Radius given Apex Distance Solution

STEP 0: Pre-Calculation Summary
Formula Used
Curve Radius = Apex Distance/(sec(Deflection Angle/2)-1)
RCurve = Lad/(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
RCurve = Lad/(sec(Δ/2)-1) --> 22/(sec(1.1344640137961/2)-1)
Evaluating ... ...
RCurve = 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 00.019 seconds)

Credits

Created by Chandana P Dev
NSS College of Engineering (NSSCE), Palakkad
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National Institute of Technology (NIT), Warangal
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11 Simple Circular Curve Calculators

Radius of Curve given Long Chord
Go Curve Radius = Length of Long Chord/(2*sin(Deflection Angle/2))
Length of Curve if 30m Chord Definition
Go Length of Curve = 30*Deflection Angle/Angle for Arc*(180/pi)
Length of Curve if 20m Chord Definition
Go Length of Curve = 20*Deflection Angle/Angle for Arc*(180/pi)
Radius given Apex Distance
Go Curve Radius = Apex Distance/(sec(Deflection Angle/2)-1)
Apex Distance
Go Apex Distance = Curve Radius*(sec(Deflection Angle/2)-1)
Mid Ordinate
Go Mid Ordinate = Curve Radius*(1-cos(Deflection Angle/2))
Radius of Curve given Tangent
Go Curve Radius = Tangent Length/tan(Deflection Angle/2)
Tangent Length
Go Tangent Length = Curve Radius*tan(Deflection Angle/2)
Deflection Angle given Length of Curve
Go Deflection Angle = Length of Curve/Curve Radius
Radius of Curve given Length
Go Curve Radius = Length of Curve/Deflection Angle
Length of Curve
Go Length of Curve = Curve Radius*Deflection Angle

Radius given Apex Distance Formula

Curve Radius = Apex Distance/(sec(Deflection Angle/2)-1)
RCurve = Lad/(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 RCurve 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 (Lad) & 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 RCurve = Lad/(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 (Lad) & 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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