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Apex Distance Formula

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

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

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

Apex Distance Example

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With units

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

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

Here is how the Apex Distance equation looks like.

37.1378 = 200 \cdot (\sec (\frac{65}{2}) - 1)

37.1378m = 200m \cdot (\sec (\frac{65°}{2}) - 1)

37.1378 = 200 \cdot (\sec (\frac{65}{2}) - 1)

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Apex Distance Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

L ad = 200m \cdot (\sec (\frac{65°}{2}) - 1)

Next Step Convert Units

∴

L ad = 200m \cdot (\sec (\frac{1.1345rad}{2}) - 1)

Next Step Prepare to Evaluate

∴

L ad = 200 \cdot (\sec (\frac{1.1345}{2}) - 1)

Next Step Evaluate

∴

L ad = 37.137809486816m

LAST Step Rounding Answer

∴

L ad = 37.1378m

Apex Distance Formula Elements

Variables

Functions

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

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

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 in Simple Circular Curve category

Go Length of Curve

L Curve = R Curve \cdot Δ

Go Radius of Curve given Length

R Curve = \frac{L Curve}{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})

How to Evaluate Apex Distance?

Apex Distance evaluator uses Apex Distance = Curve Radius*(sec(Deflection Angle/2)-1) to evaluate 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 evaluate Apex Distance using this online evaluator? To use this online evaluator for Apex Distance, enter Curve Radius (R_Curve) & Deflection Angle (Δ) and hit the calculate button.

FAQs on Apex Distance

What is the formula to find Apex Distance?

The formula of Apex Distance is expressed as Apex Distance = Curve Radius*(sec(Deflection Angle/2)-1). Here is an example- 37.13781 = 200*(sec(1.1344640137961/2)-1).

How to calculate Apex Distance?

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

Can the Apex Distance be negative?

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

Which unit is used to measure Apex Distance?

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

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