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External Distance Formula

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

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

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

External Distance Example

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With units

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Here is how the External Distance equation looks like with Values.

Here is how the External Distance equation looks like with Units.

Here is how the External Distance equation looks like.

5795.3684 = 130 \cdot ((\sec (\frac{1}{2}) \cdot 40 \cdot (\frac{180}{3.1416})) - 1)

5795.3684m = 130m \cdot ((\sec (\frac{1}{2}) \cdot 40° \cdot (\frac{180}{3.1416})) - 1)

5795.3684 = 130 \cdot ((\sec (\frac{1}{2}) \cdot 40 \cdot (\frac{180}{3.1416})) - 1)

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External Distance Solution

Follow our step by step solution on how to calculate External Distance?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

E = 130m \cdot ((\sec (\frac{1}{2}) \cdot 40° \cdot (\frac{180}{π})) - 1)

Next Step Substitute values of Constants

∴

E = 130m \cdot ((\sec (\frac{1}{2}) \cdot 40° \cdot (\frac{180}{3.1416})) - 1)

Next Step Convert Units

∴

E = 130m \cdot ((\sec (\frac{1}{2}) \cdot 0.6981rad \cdot (\frac{180}{3.1416})) - 1)

Next Step Prepare to Evaluate

∴

E = 130 \cdot ((\sec (\frac{1}{2}) \cdot 0.6981 \cdot (\frac{180}{3.1416})) - 1)

Next Step Evaluate

∴

E = 5795.36842208655m

LAST Step Rounding Answer

∴

E = 5795.3684m

External Distance Formula Elements

Variables

Constants

Functions

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

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

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 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 Radius of Curve using Degree of Curve

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

Go Central Angle of Curve for given Tangent Distance

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

How to Evaluate External Distance?

External Distance evaluator uses External Distance = Radius of Circular Curve*((sec(1/2)*Central Angle of Curve*(180/pi))-1) to evaluate the External Distance, External Distance (Exact) is defined as the distance from point of intersection of tangents to midpoint of curve. External Distance is denoted by E symbol.

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

FAQs on External Distance

What is the formula to find External Distance?

The formula of External Distance is expressed as External Distance = Radius of Circular Curve*((sec(1/2)*Central Angle of Curve*(180/pi))-1). Here is an example- 5795.368 = 130*((sec(1/2)*0.698131700797601*(180/pi))-1).

How to calculate External Distance?

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

Can the External Distance be negative?

Yes, the External Distance, measured in Length can be negative.

Which unit is used to measure External Distance?

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

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