and a self-checking mechanism (the triangle of error). Where accuracy is important, the three-point problem with Lehmann’s rules is preferred.
- Both are “orientation and resection” combined: Neither problem can be solved without simultaneously determining the correct orientation of the table. This is why Q26 states that two-point and three-point problems are methods of “orientation and resection” together.