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**Wisconsin DOT Facilities Development Manual (FDM)**

Weston Philips 1/27/05

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Superelevation Vertical Alignment

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Superelevation

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**A different angle on superelevation?**

Ch. 3 Elements of Design In Horizontal Alignment Section p. 173 Ch. 2 Alignments Section 2A-2, 2A-3

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**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)

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Axis of Rotation

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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**

Using Superelevation Tables Nomographs Simple Curve Formula

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**Superelevation Option 1**

Given: VD = 40 mph R = 700 ft. fmax = (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

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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 700 feet e = -2.5% 40mph

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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 = (VD2/15R) - fmax (English version) e = (402/15*700) = = -2.56% Where: VD = design speed R = radius e = superelevation rate fmax= maximum side friction. Note: Metric Version e = (VD2/127R) - fmax (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 Compute the theoretical point of normal crown and the theoretical point of full superelevation. Given: PC = Station 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 = = Station Theoretical point of full superelevation PC + 1/3L = = Station 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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Length of Runoff (L) The adjustment factor (α) is used to adjust for different roadway widths.

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

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Tangent Runout Lt or X

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Tangent Runout Lt or X

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Tangent Runout Lt or X

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Tangent Runout Lt or X

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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.

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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.”

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**Max % Grade By Functional Class**

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**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

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**Question: Is there more on Vertical Alignment in the Wisconsin Manual?**

p. 235 (276 pdf)

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