Optimum Vertical Curves for Highway Profiles
Publication: Journal of Surveying Engineering
Volume 125, Issue 3
Abstract
Information on the vertical alignment of existing old highways is often not available. To evaluate the highway alignment, it is necessary to fit vertical curves (parabolic curves and associated tangents) to the observed profile data. This paper presents a linear optimization model that determines the best parabolic curve/tangents that fit a given profile. The decision variables of the model are the grades of the first and second tangents and the location of the start and end of the parabolic curve. The objective function of the model minimizes the sum of the absolute deviations between the observed profile and the vertical curve. The model includes a constraint to make the point of vertical intersection lie in the middle of the curve, thus ensuring that the estimated grades are indeed tangents to the parabolic curve. Extensions of the model to accommodate another objective and multiple vertical curves are presented. The application of the model was illustrated using a numerical example involving a crest vertical curve. The proposed model can be easily solved using optimization software that are readily available in practice.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Colcord, J. E. (1962). “Vertical curve theory.” J. Surv. and Mapping, 22(4), 589–592.
2.
Easa, S. M. ( 1995). “Geometric design.” Civil engineering handbook, W. F. Chen, ed., CRC, Boca Raton, Fla.
3.
Easa, S. M., Hassan, Y., and Karim, Z. (1998). “Establishing highway vertical alignment using profile field data.” ITE J. on the Web, Aug., 81–86.
4.
Moffit, F. H., and Bossler, J. D. (1998). Surveying. Addison-Wesley, New York.
5.
Schrage, L. (1990). User's manual for LINDO. Scientific Press, Palo Alto, Calif.
6.
Schrage, L. (1991). User's manual for LINGO. Scientific Press, Palo Alto, Calif.
7.
Winston, W. L. (1994). Operations research: Applications and algorithms. Duxbury, Belmont, Calif.
Information & Authors
Information
Published In
History
Received: Sep 1, 1998
Published online: Aug 1, 1999
Published in print: Aug 1999
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.