1. Superelevation
CTC 440

2. Objectives
Know how to determine superelevation transitions on simple circular curves and spirals
Know how to use maximum relative gradients to determine superelevation length transitions

3. Superelevation
Used to partially overcome the centrifugal force on a vehicle as it goes around a curve
Transition lengths are needed to change the cross slope from normal crown to full bank and then back down to normal crown
In New York State the allowed maximum superelevation rates are:
Rural and interstates/freeways 8%
Suburban 6%
Urban 4%

4. Methods
There are various methods for transitioning pavement from normal crown to a superelevated section
The most common method is to rotate the pavement around the centerline (which is also the HCL and TGL)

7. Runout
Runout is the distance used to change the section from normal crown to where the adverse crown is removed (to level)

8. Runoff
Runoff is the distance used to change the section from where the adverse crown is removed (to level) to the point where full superelevation is achieved
Runoff length is also the length of spiral length
Refer to Exhibit 5-15 to get the length (function of e, design speed and number of lanes rotated) but first you must determine e

10. Reverse Crown
The point at which the whole pavement is sloped at 2% (in the direction of the superelevation)

11. Spirals Runout occurs before the TS (on the tangent) and after the ST
Runoff occurs on length of spiral
There is full superelevation between the SC and CS

12. Circular Curves Runout also occurs on the tangent
0.7*Runoff occurs before the PC and after the PT
0.3*Runoff occurs on the curve (right after the PC and right before the PT).
The circular arc is not fully superelevated because part of the transition falls on the curve

13. Determining Superelevation Rate, e
Use Exhibits 2-11 through 2-14 (English)
or Exhibits MT 2-11 through MT 2-14 (Metric)
2-11 (low-speed urban streets)
2-12 (emax=4%)
2-13 (emax=6%)
2-14 (emax=8%)
Function of design speed, emax and radius

14. Runoff
Refer to Exhibit 5-15 of HDM to get the length (function of e, design speed and number of lanes rotated)
Runoff length is also the length of spiral

15. Determining Runout Lengths
Rout=(Roff*NC)/e
NC is normal crown (usually 2%)
e is the superelevation rate (%)

16. Basic steps
Given: Design speed, Number of Lanes Rotated and the Radius of the Curve:
Determine e, Roff
Calculate Rout
For circular curves calculate 30% and 70% of Roff
Draw diagram working back and forth from the PC/PT or TS/SC

17. Example Last existing curve of Paris Hill project
Design speed=100 km/hr
Emax=8%
Radius=590 m
PC STA
PT STA
Curves to the RT

18. Step 1 (find e, runoff, runout)
e= (7%) (table M2-14)---see next slide
Roff= 57 m (Exhibit 5-15)---see following slide
Rout=(Roff)(NC)/e=(57m)*(2%)/7%=16 m

21. Step 2 (.7 & .3 Roff)
0.3*57m=17m
0.7*57m=40m

22. Step 3 – Draw Diagram

23. Other pavement transitions
Sometimes it makes more sense to transition directly from one curve to another
Can determine minimum length of transition by using a maximum relative gradient (Exhibit 5-12 of HDM and equation on page )

25. Equation Variables Lr=transition length w=pavement width
ed=% change in super rate
n=# of lanes
bw=adjustment factor
n*bw factor is combined see HDM page 5-59
Δ=maximum relative gradient from HDM Table 5-4 (in %); it is a function of design speed

26. Example-minimum transition lengths
A county road- reverse curves 2% rt & 3% lt
Design speed = 40 km/hr
2 lanes-3.6 m in width
What is the minimum transition length for superelevating directly from 2% to 3%

27. Example of determining minimum transition lengths using maximum relative gradient

28. Minimum transition length
Lr=w*ed*(n*bw)]/Δ
w*ed= Δ y=0.18 m
n*bw=1 (since only 1 lane is superelevated)
Δ=0.7%
Lr=26 m (compare to exh. 5-15; 40km/hr; .05)