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2 200 Horizontal and Vertical Design Vertical Considerations Coordination of Horizontal and Vertical Alignments List of Figures July 2013

3 200 Horizontal and Vertical Design Introduction This section provides a brief discussion together with several figures of design criteria needed to properly design horizontal and vertical alignments. More detailed information can be found in the 2004 edition of A Policy on Geometric Design of Highways and Streets (AASHTO Green Book) and the 2001 edition of Guidelines for Geometric Design of Very Low-Volume Local Roads (ADT 400). 201 Sight Distance General A primary feature in highway design is the arrangement of the geometric elements so that sufficient sight distance is provided for safe and efficient operation. The most important sight distance considerations are: distance required for stopping, distance required for operation at intersections, distance required for passing vehicles and distance needed for making decisions at complex locations. Stopping Sight Distance (SSD) is the cumulative distance traversed by a vehicle from the instant a motorist sights an unexpected object in the roadway, applies the brakes, and is able to bring the vehicle to a stop. Intersection Sight Distance (ISD) is the distance a motorist should be able to see other traffic operating on the intersecting roadway in order to enter or cross the roadway safely and to avoid or stop short of any unexpected conflicts in the intersection area. Passing Sight Distance (PSD) is the distance a motorist should be able to observe oncoming traffic on a two-lane, two-way road in order to pass a vehicle safely. Decision Sight Distance (DSD) is the distance needed for a motorist to detect, recognize, select, initiate and complete an appropriate course of action for an unexpected or otherwise difficult-to-perceive condition in the roadway. When evaluating sight distance, the two most critical features to be considered are the height of eye and the height of the object. The driver s height of eye remains constant at 3.5 ft. for each of the sight distance categories. The height of the object, on the other hand, varies between 2 ft. and 3.5 ft. The 2 ft. object height, used for the decision and stopping sight distances, represents the taillight of the typical passenger vehicle. Research has shown that object heights below 2 ft. would result in longer crest vertical curves without providing documented safety benefits. The 3.5 ft. height, used for the intersection and passing sight distances, represents the portion of the vehicle that needs to be visible for another driver to recognize that vehicle Stopping Sight Distance Stopping sight distance is the sum of two distances: (1) the distance traversed by the vehicle from the instant the driver sights an object necessitating a stop to the instant the brakes are applied; and, (2) the distance needed to stop the vehicle from the instant brake application begins. These two are referred to as brake reaction distance and braking distance, respectively. The recommended brake reaction time to compute the brake reaction distance is 2.5 seconds. The recommended deceleration rate to compute the braking distance is 11.2 feet per second squared. Figure lists the recommended sight distance values for the given design speeds along with the corresponding equation. July

10 200 Horizontal and Vertical Design about the outside edge of traveled way. Method 4 would apply to single-lane or multi-lane ramps or roadways that are not crowned. In reference to the above discussion on the superelevation of divided roadways, it is always preferable to use the median edge of traveled way as the rotation point. This greatly reduces the amount of distortion in grading the median area Superelevation Transition The length of highway needed to change from a normal crown pavement section to a fully superelevated pavement section is referred to as the superelevation transition. The superelevation transition is divided into two parts - the tangent runout and the superelevation runoff. The tangent runout ( Lt ) is the length required to remove the adverse pavement cross slope. As is shown on Method 1 of Figure 202-5, this is the length needed to raise the "outside" edge of traveled way from a normal slope to a half-flat section (cross section A to cross section B of Figure 202-5, Method 1). The superelevation runoff ("Lr") is the length required to raise the "outside" edge of traveled way from a "half flat" section to a fully superelevated section (cross section B to cross section E of Figure 202-5, Method 1). The length of transition required to remove the pavement crown is the distance between cross section A and cross section C Figure and is generally equal to twice the Lt distance. The minimum superelevation transition length is determined by multiplying the edge of traveled way correction by the equivalent slope rate ("G") shown on Figure The rate of change of superelevation should be constant throughout the transition. The values for "Lr" given in Figures 202-7, and are based on two 12-foot lanes revolved about the centerline. "Lr" in Figure is based on one 16-foot lane revolved about the edge of traveled way. Use the equations provided on Figure to determine Lr for cases involving other lane widths or where more than one lane is being revolved about the centerline or baseline. Figures 202-5a through 202-5d have been provided to show the designer how to develop the superelevation transitions for a two-lane undivided highway (Figure 202-5a), a four-lane divided highway (Figure 202-5b) and a six-lane divided highway (Figures 202-5c & d). Figure 202-5c could also be used for a four-lane divided highway with future median lanes and Figure 202-5d could also be used for a fourlane divided highway with future outside lanes Superelevation Position Figures 202-5a through 202-5d show the recommended positioning of the proposed superelevation transition in relationship to the horizontal curve. For those curves with spirals, the transition from adverse crown removal to full superelevation shall occur within the limits of the spiral. In other words, the spiral length shall equal the "Lr" value. For simple curves without spirals, the "Lr" transition shall be placed so that 50 percent to 70 percent of the maximum superelevation rate is outside the curve limits (P.C., P.T.). It is recommended that, whenever possible, 2/3 of the full superelevation rate be present at the P.C. and P.T. In addition, whenever possible, full superelevation should be maintained for at least 1/3 the length of the curve. July

11 200 Horizontal and Vertical Design Profiles and Elevations Breakpoints at the beginning and end of the superelevation transition should be rounded to obtain a smooth profile. One suggestion is to use a "vertical curve" on the edge of traveled way profile with a length in feet equal to the design speed in mph (i.e., 45 ft. for 45 mph). The final construction plans should have superelevation tables or pavement details showing the proposed elevations at the centerline, edges of traveled way, and if applicable, lane lines or other breaks in the cross slope. Pavement or lane widths should be included where these widths are in transition. Edge of traveled way profiles should be plotted to an exaggerated scale within the limits of the superelevation transition to check calculations and to determine the location of drainage basins. Adjustments should be made to obtain smooth profiles. These profiles should be submitted as part of the Stage 1 submission in order to facilitate review of the proposed data. Special care should be used in determining edge elevations in a transition area when the profile grade is on a vertical curve Superelevation Between Reverse Horizontal Curves Figure illustrates schematically two methods for positioning the superelevation transition between two reverse horizontal curves. In both diagrams each curve has its own "Lr" value (Lr1, Lr2) depending on the degree of curvature, and the superelevation is revolved about the centerline. The first (top) diagram involves two simple curves. In the case of new or relocated alignment, the P.T. of the first curve and P.C. of the second curve should be separated by enough distance to allow a smooth continuous transition between the curves at a rate not exceeding the "G" value in the table on Figure for the design speed. This requires that the distance be not less than 50 percent nor greater than 70 percent of Lr1 + Lr2. Two-thirds is the recommended portion. When adapting this procedure to existing curves where no alignment revision is proposed, the transition should conform as closely as possible to the above criteria. These designs will be reviewed on a case by case basis. The second (or lower) diagram involves two spiral curves. Where spiral transitions are used, the S.T. of the first curve and the T.S. of the second curve may be at, or nearly at, the same point, without causing superelevation problems. In these cases, the crown should not be re-established as shown in Figure 202-5, but instead, both edges of traveled way should be in continual transition between the curves, as shown in Figure Spirals The combination of high speed and sharp curvature leads to longer transition paths, which can result in shifts in lateral position and sometimes actual encroachment on adjoining lanes. Spirals make it easier for the driver to keep the vehicle within its own lane. Spirals are to be used on projects involving new alignment or substantial modifications to the existing alignment based on the maximum degree of curve as shown in Figure The length of the spiral should be equal or to greater than the superelevation runoff length "Lr" for the curve, as determined in Section This section also discussed the role of the spiral in attaining proper superelevation for the curve. The above criterion for using spirals is not intended to discourage their use in other design situations. In fact, spirals are recommended for use as a good mitigation feature in achieving full superelevation regardless of design speed or degree of curvature [curve radius]. See Figure of the Location and Design Manual, Volume 3, for more details on spiral curve elements and layout. July

15 200 Horizontal and Vertical Design Figure Date Title 201-1E* July 13 Stopping Sight Distance 201-2E January 06 Horizontal Sight Distance 201-3E July 12 Minimum Passing Sight Distance 201-4E January 06 Intersection Sight Triangles 201-5E* January 06 Intersection Sight Distance 201-6E July 13 Decision Sight Distance 202-1E July 13 Maximum Centerline Deflection without Horizontal Curve 202-2E July 13 Maximum Degree of Curve 202-3E July 13 Maximum Degree of Curve without Superelevation 202-4E July 13 Superelevation Transitions 202-5E January 12 Methods of Superelevation Rotation 202-5aE January 06 Superelevation Development Two-Lane Undivided 202-5bE January 06 Superelevation Development Four-Lane Divided 202-5cE January 06 Superelevation Development Six-Lane or More Divided (or Four-Lane Divided with Future Median Lanes) 202-5dE January 06 Superelevation Development Six-Lane or More Divided (or Four-Lane Divided with Future Outside Lanes) 202-6E January 06 Superelevation Transition between Reverse Horizontal Curves 202-7E* July 13 Superelevation and Runoff Lengths for Horizontal Curves on Rural Highways 202-8E* July 13 Superelevation and Runoff Lengths for Horizontal Curves on High-Speed Urban Highways 202-9E* October 09 Superelevation and Runoff Lengths for Horizontal Curves on Low-Speed Urban Streets 202-9aE* January 06 Superelevation Rates for Horizontal Curves on Low-Speed Urban Streets E January 06 Superelevation and Runoff Lengths for Horizontal Curves on Low-Speed Urban Ramps and Other Interchange Roadways E July 13 Maximum Curve Without a Spiral 203-1E July 13 Maximum Grades 203-1aE January 06 Critical Lengths of Grade 203-2E July 13 Maximum Change in Vertical Alignment without Vertical Curve 203-3E* July 13 Vertical Sight Distance: Crest Vertical Curves 203-4E January 06 Vertical Sight Distance: SSD Design Controls Crest Vertical Curves 203-6E July 13 Vertical Sight Distance: Sag Vertical Curves 203-7E January 06 Vertical Sight Distance: SSD Design Controls Sag Vertical Curves 203-8E January 06 Tangent Offsets for Vertical Curves * Note: For design criteria pertaining to Collectors and Local Roads with ADT s less than 400, please refer to the AASHTO Publication - Guidelines for Geometric Design of Very Low-Volume Local Roads (ADT 400). July

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22 DECISION SIGHT DISTANCE 201-6E REFERENCE SECTION HEIGHT OF EYE 3.50 HEIGHT OF OBJECT 2.00 DESIGN SPEED (mph) DECISION SIGHT DISTANCE (ft) AVOIDANCE MANEUVER A B C D E The Avoidance Maneuvers are as follows: A Rural Stop B Urban Stop C Rural Speed/Path/Direction Change D Suburban Speed/Path/Direction Change E Urban Speed/Path/Direction Change Decision Sight Distance (DSD) is calculated or measured using the same criteria as Stopping Sight Distance; 3.50 ft eye height and 2.00 ft object height. Use the equations on Figures 201-2, 203-3, and to determine DSD at vertical and horizontal curves.

23 MAXIMUM CENTERLINE DEFLECTION WITHOUT HORIZONTAL CURVE 202-1E REFERENCE SECTION DESIGN SPEED (mph) MAX. DEFLECTION * ' LOW SPEED ' ' HIGH SPEED ' 60 ' 65 0 ' ' * ROUNDED TO NEAREST Based on the Allowable Pavement Transition formulae ( ): High Speed: TanΔ = 1.0/V Low Speed: TanΔ = 60/V 2 Where: V = Design Speed Δ = Deflection Angle Note: The recommended minimum distances between consecutive horizontal deflections is: High Speed 200 Low Speed 100

24 MAXIMUM DEGREE OF CURVE 202-2E REFERENCE SECTION DESIGN SPEED (mph) MAX. DEGREE OF CURVE (A) RURAL HIGH- SPEED URBAN LOW- SPEED URBAN DESIGN SPEED (mph) MAX. DEGREE OF CURVE (A) RURAL HIGH- SPEED URBAN LOW- SPEED URBAN ' ' ' ' ' 6 45' ' ' 6 30' ' ' 6 15' ' ' ' 6 00' ' ' ' 5 45' ' ' ' 5 30' ' ' ' 5 15' ' ' ' 5 00' ' ' ' 4 45' ' ' ' 4 30' ' ' ' 4 15' ' ' ' 4 00' ' ' ' 4 00' ' ' ' 3 45' ' ' ' 3 30' ' ' ' 3 30' ' ' ' 3 15' ' ' ' 3 15' ' ' ' 3 00' ' ' ' 3 00' ' ' ' 2 45' ' ' 2 45' ' ' ' ' ' (A) See Superelevation Tables 202-7, 8 & 9 for corresponding radii values.

25 MAXIMUM DEGREE OF CURVE WITHOUT SUPERELEVATION 202-3E REFERENCE SECTION DEGREE OF CURVE DESIGN SPEED (mph) RURAL HIGHWAYS URBAN STREETS & HIGHWAYS ' LOW SPEED HIGH SPEED ' 29 20' ' 17 30' ' 11 28' FIGURE ' 7 42' ' 5 40' ' 0 47' ' 0 39' ' 0 33' ' 0 29' ' 0 26' 75 FIGURE FIGURE 202-8

26 SUPERELEVATION TRANSITIONS 202-4E REFERENCE SECTION & Maximum Relative Gradient for Profiles Between the Edge of Traveled Way and the Centerline or Reference Line (Axis of Rotation) Design Speed (mph) Maximum Relative Gradient (Percent) "Δ" Equivalent Maximum Relative Slope "G" : : : : : : : : : : :1 Number of Lanes, Rotated n 1 Adjustment Factors, b w Divided * Roadways b w Undivided Roadways b w * Interstates, Freeways, Expressways and Ramps In Figures 202-7, and , the table values for the Minimum Length of Superelevation Runoff, L r, were determined by the following equation: L r = (b w ) x 100 or L r = ( x n 1 )(e d )(G)(b w ) The equation can also be used to determine L r, when more than one lane is rotated about the centerline or the edge or if the lane width is other than 12 feet for Figures and or 16 feet for Figure Once L r has been determined, the Minimum Length of Tangent Runout, L t, should be determined by the following equation: L t = (e NC e d ) L r The equation for L t can be used by Figures 202-7, 202-8, and Where: L r = minimum length of superelevation runoff, ft L t = minimum length of tangent runout, ft Δ = maximum relative gradient, percent n 1 = number of lanes rotated = width of one traffic lane, ft (typically 12 ft) e d = design superelevation rate e NC = normal cross slope rate, (0.016) G = equivalent maximum relative slope, (the reciprocal of Δ) b w = adjustment factor for number of lanes rotated

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38 MAXIMUM CURVE WITHOUT A SPIRAL E REFERENCE SECTION DESIGN SPEED (mph) MAX. DEGREE OF CURVE MIN. RADIUS (feet)

39 MAXIMUM GRADES (PERCENT) 203-1E REFERENCE SECTION FUNCTIONAL CLASSIFICATION TERRAIN DESIGN SPEED (mph) URBAN RURAL INTERSTATE, (A) OTHER FREEWAYS & EXPRESSWAYS ARTERIAL STREET COLLECTOR (B) STREETS LOCAL STREETS INTERSTATE, (A) OTHER FREEWAYS & EXPRESSWAYS ARTERIALS COLLECTORS (B) LOCAL ROADS LEVEL ROLLING HILLY LEVEL ROLLING HILLY LEVEL ROLLING HILLY LEVEL ROLLING HILLY LEVEL ROLLING HILLY LEVEL ROLLING HILLY LEVEL ROLLING HILLY LEVEL ROLLING HILLY A. Grades 1% steeper may be used for extreme cases where development in urban areas precludes the use of flatter grades. Grades 1% steeper may also be used for one-way down-grades except in hilly terrain. B. Grades 1% steeper may be used for short lengths (less than 500 ft.), and on one-way downgrades. For rural highways with current ADT less than 400, grades may be 2% steeper.

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42 CREST VERTICAL CURVES 203-3E REFERENCE SECTION HEIGHT OF EYE HEIGHT OF OBJECT 2.00 DESIGN SPEED DESIGN SSD DESIGN K DESIGN SPEED DESIGN SSD Using: S = Stopping Sight Distance, ft. L = Length of Crest Vertical Curve, ft. A = Algebraic Difference in Grades (%), Absolute Value = Rate of Vertical Curvature DESIGN K - For a given design speed and an A value, the calculated length L = x A - To determine S with a given L and A, use the following: For S<L: S = 46.45, where = L/A For S>L: S = 1079/A + L/2

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