In plane surveying, level lines are considered as _________ and plumb lines are considered as _________.
Correct Answer:
D. straight; parallel
📝 Detailed Explanation: The Core Assumption of Plane Surveying
This question tests the fundamental difference between reality (geodetic surveying) and the simplifying assumption made in plane surveying. The key is to understand how we treat the Earth's surface.
Definitions in Reality (Geodetic Surveying)
- Level Line: A true level line is a curved line where every point is equidistant from the center of the Earth. It follows the mean spheroidal surface of the Earth (like the surface of a calm lake). It is perpendicular to the direction of gravity at every point.
- Plumb Line: A plumb line is a line that follows the direction of gravity. Because all plumb lines are directed towards the center of the Earth, they inevitably converge at that single point. Therefore, they are not parallel to each other.
The Plane Surveying Assumption
For surveys of small areas, the curvature of the Earth is so slight that it becomes negligible. Plane surveying simplifies reality by making a crucial assumption: the Earth's surface is considered to be a flat plane over the survey area.
This single assumption changes our geometric definitions:
- Because the Earth is now treated as flat, a curved level line is approximated as a straight line.
- Because all gravity lines are now assumed to be perpendicular to a flat plane, the converging plumb lines are considered to be parallel to each other.
💡 Key Concepts for Students
- Plane vs. Geodetic: Plane surveying is used for small-scale projects (e.g., a building site, route survey) where the Earth's curvature can be ignored. Geodetic surveying is used for large-scale projects (e.g., mapping a country, establishing national control networks) where the Earth's true shape must be considered.
- Context is Key: The answer to this question depends entirely on the context of "plane surveying." In geodetic surveying, level lines are curved and plumb lines converge.
- Practical Implication: This assumption greatly simplifies all survey calculations, allowing for the use of plane geometry and trigonometry instead of the more complex spherical trigonometry required for geodetic work.