Presentation on theme: "Quiz Answers What can be done to improve the safety of a horizontal curve? Make it less sharp Widen lanes and shoulders on curve Add spiral transitions."— Presentation transcript:
1Quiz AnswersWhat can be done to improve the safety of a horizontal curve?Make it less sharpWiden lanes and shoulders on curveAdd spiral transitionsIncrease superelevation
2Quiz Answers Increase clear zone Improve horizontal and vertical alignmentAssure adequate surface drainageIncrease skid resistance on downgrade curves
3Some of Your Answers Decrease posted speed Add rumble strips Bigger or better signsGuardrailBetter lane markersSight distanceDecrease radius
4Superelevation and Spiral Curves CE 453 Lecture 18
5ObjectivesDefine superelevation runoff length and methods of attainment (for simple and spiral curves)Calculate spiral curve length
6Other Issues Relating to Horizontal Curves Need to coordinate with vertical and topographyNot always neededMAXIMUM CENTERLINE DEFLECTIONNOT REQUIRING HORIZONTAL CURVEDesign Speed, mphMaximum Deflection255°30'303°45'352°45'402°15'451°15'50551°00'60650°45'70Source: Ohio DOT Design Manual, Figure 202-1E
7Attainment of Superelevation - General Tangent to superelevationMust be done gradually over a distance without appreciable reduction in speed or safety and with comfortChange in pavement slope should be consistent over a distanceMethods (Exhibit 3-37 p. 186)Rotate pavement about centerlineRotate about inner edge of pavementRotate about outside edge of pavement
9Tangent Runout Section Length of roadway needed to accomplish a change in outside-lane cross slope from normal cross slope rate to zeroFor rotation about centerline
10Superelevation Runoff Section Length of roadway needed to accomplish a change in outside-lane cross slope from 0 to full superelevation or vice versaFor undivided highways with cross-section rotated about centerline
11Source: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, th Ed.
12Source: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, th Ed.
14Source: CalTrans Design Manual online, http://www. dot. ca
15Same as point E of GBSource: Iowa DOT Standard Road Plans
16Attainment Location - WHERE Superelevation must be attained over a length that includes the tangent and the curve (why)Typical: 66% on tangent and 33% on curve of length of runoff if no spiralIowa uses 70% and 30% if no spiralSuper runoff is all attained in Spiral if used (see lab manual (Iowa Spiral length = Runoff length)
17Minimum Length of Runoff for curve Lr based on drainage and aestheticsrate of transition of edge line from NC to full superelevation traditionally taken at 0.5% ( 1 foot rise per 200 feet along the road)current recommendation varies from 0.35% at 80 mph to 0.80% for 15mph (with further adjustments for number of lanes)
18Minimum Length of Tangent Runout Lt = eNC x LredwhereeNC = normal cross slope rate (%)ed = design superelevation rateLr = minimum length of superelevation runoff (ft)(Result is the edge slope is same as for Runoff segment)
19Length of Superelevation Runoff α = multilane adjustment factorAdjusts for total width
20Relative Gradient (G) Maximum longitudinal slope Depends on design speed, higher speed = gentler slope. For example:For 15 mph, G = 0.78%For 80 mph, G = 0.35%See table, next page
21Maximum Relative Gradient (G) Source: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, th Ed.
22Multilane AdjustmentRunout and runoff must be adjusted for multilane rotation.See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
23Length of Superelevation Runoff Example For a 4-lane divided highway with cross-section rotated about centerline, design superelevation rate = 4%. Design speed is 50 mph. What is the minimum length of superelevation runoff (ft)Lr = 12eαG
25Tangent runout length Example continued Lt = (eNC / ed ) x Lras defined previously, if NC = 2%Tangent runout for the example is:LT = 2% / 4% * 144’ = 72 feet
26From previous example, speed = 50 mph, e = 4% From chart runoff = 144 feet, same as from calculationSource: A Policy on Geometric Design of Highways and Streets (The Green Book). Washington, DC. American Association of State Highway and Transportation Officials, th Ed.
28Spiral Curve Transitions Vehicles follow a transition path as they enter or leave a horizontal curveCombination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
29SpiralsAdvantagesProvides natural, easy to follow, path for drivers (less encroachment, promotes more uniform speeds), lateral force increases and decreases graduallyProvides location for superelevation runoff (not part on tangent/curve)Provides transition in width when horizontal curve is widenedAesthetic
30Minimum Length of Spiral Possible Equations:Larger of (1) L = 3.15 V3RCWhere:L = minimum length of spiral (ft)V = speed (mph)R = curve radius (ft)C = rate of increase in centripetal acceleration (ft/s3) use 1-3 ft/s3 for highway)
31Minimum Length of Spiral Or (2) L = (24pminR)1/2Where:L = minimum length of spiral (ft)R = curve radius (ft)pmin = minimum lateral offset between the tangent and circular curve (0.66 feet)
32Maximum Length of Spiral Safety problems may occur when spiral curves are too long – drivers underestimate sharpness of approaching curve (driver expectancy)
33Maximum Length of Spiral L = (24pmaxR)1/2Where:L = maximum length of spiral (ft)R = curve radius (ft)pmax = maximum lateral offset between the tangent and circular curve (3.3 feet)
34Length of SpiralAASHTO also provides recommended spiral lengths based on driver behavior rather than a specific equation. See Table of text and the associated tangent runout lengths in TableSuperelevation runoff length is set equal to the spiral curve length when spirals are used.Design Note: For construction purposes, round your designs to a reasonable values; e.g.Ls = 147 feet, round it toLs = 150 feet.
39Attainment of superelevation on spiral curves See sketches that follow:Normal Crown (DOT – pt A)Tangent Runout (sometimes known as crown runoff): removal of adverse crown (DOT – A to B) B = TSPoint of reversal of crown (DOT – C) note A to B = B to CLength of Runoff: length from adverse crown removed to full superelevated (DOT – B to D), D = SCFully superelevate remainder of curve and then reverse the process at the CS.
40With Spirals Same as point E of GB Source: Iowa DOT Standard Road Plans RP-2
47For:Design Speed = 50 mphsuperelevation = 0.04normal crown = 0.02Runoff length was found to be 144’Tangent runout length =0.02/ 0.04 * 144 = 72 ft.
48Where to start transition for superelevation? Using 2/3 of Lr on tangent, 1/3 on curve for superelevation runoff:Distance before PC = Lt + 2/3 Lr=72 +2/3 (144) = 168Start removing crown at:PC station – 168’ = =Station =
49Location Example – with spiral Speed, e and NC as before and = ºStationR = 1,432.4’Lr was 144’, so set Ls = 150’
50Location Example – with spiral See Iowa DOT design manual for more equations:Spiral angle Θs = Ls * D /200 = 3 degreesP = (calculated)Ts = (R + p ) tan (delta /2) + k = ft
51Location Example – with spiral TS station = PI – Ts= –=Runoff length = length of spiralTangent runout length = Lt = (eNC / ed ) x Lr= 2% / 4% * 150’ = 75’Therefore: Transition from Normal crown begins at ( ) – ( ) =
52Location Example – with spiral With spirals, the central angle for the circular curve is reduced by 2 * ΘsLc = ((delta – 2 * Θs) / D) * 100Lc = ( *3)/4)*100 = ftTotal length of curves = Lc +2 * Ls =Verify that this is exactly 1 spiral length longer than when spirals are not used (extra credit for who can tell me why, provide a one-page memo by Monday)
53Location Example – with spiral Also note that the tangent length with a spiral should be longer than the non-spiraled curve by approximately ½ of the spiral length used. (good check – but why???)
54Notes – Iowa DOT Source: Iowa DOT Standard Road Plans Note: Draw a sketch and think about what the last para is saying