Mid Ordinate Solution

STEP 0: Pre-Calculation Summary
Formula Used
Mid Ordinate = Curve Radius*(1-cos(Deflection Angle/2))
Lmo = RCurve*(1-cos(Δ/2))
This formula uses 1 Functions, 3 Variables
Functions Used
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
Variables Used
Mid Ordinate - (Measured in Meter) - Mid Ordinate is the distance from midpoint of curve to midpoint of chord.
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
Lmo = RCurve*(1-cos(Δ/2)) --> 200*(1-cos(1.1344640137961/2))
Evaluating ... ...
Lmo = 31.3217108374114
STEP 3: Convert Result to Output's Unit
31.3217108374114 Meter --> No Conversion Required
FINAL ANSWER
31.3217108374114 31.32171 Meter <-- Mid Ordinate
(Calculation completed in 00.004 seconds)

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

Mid Ordinate Formula

Mid Ordinate = Curve Radius*(1-cos(Deflection Angle/2))
Lmo = RCurve*(1-cos(Δ/2))

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 Mid Ordinate?

Mid Ordinate calculator uses Mid Ordinate = Curve Radius*(1-cos(Deflection Angle/2)) to calculate 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 Lmo symbol.

How to calculate Mid Ordinate using this online calculator? To use this online calculator for Mid Ordinate, enter Curve Radius (RCurve) & Deflection Angle (Δ) and hit the calculate button. Here is how the Mid Ordinate calculation can be explained with given input values -> 31.32171 = 200*(1-cos(1.1344640137961/2)).

FAQ

What is 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 and is represented as Lmo = RCurve*(1-cos(Δ/2)) or Mid Ordinate = Curve Radius*(1-cos(Deflection Angle/2)). 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 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 is calculated using Mid Ordinate = Curve Radius*(1-cos(Deflection Angle/2)). To calculate Mid Ordinate, you need Curve Radius (RCurve) & 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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