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Length of First Chord for given Deflection Angle of First Chord Formula

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First Sub Chord is the first chord drawn in the curve for setting out the curve using offsets from tangents. Check FAQs

C 1 = δ1 \cdot 2 \cdot R Mid Ordinate

C₁ - First Sub Chord?δ1 - Deflection Angle 1?R_{Mid Ordinate} - Radius of Curve for Mid Ordinate?

Length of First Chord for given Deflection Angle of First Chord Example

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Here is how the Length of First Chord for given Deflection Angle of First Chord equation looks like with Values.

Here is how the Length of First Chord for given Deflection Angle of First Chord equation looks like with Units.

Here is how the Length of First Chord for given Deflection Angle of First Chord equation looks like.

5 = 0.0625 \cdot 2 \cdot 40

5m = 0.0625 \cdot 2 \cdot 40m

5 = 0.0625 \cdot 2 \cdot 40

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Length of First Chord for given Deflection Angle of First Chord Solution

Follow our step by step solution on how to calculate Length of First Chord for given Deflection Angle of First Chord?

FIRST Step Consider the formula

C 1 = δ1 \cdot 2 \cdot R Mid Ordinate

Next Step Substitute values of Variables

∴

C 1 = 0.0625 \cdot 2 \cdot 40m

Next Step Prepare to Evaluate

∴

C 1 = 0.0625 \cdot 2 \cdot 40

LAST Step Evaluate

∴

C 1 = 5m

Length of First Chord for given Deflection Angle of First Chord Formula Elements

Variables

First Sub Chord

First Sub Chord is the first chord drawn in the curve for setting out the curve using offsets from tangents.

Symbol: C₁

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find First Sub Chord

Deflection Angle 1

Deflection Angle 1 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: δ1

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Deflection Angle 1

Radius of Curve for Mid Ordinate

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

Symbol: R_{Mid Ordinate}

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Radius of Curve for Mid Ordinate

Other formulas in Setting Out Curve using Offsets from Chords category

Go Deflection Angle of First Chord

δ1 = (\frac{C 1}{2 \cdot R Mid Ordinate})

Go First Offset given First Chord Length

O 1 = \frac{{C 1}^{2}}{2} \cdot R Mid Ordinate

Go Second Offset using Chord Lengths

O 2 = (\frac{C 2}{2} \cdot R Mid Ordinate) \cdot (C 1 + C 2)

Go N-th Offset using Chords Produced

O n = (\frac{C n}{2} \cdot R Mid Ordinate) \cdot (C n-1 + C n)

How to Evaluate Length of First Chord for given Deflection Angle of First Chord?

Length of First Chord for given Deflection Angle of First Chord evaluator uses First Sub Chord = Deflection Angle 1*2*Radius of Curve for Mid Ordinate to evaluate the First Sub Chord, The Length of First Chord for given Deflection Angle of First Chord formula is defined as the first sub-chord drawn on the curve for setting out the curve. The length depends on the deflection angle. First Sub Chord is denoted by C₁ symbol.

How to evaluate Length of First Chord for given Deflection Angle of First Chord using this online evaluator? To use this online evaluator for Length of First Chord for given Deflection Angle of First Chord, enter Deflection Angle 1 (δ1) & Radius of Curve for Mid Ordinate (R_{Mid Ordinate}) and hit the calculate button.

FAQs on Length of First Chord for given Deflection Angle of First Chord

What is the formula to find Length of First Chord for given Deflection Angle of First Chord?

The formula of Length of First Chord for given Deflection Angle of First Chord is expressed as First Sub Chord = Deflection Angle 1*2*Radius of Curve for Mid Ordinate. Here is an example- 5 = 0.0625*2*40.

How to calculate Length of First Chord for given Deflection Angle of First Chord?

With Deflection Angle 1 (δ1) & Radius of Curve for Mid Ordinate (R_{Mid Ordinate}) we can find Length of First Chord for given Deflection Angle of First Chord using the formula - First Sub Chord = Deflection Angle 1*2*Radius of Curve for Mid Ordinate.

Can the Length of First Chord for given Deflection Angle of First Chord be negative?

No, the Length of First Chord for given Deflection Angle of First Chord, measured in Length cannot be negative.

Which unit is used to measure Length of First Chord for given Deflection Angle of First Chord?

Length of First Chord for given Deflection Angle of First Chord is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Length of First Chord for given Deflection Angle of First Chord can be measured.

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