Plumb bob lines at two different places in plane surveying are _____.
parallel to each other
Understanding Plumb Bob Lines in Plane Surveying
A plumb bob is a weight attached to a string, used to determine the true vertical line at a point. This vertical line represents the direction of gravity at that specific location. In surveying, understanding the direction of gravity, indicated by the plumb bob line, is crucial for establishing elevations and vertical alignments.
Plane Surveying vs. Geodetic Surveying
Surveying can be broadly classified into two main types:
- Plane Surveying: This type of surveying assumes that the surface of the Earth is a plane and that all plumb bob lines within the survey area are parallel to each other. The effects of the Earth's curvature and the spheroidal shape are ignored. This method is suitable for small areas where the curvature effects are negligible.
- Geodetic Surveying: This type of surveying accounts for the true shape of the Earth (geoid/ellipsoid) and the curvature of its surface. Plumb bob lines are considered to converge towards the Earth's center. This method is used for large areas, national surveys, and establishing precise control networks.
Relationship of Plumb Bob Lines in Plane Surveying
The question specifically asks about plumb bob lines in plane surveying. Based on the definition and assumptions of plane surveying, one of the fundamental principles is treating all vertical lines (represented by plumb bob lines) within the survey area as parallel. This simplification is what distinguishes plane surveying from geodetic surveying.
Analyzing the Options for Plumb Bob Lines
Let's evaluate the given options in the context of plane surveying:
cut at the center of the earth: This describes the behavior of plumb bob lines in geodetic surveying, where they are assumed to converge at the Earth's center due to gravity acting towards the mass center. This is not the assumption in plane surveying.
inclined: While a plumb bob line indicates the local vertical, saying they are simply "inclined" is too vague and doesn't describe their relationship to each other in the context of surveying principles. They are vertical, but their relationship (parallel or converging) depends on the survey type.
parallel to each other: This is the key assumption made in plane surveying regarding plumb bob lines. For the relatively small areas covered by plane surveys, the convergence of plumb lines is considered negligible, and they are treated as parallel.
perpendicular to each other: Plumb bob lines indicate vertical direction. Two vertical lines cannot be perpendicular to each other unless they are in different planes, which is not the context here. Plumb lines at different points will be either parallel (plane surveying) or converging (geodetic surveying), but never perpendicular to each other in the same local reference plane.
Therefore, in plane surveying, the plumb bob lines at two different places are assumed to be parallel to each other.
| Feature | Plane Surveying | Geodetic Surveying |
|---|---|---|
| Earth Shape Assumption | Plane Surface | Curved Surface (Geoid/Ellipsoid) |
| Plumb Bob Lines | Parallel to each other | Converge at Earth's center |
| Suitable Area | Small areas | Large areas, national surveys |
Conclusion on Plumb Bob Lines in Plane Surveying
Based on the principles that define plane surveying, the curvature of the Earth is disregarded. This simplification means that all vertical lines, indicated by plumb bob lines, are considered to be parallel within the survey area. This fundamental assumption is essential for the calculations and methods used in plane surveying.
Revision Table: Key Concepts
| Term | Definition in Surveying | Relevance to Plumb Bob Lines |
|---|---|---|
| Plumb Bob | A weight used to establish a true vertical line. | Defines the direction of gravity at a point. |
| Vertical Line | Line aligned with the direction of gravity. | Represented by a plumb bob line. |
| Plane Surveying | Surveying ignoring Earth's curvature. | Assumes plumb lines are parallel. |
| Geodetic Surveying | Surveying accounting for Earth's curvature. | Considers plumb lines to converge. |
Additional Information: Gravity and the Geoid
The direction indicated by a plumb bob line is the direction of the local gravitational pull. This direction is perpendicular to the equipotential surface of gravity passing through that point. The equipotential surface that closely approximates mean sea level is called the Geoid. Plumb lines are always perpendicular to the Geoid surface. In geodetic surveying, the complex shape of the Geoid and how plumb lines converge are important considerations. However, in plane surveying, these complexities are simplified, treating the Earth's surface as flat and plumb lines as uniformly parallel.
The assumption of parallel plumb lines in plane surveying simplifies calculations significantly, allowing the use of plane trigonometry for distances, angles, and areas. This is why plane surveying is practical and widely used for smaller projects like property surveys, construction layouts, and topographic mapping of limited areas.
Important Questions from Fundamental Concepts
Which of the following statement is not correct for the principle of surveying?
The maximum error (mm) on the drawing should not be greater than _____.
Plumb bob lines at two different places in geodetic surveying will _____.
With an increase in the denominator of the representative fraction, the scale of the map will _____.
Calculate the length of one division of the vernier scale, if least count of the combination of main and vernier scale is 0.02 mm. The least count of the main scale is 1 mm.
