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It the presentation about highway and railway geometric design. It describes the complete criteria for designing project. It about design streets and railways. how much carriageway is required for new road

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- 1. 1 Highway and railway geometric design John Parkin Professor of Transport Engineering john.parkin@uwe.ac.uk
- 2. 1. Introduction to trunk roads and motorways 2. Introduction to urban streets 3. Design speeds and visibility 4. Horizontal geometry 5. Vertical geometry 6. Railway geometry 2
- 3. 1 Introduction to trunk roads and motorways
- 4. 4 Design Manual for Roads and Bridges: Applies to trunk roads and motorways
- 5. Main landing page https://www.standardsforhighways.co.uk/dmrb/ Road layout standards https://www.standardsforhighways.co.uk/dmrb/search?discipli ne=ROAD_LAYOUT 5
- 6. Some basic definitions Strategic Road Network: • nationally significant roads used for the distribution of goods and services, and a network for the travelling public. • In legal terms, it can be defined as those roads which are the responsibility of the Secretary of State for Transport (managed by Highways England). Trunk Road: • Any road on the Strategic Road Network 6
- 7. 7 https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachme nt_data/file/826533/Network_management_13-8-19.pdf Dark blue/red: smart motorway Thick blue: motorway Thin blue: trunk A roads
- 8. 8 Some basic definitions Single and dual carriageway roads: A dual carriageway has two carriageways (one in either direction) that are physically separated, usually by a central reservation
- 9. 9 Basic definitions cont… In the UK we make a distinction between urban and rural roads Urban roads Urban motorway: “A motorway with a speed limit of 60 mph or less within a built up area” Urban all-purpose road: “An all purpose road within a built up area, either a single carriageway with a speed limit of 40 mph or less or a dual carriageway with a speed limit of 60mph or less.” DMRB TA 79/99
- 10. 10 Basic definitions cont… In the UK we make a distinction between urban and rural roads Rural roads “All purpose roads and motorways that are not generally subject to a local speed limit” DMRB TA 46/97
- 11. 11 How much carriageway is required for a new road? This is dependent on anticipated traffic volumes
- 12. Traffic flow ranges: New rural roads Flow ranges assist designers in determining which carriageway standards are most likely to be economically/operationally acceptable Guidelines were in DMRB 5.1 – TA 46/97, but are now withdrawn (but given on next two slides as overall guidance) Recommends Annual Average Daily Traffic (AADT) flow levels for determining carriageway type/width in the case of rural roads
- 13. Traffic flow ranges: New rural roads Road Standard ID AADT Single 2-lane S2 Up to 13,000 Wide single 2-lane WS2 6,000 to 21,000 Dual 2-lane all purpose D2AP 11,000 to 39,000 Dual 3-lane all purpose D3AP 23,000 to 54,000 Dual 2-lane motorway D2M Up to 41,000 Dual 3-lane motorway D3M 25,000 to 67,000
- 14. Typical rural dual carriageway 14
- 15. 15
- 16. Typical rural single carriageway 16
- 17. 17
- 18. Traffic flow ranges – Urban roads For urban roads, flow range guidelines were given in DMRB 5.1 – TA 79/99, now withdrawn This gave maximum HOURLY vehicle capacities for determining carriageway type/width in the case of urban roads Five urban road classes are defined: UM, UAP1-UAP4...
- 19. Urban road classes
- 20. Traffic flow ranges – Urban roads Determination of class dependent on speed limit, level of frontage development, frequency of side-road accesses and level of on-street parking/loading etc. Hourly capacities sub-divided in each class according to overall carriageway width and the number of lanes Quoted ‘maximum’ capacities (vph) are the highest ‘one way’ flows achievable in the busiest direction (60/40 directional split assumed)
- 21. Traffic flow ranges – Urban roads
- 22. Typical urban road (DMRB) 22
- 23. 1. Introduction to trunk roads and motorways 2. Introduction to urban streets 3. Design speeds and visibility 4. Horizontal geometry 5. Vertical geometry 6. Railway geometry 23
- 24. 2 Introduction to urban streets
- 25. Manual for Streets and Manual for Streets 2 Applies to non-trunk roads in populated areas “The strict application of DMRB to non- trunk routes is rarely appropriate for highway design in built up areas, regardless of traffic volume”. Department for Transport (2007) Manual for Streets. Thomas Telford, London, UK. https://assets.publishing.service.gov.uk/government/uploads/sys tem/uploads/attachment_data/file/341513/pdfmanforstreets.pdf Chartered Institution of Highways and Transportation (2010) Manual for Streets 2. Chartered Institution of Highways and Transportation, London, UK. https://www.gov.uk/government/publications/manual-for- streets-2 25
- 26. Principles of inclusive design places people at the heart of the design process; acknowledges diversity and difference; offers choice where a single solution cannot accommodate all users; provides for flexibility in use; and provides buildings and environments that are convenient and enjoyable to use for everyone.
- 27. Principle functions of streets place; movement; access; parking; and drainage, utilities and street lighting.
- 37. 1. Introduction to trunk roads and motorways 2. Introduction to urban streets 3. Design speeds and visibility 4. Horizontal geometry 5. Vertical geometry 6. Railway geometry 37
- 38. Local and mode specific guidance Local authority guidance on layout of roads in residential and industrial areas – See, for example, Transport for London’s ‘Streets Toolkit’ design guidance Local Transport Note 1/20 Cycle Infrastructure Design. Also, see Parkin, J. (2018) Designing for cycle traffic, ICE Publishing, available from the ICE Virtual Library as an e-book 38
- 39. 1. Local Transport Note 1/20 Cycle infrastructure design. https://www.gov.uk/government/publications/cycle-infrastructure-design-ltn-120 2. Parkin, J. (2018) Designing for cycle traffic: international principles and practice. ICE Publishing, London. 3. CIHT (2019) Streets and transport in the urban environment. (Source documents on planning and designing for walking, cycling and public transport) https://www.ciht.org.uk/knowledge-resource-centre/resources/streets-and-transport-in-the- urban-environment/ 4. Butler, R., Salter, J., Stevens, D., Deegan, B. (2019) CYCLOPS – Creating Protected Junctions. Greater Manchester Combined Authority, Transport for Greater Manchester. http://www.jctconsultancy.co.uk/Symposium/Symposium2018/PapersForDownload/CYCLOPS %20Creating%20Protected%20Junctions%20- %20Richard%20Butler%20Jonathan%20Salter%20Dave%20Stevens%20TFGM.pdf
- 40. Accessing Designing for cycle traffic 1. Go to the UWE library home page https://www.uwe.ac.uk/study/library 2. At the bottom you will see ‘Databases A-Z at the bottom. Click the link. 3. Then click the link for ‘I’ to take you to a page with the 4. Institution of Civil Engineers…. 5. Once you have entered the virtual library put ‘Designing for cycle traffic’ in the search and you should find it.
- 41. • Design guidance is extensive and requires interpretation and evaluation. • Design requires creativity and an understanding of user needs. • Language is important because it affects thinking.
- 42. ‘vulnerable road user’: admitting the system is failing ‘Non-motorised road user’: a persuasive definition. ‘cycle path’: a path is for walking False comparisons: ‘motor traffic and cyclists’. ‘Active travel’: Cf ‘Inactive travel’ ‘cycle traffic’: Cf ‘fietsverkeer’, ‘radverkehr’, ‘cykeltrafik’. ‘cycleway’: Cf ‘carriageway’ and ‘footway’ ‘Rider’? Cf driver
- 43. Principles for designing for cycle traffic
- 44. • Cycles are vehicles capable of speed. • Cycles are heterogeneous with many different dimensions and characteristics. • The design speed is the principle characteristic of relevance for design.
- 45. Design guidance 40 km/hr 36 km/hr 30 km/hr 20 km/hr Highways England (2016) Gradients of 3% All routes Absolute minimum (see note) Cycling Embassy for Denmark (2012) Gradients of 5% Gradients of 3% Not explicitly
- 46. • In addition to the design speed, it is important within the envelope of provision to cater for cyclists of all abilities and disabilities. • Cycling is not the same as walking and separate provision is required. • Cyclists have a kinematic envelope that needs to be taken into account in design. • The environment for cycling needs to be attractive and comfortable.
- 47. 47 Where should cycle traffic be? Local Transport Note 1/20 Cycle Infrastructure Design
- 48. Speed limit (mph) Motor traffic volume (Annual Average Daily Traffic, two- way) Route type Peak hour cycle flow One-way width (metres) Two-way width (metres) Buffer distance from carriageway (metres) 70 All volumes Cycle track < 150 2.50 3.00 3.50 150 to 750 3.00 4.00 > 750 4.00 60 All volumes Cycle track < 150 2.50 3.00 2.50 150 to 750 3.00 4.00 > 750 4.00 50 All volumes Cycle track < 150 2.50 3.00 2.00 150 to 750 3.00 4.00 > 750 4.00 40 All volumes Cycle track < 150 2.50 3.00 1.00 150 to 750 3.00 4.00 > 750 4.00 30 < 5,000 Cycle Lanes All volumes 2.00 Light segregation All volumes 2.50 > 5,000 Stepped Cycle tracks < 150 2.50 150 to 750 3.00 > 750 4.00 > 5,000 Cycle track < 150 2.50 3.00 0.500 150 to 750 3.00 4.00 > 750 4.00 20 < 2,500 Mixed traffic < 75 N/A Mixed traffic or cycle street 50 to 250 N/A Cycle street > 200 N/A 2,500 to 5,000 Mixed traffic < 75 N/A Mixed traffic or cycle lane 50 to 250 2.00
- 49. Networks • Comfortable, attractive and safe networks required • Full capabilities realized through filtered permeability (new build and retro-fit) • Start building the network from major attractors • Direction signing essential • Cycle dismount signs are discriminatory, replace with warning signs
- 50. • Two-way cycle traffic in one-way streets • Opening up closures • Exemptions from banned turns • Bridges
- 51. Signing
- 52. 1. Introduction to trunk roads and motorways 2. Introduction to urban streets 3. Design speeds and visibility 4. Horizontal geometry 5. Vertical geometry 6. Railway geometry 52
- 53. 3 Design speeds and visibility
- 54. Highway Link Design concerns the geometry of the road alignment, both horizontally and vertically Alignment design must ensure that standards of curvature, visibility and super-elevation are provided for a DESIGN SPEED consistent with anticipated vehicle speeds Design process seeks to achieve value for money and acceptable standard of safety
- 55. Design Speed Road alignment should be consistent with design speed The DMRB standard provides an alignment appropriate for 85th percentile driver (in wet conditions)
- 56. Design factors Design speed dictates: Stopping sight distance (SSD) Full overtaking sight distance (FOSD) Horizontal alignment Vertical alignment Co-ordination of horizontal and vertical alignments
- 57. 57 Design speed related parameters
- 58. 58 Urban design speed determination • Design speed is linked to speed limit • Permits a small margin for speeds greater than limit
- 59. Cycle traffic design speed 59 Design guidance 40 km/hr 36 km/hr 30 km/hr 20 km/hr Highways England (2016) Gradients of 3% All routes Absolute minimum Cycling Embassy for Denmark (2012) Gradients of 5% Gradients of 3% Not explicitly stated CROW (2017) Outside built-up areas ‘Normal situations ’
- 60. Rural design speed determination 1. Select trial design speed 2. Draw up initial alignment 3. Measure alignment constraint over sections >= 2km 4. Re-calculate design speed and compare against trial design speed 5. Relax alignment to achieve cost / environmental savings 6. Re-check speeds following changes 60
- 61. Design Speed Speeds vary according to the impression of constraint that the road alignment and layout impart to the driver (CD 109) Alignment constraint (Ac) – Bendiness and forward visibility Layout constraint (Lc) – Road width, verge width, no. of access junctions V50wet = 110 – Lc - Ac
- 62. 62 Alignment constraint Dual carriageways θ1 θ2 10 6 . 6 B Ac 45 2 60 12 B VISI Ac L B 4 3 2 1 1 ... 1 1 1 V V V V n VISI Single carriageways B, Bendiness VISI, harmonic mean visibility Harmonic mean visibility: Forward visibility measured every 50m or 100m where visibility is consistent
- 63. 63 Layout constraint
- 64. 64 Original TD 9/93 chart c c A L Speed 110
- 65. CD109 chart 65
- 66. 66 Speed band determination
- 67. Relaxations • The standard provides an alignment appropriate for 85th percentile driver • A relaxation provides an alignment one or more design speed bands below this • Allowable to reduce construction cost / environmental impact Salter and Hounsell (1996) 67
- 68. Relaxations Relaxation to a number of design steps below desirable minimum may be made where cost and/or environmental savings are significant, and safety not compromised • Relaxations should only be applied to SSD, horizontal curvature, vertical curvature and superelevation. • Values for SSD, horizontal curvature and vertical curvature shall not be less than the value for 50 kph design speed • Relaxations for SSD and vertical curvature for crest and sag curves are not permitted on the immediate approaches to junctions. 68
- 69. Stopping sight distance The distance required by a driver to stop a vehicle when faced with an obstruction Includes • Perception – reaction distance: • 2 secs • Braking distance: • comfortable braking deceleration: 0.25g Salter and Hounsell (1996) 70
- 70. 71
- 71. 72 Stopping sight distance Measurement of SSD: • Drivers eye height between 1.05 – 2.0m • Object height between 0.26m – 2.0m above road surface • Checked in vertical and horizontal plane
- 72. 𝑣 = 𝑢 + 𝑎𝑡 0 = 𝑢 + 𝑎𝑡 𝑢 = −𝑎𝑡 𝑡 = 𝑢 −𝑎 73
- 73. 74 Stopping sight distance Desirable minimum (V in km/hr) One step below desirable minimum (V in km/hr) 𝑆𝑆𝐷 = 2𝑢 + 𝑢 2 . 𝑡𝑏 = 2𝑢 + 𝑢 2 . 𝑢 0.25𝑔 = 𝑢 2 + 𝑢 0.5𝑔 0.555𝑉 + 0.01573𝑉2 0.555𝑉 + 0.01049𝑉2
- 74. MfS2 stopping sight distance For light vehicles • 1.5 seconds perception and reaction time for and • 0.45g deceleration. • It is recommended that the volume and proportion of buses and heavy goods vehicles is considered when considering deceleration rates. • Account is also taken of the longitudinal gradient of the street, resulting in the formula, as follows • t is the perception and reaction time, • 𝑑 is the deceleration and • 𝑎 is the longitudinal gradient (positive for upgrades) 75 𝑆𝑆𝐷 = 𝑢𝑡 + 𝑢2 2(𝑑 + 0.1𝑎
- 75. Design Speed (km/hr ) Minimum stopping sight distance (metres) Highways England / (CROW) Sight distance in motion at 10 and 5 seconds (metres) CROW 40 47 / (-) 111 / 56 30 31 / (40) 83 / 42 20 17 / (21) 56 / 28_
- 76. Full overtaking sight distance For single carriageway roads: • Sections provided with adequate forward visibility to enable safe overtaking using opposing traffic lane • FOSD should be available between 1.05 and 2m above centre of carriageway • FOSD is greater than SSD 77
- 77. 78 Full overtaking sight distance
- 78. 79 Components of FOSD D1 is the overtaking distance D2 is the closing distance D3 is a safety margin A A B B C C D1 D3 D2
- 79. 80 Components of FOSD D1 is 10 seconds. (Assumed to starts 2 steps below design speed and accelerate to design speed, hence approximately equal to a constant speed one step below design speed) D2 is 10 seconds at design speed D3 is a safety margin equal to one fifth of D2. A A B B C C D1 D3 D2
- 80. 81 Manual for Streets visibility • It has been shown that increased forward visibility is linked to higher speeds • For urban areas MfS recommends limiting forward visibility (to manage speed) i.e. • Forward visibility = SSD
- 81. 82 Manual for Streets visibility
- 82. 20mph in urban areas DfT Circular 1/2006 ‘Setting local speed limits’ (para 89 et seq.) • mean speeds (not 85%ile speeds) now considered • mean speed of 24mph or less for a 20mph limit to be set without other self- enforcing measures. • The key factor in setting speed limits is what the road looks like to the road user. 83
- 83. • 20 mph speed limits are just signed limits • 20 mph speed zones have traffic calming and entry features • We demonstrated a statistically significant reduction in fatalities for Bristol (Bornioli, A., Bray, I., Pilkington, P., Parkin, J., 2019) • Wales has a task group now to implement 20mph national default for residential roads. • For more information see 20’s Plenty website 84
- 84. Other speed limit considerations • collision and casualty savings; • traffic flow and emissions; • journey times for motorised traffic and journey- time reliability; • the environmental impact; • the level of public anxiety; • the level of severance caused by fast-moving traffic; • conditions and facilities for vulnerable users; • the costs of measures and their maintenance; • the cost and impact of signing; • the cost of enforcement. 85
- 85. 1. Introduction to trunk roads and motorways 2. Introduction to urban streets 3. Design speeds and visibility 4. Horizontal geometry 5. Vertical geometry 6. Railway geometry 86
- 86. 4 Horizontal geometry
- 87. 89 Horizontal curves R vehicle at rest travelling around a curve of radius R
- 88. 90 Horizontal curves: Forces w=m.g N1 P N2 • N1 and N2: normal contact forces between tyres and road surface • w: weight of the object of mass m in the Earth’s gravitational field, acting from the centre of mass • P: frictional force between the tyres and the surface, acting towards the centre of the curve
- 89. 91 Slipping m.v2 R m.v2 R μ.N Force required to keep the body moving in a circle: Force provided by friction between tyres and surface: At point of slipping the speed has increased to the point where : m.v2 R μ.m.g = = μ.m.g Inertial resistance to the centripetal acceleration w=m.g N1 N2 N = N1 + N2
- 90. Overturning 92 P
- 91. Overturning: Forces 93 N1 N2 mg a a h Geometry: • h – vertical distance between road surface and centre of mass • a - horizontal distance between centre of either tyre and centre of wheel base Forces: • N1 and N2: Normal contact forces at tyres • mg: weight of vehicle in Earth’s gravitational field • F: Horizontal force required to keep the vehicle moving around a curve F
- 92. Overturning: Forces 94 N1 N2 mg a a h There is no vertical acceleration: N1 + N2 = mg (eq 1) The minimum horizontal force required to keep the vehicle moving around the curve of radius R is given by: F = mv2 / R F
- 93. Overturning: Moments 95 N1 N2 mg a a h When the vehicle is not overturning, it is in ‘rotational equilibrium’. Moments of forces, acting on either side of the vehicle’s centre of mass (clockwise and anticlockwise), will be equal: F.h + N1.a = N2.a F
- 94. Overturning: Moments 96 N1 N2 mg a a h Solving for N1: F.h + N1.a = N2.a N1.a – N2.a = - F.h N1.a – N2.a = (-m.v2/R) . h N1 – N2 = -m.v2.h / R.a (eq 2) Adding (eq 1) to (eq 2) N1 + N2 + N1 – N2 = mg - m.v2.h / R.a 2N1 = mg - m.v2.h / R.a 2N1 = m (g - v2.h / R.a) N1 = m /2 . (g - v2.h / R.a) F
- 95. Overturning: Moments 97 N1 N2 mg a a h Solving for N1: N1 = m /2 . (g - v2.h / R.a) Solving for N2: Similarly, it can be shown that N2 = m /2 . (g + v2.h / R.a) F
- 96. Overturning: Toppling 98 N1 N2 mg a a h N1 = m /2 . (g - v2.h / R.a) As the speed of the vehicle increases, N1 tends to zero. The point of toppling around the outer wheel occurs when N=0. This is when the inner tyre is no longer in contact with the road surface i.e. when: g = v2.h / R.a Solving for the toppling speed v gives: v = √g.R.a / h F
- 97. Super-elevation • With super-elevation, a vehicle’s weight contributes to the force required to keep the body moving around a horizontal curve, in addition to the frictional force 99
- 98. 100 N w=m.g P Super-elevation α To move around a curve, we need to generate a horizontal force equivalent to mv2/R With super-elevation, this force is generated by: i) the horizontal component of the Normal force (N), plus ii) the horizontal component of friction (P)
- 99. 101 N w=m.g P Super-elevation α Horizontal component of Normal: N sin α α
- 100. 102 N w=m.g P Super-elevation α Horizontal component of Friction: P cos α α Horizontal component of Normal: N sinα
- 101. 103 N w=m.g P Super-elevation α α N sin + P cos = mv2/R α α N sin + 𝜇 N cos = mv2/R α α The point of slipping occurs when:
- 102. 104 N w=m.g P Super-elevation α There is no vertical acceleration Therefore, resolving vertically( & ignoring negligible vertical component of P): N cos - mg = 0 Hence: N=mg / cos α α α
- 103. 105 Super-elevation N sin + 𝜇 N cos = mv2/R α α (mg . sin / cos ) + (𝜇 mg cos / cos ) = mv2/R α α α α 𝑣2 𝑔. 𝑅 = 𝑇𝑎𝑛𝛼 + 𝜇 Substituting for N and simplifying:
- 104. Converting v(m/s) to V(kph)and setting g = 9.81 gives Where “e” is the superelevation. In the UK superelevation, e, is limited to generating 0.45 of the centripetal force, F. Hence superelevation e, is given by As a percentage this is: 106 𝑉2 3.62 × 9.81 × 𝑅 = 𝑒 + 𝜇 = 𝑉2 127𝑅 𝑒 = 0.45. 𝑉2 127𝑅 = 𝑉2 283𝑅 𝑒% = 100. 𝑉2 283𝑅 = 𝑉2 2.83𝑅 = 0.353. 𝑉2 𝑅
- 105. 107 Design speed related parameters
- 106. • There are is minimum horizontal and vertical geometry for cycle traffic that should be adhered to. Design speed (km/hr) Minimum horizontal curve radius (metres) Highways England / (CROW) Minimum taper 40 57 / (-) 1:11 30 32 / (20) 1:8 20 14 / (10) 1:6 Lower limit for stability (12) 5 / (5) N/A
- 107. Transition curves • Transition curves are provided to enable vehicles moving at high speeds to make the change from a tangent (straight) section to the curved section in a safe and comfortable way. 110
- 108. 111
- 109. Transition curves • Transitions are a spiral shape. • There are many types of spiral, but the one used for transitions in alignment design is the Clothoid Spiral (also known as Euler’s spiral or the Cornu Spiral) because its curvature increases linearly with the distance along the spiral. 112
- 110. 113 The radius of curve rises linearly with distance along transition, hence: Where R is the circular curve radius in metres and L is the length of the Clothoid Spiral in metres. A is the Clothoid Parameter in metres squared Many characteristics of the spiral can be derived from this parameter Source: https://pwayblog.com/2016/07/03/the- clothoid/ L R A . 2
- 111. 114 Transition curves Rate of gain (or loss) of radial acceleration is given by Re-arranging to make L the subject Hence, from the Clothoid Spiral equation 𝐴2 = 𝑣3 𝑞. Converting so speed is in 𝑘𝑚 ℎ𝑟 (𝑣 = 𝑉 3.6) gives the following equation as used in the UK: Where q is the rate of gain of radial acceleration and is usually limited to 0.3m/s3 in the UK. In difficult circumstances it may be increased to 0.45 or 0.6 m/s3. R q V L . . 7 . 46 3 𝑞 = 𝑣2 𝑅 𝑡 = 𝑣2 𝑅 𝐿 𝑣 𝐿 = 𝑣3 𝑞. 𝑅
- 112. Superelevation and crossfall • Crossfall is applied to allow for drainage • Super-elevation is achieved by incrementally ‘rolling-over’ the drainage crossfall: 115 Rollover Drainage crossfall on straight Super-elevation on curve
- 113. 116
- 114. Application of superelevation 117 Superelevation applied within the transition
- 115. 1. Introduction to trunk roads and motorways 2. Introduction to urban streets 3. Design speeds and visibility 4. Horizontal geometry 5. Vertical geometry 6. Railway geometry 118
- 116. 5 Vertical geometry
- 117. Vertical curves Vertical curves are parabolic, although very gentle ones approximate to a circular arc. The formula: gives the length of the curve (metres) connecting an entry grade of g1% to an exit grade of g2%. 120 𝐿 = 𝐾(𝑔1 − 𝑔2 g1 g2 K L
- 118. Vertical curves • ‘K’ values are given in Table 3 of TD9/93 for crest and sag curves. • The ‘K’ values refer to the radius of the vertical curve • All K values satisfy comfort requirement of 0.3m/s2 vertical radial acceleration 121 g1 g2 K L
- 119. Vertical curves The curvature equation is: where y is a vertical offset distance from the projected entry gradient and x is a horizontal distance. 122 𝑦 = 𝑔2 − 𝑔1 . 𝑥2 200. 𝐿
- 120. Vertical curves The curvature equation is: where y is a vertical offset distance from the projected entry gradient and x is a horizontal distance. Hence to calculate centreline levels along the curve, where A is the level at the start of the curve, use the equation: 123 𝑦 = 𝑔2 − 𝑔1 . 𝑥2 200. 𝐿 A + 𝑔1.𝑥 100 + 𝑔2−𝑔1 .𝑥2 200.𝐿 level along line of projected entry gradient the y offset (-ve for a crest curve, +ve for a sag curve)
- 121. 124 Design speed related parameters
- 122. 125 Design speed related parameters
- 123. Vertical curves The curvature equation is: where y is a vertical offset distance from the projected entry gradient and x is a horizontal distance. Gradients are normally limited in the following ways: • 3% for motorways (max. to 4%) • 4% for all-purpose dual carriageways (max. 8%) • 6% for all purpose single carriageways (max. 8%) 126 𝑦 = 𝑔2 − 𝑔1 . 𝑥2 200. 𝐿
- 124. Vertical curves • The FOSD value allows for overtaking on a crest and the vertical curvature values allow for stopping. • For sag curves, headlight distance governs the K values up to 70km/hr and above this comfort is the ruling criterion. 127 g1 g2 K L
- 125. CROW (2017) Celis Consult (2014) Target severity (0.075) Upper limit of severity (0.200) Gradi ent Height differe nce Maxim um length of gradie nt (metre s) Height differe nce Maxim um length of gradie nt (metre s) Height differe nce Maxim um length of gradie nt (metre s) Sever ity 2.00 % 3.8 188 10.0 500 2.50 % 3.0 120 8.0 320 3.00 % 2.5 83 6.7 222 15 500 0.45 3.50 % 2.1 61 5.7 163 10.5 300 0.367 5 4.00 % 1.9 47 5.0 125 8 200 0.32 4.50 % 1.7 37 4.4 99 4.5 100 0.202 5 5.00 % 1.5 30 4.0 80 2.5 50 0.125 5.50 % 1.4 25 3.6 66 6.00 % 1.3 21 3.3 56
- 126. Plan Part of layout of A30 improvement scheme, Cornwall. Drawings by CORMAC 129 https://infrastructure.planninginspectorate.gov.uk/wp- content/ipc/uploads/projects/TR010014/TR010014-000129- 2.05%20Long%20Sections%20and%20Cross%20Sections.pdf
- 127. Long section 130
- 128. Cross- Section 131
- 129. 6 Railway geometry
- 130. Introduction 133 • A train driver cannot vary the horizontal movement of the train, so speed and alignment have to be more closely aligned than for highways • Aim is to achieve constant running speed • Gradients are limited to minimise tractive and braking effort required. • Train traffic is of different types (passenger, freight, light rail etc.), and the mix of traffic and its speed determines the alignment.
- 131. Horizontal Alignment Elements Three elements: 1. Straights 2. Curves 3. Transition curves Rule of thumb: Practical minimum element length: • Length in metres is half design speed in km/hr • E.g. 40m for a design speed of 80kph • Absolute minimum is 20 metres 135
- 132. Horizontal Alignment Elements Left and Right Hand Curves • Maximum radius: 10,000m • Not possible to construct a more gentle curve to line and level • Minimum radius: • Determined by design speed and cant (super-elevation); and • Curving ability of rolling stock 136
- 133. Cant (E): Super-elevation 137 The difference in height between the inside rail head and outside rail head - E
- 134. UK Track Gauge 138 1502mm between centre line 1435mm
- 135. Equilibrium Cant The cant that would need to be applied such that: The effect of the inertial resistance to the centripetal force is balanced by the component of the vehicle’s weight acting in the opposite direction 139
- 136. Equilibrium Cant 140 𝐸𝑞 = 11.82 𝑉2 𝑅 B
- 137. θ mv2 / R mg Equilibrium Cant - Derivation Resolve the two forces horizontal to the banked track and equate the horizontal components
- 138. θ mv2 / R mg Equilibrium Cant - Derivation Resolve the two forces horizontal to the banked track and equate the horizontal components 𝑚. 𝑔. 𝑠𝑖𝑛𝜃 = 𝑚. 𝑣2 𝑅 . 𝑐𝑜𝑠𝜃
- 139. θ mv2 / R mg Equilibrium Cant - Derivation Now rearrange in terms of θ and simplify 𝑚. 𝑔. 𝑠𝑖𝑛𝜃 = 𝑚. 𝑣2 𝑅 . 𝑐𝑜𝑠𝜃
- 140. θ mv2 / R mg Equilibrium Cant - Derivation Now rearrange in terms of θ and simplify 𝑠𝑖𝑛𝜃 𝑐𝑜𝑠𝜃 = 𝑣2 𝑔. 𝑅
- 141. θ mv2 / R mg Equilibrium Cant - Derivation Now rearrange in terms of θ and simplify 𝑠𝑖𝑛𝜃 𝑐𝑜𝑠𝜃 = 𝑣2 𝑔. 𝑅 tan 𝜃 = 𝑣2 𝑔. 𝑅
- 142. θ mv2 / R mg Equilibrium Cant - Derivation What is tan approximately equal to in relation to the track geometry (the equilibrium cant E, and the distance between the rail head centre line B)? tan 𝜃 ≈? ~B (=1.502m) E θ
- 143. θ mv2 / R mg Equilibrium Cant - Derivation What is tan approximately equal to in relation to the track geometry (the equilibrium cant E, and the distance between the rail head centre line B)? tan 𝜃 ≈ 𝐸 𝐵 ~B (=1.502m) E θ
- 144. θ mv2 / R mg Equilibrium Cant - Derivation Substitute for tan in tan 𝜃 ≈ 𝐸 𝐵 ~B (=1.502m) E θ tan 𝜃 = 𝑣2 𝑔. 𝑅 Using: And express in terms of E Then substitute for B=1.502m , g=9.80655 m/s2
- 145. Equilibrium Cant - Derivation UK standard gauge, G, is 1435 mm between rail heads. Dimension between centre lines of the rail heads is 1502 mm. Resolving parallel to banking: 𝑚. 𝑔. 𝑠𝑖𝑛𝜃 = 𝑚. 𝑣2 𝑅 . 𝑐𝑜𝑠𝜃 As 𝐸𝑞 𝐵 ≈ 𝑡𝑎𝑛𝜃 = 𝑣2 𝑅. 𝑔 where 𝐸𝑞 is the equilibrium cant 𝐸𝑞 = 𝐵. 𝑣2 𝑅𝑔 = 0.1532. 𝑣2 𝑅 Where 𝐵 = 1.502𝑚 and 𝑣 is in m/s and 𝑅 is in metres. 149
- 146. Equilibrium Cant - Derivation Now convert for 𝑣 (m/s) in km/hr: [Hint what factor do you multiply km/hr by to convert to m/s?] 𝐸𝑞 = 0.1532. 𝑣2 𝑅 =? 150
- 147. Equilibrium Cant - Derivation Now convert for 𝑣 (m/s) in km/hr: 𝐸𝑞 = 0.1532. 𝑣2 𝑅 = 0.1532. 𝑉2 𝑅 . 10002 36002 = 0.01182 𝑉2 𝑅 151
- 148. Equilibrium Cant - Derivation Converting for 𝑣 (m/s) in km/hr, the equation becomes: 𝐸𝑞 = 0.1532. 𝑣2 𝑅 = 0.1532. 𝑉2 𝑅 . 10002 36002 = 0.01182 𝑉2 𝑅 Finally, convert for 𝐸𝑞 (m) in mm: 𝐸𝑞 =? 152
- 149. Equilibrium Cant - Derivation Converting for 𝑣 (m/s) in km/hr, the equation becomes: 𝐸𝑞 = 0.1532. 𝑣2 𝑅 = 0.1532. 𝑉2 𝑅 . 10002 36002 = 0.01182 𝑉2 𝑅 Converting for 𝐸𝑞 (m) in mm, the equation becomes: 𝐸𝑞 = 1000 × 0.01182 𝑉2 𝑅 = 11.82 𝑉2 𝑅 153
- 150. Cant deficiency On single speed lines, cant can be designed so that it precisely counteracts the inertial resistance to the centripetal force On mixed traffic lines with different train speeds, a ‘deficiency’ of cant can be allowed But ‘cant deficiency’ has to be limited to limit the maximum force (acting outwards) created at the rail. The applied cant plus the deficiency equals Equilibrium Cant, as follows 𝐸𝑞 = 𝐸𝑎 + 𝐷 = 11.82. 𝑉2 𝑅 Where 𝐸𝑎 is the applied cant and 𝐷 is the deficiency. 154
- 151. Why allow ‘cant deficiency’? For mixed traffic lines • Equilibrium cant will apply to the maximum running speed (to counter the centrifugal force) • How will the banked track ‘feel’ at lower running speeds [consider the extreme case of a stationary train on a banked track]? 155
- 152. Why allow ‘cant deficiency’? • Allows higher running speeds and hence greater line capacity • Too much banking is uncomfortable, particularly at lower speeds 156
- 153. Description All locations Continuously Welded Rail Jointed track Maximum cant: On curved track At station platforms 150mm 110mm Deficiency on plain line 110mm 90mm Deficiency on switches and crossings: On through line On turnout With negative cant on turnout At switch toes 110mm 90mm 90mm 125mm 90mm 90mm 90mm 125mm Maximum cant gradient not steeper than: Desirable Absolute 1 in 600 1 in 400 Cant gradient not flatter than: Desirable Absolute 1 in 1500 1 in 2500 Rate of change of cant and cant deficiency on plain line and switches and crossings Desirable Absolute 35mm/s 55mm/s 157 Source: Network Rail (2010) Track Design Handbook
- 154. Applied Cant The amount of cant applied in practice is usually the lesser of: 𝐸𝑎 = 2 3 . 𝐸𝑞 and maximum allowable cant (150 mm). 158
- 155. Line speed and cant To ensure that safety limits and comfort criteria are not exceeded, limits are placed on the line speed based on the cant. Re-arranging the equation for cant, we get: 𝑉 𝑚𝑎𝑥 = 0.29 𝑅 𝐸𝑎 + 𝐷𝑚𝑎𝑥 As an example, with a maximum applied cant of 150mm, and a maximum cant deficiency of 110mm (on continuously welded rail), the maximum speed on a curve of 2km radius would be 209 km/hr (130 mph). 159
- 156. Horizontal Alignment Elements Curves • Maximum radius: 10,000m • Minimum determined by design speed and cant and curving ability of rolling stock On tight bends gauge widening to overcome screech (for trains without bogies) • 140 – 200 m Radius: 6 mm widening • 110 – 140 m Radius: 12 mm widening • <100 m Radius: 18 mm widening 160
- 157. 161 Corner wear Level track Curved track Outer rail head wears on the inside top face and the inner rail wears across the whole rail head. Contributing to wear are: • Wheels of different size • Tyres in different stages of wear • Wagons of different wheelbases • Varying amounts of play in the axle boxes
- 158. Cant Gradient The rate at which applied cant is ‘built up’ over a transition curve 162
- 159. Cant Gradient Cant is applied in 5 mm increments. The cant gradient depends on: • The line speed limit; • The proximity of permanent speed restrictions e.g. at junctions and tunnels); • Track longitudinal gradients (that may cause reduction below line speed limit); • Relative importance of types of traffic. 163
- 160. Cant Gradient Cant is applied over the transition curve length, where a transition exists, and can be expressed as: 𝐶𝑎𝑛𝑡 𝐺𝑟𝑎𝑑𝑖𝑒𝑛𝑡 = 1 𝑖𝑛 𝑇𝐿 𝐶 Where 𝑇𝐿 is the transition length and 𝐶 is the cant. Generalising and taking account of units, a cant gradient of 1 to N may have N calculated as follows: 𝑁 = 1000. 𝐿 𝐸𝑎 Where 𝐿 is the length over which the cant is applied in metres and 𝐸𝑎 is in millimetres. Maximum and minimum cant gradients are specified 164
- 161. Description All locations Continuously Welded Rail Jointed track Maximum cant: On curved track At station platforms 150mm 110mm Deficiency on plain line 110mm 90mm Deficiency on switches and crossings: On through line On turnout With negative cant on turnout At switch toes 110mm 90mm 90mm 125mm 90mm 90mm 90mm 125mm Maximum cant gradient not steeper than: Desirable Absolute 1 in 600 1 in 400 Cant gradient not flatter than: Desirable Absolute 1 in 1500 1 in 2500 Rate of change of cant and cant deficiency on plain line and switches and crossings Desirable Absolute 35mm/s 55mm/s 165 Source: Network Rail (2010) Track Design Handbook
- 162. Rate of change of cant • Is limited to 35 – 55 mm/s • Why does the ‘rate of change of cant’ & ‘rate of change of cant deficiency’ need to be limited? 166
- 163. Rate of change of cant • Is limited to 35 – 55 mm/s • Why does the rate of change of cant need to be limited? i. To reduce ‘roller coaster’ effect if cant is applied to quickly ii. If ‘cant deficiency’ builds up too quickly passengers will feel a sharp outwards force • The rate at which cant can be comfortably built up may determine the transition curve length 167
- 164. Can be expressed in terms of transition length: 𝑑𝐸 𝑑𝑡 = ∆𝐸.𝑉 3.6𝐿 𝑑𝐷 𝑑𝑡 = ∆𝐷.𝑉 3.6𝐿 Where Δ𝐸 is the change in cant over the transition length (mm) Δ𝐷 is the change in cant deficiency over the transition length (mm) 𝑉 is the design speed (km/hr) 𝐿 is the length of the transition curve (m) 168 Rate of change of cant
- 165. The transition length may be given by the following equation 𝑇𝐿 = 𝐶 𝑟 . 𝑣 Where 𝑇𝐿 is the transition length in m 𝐶 is the cant or cant deficiency whichever is the greater (mm), 𝑟 is the rate of change of cant (mm/s) 𝑣 is the line speed in m/s. 169 Transition length
- 166. Transition setting out Cubic parabola if 𝛼 is less than 4°. 170
- 167. Transition setting out 𝜙 = 𝑙2 2𝑅𝐿 𝑟𝑎𝑑𝑖𝑎𝑛𝑠 = 90𝐿 𝜋𝑅 𝑑𝑒𝑔𝑟𝑒𝑒𝑠 𝑋 = 𝑙 − 𝑙5 40 𝑅𝐿 2 𝑆 = 𝐿2 24𝑅 − 𝐿4 2668 𝑅3 𝑌 = 𝑙3 6𝑅𝐿 − 𝑙7 336 𝑅𝐿 3 𝐶 = 𝐿 2 − 𝐿3 240𝑅2 Source: Network Rail track design handbook, Section C2.5 171 Clothoid spiral if 𝛼 is more than 4°.
- 168. Virtual transition length • On larger radius curves and lower designs speeds, transitions may be omitted. • If so, two thirds of the cant is developed on the straight with the remainder developed on the curve. • As the first bogie enters the curve, the rail vehicle will experience increasing inertial resistance to the centripetal force up to the maximum centrifugal force when the rear bogies has joined the curve. • As a result of the above, the wheelbase between the bogies is in effect a virtual transition length. • Bogie wheelbase for design is assumed to be 12.2m on the mainline and 10.06m on London Underground. 172
- 169. 173
- 170. Reverse curves: buffer locking Value of 𝐵 should be less than 300 mm calculated as follows. 𝐵 = 𝐿2−𝑊2−𝐷2 8𝑅𝑒 for the condition where 𝐷 < 𝐿 − 𝑊 𝐵 = 𝐿−𝑊 𝐿+𝑊−𝐷 2 16𝑊𝑅𝑒 for the condition where 𝐷 > 𝐿 − 𝑊 < 𝐿2−𝑊2 2 Where, 𝐵 , 𝐿 , 𝑊 and 𝐷 are defined in Figure 5.6 and the equivalent radius of the two curves is given as 𝑅𝑒 = 𝑅1𝑅2 𝑅1+𝑅2 . 174
- 171. Gradients The gradient: percentage or ‘rise over the run’, 1 in N. A rise of 1.5 metres over 750 metres gives a percentage of 0.2%, or a rise over run of 1 in 500. Note that 𝑁 = 100 𝐺% Gradients: as flat as possible • Usually: 0.2% and 1.5% (1 in 500 to 1 in 66) • Absolute maximum: 2.5% (1 in 40) • At station platforms and in sidings: less than 0.2% (1 in 500) • In tunnels: greater than 0.5% (1 in 200) for drainage reasons. 175
- 172. Ruling and compensated gradients Ruling grade: maximum gradient on straight track at which the heaviest train can maintain speed using its maximum tractive effort. On a curve, there will be more resistance and so maximum a ‘compensated grade’ calculated: 𝐺𝑐 = 𝐺 − 70 𝑅 Where 𝐺𝑐 is the compensated grade, 𝐺 is the grade and 𝑅 is the curve radius in metres. 176
- 173. Vertical alignment Instantaneous grade change of less than 0.15% are acceptable. Otherwise, vertical curves are provided to connect grades of different gradient: • Minimum radius of a vertical curve is normally 1,000m • Practical maximum is 40,000m. 177
- 174. General form of a parabolic curve is a quadratic of the form: 𝑦 = 𝑎. 𝑥2 + 𝑏. 𝑥 + 𝑐 Differentiating with respect to 𝑥, where 𝑥 is the (horizontal) length of the curve gives the gradient at points on the curve: 𝑑𝑦 𝑑𝑥 = 2. 𝑎𝑥 + 𝑏 At the origin (0,0) (and assuming no vertical shift, i.e. c=0) and the gradient, 𝑑𝑦 𝑑𝑥 , is = 𝑏 We can express the gradient as a 1 in N, so 𝑏 = 1 𝑁1 And at some distance 𝑙 along L, the gradient is 1 𝑁2 = 2𝑎𝑙 + 1 𝑁1 Differentiating again with respect to 𝑥 gives the rate of change of gradient, and this is the inverse of the radius of the curve because curvature is the inverse of the radius of curvature. 𝑑2𝑦 𝑑𝑥2 = 2𝑎 = − 1 𝑅𝑣 178
- 175. As vertical acceleration, assuming a design limit of 3% of g: 𝑣2 𝑅𝑣 ≤ 0.03𝑔 So: 𝑅𝑣 ≥ 𝑣2 0.03𝑔 As, from above 1 𝑁1 − 1 𝑁2 = −2𝑎𝑙 = 𝑙 𝑅𝑣 So: 𝐿 ≥ 1 𝑁1 − 1 𝑁2 . 𝑣2 0.03𝑔 179
- 176. 181 The levels along the vertical curve at points 𝑙 along the curve are calculated as follows: 𝐴 + 𝐺1. 𝑙1 100 + 𝐺1 − 𝐺2 . 𝑙2 200. 𝐿 Where 𝐴 is the reduced level at the origin of the vertical curve. The length, 𝐿, of the vertical curve is calculated based on a limit on the maximum vertical acceleration as follows • Desirable 0.0225g • Maximum for sag 0.0325g; for a crest 0.0425g • Exceptionally, 0.06g
- 177. High speed lines • French TGV: PAX only; 3.5% maximum gradient; 300 km/hr; minimum curve radius is 6000m (TGV Atlantique has a 4500 metre minimum curve and maximum gradient of 2.5%.) • Japanese Shinkansen (bullet train): PAX only • German Deutsche Bahn Inter-City Express: PAX and freight; 317 km/hr; third of route in tunnel; mixed traffic means gentler gradients. 182
- 178. High Speed 2 Is 360 km/hr too fast? • Very gentle curves mean more tunnel needed • Longer braking distances mean fewer trains per hour • Acceleration and deceleration energy intensive • Speed limited at points • Maximum tractive effort on gradients reduces maximum speed • Ballast blown by high speeds may mean solid track bed 183