Tangential Angle Method for setting out circular curves

This calculator checks the alignment and geometry of circular curves, which is used in fields such as civil engineering, construction and surveying. It provides a visual of a curve based on the input parameters: radius of the circle, chord length and number of points. 
CalculationInputs﻿﻿Radius, R
:25.00m​
﻿
﻿﻿L
:0.10m​
﻿
﻿﻿Number of Points
:100​
﻿
﻿
﻿
Input parameters in the set out of curves
OutputFor the set out curve to be valid, this condition must be satisfied:
﻿﻿L<20R​
 
﻿﻿Check condition
:Condition Satisfied​
﻿
Set out curve using Tangential Angles Method:
Can’t display the image because of an internal error. Our team is looking at the issue.
﻿
ExplanationThe Tangential Angles Method, also referred to as the Rankine Method, uses a known value (chord length) and desired value (radius) to set out circular curves. 
Here is all the parameter symbols you need to know.
﻿
Parameters for the Tangential Angles Method to set out curves
Where:
﻿﻿A,B
 or ﻿C
 are example of points, where the number of points is inputted by the user
﻿﻿L
 is a chord length, which are distances between two points. The notation is written as ﻿AB
 for distance between points ﻿A
 and ﻿B
﻿
﻿﻿R
 is the desired radius of the circle
﻿﻿O
 is the centre of the circle
﻿﻿TP
 is the tangent point, from which the tangent line is drawn and the setting out starts 
﻿﻿δi​
 is the half-angle, which is the angle between the current chord and the line connecting points ﻿TP
 and the current point. 
﻿﻿Δi​
 is the tangential angle, which is the angle between the tangent line from point ﻿TP
 and the line connecting points ﻿TP
 and the current point. You will notice ﻿Δ1​=δ1​
.
Set out curve using the Tangential Angles MethodFollow these steps to successfully set out your curve:
Select the chord length (﻿L
) and a desired radius (﻿R
) ensuring ﻿L< 20R​
﻿
Find the half angles (﻿δi​)
 for each chord using: ﻿δi​=π90​×RL​
, which will be a constant value as our chord length and radius are constants
Find the tangential angles (﻿Δi​
) for each chord using: ﻿Δi​=δi−1​+δi​
﻿
Plot the ﻿x
 and ﻿y
 coordinates of the points, which are the ﻿x
 and ﻿y
 distances from the centre of the circle, using:
﻿
x=R×cos⁡(Δi)y=R×sin⁡(Δi)x=R\times\cos(\Delta_i)\\y=R\times\sin(\Delta_i)x=R×cos(Δi​)y=R×sin(Δi​)
Iterate over all points up to ﻿n
 number of points, which is a value selected by the user
💡Assumptions of Tangential Angles Method
Related ResourcesCheck out our full library of CalcTree templates here!
Explanation by Engineering Notes here!
Explanation by Engineering Infinity here!
Rankine's Method Explained here!
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