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Mid Ordinate Formula

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Mid Ordinate is the distance from midpoint of curve to midpoint of chord. Check FAQs

L mo = R Curve \cdot (1 - \cos (\frac{Δ}{2}))

L_mo - Mid Ordinate?R_Curve - Curve Radius?Δ - Deflection Angle?

Mid Ordinate Example

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With units

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Here is how the Mid Ordinate equation looks like with Values.

Here is how the Mid Ordinate equation looks like with Units.

Here is how the Mid Ordinate equation looks like.

31.3217 = 200 \cdot (1 - \cos (\frac{65}{2}))

31.3217m = 200m \cdot (1 - \cos (\frac{65°}{2}))

31.3217 = 200 \cdot (1 - \cos (\frac{65}{2}))

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Mid Ordinate Solution

Follow our step by step solution on how to calculate Mid Ordinate?

FIRST Step Consider the formula

L mo = R Curve \cdot (1 - \cos (\frac{Δ}{2}))

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

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

Next Step Prepare to Evaluate

∴

L mo = 200 \cdot (1 - \cos (\frac{1.1345}{2}))

Next Step Evaluate

∴

L mo = 31.3217108374114m

LAST Step Rounding Answer

∴

L mo = 31.3217m

Mid Ordinate Formula Elements

Variables

Functions

Mid Ordinate

Mid Ordinate is the distance from midpoint of curve to midpoint of chord.

Symbol: L_mo

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Mid Ordinate

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

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(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 Mid Ordinate?

Mid Ordinate evaluator uses Mid Ordinate = Curve Radius*(1-cos(Deflection Angle/2)) to evaluate the Mid Ordinate, The Mid Ordinate formula is defined as the distance from the midpoint of a curve to the midpoint of a chord. It is found by drawing the long chord and finding the distance from its midpoint to the apex of the curve. Mid Ordinate is denoted by L_mo symbol.

How to evaluate Mid Ordinate using this online evaluator? To use this online evaluator for Mid Ordinate, enter Curve Radius (R_Curve) & Deflection Angle (Δ) and hit the calculate button.

FAQs on Mid Ordinate

What is the formula to find Mid Ordinate?

The formula of Mid Ordinate is expressed as Mid Ordinate = Curve Radius*(1-cos(Deflection Angle/2)). Here is an example- 31.32171 = 200*(1-cos(1.1344640137961/2)).

How to calculate Mid Ordinate?

With Curve Radius (R_Curve) & Deflection Angle (Δ) we can find Mid Ordinate using the formula - Mid Ordinate = Curve Radius*(1-cos(Deflection Angle/2)). This formula also uses Cosine (cos) function(s).

Can the Mid Ordinate be negative?

No, the Mid Ordinate, measured in Length cannot be negative.

Which unit is used to measure Mid Ordinate?

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

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