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Radius given Apex Distance Formula

GoRadius of Curve given Length Formula

GoRadius of Curve given Tangent Formula

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

R Curve = \frac{L ad}{\sec (\frac{Δ}{2}) - 1}

R_Curve - Curve Radius?L_ad - Apex Distance?Δ - Deflection Angle?

Radius given Apex Distance Example

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Here is how the Radius given Apex Distance equation looks like with Values.

Here is how the Radius given Apex Distance equation looks like with Units.

Here is how the Radius given Apex Distance equation looks like.

118.4776 = \frac{22}{\sec (\frac{65}{2}) - 1}

118.4776m = \frac{22m}{\sec (\frac{65°}{2}) - 1}

118.4776 = \frac{22}{\sec (\frac{65}{2}) - 1}

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Radius given Apex Distance Solution

Follow our step by step solution on how to calculate Radius given Apex Distance?

FIRST Step Consider the formula

R Curve = \frac{L ad}{\sec (\frac{Δ}{2}) - 1}

Next Step Substitute values of Variables

∴

R Curve = \frac{22m}{\sec (\frac{65°}{2}) - 1}

Next Step Convert Units

∴

R Curve = \frac{22m}{\sec (\frac{1.1345rad}{2}) - 1}

Next Step Prepare to Evaluate

∴

R Curve = \frac{22}{\sec (\frac{1.1345}{2}) - 1}

Next Step Evaluate

∴

R Curve = 118.477639386944m

LAST Step Rounding Answer

∴

R Curve = 118.4776m

Radius given Apex Distance Formula Elements

Variables

Functions

Curve Radius

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

Symbol: R_Curve

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Curve Radius

Apex Distance

Apex Distance is the distance from the point of intersection to the apex of the curve.

Symbol: L_ad

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Apex Distance

Deflection Angle

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.

Symbol: Δ

Measurement: AngleUnit: °

Note: Value should be between 0 to 360.

Formulas to find Deflection Angle

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 Curve Radius

Go Radius of Curve given Length

R Curve = \frac{L Curve}{Δ}

Go Radius of Curve given Tangent

R Curve = \frac{T}{\tan (\frac{Δ}{2})}

Go Radius of Curve given Long Chord

R Curve = \frac{C}{2 \cdot \sin (\frac{Δ}{2})}

Other formulas in Simple Circular Curve category

Go Length of Curve

L Curve = R Curve \cdot Δ

Go Deflection Angle given Length of Curve

Δ = \frac{L Curve}{R Curve}

Go Length of Curve if 30m Chord Definition

L Curve = 30 \cdot \frac{Δ}{D} \cdot (\frac{180}{π})

Go Length of Curve if 20m Chord Definition

L Curve = 20 \cdot \frac{Δ}{D} \cdot (\frac{180}{π})

How to Evaluate Radius given Apex Distance?

Radius given Apex Distance evaluator uses Curve Radius = Apex Distance/(sec(Deflection Angle/2)-1) to evaluate the Curve Radius, The Radius given Apex Distance formula is defined as it determines the “sharpness” or “flatness” of the curve, larger radius, “flatter” curve. Curve Radius is denoted by R_Curve symbol.

How to evaluate Radius given Apex Distance using this online evaluator? To use this online evaluator for Radius given Apex Distance, enter Apex Distance (L_ad) & Deflection Angle (Δ) and hit the calculate button.

FAQs on Radius given Apex Distance

What is the formula to find Radius given Apex Distance?

The formula of Radius given Apex Distance is expressed as Curve Radius = Apex Distance/(sec(Deflection Angle/2)-1). Here is an example- 118.4776 = 22/(sec(1.1344640137961/2)-1).

How to calculate Radius given Apex Distance?

With Apex Distance (L_ad) & Deflection Angle (Δ) we can find Radius given Apex Distance using the formula - Curve Radius = Apex Distance/(sec(Deflection Angle/2)-1). This formula also uses Secant (sec) function(s).

What are the other ways to Calculate Curve Radius?

Here are the different ways to Calculate Curve Radius-

Curve Radius=Length of Curve/Deflection Angle
Curve Radius=Tangent Length/tan(Deflection Angle/2)
Curve Radius=Length of Long Chord/(2*sin(Deflection Angle/2))

Can the Radius given Apex Distance be negative?

No, the Radius given Apex Distance, measured in Length cannot be negative.

Which unit is used to measure Radius given Apex Distance?

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

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