RT Journal Article
T1 Numerical Computation of Egg and Double-Egg Curves with Clothoids
A1 Vázquez Méndez, Miguel Ernesto
A1 Casal Urcera, Gerardo
A1 Ferreiro Darriba, Juan Bosco
K1 Clothoid
K1 Cornu spiral
K1 Euler spiral
K1 Highway connections and interchanges
K1 Egg and double-egg curves
AB The clothoid, also known as Cornu spiral or Euler spiral, is a curve widely used as a transition curve when designing the layout of railway tracks and roads because of a key feature: its curvature is proportional to its length. The classical method to compute a clothoid is based on the use of Taylor expansions of sine and cosine functions, usually starting with zero curvature at the initial point. In this paper the clothoid is presented as the only curve with a constant rate of change of curvature, which parametrization can be obtained by solving an initial value problem. In this initial value problem the curvature at the starting point can be chosen, being able to develop simple, efficient, and accurate algorithms to connect two oriented circumferences by means of clothoids. These algorithms are presented as a useful tool for designing egg and double-egg curves in highway connections and interchanges
PB American Society of Civil Engineers
SN 0733-9453
YR 2020
FD 2020
LK http://hdl.handle.net/10347/32521
UL http://hdl.handle.net/10347/32521
LA eng
NO Vázquez-Méndez, M. E., Casal, G., & Ferreiro, J. B. (2020). Numerical computation of egg and double-egg curves with clothoids. Journal of Surveying Engineering, 146(1), 04019021
NO Revised version (June, 2021) of the preprint corresponding to the paperpublished in Journal of Surveying Engineering.
NO The authors would like to thank Loris Lori from Terni, Italy (Centro SviluppoMateriali and ThyssenKrupp Acciai Speciali Terni), for replicating all examples andpointing out the misprints corrected in red in this revised version. M.E. VázquezMéndez thanks the funding support from project MTM2015-65570-P of Ministerio deEconomía y Competitividad (Spain)/FEDER.
DS Minerva
RD 28 abr 2026