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Radius of Curve using Tangent Distance Formula

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GoRadius of Curve Formula

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Radius of Circular Curve is the radius of a circle whose part, say, arc is taken for consideration. Check FAQs

R c = \frac{T}{\sin (\frac{1}{2}) \cdot (I)}

R_c - Radius of Circular Curve?T - Tangent Distance?I - Central Angle of Curve?

Radius of Curve using Tangent Distance Example

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Here is how the Radius of Curve using Tangent Distance equation looks like with Values.

Here is how the Radius of Curve using Tangent Distance equation looks like with Units.

Here is how the Radius of Curve using Tangent Distance equation looks like.

148.1317 = \frac{49.58}{\sin (\frac{1}{2}) \cdot (40)}

148.1317m = \frac{49.58m}{\sin (\frac{1}{2}) \cdot (40°)}

148.1317 = \frac{49.58}{\sin (\frac{1}{2}) \cdot (40)}

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Radius of Curve using Tangent Distance Solution

Follow our step by step solution on how to calculate Radius of Curve using Tangent Distance?

FIRST Step Consider the formula

R c = \frac{T}{\sin (\frac{1}{2}) \cdot (I)}

Next Step Substitute values of Variables

∴

R c = \frac{49.58m}{\sin (\frac{1}{2}) \cdot (40°)}

Next Step Convert Units

∴

R c = \frac{49.58m}{\sin (\frac{1}{2}) \cdot (0.6981rad)}

Next Step Prepare to Evaluate

∴

R c = \frac{49.58}{\sin (\frac{1}{2}) \cdot (0.6981)}

Next Step Evaluate

∴

R c = 148.131697183343m

LAST Step Rounding Answer

∴

R c = 148.1317m

Radius of Curve using Tangent Distance Formula Elements

Variables

Functions

Radius of Circular Curve

Radius of Circular Curve is the radius of a circle whose part, say, arc is taken for consideration.

Symbol: R_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius of Circular Curve

Tangent Distance

Tangent distance can be defined as the distance from point of intersection of tangents to point of curvature.

Symbol: T

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Tangent Distance

Central Angle of Curve

Central angle of curve can be described as the deflection angle between tangents at point of intersection of tangents.

Symbol: I

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Central Angle of Curve

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.

Syntax: sin(Angle)

Other Formulas to find Radius of Circular Curve

Go Radius of Curve using Degree of Curve

R c = \frac{50}{\sin (\frac{1}{2}) \cdot (D)}

Go Radius of Curve

R c = \frac{5729.578}{D \cdot (\frac{180}{π})}

Go Radius of Curve Exact for Chord

R c = \frac{50}{\sin (\frac{1}{2}) \cdot (D)}

Go Radius of Curve using External Distance

R c = \frac{E}{(\sec (\frac{1}{2}) \cdot (I \cdot (\frac{180}{π}))) - 1}

Other formulas in Circular Curves on Highways and Roads category

Go Exact Tangent Distance

T = R c \cdot \tan (\frac{1}{2}) \cdot I

Go Degree of Curve for given Radius of Curve

D = (\frac{5729.578}{R c}) \cdot (\frac{π}{180})

Go Central Angle of Curve for given Tangent Distance

I = (\frac{T}{\sin (\frac{1}{2}) \cdot R c})

Go External Distance

E = R c \cdot ((\sec (\frac{1}{2}) \cdot I \cdot (\frac{180}{π})) - 1)

How to Evaluate Radius of Curve using Tangent Distance?

Radius of Curve using Tangent Distance evaluator uses Radius of Circular Curve = Tangent Distance/(sin(1/2)*(Central Angle of Curve)) to evaluate the Radius of Circular Curve, The Radius of Curve using Tangent Distance can be defined as the absolute value of the reciprocal of the curvature at a point on a curve. Radius of Circular Curve is denoted by R_c symbol.

How to evaluate Radius of Curve using Tangent Distance using this online evaluator? To use this online evaluator for Radius of Curve using Tangent Distance, enter Tangent Distance (T) & Central Angle of Curve (I) and hit the calculate button.

FAQs on Radius of Curve using Tangent Distance

What is the formula to find Radius of Curve using Tangent Distance?

The formula of Radius of Curve using Tangent Distance is expressed as Radius of Circular Curve = Tangent Distance/(sin(1/2)*(Central Angle of Curve)). Here is an example- 143.4111 = 49.58/(sin(1/2)*(0.698131700797601)).

How to calculate Radius of Curve using Tangent Distance?

With Tangent Distance (T) & Central Angle of Curve (I) we can find Radius of Curve using Tangent Distance using the formula - Radius of Circular Curve = Tangent Distance/(sin(1/2)*(Central Angle of Curve)). This formula also uses Sine (sin) function(s).

What are the other ways to Calculate Radius of Circular Curve?

Here are the different ways to Calculate Radius of Circular Curve-

Radius of Circular Curve=50/(sin(1/2)*(Degree of Curve))
Radius of Circular Curve=5729.578/(Degree of Curve*(180/pi))
Radius of Circular Curve=50/(sin(1/2)*(Degree of Curve))

Can the Radius of Curve using Tangent Distance be negative?

No, the Radius of Curve using Tangent Distance, measured in Length cannot be negative.

Which unit is used to measure Radius of Curve using Tangent Distance?

Radius of Curve using Tangent Distance is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Radius of Curve using Tangent Distance can be measured.

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