Horizontal Curves (Simple, Compound, Reverse) - Concept Map
Horizontal Curves in Road & Rail Alignment Design
Related concepts
Simple Circular Curve
Sub concepts
- Curve Geometry & Elements
- Radius & Deflection Angle
- Degree of Curve
- Stationing System
Relationship to central
Fundamental element; connects two tangent lines with constant radius
Curve Elements & Formulas
Sub concepts
- Tangent Distance (T)
- Length of Curve (Lc)
- Long Chord (LC)
- External Distance (E)
- Middle Ordinate (M)
Relationship to central
Define physical dimensions and positions of curve features
Degree of Curve
Sub concepts
- Arc Definition (20 m standard)
- Chord Definition
- Radius Calculation
- Curvature Comparison
Relationship to central
Specifies sharpness; inverse relationship with radius
Stationing & Layout
Sub concepts
- Point of Curvature (PC)
- Point of Intersection (PI)
- Point of Tangency (PT)
- Station Calculations
- Field Marking
Relationship to central
Locates curve features along route; essential for construction
Compound Curves
Sub concepts
- Definition & Purpose
- Common Tangent Point
- Radius Combination
- Design Constraints
Relationship to central
Two simple curves in same direction; handles complex terrain
Reverse Curves
Sub concepts
- Definition & S-Curve Geometry
- Superelevation Runoff
- Tangent Requirements
- Safety Considerations
Relationship to central
Two curves in opposite directions (S-shape); spiral transition needed
Practical Applications
Sub concepts
- Highway Design Standards
- Railway Alignment
- Urban Road Networks
- Safety & Comfort
Relationship to central
Real-world road & rail design scenarios
Common Errors & Verification
Sub concepts
- PT Stationing Mistakes
- Degree Definition Confusion
- Angle Unit Conversion
- Formula Selection
Relationship to central
Quality control in calculations and field work
Concept connections
- Simple Circular CurveCurve Elements & FormulasFormulas define all geometric properties of a simple curve
- Degree of CurveRadius & SharpnessD is the measure of curvature; inversely proportional to R
- Tangent Distance (T)Stationing & LayoutT is used to calculate PC station from PI
- Length of Curve (Lc)Stationing & LayoutLc is added to Sta PC to find Sta PT
- Simple Circular CurveCompound CurvesCompound curves are combinations of two simple curves with different radii
- Simple Circular CurveReverse CurvesReverse curves are two simple curves in opposite directions
- Curve Elements & FormulasStationing & LayoutAll calculated elements are used to determine station positions
- Degree of CurveCurve Elements & FormulasD values affect the selection of R, which affects all element calculations
- Compound CurvesCurve Elements & FormulasEach curve in a compound uses the same formulas independently
- Reverse CurvesSuperelevation RunoffReverse curves require tangent segments for safe superelevation transitions
- Stationing & LayoutPractical ApplicationsCorrect stationing enables accurate field construction and layout
- Common Errors & VerificationStationing & LayoutMost common errors occur in stationing calculations; verification prevents them
- External Distance (E)Practical ApplicationsE determines clearance requirements for buildings and obstacles
- Middle Ordinate (M)Curve Elements & FormulasM provides midpoint verification for curve shape accuracy
- Long Chord (LC)Stationing & LayoutLC is used in chord surveys to verify curve geometry in the field
Diagrams
Complete Concept Hierarchy — Horizontal Curves
Comprehensive mind map showing the hierarchical structure of horizontal curve concepts, from simple curves through compound and reverse curves, with detailed sub-elements for each category.
Simple Curve Design & Calculation Workflow
Step-by-step workflow for designing and calculating simple circular curve elements, from parameter definition through verification and field layout.
Curve Type Selection Decision Tree
Decision tree for selecting the appropriate curve type based on alignment geometry and design requirements.
Critical Stationing Calculation (Common Pitfall Avoidance)
Detailed workflow highlighting the most common stationing calculation error: using 2T instead of Lc for PT location. Essential for exam success.
Formula Selection Guide: When to Use Each Element
Decision guide for selecting the correct formula based on what curve dimension or property is needed.
Degree of Curve Conversion & Radius Relationship
Visual explanation of degree of curve concept using the 20-meter arc definition, showing the inverse relationship between D and R, with practical examples.
Compound Curve Layout: Two Radii, One Direction
Systematic layout of compound curve geometry showing how two different radii curve in the same direction with a common tangent point.
Reverse Curve with Superelevation Runoff
Detailed layout showing reverse curve geometry with emphasis on superelevation runoff and safety requirements for vehicle dynamics.
Curve Elements: Formulas & Physical Meanings
Mind map organizing the five primary curve elements with their formulas, units, meanings, and practical applications.
Common Exam Errors & Prevention Strategies
Common mistakes in horizontal curve problems with prevention and verification strategies specific to PRC board exam context.