Curve Setting - Angular and linear Methods of Settings out curves (2024)

Linear Method of Curve Setting

The linear method, also known as the chord method or the tangent-offset method, is one of the techniques used in surveying and engineering to determine and mark points along a curved path, such as a circular curve or an arc. It is a straightforward and practical method for setting out curves, particularly in field surveying or construction applications where precision is not the primary concern.

The various types of linear methods of curve setting include:

  • Offsets from Long Chord
  • Offsets from Chord Produced
  • Radial Offset from Tangent
  • Successive Bisection of Chords
  • Perpendicular Offset from Tangent

Steps involved in the curve setting by Linear Methods

  • Establishing the center of the curve.
  • Determination of the radius and degree of the curve.
  • Calculation and marking of the tangent points, offset distances, etc according to the method employed.
  • Marking the curve points by employing different surveying techniques.
  • Establish the transition curves (if applicable).
  • Checking and verifying the layout.

Types of Linear Methods of Curve Setting

Offsets from long chord

Curve Setting - Angular and linear Methods of Settings out curves (1)

Fig: Offsets from long chord

Offsets from the long chord method, also known as the radial offset method, is a linear method of curve setting which provides a closer approximation to the true curve.

Ordinate at a distance x from the midpoint of the long chord is given by:

\(O_x=\sqrt{R^2-x^2}-\sqrt{R^2-\left(\frac{L}{2}\right)^2}\)

Perpendicular Offset From Tangent

The perpendicular offset from the tangent method is a linear method of curve setting which involves calculating and measuring the perpendicular distances from the tangent line to the curve at specific points. Since this method takes into account the perpendicular distances from the tangent line to the curve, it provides accurate positioning of points along the curve.

Curve Setting - Angular and linear Methods of Settings out curves (2)

Fig: Perpendicular Offset from Tangent

In the figure above,

\(\mathrm{O}_{\mathrm{x}}=\mathrm{T}_1 \mathrm{E}_1=\mathrm{T}_1 \mathrm{O}-\mathrm{E}_1 \mathrm{O}\)

The exact formula is given by:

\(O_x=R-\sqrt{R^2-x^2}\)

The approximate formula is:

\(O_x=\frac{x^2}{2 R}\)

Offset From Chord Produced

The offset from chord produced method is another linear method of curve setting which involves calculating and measuring the perpendicular distances from a produced chord to the curve at specific points. This method is generally employed for longer curves having larger radius.

Curve Setting - Angular and linear Methods of Settings out curves (3)

Fig: Offset from Chord Produced

\(O_n=\frac{C_n}{2 R}\left(C_{n-1}+C_n\right)\)

Radial Offset from Tangent

The radial offset from the tangent method involves calculating and measuring the radial distances from the tangent line to the curve at specific points.

Curve Setting - Angular and linear Methods of Settings out curves (4)

Fig: Radial Offset from Tangent

The exact formula is given by:

\(O_x=\left(R^2+x^2\right)^{1 / 2}-R\)

The approximate formula is:

\(O_x=\frac{x^2}{2 R}\)

Curve Setting - Angular and linear Methods of Settings out curves (2024)

FAQs

Curve Setting - Angular and linear Methods of Settings out curves? ›

Curve Setting

What are the different linear methods of setting out a curve? ›

There are two main methods: linear and angular. The linear method uses only a tape or chain and does not require angle measurement. It includes setting out curves by offsets from the long chord, by successive bisection of arcs, and by offsets from the tangents.

What angular methods are used for setting out curves? ›

The Angular methods are:
  • Rankine method of tangential angles.
  • Two theodolite method.
  • Tacheometric method.

What are the different methods of designating a curve? ›

A curve may be designated either by the radius or by the angle subtended at the centre by a chord of particular length In India, a curve is designated by the angle (in degrees) subtended at the centre by a chord of 30 metres (100 ft.) length. This angle is called the degree of the curve (D).

What are the methods of setting out offset? ›

There are 3 methods by which pegs on the centreline of circular curves can be set out:1. Tangential angle method2. Offsets from the tangent lengths 3. Offsets from the long chordWhen traditional methods are being used it is first necessary to locate the intersection and tangent points of a curve.

What is the difference between linear method and angular method? ›

Linear methods determine the coordinates of points along the curve, while angular methods use deflection angles and tangent offsets. Each method has its advantages and is selected based on project requirements and terrain characteristics.

What is the angular method of surveying? ›

plane perpendicular to the vertical axis (plumb line).
  • Vertical angular measurements are measured to determine slope of.
  • survey lines from the horizontal plane (level line). ...
  • is applied to the slope distance, the horizontal and vertical distances may.
  • be calculated. ...
  • the vertical axis perpendicular to the horizontal plane.

What are the methods of setting out? ›

The three methods of setting out are HORIZONTAL ALIGNMENT, VERTICAL ALIGNMENT, and CROSS-SECTIONS. Horizontal alignment involves establishing the position of a structure on its baseline, while vertical alignment is used to establish the position of a building or other structure at an angle relative to it.

What is Rankine's method of curve setting used for? ›

Rankine's method or tangential angle method is an angular technique for laying out circular curves by a combination of chaining and angles at circumference, fully exploiting the theodolite and making a substantial improvement in accuracy and productivity over existing methods.

What is the two theodolite method of setting out a curve? ›

In two theodolite method, curves are staked out by angular measurements only. Accuracy attained in this method is quite high. Thus, the method is used when higher accuracy is required and when the topography is rough or field condition is difficult.

What are the 4 curve types? ›

Types of Curves in Surveying
  • Circular Curve: A circular curve is the most basic type of curve used in surveying and engineering. ...
  • Compound Curve: A compound curve consists of two or more circular curves connected end to end with different radii and centers. ...
  • Reverse Curve: ...
  • Spiral Curve: ...
  • Transition Curve (Easem*nt Curve):
Oct 15, 2023

What is the procedure of setting out curves? ›

Procedure of setting out the Curve: (i) Divide the long chord into an even number of equal parts. (ii) Calculate the offsets by equation (5.10) at each of the points of division. () Set out the offsets at respective points to obtain the required points on the curve.

What are the three different classification of curves? ›

Answer: The different types of curves are Simple curve, Closed curve, Simple closed curve, Algebraic and Transcendental Curve. Question 4: Is straight line is a curve? Answer: No. A curve is not a straight line, at the same time as a straight line is not a curve.

What is the linear method of setting out a curve? ›

The methods used in setting out a curve are classified as linear method and angular methods. 1. Linear method adopts the usage of chain or tape in which only distance can be found but not angles. Moreover, this process is used when accuracy is not required and speed of work is concerned.

What are the 3-4-5 methods of setting out? ›

Ensuring right angles (90 degrees) is important when setting out the initial perimeter of the house. This can easily be achieved using the 3:4:5 triangle method. A triangle, which has sides of length 3 metres, 4 metres and 5 metres, will always have a right angle between the 3-metre side and the 4-metre side.

What are the methods of setting offsets? ›

Offset Method
  • Set up two control points on site, through the middle of the area to be recorded ensuring a clear line of sight between them.
  • Lay a tape measure between the two points, ensure that the tape is at the correct tension.
  • Ensure each point is securely fixed, as it will be pulled on by the tape measure.

What are the types of linear method? ›

Linear measurement is achieved by various instruments, depending on the type of instrument used for measurement. It can be divided into a direct measurement method, an optical measurement method, and an electronic measurement method. It is obtained by using some simple measurement equipment.

What are the methods of mathematical curve? ›

The Wavy Curve Method (also known as the Method of Intervals) is a mathematical technique widely applied to solve inequalities of the form f(x)g(x)> 0, f(x)g(x)< 0, f(x)g(x) 0, or f(x)g(x) 0. By using the zeroes (roots) of the functions f(x) and g(x), a graph over different intervals is sketched.

What are the different types of curves? ›

Answer: The different types of curves are Simple curve, Closed curve, Simple closed curve, Algebraic and Transcendental Curve. Question 4: Is straight line is a curve? Answer: No.

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