Geometric Design It deals with visible elements of a highway. It is influenced by: Nature of terrain. Type Composition and hourly volume / capacity of traffic Traffic Factors Operating speed (Design Speed) Landuse characteristics (Topography) Environmental Factors (Aesthetics).

TERRAIN CLASSIFICATION Terrain type Percentage cross slope of the country Plain 0-10 Rolling 10-25 Mountainous 25-60 Steep >60

goals of geometric design Maximize the comfort Safety, Economy of facilities Sustainable Transportation Planning.

FUNDAMENTALS OF GEOMETRIC DESIGN geometric cross section vertical alignment horizontal alignment super elevation intersections various design details.

HIGHWAY GEOMETRIC DESIGN Cross sectional elements Sight distance Horizontal curves Vertical curves

Comparision of Urban and Rural Roads Section Capacity Peak Hour flow Traffic fluctuations Design Based on ADT Speed

Urban Road Classification ARTERIAL ROADS SUB ARTERIAL COLLECTOR LOCAL STREET CUL-DE-SAC PATHWAY DRIVEWAY

Urban Road Classification ARTERIAL ROADS SUB ARTERIAL COLECTOR LOCAL STREET CUL-DE-SAC PATHWAY DRIVEWAY

ARTERIAL No frontage access, no standing vehicle, very little cross traffic. Design Speed : 80km/hr Land width : 50 – 60m Spacing 1.5km in CBD & 8km or more in sparsely developed areas. Divided roads with full or partial parking Pedestrian allowed to walk only at intersection

SUB ARTERIAL Bus stops but no standing vehicle. Less mobility than arterial. Spacing for CBD : 0.5km Sub-urban fringes : 3.5km Design speed : 60 km/hr Land width : 30 – 40 m

Collector Street Collects and distributes traffic from local streets Provides access to arterial roads Located in residential, business and industrial areas. Full access allowed. Parking permitted. Design speed : 50km/hr Land Width : 20-30m

Local Street Design Speed : 30km/hr. Land Width : 10 – 20m. Primary access to residence, business or other abutting property Less volume of traffic at slow speed Origin and termination of trips. Unrestricted parking, pedestrian movements. (with frontage access, parked vehicle, bus stops and no waiting restrictions)

CUL–DE- SAC Dead End Street with only one entry access for entry and exit. Recommended in Residential areas

HIGHWAY CROSS SECTIONAL ELEMENTS 1.Carriage way (Pavement width) 2.Camber 3.Kerb 4.Traffic Separators 5.Width of road way or formation width 6.Right of way (Land Width) 7.Road margins 8.Pavement Surface (Ref: IRC 86 – 1983)

GEOMETRIC CROSS SECTION The primary consideration in the design of cross sections is drainage. Highway cross sections consist of traveled way, shoulders (or parking lanes), and drainage channels. Shoulders are intended primarily as a safety feature. Shoulders provide: accommodation of stopped vehicles emergency use, and lateral support of the pavement. Shoulders may be either paved or unpaved. Drainage channels may consist of ditches (usually grassed swales) or of paved shoulders with berms of curbs and gutters.

Two-lane highway cross section, with ditches. Two-lane highway cross section, curbed. Two-lane highway cross section, with ditches. Two-lane highway cross section, curbed.

Divided highway cross section, depressed median, with ditches.

Geometric cross section cont.. Standard lane widths are 3.6 m (12 ft). Shoulders or parking lanes for heavily traveled roads are 2.4 to 3.6 m (8 to 12 ft) in width. narrower shoulders used on lightly traveled road.

CARRIAGE WAY (IRC RECOMMENDATIONS) Single lane without Kerbs = 3.50m Two lane without kerbs = 7m Two lane with kerbs = 7.5m 3 lane with or without kerbs = 10.5 /11.0 4 lane with or without kerbs = 14.0m 6 lane with or without kerbs = 21.0 m Intermediate carriage way = 5.5m Multilane pavement = 3.5m/lane

Footpath (Side walk) No of Persons/Hr Required Width of footpath (m) All in one direction In both direction 1200 800 1.5 2400 1600 2.0 3600 2.5 4800 3200 3.0 6000 4000 4.0

Cycle Track Minimum = 2m Each addln lane = 1m Separate Cycle Track for peak hour cycle traffic more than 400 with motor vehicle of traffic 100 – 200 vehicles/Hr. Motor Vehicles > 200; separate cycle track for cycle traafic of 100 is sufficient.

Median Width of Median Depends on: Mim Width of Median: Available ROW Terrain Turn Lanes Drainage. Mim Width of Median: Pedestrian Refuge =1.2m To protect vehicle making Right turn = 4.0m (Recc – 7.0m) To protect vehicle crossing at grade = 9 – 12m. For Urban area 1.2 to 5m

KERBS Road kerbs serve a number of purposes: - retaining the carriageway edge to prevent 'spreading' and loss of structural integrity - acting as a barrier or demarcation between road traffic and pedestrians or verges - providing physical 'check' to prevent vehicles leaving the carriageway - forming a channel along which surface water can be drained

KERBS Low or mountable kerbs : height = 10 cm provided at medians and channelization schemes and also helps in longitudinal drainage. Semi-barrier type kerbs : When the pedestrian traffic is high. Height is 15 cm above the pavement edge. Prevents encroachment of parking vehicles, but at acute emergency it is possible to drive over this kerb with some difficulty. Barrier type kerbs : Designed to discourage vehicles from leaving the pavement. They are provided when there is considerable amount of pedestrian traffic. Height of 20 cm above the pavement edge with a steep batter. Submerged kerbs : They are used in rural roads. The kerbs are provided at pavement edges between the pavement edge and shoulders. They provide lateral confinement and stability to the pavement.

CAMBER (OR) CROSS FALL S. No Type of Surface % of camber in rainfall range Heavy to light 1 Gravelled or WBM surface 2.5 % - 3 % ( 1 in 40 to 1 in 33) 2 Thin bituminous Surface 2.0 % - 2.5 % ( 1 in 50 to 1 in 40) 3 Bituminous Surfacing or Cement Concrete surfacing 1.7 % - 2.0 % 4 Earth 4 % - 3 %

Types of Camber Parabolic or Elliptic Straight Line Straight and Parabolic

Sight Distances The actual distance along the road surface up to which the driver of a vehicle sitting at a specified height has visibility of any obstacle. The visibility ahead of the driver at any instance. 29

SIGHT DISTANCE THE SIGHT DISTANCE AVAILABLE ON A ROAD TO A DRIVER DEPENDS ON FEATURE OF ROAD AHEAD HEIGHT OF THE DRIVER’S EYE ABOVE THE ROAD SURFACE

Sight Distances 1. Stopping Sight distance 2. Over Taking Sight distance 3. Passing 4. Intermediate 31

Sight Distance in Design Stopping Sight Distance (SSD) – object in roadway Passing Sight Distance (PSD) – pass slow vehicle 32

Stopping Sight Distance (SSD) THE DISTANCE WITHIN WHICH A MOTOR VEHICLE CAN BE STOPPED DEPENDS ON Total reaction time of driver Speed of vehicles Efficiency of brakes Gradient of road Frictional resistance

TOTAL REACTION TIME PERCEPTION TIME BRAKE REACTION TIME

TOTAL REACTION TIME DEPENDS ON PIEV THEORY PERCEPTION INTELLECTION EMOTION VOLIATION

Perception-Reaction Process Identification Emotion Reaction (volition) PIEV Used for Signal Design and Braking Distance 36 36

Perception-Reaction Process Sees or hears situation (sees deer) Identification Identify situation (realizes deer is in road) Emotion Decides on course of action (swerve, 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 37 37

0.5 to 7 seconds Affected by a number of factors. Typical Perception-Reaction time range 0.5 to 7 seconds Affected by a number of factors. 38 38

Perception-Reaction Time Factors Environment Urban vs. Rural Night vs. Day Wet vs. Dry Age Physical Condition Fatigue Drugs/Alcohol Distractions 39 39

Age Older drivers May perceive something as a hazard but not act quickly enough More difficulty seeing, hearing, reacting Drive slower Less flexible 40 40

Age Younger drivers Quick Response but not have experience to recognize things as a hazard or be able to decide what to do Drive faster Are unfamiliar with driving experience Are less apt to drive safely after a few drinks Are easily distracted by conversation and others inside the vehicle May be more likely to operate faulty equipment. Poorly developed risk perception Feel invincible, the "Superman Syndrome” 41 41

Alcohol Affects each person differently Slows reaction time Increases risk taking Dulls judgment Slows decision-making Presents peripheral vision difficulties 42 42

Stopping Sight Distance (SSD) Required for every point along alignment (horizontal and vertical) – Design for it, or sign for lower, safe speed. Available SSD = f(roadway alignment, objects off the alignment, object on road) SSD = LD + BD Lag distance Braking Distance 43

Lag Distance Speed of the vehicle = v m/sec Reaction Time of Driver = t sec ; (2.5 sec) Lag Distance = v t m If the design speed is V kmph, Lag Distance = V x 1000 x t 60 x 60 = 0.278 V t m

Braking Distance Kinetic Energy at the design speed of v m/sec= ½ m v2 = W v2 ; m = W/g 2g W = weight of the Vehicle G = acceleration due to gravity (9.9 m/sec2) Work done in stopping the vehicle = F x l F = Frictional force L = braking distance F = coeff of friction = 0.35 Wv2 = fWl ; l = v2 2g 2fg

SSD Equation SSD,m = 0.278V t + _____V2_____ 254f SSD in meter V = speed in kmph T = perception/reaction time (in seconds) f = design coefficient of friction 46

STOPPING SIGHT DISTANCE FOR ASCENDING GRADIENT AND DESCENDING GRADIENT SSD = 0.278vt + v2 2g(f+ (n/100)) (or) SSD = 0.278Vt + V2 254(f - n/100)

Passing Distance Applied to rural two-lane roads The distance required for a vehicle to safely overtake another vehicle on a two lane, two-way roadway and return to the original lane without interference with opposing vehicles Designers assume single vehicle passing Several assumptions are considered (vehicle being passed s traveling at a uniform speed, and others) Normally use car passing car Passing distance increased by type of vehicle Minimum passing distance currently used are conservative

Geometric Design of Highways Highway Alignment is a three-dimensional problem Design & Construction would be difficult in 3-D so highway alignment is split into two 2-D problems

Horizontal Alignment Components of the horizontal alignment. Properties of a simple circular curve.

Horizontal Alignment Tangents Curves

Tangents & Curves Tangent Curve Tangent to Circular Curve Tangent to Spiral Curve to Circular Curve

TWO CURVES HORIZONTAL CURVES VERTICAL CURVES

Stationing Horizontal Alignment Vertical Alignment Therefore, roads will almost always be a bit longer than their stationing because of the vertical alignment Draw in stationing on each of these curves and explain it

Alignment Design Definition of alignment: Definitions from a dictionary In a highway design manual: a series of straight lines called tangents connected by circular curves or transition or spiral curves in modern practice Definition of alignment design: also geometric design, the configuration of horizontal, vertical and cross-sectional elements (first treated separately and finally coordinated to form a continuous whole facility) Horizontal alignment design Components of horizontal alignment Tangents (segments of straight lines) Circular/simple curves Spiral or transition curves

Alignment Design Horizontal curves Simple curves This consists of a single arc of uniform radius connecting two tangents Compound curves A compound curve is formed by joining a series of two or more simple curves of different radius which turn in same direction..

Simple curve elements

Simple curve in full superelevation

Compound curve

Alignment Design Horizontal curves TRANSITION CURVE Reverse curves A curve having its radius varying gradually from a radius equal to infinity to a finite value equal to that of a circular curve Reverse curves A circular curve consistings of two simple curves of same or different radii and turn in the opposite direction is called reverse curve 61 Saturday, March 25, 2017

Reverse curves

VERTICAL ALIGNMENT The vertical alignment of a transportation facility consists of tangent grades (straight line in the vertical plane) vertical curves. Vertical alignment is documented by the profile.

Vertical Alignment

Vertical curves

Convex and concave curves

Vertical Alignment Objective: Primary challenge Determine elevation to ensure Proper drainage Acceptable level of safety Primary challenge Transition between two grades Vertical curves Sag Vertical Curve G1 G2 G1 G2 Crest Vertical Curve

Coordination of vertical and horizontal alignments

Outline Concepts Vertical Alignment Horizontal Alignment Fundamentals Crest Vertical Curves Sag Vertical Curves Examples Horizontal Alignment Superelevation Other Non-Testable Stuff

Concepts Alignment is a 3D problem broken down into two 2D problems Horizontal Alignment (plan view) Vertical Alignment (profile view) Stationing Along horizontal alignment 12+00 = 1,200 ft. Piilani Highway on Maui

Stationing Horizontal Alignment Vertical Alignment Therefore, roads will almost always be a bit longer than their stationing because of the vertical alignment Draw in stationing on each of these curves and explain it

From Perteet Engineering Typical set of road plans – one page only From Perteet Engineering

Vertical Alignment

Vertical Alignment Objective: Primary challenge Determine elevation to ensure Proper drainage Acceptable level of safety Primary challenge Transition between two grades Vertical curves Sag Vertical Curve G1 G2 G1 G2 Crest Vertical Curve

Vertical Curve Fundamentals Parabolic function Constant rate of change of slope Implies equal curve tangents y is the roadway elevation x stations (or feet) from the beginning of the curve

Vertical Curve Fundamentals PVI G1 δ PVC G2 PVT L/2 L x Choose Either: G1, G2 in decimal form, L in feet G1, G2 in percent, L in stations

Relationships Choose Either: G1, G2 in decimal form, L in feet G1, G2 in percent, L in stations Relationships

Example A 400 ft. equal tangent crest vertical curve has a PVC station of 100+00 at 59 ft. elevation. The initial grade is 2.0 percent and the final grade is -4.5 percent. Determine the elevation and stationing of PVI, PVT, and the high point of the curve. PVI PVT G1=2.0% G2= - 4.5% PVC: STA 100+00 EL 59 ft.

PVI G1=2.0% PVT G2= -4.5% PVC: STA 100+00 EL 59 ft. 400 ft. vertical curve, therefore: PVI is at STA 102+00 and PVT is at STA 104+00 Elevation of the PVI is 59’ + 0.02(200) = 63 ft. Elevation of the PVT is 63’ – 0.045(200) = 54 ft. High point elevation requires figuring out the equation for a vertical curve At x = 0, y = c => c=59 ft. At x = 0, dY/dx = b = G1 = +2.0% a = (G2 – G1)/2L = (-4.5 – 2)/(2(4)) = - 0.8125 y = -0.8125x2 + 2x + 59 High point is where dy/dx = 0 dy/dx = -1.625x + 2 = 0 x = 1.23 stations Find elevation at x = 1.23 stations y = -0.8125(1.23)2 + 2(1.23) + 59 y = 60.23 ft

Other Properties G1, G2 in percent L in feet G1 x PVT PVC Y Ym G2 PVI Yf Last slide we found x = 1.23 stations

Other Properties K-Value (defines vertical curvature) The number of horizontal feet needed for a 1% change in slope G is in percent, x is in feet G is in decimal, x is in stations

Crest Vertical Curves For SSD < L For SSD > L SSD h2 h1 L PVI Line of Sight PVC G1 PVT G2 h2 h1 L For SSD < L For SSD > L

Crest Vertical Curves Assumptions for design Simplified Equations h1 = driver’s eye height = 3.5 ft. h2 = tail light height = 2.0 ft. Simplified Equations Minimum lengths are about 100 to 300 ft. Another way to get min length is 3 x (design speed in mph) For SSD < L For SSD > L

Crest Vertical Curves Assuming L > SSD…

Design Controls for Crest Vertical Curves from AASHTO’s A Policy on Geometric Design of Highways and Streets 2001

Design Controls for Crest Vertical Curves from AASHTO’s A Policy on Geometric Design of Highways and Streets 2001

Light Beam Distance (SSD) Sag Vertical Curves Light Beam Distance (SSD) G1 headlight beam (diverging from LOS by β degrees) G2 PVC PVT h1 PVI h2=0 L For SSD < L For SSD > L

Sag Vertical Curves Assumptions for design Simplified Equations h1 = headlight height = 2.0 ft. β = 1 degree Simplified Equations What can you do if you need a shorter sag vertical curve than calculated? Provide fixed-source street lighting Minimum lengths are about 100 to 300 ft. Another way to get min length is 3 x design speed in mph For SSD < L For SSD > L

Sag Vertical Curves Assuming L > SSD…

Design Controls for Sag Vertical Curves from AASHTO’s A Policy on Geometric Design of Highways and Streets 2001

Design Controls for Sag Vertical Curves from AASHTO’s A Policy on Geometric Design of Highways and Streets 2001

Example 1 A car is traveling at 30 mph in the country at night on a wet road through a 150 ft. long sag vertical curve. The entering grade is -2.4 percent and the exiting grade is 4.0 percent. A tree has fallen across the road at approximately the PVT. Assuming the driver cannot see the tree until it is lit by her headlights, is it reasonable to expect the driver to be able to stop before hitting the tree? Assume that S>L (it usually is not but for example we’ll do it this way), therefore S = 146.23 ft. which is less than L Must use S<L equation, it’s a quadratic with roots of 146.17 ft and -64.14 ft. The driver will see the tree when it is 146.17 feet in front of her. Available SSD is 146.17 ft. Required SSD = (1.47 x 30)2/2(32.2)(0.35 + 0) + 2.5(1.47 x 30) = 196.53 ft. Therefore, she’s not going to stop in time. OR L/A = K = 150/6.4 = 23.43, which is less than the required K of 37 for a 30 mph design speed Stopping sight distance on level ground at 30 mph is approximately 200 ft.

Example 2 Similar to Example 1 but for a crest curve. A car is traveling at 30 mph in the country at night on a wet road through a 150 ft. long crest vertical curve. The entering grade is 3.0 percent and the exiting grade is -3.4 percent. A tree has fallen across the road at approximately the PVT. Is it reasonable to expect the driver to be able to stop before hitting the tree? Assume that S>L (it usually is), therefore SSD = 243.59 ft. which is greater than L The driver will see the tree when it is 243.59 feet in front of her. Available SSD = 243.59 ft. Required SSD = (1.47 x 30)2/2(32.2)(0.35 + 0) + 2.5(1.47 x 30) = 196.53 ft. Therefore, she will be able to stop in time. OR L/A = K = 150/6.4 = 23.43, which is greater than the required K of 19 for a 30 mph design speed on a crest vertical curve Stopping sight distance on level ground at 30 mph is approximately 200 ft.

Example 3 A roadway is being designed using a 45 mph design speed. One section of the roadway must go up and over a small hill with an entering grade of 3.2 percent and an exiting grade of -2.0 percent. How long must the vertical curve be? For 45 mph we get K=61, therefore L = KA = (61)(5.2) = 317.2 ft.

Trinity Road between Sonoma and Napa valleys Horizontal Alignment

Horizontal Alignment Objective: Primary challenge Fundamentals Geometry of directional transition to ensure: Safety Comfort Primary challenge Transition between two directions Horizontal curves Fundamentals Circular curves Superelevation Δ

Horizontal Curve Fundamentals PI T Δ E M L PC Δ/2 PT D = degree of curvature (angle subtended by a 100’ arc) R R Δ/2 Δ/2

Horizontal Curve Fundamentals PI T Δ E M L PC Δ/2 PT R R Δ/2 Δ/2

Example 4 A horizontal curve is designed with a 1500 ft. radius. The tangent length is 400 ft. and the PT station is 20+00. What are the PI and PT stations? Since we know R and T we can use T = Rtan(delta/2) to get delta = 29.86 degrees D = 5729.6/R. Therefore D = 3.82 L = 100(delta)/D = 100(29.86)/3.82 = 781 ft. PC = PT – PI = 2000 – 781 = 12+18.2 PI = PC +T = 12+18.2 + 400 = 16+18.2. Note: cannot find PI by subtracting T from PT!

Superelevation Rv ≈ Fc α Fcn Fcp α e W 1 ft Wn Ff Wp Ff α

Superelevation Divide both sides by Wcos(α) Assume fse is small and can be neglected – it is the normal component of centripetal acceleration

Selection of e and fs Practical limits on superelevation (e) Climate Constructability Adjacent land use Side friction factor (fs) variations Vehicle speed Pavement texture Tire condition The maximum side friction factor is the point at which the tires begin to skid Design values of fs are chosen somewhat below this maximum value so there is a margin of safety

Side Friction Factor New Graph from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004

New Table Minimum Radius Tables

WSDOT Design Side Friction Factors New Table WSDOT Design Side Friction Factors For Open Highways and Ramps from the 2005 WSDOT Design Manual, M 22-01