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

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Superelevation Vertical Alignment

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Superelevation

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

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Axis of Rotation 1.Rotate pavement about centerline 2.Rotate about inner edge of pavement 3.Rotate about outside edge of pavement 4.Rotate about center of median (Divided)

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Axis of Rotation

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Superelevation Profile Two-Lane Highway – Centerline Rotation

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Normal Crown

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Tangent Runout/Crown Runoff Horizontal

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Superelevation Runoff Superelevation = Cross Slope

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Superelevation Achieved

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Max Superelevation Rate Nomograph (Discussed Later)

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Max Superelevation Rate Cont’d

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How to Calculate Superelevation 1. Using Superelevation Tables 2. Nomographs 3. Simple Curve Formula

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

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Iowa has ramp tables.

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

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

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Note: Greenbook contains derivation of equations/graphs.

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Superelevation Option 3 Third solution is obtained from the simplified curve formula: e = (VD 2 /15R) - f max (English version) e = (40 2 /15*700) - 0.178 = 0.152 - 0.178 = -0.0256 -2.56% Where: VD = design speed R = radius e = superelevation rate f max = maximum side friction. Note: Metric Version e = (VD 2 /127R) - f max (metric version).

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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.

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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.

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Calculations 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 ► Compute the theoretical point of normal crown and the theoretical point of full superelevation. Where: PC = Point of Curvature L = Length of Runoff X = Length of Tangent Runout NC = Normal Crown of 2%

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Length of Runoff (L)

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

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

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Tangent Runout L t or X

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

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► ► 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

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

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Max % Grade By Functional Class

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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

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Question: Is there more on Vertical Alignment in the Wisconsin Manual? 2A-1 p. 235 (276 pdf)

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