Highway Geometric Design

Table of Contents
1. Introduction
2. Factors that govern geometric elements
3. Cross-section elements
4. Sight distance
5. Design of horizontal alignment
6. Gradient (longitudinal slope)
7. Vertical alignment - vertical curves
8. Summary
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Introduction

The geometric design of a highway deals with the dimensions and layout of visible features of the highway such as alignment, sight distances and intersections. The geometrics of a highway should be designed to provide optimum efficiency in traffic operations with maximum safety at reasonable cost. Geometric design deals with the following main elements:

• Cross-section elements (widths of carriageway, shoulders, medians, kerbs, footpaths, cycle tracks, etc.).
• Sight-distance considerations (stopping sight distance, overtaking sight distance, headlight sight distance, intermediate sight distance).
• Horizontal alignment (horizontal curves, superelevation, transition curves, widening on curves).
• Vertical alignment (gradients, vertical curves - summit and valley curves, grade compensation on curves).
• Intersection elements (layout of intersections, channelisation, spacing, turning lanes and islands).

Factors that govern geometric elements

• Design speed: the most important factor controlling geometric design elements. It is chosen according to the type/class of road (for example national highway, state highway, major district road, village road) and the topography of the region. Nearly every geometric element depends on the design speed.
• Topography: typical ruling speeds for main roads on different terrains (IRC guidance): plain terrain (cross slope up to 10%) - 100 km/h; rolling terrain (cross slope 10-25%) - 80 km/h; mountainous terrain (cross slope 25-60%) - 50 km/h.
• Traffic factors: vehicular characteristics (size, performance), human characteristics (driver perception and reaction), traffic composition and mix.
• Design hourly volume and capacity: traffic flow varies over the day; design is normally based on a representative design hour rather than absolute peak hour to remain economical.
• Environmental and other considerations: aesthetics, landscaping, air and noise pollution, and local land-use constraints influence geometric choices.

Cross-section elements

Friction, skid and slip

• Friction between tyre and pavement governs operating speeds and distances required for stopping and accelerating.
• Skid occurs when tyres slide without proper rolling; lateral skids at curves are particularly dangerous. The lateral skid coefficient can be equal to or slightly higher than the forward skid coefficient measured in braking tests.
• Slip occurs when wheels revolve more than the corresponding movement along the road (opposite tendency to skid).

Pavement unevenness

• Pavement surface conditions are commonly measured by instruments such as a bump integrator and expressed as an unevenness index (cumulative vertical undulations per unit horizontal length).
• Recommended values: keep unevenness index below 150 cm/km for good surfaces on high-speed highways; 250 cm/km is satisfactory up to about 100 km/h. Values above 350 cm/km are very uncomfortable even at 50 km/h.

Cross slope (camber)

• Purpose: camber provides drainage of surface water from the carriageway.
• Required camber depends on pavement type and rainfall intensity. Typical values:
  • Cement concrete and high-type bituminous surface: about 1.7% (flat camber 1.7-2.0% often adequate).
  • Water bound macadam and gravel pavement: up to about 2.5%.
  • Thin bituminous surface: 2.0-2.5% (dependant on rainfall).
  • Earth roads: 3.0-4.0%.
• Camber may be parabolic, elliptical or straight; parabolic/elliptical forms are preferred where high speeds and overtaking are frequent, since vehicles cross the crown frequently during overtaking. Where cross slope is very flat (e.g. RCC pavements) a straight line camber may be used.
• Shoulder cross slope: shoulder slope is typically 0.5% steeper than the adjoining carriageway; for earth shoulders a minimum of 3% and maximum of 5% is often used for drainage.

Carriageway and lane widths

• Lane width: depends on road category, design speed and vehicle mix. Typical values:
  • Single lane carriageway: 3.75 m.
  • Two-lane carriageway with raised kerbs: 7.50 m.
  • Two lanes without raised kerbs: 7.00 m.
  • Intermediate carriageway (single lane in urban situations): 5.5 m.
  • Multi-lane pavement lane width: typically 3.5 m per lane.
• For village roads, a single lane width of 3.0 m is commonly used.
• Minimum kerbed urban road width recommended is 5.5 m to allow for a stalled vehicle.
• Typical vehicle width is about 2.44 m.

Medians (traffic separators)

• Medians separate opposing traffic and reduce head-on collision risk.
• IRC recommendations for rural highways: desirable median width = 5.0 m; may be reduced to 3.0 m where land is restricted. On long bridges medians may be reduced to 1.2-1.5 m.
• Minimum median widths at urban intersections vary by function: 1.2 m for pedestrian refuge, 4.0-7.5 m where protection for right-turning vehicles is required, and 9.0-12.0 m for protection for crossing vehicles. Absolute minimum urban median width is 1.2 m and desirable is 5.0 m.

Kerbs

• Kerb marks the boundary between carriageway and shoulder, or islands, footpaths or kerb parking areas.
• Types:
  • Low or mountable kerb: height about 10 cm.
  • Semi-barrier kerb: height about 15 cm above pavement edge; top 7.5 cm with 1:1 batter where pedestrians are numerous.
  • Barrier kerb: height about 20 cm above pavement edge with a steep batter (approx. 1 vertical : 0.25 horizontal); used in built-up areas where vehicular separation is required.

Road margins and other elements

• Shoulders: provided along the road edge as emergency lanes and for additional lateral support. Minimum shoulder width recommended is 4.6 m so that a truck stationed on the shoulder has approx. 1.85 m clearance from the pavement edge.
• Parking lanes: provided on urban roads for kerb parking; parallel parking requires about 3.0 m width.
• Lay-bys: short stopping places near facilities; a typical lay-by is 3.0 m wide and at least 30 m long, with 15 m end tapers on both ends.
• Bus bays: provided to avoid conflict with moving traffic; often located about 75 m away from intersections.
• Driveways: connect the highway to commercial establishments (fuel stations, service stations); they should be located away from intersections. Driveway curves should have the largest practical radius, and driveway width kept minimum to reduce crosswalk length.
• Cycle tracks: minimum width 2.0 m; add 1.0 m for each additional cycle lane where required.
• Footpaths: minimum width 1.5 m.
• Guard rails: provided on fills where embankment height exceeds about 3 m to prevent vehicles running off the embankment.

Formation width (roadway)

• Formation width is the sum of carriageway widths (including any separators) and shoulders.
• Typical recommended formation widths (examples):
  • National & State Highways (single lane): about 6.25 m in plain/rolling terrain; two-lane carriageway 12.0 m in plain/rolling terrain; in mountainous/steep terrain lower values (for example single lane 4.75 m) are used where necessary.
  • Major District Roads, Other District Roads and Village Roads have formation widths appropriate to their traffic and terrain; for village roads (single lane) formation width may be about 4.75 m in mountainous terrain and 7.5 m in plain terrain.
• Minimum roadway width on a single-lane bridge is often specified as 4.25 m.

Right of way

• Right of way (ROW) is the area of land acquired for the road along its alignment. Land width depends on road importance and future development potential.
• Typical normal ROW for NH and SH on open plain terrain: 45 m (normal) up to 60 m (maximum). Corresponding widths between building lines and control lines are larger to allow setbacks.
• Recommended land widths for urban roads:
  • Arterial roads: 50-60 m.
  • Sub-arterial: 30-40 m.
  • Collector streets: 20-30 m.
  • Local streets: 10-20 m.

Sight distance

Sight distance is the length of road visible ahead to a driver at any instant. Design considers several types of sight distances:

• Stopping sight distance (SSD) - minimum distance required to stop a vehicle travelling at design speed without collision.
• Overtaking (or passing) sight distance (OSD) - distance required to overtake a slower vehicle safely on two-way roads.
• Sight distance for entering uncontrolled intersections - safe gap acceptance distances.
• Intermediate sight distance (ISD) - defined as twice the SSD; used to provide limited overtaking opportunities when full OSD is not available.
• Headlight sight distance - distance visible to the driver at night under vehicle headlight illumination; important on up gradients and sag curves.

Stopping sight distance (SSD)

• SSD must be present at all points and is sometimes referred to as absolute minimum sight distance.
• SSD depends on road features ahead, driver eye height, object height, reaction time, vehicle speed, brake efficiency, tyre-pavement friction and longitudinal gradient.
• IRC recommended values: driver eye height = 1.2 m; object height = 0.15 m above the road surface.
• Total reaction time comprises perception time and brake reaction time. The PIEV model splits reaction into Perception, Intellection, Emotion and Volition. IRC commonly recommends a design total reaction time t = 2.5 s.
• Lag (reaction) distance (distance travelled during reaction time):
  lag distance = v × t = 0.278 × V × t (where V is km/h, v is m/s).
• Braking distance (assuming constant longitudinal friction f):
  work done against friction = initial kinetic energy
  => f.W.l = W.v²/(2g) => l = v²/(2g f).
  If V is in km/h, then braking distance l = V²/(254 f) (metres).
• Total SSD = reaction (lag) distance + braking distance.
  SSD = 0.278 V t + V²/(254 f), where t is reaction time in s, f is longitudinal friction coefficient, V is km/h.
• Typical IRC friction values: f ≈ 0.40 at 20-30 km/h; f ≈ 0.34 at 100 km/h (friction decreases with speed).
• Effect of gradient: on an uphill or downhill grade the braking distance is affected. The SSD equation may be adjusted by adding the component due to gradient n (%):
  SSD = 0.278 V t + V²/(254 f ± 0.01 n)
  use + for ascending grades and - for descending grades.
• Notes:
  • On narrow or single-lane two-way roads where two vehicles travel toward each other, the minimum SSD should be twice the SSD so both vehicles can stop.
  • If SSD for design speed cannot be provided on a section, the speed should be restricted by signs and/or geometric changes provided.
• Approximate SSD values (IRC typical values) - examples:
  • For V = 20 km/h, SSD ≈ 20 m.
  • For V = 40 km/h, SSD ≈ 40-45 m.
  • For V = 65 km/h, SSD ≈ 90 m.
  • For V = 80 km/h, SSD ≈ 120 m.
  • For V = 100 km/h, SSD ≈ 180 m.

Overtaking sight distance (OSD)

• OSD (or passing sight distance) is the minimum clear distance ahead required by a driver to overtake a slower vehicle safely against traffic in the opposing direction.
• OSD depends on the speeds of the overtaking vehicle, the overtaken vehicle and the oncoming vehicle; driver reaction time; spacing required before and after overtaking; acceleration capability of the overtaking vehicle; and gradient.
• Conceptually OSD = d1 + d2 + d3, where:
  • d1 = distance travelled by the overtaking vehicle during the reaction time before initiating the overtake.
  • d2 = distance required for the overtaking vehicle to accelerate, overtake and return to the lane ahead of the slower vehicle.
  • d3 = distance the oncoming vehicle travels while the overtaking is being carried out.
• Practical design uses simplified formulae and standard assumptions for guard spacing S and acceleration; if Vb (speed of slow vehicle) is not known, Vb ≈ V - 16 km/h and corresponding conversions are used.
• Signage: locations where safe overtaking cannot be provided should be signed "No Passing" or "Overtaking Prohibited" in advance; overtaking zones (signed "Overtaking Zone Ahead" and "End of Overtaking Zone") should be provided at suitable intervals where safe passing is possible.
• Overtaking zone maximum length: often recommended as up to 50 × OSD (practical considerations determine actual lengths and frequency).

Design of horizontal alignment

Ruling design speeds

• IRC guidance for ruling design speeds (examples):
• Open roads:
  • NH & SH: 100 km/h (plain), 80 km/h (rolling).
  • MDR: 80 km/h (plain), 65 km/h (rolling).
  • ODR: 65 km/h (plain).
  • VR (village roads): 30 km/h (plain).
• Urban roads:
  • Arterial roads: 80 km/h.
  • Sub-arterial roads: 60 km/h.
  • Collector streets: 50 km/h.
  • Local streets: 30 km/h.

Horizontal curves and centrifugal effect

• A vehicle negotiating a horizontal curve experiences a centrifugal force which must be resisted by friction and/or by superelevation.
• Centrifugal force P acting on a vehicle of weight W at speed v negotiating a circular curve of radius R:
  P = W·v² / (g·R)
  where v is m/s, g ≈ 9.8 m/s² and R is in metres. The ratio P/W = v²/(gR) is often called the centrifugal ratio.
• The centrifugal force tends to:
  • Overturn the vehicle (tendency to roll outward).
  • Cause lateral skid (tyre lateral force requirement).
• Overturning condition (simplified): equilibrium when P·h = W·(b/2), where h is height of centre of gravity and b is the track width. This gives a limit on permissible combinations of speed and radius for a given vehicle geometry.
• Skidding (no lateral skid) condition: P ≤ f·W where f is the lateral friction coefficient. Hence v²/(gR) ≤ f.

Superelevation (banking)

• Purpose: to counteract centrifugal force by inclining the pavement so that part of the lateral force is taken by the component of weight, reducing reliance on friction.
• Superelevation rate e is expressed as the ratio of difference in outer and inner edge elevation to the pavement width (i.e. e = tan θ, θ being the pavement cross-slope angle on the curve).
• Equilibrium consideration combining superelevation and lateral friction gives:
  e + f ≈ v²/(127 R) (where v is in km/h, R in m and f is the lateral friction coefficient).
• Design steps (practical IRC procedure):
  • Compute superelevation e required for 75% of design speed without considering friction: e ≈ (0.75 V)²/(127 R).
  • If computed e ≤ 0.07 (7%), provide that e. If e > 0.07, limit e to maximum emax = 0.07 and check friction requirement at full design speed.
  • If required lateral friction f for e = 0.07 is less than allowable f (commonly taken as f = 0.15), then e = 0.07 and f = 0.15 are acceptable. If not, the permissible speed on the curve should be reduced.
• IRC recommended limits:
  • Maximum superelevation emax = 0.07 (7%) for plain and rolling terrain.
  • emax = 0.10 (10%) for certain hilly terrain not subject to snow.
  • emax = 0.04 (4%) for urban roads with frequent intersections.
  • Minimum superelevation emin is governed by drainage (equal to camber where necessary).
• Attainment of superelevation: full superelevation is usually attained by the end of the transition curve or at the start of the circular curve. Two common methods of rotating the pavement to achieve super-elevation:
  • Rotation about the centre line - inner edge depressed and outer edge raised by equal amounts (advantage: earthwork balance; disadvantage: inner edge depression can create drainage problems).
  • Rotation about the inner edge - outer edge raised only (suitable in high rainfall or level terrain to avoid drainage problems).

Minimum (ruling) radius of horizontal curves

• For given superelevation e and lateral friction f the minimum radius R for a design (ruling) speed V (km/h) is given from the relation:
  R ≥ V² / [127 (e + f)].
• IRC recommended ruling minimum radii (approximate examples):
  • NH & SH : 360 m (minimum for certain categories).
  • MDR : 230 m.
  • ODR : 155 m.
  • VR : 90 m.

Extra widening of pavement on curves

• Extra pavement widening on curves is provided to:
  • accommodate vehicle off-tracking (mechanical widening),
  • allow ease of overtaking and driver psychology (psychological widening),
  • increase safety and visibility at curves.
• Extra widening We consists of two parts: mechanical widening Wm and psychological widening Wps, so We = Wm + Wps.
• Typical practical values (IRC and widely used practice):
  • We ≈ 0.6 m for R = 100-300 m.
  • We ≈ 0.9 m for R = 60-100 m.
  • We ≈ 1.5 m for R < 60 m.
• Psychological widening is more important for multi-lane pavements and higher speeds.

Transition curves (horizontal)

• Transition curves gradually introduce curvature (and hence centrifugal acceleration and superelevation) so the lateral acceleration increases smoothly, improving ride comfort and safety.
• Typical transition curve types: clothoid (spiral), lemniscate, cubic parabola. The clothoid is most commonly used because the centrifugal acceleration increases roughly linearly with distance along the spiral.
• Functions of transition curves:
  • Introduce centrifugal force gradually to avoid jerk;
  • Improve driver comfort and vehicle stability;
  • Allow gradual introduction of superelevation and extra widening;
  • Improve aesthetic appearance of alignment.
• Length of transition curve is chosen to satisfy one or more of the following criteria:
  • Allowable rate of change of centrifugal acceleration: for clothoid design a practical formula used in many guidelines is
    L = 0.0215 × V³ / (C × R)
    where L (m) is length of transition, V is design speed in km/h, R is radius in m and C is the allowable rate of change of centrifugal acceleration (typically C ≈ 0.5-0.8 m/s³; a common design value is C = 0.6 m/s³).
  • Rate of introduction of superelevation: when pavement is rotated the length Ls is related to the allowable rate of rotation. Common practical parameter N (the number of metres required per unit change) varies approximately from 150 (plain) to 60 (hilly). A commonly used relation is:
    Ls ≈ N × e × (W + We)
    where e is superelevation, W is carriageway width and We is extra widening. N varies by terrain (about 150 in plain to 60 in hilly terrain).
  • Empirical IRC recommendations:
    For plain and rolling terrain a recommended minimum transition length is Ls ≥ 2.7 V² / R (V in km/h, R in m).
    For mountainous and steep terrain a conservative recommendation is Ls ≥ V² / R.
• The final Ls adopted should be the largest value obtained from the applicable criteria.

Curve resistance

• Curve resistance is the loss of tractive force due to turning a vehicle on a horizontal curve and is equal to T - T cos α = T (1 - cos α), where T is the tractive effort and α is the turning angle.

Gradient (longitudinal slope)

• Gradient is the rate of rise or fall along the length of the road measured with respect to the horizontal; usually expressed as a percentage or as 1 in n.
• Gradients are categorised:
  • Ruling gradient - the maximum gradient that the designer attempts to adopt as the standard design gradient.
  • Limiting gradient - steeper than ruling gradient and used where gentler gradients would be very expensive to achieve.
  • Exceptional gradient - steeper still and used only for short stretches (usually limited to lengths not exceeding about 100 m).
  • Minimum gradient - required for drainage; typical values: 1 in 500 for good concrete drains, about 1 in 200 (0.5%) for inferior drains, up to 1 in 100 (1%) for kutcha drains.
• Typical gradient recommendations by terrain:
  • Plain/rolling terrain: ruling 3.3% (≈1 in 30), limiting 5% (1 in 20), exceptional 6.7% (1 in 15).
  • Mountainous terrain (high elevations > 3000 m): ruling 5%, limiting 6%, exceptional 7%.
  • Steep terrain up to 3000 m: ruling 6%, limiting 7%, exceptional 8%.
• Grade (gradient) compensation on horizontal curves:
  • Due to curve resistance, the effective tractive effort is reduced on horizontal curves. A reduction in gradient (grade compensation) is therefore sometimes provided on sharp curves to compensate for loss of tractive effort.
  • IRC practice: grade compensation is generally not necessary for gradients flatter than about 4%. For sharper curves some numerical compensation is applied as per detailed design charts and local guidance.

Vertical alignment - vertical curves

Vertical curves provide smooth transition where two grades meet. They are essential to ensure comfort, safety and adequate sight distance. Two main types are:

• Summit (crest) curves - convex upwards; main requirement is adequate sight distance (SSD, OSD).
• Valley (sag) curves - concave upwards; main concerns are headlight sight distance at night and comfort (rate of change of vertical acceleration).

Summit (crest) curves

• Summit curves are commonly provided as parabolic curves: y = a x² where a = N/(2 L) and N is the algebraic difference between approaching and leaving grades (in percent) and L is length of curve in metres.
• Design of summit curve length must ensure adequate sight distance:
  • For SSD: when L ≥ SSD the length of parabolic summit curve can be related to SSD and deviation angle. Using driver eye height H = 1.2 m and object height h = 0.15 m, a simplified relation commonly used is:
    L = N · S² / 4.4
    where S is the stopping sight distance and N is the deviation angle in suitable units (algebraic sum of grades in percent). (This formula corresponds to standard simplifications with H = 1.2 m and h = 0.15 m.)
  • When L < SSD a different relation applies and design must ensure that the available sight distance over the curve meets SSD; refer to standard equations that include H and h explicitly.
• For overtaking/intermediate sight distance (ISD/OSD) similar relations are used with S representing OSD (or ISD). For H = h = 1.2 m and for OSD the simplified relation often used is:
  L = N · S² / 9.6
  when L ≥ S and H = h.
• Circular summit curves provide constant sight distance but parabolic curves are simpler to construct and are commonly used.

Valley (sag) curves

• Valley curves are often designed to control the rate of change of vertical acceleration and to provide headlight sight distance at night. The best shape for gradual introduction of centrifugal force is a transition (cubic parabola is commonly preferred for sag curves).
• Design criteria:
  • Allowable rate of change of centrifugal acceleration (comfort): commonly C ≈ 0.6 m/s³.
  • Headlight sight distance: the distance illuminated by vehicle headlight must be sufficient (at least equal to SSD for safety).
• Length criteria: the length L of a valley curve is chosen as the higher of values obtained from the comfort criterion and headlight sight distance criterion. For comfort, transition length is often obtained from relations analogous to the horizontal transition expression, for example:
  L ≈ 0.38 × (N·V³)½ (empirical form used in some guidelines)
  where N is deviation angle and V is speed; consult detailed standards for exact use and units.
• When L is large the sag curve can be made fully transitional with equal lengths of transition on both sides; for valley curves the lowest point normally lies at the bisector of the angle between grades if grades are equal, otherwise it is shifted toward the flatter grade.
• Cubic parabola equation often used for sag curves: y = b x³, with b related to the total deviation and length as per standard derivation.

Summary

This chapter presented the primary elements of highway geometric design: cross-sectional components, sight distances, horizontal and vertical alignment design, superelevation, transition curves and gradients. Design depends principally on the chosen design speed, terrain, traffic characteristics and environmental constraints. IRC recommendations for speeds, superelevation limits, driver eye and object heights (H = 1.2 m, h = 0.15 m), reaction time (commonly 2.5 s), and typical dimensional values (lane widths, shoulder widths, median widths) are widely used in practice. For detailed numerical design and working examples, refer to the relevant standards and design charts of the Indian Roads Congress and standard textbooks on highway engineering.