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Radius of Curve using External Distance Formula

GoRadius of Curve using Degree of Curve Formula

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

R_c - Radius of Circular Curve?E - External Distance?I - Central Angle of Curve?π - Archimedes' constant?

Radius of Curve using External Distance Example

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

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

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

129.9917 = \frac{5795}{(\sec (\frac{1}{2}) \cdot (40 \cdot (\frac{180}{3.1416}))) - 1}

129.9917m = \frac{5795m}{(\sec (\frac{1}{2}) \cdot (40° \cdot (\frac{180}{3.1416}))) - 1}

129.9917 = \frac{5795}{(\sec (\frac{1}{2}) \cdot (40 \cdot (\frac{180}{3.1416}))) - 1}

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Radius of Curve using External Distance Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

R c = \frac{5795m}{(\sec (\frac{1}{2}) \cdot (40° \cdot (\frac{180}{π}))) - 1}

Next Step Substitute values of Constants

∴

R c = \frac{5795m}{(\sec (\frac{1}{2}) \cdot (40° \cdot (\frac{180}{3.1416}))) - 1}

Next Step Convert Units

∴

R c = \frac{5795m}{(\sec (\frac{1}{2}) \cdot (0.6981rad \cdot (\frac{180}{3.1416}))) - 1}

Next Step Prepare to Evaluate

∴

R c = \frac{5795}{(\sec (\frac{1}{2}) \cdot (0.6981 \cdot (\frac{180}{3.1416}))) - 1}

Next Step Evaluate

∴

R c = 129.991735664109m

LAST Step Rounding Answer

∴

R c = 129.9917m

Radius of Curve using External Distance Formula Elements

Variables

Constants

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

External Distance

External distance can be described as distance from point of intersection of tangents to midpoint of curve.

Symbol: E

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find External 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

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

sec

Secant is a trigonometric function that is defined ratio of the hypotenuse to the shorter side adjacent to an acute angle (in a right-angled triangle); the reciprocal of a cosine.

Syntax: sec(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 Tangent Distance

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

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 External Distance?

Radius of Curve using External Distance evaluator uses Radius of Circular Curve = External Distance/((sec(1/2)*(Central Angle of Curve*(180/pi)))-1) to evaluate the Radius of Circular Curve, The Radius of Curve using External 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 External Distance using this online evaluator? To use this online evaluator for Radius of Curve using External Distance, enter External Distance (E) & Central Angle of Curve (I) and hit the calculate button.

FAQs on Radius of Curve using External Distance

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

The formula of Radius of Curve using External Distance is expressed as Radius of Circular Curve = External Distance/((sec(1/2)*(Central Angle of Curve*(180/pi)))-1). Here is an example- 129.9917 = 5795/((sec(1/2)*(0.698131700797601*(180/pi)))-1).

How to calculate Radius of Curve using External Distance?

With External Distance (E) & Central Angle of Curve (I) we can find Radius of Curve using External Distance using the formula - Radius of Circular Curve = External Distance/((sec(1/2)*(Central Angle of Curve*(180/pi)))-1). This formula also uses Archimedes' constant and Secant (sec) 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 External Distance be negative?

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

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

Radius of Curve using External 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 External Distance can be measured.

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