Elements of DesignThis chapter discusses the elements common to all classes of highways and streets including

Sight DistanceSuperelevationTraveled Way WideningGradesHorizontal and Vertical Alignments

Sight DistanceA drivers ability to see ahead is of the utmost importance in the safe and efficient operation of a vehicle on a highway.

Four aspects of sight distance are sight distances needed for stopping (all highways), passing sight distances (2-lane highways), decision sight distances (complex locations), and criteria for measuring these sight distances for use in design.

Stopping Sight Distance: 1) the distance traversed by the vehicle from the instant the driver sights an object necessitating a stop to the instant the brakes are applied and 2) the distance needed to stop the vehicle from the instant brake application begins.

The height of the drivers eye is 1080 mm (3.5 ft) and the height of the object to be seen by the driver is 600 mm (2.0 ft).

More on Stopping Sight Distance

More on Stopping Sight DistanceOne or Two-way FlatG= 0+2%-3.5%One-way orTwo wayG = 0.02 orG = 0.035+4%-3.5%One-Way

G = 3.5%+4%-3.5%Two-Way

G = 4%Case 1Case 2Case 3Case 4SSD = 0.278Vt + 0.039 V2/aGrade zeroSSD = 0.278Vt + V2/ (254 (a/9.81)G)Grade is Ga = 3.4m/s2

Decision Sight DistanceDecision Sight Distance The distance needed for a driver to detect an expected or otherwise difficult-to-perceive information source or condition in a roadway environment that may be visually cluttered, recognize the condition or its potential threat, select an appropriate speed and path, and initiate and complete the maneuver safely and efficiently.

PlacementCritical Locations such as land drops and tool plazas, where driver errors may be experienced in digesting complicated traffic information. The locations

More on Decision Sight Distance

More on Decision Sight DistanceDecision Sight Distance

DSD = 0.278Vt + 0.039 V2/aAvoidance Maneuvers A and BWhere a = 3.4 m/s2

DSD = 0.278 VtAvoidance Maneuvers C, D, and E

Two Examples

Passing Sight Distance for Two-Lane Highways

More on Passing Sight DistanceAssumptions:

The overtaken vehicle travels at uniform speed

The passing vehicle has reduced speed and trails the overtaken vehicle as it enters a passing section

When the passing section is reached, the passing driver needs a short period of time to perceive the clear passing section and to react to start his/her maneuver.

The passing vehicle accelerates during the maneuver and its average speed during the occupation of the left lane is 15 km/h higher than that of the overtaken vehicle.

When the passing vehicle returns to its lane, there is a suitable clearance length between it and an oncoming vehicle in the other lane

More on Passing Sight DistanceExhibit 3-5 on Page 120 shows the elements of Safe Passing Sight Distance for Design of Two-Lane Two-Way Highways

d1 = 0.278ti(v-m+ati/2)

a 2.25 2.41 km/h/s, m 15 km/hv and t see Exhibit 3-5.

d2 = 0.278Vt2t2 see Exhibit 3-5.

d3 = see Exhibit 3-5

d4 = 2d2/3

More on Passing Sight DistanceExhibit 3-6 on Page 124 shows the design value of Passing Sight Distance for Design of Two-Lane Two-Way Highways

Insert the Table here

More on Passing Sight DistanceEffect of Grade on Passing Sight Distance

Downgrade Passed and Passing Vehicles easy to speed upOpposite vehicle slow down

UpgradePassed and passing vehicles slow downOpposite vehicle speed up.

Frequency and Length of Passing Sections

f(topography, design speed, cost and/or intersection spacing)

% time spent following and Average travel speed

Measuring Sight DistanceDesigners should check if the available sight distance is greater than the minimum sight distance. The available sight distance is dependent on the height of the drivers eye above the road surface, the specified object height above the road surface, and the height and lateral position of the sight obstructions within the drivers line of sight.

Height of Drivers Eye1080 mm (3.5 ft) for passenger cars2330 mm (7.6 ft) for trucks

Height of Object600 mm (2.0 ft) for SSD1080 mm (3.5 ft) for PSD

Sight ObstructionsCrest vertical curves for tangent roadwaysPhysical features outside the traveled way

Procedures for Measuring Sight DistanceExhibit 3-8 shows the methods for scaling sight distance on plans

Check on Horizontal Alignments

Step One At each station, identify potential obstructions outside the traveled way downward and upward (in two directions) and estimate available sight distance between the station and the ending point of the line of sight that is controlled by every obstruction.

Step TwoCompare the available sight distance to the minimum sight distance

QuestionHow to use computer (with a digital straightedge) to check the Sight Distance Requirements

Procedures for Measuring Sight DistanceCheck on Vertical Alignments

Step One Each each vertical curve, 1) find the highest or lowest point 2) draw a tangent line from the point downward and upward3) find the point where the offset of the tangent from the vertical curve is 1080 mm and get the station of the point4) find the point where the offset of the tangent from the vertical curve is 600 mm and get the station of the point5) Calculate the difference between the stations. The difference will be the available sight distance

Step TwoCompare the available sight distance to the minimum sight distance

QuestionHow to use computer (with a digital transparent strip) to check the Sight Distance Requirements

Horizontal AlignmentCurve Design Controls

The design of roadway curves should be based on an appropriate relationship between design speed and curvature and on their joint relationships with superelevation and side friction.

Centripetal or lateral acceleration is balanced by side friction and superelevation in geometric design.Lateral Acceleration = side friction + superelevationor0.01e + f = V2/127RSide friction varies from 0 to fmax depending on the speed of the vehicle

Superelevation rate or cross slope has its limit or emax that is controlled by emax = f (weather, adjacent land use, frequency of slow-moving vehicles, construct ability)

Horizontal AlignmentA design agency normally sets up emax based on facility type. Caltrans has set up emax in its highway design manual.

With the emax is defined and pre-selected, designers can choose superelevation rate e which is less than emax. The sum of e and side friction (f) balances the lateral acceleration.

f = f(V, surface, and tire)Wet surface is the worse case

Several rates, rather than a single rate, of maximum superelevation should be recognized in establishing design controls for highway curves. A rate of 12% should not be exceeded. A rate of 4-6% is applicable for urban design. Superelevation may be omitted on low-speed urban streets.

Horizontal AlignmentBall-bank indicator is a testing tool for determining comfortable f for drivers. The comfortable f is 0.21 for 40-50 km/h

Electronic accelerometer is another testing tool used in determining advisory speeds for horizontal curves and ramps.

Testing results are shown in Exhibits 3-10 and 3-11.

Horizontal curves should not be designed directly on the basis of the maximum available side friction factor. Rather, the maximum side friction factor used in design should be that portion of the maximum available side friction that can be used with comfort and safety by vast majority of drivers.

Horizontal AlignmentDistribution of Superelevation (e) and side friction (f)

There are five methods for the distribution of e and f (see Exhibit 3-12)Application

M 1e and f to 1/RHighways with uniform speed flowsuch as rural highways

M2fmax first & e make upUrban streets with speeds not uniform

M3 emax first & f make upNegative friction for curves with flat radii

M4emax first & f make up A solution to M3 but still with negative on average speedfrictions problemM5curvilinear relation to A practical distribution for e over the range of 1/Rcurvature.

Horizontal AlignmentDesign Considerations

Design considerations in horizontal alignment involves the determination of maximum superelevation rates, minimum radius, and others

The minimum radius is the limiting value of curvature for a given design speed and is determined from the maximum rate of superelevation and the maximum side friction factor selected for design Rmin = V2/(127(0.01emax+fmax)

Horizontal AlignmentF value for these facilities is shown in Exhibit 3-13. The minimum radius for each of the five maximum superelevation rates (4%, 6%, 8%, 10%, 12%) is shown in Exhibit 3-14 for design of Rural Highways, Urban Freeways, and High-Speed Urban Streets.

Method 5 is recommended for use for these facilities. Method 5 assumes the f curve is shown in Exhibit 3-13 (dark solid line). The e value is the difference of the lateral acceleration rate and the f value for a certain speed.

Exhibits 3-16 to 3-25 show the tables and curves derived from the Method 5 procedure.

Very flat horizontal curves need no superelevation. Traffic entering a curve to the right has some superelevation provided by the normal cross slope. Traffic entering a flat curve to the left uses friction to sustain the lateral acceleration and counteract the negative superelevation due to the normal cross slope.

Horizontal AlignmentRRNo SE neededSE adjustmentSE needed

Horizontal AlignmentTransition Design Controls

Transition from a tangent to a curve or from a curve to a tangent has two parts: superelevation transition (transition in the roadway cross slope) and alignment transition (transition curves incorporated in the horizontal alignments)

Superelevation transition involves superelevation runoff and tangent run out.

Alignment transition is made of a spiral or compound transition curve. When no spiral curve is used, the transition is called tangent-to-curve transition.

Horizontal AlignmentTangent-to-curve transitionTangentRun outSuperelevation Runoff1251Old Policy:Superelevation Runoff Length is at least the distance traveled in 2.0 s at the design speedNew Policye%20

Horizontal AlignmentTangent-to-curve transitionLr = (wn1)edbw/Example 1:Assume a circular curve is designed on a two-lane two-wayundivided highway with design speed of 40 km/h. The design e is 6%. Lr =?

Example 2:Assume a circular curve is design on a four-lane undivided highway with design speed of 100km/h. The design e is 10%.Lr = ?

Horizontal AlignmentMinimum Length of Tangent RunoutLt = encLr/edExample 1:Assume a circular curve is designed on a two-lane two-wayundivided highway with design speed of 40 km/h. The design e is 6%. Lt =?

Example 2:Assume a circular curve is design on a four-lane undivided highway with design speed of 100km/h. The design e is 10%.Lt = ?

Horizontal AlignmentDistribution of Runoff on Tangent and CurveLr Distribution 0%100%100%0%

67%33%Design Portion of runoff located priorSpeed to the curveNo. of lanes rotated1.01.52.0-2.53.0-3.520-70 km/h0.800.850.900.9080-1300.700.750.800.85Lr

Horizontal AlignmentSpiral Curve Transitions

The Euler spiral, also known as the clothoid, is used in the design of spiral transition curves.

The radius varies from infinity at the tangent end of the spiral to the radius of the circular arc at the end that adjoins that circular arc.

L = 0.0214V3/RC

Rmaxsee Exhibit 3-33 on Page 179

Given R, the minimum length of spiral is as followLmin,s = (24PminR)0.5 where Pmin = 0.2Lmin,s = 0.0214V3/RC where C = 1.2 m/s3

Horizontal AlignmentSpiral Curve Transitions

Given R, the maximum length of spiral is as followLmin,s = (24PmaxR)0.5 where Pmax = 1.0

The desirable length of spiral is as follows:

The distance traveled in 2 s at the design speed of the roadway. Exhibit 3-34 on Page 181 shows the list of the desirable length at different design speed.

Length of superelevation runoff is the minimum length of spiral.

Length of Tangent Run Out:Lt = encLr/ed

Horizontal AlignmentMethods of Attaining Superelevation

Four methods are used to transition the pavement to a superelevated cross section.

Method 1Revolve a traveled way about centerline

Method 2Revolve a traveled way about the inside-edge profile

Method 3Revolve a traveled way about the outside-edge profile

Method 4Revolve a straight cross slope traveled way about theoutside-edge profile

Exhibit 3-37 shows these four methods on Page 185.

Horizontal AlignmentAxis of Rotation with a Median

The inclusion of a median in the cross section influences the superelevation transition design of divided highways, streets and parkways

Case IThe whole of the traveled way including the median is superelevated as a plane sectionMedians: < 4m and e: moderate

Case IIThe median is held in a horizontal plane and the two traveled ways are rotated separately around the median edges. Median: 4-18 m.

Case IIIThe two traveled ways are treated separately for runoff with a resulting variable difference in elevations at the median edges. Median > 18 m

Horizontal AlignmentMinimum Transition Grades

Criteria 1Maintain minimum profile grade of 0.5 % through the transition section

Criteria 2maintain minimum edge of pavement grade of 0.2 % (0.5% for curbed streets) through the transition section

Example:An uncurbed transition section with = 0.65%

Criteria 1any grade but -0.5% - 0.5% Criteria 2any grade but 0.85% - -0.45%and 0.45% 0.85%

Horizontal AlignmentTurning Roadway Design

Turning Roadways consist of interchange ramps, roadways, or intersection curves for right turning vehicles.Turning roadway design does not apply to minimum edge-of-traveled-way design for turns at intersections

Turning roadways with V 70 km/h, compound curves OK V > 70 km/h, compound curves not OK

When compound curves are considered,2: 1 for the radius of the Intersectionslarge curve and smaller curve

1.75 : 1Interchanges

The minimum arc length for the curve is given in Exhibit 3-38 on Page 192.

Horizontal AlignmentDesign for Low-Speed Urban Streets

Method 2 is often used for the design of horizontal curves on low-speed urban streets.

Exhibit 3-39 on Page 193 shows the design values of f that are applicable to low-speed urban streets (solid line)

Superelevation is impractical in many built-up areas. Very often superelevation is not considered in urban streets design

When superelevation is considered, Exhibit 3-41 should be used in selecting e given the minimum R or r given a pre-selected e.

Horizontal AlignmentDesign for Low-Speed Urban Streets

Maximum Comfortable Speed on Horizontal Curves is derived from the following formula (see Exhibit 3-40):

0.01 e + f max = V2/127R

Minimum Superelevation Runoff Length (when e is used in design)

L = 2.72fVd/C

Horizontal AlignmentCurvature of Turning Roadways and Curvature at Intersections

Minimum radius for turning speeds is controlled by the turning speed of the vehicle, normally 15 km/h.

Exhibit 3-43 shows the minimum radius given design speed for intersection curves.

Transitions and Compound Curves are often considered in design of turning roadways and urban streets.

When spirals are used for a transition section, the minimum length of the spiral is given in Exhibit 3-45 on Page 204.

Compound circular curves keep the radius ratio to be 1.5 : 1.

Horizontal AlignmentOfftracking

Offtracking is the characteristics, common to all vehicles, although much more related to the large design vehicles, in which the rear wheels do not follow precisely the same path as the front wheels when the vehicle takes a horizontal curve or makes a turn.

W = Wc WnWc = N(U+C) + (N-1)Fa +ZU = u+R (R2-li2)0.5 Fa = R2+A(2L+A)0.5 RZ = 0.1(V/R0.5)

Example on Page 215.

Horizontal AlignmentSight Distance on Horizontal Curves

Stopping Sight Distance

Relationships among, R, M, and S is shown in Exhibit 3-58The sight line is the line whose two ends have 1080 mm eye height and 600 mm object height and whose midpoint is 840 mm high.

Passing Sight Distance

The sigh line has its two ends with an eye height of 1080 mm, an object height of 1080 mm and a midpoint of 1080 mm.

Horizontal AlignmentGeneral Controls for Horizontal Alignment

Alignment should be as directional as practical but should be consistent with the topography and with preserving developed properties and community values

Rmin should be avoided for a given design speed. Use R > Rmin

Consistent alignment should be sought. Sharp curves should not be introduced at the ends of long tangent.

For small deflection angles, curves should be sufficiently long to avoid the appearance of a kink.

Sharp curvature should be avoided on long hill fills.

Compound curves should be cautiously considered.