Rankine's method

<h2 id="background">Background</h2>
<p>This method makes sure that any line drawn from the known tangent to curve is a chord of the curve by constraining the deflection angle of line. Since end points of chords lie on the curve this can be used to approximate the shape of actual curve.<a class="footnote-ref" id="fnref:1" href="#fn:1"><sup>1</sup></a>
</p>
<h2 id="procedure">Procedure</h2>
<p>Let AB be a tangent line/path of communication or start of a curve, then successive points on the curve can be obtained by drawing an arbitrary line of length 
  
    
      
        
          C
          
            i
          
        
      
    
    {\displaystyle C_{i}}
  
 from point A with an angle 
  
    
      
        
          Δ
          
            i
          
        
        =
        
          ∑
          
            j
            =
            0
          
          
            i
          
        
        
          δ
          
            j
          
        
      
    
    {\displaystyle \Delta _{i}=\sum _{j=0}^{i}\delta _{j}}

</p><p>
  
    
      
        
          δ
          
            i
          
        
        =
        
          
            
              
                C
                
                  i
                
              
              ×
              180
            
            
              2
              π
              R
            
          
        
      
    
    {\displaystyle \delta _{i}={\frac {C_{i}\times 180}{2\pi R}}}
  
<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a>
</p><p>where 
  
    
      
        
          δ
          
            i
          
        
      
    
    {\displaystyle \delta _{i}}
  
 is deflection from nth chord in degrees.
</p><p>R is the radius of circular curve
</p><p>
  
    
      
        
          C
          
            i
          
        
      
    
    {\displaystyle C_{i}}
  
 is arbitrary length of chord
</p>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Dublin_and_Drogheda_Railway/wV7cm5st">Dublin and Drogheda Railway</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Schofield, W.; M. Breach (2007). Engineering surveying (6th ed.). Oxford: Butterworth-Heinemann. ISBN 978-0-7506-6949-8. OCLC 71284936. <a href="978-0-7506-6949-8" target="_blank">978-0-7506-6949-8</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Schofield, W.; M. Breach (2007). Engineering surveying (6th ed.). Oxford: Butterworth-Heinemann. ISBN 978-0-7506-6949-8. OCLC 71284936. <a href="978-0-7506-6949-8" target="_blank">978-0-7506-6949-8</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
</ol>

Rankine's method open-in-new

Rankine's method