HORIZONTAL CURVE DATA COLLECTION BY REMOTE SENSING TECHNIQUE

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HORIZONTAL CURVE DATA COLLECTION BY

REMOTE SENSING TECHNIQUE

Arichandr an Ramachandr an1*, Lakshmi S2, Velumani D3, Anupri ya Srini vasan4, S arojini T5 and

Umashankar S6

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 & 4,5Under 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. *

Email: 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 lik e 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. Intr oduc tion

Horizontal curves provide a transition fro m one tangent segment of roadway to the next. When a highway changes horizontal direction, ma king 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 Ka mara j co llege 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 esti mating r adius of cur ves

2.1. Using Arc length and Long chor d

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 fro m the basic geometric characteristics of the circ le as shown in (Fig 1)

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Fig 1. Ge ometric characte ristics 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 A OD as X and solve it to get X value by Newton Raphson’s Method

Starts the iteration by guessing X0 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 a ll

close all clc

% Arc length of the Cu rve 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;

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X=1; for i=1:1:500 X1=X-(y(X)/dy(X)); X=X1; end Indegree=X*180/ 3.141592654; I=Indegree; IntersectionAngle=2*I Radius=LC/(2*sin(X))

2.2. Using Long Chor d and Mi d Or dinate :

By measuring the long chord and mid ordinate of the curve, the rad ius can be estimated by solving following equation by using program in Mat Lab software.

Matlab Code : clear a ll 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/2

2.3. Using Mi d-or dinate and Angle of De viation

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 a ll close all clc

% Mid Ordinate of the Curve as M % Angle of Dev iation 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 fro m the drawing.

3. Es timati on of ‘Cur ve A’ Radi us

The curve A includes two curves which named as curve A1 and A2 (Fig 2).These two curves are present in front of Main Bloc k at Ka ma raj 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 rad ius values and the comparison of the radius of the curve A1 & A2 are given in the Table 1 & Table 2 respectively.

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Fig 2. Curve A1 & Curve A2

3.1. Es timation of Curve ‘B’ Radius

The curve B inc ludes five curves which named as curve B1, B2, B3, B4 and B5 (Fig 3 & Fig 4).These five curves are drawn in ground at Kama raj College of Engineering and Technology. These five curves B1, B2, B3, B4 and B5 are dra wn 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 estimate d for the curve s A1

Parame ters Manual me asurements (Tape) Total Station

Arc Length (m) 15.25 16.93

Chord Length (m) 14.75 14.39

Mid Ordinate (m) 1.670 1.720

Angle of Deviat ion (degree) _51.080 ₅₂0

R a d iu s (m

) _{Using Long Chord & Arc Length} _17.11

19.25 Using Long Chord & M id Ordinate 17.12

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Table . 2: Comparison of the radius estimate d for the curve s A2

Arc Length (m) 29.60 25.42

Angle of Deviat ion (degree) 117.870 1030

R a d iu s (m

) Using Long Chord & Arc Length 14.39

Using Mid Ordinate & Angle o f Deviation 14.32

Table . 3: Comparison of the radius estimate d for the curve s B1

Arc Length (m) 7.02 6.865

Angle of Deviat ion (degree) _41.160 ₄₀0

R a d iu s (m

Arc Length (m) 13.99 14.045

Angle of Deviat ion (degree) 390 400

R a d iu s (m

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Arc Length (m) 20.95 21.165

R a d iu s (m

Arc Length (m) 28 28.398

R a d iu s (m

Arc Length (m) 35.18 35.319

R a d iu s (m

3.2. Es timation of Curve ‘C’ Radius

The curve C (Fig 5) is e xisting at Ch itoor, which is located about 0.5 km away fro m NH-7 (Near Virudhunagar). The latitude and longitude of the curve location are 9.646401 & 77.958792.

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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 ru ler. 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 estimate d for the curve s C

Parame ters Using Google

Ear th ruler Total Station

Arc Length (m) 43.14 43.27

Angle of Deviat ion (degree) 54˚ 52˚

R a d iu s (m )

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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 fro m 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.

 Simp le curve is only considered for this study.

 As per IRC:SP:20, the absolute min imu m radius for v illage road is 60m. But, the obtained radius for the curve C is 45m. Thus, the curve “C” has to be smoothened.

REFER ENCE

[1] Paul J. Ca rlson, Mark Burris, Kit Blac k, and Elisabeth R. Rose, “Co mparison of Radius -Estimat ing Techniques for Horizontal Curves” Dec. 2005.

[2] Willia m Rasdorf, Ph.D., P.E.; Danie l J. Findley, P.E.; Charles V. Zegeer, P.E.; Ca rl A. Sundstrom, P.E.; and Joseph E. Hu mme r, Ph.D., P.E., F.ASCE, “ Evaluation of GIS Applications for Horizontal Curve Data Co llection” March 1, 2012.

[3] Asma Th. Ibraheem and Waseem Wathiq Hammodat, “ Review And Modeling The Methods of Radius Estimatingtechniques for Horizontal Curves” Dec 2011.

[4] Zhixia Li, Madhav V. Ch itturi, Andrea R. Bill, and David A. Noyce, “Automated Identification and Extraction of Horizontal Curve Information fro m Geographic Information System Roadway Maps” Dec 2012.

[5] Dr. B.C. Pun mia , Su rveying Volu me II, La xmi Publishers.

[6] N N Basak, Surveying and Levelling, Tata Mc GRAW Hill Publisher. [7] IRC :SP- 20-2002 - Guide Lines and Construction of Rural Roads