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310/3339–14FE Reference Handbook 10.4 · Civil · Transportation · Horizontal Alignment
1. Stopping Sight Distance2. Superelevation & Side Friction3. Traffic Flow Fundamental4. Density and Spacing5. Peak-Hour Factor6. Crest Vertical Curve (SSD Controls)7. Degree of Curve (Arc Definition)8. Time-Mean and Space-Mean Speed9. Design Hourly Volume from AADT10. Braking Distance11. Passing Sight Distance12. ESAL and Structural Number13. Sag Vertical Curve Length (Headlight)14. Horizontal-Curve Middle Ordinate (Sight)15. Webster Optimum Cycle Length16. Passenger-Car Equivalent and HVF17. Decision Sight Distance18. Lane Capacity from Saturation Flow19. Uniform Intersection Delay (Webster d1)20. Crash Rate21. Spiral (Transition) Curve Length22. Flexible Pavement SN and ESALs

Handbook formula

Spiral (Transition) Curve Length

Clothoid: curvature increases linearly from 0 to 1/R. Ls also from superelevation runoff. C is the rate of change of centripetal acceleration (comfort).

(mph)
Speed
(ft)
Circular radius
Comfort jerk parameter

Step-by-step solved example

V=60 mph, R=1200 ft, C=2 ft/s³. Ls?

PCPTRΔ
Clothoid TS–SC: curvature ramps from 0 to 1/R over Ls.

  1. 1. V³

    216000.

  2. 2. Ls

    3.15×216000/(1200×2)=3.15×90=283.5 ft.

Answer: Ls ≈ 284 ft

10 practice questions

0/10 correct

1.If R doubles, Ls

2.A compound curve is

3.Superelevation runoff e from 0 to e_max often sets

4.V=40, R=800, C=2: Ls nearest

5.θs spiral angle =

6.Without a spiral, drivers jump from

7.V³ means high-speed ramps need

8.C=1 vs C=3: smaller C is

9.Stations: TS → SC → CS → ST

10.Metric form uses a different constant than 3.15 because