Geometric design of Highway Chapter-3-pptx

Geometric design

1. Chapter Three Geometric Design of Highways 1

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3. DESIGN CONTROLS AND CRITERIA The choice of design controls and criteria is influenced by the following factors: The functional classification of the road; the nature of the terrain; the design vehicle; the traffic volumes expected on the road; the design speed; the density and character of the adjoining land use; and economic and environmental considerations 3

4. Road Functional Classification As stated in previous chapters ERA classifies roads in the country into five functional classes. These are Trunk roads, Link roads, Main Access roads, Collector roads and Feeder roads. 4

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6. The geometric design elements of a road depend on the transverse terrain through which the road passes. Transverse terrain properties are categorized into four classes as follows: Flat Terrain Rolling Terrain Mountainous Terrain Escarpment Terrain 6

7. Flat or gently rolling country, which offers few obstacles to the construction of a road, having continuously unrestricted horizontal and vertical alignment (transverse terrain slope up to 5 percent). 7

8. ROLLING : Rolling, hilly or foothill country where the slopes generally rise and fall moderately and where occasional steep slopes are encountered, resulting in some restrictions in alignment (transverse terrain slope from 5 percent to 25 percent). 8

9. MOUNTAINOUS : Rugged, hilly and mountainous country and river gorges. This class of terrain imposes definite restrictions on the standard of alignment obtainable and often involves long steep grades and limited sight distance (transverse terrain slope from 25 percent to 50 percent). 9

10. ESCARPMENT : We refer to escarpment situations inclusive of switchback roadway sections, or side hill transverse sections where earthwork quantities are considerable, with transverse terrain slope in excess of 50 percent). 10

11. In general, construction costs will be greater as the terrain becomes more difficult and higher standards will become less justifiable or achievable in such situations than for roads in either flat or rolling terrain. Drivers accept lower standards in such conditions and therefore adjust their driving accordingly, so minimizing accident risk. Design speed will therefore vary with transverse terrain. 11

12. Design Vehicle Both the physical characteristics and turning capabilities of vehicles are controls in geometric design. Vehicle characteristics and dimensions affecting design include power to weight ratio, minimum turning radius and travel path during a turn, and vehicle height and width. The road elements affected include the selection of maximum gradient, lane width, horizontal curve widening, and junction design. 12

13. The present vehicle fleet in Ethiopia includes a high number of four-wheel drive utility vehicles and overloaded trucks. Until more detailed information becomes available regarding the makeup of the vehicle fleet in Ethiopia, the four design vehicles indicated in Table below should be used in the control of geometric design: 13

14. List of Design Vehicles 14

15. Minimum turning radius of DV1 passenger car 15

16. Minimum turning radius of DV2 16

17. Roads conforming to Design Standards DS1 trough DS5 should be designed to accommodate the most restrictive of the above design vehicle. Standards DS6 and DS7, two lane roads should accommodate all but the semi-trailer combination DV4. Standards DS8 and DS9, for single lane roads should be designed similarly to DS6 and DS7; and Standard DS10 roads need only accommodate the requirements for utility vehicle and passenger cars -DV1. 17

18. Density and Character of Adjoining Land Use For urban or peri-urban conditions, the design speed selection is influenced by other factors. In such areas, speed controls are frequently included. Traffic speeds are in fact influenced by the presence of other vehicles traveling in and across the through lanes, physical and right of- way constraints, together with pedestrian and safety considerations. 18

19. Design Traffic Volume A further factor influencing the development of road design standards, and in particular the design speed, is the volume and composition of traffic. Traffic indicates the need for improvement and directly affects features of design such as widths, alignments, and gradients. Traffic data for a road or section of road, including traffic trends, is generally available in terms of annual average daily traffic (AADT). 19

20. Design classes DS1 to DS10 have associated bands of traffic flow as was shown in Table below The range of flows extends from less than 20 to 15,000 motorized vehicles per day (excluding motorcycles), and covers the design conditions for all single and dual carriageway roads. 20

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22. Design Speed The Design Speed is used as an index which links road function, traffic flow and terrain to the design parameters of sight distance and curvature to ensure that a driver is presented with a reasonably consistent speed environment. Design elements such as lane and shoulder widths, horizontal radius, super elevation, sight distance and gradient are directly related to, and vary, with design speed. Thus all of the geometric design parameters of a road (such as curve radius, gradient and tangent length which is between same direction adjacent curves and reverse curves) are directly related to the selected design speed. 22

23. The design speeds given in ERA manual have been determined in accordance with the following guidelines: Drivers on long-distance journeys are apt to travel at higher speeds than local traffic. On local roads whose major function is to provide access, high speeds are undesirable. Drivers usually adjust their speeds to physical limitations and prevailing traffic conditions. Where a difficult location is obvious to the driver , he/she is more apt to accept a lower speed of operation. 23

24. Economic considerations (road user savings vs. construction costs) may justify a higher design speed for a road carrying large volumes of traffic than for a less heavily trafficked road in similar topography. Change in design speed, if required due to a change in terrain class, should not be effected abruptly, but over sufficient distances to enable drivers to change speed gradually. The change in design speed should not be greater than one design speed step, and the section with the lower geometric standards should be long enough to be clearly recognizable by drivers (not, for example, just one single curve). It is often the case that the physical terrain changes two steps, i.e.- from mountainous to flat terrain. Where possible in such circumstances, a transition section of road shall be provided with limiting parameters equivalent to the rolling terrain type. Where this is not possible, i.e.- a Departure from Standards, special attention shall be given to the application of warning signs and/or rumble strips to alert the driver to the changing conditions. 24

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26. CROSS SECTION ELEMENTS A cross-section will normally consist of the carriageway , shoulders or curbs , drainage features , and earthwork profiles . Carriageway- the part of the road constructed for use by moving traffic, including traffic lanes, auxiliary lanes such as acceleration and deceleration lanes, climbing lanes, and passing lanes, and bus bays and lay-byes. Roadway- consists of the carriageway and the shoulders, parking lanes and viewing areas Earthwork profiles- includes side slopes and back slopes 26

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28. For urban cross-sections, cross-section elements may also include facilities for pedestrians, cyclists, or other specialist user groups. These include curbs, footpaths, and islands. It may also provide for parking lanes. For dual carriageways, the cross-section will also include medians. Lane and shoulder widths should be adjusted to traffic requirements and characteristics of the terrain. 28

29. Lane Widths A feature of a highway having great influence on safety and comfort is the width of the carriageway. Lane widths of 3.65m are used for Design Classes DS1 and DS2. Narrower lanes are appropriate on lower volume roads. 29

30. Shoulders A shoulder is the portion of the roadway contiguous to the carriageway for the accommodation of stopped vehicles; traditional and intermediate non-motorized traffic, animals, and pedestrians; emergency use; the recovery of errant vehicles; and lateral support of the pavement courses. Where the carriageway is paved, the shoulder should also be sealed with a single bituminous surface treatment. This has several advantages. It would prevent edge raveling and maintenance problems associated with parking on a gravel shoulder. 30

31. Normal Cross fall Normal cross fall (or camber, crown) should be sufficient to provide adequate surface drainage whilst not being so great as to make steering difficult. On unpaved roads, the minimum acceptable value of cross fall should be related to the need to carry surface water away from the pavement structure effectively, with a maximum value above which erosion of material starts to become a problem. The normal cross fall should be 2.5 percent on paved roads and 4 percent on unpaved roads. Shoulders having the same surface as the roadway should have the same normal cross fall. Unpaved shoulders on a paved road should be 1.5 percent steeper than the cross fall of the roadway. 31

32. The precise choice of normal cross fall on unpaved roads will vary with construction type and material rather than any geometric design requirement. In most circumstances, cross falls of 4 percent should be used, although the value will change throughout the maintenance cycle. 32

33. Side Slopes and Back Slopes Side slopes should be designed to insure the stability of the roadway and to provide a reasonable opportunity for recovery of an out-of-control vehicle. Three regions of the roadside are important when evaluating the safety aspects: the top of the slope (hinge point), the side slope, and the toe of the slope (intersection of the fore slope with level ground or with a back slope, forming a ditch). Research has found that rounding at the hinge point can significantly reduce the hazard potential. Similarly, rounding at the toe of the slope is also beneficial. 33

34. Designation of Roadside Regions 34

35. Embankment or fill slopes parallel to the flow of traffic may be defined as recoverable, non recoverable, or critical. Recoverable slopes include all embankment slopes 1:4 or flatter. Motorists who encroach on recoverable slopes can generally stop their vehicles or slow them enough to return to the roadway safely. Fixed obstacles such as culvert head walls should not extend above the embankment within the clear zone distance. 35

36. A non-recoverable slope is defined as one which is traversable, but from which most motorists will be unable to stop or to return to the roadway easily. Typically, vehicles on such slopes typically can be expected to reach the bottom. Embankments between 1:3 and 1:4 generally fall into this category. A critical slope is one on which a vehicle is likely to overturn. Slopes steeper than 1:3 generally fall into this category. The selection of a side slope and back slope is dependent on safety considerations, height of cut or fill, and economic considerations. 36

37. Slope Ratio Table – Vertical to Horizontal 37

38. Roadside Ditches Will be discussed in drainage design in last chapter Clear Zone Once a vehicle has left the roadway, an accident may occur. The end result of an encroachment depends upon the physical characteristics of the roadside environment. Flat, traversable, stable slopes will minimize overturning accidents, which are usually severe. Elimination of roadside furniture or its relocation to less vulnerable areas are options in the development of safer roadsides. For adequate safety, it is desirable to provide an unencumbered roadside recovery area that is as wide as practical on a specific highway section. The cleared width should be a minimum of 15 meters each side from the edge of the roadway for the higher road standards. 38

39. For lower standard roads, the clear zone can be reduced as practical. It should extend beyond the toe of the slope. Lateral clearances between roadside objects and obstructions and the edge of the carriageway should normally be not less than 1.5 meters. At existing pipe culverts, box culverts and bridges, the clearance cannot be less than the carriageway width; if this clearance is not met, the structure must be widened. New pipe and box culvert installations, and extensions to same, must be designed with a 1.5-meter clearance from the edge of the shoulder. 39

40. Elements of Geometric Design The principal elements of geometric design include:- Sight distance Horizontal alignments and vertical alignments 40

41. Sight Distances The path and speed of motor vehicles on highways and streets are subject to the control of drivers whose ability, training, and experience are quite varied. For safety on highways, 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. Certain two-lane highways should also have sufficient sight distance to enable drivers to occupy the opposing traffic lane for passing other vehicles without risk of a crash. 41

42. There are basically three types of sight distances Stopping Sight distances : the sight distances needed for stopping, which are applicable on all highways Passing Sight Distances : the sight distances needed for the passing of overtaken vehicles, applicable only on two-lane highways Decision Sight Distances: the sight distances needed for decisions at complex locations 42

43. Stopping Sight Distance It is the available sight distance on a roadway that should be sufficiently long to enable a vehicle traveling at or near the design speed to stop before reaching a stationary object in its path. Stopping sight distance is the sum of two distances: Brake reaction distance : 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 Braking distance : the distance needed to stop the vehicle from the instant brake application begins. 43

44. ERA provides the following equation to determine stopping sight distance where d = distance (meter) t = driver reaction time, generally taken to be 2.5 seconds V = initial speed (km/h) f = coefficient of friction between tires and roadway 44

45. Coefficient of friction f by ERA is given as:- 45

46. When the road is not flat and has some grade then the stopping sight distance equation is modified as: where, d = distance (meters) t = driver reaction time, generally taken to be 2.5 seconds V = initial speed (km/h) f = coefficient of friction between tyres and roadway g = gradient of road as a percentage (downhill is negative) 46

47. Ex-1 Determine the stopping sight distance for a design of 30km/hr for a flat terrain Ex-2 Determine the stopping sight distance for a design speed of 40km/hr and an uphill slope of 20%. 47

48. Control of Sight Distance Sight distances should be checked during design and adjustments made to meet the minimum requirements. The following values should be used for the determination of sight lines. (a) Driver's eye height: 1.05 meters (b) Object height for stopping sight distance: 0.2 meters (c) Object height for passing sight distance: 1.30 meters (d) Object height for decision sight distance 0.00 meters 48

49. On the inside of horizontal curves, it may be necessary to remove buildings, trees or other sight obstructions or widen cuts on the insides of curves to obtain the required sight distance Sight Distance for Horizontal Curves 49

50. Length of Sight Line (S) = 2R sin( Δ /2) where Δ = Deflection angle Length of Middle Ordinate (M) = R(1-cos( Δ /2) Ex-3 If the radius of an alignment is 1000m and the deflection angle is 20 o determine the required sight distance and the required clearance (Middle Ordinate) 50

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52. Stopping Sight Distance: Single Lane Roads Certain classes of roads only have a single lane, with passing pullouts. In these circumstances, a stopping sight distance is required to enable both approaching drivers to stop. This distance is the sum of the stopping sight distance for the two vehicles, plus a 30- meter safety distance. The resultant distance is that shown in Table 7-1, doubled, plus 10meters. This distance is the sum of the stopping sight distance for the two vehicles, plus a 30- meter safety distance. Design speed = 50 km/hr. SSD = (55 x 2) + 30 = 140 meters 52

53. Passing Sight Distance Passing Sight Distance is the minimum sight distance on two-way single roadway roads that must be available to enable the driver of one vehicle to pass another vehicle safely without interfering with the speed of an oncoming vehicle traveling at the design speed. Within the sight area the terrain should be the same level or a level lower than the roadway. Otherwise, for horizontal curves, it may be necessary to remove obstructions and widen cuttings on the insides of curves to obtain the required sight distance. 53

54. The passing sight distance is generally determined by a formula with four components, as follows: d1 = initial maneuver distance, including a time for perception and reaction d2 = distance during which passing vehicle is in the opposing lane d3 = clearance distance between vehicles at the end of the maneuver d4 = distance traversed by the opposing vehicle 54

55. The formulae for these components are as indicated below: d1 = 0.278 t1 (v – m + a.t1/2) Where t1 = time of initial manoeuvre, s a = average acceleration, km/h/s v = average speed of passing vehicle, km/h m = difference in speed of passed vehicle and passing vehicle, km/h 55

56. d2 = 0.278 v.t2. Where t2 = time passing vehicle occupies left lane, s v = average speed of passing vehicle, km/h d3 = safe clearance distance between vehicles at the end of the manoeuvre, and is dependent on ambient speeds as per Table 7.5: d4 = distance traversed by the opposing vehicle, which is approximately equal to d2 minus the portion of d2 whereby the passing vehicle is entering the left lane, estimated as: d4 = 2d2/3 56

57. The minimum Passing Sight Distance (PSD) for design is therefore: PSD = d1+ d2 + d3 + d4 57

58. Ex-4 Determine minimum passing sight distance based on the following study on a certain proposed road alignment Overtaken vehicle Speed= 55km/hr Passing Vehicle Initial Maneuver Average Speed = 70km/hr Average acceleration = 2.3km/h/s T1= 4sec d1=? Occupation of left turn T2= 10sec d2=? Clearance length d3=? Opposing Vehicle d4= ? 58

59. The usual values resulting from application of the formulae are reduced in ERA manual, as it is deemed appropriate to address the distances covered by twice the d4 distance and the clearance distance d3. A driver finding that he has insufficient distance after initiating the passing maneuver can choose to abort the maneuver The reduced passing sight distance is shown on the fifth column in the following table. 59

60. ERA provides the following table for quick determination of SSD and PSD 60

61. Passing Sight distance 61

62. Decision Sight Distances Decision sight distance, sometimes termed ‘anticipatory sight distance’, is the distance required for a driver to: detect an unexpected or otherwise ‘difficult-to-perceive’ information source or hazard in a roadway environment that may be visually cluttered; recognize the hazard or its potential threat; select an appropriate speed and path; and initiate and complete the required safety manoeuvre safely and efficiently. 62

63. Because decision sight distance gives drivers additional margin for error and affords them sufficient length to manoeuvre their vehicles at the same or reduced speed rather than to just stop, it is substantially longer than stopping sight distance. Drivers need decision sight distances whenever there is likelihood for error in information reception, decision-making, or control actions. Critical locations where these kinds of errors are likely to occur, and where it is desirable to provide decision sight distance include: Approaches to interchanges and intersections; Changes in cross-section such as at toll plazas and lane drops; Design speed reductions; and Areas of concentrated demand where there is likely to be ‘visual noise’, e.g. where sources of information, such as roadway elements, opposing traffic, traffic control devices, advertising signs and construction zones, compete for attention. 63

64. ERA provides the following decision sight distances in meters for different design speeds 64

65. Horizontal Alignment The horizontal alignment consists of a series of straight sections (tangents), circular curves, transition curves (spirals) and super-elevation. Tangent Sections From an aesthetic point of view, tangent sections may often be beneficial in flat country but are less so in rolling or mountainous terrain. From a safety standpoint, they provide better visibility and more passing opportunities. However, long tangent sections increase the danger from headlight glare and usually lead to excessive speeding. Hence ERA states the maximum length of a tangent section not to exceed 4.0 kilometers. ERA 2013 states the length of tangent sections should not exceed 20 times the design speed. Thus if the design speed is 100km/hr the length should not exceed 2000 meters or 2 kilometers. 65

66. Circular Curve When a vehicle moves in a circular path, it is forced radially outward by centrifugal force. The centrifugal force is counter balanced by super elevation of the roadway and/or the side friction developed between the tires and the road surface. 66

67. For calculation of the minimum horizontal radius, R min, for a particular design speed, ERA provides the following equation: Where VD = Design Speed (km/h) e = Maximum superelevation (%/100) f = Side friction coefficient 67

68. Side friction coefficients are dependent on i ) vehicle speed; ii) type, condition and texture of roadway surface; iii) weather conditions; and iv) type and condition of tyres. 68

69. Ex-5 Determine the minimum radius that should be provided in a circular alignment for a design speed of 50 km/hr and super-elevation of 8% with a side friction of o.17 69

70. ERA provides the following side friction factors and calculated minimum radius to different super-elevations for paved and unpaved roads. Table: Minimum Turning radius for paved roads Table: Minimum Turning radius for unpaved roads 70

71. Elements of a Circular Curve Δ is the Deflection Angle (in degrees). R is the Radius of the curve. T is the Tangent Distance PC to PI; T = R.tan( Δ /2) E is the External Distance: E = R.[sec( Δ /2) – 1] L is the Curve Length. L = 2.π.R. Δ /360 M is the Middle Ordinate M = R.[1 – cos ( Δ /2)] C is the Chord Length from PC to PT C = 2.R.sin( Δ /2) Point PC is the Point-of-Curvature Station PC = PI – T PT is the Point-of-Tangency Station PT = PC+ L 71

72. Ex-6 A curve has a deflection angle of = 23 o 18’ 02”, and a radius of 1432.6m. The Point of Intersection (PI) is 5+053.87. Calculate the tangent distance (T), external distance (E),curve length (L), Point of Curvature (PC), and Point of Tangent (PT). 72

73. 4 x 4 utility vehicles, buses and trucks, and trucks with trailers (DV1, DV2/3,and DV4) require minimum design turning radii of 7.3, 12.8, and 13.7m, respectively. As it is not practically possible to exclude any of these categories from the lower standard roads, and as a certain amount of tolerance is required for safe operations, the minimum horizontal curve radius of 15m is specified in ERA manual for all design standards. 73

74. Isolated Curves The horizontal curvature over a particular road section should be as consistent as possible. Long tangent roadway segments joined by an isolated curve designed at or near the minimum radius are unsafe. Long straight sections encourage drivers to drive at speeds in excess of the design speed, hence sudden and unexpected sharp curves are dangerous. Good design practice is to avoid the use of minimum standards in such conditions. For isolated curves, the minimum horizontal curve radius should be increased by 50 percent. This will usually result in the ability to negotiate the curve at a speed approximately 10 km/hr higher than the design speed. 74

75. Isolated curves 75

76. Reverse Curves, Broken-Back Curves, and Compound Curves Curves are more frequent in rugged terrain. Tangent sections are shortened, and a stage may be reached where successive curves can no longer be dealt with in isolation. Three cases of successive curves are i ) Reverse Curve: a curve followed by another curve in the opposite direction. ii) Broken-back Curve: a curve followed by another curve in the same direction but with only a short tangent in-between. iii) Compound curve: curves in the same direction but of different radii, and without any intervening tangent section. 76

77. Reverse Curves, Broken-Back Curves, and Compound Curves 77

78. The occurrence of abrupt reverse curves (having a short tangent between two curves in opposite directions) should be avoided. Such geometrics make it difficult for the driver to remain within his lane. It is also difficult to super-elevate both curves adequately, and this may result in erratic operation. The broken-back arrangement of curves (having a short tangent between two curves in the same direction) should also be avoided except where very unusual topographical or right of way conditions dictate otherwise. Drivers do not generally anticipate successive curves in the same direction hence safety is compromised. Problems also arise associated with super-elevation and drainage. 78

79. The use of compound curves affords flexibility in fitting the road to the terrain and other controls. Caution should, however, be exercised in the use of compound curves because the driver does not expect to be confronted by a change in radius once he has entered a curve, hence safety is compromised. Their use should also be avoided where curves are sharp. Compound curves with large differences in curvature introduce the same problems as are found at the transition from a tangent to a small-radius curve. Where the use of compound curves cannot be avoided, the radius of the flatter circular arc should not be more than 50 percent greater than the radius of the sharper arc; ie . R1 should not exceed 1.5.R2. 79

80. Minimum Length of Curve For small changes of direction it is desirable to use large radius curves. This improves the appearance of the road by removing rapid changes in edge profile. It also reduces the tendency for drivers to cut the corners of small radius curves. Providing the curve radii are sufficiently large, it may be possible to maintain a passing zone through a curve. The minimum length of curve for a deflection angle of 5 o or less is 300 meters. 80

81. Widening on Curves and Embankments The use of long curves of tight radii should be avoided where possible because drivers following the design speed will find it difficult to remain in the traffic lane. Widening of the carriageway where the horizontal curve is tight is usually necessary to ensure that the rear wheels of the largest vehicles remain on the road when negotiating the curve; and, on two lane roads, to ensure that the front overhang of the vehicle does not encroach on the opposite lane. Widening is therefore also important for safety reasons. 81

82. Curve widening is required on all standards of roads and should be sufficient to cater for the design vehicle. Widening is also required for Design Standards DS1 through DS5 at high fills for the psychological comfort of the driver. The steep drops from high embankments un nerve some drivers and the widening is primarily for psychological comfort although it also has a positive effect on safety. Widening for curvature and for high embankments should be added where both cases apply. Widening is provided to make driving on a curve comparable with that on a tangent. Where a road has to be rehabilitated and it is not possible to increase the radius of curvature, the designer could consider the need for curve widening. 82

83. ERA provides the following table for curve widening:- 83 Widening should transition gradually on the approaches to the curve so that the full additional width is available at the start of the curve.

84. Switchback Curves Switchback or hairpin curves are used where necessary in traversing mountainous and escarpment terrain. Employing a radius of 20m or less, with a minimum of 10m, they are generally outside of the standards for all road designs Switchback curves require careful design to ensure that all design vehicles can travel through the curve. They must therefore provide for the tracking widths of the design vehicles 84

85. Switch-back curve 85

86. Switchback requirements can be determined which allow for: Passage of two opposing DV4 vehicles. This is recommended for Design Standards DS1- DS3 Passage of a single DV4 and a DV1. This is recommended for Design Standards DS4- DS5 Passage of only a single DV4. This is recommended to Design Standards DS6- DS9 86

87. Transition Curves The characteristic of a transition curve is that it has a constantly changing radius. Transition curves may be inserted between tangents and circular curves to reduce the abrupt introduction of lateral acceleration. They may also be used between two circular curves. For large radius curves, the rate of change of lateral acceleration is small and transition curves are not normally required. If the choice is made to employ a transition curve, the Euler(An Euler spiral is a curve whose curvature changes linearly with its curve length (the curvature of a circular curve is equal to the reciprocal of the radius). Euler spirals are also commonly referred to as spiros,  clothoids , or Cornu spirals.) spiral, which is also known as the clothoid, shall be used. 87

88. The equation of clothoid is in the form of RL = A 2 where A 2 is a constant that controls the scale of the clothoid R is the radius of the horizontal curve L is the length of the clothoid 88

89. Two formulae are required for the analysis of transition curves: S = L 2 /24R L = V 3 /(3.6 3 x C x R) where S is the shift (m) L is the length of the transition curve (m) R is the radius of the circular curve (m) V is the design speed (km/hr) C is the rate of change of radial acceleration (m/s3) c should normally not be less than 0.3 m/s3 for unrestricted design, although in urban areas it may be necessary to increase it to 0.6 m/s3 or even higher, for sharp curves in tight locations. The length of transition should normally be limited to Lmax = √ ( 24R ) 89

90. Transition curve 90

91. From the geometry of the above figure: IB = ( R + S)tan( ϴ /2) It has been proved that B is the mid-point of the transition Therefore: BT = L/2 Combining these two equations, the length of the line IT is obtained: IT = ( R + S)tan( ϴ /2) + L/2 If a series of angles and chord lengths are used, the spiral is the preferred form. If, as is the case here, x and y co-ordinates are being used, then any point on the transition curve can be estimated using the following equation of the curve x = y 3 ÷ 6 RL When y attains its maximum value of L (the length of the transition curve), then the maximum offset is calculated as follows: x = L 3 ÷ 6RL = L 2 ÷ 6R 91

92. Generation of offset values for plotting a transition curve. 92

93. ERA provides the following requirement of transition curves for different design speeds 93

94. Ex A transition curve is required for a single carriageway road with a design speed of 85 km/hr. The bearings of the two straights in question are 17° and 59° . Assume a value of 0.3 m/s3 for C. Calculate the following: (1) The transition length, L (2) The shift, S (3) The length along the tangent required from the intersection point to the start of the transition, IT (4) The form of the cubic parabola and the co-ordinates of the point at which the transition becomes the circular arc of radius R. 94

95. Bonus Assignment For the above example drive an equation for the three alignments tangent, transition and circular curve in terms of x and y form and draw the alignment on graph paper in scale. 95

96. Super-elevation A tighter curve can be designed if higher values of super-elevation are used, but high values of super-elevation are not recommended if the friction is low, such as in locations where mud is likely to contaminate the road surface regularly. High values are also not recommended where mixed traffic and/or roadside development severely limit the speed of vehicles. In urban areas an upper limit of 4 percent should be used. Similarly, either a low maximum rate of super-elevation or no super-elevation is employed within important intersection areas or where there is a tendency to drive slowly because of turning and crossing movements, warning devices, and signals. 96

97. Super-elevation Runoff In alignment design with spirals, the super-elevation runoff is provided over the whole of the transition curve. The length of runoff is the spiral length, with the tangent to spiral (TS) transition point at the beginning and the spiral to curve (SC) transition point at the end. The change in cross slope begins by removing the adverse cross slope from the lane or lanes on the outside of the curve on a length of tangent just ahead of TS (the tangent runout ). Between the TS and SC (the super-elevation runoff) the travelled way is rotated to reach the full super-elevation at the SC. The procedure is reversed on leaving the curve. 97

98. Spiral Curve transition 98

99. In the design of curves without spirals the super-elevation runoff is considered to be that length beyond the tangent run-out. Empirical methods are employed to locate the super-elevation runoff length with respect to the point of curvature (PC). Current design practice is to place approximately two-thirds of the runoff on the tangent approach and one-third on the curve 99

100. Circular Curve Transition 100

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103. Shoulder Super-elevation Shoulder super-elevation rates corresponding to carriageway super-elevation rates. On the low side (inner shoulder) of super-elevated curves, the shoulder super-elevation matches the roadway super-elevation. On the high side (outer shoulder), the super-elevation is set such that the grade break between the An exception to this occurs at a maximum super-elevation of 8 percent, where the resultant shoulder super-elevation would be an undesirable flat configuration. Here the super-elevation is set at -1% to drain the shoulder. 103

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105. VERTICAL ALIGNMENT Vertical alignment is the combination of parabolic vertical curves and tangent sections of a particular slope. The selection of rates of grade and lengths of vertical curves is based on assumptions about characteristics of the driver, the vehicle and the roadway. Vertical curvature may impose limitations on sight distance, particularly when combined with horizontal curvature. 105

106. Thus the two major aspects of vertical alignment are Vertical curvature, which is governed by sight distance criteria, and Gradient, which is related to vehicle performance and level of service. 106

107. Vertical Curve Formula Vertical curves are required to provide smooth transitions between consecutive gradients. The simple parabola is specified for these because the parabola provides a constant rate of change of curvature and, hence, acceleration and visibility, along its length. 107

108. Equations relating the various aspects of the vertical curve are as follows Y(x) = r.X 2 /200 + X.g1/100 + YBVC r = (g2 – g1)/L = G/L Where BVC = Beginning of the vertical curve. The coordinates are normally (0,Y(0)), EVC = End of the vertical curve. The coordinates are normally (L, Y(L)), Y(X) = Elevation of a point on the curve ( metres ) X = Horizontal distance from the (BVC) ( metres ) g1 = Starting gradient (%), g2 = Ending gradient (%), r = Rate of change of grade per section (% per metre ), L = Length of curve (horizontal distance) in metres , G = g1 - g2 (%), 108

109. K = L/G = horizontal distance required to achieve a 1% change in grade (metres), Z = vertical distance from the tangent to the curve ( metres ) Some useful relationships are; Equation of tangent g1 is Y(X) = Y(0) +g1.X/100 Equation of tangent g2 is Y(X) = Y(L) + g2.(X-L)/100 The y coordinate of the EVC is Y(L) = (g1+g2)L/200+Y(0) The Intersection Point always occurs at an x coordinate of 0.5L hence the elevation is always; Y(IP) = (g2+3.g1)L/800 + Y(0) 109

110. There are two types of vertical curve crest and sag vertical curves 110 Crest Curve

111. 111 Sag Curve

112. Ex.Two grade lines intersect at Station 2+200 where the point of vertical intersection(PVI) elevation is 239.5 m. The starting grade is –6 percent and the ending grade is +2 percent. The length of curve is 400 m. Compute the elevation at station 2+200. 112

113. Ex. For the crest curve two tangent grade lines are +6% and -3%. The Beginning of the Vertical Curve is at chainage 0.000 and its elevation 100.0m. The length of the vertical curve is 400m. Compute the End of Vertical Curve and the coordinates of the Intersection Point. 113

114. Crest curves Two conditions exist when considering the minimum sight distance criteria on vertical curves. The first is where the sight distance (S) is less than the length of the vertical curve (L), and The second is where sight distance extends beyond the vertical curve. 114

115. Consideration of the properties of the parabola results in the following relationships for minimum curve length to achieve the required sight distances: For S < L (the most common situation in practice): Lm = (G.S 2 )/[200(h 1 0.5 + h 2 0.5 ) 2 ] Lm = K.G where Lm = minimum length of vertical crest curve ( metres ) S = required sight distance ( metres ) h1 = driver eye height ( metres ) h2 = object height (metres) G= g1-g2 K = is a constant for given values of h1 and h2 and stopping sight distance (S) and therefore speed and surface friction. For S > L Lm = 2S - [200.(h 1 0.5 + h 2 0.5 ) 2 ]/G ] Eye height (h1) has been taken as 1.05 metres , and object heights h2 of 0.6 metres above the road surface. 115

116. Ex A vertical crest curve on a single carriageway road with a design speed of 85 km/hr is to be built in order to join an ascending grade of 4% with a descending grade of 2.5%. The motorist’s eye height is assumed to be 1.05m while the object height is assumed to be 0.6m. Calculate the minimum curve length required in order to satisfy the requirements of minimum sight stopping distance 116

117. ERA provides the following minimum values of K values for crest curves 117 Minimum K values for Unpaved roads

118. Minimum K values for Unpaved roads 118

119. Sag Curves It is assumed that adequate sight distance will be available on sag curves in daylight. However, at night, visibility is limited by the distance illuminated by the headlamp beams. Assumptions concerning the brightness of the headlights, their height above the road and the divergence of the beams have been made and minimum sag curve lengths for this condition have been computed. However the results lead to unrealistically long vertical curves, especially at higher speeds, and the required sight distances may be in excess of the effective range of the headlamp beam. Thus, the only likely situation when the calculations are useful is on the approaches to fords and drifts and other similar locations where flowing or standing water may be present on the road surface. 119

120. It is therefore recommended that, for most situations, sag curves are designed using a driver comfort criterion of vertical acceleration. A maximum acceleration of 0.3m/sec2 is often used. K > V 2 /395 120

121. Minimum Lengths of Vertical Curves Especially for trunk and link roads, where the algebraic difference between successive gradients is often small, the intervening minimum vertical curve, obtained by applying the above formulae in previous slides, becomes very short. This can create the impression of a kink in the grade-line. If the vertical alignment is allowed to contain many curves of short length, the result can be a ‘hidden dip’ profile, and/or a ‘roller coaster’ type profile. For this reason, where the algebraic difference in gradient is less than 0.5 percent, a minimum curve length is recommended for purely aesthetic reasons. The minimum length should not be less than twice the design speed in km/h and, for preference, should be 400 metres or longer, except in mountainous or escarpment terrain. 121

122. Hidden Dip and Roller Coaster Profiles 122

123. Where a crest curve and a succeeding sag curve have a common beginning and end, the visual effect created is that the road has suddenly dropped away. In the reverse case, the illusion of a hump is created. Either effect is removed by inserting a short length of straight grade between the two curves. Typically, 60 m to 100 m is adequate for this purpose 123

124. Maximum Gradients Vehicle operations on gradients are complex and depend on a number of factors: severity and length of gradient; level and composition of traffic; and the number of overtaking opportunities on the gradient and in its vicinity. ERA provides the following table of maximum gradient for different terrains 124

125. Maximum Gradients 125

126. PHASING OF HORIZONTAL AND VERTICAL ALIGNMENT Phasing of the vertical and horizontal curves of a road implies their coordination so that the line of the road appears to a driver to flow smoothly, avoiding the creation of hazards and visual defects. It is particularly important in the design of high-speed roads on which a driver must be able to anticipate changes in both horizontal and vertical alignment well within the safe stopping distance. It becomes more important with small radius curves than with large. Defects may arise if an alignment is mis -phased. Defects may be purely visual and do no more than present the driver with an aesthetically displeasing impression of the road. 126

127. When the horizontal and vertical curves are adequately separated or when they are coincident, no phasing problem occurs and no corrective action is required. Where defects occur, phasing may be achieved either by separating the curves or by adjusting their lengths such that vertical and horizontal curves begin at a common station and end at a common station 127

128. Types of Mis -phasing and Corrective Action Vertical Curve Overlaps One End of the Horizontal Curve : If a vertical curve overlaps either the beginning or the end of a horizontal curve, a driver’s perception of the change of direction at the start of the horizontal curve may be delayed because his sight distance is reduced by the vertical curve. This defect is hazardous. The defect may be corrected in both cases by completely separating the curves. If this is uneconomic, the curves must be adjusted so that if the horizontal curve is of short radius they are coincident at both ends, or if the horizontal curve is of longer radius they need be coincident at only one end. 128

129. Deformation: End of horizontal curve follows vertical curve 129

130. Insufficient Separation between the Curves: If there is insufficient separation between the ends of the horizontal and vertical curves, a false reverse curve may appear on the outside edge-line at the beginning of the horizontal curve. Corrective action consists of increasing the separation between the curves, or making the curves concurrent 130

131. Both Ends of the Vertical Curve Lie on the Horizontal Curve If both ends of a crest curve lie on a sharp horizontal curve, the radius of the horizontal curve may appear to the driver to decrease abruptly over the length of the crest curve. If the vertical curve is a sag curve, the radius of the horizontal curve may appear to increase. The corrective action is to make both ends of the curves coincident or to separate them. 131

132. Vertical Curve Overlaps Both Ends of the Horizontal Curve If a vertical crest curve overlaps both ends of a sharp horizontal curve, a hazard may be created because a vehicle has to undergo a sudden change of direction during the passage of the vertical curve while sight distance is reduced. The corrective action is to make both ends of the curves coincident. 132

133. The Economic Penalty Due to Phasing The correct phasing of vertical curves restricts the designer in fitting the road to the topography at the lowest cost. Therefore, phasing is usually bought at the cost of extra earthworks and the designer must decide at what point it becomes uneconomic. 133