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+16.62 | |||
| 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 |
 |
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Figure E-14
Staking a Spiraled Horizontal Curve
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