The geometric design of roads is the branch of highway engineering concerned with the positioning of the physical elements of the roadway according to standards and constraints. The basic objectives in geometric design are to optimize efficiency and safety while minimizing cost and environmental damage. Geometric design also affects an emerging fifth objective called "livability", which is defined as designing roads to foster broader community goals, including providing access to employment, schools, businesses and residences, accommodate a range of travel modes such as walking, bicycling, transit, and automobiles, and minimizing fuel use, emissions and environmental damage.
Geometric roadway design can be broken into three main parts: alignment, profile, and cross-section. Combined, they provide a three-dimensional layout for a roadway.
The alignment is the route of the road, defined as a series of horizontal tangents and curves.
The profile is the vertical aspect of the road, including crest and sag curves, and the straight grade lines connecting them.
The cross section shows the position and number of vehicle and bicycle lanes and sidewalks, along with their cross slope or banking. Cross sections also show drainage features, pavement structure and other items outside the category of geometric design.
Design standards Roads are designed in conjunction with design guidelines and standards. These are adopted by national and sub-national authorities (e.g., states, provinces, territories and municipalities). Design guidelines take into account speed, vehicle type, road grade (slope), view obstructions, and stopping distance. With proper application of guidelines, along with good engineering judgement, an engineer can design a roadway that is comfortable, safe, and appealing to the eye.
The primary US guidance is found in A Policy on Geometric Design of Highways and Streets published by the American Association of State Highway and Transportation Officials (AASHTO).Garber, N.J., and Hoel, L., A., Traffic and Highway Engineering, 3rd Edition. Brooks/Cole Publishing, 2001 Other standards include the Australian Guide to Road Design , and the British Design Manual for Roads. An open source version of the green book is published online by The Council for Scientific and Industrial Research (CSIR) office in Zimbabwe.
Profile The profile of a road consists of road slopes, called grades, connected by parabolic vertical curves. Vertical curves are used to provide a gradual change from one road slope to another, so that vehicles may smoothly navigate grade changes as they travel.
Sag vertical curves are those that have a tangent slope at the end of the curve that is higher than that of the beginning of the curve. When driving on a road, a sag curve would appear as a valley, with the vehicle first going downhill before reaching the bottom of the curve and continuing uphill or level.
Crest vertical curves are those that have a tangent slope at the end of the curve that is lower than that of the beginning of the curve. When driving on a crest curve, the road appears as a hill, with the vehicle first going uphill before reaching the top of the curve and continuing downhill.
The profile also affects road drainage.
Symbols used
Sag curves Sag vertical curves are curves which, when viewed from the side, are concave upwards. This includes vertical curves at valley bottoms, but it also includes locations where an uphill grade becomes steeper, or a downhill grade becomes less steep.
The most important design criterion for these curves is headlight sight distance. When a driver is driving on a sag curve at night, the sight distance is limited by the higher grade in front of the vehicle. This distance must be long enough that the driver can see any obstruction on the road and stop the vehicle within the headlight sight distance. The headlight sight distance (S) is determined by the angle of the headlight and angle of the tangent slope at the end of the curve. By first finding the headlight sight distance (S) and then solving for the curve length (L) in each of the equations below, the correct curve length can be determined. If the curve length is greater than the headlight sight distance, then this number can be used. If it is smaller, this value cannot be used. Similarly, if the S>L curve length is smaller than the headlight sight distance, then this number can be used. If it is larger, this value cannot be used.Homburger, W.S., Hall, J.W., reilly, W.R. and Sullivan, E.C., Fundamentals of Traffic Engineering (15th ed), ITS Course Notes UCB-ITS-CN-01-1, 2001
Units Sight distance < curve length (S < L) Sight distance > curve length (S > L) Metric(S in metres) US customary(S in feet)
These equations assume that the headlights are above the ground, and the headlight beam diverges 1 degree above the longitudinal axis of the vehicle.
Crest curves Crest vertical curves are curves which, when viewed from the side, are convex upwards. This includes vertical curves at hill crests, but it also includes locations where an uphill grade becomes less steep, or a downhill grade becomes steeper.
The most important design criterion for these curves is stopping sight distance. This is the distance a driver can see over the crest of the curve. If the driver cannot see an obstruction in the roadway, such as a stalled vehicle or an animal, the driver may not be able to stop the vehicle in time to avoid a crash. The desired stopping sight distance (S) is determined by the speed of traffic on a road. By first finding the stopping sight distance (S) and then solving for the curve length (L) in each of the equations below, the correct curve length can be determined. The proper equation depends on whether the vertical curve is shorter or longer than the available sight distance. Normally, both equations are solved, then the results are compared to the curve length.
sight distance > curve length (S > L)
sight distance < curve length (S < L)
US standards specify the height of the driver's eye is defined as 1080 mm (3.5 ft) above the pavement, and the height of the object the driver needs to see as 600 mm (2.0 ft), which is equivalent to the taillight height of most passenger cars.
For bicycle facilities, the cyclist's eye height is assumed to be at 1.4 m (4.5 ft), and the object height is 0 inches, since a pavement defect can cause a cyclist to fall or lose control.Minnesota Department of Transportation, Bikeway Facility Design Manual, section 5-3.5.1, http://www.dot.state.mn.us/bike/pdfs/Chapter5_Bw.pdf, retrieved 4/20/2010
Alignment Horizontal alignment in road design consists of straight sections of road, known as tangents, connected by circular horizontal curves. Circular curves are defined by radius (tightness) and deflection angle (extent). The design of a horizontal curve entails the determination of a minimum radius (based on speed limit), curve length, and objects obstructing the view of the driver.
Using AASHTO standards, an engineer works to design a road that is safe and comfortable. If a horizontal curve has a high speed and a small radius, an increased superelevation (bank) is needed in order to assure safety. If there is an object obstructing the view around a corner or curve, the engineer must work to ensure that drivers can see far enough to stop to avoid an accident or accelerate to join traffic.
Terminology
Geometry
The quantity is the versine and is the exsecant.
Curve sight distance
Cross section
The cross section of a roadway can be considered a representation of what one would see if an excavator dug a trench across a roadway, showing the number of lanes, their widths and cross slopes, as well as the presence or absence of shoulders, curbs, sidewalks, drains, ditches, and other roadway features. The cross-sectional shape of a road surface, in particular in connection to its role in managing runoff, is called "".
Lane width The selection of lane width affects the safety, maximum capacity, and cost, of a highway.
Safety is best at a width of in urban settings, where both narrow (less than ) and wide (over ) lanes have higher crash risks. Lanes wider than 3.3~3.4m (10.8-11.2 ft)) are also associated with 33% higher impact speeds and more severe collisions, as well as higher crash rates.Dewan Masud Karim. Narrower Lanes, Safer Streets. June 2015 Conference: Canadian Institute of Transportation Engineers, Regina 2015, accessed 14th March 2022
Carrying capacity is also optimal at a width of , both for motor traffic and for bicycles. Throughput is maximal at ; as lane width decreases to , traffic speed diminishes, and so does the interval between vehicles.
Pedestrian volume also increases as lanes narrow, and intersections with narrower lanes provide higher capacity for bicycles.
Narrow lanes typically cost less to build and maintain.Theodore A. Petritsch, "The Influence of Lane Widths on Safety and Capacity: A Summary of the Latest Findings", n.d., Sprinkle Consulting They lessen the time needed to walk across, and reduce stormwater runoff.
Lane widths in Northern America are typically greater than optimum, ranging from to . Wider lanes and shoulders are usually used on roads with higher speed and higher volume traffic, and with significant numbers of trucks and other large vehicles.
Cross slope
Cross slope describes the slope of a roadway perpendicular to the centerline. If a road were completely level, water would drain off it very slowly. This would create problems with hydroplaning, and ice accumulation in cold weather.
In tangent (straight) sections, the road surface cross slope is commonly 1—2% to enable water to drain from the roadway. Cross slopes of this size, especially when applied in both directions of travel with a crown point along the centerline of a roadway are commonly referred to as "normal crown" and are generally unnoticeable to traveling motorists.
In curved sections, the outside edge of the road is superelevated above the centerline. Since the road is sloped down toward the inside of the curve, gravity draws the vehicle toward the inside of the curve. This causes a greater proportion of centripetal force to supplant the tyre friction that would otherwise be needed to negotiate the curve.
Superelevation slopes of 4 to 10% are applied in order to aid motorists in safely traversing these sections, while maintaining vehicle speed throughout the length of the curve. An upper bound of 12% was chosen to meet the demands of construction and maintenance practices, as well as to limit the difficulty of driving a steeply cross-sloped curve at low speeds. In areas that receive significant snow and ice, most agencies use a maximum cross slope of 6 to 8%. While steeper cross slope makes it difficult to traverse the slope at low speed when the surface is icy, and when accelerating from zero with warm tyres on the ice, lower cross slope increases the risk of loss-of-control at high speeds, especially when the surface is icy. Since the consequence of high speed skidding is much worse than that of sliding inward at a low speed, sharp curves have the benefit of greater net safety when designers select up to 8% superelevation, instead of 4%. A lower slope of 4% is commonly used on urban roadways where speeds are lower, and where a steeper slope would raise the outside road edge above adjacent terrain.
The equation for the desired radius of a curve, shown below, takes into account the factors of speed and superelevation (e). This equation can be algebraically rearranged to obtain desired rate of superelevation, using input of the roadway's designated speed and curve radius.