Central Angle of Curve for given Length of Long Chord Calculator

✖Length of long chord can be described as the distance from point of curvature to point of tangency.ⓘ Length of long Chord [C]			+10% -10%
✖Radius of Circular Curve is the radius of a circle whose part, say, arc is taken for consideration.ⓘ Radius of Circular Curve [R_c]			+10% -10%

✖Central angle of curve can be described as the deflection angle between tangents at point of intersection of tangents.ⓘ Central Angle of Curve for given Length of Long Chord [I]

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Formula

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Central Angle of Curve for given Length of Long Chord

Formula

`"I" = ("C"/(2*"R"_{"c"}*sin(1/2)))`

Example

`"46.42474°"=("101m"/(2*"130m"*sin(1/2)))`

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Download Circular Curves on Highways and Roads Formulas PDF

Central Angle of Curve for given Length of Long Chord Solution

STEP 0: Pre-Calculation Summary

Formula Used

Central Angle of Curve = (Length of long Chord/(2*Radius of Circular Curve*sin(1/2)))
I = (C/(2*R_c*sin(1/2)))
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

Central Angle of Curve - (Measured in Radian) - Central angle of curve can be described as the deflection angle between tangents at point of intersection of tangents.
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.
Radius of Circular Curve - (Measured in Meter) - Radius of Circular Curve is the radius of a circle whose part, say, arc is taken for consideration.

STEP 1: Convert Input(s) to Base Unit

Length of long Chord: 101 Meter --> 101 Meter No Conversion Required
Radius of Circular Curve: 130 Meter --> 130 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I = (C/(2*R_c*sin(1/2))) --> (101/(2*130*sin(1/2)))

Evaluating ... ...

I = 0.810264592062624

STEP 3: Convert Result to Output's Unit

0.810264592062624 Radian -->46.4247414140864 Degree (Check conversion here)

FINAL ANSWER

46.4247414140864 ≈ 46.42474 Degree <-- Central Angle of Curve

(Calculation completed in 00.004 seconds)

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Created by M Naveen

National Institute of Technology (NIT), Warangal

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National Institute Of Technology (NIT), Hamirpur

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< 25 Circular Curves on Highways and Roads Calculators

Radius of Curve using External Distance

Go Radius of Circular Curve = External Distance/((sec(1/2)*(Central Angle of Curve*(180/pi)))-1)

External Distance

Go External Distance = Radius of Circular Curve*((sec(1/2)*Central Angle of Curve*(180/pi))-1)

Central Angle of Curve for given Length of Long Chord

Go Central Angle of Curve = (Length of long Chord/(2*Radius of Circular Curve*sin(1/2)))

Radius of Curve given Length of Long Chord

Go Radius of Circular Curve = Length of long Chord/(2*sin(1/2)*(Central Angle of Curve))

Length of Long Chord

Go Length of long Chord = 2*Radius of Circular Curve*sin((1/2)*(Central Angle of Curve))

Central Angle of Curve for given Tangent Distance

Go Central Angle of Curve = (Tangent Distance/(sin(1/2)*Radius of Circular Curve))

Radius of Curve using Tangent Distance

Go Radius of Circular Curve = Tangent Distance/(sin(1/2)*(Central Angle of Curve))

Radius of Curve using Midordinate

Go Radius of Circular Curve = Midordinate/(1-(cos(1/2)*(Central Angle of Curve)))

Exact Tangent Distance

Go Tangent Distance = Radius of Circular Curve*tan(1/2)*Central Angle of Curve

Length of Curve or Chord by Central Angle given Tangent Offset for Chord of Length

Go Length of Curve = sqrt(Tangent Offset*2*Radius of Circular Curve)

Length of Curve or Chord determined by Central Angle given Chord Offset for Chord of Length

Go Length of Curve = sqrt(Chord Offset*Radius of Circular Curve)

Length of Curve or Chord by Central Angle given Central Angle for Portion of Curve

Go Length of Curve = (100*Central Angle for Portion of Curve)/Degree of Curve

Central angle for Portion of Curve Approximate for Chord definition

Go Central Angle for Portion of Curve = (Degree of Curve*Length of Curve)/100

Central Angle for Portion of Curve Exact for Arc definition

Go Central Angle for Portion of Curve = (Degree of Curve*Length of Curve)/100

Length of Curve given Central Angle for portion of Curve

Go Length of Curve = (Central Angle for Portion of Curve*100)/Degree of Curve

Degree of Curve when Central Angle for Portion of Curve

Go Degree of Curve = (100*Central Angle for Portion of Curve)/Length of Curve

Degree of Curve for given Radius of Curve

Go Degree of Curve = (5729.578/Radius of Circular Curve)*(pi/180)

Radius of Curve

Go Radius of Circular Curve = 5729.578/(Degree of Curve*(180/pi))

Tangent Offset for Chord of Length

Go Tangent Offset = Length of Curve^2/(2*Radius of Circular Curve)

Central Angle of Curve for given Length of Curve

Go Central Angle of Curve = (Length of Curve*Degree of Curve)/100

Degree of Curve for given Length of Curve

Go Degree of Curve = (100*Central Angle of Curve)/Length of Curve

Exact Length of Curve

Go Length of Curve = (100*Central Angle of Curve)/Degree of Curve

Radius of Curve using Degree of Curve

Go Radius of Circular Curve = 50/(sin(1/2)*(Degree of Curve))

Radius of Curve Exact for Chord

Go Radius of Circular Curve = 50/(sin(1/2)*(Degree of Curve))

Approximate Chord Offset for Chord of Length

Go Chord Offset = Length of Curve^2/Radius of Circular Curve

Central Angle of Curve for given Length of Long Chord Formula

Central Angle of Curve = (Length of long Chord/(2*Radius of Circular Curve*sin(1/2)))
I = (C/(2*R_c*sin(1/2)))

What is length of long chord?

Length of long chord can be described as distance from point of curvature to point of tangency, end of curve.

How to Calculate Central Angle of Curve for given Length of Long Chord?

Central Angle of Curve for given Length of Long Chord calculator uses Central Angle of Curve = (Length of long Chord/(2*Radius of Circular Curve*sin(1/2))) to calculate the Central Angle of Curve, Central Angle of Curve for given Length of Long Chord can be defined as the deflection angle between tangents at the point of intersection of tangents. Central Angle of Curve is denoted by I symbol.

How to calculate Central Angle of Curve for given Length of Long Chord using this online calculator? To use this online calculator for Central Angle of Curve for given Length of Long Chord, enter Length of long Chord (C) & Radius of Circular Curve (R_c) and hit the calculate button. Here is how the Central Angle of Curve for given Length of Long Chord calculation can be explained with given input values -> 2659.942 = (101/(2*130*sin(1/2))).

FAQ

What is Central Angle of Curve for given Length of Long Chord?

Central Angle of Curve for given Length of Long Chord can be defined as the deflection angle between tangents at the point of intersection of tangents and is represented as I = (C/(2*R_c*sin(1/2))) or Central Angle of Curve = (Length of long Chord/(2*Radius of Circular Curve*sin(1/2))). Length of long chord can be described as the distance from point of curvature to point of tangency & Radius of Circular Curve is the radius of a circle whose part, say, arc is taken for consideration.

How to calculate Central Angle of Curve for given Length of Long Chord?

Central Angle of Curve for given Length of Long Chord can be defined as the deflection angle between tangents at the point of intersection of tangents is calculated using Central Angle of Curve = (Length of long Chord/(2*Radius of Circular Curve*sin(1/2))). To calculate Central Angle of Curve for given Length of Long Chord, you need Length of long Chord (C) & Radius of Circular Curve (R_c). With our tool, you need to enter the respective value for Length of long Chord & Radius of Circular Curve 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 Central Angle of Curve?

In this formula, Central Angle of Curve uses Length of long Chord & Radius of Circular Curve. We can use 2 other way(s) to calculate the same, which is/are as follows -

Central Angle of Curve = (Tangent Distance/(sin(1/2)*Radius of Circular Curve))
Central Angle of Curve = (Length of Curve*Degree of Curve)/100

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