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Generalized Method for Estimating Best-Fit Vertical Alignments for Profile Data

Authors: Said M. Easa, Shinya Kikuchi


When the profile information of an existing road is missing or not up-to-date and the parameters of the vertical alignment are needed for engineering analysis, the engineer has to recreate the geometric design features of the road alignment using collected profile data. The profile data may be collected using traditional surveying methods, global positioning systems, or digital imagery. This paper develops a method that estimates the parameters of the geometric features that best characterize the existing vertical alignments in terms of tangents and the expressions of the curve, that may be symmetrical, asymmetrical, reverse, and complex vertical curves. The method is implemented using an Excel-based optimization method that minimizes the differences between the observed profile and the profiles estimated from the equations of the vertical curve. The method uses a 'wireframe' representation of the profile that makes the proposed method applicable to all types of vertical curves. A secondary contribution of this paper is to introduce the properties of the equal-arc asymmetrical curve that has been recently developed in the highway geometric design field.

Keywords: Optimization, parameters, data, reverse, spreadsheet, vertical curves

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[1] S. M. Easa, Y. Hassan, and Z. Karim, "Establishing highway vertical alignment using field data," ITE J. on the Web, 1998, pp. 81-86.
[2] D. Ben-Arieh, S. Chang, M. Rys, and G. Zhang, "Geometric modeling of highways using GPS data and B-spline approximation," J. Transp. Eng., vol. 130, no. 5, 2004, pp. 632-636.
[3] J. M. Anderson, and E. M. Mikhail, Surveying: Theory and Practice. New York: McGraw-Hill, 1998, ch. 16.
[4] B. F. Kavanagh, Surveying: Principles and Applications. New York: Prentice Hall, 2005, ch. 10.
[5] F. H. Moffitt, and J. D. Bossler, Surveying. New York: Addison Wesley, 1998, ch. 13.
[6] C. D. Ghilani, and P. R. Wolf, Elementary Surveying: An Introduction to Geomatics. 12th Edition, Upper Saddle River, New Jersey: Pearson Prentice-Hall, 2008, ch. 25.
[7] T. Hickerson, Route Location and Design. New York: McGraw-Hill, 1964, ch. 5.
[8] S. M. Easa, "New and improved unsymmetrical vertical curve for highways," J. Transp. Res. Rec., TRB, no. 1445, 1994, pp. 94-100.
[9] S. M. Easa, "Sight distance model for unsymmetrical crest curves," J. Transp. Res. Rec., TRB, no. 1303, 1991, pp. 39-49.
[10] S. M. Easa, "Sight distance models for unsymmetrical sag curves," J. Transp. Res. Rec., TRB, no. 1303, 1991, pp. 51-62.
[11] S. M. Easa, and Y. Hassan, "Design requirements of equal-arc unsymmetrical curves," J. Transp. Eng., ASCE, vol. 124, no. 5, 1998, pp. 404-410.
[12] S. M. Easa, "Optimum vertical curves for highway profiles," J. Surv. Eng., ASCE, vol. 125, no. 3, 1999, pp. 147-157.
[13] L. Schrage, Optimization Modeling with LINGO. Palo Alto, California: LINDO Systems, 2006, ch. 1-5.
[14] W. C. Hu, F. Tan, A. and Barnes, "New solutions to vertical curve problem," J. Surv. Eng., ASCE, vol. 130, no. 3, 2004, pp. 119-125.
[15] S. M. Easa, "Efficient method for estimating globally optimal simple vertical curves," J. Surv. Eng., ASCE, vol. 134, no. 1, 2008, pp. 33-37.
[16] G. Nehate, and M. Rys, "3D calculation of stopping-sight distance from GPS data," J. Transp. Eng., vol. 132, no. 9, 2006, pp. 691-698.
[17] J. Marshall, and J. Bethel, "Basic concepts of L1 norm minimization for surveying applications," J. Surv. Eng., ASCE, vol. 122, no. 4, 1996, pp. 168-179.
[18] Frontline Systems. Premium Solver Platform - User Guide. Incline Village, Nevada: Frontline Systems, Inc., 2005.
[19] B. P. Carlin, and T. A. Louis, Bayesian Methods for Data Analysis. Boca Raton, Florida: Chapman & Hall/CRC, 2008.