Alighnment & horizontal alignment of highway (transportation engineering)

Alighnment & horizontal alignment of highway (transportation engineering)

1. Transportation Engineering (CE-421) Alignment Of Highways

2. Topics; __Alignment Of Highways __ Grade Line __Horizontal & Vertical Curves (1) Super Elevation (2) Transition Curve (3) Curve Widening __Sight Distance Requirements

3. Alignment Of Highways The  alignment  is the route of the road, defined as a series of horizontal tangents and curves .

4. Alignment Of Highways Grade Line: is a line or slope used as a longitudinal reference for a railroad or highway. Inclinations with the horizontal of a road, railroad, etc., usually expressed by stating the vertical rise or fall as a percentage of the horizontal distance; slope . Main consideration while selecting grade line are, Amount of earth work Natural Terrain Minimum sight distance requirement Flood water level Maximum Level of ground water Profile grade line (PGL) - This is a single line, straight or curved, along the length of the highway, sometimes but not always on the center of the highway.

5. Alignment Of Highways The alignment of a highway is composed of horizontal and vertical elements The horizontal alignment : includes the straight ( tangent ) sections of the roadway circular curves that connect their change in direction The vertical alignment : includes straight (tangent) highway grades parabolic curves that connect these grades

6. Alignment Of Highways Highway alignment is in reality a three-dimensional problem Design & construction is difficult in 3-D so highway design is typically treated as two 2-D problems: Horizontal alignment, vertical alignment

7. Alignment Of Highways Vertical Alignment Horizontal Alignment Horizontal Alignment Cor r esponds t o “X ” a n d “ Z ” Coordinates Plan vi e w – R o u ghly Equivalent to perspective view of an aerial photograph of highway. Vertical Alignment Corresponds to highway length and “Y” coordinate. Presented in a profile view. Gives elevation of all points measured along the of a highway.

8. Alignment Of Highways Instead of using the coordinates system, highway positioning and length are defined as the distance usually measured along the center line of the highway from a specified point ( also called “Reduced Distance” or ‘RD’) The notation for stationing distance is such that a point on highway 4250 ft (1295.3 m) from a specified origin (0+00 or 0+000) is said to be at station: 42+50 ft (42 stations and 50 feet) I + 295.300 meter( 1 station and 295.300 meters)

9. Alignment Of Highways The horizontal alignment consists of tangents and curves The curves are usually segments of circles, which have radii that will provide for a smooth flow of traffic The critical design feature of horizontal alignment: ho r i z o n t al cu r v e th a t t r ansit i o n s the r o a d wa y b e t w een two straight (tangent) sections f ocu s o n the des i g n of di r ectional t r ansit i o n o f the roadway in a horizontal plan A key concern in the directional transition is the ability of the vehicle to negotiate the horizontal curve

10. Alignment Of Highways

11. Alignment Of Highways Horizontal alignment to accommodate the cornering capability of a variety of vehicles (cars to combination trucks) T h e d esi g n o f the hori z o n t al alig nm e n t e n t ails t h e determination of: the minimum radius of the curve determination of the length of the curve Side friction factor Superelevation Adequate stopping sight distance

12. Horizontal Alignment

13. (1) Simple horizontal curve Horizontal Curves - Types of Curves Horizontal Curves : curves used in horizontal planes to connect two straight tangent sections Simple Curve : circular arc connecting two tangents

14. Horizontal Curves A properly designed transition curve provides a natural , easy-to-follow path for drivers, such that the lateral force increases and decreases gradually as a vehicle enters and leaves a circular curve. Transition curves minimize encroachment on adjoining traffic lanes and tend to promote uniformity in speed. A spiral transition curve simulates the natural turning path of a vehicle.

15. (2) Compound curve R1 R2 Horizontal Curves Compound Curve : a curve which is composed of two or more circular arcs of different radii, with centers on the same side of the alignment Compound curves are used to fit horizontal curves to very specific alignment needs …..interchange ramps, intersection curves etc. Radii should not be very different- difficult for drivers to maintain lane position during transition from one to another curve

16. Horizontal Curves - Types of Curves Spiral Curve : A curve with constantly changing radius a cu r v e who s e r adius de c r ea s es uni f ormly f r om i n finit y a t the tangent to that of the curve it meets Motorist usually create their own transition path while moving from tangent section to curve….spiral curves not often used Special case use: used to gradually introduce superelevation Spiral curve Horizontal Curves

17. Horizontal Curves - Types of Curves R1 R2 R1 R2 (4) Reverse Curve (a) With tangent (b) Without tangent Reverse Curve : Two circular arcs tangent to each other, with their centers on opposite sides of the alignment Two consecutive curves that turn in opposite direction Not recommended- drivers may find it difficult to stay in their lane as a result of sudden change in alignment Horizontal Curves

18. Horizontal Curves - Types of Curves o Easement Curves : curves used to lessen the effect of the sudden change in curvature at the junction of either a tangent and a curve, or of two curves. Horizontal Curves

19. Properties of Circular Curves Degree of Curvature Traditionally, the “steepness” of the curvature is defined by either the radius (R) or the degree of curvature (D) In highway work we use the ARC definition Degree of curvature = angle subtended by an arc of length 100 feet Horizontal Curves

20. Properties of Circular Curves Degree of curvature = angle subtended by an arc of length 100 feet By simple ratio: D /360 = 100 /2*Pi*R Therefore R = 5730 / D D = Degree of curvature - degrees R = Radius of curvature - feet Horizontal Curves

21. o Le ng th o f Cu r v e : The l en g t h o f the cu r v e derives directly from the arc definition of degree of curvature A central angle equal to the degree of curvature subtends an arc of 100 ft, while the actual central angle (Δ) subtends the length of the curve (L). By simple ratio D/100=Δ/L L = 100 Δ / D Or (from R = 5730 / D, substitute for D = 5730/R) o L = Δ R / 57.30 (note: D is not Δ – the two are often confused ) Horizontal Curves

22. Horizontal Curves Fundamentals -Layout R = Radius of Circular Curve (ft) PC = Point of Curvature ( Beginning of Curve) PT = Point of Tangency (End of Curve) PI = Point of Intersection T = Tangent Length (T = PI – PC ) L = Length of Curvature (L = PT– PC) M = Middle Ordinate E = External Distance L.C = Chord Length Δ = Deflection Angle or external angle

23. Useful Formulas… Tangent: T = R tan(Δ/2) (Triangle 143) Chord: L.C = 2R sin(Δ/2) (Triangle 364) Mid Ordinate: M = R – R cos(Δ/2) External Distance: E = R sec(Δ/2) - R Horizontal Curves Fundamentals -Layout

24. Deflection angle of a 4º curve is 55º25’, PI at station 24 5 + 9 7.0 4 . F in d len g th of cu r v e , T , a n d st a tion of PT. D = 4º ,  = 55º25’ = 55.417º R D  5729.58 R  5729.58  1432.3 ft. 4 Horizontal Curves Fundamentals -Layout

25. Horizontal Curves – Example1 D = 4º  = 55.417º R = 1,432.4 ft L = 2  R  360 = 2  (1,432.4 ft)(55.417º) = 1385.42ft 360

26. Horizontal Curves – Example1 D = 4º  = 55.417º R = 1,432.4 ft L = 1385.42 ft T = R tan  = 1,432.4 ft tan (55.417) = 752.29 ft 2 2

27. Horizontal Curves – Example A horizontal curve is designed with a 2000-ft radius. The curve has a tangent length of 400 ft. and the PI is at station 103 + 00. Determine the stationing of PT Formulas… Tangent: T = R tan(Δ/2) (Triangle 143) Chord: L.C = 2R sin(Δ/2) (Triangle 364) Mid Ordinate: M = R – R cos(Δ/2) External Distance: E = R sec(Δ/2) - R Horizontal Curves – Example 2

28. Alignment Of Highways

29. The presence of horizontal curve imparts centrifugal force which is a reactive force acting outward on a vehicle negotiating it Centrifugal force depends on speed and radius of the horizontal curve and is counteracted to a certain extent by transverse friction between the tyre and pavement surface On a curved road, this force tends to cause the vehicle to overrun or to slide outward from the center of road curvature For proper design of the curve, an understanding of the forces acting on a vehicle taking a horizontal curve is necessary. From the basic laws of physics ….centrifugal force is as: Concept of Super-elevation

30. Super-elevation

31. Super-elevation Forces acting on a vehicle on horizontal curve of radius R (m) at a speed of V m/sec^2 P = centrifugal force acting horizontally out-wards through the center of gravity W = weight of the vehicle acting down-wards through the center of gravity, and F = friction force between the wheels and the pavement, along the surface inward

32. Super-elevation

33. Super-elevation The exact expression for superelevation For small ϴ (ϴ < 4 degrees and f=0.15 (generally) ) 1- f tan ϴ = 1 (f tan ϴ =0) tan ϴ = ϴ = e ……………..above expression can be written as V 2   0.01 e f gR e = rate of roadway superelevation, percent (number of vertical feet of rise per 100 feet of horizontal distance) f = side friction factor g = gravitational constant V = vehicle speed R = radius of curve measured to a vehicle’s center of gravity

34. Super-elevation e = rate of roadway superelevation, % f = side friction (demand) factor v = vehicle speed, m/s g = gravitational constant, 9.81 m/s2 V = vehicle speed, Kmph R = radius of curve measured to a vehicle’s center of gravity, meter e = rate of roadway superelevation, % f = side friction (demand) factor v = vehicle speed, ft/s g = gravitational constant, 32.2 ft/s2 V = vehicle speed, mph R = radius of curve measured to a vehicle’s center of gravity, ft AASHTO expression for superelevation after simplification

35. Superelevation Example -1 A roadway is being designed for a speed of 70 mi/h. At one horizontal curve, it is known that the superelevation is 8.0% and the coefficient of side friction is 0.10. Determine the minimum radius of curve (measured to the traveled path) that will provide for safe vehicle operation

36. Superelevation Example -2 Determine the proper superelevation rate for an urban highway with a design speed of 50 mph and degree of curvature of 8 degrees Super elevation Examples

37. Superelevation Example -3 A 1.0-km long racetrack is to be designed with turns 250 m in length at each end. Determine the superelevation rate you would recommend for a design speed of 130 km/h. Super elevation Examples

38. Maximum Super-elevation The maximum rates of superelevation: Climate conditions: (i.e., frequency and amount of snow and ice) Terrain conditions (i.e., flat, rolling, or mountainous) Type of area (i.e., rural or urban) Frequency of very slow-moving vehicles whose operation might be affected by high superelevation rates No single maximum superelevation rate is universally applicable Design consistency : Using only one maximum superelevation rate within a region of similar climate and land use is desirable

39. Maximum Super-elevation AASHTO recommendation: 4% and 12% Increments of 2% Maximum rates adopted vary from region to region 12% - maximum superelevation rate. Drivers feel uncomfortable on sections with higher rates, and driver effort to maintain lateral position is high when speeds are reduced on such curves Snow and Ice Conditions: 8% is generally used Ice on the road can reduce friction force and vehicle travelling at less than the design speed on the excessively superelevated curve slide inward off the curve due to gravitational forces Urban areas : 4%-6% Low-speed urban streets or at intersections : may be eliminated

40. Minimum Super-elevation It should be noted that on open highway sections, there is generally a minimum superelevation maintained, even on straight sections This is to provide for cross drainage of water to the appropriate roadside(s) where sewers or drainage ditches are present for longitudinal drainage This minimum rate is usually in the range of 1.5% for high-type surfaces and 2.0% for low-type surfaces.

41. Maximum Super-elevation

42. Side-Friction Factor

43. Side-Friction Factor With the wide variation in vehicle speeds on curves, there usually is an unbalanced force whether the curve is superelevated or not. This force results in tire side thrust , which is counterbalanced by friction between the tires and the pavement surface This frictional counterforce is developed by distortion of the contact area of the tire The upper limit of the side friction factor is the point at which the tire would begin to skid; this is known as the point of impending skid Because highway curves are designed so vehicles can avoid skidding with a margin of safety, the “f” values used in design should be substantially less than the coefficient of friction at impending skid

44. Side-Friction Factor o Important factors affecting side friction factor at impending skid : o spe e d o f the v ehi c le ( f de c re ases as speed in c rea s es ( l ess tire/pavement contact)) o the type and condition of the roadway surface o type and condition of the vehicle tires Design values represent wet pavements and tires in reasonable but not top condition Values also represent frictional forces that can be comfortably achieved; they do not represent, for example, the maximum side friction that is achieved the instant before skidding Design values for the coefficient of side friction (f) vary with speed from 0.38 at 10 mph to 0.08 at 80 mph

45. Side-Friction Factor

46. OFFFF Off Tracking Off tracking is the characteristic, common to all vehicles, although much more pronounced with the larger design vehicles, in which the rear wheels do not precisely follow the same path as the front wheels when the vehicle traverses a horizontal curve or makes a turn. At slow speed, off track inward At higher speeds, the rear wheels may even track outside the front wheels.

47. Curve Widening On horizontal curves , especially when they are not of very large radius, it is a common practice to widen the pavement slightly more than the normal width, the object of providing Extra Widening of pavements on horizontal curves are due to the following reasons .... An automobile such as car, bus or truck has a rigid wheel base and only the front wheels can be turned. When the vehicle takes a turn to negotiate a horizontal curve, the rear wheels do not follow the same path as that of the front wheels. This phenomenon is called ‘off tracking’. The off tracking depends on the length of the wheel base of the vehicle the turning angle or the radius of the horizontal curves.

48. Curve Widening At more than design speed if super elevation and lateral friction jointly cannot counteract the centrifugal force, full outward slipping of rear wheels may occur and thus more width of road is covered. This condition occurs at very high speeds. At start of the curves drivers have a tendency to follow outer edge of the pavement to have better visibility and large radius curved path. This also necessitates extra width of the road. Trailer units require even larger extra width at curves.

49. Curve Widening Analysis of extra widening on horizontal curves The extra widening of pavement on horizontal curves is divided into two parts Mechanical widening and (ii) Psychological widening. Here, n =number of traffic lanes l = length of wheel base of longest vehicle in m R= radius of horizontal curves in m The widening required to account for the off tracking due to the rigidity of wheel base is called ‘Mechanical widening ‘.

50. Curve Widening (ii) Psychological widening :- At horizontal curves driveres have a tendency to maintain a greater clearance between the vehicles than on straight stretches of road. Therefore an extra width of pavement is provided for psychological reasons for greater manoeuvrability of steering at higher speeds and to allow for the extra space requirements for the overhangs of vehicles. Psychological widening is therefore important in pavements with more than one lane. An empirical formula has been recommended byt IRC for deciding the additional psychological widening ‘W ps ’ which is dependent on the design speed, V of the vehicle and the radius. R of the curve. The psychological widening is given by the formula :

51. Curve Widening Hence the total widening We required on a horizontal curve is given by: Here, n =number of traffic lanes l = length of wheel base of longest vehicle in m R= radius of horizontal curves in m V= design speed Kmph

52. Sight Distances

53. Sight Distances Sight distance is the length of the road way section visible to the road user . A driver’s ability to see ahead is needed for safe and efficient operation of a vehicle on a highway. For example, on a railroad, trains are confined to a fixed path, yet a block signal system and trained operators are needed for safe operation.

54. Sight Distances The designer should provide sight distance of sufficient length that drivers can control the operation of their vehicles to avoid striking an unexpected object in the traveled way . Sight distance is the distance along a roadway throughout which an object of specified height is continuously visible to the driver. This distance is dependent on the height of the driver’s eye above the road surface , the specified object height above the road surface, and the height and lateral position of sight obstructions within the driver’s line of sight

55. Sight Distances Criteria For Sight Distances Height of Driver’s Eye For all sight distances calculations the height of the driver’s eye is considered to be 1.08 m [3.50 ft.] above the road surface. This value is based on a study ( 17 ) that found average vehicle heights have decreased to 1.30 m [4.25 ft.] with a comparable decrease in average eye heights to 1.08 m [3.50 ft.]. For large trucks , the driver eye height ranges from 1.80 to 2.40 m [3.50 to 7.90 ft ]. The recommended value of truck driver eye height for design is 2.33 m [ 7.60ft] above the road surface. Green Book (AASHTO,2011) Height of Object For stopping sight distance and decision sight distance calculations, the height of object is considered to be 0.60 m [2.00 ft ] above the road surface. For passing sight distance calculations, the height of object is considered to be 1.08 m [3.50 ft ] above the road surface. Green Book (AASHTO,2011)

56. Sight Distances Stopping Sight Distance (SSD) It is the minimum required distance by a drive travelling at a given speed to stop vehicle after seeing an object on highway from a specific height. Two most important driver characteristics Visual and hearing perceptions Perception-Reaction Process

57. Sight Distances Perception-Reaction Process Perception Identification Emotion Reaction (volition) PIEV or PRT Used for Signal Design and Braking Distance

58. Sight Distances Perception Sees or hears situation (sees deer) Identification Identify situation (realizes deer is in road) Emotion Decides on course of action (stop, change lanes, etc) Reaction (volition) Acts (time to start events in motion but not actually do action) Foot begins to hit brake, not actual deceleration

59. Sight Distances PRT is important factor: Determination of braking distances Establishing minimum sight distance on highway Length of the yellow phase at a signalized intersection Typical Perception-Reaction time range - 0.5 to 7 seconds For stopping sight distance - AASHTO recommends 2.5 sec PRT

60. Sight Distances Perception-Reaction Time Factors Environment ( Urban vs. Rural, Night vs. Day, Wet vs. Dry) Driver Age Physical Condition Medical Conditions (Visual Acuity) Complexity Of Situation Expected v/s Unexpected Distractions

61. Sight Distances Perception-Reaction Process –Reaction Distance Stopping Sight Distance (SSD) - Length of the roadway ahead that is visible to the driver or the distance along a roadway throughout which an object of specified height is continuously visible to the driver. Composed of Two Parts Distance traveled during perception/reaction time Distance required to physically brake vehicle SSD = PRD + BD PRD = d r = 1.47(V i )(t) d r = Distance traveled during PRT(feet) V i = velocity (mph), t = PRT= 2.5s (generally)

62. Sight Distances

63. Sight Distances

64. Sight Distances Effect Of Gravity On BD

65. Sight Distances Use basic assumptions to determine SSD at 60 mph on and a=11.2 ft /s 0% grade, b) 3% grade G  % b ) 3% grade 2 Effect Of Gravity On BD

66. Sight Distances Passing Sight Distance (PSD) The passing sight distance is the minimum sight distance required on a two-lane , two way highway that will permit a driver to complete a passing maneuver without colliding with an opposing vehicle and without cutting off the passed vehicle

67. Sight Distances Two Lane Highway

68. Sight Distances d(1) = distance traversed during perception and reaction time and during the initial acceleration to the point of encroachment on the right lane d(2) = distance traveled while the passing vehicle occupies the right lane Passing Sight Distance (PSD)

69. Sight Distances d(3) = distance between the passing vehicle at the end of its maneuver and the opposing vehicle d(4) = distance traversed by the opposing vehicle for two-thirds of the time the passing vehicle occupies the right lane Passing Sight Distance (PSD)

70. Sight Distances Passing Sight Distance for Design of Two-Lane Highways

71. Sight Distances Decision Sight Distance D e c ision sight d i stance i s the dis t a n ce re q u i r e d for a driver to: D etect an unexpected or otherwise difficult-to-perceive information source or hazard in a roadway environment hazard may be visually cluttered recognize the hazard or its potential threat select an appropriate speed and path init i ate and c o mplete the requi re d s a fety man e uv e r safely and efficiently

72. Sight Distances Where to Provide…….? AASHTO recommends that decision sight distance be provided A t i n ter c han g es o r i n terse c tion l ocat i o n s where unusual or unexpected maneuvers are required; Changes i n cro ss -s e ction such a s lane d r o p s and add i t i o ns, t o l l pl a z a s, and i n t ense-d em and area s where there is a substantial ‘visual noise’ from competing information (e.g. control devices, advertising roadway elements)

73. Sight Distances Decision Sight Distance Avoidance Maneuvers A& B Avoidance Maneuvers C, D & E Metric U.S. Customary

74. Sight Distances Decision Sight Distance