Chapter 2 Geometric Design 2.1 SIGHT DISTANCE Stopping Sight Distance Passing Sight Distance Intersection Sight Distance Sight Distance on Horizontal Curves Sight Distance on Vertical Curves 2.2 HORIZONTAL ALIGNMENT 2.3 VERTICAL ALIGNMENT What you will be learning from this chapter …

SIGHT DISTANCE “The longest distance a driver can see in front of him” “The length of carriageway visible to a driver in both horizontal and vertical planes” “Sight distance is the length of roadway visible to a driver” Sight distance is the most important feature for safe and efficient operation of a highway. Obstructions to sight distance may be in the form of parked vehicles, plants, buildings, cut sections, etc. For safe driving, minimum sight distances must be prescribed. The three types of sight distance common in roadway design : intersection sight distance, stopping sight distance, and passing sight distance

1 STOPPING SIGHT DISTANCE (SSD) The clear distance ahead needed by a driver to bring his vehicle to a stop before meeting a stationary or slow-moving object on his way is known as the safe stopping sight distance. The calculation of the minimum distance required to stop a vehicle before it hits a stationary or slow-moving object involves establishing values for speed (design speed is used), perception-reaction time, braking distance and eye and object heights. Minimum distance required to stop ?

Perception-reaction time = Perception time + Reaction time is the time which elapses between the instant the driver sees the hazard and the realization that brake action is required. Reaction time is the time taken by the driver to actuate the brake pedal, after realizing the need to brake, until the brakes start to take effect. Field measurements indicate that combined perception-reaction time typically vary form 0.5 s in difficult terrain where drivers are more alert, to 1.5 s under normal road conditions. For safe and comfortable design, a combined time of 2s is suggested. For design purposes : perception-reaction = 1.5 s is assumed for urban areas 2.5 s is assumed for rural areas.

Perception-reaction distance = 0.278tV Perception-reaction Distance is the distance traveled during perception-reaction time. Perception-reaction distance = 0.278tV t = perception-reaction time (in seconds) V= initial speed (in km/h) Braking Distance is the distance needed by a vehicle to decelerate to a stop after the brakes have been applied. Braking distance = V2 254f V = initial speed (in km/h) f= longitudinal coefficient of friction (developed between the tyres and the road surface)

Longitudinal coefficient of friction (f) can be obtained from the following table: Design speed, V (km/hr) 30 40 50 60 70 80 90 100 110 120 Coefficient of friction, f 0.40 0.38 0.35 0.33 0.31 0.30 0.29 0.28 f depends on road conditions, tyre quality, speed, and mactrotexture and microtexture of the pavement. Eye and object heights used should ensure that there is an envelope of clear visibility which enables drivers of low cars to see low objects on the carriageway, and drivers of high vehicles to see portions of other vehicles, even though bridge soffits at sag curves and overhanging tree branches may be in the way. Eye heights are generally between 1.05 m – 2.00 m, while object heights are between 0.26 m – 2.00 m.

Generally, Stopping Sight Distance = Perception-reaction Distance + Braking Distance On flat roads: On sloped roads: where n = gradient (%)

Exercise: A motorist, traveling at 60 km/hr on a steep rural road with a gradient of 8%, sees an obstruction on the carriageway ahead of him. Calculate the minimum stopping sight distance required. Stopping sight distance on slopes: SSD = 81.1 m

Minimum distance required to overtake? 2 PASSING SIGHT DISTANCE (PSD) Fast vehicle Slow vehicle Oncoming vehicle Minimum distance required to overtake?

Components of minimum safe passing sight distance 2 PASSING SIGHT DISTANCE (PSD) Components of minimum safe passing sight distance

Generally, Passing Sight Distance, PSD = d1 + d2 + d3 + d4 Exercise: A vehicle traveling at 80 km/hr wants to overtake a slower vehicle in front. The speed of the oncoming vehicle is 70 km/hr. Calculate the minimum passing sight distance required for this maneuver. (Assume the acceleration, a is 1.0 m/s2, and the speed difference between the faster vehicle and the slower vehicle is 16 km/h)

Speed of slower vehicle (Vs) = 80 – 16 = 64 km/hr Vs = 64 km/hr  vs = 0.278  64 = 17.79 m/s d1 = vs  t1 = 17.79  3.5 = 62.27 m s = 0.7vs + 6 = 0.7(17.79) + 6 = 18.45 m d2 = 2s + vs = 2(18.45) + 17.79 = 189.7 m Speed of oncoming vehicle, Vo = 70 km/hr  vo = 0.278  70 = 19.46 m/s d3 = vo  t3 = 19.46  1.5 = 29.19 m

d4 = = 126.5 m Therefore, the minimum passing sight distance, PSD = d1 + d2 + d3 + d4 = 62.27 + 189.7 + 29.19 + 126.5 = 403.13 m

3 INTERSECTION SIGHT DISTANCE (ISD) The operator of a vehicle approaching an intersection at grade should have an unobstructed view of the whole intersection and a length of the intersecting road sufficient to permit control of the vehicle to avoid collision. For the sight of distance of the driver of a vehicle passing through an intersection, two aspects must be considered: there must be a sufficient unobstructed view to recognize the traffic signs or traffic signals at the intersection there must also be a sufficient sight distance to make a safe departure after the vehicle has stopped at the stop line In order that drivers will see the appropriate traffic there should be an area of sight unobstructed by buildings or other objects across the corners of an intersection. This is known as the sight triangle.

Sight Triangle AB = stopping sight distance based on operating speed on road X BC = stopping sight distance based on operating speed on road Y AC = sight line These areas should be clear of obstructions that might block a driver’s view of conflicting vehicles or pedestrians Parking within the sight triangle should also be eliminated.

Approach Sight Triangles Approach sight triangles provide the driver of a vehicle approaching an intersection an unobstructed view of any conflicting vehicles or pedestrians. These triangular areas should be large enough that drivers can see approaching vehicles and pedestrians in sufficient time to slow or stop and avoid a crash

Approach Sight Triangles

Sight Distance for Approach, SA For Signalized Intersections: where, t = total reaction time (urban = 6 s, rural = 10 s) a = acceleration (maximum allowable acceleration = 1.96 m/s2) V = vehicle speed or design speed (in km/hr) For Priority Intersections: Use the similar equation as for sight distance of approach at signalized intersections. However, total reaction time is taken as 2 s because decision making is not required as every driver must stop.

Departure Sight Triangles Departure sight triangles provide adequate sight distance for a stopped driver on a minor roadway to depart from the intersection and enter or cross the major roadway These sight triangles should be provided in each quadrant of a controlled intersection

Departure Sight Triangles

Sight Distance for Departure, SD V = vehicle speed or design speed (in km/h J = sum of perception time and the time required to shift to first gear or actuate an automatic shift (in seconds) ta = time required to accelerate and traverse the distance S to clear the major road (in seconds) J-value for rural areas is 2 s, while for urban and suburban areas is 1.0 s to 1.5 s ta values can be obtained from the following figure. It depends on the distance S which the crossing vehicle must travel to cross the major road.

Figure 1:Time required to accelerate and traverse the distance S ( ta )

Distance traveled during crossing maneuver, S = D + W + L where, D = distance from near edge of pavement of front of stopped vehicle (for design purposes, taken as 3 m) W = width of pavement along path of crossing vehicle (in m) L = overall length of vehicle (5 m for passenger cars, 10 m for single unit trucks and 15 m for semi-trailers)

Obstructions within Sight Triangles To determine whether an object is a sight obstruction, consider: The horizontal and vertical alignment of both roadways, The height and position of the object For passenger vehicles, it is assumed that the driver’s eye height is 3.5 feet and the height of an approaching vehicle is 4.25 feet above the roadway surface

Obstructions within Sight Triangles At the decision point, as shown in Figure, the driver’s eye height is used for measurement.

Clear versus Obstructed Sight Triangles

Exercise: A car is traveling at 75 km/hr along a secondary road approaching an intersection with priority control. The car will cross the intersection and reach the same speed after departing from the intersection. The width of pavement along the path where the vehicle crosses is 7.0 m. Calculate the required sight distance for approach and departure. Sight distance for approach, = 152.4 m

Distance traveled during crossing maneuver, S = D + W + L = 3.0 + 7.0 + 5.0 = 15 m From Figure 1, time required to accelerate and traverse the distance S, ta = 4.8 s Sight distance for departure, = 0.278(75)(2.0 + 4.8) = 141.8 m

Sight Distance on Horizontal Curves Objects such as cut slopes, walls, buildings, bridge piers, and longitudinal barriers can create sight obstructions on the inside of curves (or the inside of a median lane on a divided highway). If removal of the object is not a possibility, then the alignment of the roadway may need to be altered to provide adequate sight distance.

Sight Distance on Horizontal Curves The distance M is the minimum distance an object needs to be located from the center of the inside lane to provide adequate sight distance. Sight distance is measured along the centerline of the inside lane around the curve

4 SIGHT DISTANCE ON HORIZONTAL CURVE The figure illustrates the situation where the required sight distance lies wholly within the length of the curve, normally L is assumed to be equal to the required sight distance, S. However in the case of S ≤ L : L = Length of curve M can be calculated as: where R = horizontal curve radius

The figure illustrates the situation where S is greater than the available length of curve, L and overlaps onto the tangents for a distance of l on either side. (S > L) Therefore when S > L: where R = horizontal curve radius

Exercise: The figure below illustrates the proposed site for the construction of a building that is adjacent to a horizontal curve section of a rural highway. The suggested offset clearance is 10 m. The highway design speed is 100 km/hr, while the curve length and curve radius is 200 m and 600 m respectively. Drivers’ perception-reaction time is taken as 2.5 seconds and the coefficient of friction between the tyres and the road surface is 0.28. Is the suggested offset clearance adequate to allow for safe stopping sight distance?

Safe stopping sight distance = perception reaction distance + braking distance Given that, curve length, L = 200 m For S (210) > L: (100) Minimum offset clearance, = 9.175 m The provided minimum offset clearance is 10.0 m, which is adequate.

Additional Notes: Sight Distance on Horizontal Curve Based on the diagram,

Substitute into SSD = stopping sight distance on horizontal curve Ms = middle ordinate necessary to provide adequate stopping sight distance Rv = radius to the vehicle’s traveled path

Example: A horizontal curve on a U5 highway is designed with a 700 m radius, 3.6 m lanes, and a 100km/hr design speed. Determine the distance that must be cleared from the inside edge lane to provide sufficient sight distance for desirable and minimum SSD. Rv = 700 – 3.6/2 = 698.2 m From standard produced by public of work Malaysia, the distance that must be cleared from the inside edge lane to provide sufficient sight distance for desirable SSD = 205 m: (refer table in appendix)

The distance that must be cleared from the inside edge lane to provide sufficient sight distance for minimum SSD = 157 m: (refer table in appendix)

Quiz 3 Given, Lane width = 3.5 m Curve radius, R = 400 m Calculate the following: length of the sight line if clearance of 25 m from the road centreline is required. SSD. 25 m

Rv = 400 – (3.5/2) = 398.25 m Sight line Ms = 25 – (3.5/2) = 23.25 m SSD Ms = Rv [1 - cos(s/2)] 23.25 = 398.25 [1 - cos(s/2)] 25 m cos(s/2) = 1 - (23.25/398.25) = 0.94162 s/2 = 19.67 s = 39.34 s Rv Length of sight line, l = 2Rvsin(s/2) = 2(398.25)sin19.67 = 268.14 m

Stopping Sight Distance (m) Passing Sight Distance (m) Appendix Stopping Sight Distance (Source: JKR & LLM) Passing Sight Distance (Source: JKR) Highway Agency Design Speed (km/h) Stopping Sight Distance (m) Malaysian Highway Authority (LLM) 140 120 100 80 325 225 150 Public Works Department (JKR) 60 50 40 30 20 285 205 85 65 45 Design Speed (km/h) Passing Sight Distance (m) 120 100 80 60 50 40 30 20 800 700 550 450 350 300 250 200

Stopping Sight Distance (m) Stopping Sight Distance (Source: AASHTO) Design speed (km/h) Stopping Sight Distance (m) AASHTO 2001 AASHTO 1994 Design Desirable Minimum 30 40 50 60 70 80 90 100 35 65 85 105 130 160 185 29.6 44.4 62.8 84.6 110.8 139.4 168.7 205.0 57.4 74.3 94.1 112.8 131.2 157.0

5 SIGHT DISTANCE ON VERTICAL CURVE For Crest Curves: (a) When S < L: where, A = difference in grades h1 = eye height h2 = object height

(b) When S > L: where, A = difference in grades h1 = eye height h2 = object height

For Sag Curves: (a) When S < L: (b) When S > L: where D = vertical clearance (ideally taken as 5.7 m)

Exercise: A car is traveling at 90 km/hr on a crest vertical curve connecting grades of +1% and -2% and having a curve length of 300 m. Further ahead of the car, a box from a truck has fallen onto the travel lane. The height of the box is 500 cm. Eye height is taken as 1.06 m. Ignore the effects of grades on stopping sight distance. The road is in a rural area. Calculate the minimum length required for the car to stop safely and avoid colliding with the box. Stopping sight distance, = 168.8 m

Since SSD < L, Minimum length required for safe stopping (on crest curve), = 141.7 m

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