Ogólne krzywe przejściowe jako alternatywa dla tradycyjnych łuków poziomych w trasowaniu dróg

Andrzej Kobryń

doi:10.7409/rabdim.024.005

Published: 2024-04-10

Vol. 23 No. 1 (2024)

General transition curves as an alternative to traditional horizontal curves in road alignment

Andrzej Kobryń

Section: Articles

https://doi.org/10.7409/rabdim.024.005

Abstract

The article presents selected solutions of the so-called general transition curves, used as an alternative to traditional horizontal curves. General transition curves enable description of the entire curvilinear transition between the two straight-line sections by means of only one equation. Analysis presented in this paper pertained to the specific case of symmetrical curves. It encompassed comparison of the basic geometric parameters of conventional curves and general transition curves based on a chord of the same length. The compared parameters included minimum radius values and middle ordinates for various curves with the same chord length, as well as chord lengths corresponding to various curves with the same radius. The analyses indicated that the greater the central angle of the entire curve, the greater the difference in geometry between traditional curves and those created using general transition curves. Consequently, use of general transition curves provides greater flexibility in shaping of horizontal alignment, which may prove advantageous in difficult terrain conditions.

Keywords:

general transition curves, horizontal curves, road alignment.

Most read articles by the same author(s)

Andrzej Kobryń, Use of polynomial transition curves in the design of horizontal arcs , Roads and Bridges - Drogi i Mosty: Vol. 16 No. 1 (2017)
Andrzej Kobryń, Selection of the transition curve on the basis of dynamic criteria of driving , Roads and Bridges - Drogi i Mosty: Vol. 7 No. 1-2 (2008)
Andrzej Kobryń, New transition curve types for road design , Roads and Bridges - Drogi i Mosty: Vol. 7 No. 3 (2008)

Download files

PDF

Citation rules

Kobryń, A. (2024). General transition curves as an alternative to traditional horizontal curves in road alignment. Roads and Bridges - Drogi I Mosty, 23(1), 99–116. https://doi.org/10.7409/rabdim.024.005

Cited by / Share

Licence

This work is licensed under a Creative Commons Attribution 4.0 International License.

References

Lipiński M.: Geometria i tyczenie tras drogowych, w: Geodezja inżynieryjna, tom 3, Polskie Przedsiębiorstwo Wydawnictw Kartograficznych im. Eugeniusza Romera, Warszawa- Wrocław, 1993
Google Scholar

Przewłocki S.: Geodezja inżynieryjno-drogowa. Wydawnictwo Naukowe PWN, Warszawa, 2000
Google Scholar

Rogers M.: Highway engineering. Blackwell Publishing, Oxford, 2003
Google Scholar

Brockenbrough R.L. (Ed.): Highway engineering handbook. McGraw-Hill, New York, 2009
Google Scholar

Wolhuter K.M.: Geometric design of roads handbook. CRC Press, Taylor & Francis, London, 2015 DOI: https://doi.org/10.1201/b18344
Google Scholar

Rogers M., Enright B.: Highway engineering. John Wiley & Sons Inc., New York, 2016
Google Scholar

Kobryń A.: Krzywe przejściowe w trasowaniu dróg – teoria i praktyka. Wydawnictwo Naukowe PWN, Warszawa, 2023
Google Scholar

Vázquez-Méndez M.E., Casal G.: The clothoid computation: a simple efficient numerical algorithm. Journal of Surveying Engineering, 142, 3, 2016, ID article: 04016005:1-9, DOI: 10.1061/(ASCE)SU.1943-5428.0000177 DOI: https://doi.org/10.1061/(ASCE)SU.1943-5428.0000177
Google Scholar

Casal G., Santamarina D., Vázquez-Méndez M.E.: Optimization of horizontal alignment geometry in road design and reconstruction. Transportation Research Part C: Emerging Technologies, 74, 2017, 261-274, DOI: 10.1016/j.trc.2016.11.019 DOI: https://doi.org/10.1016/j.trc.2016.11.019
Google Scholar

Vázquez-Méndez M.E., Casal G., Ferreiro J.B.: Numerical computation of egg and double-egg curves with clothoids. Journal of Surveying Engineering, 146, 1, 2020, ID article: 04019021:1-8, DOI: 10.1061/(ASCE)SU.1943-5428.0000299 DOI: https://doi.org/10.1061/(ASCE)SU.1943-5428.0000299
Google Scholar

Baykal O., Tari E., Coskun Z., Sahin M.: New transition curve joining two straight lines. Journal of Transportation Engineering 123, 5, 1997, 132-141, DOI: 10.1061/(ASCE)0733-947X(1997)123:5(337) DOI: https://doi.org/10.1061/(ASCE)0733-947X(1997)123:5(337)
Google Scholar

Tari E., Baykal O.: An alternative curve in the use of high speed transportation systems. ARI – An International Journal for Physical and Engineering Sciences, 51, 1998, 126-135, DOI: 10.1007/s007770050044 DOI: https://doi.org/10.1007/s007770050044
Google Scholar

Tari E., Baykal O.: The new generation transition curves. 5th International Congress on Advances in Civil Engineering, Istanbul, 2002
Google Scholar

Tari E., Baykal O.: A new transition curve with enhanced properties. Canadian Journal of Civil Engineering 32, 5, 2005, 913-923, DOI: 10.1139/l05-051 DOI: https://doi.org/10.1139/l05-051
Google Scholar

Bosurgi G., D’Andrea A.: A Polynomial Parametric Curve (PPC-CURVE) for the design of horizontal geometry of highways. Computer Aided Civil and Infrastructure Engineering, 27, 4, 2012, 304-312, DOI: 10.1111/j.1467-8667.2011.00750.x DOI: https://doi.org/10.1111/j.1467-8667.2011.00750.x
Google Scholar

Kisgyörgy L.: Hyperbolic transition curve. Periodica Polytechnica Civil Engineering, 58, 1, 2014, 63-69, DOI: 10.3311/PPci.7433 DOI: https://doi.org/10.3311/PPci.7433
Google Scholar

Bosurgi G., D’Andrea A., Pellegrino O., Solazzo G.: An algorithm based on the PPC (Polynomial Parametric Curve) for designing horizontal highway alignments. Advances in Transportation Studies – An International Journal, 36, 2015, 5-20
Google Scholar

Grabowski R.J.: Gładkie przejścia krzywoliniowe w drogach kołowych i kolejowych. Zeszyty Naukowe AGH, Geodezja nr 82, Kraków, 1984
Google Scholar

Kobryń A.: Wielomianowe krzywe przejściowe w projektowaniu niwelety tras drogowych. Wydawnictwa Politechniki Białostockiej, Rozprawy Naukowe nr 100, Białystok, 2002
Google Scholar

Grabowski R.J.: Ogólne krzywe przejściowe. Geodezja i Kartografia, 20, 3, 1975, 235-246
Google Scholar

Kobryń A.: Nowe typy krzywych przejściowych do definiowania tras komunikacyjnych. Roads and Bridges – Drogi i Mosty, 7, 3, 2008, 5-8
Google Scholar

Kobryń A.: Allgemeine mathematische Übergangskurven als Trassierungselement. Zeitschrift für Vermessungswesen, 93, 5, 1993, 227-242
Google Scholar

Morlok E.K.: Introduction to transportation engineering and planning. McGraw-Hill, New York, 1978
Google Scholar

Sharpe R.J., Thorne R.W.: Numerical method for extracting an arc length parameterization from parametric curves. Computer Aided Design, 14, 2, 1982, 79-81 DOI: https://doi.org/10.1016/0010-4485(82)90171-3
Google Scholar

Shoup T.E.: Applied numerical methods for the microcomputer, Prentice-Hall, Englewood Cliffs, 1984
Google Scholar

Ali J.M., Tookey R.M., Ball J.V., Ball A.A.: The generalized Cornu spiral and its application to span generation. Journal of Computational and Applied Mathematics, 102, 1, 1999, 37-47 DOI: https://doi.org/10.1016/S0377-0427(98)00207-6
Google Scholar

Meek D.S., Thomas R.S.: A guided clothoid spline. Computer Aided Geometric Design, 8, 2, 1991, 163-174 DOI: https://doi.org/10.1016/0167-8396(91)90042-A
Google Scholar

Meek D.S., Walton D.J.: Clothoid spline transition spirals. Mathematics of Computation, 199, 59, 1992, 117-133 DOI: https://doi.org/10.1090/S0025-5718-1992-1134736-8
Google Scholar

Meek D.S., Walton D.J.: A note on finding clothoids. Journal of Computational and Applied Mahematics, 170, 2, 2004, 433-453, DOI: 10.1016/j.cam.2003.12.047 DOI: https://doi.org/10.1016/j.cam.2003.12.047
Google Scholar

Walton D.J.: Spiral spline curves for highway design. Computer-Aided Civil and Infrastructure Engineering, 4, 2, 1989, 99-106, DOI: 10.1111/j.1467-8667.1989.tb00012.x DOI: https://doi.org/10.1111/j.1467-8667.1989.tb00012.x
Google Scholar

Walton D.J., Meek D.S.: Computer aided design for horizontal alignment. Journal of Transportation Engineering, 115, 4, 1989, 411-424, DOI: 10.1061/(ASCE)0733-947X(1989)115:4(411) DOI: https://doi.org/10.1061/(ASCE)0733-947X(1989)115:4(411)
Google Scholar

Walton D.J., Meek D.S.: Clothoidal splines. Computers and Graphics, 14, 1, 1990, 95-100 DOI: https://doi.org/10.1016/0097-8493(90)90013-N
Google Scholar

Walton D.J., Meek D.S.: Curvature extrema of planar parametric polynomial cubic curves. Journal of Computational and Applied Mahematics, 134, 1-2, 2001, 69-83, DOI: 10.1016/S0377-0427(00)00529-X DOI: https://doi.org/10.1016/S0377-0427(00)00529-X
Google Scholar

Wang L.Z., Miura K.T., Nakamae E., Yamamoto T., Wang T.J.: An approximation approach of the clothoid curve defined in the interval [0, /2] and its offset by free-form curves. Computer Aided Design, 33, 14, 2001, 1049-1058, DOI: 10.1016/S0010-4485(00)00142-1 DOI: https://doi.org/10.1016/S0010-4485(00)00142-1
Google Scholar

Kobryń A.: Wielomianowe kształtowanie krzywych przejściowych. Wydawnictwa Politechniki Białostockiej, Rozprawy Naukowe nr 167, Białystok, 2009
Google Scholar

Kobryń A.: Transition curves for highway geometric design. Springer Tracts on Transportation and Traffic, 14, Springer International Publishing, Cham, 2017 DOI: https://doi.org/10.1007/978-3-319-53727-6
Google Scholar

Kobryń A.: Krzywe przejściowe w trasowaniu dróg. Teoria i praktyka. Wydawnictwo Naukowe PWN, Warszawa, 2023
Google Scholar

Sánchez-Reyes J., Chacón J.M.: Nonparametric Bézier representation of polynomial transition curves. Journal of Surveying Engineering, 144, 2, 2018, ID article: 04018001, DOI: 10.1061/(ASCE)SU.1943-5428.0000251 DOI: https://doi.org/10.1061/(ASCE)SU.1943-5428.0000251
Google Scholar

Brzeziński A., Cielecki A., Dąbkowski P., Jesionkiewicz-Niedzińska K., Olszewski P., Osińska B., Sandecki T., Szagała P., Więckowski M., Włodarek P., Zieliński T.: Wytyczne projektowania odcinków dróg zamiejskich. Część 2: Kształtowanie geometryczne (WR-D-22-2). Wzorce i standardy rekomendowane przez Ministra właściwego ds. transportu, Ministerstwo Infrastruktury, Warszawa, 2023
Google Scholar

Kruszyna M., Suchy G.: Propozycja metody oceny wariantów przebiegu inwestycji drogowej w fazie planistycznej, Roads and Bridges - Drogi i Mosty, 17, 2, 2018, 159-176, DOI: 10.7409/rabdim.018.010
Google Scholar

General transition curves as an alternative to traditional horizontal curves in road alignment

Abstract

Keywords:

Similar Articles

Most read articles by the same author(s)

Downloads

Andrzej Kobryń