Apex Distance Calculator

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

✖Apex Distance is the distance from the point of intersection to the apex of the curve.ⓘ Apex Distance [L_ad]

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Formula

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Apex Distance

Formula

`"L"_{"ad"} = "R"_{"Curve"}*(sec("Δ"/2)-1)`

Example

`"37.13781m"="200m"*(sec("65°"/2)-1)`

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Apex Distance Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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

Curve Radius: 200 Meter --> 200 Meter No Conversion Required
Deflection Angle: 65 Degree --> 1.1344640137961 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L_ad = R_Curve*(sec(Δ/2)-1) --> 200*(sec(1.1344640137961/2)-1)

Evaluating ... ...

L_ad = 37.137809486816

STEP 3: Convert Result to Output's Unit

37.137809486816 Meter --> No Conversion Required

FINAL ANSWER

37.137809486816 ≈ 37.13781 Meter <-- Apex Distance

(Calculation completed in 00.004 seconds)

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Credits

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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< 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

Apex Distance Formula

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

What are the Various Parts of a Curve?

(i) Tangents: The straight lines at the ends of curve or lines connected by the curves. The tangent drawn to the first point of curve is the first tangent and similarly the second tangent.
(ii) Vertex: The points of intersection of the two straights is called the intersection point or the vertex.
(iii) Long chord: Line joining both the tangents.
(iv) Mid point: It is the summit or apex of the curve.
(v) Apex distance: The distance from the point of intersection to the apex of the curve.
(vi) Central angle: The angle subtended at the centre of the curve by the arc.

How to Calculate Apex Distance?

Apex Distance calculator uses Apex Distance = Curve Radius*(sec(Deflection Angle/2)-1) to calculate the Apex Distance, The Apex Distance formula is defined as the distance from the point of intersection to the apex of the curve. The midpoint of the arc is termed as apex of the curve. Apex Distance is denoted by L_ad symbol.

How to calculate Apex Distance using this online calculator? To use this online calculator for Apex Distance, enter Curve Radius (R_Curve) & Deflection Angle (Δ) and hit the calculate button. Here is how the Apex Distance calculation can be explained with given input values -> 37.13781 = 200*(sec(1.1344640137961/2)-1).

FAQ

What is Apex Distance?

The Apex Distance formula is defined as the distance from the point of intersection to the apex of the curve. The midpoint of the arc is termed as apex of the curve and is represented as L_ad = R_Curve*(sec(Δ/2)-1) or Apex Distance = Curve Radius*(sec(Deflection Angle/2)-1). Curve Radius is the radius of a circle whose part, say, arc is taken for consideration & 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 Apex Distance?

The Apex Distance formula is defined as the distance from the point of intersection to the apex of the curve. The midpoint of the arc is termed as apex of the curve is calculated using Apex Distance = Curve Radius*(sec(Deflection Angle/2)-1). To calculate Apex Distance, you need Curve Radius (R_Curve) & Deflection Angle (Δ). With our tool, you need to enter the respective value for Curve Radius & Deflection Angle and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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