Survey Curve Calculator

A survey curve calculator is a vital tool used primarily in the fields of civil engineering and land surveying. It facilitates the precise calculation of various properties of a curve that is often required in constructing roads, railways, and other infrastructure projects. The calculations enable surveyors and engineers to map out curves accurately on the ground, ensuring that designs conform to safety standards and practical specifications.

Understanding the Purpose and Functionality

Curves are ubiquitous in infrastructure projects, providing transitions between straight sections of roads or tracks. The main challenge lies in designing these curves so they are safe and efficient. The survey curve calculator tackles this by computing several critical elements:

• Radius of the Curve: Determines how sharp or broad the curve is.
• Tangent: Measures the straight distance from the beginning of the curve to where it intersects with an imaginary line through the curve’s endpoint.
• Chord: The straight line distance between the curve’s start and endpoint.
• Middle Ordinate: The distance from the chord to the deepest point of the curve.
• External Distance: The distance from the intersection of the tangents to the curve’s midpoint.

Formulas Used in Calculations

The calculator employs specific mathematical formulas to determine the properties of a circular curve:

• Radius of the Curve (R): Calculated as 𝑅=180𝜋×𝐷R=π×D180​ where 𝐷D is the Degree of Curve.
• Tangent (T): Given by 𝑇=𝑅×tan⁡(Δ2)T=R×tan(2Δ​), with ΔΔ being the central angle in radians.
• Length of Curve (L): Found using 𝐿=𝜋×𝑅×Δ180L=180π×R×Δ​.
• Chord (C): Calculated as 𝐶=2×𝑅×sin⁡(Δ2)C=2×R×sin(2Δ​).
• Middle Ordinate (M): 𝑀=𝑅(1−cos⁡(Δ2))M=R(1−cos(2Δ​)).
• External Distance (E): 𝐸=𝑅(sec⁡(Δ2)−1)E=R(sec(2Δ​)−1).

Step-by-Step Example

Let’s calculate the elements of a circular curve where the Degree of Curve 𝐷D is 2 degrees per 100 ft arc, and the central angle ΔΔ is 30 degrees.

1. Calculate the Radius:𝑅=180𝜋×2≈28.65 feetR=π×2180​≈28.65 feet
2. Calculate the Tangent:𝑇=28.65×tan⁡(15∘)≈7.56 feetT=28.65×tan(15∘)≈7.56 feet
3. Calculate the Length of the Curve:𝐿=𝜋×28.65×30180≈14.98 feetL=180π×28.65×30​≈14.98 feet
4. Calculate the Chord:𝐶=2×28.65×sin⁡(15∘)≈14.68 feetC=2×28.65×sin(15∘)≈14.68 feet
5. Calculate the Middle Ordinate:𝑀=28.65×(1−cos⁡(15∘))≈1.20 feetM=28.65×(1−cos(15∘))≈1.20 feet
6. Calculate the External Distance:𝐸=28.65×(sec⁡(15∘)−1)≈1.25 feetE=28.65×(sec(15∘)−1)≈1.25 feet

Information Table

Here is a table summarizing the input and output for this example:

Conclusion

The survey curve calculator is an indispensable tool for modern construction and land surveying. It ensures that curves are laid out with precision, enhancing both the safety and aesthetics of infrastructure projects. By automating complex calculations, the tool saves time and reduces errors, making it an essential asset for professionals in the field. Its applications span various projects, from simple road curves to complex