This document discusses simple circular curves, which are curves consisting of a single arc with a constant radius connecting two tangents. It defines key elements of circular curves such as deflection angle, radius of curvature, chord length, and tangent length. Circular curves are used to impose curves between two straight lines in roads and railways. The document also discusses designating curves by their degree or radius, with degree defined as the angle subtended by a 30m chord at the curve's center. Fundamental geometry rules for circular curves are provided.

1. SNPIT AND RC
SURVEYING(2130601)
NAME PEN NO.
•SINDHVAD KATHAN 160490106087
•VISHAL SHARMA 160490106085
•MALHAR SHUKLA 160490106086
•UPADHYAY NISHANK 160490106092

2. WHAT IS SIMPLE CIRCULAR CURVE?
 It is a curve consists of a single arc with a constant radius
connecting the two tangents.
 It is a type of horizontal curve used most in common.
 A simple arc provided in the road or railway track to impose a
curve between the two straight lines is the simple circular curve.

3. SIMPLE CIRCULAR CURVE
o Once the alignment of a route is finalized, such as AVCD in Figure, the
change in direction is achieved through provision of circular curves. In
Figure, to change the direction from AV to VC, a circular curve T1 GT2 is
provided. Similarly, from VC to CD, T'1G'T'2 is provided. The straight
alignments, between which a curve is provided, are tangential to the curve.
o Thus, AT1 V and VT2C are tangential to T1 GT2 . The tangent line before
the beginning of the curve is called the Back tangent or the rear tangent. The
tangent line after the end of the curve is called the Forward tangent.

4. ELEMENTS OF A SIMPLE CIRCULAR CURVE
 Let T1GT2 be the circular curve that has been provided between the tangents
AV and VC. The deflection angle, D between the tangents is measured in the
field.
 The radius of curvature is the design value as per requirement of the route
operation and field topography. The line joining O and V bisects the internal
angles at V and at O, the chord T1T2 and arc T1GT2 . It is perpendicular to
the chord T1T2 at F. From the Figure 37.1, RT1 O T2 = D and

5. FIGURE OF ELEMENTS OF CIRCULAR CURVE

6. TANGENT LENGTH
• T = length T1 V = length T2
• Chainages of tangent point : The chainage of the point of intersection (V) is
generally known. Thus,
• Chainageof T1 = Chainage of V - tangent length (T)
• Chainage of T2 = Chainage of T1 + length of curve (l)
• Length of the long chord (L) : Length of the long chord,
• L = length T1 FT2
• External distance (E) :
• E = length VG
• = VO - GO
• Mid-ordinate (M) :
• M = length GF = OG-OF

7. DESIGNATION OF A CURVE
 A curve is designated either in terms of its degree (D) or by its radius (R).

8. DEGREE OF CURVE
 The degree of a curve (D) is defined as the angle subtended at the centre of
the curve by a chord or an arc of specified length.

9. CHORD DEFINITION
 The degree of a curve is defined as the angle subtended at the centre of the
curve by a chord of 30 m length.
 Let D be the degree of a curve i.e., it is the angle subtended at its centre O by
a chord C1C2 of 30 m length.
 Hence degree of curve is given by,
D = 360*length of chord/2πR
D = 1718.9/R (for 30m chainage)
D = 1145.9/R (for 20m chainage)

10. RADIUS OF CURVE
 In this convention, a curve is designated by its radius. The sharpness of the
curve depends upon its radius. A sharp curve has a small radius. On the other
hand, a flat curve has a large radius. Moreover, from, it can be found that the
degree of curve is inversely proportional to the radius of curve. Thus, a sharp
curve has a large degree of curve, whereas a flat curve has a small degree of
curve.

11. FUNDAMENTAL GEOMETRY OF CIRCULAR CURVE
• The fundamentals of geometry of a circular curve those required to
understand the fundamentals of laying out of a circular curve are as follows:
• Rule 1 : The angle subtended by any chord at the centre of the circle is twice
the angle between the chord and a tangent at one of its ends. For example, in
Figure, the angle subtended by the chord AB at the centre of the circle,
RAOB (d) is twice the angle RVAB between the chord AB and the tangent
AV at end A (d / 2).
• Rule 2 : Inscribed angles subtended by the same or equal arc or chord are
equal. In Figure 37.4, inscribed angles at C and E subtended by the chord AB
are equal and both are (d / 2).

12. • Rule 3 : Inscribed angle subtended by the same or equal arc or chord is half
the angle subtended (by the arc or chord) at the centre of the circle. In Figure,
the inscribed angles at C and E (d / 2) is half the angle subtended by the
chord AB at the centre of the circle, AOB (d).
• Rule 4 : The deflection angle between a tangent (at any point on a circle) and
a chord is equal to the angle which the chord subtends in the alternate
segment. For example, in Figure 37.4, the deflection angle at D from the
tangent at A (RVAD) is equal to the angle subtended by the chord AD at B
(RABD) i.e., RVAD = RABD.

13. FIGURE OF GEOMETRY OF CIRCULAR CURVE