Radius of Curve given Long Chord Solution

STEP 0: Pre-Calculation Summary
Formula Used
Curve Radius = Length of Long Chord/(2*sin(Deflection Angle/2))
RCurve = C/(2*sin(Δ/2))
This formula uses 1 Functions, 3 Variables
Functions Used
sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
Variables Used
Curve Radius - (Measured in Meter) - Curve Radius is the radius of a circle whose part, say, arc is taken for consideration.
Length of Long Chord - (Measured in Meter) - Length of Long Chord can be described as the distance from point of curvature to point of tangency.
Deflection Angle - (Measured in Radian) - Deflection Angle is the angle between the first sub chord of curve and the deflected line with equal measurement of first sub chord from tangent point.
STEP 1: Convert Input(s) to Base Unit
Length of Long Chord: 65.5 Meter --> 65.5 Meter No Conversion Required
Deflection Angle: 65 Degree --> 1.1344640137961 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
RCurve = C/(2*sin(Δ/2)) --> 65.5/(2*sin(1.1344640137961/2))
Evaluating ... ...
RCurve = 60.9529571420524
STEP 3: Convert Result to Output's Unit
60.9529571420524 Meter --> No Conversion Required
FINAL ANSWER
60.9529571420524 60.95296 Meter <-- Curve Radius
(Calculation completed in 00.004 seconds)

Credits

Created by Chandana P Dev
NSS College of Engineering (NSSCE), Palakkad
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National Institute of Technology (NIT), Warangal
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11 Simple Circular Curve Calculators

Radius of Curve given Long Chord
Go Curve Radius = Length of Long Chord/(2*sin(Deflection Angle/2))
Length of Curve if 30m Chord Definition
Go Length of Curve = 30*Deflection Angle/Angle for Arc*(180/pi)
Length of Curve if 20m Chord Definition
Go Length of Curve = 20*Deflection Angle/Angle for Arc*(180/pi)
Radius given Apex Distance
Go Curve Radius = Apex Distance/(sec(Deflection Angle/2)-1)
Apex Distance
Go Apex Distance = Curve Radius*(sec(Deflection Angle/2)-1)
Mid Ordinate
Go Mid Ordinate = Curve Radius*(1-cos(Deflection Angle/2))
Radius of Curve given Tangent
Go Curve Radius = Tangent Length/tan(Deflection Angle/2)
Tangent Length
Go Tangent Length = Curve Radius*tan(Deflection Angle/2)
Deflection Angle given Length of Curve
Go Deflection Angle = Length of Curve/Curve Radius
Radius of Curve given Length
Go Curve Radius = Length of Curve/Deflection Angle
Length of Curve
Go Length of Curve = Curve Radius*Deflection Angle

Radius of Curve given Long Chord Formula

Curve Radius = Length of Long Chord/(2*sin(Deflection Angle/2))
RCurve = C/(2*sin(Δ/2))

What are the Various Parts of a Curve?

(i) Tangents: The straight lines at the ends of curve or lines connected by the curves. The tangent drawn to the first point of curve is the first tangent and similarly the second tangent.
(ii) Vertex: The points of intersection of the two straights is called the intersection point or the vertex.
(iii)Long chord: Line joining both the tangents.
(iv) Mid point: It is the summit or apex of the curve.
(v) Apex distance: The distance from the point of intersection to the apex of the curve.
(vi)Central angle: The angle subtended at the centre of the curve by the arc.

How to Calculate Radius of Curve given Long Chord?

Radius of Curve given Long Chord calculator uses Curve Radius = Length of Long Chord/(2*sin(Deflection Angle/2)) to calculate the Curve Radius, The Radius of Curve given Long Chord formula is defined as the same as the radius of a circle from which part is taken as an arc or curve. Curve Radius is denoted by RCurve symbol.

How to calculate Radius of Curve given Long Chord using this online calculator? To use this online calculator for Radius of Curve given Long Chord, enter Length of Long Chord (C) & Deflection Angle (Δ) and hit the calculate button. Here is how the Radius of Curve given Long Chord calculation can be explained with given input values -> 60.95296 = 65.5/(2*sin(1.1344640137961/2)).

FAQ

What is Radius of Curve given Long Chord?
The Radius of Curve given Long Chord formula is defined as the same as the radius of a circle from which part is taken as an arc or curve and is represented as RCurve = C/(2*sin(Δ/2)) or Curve Radius = Length of Long Chord/(2*sin(Deflection Angle/2)). Length of Long Chord can be described as the distance from point of curvature to point of tangency & Deflection Angle is the angle between the first sub chord of curve and the deflected line with equal measurement of first sub chord from tangent point.
How to calculate Radius of Curve given Long Chord?
The Radius of Curve given Long Chord formula is defined as the same as the radius of a circle from which part is taken as an arc or curve is calculated using Curve Radius = Length of Long Chord/(2*sin(Deflection Angle/2)). To calculate Radius of Curve given Long Chord, you need Length of Long Chord (C) & Deflection Angle (Δ). With our tool, you need to enter the respective value for Length of Long Chord & Deflection Angle and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Curve Radius?
In this formula, Curve Radius uses Length of Long Chord & Deflection Angle. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Curve Radius = Length of Curve/Deflection Angle
  • Curve Radius = Tangent Length/tan(Deflection Angle/2)
  • Curve Radius = Apex Distance/(sec(Deflection Angle/2)-1)
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