Mid Ordinate given Ox Calculator

Mid Ordinate given Ox Formula:

\[ L_{mo} = -\sqrt{R_{Mid Ordinate}^2 - x^2} + O_x + R_{Mid Ordinate} \]

Mid Ordinate:

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1. What is the Mid Ordinate given Ox Formula?

The Mid Ordinate given Ox formula calculates the distance from the midpoint of a curve to the midpoint of a chord in a circular curve, given the radius, distance from midpoint, and offset at that distance.

2. How Does the Calculator Work?

The calculator uses the Mid Ordinate given Ox formula:

\[ L_{mo} = -\sqrt{R_{Mid Ordinate}^2 - x^2} + O_x + R_{Mid Ordinate} \]

Where:

\( L_{mo} \) — Mid Ordinate (m)
\( R_{Mid Ordinate} \) — Radius of Curve for Mid Ordinate (m)
\( x \) — Distance x (m)
\( O_x \) — Offset at x (m)

Explanation: The formula calculates the mid ordinate by considering the geometric relationship between the radius, distance from midpoint, and offset at that point in a circular curve.

3. Importance of Mid Ordinate Calculation

Details: Accurate mid ordinate calculation is crucial for road and railway curve design, surveying, and construction projects where precise curve measurements are required for proper alignment and safety.

4. Using the Calculator

Tips: Enter radius in meters, distance x in meters, and offset at x in meters. All values must be valid (radius > 0, distance x ≥ 0).

5. Frequently Asked Questions (FAQ)

Q1: What is Mid Ordinate in curve design?
A: Mid Ordinate is the perpendicular distance from the midpoint of a curve to the midpoint of the chord connecting the curve's endpoints.

Q2: When is this formula typically used?
A: This formula is commonly used in civil engineering and surveying for setting out curves and verifying curve geometry during construction.

Q3: What are the limitations of this formula?
A: The formula assumes a perfect circular curve and may not be accurate for spiral curves or curves with varying radii.

Q4: How does offset affect the mid ordinate calculation?
A: The offset value directly influences the calculated mid ordinate, with larger offsets resulting in larger mid ordinate values.

Q5: Can this formula be used for both horizontal and vertical curves?
A: While primarily used for horizontal curves, the geometric principles can be adapted for vertical curves with appropriate modifications.