CTC 440

Superelevation

ObjectivesKnow how to determine superelevation

transitions on simple circular curves and spirals

Know how to use maximum relative gradients to determine superelevation length transitions

SuperelevationUsed 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%

MethodsThere 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)

RunoutRunout is the distance used to change the

section from normal crown to where the adverse crown is removed (to level)

RunoffRunoff 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 CrownThe point at which the whole pavement is

sloped at 2% (in the direction of the superelevation)

SpiralsRunout occurs before the TS (on the

tangent) and after the ST Runoff occurs on length of spiralThere is full superelevation between the SC

and CS

Circular CurvesRunout also occurs on the tangent 0.7*Runoff occurs before the PC and after

the PT0.3*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

RunoffRefer 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 LengthsRout=(Roff*NC)/eNC is normal crown (usually 2%)e is the superelevation rate (%)

Basic stepsGiven: 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

ExampleLast existing curve of Paris Hill projectDesign speed=100 km/hrEmax=8%Radius=590 mPC STA 4+340.78PT STA 4+901.88Curves to the RT

Step 1 (find e, runoff, runout)e= (7%) (table M2-14)---see next slideRoff= 57 m (Exhibit 5-15)---see following

slideRout=(Roff)(NC)/e=(57m)*(2%)/7%=16 m

Step 2 (.7 & .3 Roff)0.3*57m=17m0.7*57m=40m

Step 3 – Draw Diagram

Other pavement transitionsSometimes 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 VariablesLr=transition lengthw=pavement widthed=% change in super raten=# of lanesbw=adjustment factor

n*bw factor is combined see HDM page 5-59Δ=maximum relative gradient from HDM

Table 5-4 (in %); it is a function of design speed

Example-minimum transition lengthsA county road- reverse curves 2% rt & 3% ltDesign speed = 40 km/hr2 lanes-3.6 m in widthWhat is the minimum transition length for

superelevating directly from 2% to 3%

Example of determining minimum transition lengths using maximum relative gradient

Minimum transition lengthLr=w*ed*(n*bw)]/Δw*ed= Δ y=0.18 mn*bw=1 (since only 1 lane is

superelevated)Δ=0.7%Lr=26 m (compare to exh. 5-15;

40km/hr; .05)