Polynomial Solutions of Transition Curves
Publication: Journal of Surveying Engineering
Volume 137, Issue 3
Abstract
The solutions of transition curves presented in this paper are new geometric solutions that can be used in various tasks related to road designing. Their basic advantage is that they form groups of transition curves. This paper is concerned with transition curves with the classical curvature diagram and so-called general transition curves. These can be a valuable alternative for the traditional solutions (first transition curve–circular arc–second transition curve or first transition curve–second transition curve). As a result, they are particularly useful when it comes to solving road design–related tasks, e.g., location of siding within road junctions when there are land limitations or for grade-line setting out through assigned points of set elevations. As for the presented solutions of general transition curves, they add to the range of geometric tools that can be used for road designing in a site plan and a longitudinal profile. The solutions of general transition curves described are well-suited for special areas of road designing, such as forming a completely curvilinear road design. It is equivalent to the solutions presented in the literature called polynomial location.
Get full access to this article
View all available purchase options and get full access to this article.
References
Ali, J. M., Tookey, R. M., Ball, J. V., and Ball, A. A. (1999). “The generalized Cornu spiral and its application to span generation.” J. Comput. Appl. Math., 102(1), 37–47.
Calogero, V. (1969). “A new method in road design—Polynomial alignment.” Comput. Aided Des., 1(2), 19–29.
Cantisani, G., Dondi, D., Loprencipe, G., and Ranzo, A. (2004). “Spline curves for geometric modeling of highway design.” Proc., II Convegno Internazionale, S. I. I.V.: New Technologies and Modeling Tools For Road Applications to Design and Management, Società Italiana di Infrastructture Viarie, Monte Dago, Italy.
Easa, S. M., and Hassan, Y. (2000a). “Development of transitioned vertical curve. I. Properties.” Transp. Res. Part A, 34(6), 481–486.
Easa, S. M., and Hassan, Y. (2000b). “Development of transitioned vertical curve. II. Sight distance.” Transp. Res. Part A, 34(7), 565–584.
Fulczyk, A. G. (1977). “Trassenausgleich nach spline-algorithmen (TRANSA).” Die Straße, 17(2), 65–67 (in German).
Grabowski, R. J. (1984). “Gładkie przejścia krzywoliniowe w drogach kołowych i kolejowych.” Zeszyty Naukowe Akademii Gorniczo-Hutniczej w Krakowie, Rozprawa naukowa nr 82 Geodezja, Krakow, Poland (in Polish).
Kobryń, A. (1999). “Geometryczne kształtowanie krzywoliniowych odcinków niwelety tras drogowych.” Wydawnictwa Politechniki Białostockiej, Rozprawy Naukowe nr 60, Białystok, Poland (in Polish).
Kobryń, A. (2000). “Modified general transition curves in grade line designing.” Geodezja i Kartografia; Kwartalnik Naukowy, 49(3), 145–157.
Kobryń, A. (2002). “Wielomianowe krzywe przejściowe w projektowaniu niwelety tras drogowych.” Wydawnictwa Politechniki Białostockiej, Rozprawy Naukowe nr 100, Białystok, Poland (in Polish).
Kühn, W. (1983a). “Anwendung verallgemeinerter kubischer Spline-funktionen für achsberechnung von straßen.” Die Straße, 23(2), 68–71 (in German).
Kühn, W. (1983b). “Entwurfstechnische parameter und kontrollgrößen zur beurteilung einer polynomialer trasse.” Die Straße, 23(1), 9–13 (in German).
Lamin, R., Psarianos, B., and Mailänder, T. (1999). Highway design and traffic safety engineering handbook, McGraw-Hill, Professional Book Group, New York.
Walton, D. J. (2008). “Spiral spline curves for highway design.” Comput. Aided Civ. Infrastruct. Eng., 4(2), 99–106.
Walton, D. J., and Meek, D. S. (1986). “Computer aided design for horizontal alignment.” J. Transp. Eng., 115(4), 411–424.
Wang, L. Z., Miura, K. T., Nakamae, E., Yamamoto, T., and Wang, T. J. (2001). “An approximation approach of the clothoid curve defined in the interval [0,] and its offset by free-form curves.” Comput. Aided Geom. Des., 33(14), 1049–1058.
Wenderlein, W. (1968). “Klothoiden-kreis-trassierung und allgemeine mathematische übergangskurven.” Zeitschrift für Vermessungswesen, 93(4), 139–144 (in German).
Wenderlein, W. (1970). “Anwendung allgemeiner übergangskurven bei der trassierung von verkehrswegen.” Zeitschrift für Vermessungswesen, 95(10), 446–449 (in German).
Information & Authors
Information
Published In
Copyright
© 2011 American Society of Civil Engineers.
History
Received: Apr 2, 2010
Accepted: Sep 8, 2010
Published online: Jul 15, 2011
Published in print: Aug 1, 2011
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.