What is a Horizontal Curve?
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1 Paul Deutsch
2 What is a Horizontal Curve? Provides a transition between two tangent lengths of roadway. PI PC PT PC (Point of Curvature at beginning of curve) PI (Point of Intersection of tangents) PT (Point of Tangency at end of curve)
3 Why are Horizontal Curves Needed? Necessary for gradual change in direction when a direct point of intersection is not feasible Ex. Highways, Interstates, high speed roads with constant flow of traffic
4 Types of Curves Simple Curve Compound Curve Reverse Curve Spiral Curve
5 Guidelines to Horizontal Curves A Policy on Geometric Design of Highways and Streets Horizontal Alignment (pg ) Considerations Radius Design Speed Side Friction Factor Superelevation Runoff Runout Equation on pg. 133
6 Design Considerations Safe Economically Practical For the most part, Design Speed is used as the overall design control Radius
7 Parameters Design of roadway curves should be based on an appropriate relationship between design speed and curvature and on their joint relationships with superelevation and side friction
8 Superelevation Super elevation is tilting the roadway to help offset centripetal forces developed as the vehicle goes around a curve. Along with friction, they are what keeps a vehicle from going off the road. Must be done gradually over a distance without noticeable reduction in speed or safety
9
10 Superelevation Practical upper limits 6% (NDDOT) Climate Water Ice Terrain conditions Flat Mountainous Adjacent land use (rural or urban) Frequency of slow moving vehicles Tractors, Etc.
11 Methods of Attaining Superelevation Revolve traveled way with normal cross slopes about the centerline profile Revolve traveled way with normal cross slope about the inside-edge profile Revolve traveled way with normal cross slope about the outside-edge profile Revolve traveled way with straight cross slope about the outside edge profile
12 Superelevation Transitions Consists of Runoff and Tangent Runout sections Runoff: length of roadway needed to accomplish a change in outside lane cross slope from zero to full Runout: length of roadway needed to accomplish a change in outside lane cross slope from normal rate to zero
13 Full Superelevation Runoff Runout
14 Runoff For appearance and comfort, the length of superelevation runoff should be based on a maximum acceptable difference between the longitudinal grades of the axis of rotation and the edge of pavement Proper runoff design can be attained through the exclusive use of the maximum relative gradient.
15 Runoff Locating a portion of the runoff on the tangent, in advance of the PC, is preferable, since this tends to minimize the peak lateral acceleration and resulting side friction demand. For non-spiral curves, the NDDOT places 2/3 of the runoff on the tangent, and 1/3 of the runoff on the curve.
16 Runout
17 Runoff Placing a larger portion of the runoff length on the approach tangent is desirable. It decreases lateral velocity in an outward direction, which can lead to undesirable side friction due to corrective steer by the driver.
18 Equation for minimum length of superelevation runoff Where w = width of one traffic lane (ft) N = number of lanes rotated e = design superelevation rate (%) b = adjustment factor for # of lanes G = max relative gradient (%)
19 Runout Determined by the amount of adverse cross slope to be removed and the rate at which is removed. To effect a smooth edge of pavement profile, the rate of removal should equal the relative gradient used to define the superelevation runoff length
20 Methods of Distribution of Superelevation and Side Friction 5 methods Methods #2 and #5 are the most common Method #2: Side friction is such that a vehicle has all lateral acceleration sustained by side friction. Superelevation is used once f is equal to f_max. Method #5: Side friction and superelevation are in a curvilinear relation with the inverse of the radius of the curve.
21 Methods of Distribution of Superelevation and Side Friction Method #2 Used mostly for urban streets Where speed is not uniform Where constraints do not allow for superelevation Superelevation is not needed on flatter curves that need less than maximum side friction for vehicles.
22 Methods of Distribution of Superelevation and Side Friction Method #5 Superelevation and side friction distributed concurrently Most practical
23 Finding Minimum Radius Minimum Radius and Design Speeds are the common limiting values of curvature determined from max rate of superelevation and max side friction factor Equation found on pg. 133 and pg. 143 Can use this equation to solve for R_min 2 R_min = V 15(.01e_max + f_max)
24 Example/Handout According to NDDOT Cadd Standards 6% max table on pg. 159 Max Relative Gradient (MRG) table on pg. 170 Determine Desired Relative Gradient (DRG) NDDOT uses DRG as 83.3 % of MRG
25 Main Points Horizontal curves provide transitions between two tangent lengths of roadway Simple Curves have 4 variables Radius Design Speed Side Friction Factor Superelevation
26 Main Points Considerations for Horizontal Curves Safety Economically Practical Superelevation Transitions Runout Runoff
27 Sources A Policy on Geometric Design of Highways and Streets, 2001 Cadd Standards anual/caddmanual.pdf
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Lecture 24 Flumes & Channel Transitions. I. General Characteristics of Flumes. Flumes are often used:
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