Mid Ordinate given Ox Calculator

✖Radius of Curve for Mid Ordinate is the radius of a circle whose part, say, arc is taken for consideration.ⓘ Radius of Curve for Mid Ordinate [R_{Mid Ordinate}]			+10% -10%
✖Distance x is the length from midpoint to a point anywhere in long chord where offset need to be drawn for setting out the curve.ⓘ Distance x [x]			+10% -10%
✖Offset at x is the length of offset drawn at a distance x from midpoint for setting out the curve.ⓘ Offset at x [O_x]			+10% -10%

✖Mid Ordinate is the distance from midpoint of curve to midpoint of chord.ⓘ Mid Ordinate given Ox [L_mo]

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Formula

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Mid Ordinate given Ox

Formula

`"L"_{"mo"} = -sqrt("R"_{"Mid Ordinate"}^2-"x"^2)+"O"_{"x"}+"R"_{"Mid Ordinate"}`

Example

`"2.012659m"=-sqrt(("40m")^2-("3m")^2)+"1.9m"+"40m"`

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Mid Ordinate given Ox Solution

STEP 0: Pre-Calculation Summary

Formula Used

Mid Ordinate = -sqrt(Radius of Curve for Mid Ordinate^2-Distance x^2)+Offset at x+Radius of Curve for Mid Ordinate
L_mo = -sqrt(R_{Mid Ordinate}^2-x^2)+O_x+R_{Mid Ordinate}
This formula uses 1 Functions, 4 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Mid Ordinate - (Measured in Meter) - Mid Ordinate is the distance from midpoint of curve to midpoint of chord.
Radius of Curve for Mid Ordinate - (Measured in Meter) - Radius of Curve for Mid Ordinate is the radius of a circle whose part, say, arc is taken for consideration.
Distance x - (Measured in Meter) - Distance x is the length from midpoint to a point anywhere in long chord where offset need to be drawn for setting out the curve.
Offset at x - (Measured in Meter) - Offset at x is the length of offset drawn at a distance x from midpoint for setting out the curve.

STEP 1: Convert Input(s) to Base Unit

Radius of Curve for Mid Ordinate: 40 Meter --> 40 Meter No Conversion Required
Distance x: 3 Meter --> 3 Meter No Conversion Required
Offset at x: 1.9 Meter --> 1.9 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L_mo = -sqrt(R_{Mid Ordinate}^2-x^2)+O_x+R_{Mid Ordinate} --> -sqrt(40^2-3^2)+1.9+40

Evaluating ... ...

L_mo = 2.01265864964174

STEP 3: Convert Result to Output's Unit

2.01265864964174 Meter --> No Conversion Required

FINAL ANSWER

2.01265864964174 ≈ 2.012659 Meter <-- Mid Ordinate

(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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< 3 Offsets from Long Chord Calculators

Offset at Distance x from Mid-Point

Go Offset at x = sqrt(Radius of Curve for Mid Ordinate^2-Distance x^2)-(Radius of Curve for Mid Ordinate-Mid Ordinate)

Mid Ordinate given Ox

Go Mid Ordinate = -sqrt(Radius of Curve for Mid Ordinate^2-Distance x^2)+Offset at x+Radius of Curve for Mid Ordinate

Mid Ordinate when Offsets from Long Chord is Used for Setting Out

Go Mid Ordinate = Radius of Curve for Mid Ordinate-sqrt(Radius of Curve for Mid Ordinate^2-(Length of Long Chord/2)^2)

Mid Ordinate given Ox Formula

Mid Ordinate = -sqrt(Radius of Curve for Mid Ordinate^2-Distance x^2)+Offset at x+Radius of Curve for Mid Ordinate
L_mo = -sqrt(R_{Mid Ordinate}^2-x^2)+O_x+R_{Mid Ordinate}

What are the methods of Curve Ranging?

A curve may be set out:
1. By linear methods, where chain and tape are used.
2. By angular or instrumental methods, where a theodolite with or without a chain is used.
Before starting to set out a curve by any method, the exact positions of the tangent points between which the curve lies must be determined.

What is Setting Out using Offsets from Long Chord?

Setting out a curve means locating various points at equal and convenient distances along the length of a curve. The methods of setting out a simple circular curve are broadly classified as linear and angular methods. In the former method, only a chain or a tape is used and no angle measuring instrument is used. In the latter method, an angle-measuring instrument, such as a theodolite is used. The offset from a long chord is one of the linear techniques used. Once the mid ordinate is known, the offset at any distance x from the midpoint can be calculated and thus a curve can be set out.

How to Calculate Mid Ordinate given Ox?

Mid Ordinate given Ox calculator uses Mid Ordinate = -sqrt(Radius of Curve for Mid Ordinate^2-Distance x^2)+Offset at x+Radius of Curve for Mid Ordinate to calculate the Mid Ordinate, The Mid Ordinate given Ox formula is defined as the distance from the midpoint of a chord to the apex of the curve when setting out offset is established. Mid Ordinate is denoted by L_mo symbol.

How to calculate Mid Ordinate given Ox using this online calculator? To use this online calculator for Mid Ordinate given Ox, enter Radius of Curve for Mid Ordinate (R_{Mid Ordinate}), Distance x (x) & Offset at x (O_x) and hit the calculate button. Here is how the Mid Ordinate given Ox calculation can be explained with given input values -> 2.012659 = -sqrt(40^2-3^2)+1.9+40.

FAQ

What is Mid Ordinate given Ox?

The Mid Ordinate given Ox formula is defined as the distance from the midpoint of a chord to the apex of the curve when setting out offset is established and is represented as L_mo = -sqrt(R_{Mid Ordinate}^2-x^2)+O_x+R_{Mid Ordinate} or Mid Ordinate = -sqrt(Radius of Curve for Mid Ordinate^2-Distance x^2)+Offset at x+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, Distance x is the length from midpoint to a point anywhere in long chord where offset need to be drawn for setting out the curve & Offset at x is the length of offset drawn at a distance x from midpoint for setting out the curve.

How to calculate Mid Ordinate given Ox?

The Mid Ordinate given Ox formula is defined as the distance from the midpoint of a chord to the apex of the curve when setting out offset is established is calculated using Mid Ordinate = -sqrt(Radius of Curve for Mid Ordinate^2-Distance x^2)+Offset at x+Radius of Curve for Mid Ordinate. To calculate Mid Ordinate given Ox, you need Radius of Curve for Mid Ordinate (R_{Mid Ordinate}), Distance x (x) & Offset at x (O_x). With our tool, you need to enter the respective value for Radius of Curve for Mid Ordinate, Distance x & Offset at x and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Mid Ordinate?

In this formula, Mid Ordinate uses Radius of Curve for Mid Ordinate, Distance x & Offset at x. We can use 1 other way(s) to calculate the same, which is/are as follows -

Mid Ordinate = Radius of Curve for Mid Ordinate-sqrt(Radius of Curve for Mid Ordinate^2-(Length of Long Chord/2)^2)

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