7. Example Spiraled Horizontal Curve Computation

 

a. Set up

A N75°00'00"E tangent intersects a S60°00'00"E tangent at station 43+31.10. A circular arc with a 9°00'00 degree of curvature will be used together with 300.00 ft entrance and exit spirals.

Compute radial stake out notes using 5-chord spirals and arc half stations.

   

b. Spiral components

 

 

c. Circular curve components

 

 

 

d. Stationing

StaPI      43+31.10   StaPI 43+31.10  
-Ts   4+16.62   +Ts 4+46.62  
StaTS   39+14.48   StaST 47+47.72 Ahead
+Ls   3+00.00        
StaSC   42+14.48        
+Lc   2+00.00        
StaCS   44+14.48        
+Ls   3+00.00        
StaST   47+14.48  Back      

e. Five-chord spiral

Length of each chord:

Deflection angle equation

Set up the curve table and solve ai for each curve point. Indicate appropriate math checks.

Chord Num li, ft   ai  
1 60.00   0°10'48"  
2 120.00   0°43'12"  
3 180.00   1°37'12"  
4 240.00   2°52'48"  
5 300.00 = Ls 4°30'00" = Δs/3

 

Set up and solve Equations E-21 through E-23 for radial chords:

 

Chord Num li, ft ai xi, ft   yi, ft   ci, ft   
1 60.00 0°10'48" 60.00   0.00   60.00
2 120.00 0°43'12" 119.99   1.51   120.00
3 180.00 1°37'12" 179.93   5.09   180.00
4 240.00 2°52'48" 239.71   12.06   240.00
5 300.00 4°30'00" 299.07 = Y 23.56 = X 300.00

 

Notice that the radial chord to each point is the same as its spiral distance. Because the spiral is short and flat, spiral arc and radial chord distances are (essentially) the same. That simplifies spiral computations and staking considerably: use arc distance as radial chord for each point.

f. Circular arc deflections

Set up Equations C-12 through C-15 from Chapter C. Horizontal Curves:

 

The curve table, with appropriate math checks, is:

  Stai li, ft   defl angi   ci, ft  
CS 44+14.48 200.00 = Lc 9°00'00" = Δc/2 199.18 = LC
  44+00 185.52   8°20'54"   184.86  
  43+50 135.52   6°05'54"   135.26  
  43+00 85.52   3°50'54"   85.46  
  42+50 35.52   1°35'54"   35.52  
SC 42+14.48 0.00   0°00'00"   0.00  

g. Stake out notes

Now to assemble the information into a single set of notes:

  Station Defl Ang Radial chord, ft
Exit Spiral
Occupy ST, Backsight CS
ST 47+14.48 0°00'00" 0.00
  46+54.48 0°10'48" 60.00
  45+94.48 0°43'12" 120.00
  45+34.48 1°37'12" 180.00
  44+74.48 2°52'48" 240.00
CS 44+14.48 4°30'00" 300.00
Circular Arc
Occupy SC, Backsight CS
CS 44+18.48 9°00'00" 199.18
  44+00 8°20'54" 184.86
  43+50 6°05'54" 135.26
  43+00 3°50'54" 85.26
  42+50 1°35'54" 35.52
SC 42+14.48 0°00'00 0.00
Entrance Spiral
Occupy TS,Bbacksight SC
SC 42+14.48 4°30'00" 300.00
  41+54.48 2°52'48" 240.00
  40+94.48 1°37'12" 180.00
  40+34.48 0°43'12" 120.00
  39+74.48 0°10'48" 60.00
TS 39+14.48 0°00'00" 0.00

 

Figure E-14
Staking a Spiraled Horizontal Curve