Radius given Apex Distance Calculator

✖Apex Distance is the distance from the point of intersection to the apex of the curve.ⓘ Apex Distance [L_ad]			+10% -10%
✖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.ⓘ Deflection Angle [Δ]			+10% -10%

✖Curve Radius is the radius of a circle whose part, say, arc is taken for consideration.ⓘ Radius given Apex Distance [R_Curve]

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Radius given Apex Distance Solution

STEP 0: Pre-Calculation Summary

Formula Used

Curve Radius = Apex Distance/(sec(Deflection Angle/2)-1)
R_Curve = L_ad/(sec(Δ/2)-1)
This formula uses 1 Functions, 3 Variables

Functions Used

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., sec(Angle)

Variables Used

Curve Radius - (Measured in Meter) - Curve Radius is the radius of a circle whose part, say, arc is taken for consideration.
Apex Distance - (Measured in Meter) - Apex Distance is the distance from the point of intersection to the apex of the curve.
Deflection Angle - (Measured in Radian) - 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.

STEP 1: Convert Input(s) to Base Unit

Apex Distance: 22 Meter --> 22 Meter No Conversion Required
Deflection Angle: 65 Degree --> 1.1344640137961 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_Curve = L_ad/(sec(Δ/2)-1) --> 22/(sec(1.1344640137961/2)-1)

Evaluating ... ...

R_Curve = 118.477639386944

STEP 3: Convert Result to Output's Unit

118.477639386944 Meter --> No Conversion Required

FINAL ANSWER

118.477639386944 ≈ 118.4776 Meter <-- Curve Radius

(Calculation completed in 00.020 seconds)

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Created by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

Chandana P Dev has created this Calculator and 500+ more calculators!

Verified by M Naveen

National Institute of Technology (NIT), Warangal

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< Simple Circular Curve Calculators

Length of Curve if 30m Chord Definition

LaTeX Go Length of Curve = 30*Deflection Angle/Angle for Arc*(180/pi)

Deflection Angle given Length of Curve

LaTeX Go Deflection Angle = Length of Curve/Curve Radius

Radius of Curve given Length

LaTeX Go Curve Radius = Length of Curve/Deflection Angle

Length of Curve

LaTeX Go Length of Curve = Curve Radius*Deflection Angle

Radius given Apex Distance Formula

LaTeX Go

Curve Radius = Apex Distance/(sec(Deflection Angle/2)-1)
R_Curve = L_ad/(sec(Δ/2)-1)

How can the Accuracy of the Length of Curve Calculation be Improved?

The accuracy of the Length of Curve calculation can be improved by using more advanced surveying methods, such as the compound curve method, which can account for changes in the deflection angle along the curve.

How to Calculate Radius given Apex Distance?

Radius given Apex Distance calculator uses Curve Radius = Apex Distance/(sec(Deflection Angle/2)-1) to calculate 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 calculate Radius given Apex Distance using this online calculator? To use this online calculator for Radius given Apex Distance, enter Apex Distance (L_ad) & Deflection Angle (Δ) and hit the calculate button. Here is how the Radius given Apex Distance calculation can be explained with given input values -> 118.4776 = 22/(sec(1.1344640137961/2)-1).

FAQ

What is Radius given Apex Distance?

The Radius given Apex Distance formula is defined as it determines the “sharpness” or “flatness” of the curve, larger radius, “flatter” curve and is represented as R_Curve = L_ad/(sec(Δ/2)-1) or Curve Radius = Apex Distance/(sec(Deflection Angle/2)-1). Apex Distance is the distance from the point of intersection to the apex of the curve & 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.

How to calculate Radius given Apex Distance?

The Radius given Apex Distance formula is defined as it determines the “sharpness” or “flatness” of the curve, larger radius, “flatter” curve is calculated using Curve Radius = Apex Distance/(sec(Deflection Angle/2)-1). To calculate Radius given Apex Distance, you need Apex Distance (L_ad) & Deflection Angle (Δ). With our tool, you need to enter the respective value for Apex Distance & Deflection Angle 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 Curve Radius?

In this formula, Curve Radius uses Apex Distance & Deflection Angle. We can use 3 other way(s) to calculate the same, which is/are as follows -

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))

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