HORIZONTAL CURVE DATA COLLECTION BY REMOTE SENSING TECHNIQUE

Transcription

1 Paper Number:121 HORIZONTAL CURVE DATA COLLECTION BY REMOTE SENSING TECHNIQUE Arichandran Ramachandran 1*, Lakshmi S 2, Velumani D 3, Anupriya Srinivasan 4, S arojini T 5 and Umashankar S 6 1 Lecturer, Department of Civil Engineering, University of Gondar, Gondar, Ethiopia. 2 Professor, Division of Transportation Engineering, Department of Civil Engineering, Anna University, Chennai, Tamilnadu, India. 3 Assistant Professor & 4,5 Under Graduate Student, Department of Civil Engineering, Kamaraj College of Engineering and Technology, Virudhunagar, Tamilnadu, India. 6 Assistant Professor, Department of Civil Engineering, Krishna Institute of Engineering and Technology, Ghaziabad, Uttar Pradesh, India. * arichandrangct@gmail.com Keywords: Horizontal curves, Newton Raphson s method, Arc length, Long chord length, Mid -ordinate length. Abstract: Horizontal curves are being used in roadway during transition between straight segments. These curves exert forces on vehicles that vary considerably from a tangent section. Drivers must respond appropriately to horizontal curves to safely traverse them. Implemented highway curve details on field need to be verified with design standards. Therefore, determining the characteristics of curves (including location, length and radius) is an important task. Existing methods to assess horizontal curves are Field methods and Geographical Information System applications like Curve Calculator, Curve Finder and Curvature Extension. Field methods are cost expensive, more dangerous and time consuming process. A new method, Newton Raphson s method, is attempted to find radius of highway horizontal curves. Angle of deviation and radius of horizontal curve have been obtained using Newton Raphson s method in MATLAB by measuring arc length and chord length. Few curves were selected and surveyed for their arc length, long chord length and mid-ordinate length. And by using those values radius is calculated and compared with the radius obtained by using total station. 1. Introduction Horizontal curves provide a transition from one tangent segment of roadway to the next. When a highway changes horizontal direction, making the point where it changes direction a point of intersection between two straight lines is not feasible. The change in direction would be too abrupt for the safety of modern, high -speed vehicles. It is therefore necessary to interpose a curve between the straight lines. The straight lines of a road are called tangents because the lines are tangent to the curves used to change direction. The radius of the curves can be estimated using the methods, Arc length & Long chord, Long cord and Mid-ordinate and Mid-ordinate & Angle of Deviation. There are eight curves, which are surveyed and its radiuses are estimated. The eight curves are named as curve A1, A2, B1, B2, B3, B4, B5 and C. In which, Curve A1 & A2 are foot path kerbs located at Kamaraj college of Engineering and Technology, Virudhunagar, B1, B2, B3, B4 & B5 are the curves marked on ground for known radius and C is the curve of a village road near NH7. 2. Methods of estimating radius of curves 2.1. Using Arc length and Long chord By measuring the long chord and arc length of the curve, the radius can be estimated by solving following function using Newton Raphson's method. A program has been developed to solve the above said process in the MATLAB software for the accuracy. The principles are derived from the basic geometric characteristics of the circle as shown in (Fig 1) Page 1 of 8

2 Paper Number:121 Fig 1. Geometric characteristics of circle The radius can be estimated by solving the following equations, Equating the equations 1 and 2, Then write the above equation as, Let angle AOD as X and solve it to get X value by Newton Raphson s Method Starts the iteration by guessing X 0 value as 1and continue iteration until the concurrent value is obtained. This iteration process was done by the computer program in Mat Lab. A sample coding is given for the curve B3 (Table 3) Matlab Code The code for solving the above equation, clear all close all clc % Arc length of the Curve as L % Long chord length of the Curve as LC L=7.02; LC=6.87; n=lc/l; y=@(x)sin(x)-n*(x); dy=@(x)cos(x)-n; Page 2 of 8

3 Paper Number:121 X=1; for i=1:1:500 X1=X-(y(X)/dy(X)); X=X1; end Indegree=X*180/ ; I=Indegree; IntersectionAngle=2*I Radius=LC/(2*sin(X)) 2.2. Using Long Chord and Mid Ordinate: By measuring the long chord and mid ordinate of the curve, the radius can be estimated by solving following equation by using program in MatLab software. Matlab Code: clear all close all clc % Long chord length of the Curve as LC % Mid Ordinate of the Curve as M LC=6.87; M=0.58; Radius = [(LC*LC)/(8*M)]+M/ Using Mid-ordinate and Angle of Deviation By measuring the mid-ordinate and angle of deviation value of the curve, the radius can be estimated by using the Matlab software. Matlab Code: clear all close all clc % Mid Ordinate of the Curve as M % Angle of Deviation as D M=0.58; D=40; I=D*3.14/180; R=M/[1-cos(I)/2]; Radius =R 2.4. Using Total Station: By using the total station the co-ordinate points of the curves are recorded and those points are transferred to Auto CAD as drawing and then the required values are measured from the drawing. 3. Es timation of Curve A Radius The curve A includes two curves which named as curve A1 and A2 (Fig 2).These two curves are present in front of Main Block at Kamaraj College of Engineering and Technology. These two curves are surveyed to find out their Arc Length, Long Chord Length, Mid-ordinate and Angle of Deviation by using the tape and total station. The measured values, the estimated radius values and the comparison of the radius of the curve A1 & A2 are given in the Table 1 & Table 2 respectively. Page 3 of 8

4 Radius (m) Paper Number:121 Fig 2. Curve A1 & Curve A Es timation of Curve B Radius The curve B includes five curves which named as curve B1, B2, B3, B4 and B5 (Fig 3 & Fig 4).These five curves are drawn in ground at Kamaraj College of Engineering and Technology. These five curves B1, B2, B3, B4 and B5 are drawn for the known radius of 10m, 20m, 30m, 40m and 50m respectively within an interior angle of 40. These fives curves are surveyed to find out their Arc Length, Long Chord Length, Mid-ordinate and Angle of Deviation by using the tape and total station. The table 3, 4, 5, 6 & 7 show the comparison of the radius estimated for the curves B1, B2, B3, B4 and B5 respectively. Fig 3. Co-ordinate points of the Curve B using Total Station Fig 4. Interior Angle of the Curve B Table. 1: Comparison of the radius estimated for the curves A1 Arc Length (m) Chord Length (m) Mid Ordinate (m) Angle of Deviat ion (degree) Using Long Chord & Arc Length Using Long Chord & Mid Ordinate Using Mid Ordinate & Angle of Deviation Page 4 of 8

5 Radius (m) Radius (m) Radius (m) Paper Number:121 Table. 2: Comparison of the radius estimated for the curves A2 Arc Length (m) Chord Length (m) Mid Ordinate (m) Angle of Deviation (degree) Using Long Chord & Arc Length Using Long Chord & Mid Ordinate Using Mid Ordinate & Angle of Deviation Table. 3: Comparison of the radius estimated for the curves B1 Arc Length (m) Chord Length (m) Mid Ordinate (m) Angle of Deviat ion (degree) Using Long Chord & Arc Length 9.77 Using Long Chord & Mid Ordinate Using Mid Ordinate & Angle of Deviation 9.40 Table. 4: Comparison of the radius estimated for the curves B2 Arc Length (m) Chord Length (m) Mid Ordinate (m) Angle of Deviation (degree) Using Long Chord & Arc Length 20.5 Using Long Chord & Mid Ordinate Using Mid Ordinate & Angle of Deviation Page 5 of 8

6 Radius (m) Radius (m) Radius (m) Paper Number:121 Table. 5: Comparison of the radius estimated for the curves B3 Arc Length (m) Chord Length (m) Mid Ordinate (m) Angle of Deviation (degree) Using Long Chord & Arc Length Using Long Chord & Mid Ordinate Using Mid Ordinate & Angle of Deviation Table. 6: Comparison of the radius estimated for the curves B4 Arc Length (m) Chord Length (m) Mid Ordinate (m) Angle of Deviation (degree) Using Long Chord & Arc Length Using Long Chord & Mid Ordinate Using Mid Ordinate & Angle of Deviation Table. 7: Comparison of the radius estimated for the curves B5 Arc Length (m) Chord Length (m) Mid Ordinate (m) Angle of Deviation (degree) Using Long Chord & Arc Length Using Long Chord & Mid Ordinate Using Mid Ordinate & Angle of Deviation Es timation of Curve C Radius The curve C (Fig 5) is existing at Chitoor, which is located about 0.5 km away from NH-7 (Near Virudhunagar). The latitude and longitude of the curve location are & Page 6 of 8

7 Radius (m) Paper Number:121 Fig 5. Curve C at Chitoor The above curve is surveyed by using both Total Station and by measuring long chord (Fig 7) and arc length (Fig 6) using Google earth ruler. The table 8 shows the comparison of measured radiuses. Fig 6. Arc Length of Curve C Fig 7. Long Chord Length of Curve C Table. 8: Comparison of the radius estimated for the curves C Parameters Using Google Earth ruler Total Station Arc Length (m) Chord Length (m) Angle of Deviation (degree) Using Long Chord & Arc Length Page 7 of 8

8 Paper Number:121 Fig 8. Difference of radius in percentage by various methods 4. Conclusion: The radius obtained from the three methods is almost equal to the radius obtained from total station. All the three methods are much more cost effective, less time consuming, less human resource consumption. Arc length & Long chord method is the easy one among three methods to estimate horizontal curve radius & angle of deviation. Because, direct measurement of angle of deviation and mid ordinate is not an accurate. Simple curve is only considered for this study. As per IRC:SP:20, the absolute minimum radius for village road is 60m. But, the obtained radius for the curve C is 45m. Thus, the curve C has to be smoothened. REFERENCE [1] Paul J. Carlson, Mark Burris, Kit Black, and Elisabeth R. Rose, Comparison of Radius-Estimating Techniques for Horizontal Curves Dec [2] William Rasdorf, Ph.D., P.E.; Daniel J. Findley, P.E.; Charles V. Zegeer, P.E.; Carl A. Sundstrom, P.E.; and Joseph E. Hummer, Ph.D., P.E., F.ASCE, Evaluation of GIS Applications for Horizontal Curve Data Collection March 1, [3] Asma Th. Ibraheem and Waseem Wathiq Hammodat, Review And Modeling The Methods of Radius Estimatingtechniques for Horizontal Curves Dec [4] Zhixia Li, Madhav V. Chitturi, Andrea R. Bill, and David A. Noyce, Automated Identification and Extraction of Horizontal Curve Information from Geographic Information System Roadway Maps Dec [5] Dr. B.C. Punmia, Surveying Volume II, Laxmi Publishers. [6] N N Basak, Surveying and Levelling, Tata McGRAW Hill Publisher. [7] IRC :SP Guide Lines and Construction of Rural Roads Page 8 of 8