Calculating Radius of Curvature of Existing road Using Simple survey Instruments and Excel or using Google earth also

  Calculation of Radius of Curvature of Existing roads

In India generally a VR (Village Road) is upgraded to ODR (Other District Road) which further upgraded to MDR (Major District Road) and then to SH (State Highway) and so on.

Now a simple road which is constructed in schemes like MGNREGA, employment generation is in focus than engineering a structure hence roads of VR category do not follow standard Norms of IRC (Indian Road Congress) or MORTH specifications.

Hence the Government Engineers face several problems in later stages in improving Road Geometrics such as

1) Radius of Curvature :- For smooth transition of Vehicles, Transition curves are provided which has Radius as Infinity and gradually attains the Radius according to vehicle Parameters.

Calculator for Radius of Curvature (Input Values in Red only, select speed from dropdown list only)

2) Super elevation:- To counter Centrifugal force road level at outer edge is raised, to calculate Rate of Super elevation we need to know the Radius of curvature of road.

3) Widening on curves :- As we know the centrifugal force acts on the vehicle on the curved roads, The driver has the tendency to shift inwards, so the combined effects needs two types of widening Mechanical and Psychological Widening.

As all These values are related to Radius of Curvature, the method of calculating radius of curvature should have known to every Civil Engineer.

General Method is we try to find Chord of Circle by approximations as shown in below diagram

The Solution by this method may be approximate but quite reliable.

I prefer to find out another method which in terms of logic quite similar to it, but mathematically totally different. It also finds out  radius of Approximate Circle but by Differentials. The beauty of this method is that u can find out Radius at any point on the curve. So the steps of this method are as follows

Step 1) Calculate X, Y coordinates of curves :- It can be used using Google Earth Pro software by just sitting in office or by actual taking readings by any simple survey Instrument such as Auto level, Dumpy Level, Theodolite , Total station etc.

Video Shows how to get X,Y coordinates from Google Earth Pro.

The coordinates which we get are in Horizontal Line and Latitude1 ,Longitude1, latitude2, longitude 2.... in this manner we need to bring it to Separate X and Y excel column format, for which i have written 2 simple VBA codes as below

Sub COUNTCOLUMNS() Dim i Sheet2.Activate Do If Cells(47, i + 1) = "" Then ' instead of 47 row reference formula can be given GoTo YOGI Else i = i + 1 Sheet3.Cells(1, 3) = i End If Loop Until Cells(47, i + 1) = "" YOGI: End Sub above code to calculate number of columns in which coordinates are present below code arranges it in required format to draw excel graph. Sub arrangedata() Dim i, j Dim row_num Sheet2.Activate row_num = Sheet3.Cells(1, 2).Value j = 1 For i = 1 To Sheet3.Cells(1, 3).Value Step 2 j = j + 1 Sheet3.Cells(j, 2) = Sheet2.Cells(row_num, i) * 10000 Sheet3.Cells(j, 3) = Sheet2.Cells(row_num, i + 1) * 10000 Sheet3.Cells(j, 1) = j - 1 Next i Sheet3.Activate End Sub

Step 2) Get Equation of Curve :- Polynomial Equation of order upto 6 is possible on Excel, it can be achieved by Linest formula or can be taken from Graph which can be Plotted using Insert tab then graph section or using VBA code as below

Option Explicit

Sub TrendCordinate()

Dim C, i As Integer

i = 0

'

    Sheets(26).Activate

    Range("R6", Range("R6").End(xlDown).Offset(0, 1)).Select

    ActiveSheet.Shapes.AddChart.Select

    ActiveChart.SetSourceData Source:=Range("R6", Range("R6").End(xlDown).Offset(0, 1))

    ActiveChart.ChartType = xlXYScatterLines

    ActiveChart.SeriesCollection(1).Select

    ActiveSheet.ActiveSheet.Shapes.Chart.Select

    ActiveChart.SeriesCollection(1).Trendlines.Add

    ActiveSheet.Shapes.Chart.Select

    ActiveChart.SeriesCollection(1).Trendlines(1).Select

    With Selection

        .Type = xlPolynomial

        .Order = 2

    End With

    With Selection

        .Type = xlPolynomial

        .Order = 3

    End With

    With Selection

        .Type = xlPolynomial

        .Order = 4

    End With

    With Selection

        .Type = xlPolynomial

        .Order = 5

    End With

    With Selection

        .Type = xlPolynomial

        .Order = 6

    End With

    Selection.DisplayEquation = True

    Selection.DisplayRSquared = True

    ActiveSheet.ChartObjects("Chart 1").Activate

    ActiveChart.SeriesCollection(1).Trendlines(1).DataLabel.Select

    ActiveSheet.ChartObjects("Chart 1").Activate

    ActiveChart.ChartArea.Copy

    Range("C13").Select

    ActiveSheet.Paste

End Sub

Step 3) the formula for radius of curvature at any point x for the curve y=f(x) is given by

We need to use distance formula in some calculations which can be taken as

Then R value can be found, which can be further used to calculate rate of Super elevation and Widening required

Any Corrections or Suggestions are appreciated.