Wisconsin DOT Facilities Development Manual (FDM) Weston Philips 1/27/05 http://www.dot.ca.gov/dist1/d1traffic/cap/curve.jpg

Superelevation Vertical Alignment

Superelevation

A different angle on superelevation? Ch. 3 Elements of Design In Horizontal Alignment Section p. 173 Ch. 2 Alignments Section 2A-2, 2A-3

Axis of Rotation Rotate pavement about centerline Rotate about inner edge of pavement Rotate about outside edge of pavement Rotate about center of median (Divided)

Axis of Rotation

Axis of Rotation

Superelevation Profile Two-Lane Highway – Centerline Rotation

Normal Crown

Tangent Runout/Crown Runoff Horizontal

Superelevation Runoff Superelevation = Cross Slope

Superelevation Achieved

Max Superelevation Rate Nomograph (Discussed Later)

Max Superelevation Rate Cont’d

How to Calculate Superelevation Using Superelevation Tables Nomographs Simple Curve Formula

Superelevation Option 1 Given: VD = 40 mph R = 700 ft. fmax = 0.178 (from Table 7) First solution is obtained from the superelevation tables, emax = 0.04 (Figure 9) R = 700.; e = 0.039 3.9% Note: Choose Table emax = 0.04

Iowa has ramp tables.

Minimum Radius Greenbook p. 145 (186 pdf) Minimum Radius Table

Superelevation Option 2 Radius 700 feet e = -2.5% 40mph

Note: Greenbook contains derivation of equations/graphs.

Superelevation Option 3 Third solution is obtained from the simplified curve formula: e = (VD2/15R) - fmax (English version) e = (402/15*700) - 0.178 = 0.152 - 0.178 = -0.0256 -2.56% Where: VD = design speed R = radius e = superelevation rate fmax= maximum side friction. Note: Metric Version e = (VD2/127R) - fmax (metric version).

Superelevation Transition Superelevation transition is the length required to rotate the cross slope of a highway from a normal crowned slope to a fully superelevated cross slope.

Transition Placement WisDOT practice is to place the tangent runout and approximately two-thirds of the length of runoff on the tangent approach and one-third of the length of runoff on the curve.

Calculations Compute the theoretical point of normal crown and the theoretical point of full superelevation. Given: PC = Station 870+00.00 L = 115 ft. (Table 7, 40mph design speed) X = L * NC/ e = 115 * .02/.02 = 115ft Theoretical point of normal crown PC - 2/3L - X = 870+00.00 - 76.67 - 115 = Station 868+08.33 Theoretical point of full superelevation PC + 1/3L = 870+00.00 + 38.33 = Station 870+38.33 Where: PC = Point of Curvature L = Length of Runoff X = Length of Tangent Runout NC = Normal Crown of 2%

Length of Runoff (L)

Length of Runoff (L) The adjustment factor (α) is used to adjust for different roadway widths.

Length of Runoff (L) Greenbook p. 171 (pdf 212)

Tangent Runout Lt or X

Tangent Runout Lt or X

Tangent Runout Lt or X

Tangent Runout Lt or X

Vertical Alignment http://www.scvresources.com/highways/sr_23.htm

The highway vertical alignment consists of tangents or grades and vertical curves. Design vertical curves to provide adequate sight distance, safety, comfortable driving, good drainage, and pleasing appearance. http://listproc.ucdavis.edu/archives/cbximages/log0306/att-0011/01-CoolRide.jpg

No Vertical Curves? “Although grade changes without a vertical curve are discouraged, there may be situations where it is necessary.” “Some rounding of the deflection point is anticipated during construction.”

Max % Grade By Functional Class

K Vertical Curves Vertical curves are generally identified by their K values. K is the rate of curvature and is defined as the length of the vertical curve divided by the algebraic difference in grade Note: For Drainage, use K > 167 K

Question: Is there more on Vertical Alignment in the Wisconsin Manual? p. 235 (276 pdf)