________ is the method of locating an offset point from 2 different points on a chain line in such a way that all the three points form a near-equilateral triangle.

Question

Prepp Team · Accepted Answer

Understanding Point Location in Surveying: Method of Ties

Surveying involves determining the relative positions of points on or near the surface of the earth. When performing chain surveying, which primarily relies on linear measurements, it is often necessary to locate details or specific points that are not directly on the main survey line (chain line).

These points are located by taking measurements from the chain line. Various methods exist for this purpose, commonly referred to as offset methods or tie methods.

Exploring Different Methods for Locating Points

Let's consider the methods mentioned in the options:

Perpendicular Offset Method: This is the most common method. It involves measuring the shortest distance from the point to the chain line, which means the measurement is taken perpendicular (at 90 degrees) to the chain line.
Oblique Offset Method: When it is difficult or impossible to take a perpendicular offset (e.g., due to obstacles), offsets are measured at an angle other than 90 degrees to the chain line.
Swing Offset Method: This method is used to find the foot of the perpendicular from a point to the chain line without using an instrument to set out a right angle. The end of the tape is held at a point on the chain line, and an arc is swung with the measured offset distance. The shortest distance (perpendicular) is where the arc just touches the line.
Method of Ties: This method involves locating a point by measuring the distance from that point to two established points on the chain line. These two measurements are called 'ties' or 'tie lines'. The point is located by the intersection of two arcs drawn from the two points on the chain line with radii equal to the measured tie distances. These two tie measurements, along with the distance between the two points on the chain line, form a triangle.

Analyzing the Method Described in the Question

The question describes a method where an offset point is located from 2 different points on a chain line. Measurements are taken from these two points to the offset point. This clearly aligns with the description of the Method of ties, where two tie measurements are taken from the chain line to locate the point.

Furthermore, the question specifies that these three points (the offset point and the two points on the chain line) form a near-equilateral triangle. In the method of ties, the geometry formed by the two tie measurements and the segment of the chain line between the two reference points is indeed a triangle. Choosing the two reference points on the chain line such that the resulting triangle is nearly equilateral is a surveying practice aimed at achieving good geometric strength. A near-equilateral triangle provides a stable intersection for locating the point and minimizes errors compared to very acute or obtuse triangles.

Conclusion

Based on the description of locating an offset point from two points on a chain line using tie measurements to form a near-equilateral triangle, the method being described is the Method of ties.

Comparison of Point Location Methods
Method	Description	Measurements	Geometry
Perpendicular Offset	Locating a point by its shortest distance to the line.	One distance (perpendicular) and position along the line.	Right-angled triangle (implicitly).
Oblique Offset	Locating a point by its distance and angle (not 90°) to the line.	One distance (oblique) and angle/position along the line.	Triangle.
Swing Offset	Finding the foot of the perpendicular by swinging an arc.	One distance swung from a point on the line.	Arc intersection to define perpendicular.
Method of Ties	Locating a point by measuring distances from two points on the line.	Two distances (ties) from two points on the line.	Triangle formed by the point and the two points on the line.

Revision Table: Surveying Point Location Methods

Method Name	Key Principle	Measurements Required
Perpendicular Offset	Locating relative to a 90° line from the baseline.	Distance along baseline, perpendicular distance to point.
Method of Ties	Locating using distances from two known points on the baseline.	Distances from point to two baseline points.
Oblique Offset	Locating relative to a line at an angle ≠ 90° from baseline.	Distance along baseline, oblique distance to point.
Swing Offset	Finding perpendicular by swinging tape from baseline point.	Swung distance to touch baseline (determines perpendicular location).

Additional Information: Importance of Triangle Geometry in Surveying

In surveying techniques that rely on triangulation or creating triangles (like the method of ties or larger triangulation networks), the shape of the triangle significantly impacts the accuracy of the located points.

Triangles that are very acute (having a very small angle) or very obtuse (having an angle close to 180 degrees) are considered geometrically weak.
Small errors in measuring distances or angles in weak triangles can lead to large errors in the calculated positions of points.
Isosceles triangles with apex angles between 30° and 150° are generally considered good.
The strongest triangle shape for locating a point is an equilateral triangle, where all angles are 60°. A "near-equilateral" triangle aims for this optimal geometry to minimize the propagation of errors in the measurements. This is why it is preferred in the method of ties when possible.