Analyzing the Impact of Geometrophysical Modeling on Highway Design Speeds: A Comparative Study for Mexico’s Case
Abstract
:1. Introduction and Antecedents
2. A Brief Comment on Geometrophysical Modeling
2.1. Fundamental Principles
2.2. Modeling Dynamics
2.3. Application to Highway Regulations
2.4. Comparative Analysis
2.5. Relevance of Geometrophysical Modeling/Examples
3. Analytical Model Conceptual Development and Discussion
3.1. Instantaneous Radius of Curvature Model (IRCM) for Highway Vehicle Dynamics: Normal and Tangential Coordinates
- (i)
- A 2D model is used to ascertain a 3D situation. The motion of a vehicle on the highway can not be reduced to normal and tangential components. For the model to make sense, another coordinate along is used.
- (ii)
- A radius of the curvature (R) notion only makes sense when considering sequences of precise segments of circular/curvilinear sections; that is, definite arc segments of the vehicle’s trajectory, as shown in Figure 3.
- (iii)
3.2. Highway Vehicle Dynamics Studied by Cylindrical-Polar Coordinates: Plane of Vehicle Motion Rotated with Respect to Horizontal Plane
3.3. Highway Vehicle Dynamics Studied by Cylindrical-Polar Coordinates: Plane of Motion Unrotated with Respect to the Horizontal Plane (i.e., Parallel to It)
3.4. Highway Vehicle Dynamics Studied by Spherical Coordinates
4. Results Comparative Presentation and Discussion
5. Parametric Sweep: Visualization and Analysis
6. Observations/Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Geometric Model | Curvature Parameter | Maximum Speed |
---|---|---|
“n & t”/unrotated cylindrical-polar system (Equation (7)/Equation (16)) | R | |
Rotated cylindrical-polar system (Equation (13)) | r | |
Rotated cylindrical-polar system (Equation (14)) | R | |
Spherical system (Equation (21)) | R | |
Spherical system (Equation (22)) | r |
Parameter | Parametric Range | Parameter Mean |
---|---|---|
Curvature radius | ∼ | |
Super-elevation | ∼ | |
Maximum speed | ∼ |
Pavement Particular Conditions | Parametric Range | Parameter Mean | Mean Particle Diameter |
---|---|---|---|
Iced, no sand | ∼ | Not applicable. | |
Dry, sandy | ∼ | ∼ | |
Dry, sandy | ∼ | ∼ |
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Anaya Rivera, E.; Isaza, C.; Ramirez-Gutierrez, C.F.; Zavala-De Paz, J.P.; Ibarra Tapia, P.R.; Rizzo-Sierra, J.A. Analyzing the Impact of Geometrophysical Modeling on Highway Design Speeds: A Comparative Study for Mexico’s Case. Appl. Sci. 2024, 14, 4064. https://doi.org/10.3390/app14104064
Anaya Rivera E, Isaza C, Ramirez-Gutierrez CF, Zavala-De Paz JP, Ibarra Tapia PR, Rizzo-Sierra JA. Analyzing the Impact of Geometrophysical Modeling on Highway Design Speeds: A Comparative Study for Mexico’s Case. Applied Sciences. 2024; 14(10):4064. https://doi.org/10.3390/app14104064
Chicago/Turabian StyleAnaya Rivera, Ely, Cesar Isaza, Cristian Felipe Ramirez-Gutierrez, J. P. Zavala-De Paz, Pamela Rocío Ibarra Tapia, and Jose Amilcar Rizzo-Sierra. 2024. "Analyzing the Impact of Geometrophysical Modeling on Highway Design Speeds: A Comparative Study for Mexico’s Case" Applied Sciences 14, no. 10: 4064. https://doi.org/10.3390/app14104064
APA StyleAnaya Rivera, E., Isaza, C., Ramirez-Gutierrez, C. F., Zavala-De Paz, J. P., Ibarra Tapia, P. R., & Rizzo-Sierra, J. A. (2024). Analyzing the Impact of Geometrophysical Modeling on Highway Design Speeds: A Comparative Study for Mexico’s Case. Applied Sciences, 14(10), 4064. https://doi.org/10.3390/app14104064