Superelevation CTC 440

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

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%

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)

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

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

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

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

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

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

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

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

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

Example Last existing curve of Paris Hill project Design speed=100 km/hr Emax=8% Radius=590 m PC STA 4+340.78 PT STA 4+901.88 Curves to the RT

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

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

Step 3 – Draw Diagram

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 5.7.3.3)

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

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%

Example of determining minimum transition lengths using maximum relative gradient

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)