Length Of First Chord For Given Deflection Angle Of First Chord Calculator

Formula Used:

\[ First Sub Chord = Deflection Angle 1 \times 2 \times Radius of Curve for Mid Ordinate \]

First Sub Chord:

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1. What is the First Sub Chord Formula?

The First Sub Chord formula calculates the length of the first chord in a curve for setting out the curve using offsets from tangents. It is derived from the relationship between the deflection angle, radius of curvature, and the chord length.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ First Sub Chord = Deflection Angle 1 \times 2 \times Radius of Curve for Mid Ordinate \]

Where:

\( Deflection Angle 1 \) — Angle between the first sub chord and the deflected line (radians)
\( Radius of Curve for Mid Ordinate \) — Radius of the circular curve (meters)

Explanation: This formula establishes the relationship between the deflection angle at the beginning of a curve and the corresponding chord length, which is essential for accurate curve setting in surveying and engineering applications.

3. Importance of First Sub Chord Calculation

Details: Accurate calculation of the first sub chord is crucial for proper curve layout in road construction, railway design, and other civil engineering projects. It ensures precise alignment and smooth transitions between straight and curved sections.

4. Using the Calculator

Tips: Enter the deflection angle in radians and the radius in meters. Both values must be positive numbers greater than zero for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What units should be used for the deflection angle?
A: The deflection angle should be entered in radians for this calculation.

Q2: Can this formula be used for any type of curve?
A: This formula is specifically designed for circular curves commonly used in civil engineering and surveying applications.

Q3: What is the practical significance of the first sub chord?
A: The first sub chord helps in establishing the initial tangent offset points for accurate curve setting and alignment.

Q4: How does radius affect the first sub chord length?
A: The first sub chord length is directly proportional to the radius - larger radii result in longer chord lengths for the same deflection angle.

Q5: Is this calculation applicable for both horizontal and vertical curves?
A: This formula is primarily used for horizontal curves, though similar principles may apply to vertical curves with appropriate modifications.