Roads and Bridges - Drogi i Mosty
23, 1, 2024, 99-116

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

Andrzej Kobryń Mail
https://orcid.org/0000-0002-4775-8164
Bialystok University of Technology, Faculty of Civil Engineering and Environmental Sciences, 45E Wiejska St., 15-351 Białystok
Published: 2024-04-10

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.

Full Text:

PDF PDF

References


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

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

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

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

Wolhuter K.M.: Geometric design of roads handbook. CRC Press, Taylor & Francis, London, 2015

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

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

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

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

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

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)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Meek D.S., Thomas R.S.: A guided clothoid spline. Computer Aided Geometric Design, 8, 2, 1991, 163-174

Meek D.S., Walton D.J.: Clothoid spline transition spirals. Mathematics of Computation, 199, 59, 1992, 117-133

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

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

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)

Walton D.J., Meek D.S.: Clothoidal splines. Computers and Graphics, 14, 1, 1990, 95-100

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

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

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

Kobryń A.: Transition curves for highway geometric design. Springer Tracts on Transportation and Traffic, 14, Springer International Publishing, Cham, 2017

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

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

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

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


1. Figure 1

  Figure 1
View (18KB)

2. Figure 2

  Figure 2
View (26KB)

3. Propozycja potencjalnych recenzentów

  Propozycja potencjalnych recenzentów
Download (30KB)

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

  
Kobryń, Andrzej. General transition curves as an alternative to traditional horizontal curves in road alignment. Roads and Bridges - Drogi i Mosty, [S.l.], v. 23, n. 1, p. 99-116, apr. 2024. ISSN 2449-769X. Available at: <>. Date accessed: 26 May. 2024. doi:http://dx.doi.org/10.7409/rabdim.024.005.