Curves in Surveying – Complete Guide for JKSSB Civil Engineering Aspirants

🔍 Introduction

In surveying and civil engineering, curves are essential components in the design of highways, railways, canals, and pipelines. They allow smooth and safe transitions between two straight paths, ensuring that vehicles can turn or ascend/descend gradually without sudden changes in direction or slope.

For JKSSB JE Civil aspirants, questions on curves in surveying are frequently asked in both objective (MCQ) and conventional sections. Understanding this topic not only helps in exams but also builds a solid foundation for practical fieldwork.

🧭 What Are Curves in Surveying?

A curve is a line that deviates from a straight path in a smooth and continuous manner. In surveying, curves are used to connect two straight alignments with a smooth transition, either in horizontal or vertical direction.

In simple terms: Curves make roads, railways, and canals safer and more comfortable to travel on.

🛣️ Types of Curves in Surveying

Curves are broadly classified into two major categories:

1. Horizontal Curves

These curves lie in the horizontal plane and are used when there’s a change in direction.

a) Simple Curve

• Definition: A curve with a single radius connecting two tangents.
• Use: When the deflection angle is small.
• Key Elements:
  • Radius (R)
  • Tangent (T)
  • Length (L)
  • Point of Curvature (PC)
  • Point of Tangency (PT)
  • Point of Intersection (PI)

📌 Formula:

• Tangent (T) = R × tan(Δ/2)
• Length of Curve (L) = (π × R × Δ) / 180

b) Compound Curve

• Made of two or more arcs of different radii.
• Used when alignment changes in stages or due to restricted space.
• Common in mountain roads or railways.

c) Reverse Curve (Serpentine Curve)

• Two curves of opposite curvature with a common tangent.
• No intermediate straight section.
• Used in urban streets or railway sidings.

d) Transition Curve (Spiral Curve)

• A curve with gradually changing radius from infinite (straight) to a finite value (circular curve).
• Ensures smooth entry/exit from a circular curve.
• Eliminates shock and provides comfort at high speeds.

📌 Types of Transition Curves:

• Clothoid (Spiral)
• Cubic Parabola
• Bernoulli’s Lemniscate

📌 Application:

• Expressways, national highways, railway tracks

2. Vertical Curves

These curves lie in the vertical plane and are used to connect different gradients (slopes).

a) Summit Curve (Convex)

• When ascending gradient meets a descending gradient.
• Ensures visibility and safety at hill crests.

b) Valley Curve (Concave)

• When a descending gradient meets an ascending gradient.
• Ensures comfort and safety, especially at night or during rainfall.

📌 Factors to Consider:

• Stopping Sight Distance (SSD)
• Headlight Sight Distance (HSD)
• Vertical clearance for vehicles

🧾 Important Terms & Definitions

⚙️ Methods of Setting Out Curves

This is a very important topic for JKSSB JE Civil exam. Methods include:

1. Rankine’s Method (Deflection Angle Method)

• Most commonly used.
• Based on calculating deflection angles from the tangent.

2. Offsets from Chord Produced

• Used when working with chains/tapes.
• Suitable for short curves.

3. Offsets from Tangent

• Offsets measured perpendicular from the tangent line.

4. Two Theodolite Method

• Used for precise work.
• Requires two theodolites at PC and PT.

5. Tacheometric Method

• Based on stadia readings from a tacheometer.
• Suitable for hilly terrain or inaccessible areas.

✍️ Formulas to Remember for JKSSB

1. Tangent Length (T) = R × tan(Δ/2)
2. Length of Curve (L) = (π × R × Δ) / 180
3. Degree of Curve (D) = 1718.87 / R
4. Mid Ordinate (M) = R × (1 – cos(Δ/2))
5. External Distance (E) = R × (sec(Δ/2) – 1)

🧠 Memory Tricks for Exams

• “SCT” – Simple, Compound, Transition (Sequence of increasing complexity)
• “S-V-V” – Summit, Valley → for vertical curves

🛠️ Real-Life Applications of Curves

• Highways: Transition curves prevent skidding and provide smooth travel at curves.
• Railways: Reduce risk of derailment and improve comfort.
• Canals and pipelines: Smooth direction changes without pressure buildup.
• Airport taxiways and runways: Ensure safety during turns at high speed.

📝 Summary Table for Revision

📘 Conclusion

Understanding curves in surveying is crucial for both practical engineering and JKSSB exam preparation. Focus on types, definitions, formulas, and methods of setting out curves. Practice numerical questions and revise concepts regularly to stay confident.

About The Author

Sahil Digra

See author's posts