Fibonacci-Anchored Approach to Road Curve Design: Golden Curvature with Single-Segment and G²-Continuous Composite Construction Modes
Keywords:
Golden Curvature, Fibonacci-anchored curvature; logarithmic-spiral generalisation, G²-continuous transition curve, Horizontal road alignment, Cloverleaf interchangeAbstract
Horizontal road curve design has traditionally relied on prescribed curvature laws (circular arcs, clothoids, and clothoid-arc-clothoid (SCS) hybrids) to satisfy geometric feasibility and driving-comfort requirements. These classical approaches are based on fixed or linearly evolving curvature profiles and provide limited control over how curvature is redistributed along a curve under given design constraints. This study proposes a Fibonacci-anchored curvature formulation, referred to as Golden Curvature (GC), as a parametric and curvature-continuous alternative for horizontal alignment design. The framework is governed by a single dimensionless intensity parameter β and is realized in two distinct construction modes: a Single-Segment GC in which curvature varies monotonically between two non-zero values, and a Composite Golden Curvature Spiral (GCS) in which two single-GC half-segments are joined symmetrically (optionally through a central circular arc) so that , delivering G²-continuous tangent-to-tangent transitions. Asymptotic analysis demonstrates that the framework recovers the circular arc ), the clothoid (), and the logarithmic spiral () as analytically identifiable limit cases within a single parametric family. Three case studies, moderate horizontal curves at and , and a cloverleaf interchange at per loop, are evaluated under AASHTO Green Book [1] design-speed scenarios. The Single-Segment GC achieves 25–45% shorter curve length and up to 65% smaller spatial footprint than the SCS hybrid at moderate deflections; at high deflections (270° cloverleaf loops), the small-β regime of the Single-Segment GC approaches the pure-circular geometric optimum to within 2% while satisfying the AASHTO and Lamm-et-al. operational comfort criteria. Vehicle-dynamics, side-friction, and constructability analyses confirm that the framework integrates cleanly into established design practice. The proposed Golden Curvature framework is positioned as a continuous parametric extension of the classical clothoid-based toolkit, rather than a replacement of it.
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