Lec-03 Horizontal Alignment

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Lec-03Horizontal Alignment Sight Distances
Dr. Attaullah Shah

• Transportation Engineering I

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Sight Distance For operating a motor vehicle
safely and efficiently, it is of utmost
importance that drivers have the capability of
seeing clearly ahead. Therefore, sight distance
of sufficient length must be provided so that the
drivers can operate and control their vehicles
safely. Sight distance is the length of the
highway visible ahead to the driver of the vehicle
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• Aspects of Sight Distance
• The distances required by motor vehicles to stop.
• The distances needed for decisions at complex
  locations
• The distances required for passing and overtaking
  vehicles, applicable on two-lane highways
• The criteria for measuring these distances for
  use in design.

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• Stopping Sight Distance
• At every point on the roadway, the minimum sight
  distance provided should be sufficient to enable
  a vehicle traveling at the design speed to stop
  before reaching a stationary object in its path.
  Stopping sight distance is the aggregate of two
  distances
• brake reaction distance and
• braking distance.

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Brake reaction time It is the interval between
the instant that the driver recognizes the
existence of an object or hazard ahead and the
instant that the brakes are actually applied.
Extensive studies have been conducted to
ascertain brake reaction time. Minimum reaction
times can be as little as 1.64 seconds 0.64 for
alerted drivers plus 1 second for the unexpected
signal. Some drivers may take over 3.5 seconds
to respond under similar circumstances. For
approximately 90 of drivers, including older
drivers, a reaction time of 2.5 sec is considered
adequate. This value is therefore used in Table
3.1
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The braking distance of a vehicle on a roadway
may be determined by the formula
Equation (1)
d braking distance (ft) or (m) v initial
speed (ft/s) or (m/s) a deceleration rate,
ft/s² (m/s²)
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Studies (Fambro et aI., 1997) document that most
drivers decelerate at a rate greater than 4.5
m/s² (14.8 ft/s²) when confronted with an urgent
need to stop-for example, when seeing an
unexpected object in the roadway. Approximately
90 percent of all drivers displayed deceleration
rates of at least 3.4 m/s² (11.2 ft/s²).
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Such deceleration rates are within a driver's
capability while maintaining steering control and
staying in a lane when braking on wet surfaces.
Most vehicle braking systems and tire-pavement
friction levels are also capable of providing
this level. Therefore, a deceleration rate of 3.4
m/s² (11.2 ft/s²) is recommended as a threshold
for determining stopping sight distance (AASHTO,
2004).
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Design Values The sum of the distance traversed
during the brake reaction time and the distance
to brake the vehicle to a stop is the stopping
sight distance. The computed distances for wet
pavements and for various speeds at the assumed
conditions are shown in Exhibit 3-1 and were
developed from the following equation
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Equation 2
where tr is the driver reaction time (sec). If
speed is given in miles per hour or kilometer per
hour, Equation (2) can be rewritten as
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Note that the units for S are in feet and V is in
miles per hour, assuming that 1 ft/sec 0.682
mph (or 1.466 ft/sec 1 mph).
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In computing and measuring stopping sight
distances, the height of the driver's eye is
estimated to be 1,080 mm 3.5 ft and the height
of the object to be seen by the driver is 600 mm
2.0 ft, equivalent to the tail-light height of
a passenger car.
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Effect of Grade on Stopping When a highway is on
a grade, the equation for braking distance should
be modified as follows
Eq - 3
Where G is grade or longitudinal slope of the
highway divided by 100.
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Stopping sight distances calculated as based on
Equation (2)
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However, at the end of long down- grades where
truck speeds approach or exceed passenger car
speeds, it is desirable to provide distances
greater than those recommended in Exhibit - 1 or
even those calculated based on Equation (3).
It is easy to see that under these circumstances
higher eye position of the truck driver can be of
little advantage.
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Discussion The driver's reaction time, the
condition of the road pavement, vehicle braking
system, and the prevailing weather all play a
significant role in this problem.
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Decision Sight Distance Although stopping sight
distances are generally sufficient to allow
competent and alert drivers to stop their
vehicles under ordinary circumstances, these
distances are insufficient when information is
difficult to perceive. When a driver is required
to detect an unexpected or otherwise
difficult-to-perceive information source, a
decision sight distance should be provided.
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Interchanges and intersections, changes in
cross-section such as toll plazas and lane drops,
and areas with "visual noise" are examples where
drivers need decision sight distances. Exhibit
3-3, provides values used by designers for
appropriate sight distances.
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These values are applicable to most situations
and have been developed from empirical data.
Because of additional maneuvering space needed
for safety, it is recommended that decision sight
distances be provided at critical locations or
critical decision points may be moved to where
adequate distances are available.
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If it is not practical to provide decision sight
distance because of horizontal or vertical
curvature or if relocation of decision points is
not practical, special attention should be given
to the use of suitable traffic control devices
for providing advance warning of the conditions
that are likely to be encountered.
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Distances in Exhibit 3-3 for avoidance maneuvers
A and B are calculated as based on Equation (2)
however, with modified driver reaction time as
stated in the notes for Exhibit 3-3. Decision
sight distances for maneuvers C, D, and E are
calculated from either 0.278Vt or 1.47 V t, with
t, modified as in the notes.
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In computing and measuring stopping sight
distances, driver's eye height is estimated as
1080 mm (3.5 ft) and the height of the dangerous
object seen by the driver is 600 mm (2.0 ft),
which represents the height of tail-lights of a
passenger car.
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Stopping Sight Distance on plane Road
Braking Distance on sloping Road
Decision Distance
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Passing Sight Distance for Two-Lane Highways On
most two-lane, two-way highways, vehicles
frequently overtake slower-moving vehicles by
using the lane meant for the opposing traffic. To
complete the passing maneuver safely, the driver
should be able to see a sufficient distance
ahead. Passing sight distance is determined on
the basis that a driver wishes to pass a single
vehicle, although multiple-vehicle passing is
permissible.
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Based on observed traffic behavior, the
following assumptions are made 1. The overtaken
vehicle travels at a uniform speed. 2. The
passing vehicle has reduced speed and trails the
overtaken vehicle as it enters a passing section.
3. The passing driver requires a short period of
time to perceive the clear passing section, when
reached, and to start maneuvering.
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• 4)The passing vehicle accelerates during the
  maneuver, during the occupancy of the right lane,
  at about 15 km/h (10 mph) higher than the
  overtaken vehicle.
• 5)There is a suitable clearance length between
  the passing vehicle and the oncoming vehicle upon
  completion of the maneuver.

The minimum passing sight distance for two-lane
highways is determined as the sum of the four
distances shown in Figures on next slides.
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Safe passing sight distances for various speed
ranges determined from distance and time values
observed in the field are summarized in Exhibit
3-5
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Initial maneuver distance d1 The distance d1
traveled during the initial maneuver period is
computed with the following equation
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Distance while passing vehicle occupies left lane
(d2). Passing vehicles were found in the study
to occupy the left lane from 9.3 to 10.4 s. The
distance d2 traveled in the left lane by the
passing vehicle is computed with the following
equation
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Clearance length (d3). The clearance length
between the opposing and passing vehicles at the
end of the passing maneuvers was found in the
passing study to vary from 30 to 75 m 100 to 250
ft.
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Distance traversed by an opposing vehicle (d4)
The opposing vehicle is assumed to be traveling
at the same speed as the passing vehicle, so
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Initial maneuver distance d1
Distance while passing vehicle occupies left
lane (d2).
Clearance length (d3). The clearance length
between the opposing and passing vehicles at the
end of the passing maneuvers was found in the
passing study to vary from 30 to 75 m 100 to 250
ft.
Distance traversed by an opposing vehicle
(d4) d42/3 d2
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• Estimation of Velocity of a Vehicle just Before
  it is Involved in an accident
• Some times it is necessary to determine the
  velocity of a vehicle just before it is involved
  in an accident. Following steps are involved
• Estimate length of skid marks for all the four
  tires of the vehicle and take the average length.
  This is equal to breaking distance.

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2)Find out f by performing trial runs under
same environment /weather conditions and using a
vehicle having similar conditions of tyres.
Vehicle is driven at a known speed and breaking
distance is measured. 3)The unknown speed is
than determined using the braking formula.
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Horizontal Alignment

• Along circular path, vehicle undergoes
  centripetal acceleration towards center of
  curvature (lateral acceleration).
• Balanced by superelevation and weight of vehicle
  (friction between tire and roadway).
• Design based on appropriate relationship between
  design speed and curvature and their relationship
  with side friction and super elevation.

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Vehicle Cornering
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• Figure illustrates the forces acting on a vehicle
  during cornering. In this figure, ? is the angle
  of inclination, W is the weight of the vehicle in
  pounds with Wn and Wp being the weight normal and
  parallel to the roadway surface respectively.

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• Ff is the side frictional force, Fc is the
  centrifugal force with Fcp being the centrifugal
  force acting parallel to the roadway surface, Fcn
  is the centrifugal force acting normal to the
  roadway surface, and Rv is the radius defined to
  the vehicles traveled path in ft.

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• Some basic horizontal curve relationships can be
  derived by summing forces parallel to the roadway
  surface.
• Wp Ff Fcp
• From basic physics this equation can be written as

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• Where fs is the coefficient of side friction, g
  is the gravitational constant and V is the
  vehicle speed (in ft per second).
• Dividing both the sides of the equation by W cos
  ?

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• The term tan? is referred to as the super
  elevation of the curve and is denoted by e.
• Super elevation is tilting the roadway to help
  offset centripetal forces developed as the
  vehicle goes around a curve.
• The term fs is conservatively set equal to zero
  for practical applications due to small values
  that fs and ? typically assume.

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• With e tan?, equation can be rearranged as
• Here Rv in meters
• V speed in Km/hr
• G9.8m/sec2
• e coefficient of friction
• For Imperial units
• V in mph
• And Rv in feet

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Superelevation
Road Section View
Road Plan View
CL
2
2
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Superelevation
Road Plan View
Road Section View
CL
1.5
2
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Superelevation
Road Plan View
Road Section View
CL
2
1
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Superelevation
Road Plan View
Road Section View
2
0.5
CL
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Superelevation
Road Plan View
Road Section View
2
CL
-0.0
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Superelevation
Road Plan View
Road Section View
CL
-0.5
2
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Superelevation
Road Plan View
Road Section View
CL
-1
2
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Superelevation
Road Plan View
Road Section View
-.5
2
2
CL
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Superelevation
Road Plan View
Road Section View
CL
2
-2
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Superelevation
Road Plan View
Road Section View
CL
-3
3
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Super elevation
Road Section View
Road Plan View
CL
-4
4
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Superelevation
Road Plan View
Road Section View
CL
-3
3
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Superelevation
Road Plan View
Road Section View
CL
-2
2
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Superelevation
Road Plan View
Road Section View
CL
-1.5
2
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Superelevation
Road Plan View
Road Section View
CL
-1
2
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Superelevation
Road Plan View
Road Section View
CL
-0.5
2
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Superelevation
Road Plan View
Road Section View
CL
-0.0
2
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Superelevation
Road Plan View
Road Section View
CL
0.5
2
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Superelevation
Road Plan View
Road Section View
CL
1
2
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Superelevation
Road Plan View
Road Section View
CL
1.5
2
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Superelevation
Road Plan View
Road Section View
CL
2
2
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• In actual design of a horizontal curve, the
  engineer must select appropriate values of e and
  fs.
• Super-elevation value e is critical since
• high rates of super-elevation can cause vehicle
  steering problems at exits on horizontal curves
• and in cold climates, ice on road ways can reduce
  fs and vehicles are forced inwardly off the curve
  by gravitational forces.
• Values of e and fs can be obtained from
  AASHTO standards.

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Horizontal Curve Fundamentals

• For connecting straight tangent sections of
  roadway with a curve, several options are
  available.
• The most obvious is the simple curve, which is
  just a standard curve with a single, constant
  radius.
• Other options include
• compound curve, which consists of two or more
  simple curves in succession ,
• and spiral curves which are continuously changing
  radius curves.

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Basic Geometry
Horizontal Curve
Tangent
Tangent
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Tangent Vs. Horizontal Curve

• Predicting speeds for tangent and horizontal
  segments is different
• May actually be easier to predict speeds on
  curves than tangents
• Speeds on curves are restricted to a few well
  defined variables (e.g. radius, superelevation)
• Speeds on tangents are not as restricted by
  design variables (e.g. driver attitude)

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Elements of Horizontal Curves
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• Figure shows the basic elements of a simple
  horizontal curve. In this figure
• R is the radius (measured to center line of the
  road)
• PC is the beginning point of horizontal curve
• T is tangent length
• PI is tangent intersection
• ? is the central angle of the curve
• PT is end point of curve
• M is the middle ordinate
• E is the external distance
• L is the length of the curve

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Degree of Curve

• It is the angle subtended by a 100-ft arc along
  the horizontal curve.
• Is a measure of the sharpness of curve and is
  frequently used instead of the radius in the
  actual construction of horizontal curve.
• The degree of curve is directly related to the
  radius of the horizontal curve by

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• A geometric and trigonometric analysis of figure,
  reveals the following relationships

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Stopping Sight Distance and Horizontal Curve
Design
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• Adequate stopping sight distance must also be
  provided in the design of horizontal curves.
• Sight distance restrictions on horizontal curves
  occur when obstructions are present.
• Such obstructions are frequently encountered in
  highway design due to the cost of right of way
  acquisition and/or cost of moving earthen
  materials.

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• When such an obstruction exists, the stopping
  sight distance is measured along the horizontal
  curve from the center of the traveled lane.
• For a specified stopping sight distance, some
  distance, Ms, must be visually cleared, so that
  the line of sight is such that sufficient
  stopping sight distance is available.

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• Equations for computing SSD relationships for
  horizontal curves can be derived by first
  determining the central angle, ?s, for an arc
  equal to the required stopping sight distance.

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• Assuming that the length of the horizontal curve
  exceeds the required SSD, we have
• Combining the above equation with following
• we get

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• Rv is the radius to the vehicles traveled path,
  which is also assumed to be the location of the
  drivers eye for sight distance, and is again
  taken as the radius to the middle of the
  innermost lane,
• and ?s is the angle subtended by an arc equal to
  SSD in length.

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• By substituting equation for ?s in equation of
  middle ordinate, we get the following equation
  for middle ordinate
• Where Ms is the middle ordinate necessary to
  provide adequate stopping sight distance. Solving
  further we get

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Max e

• Controlled by 4 factors
• Climate conditions (amount of ice and snow)
• Terrain (flat, rolling, mountainous)
• Frequency of slow moving vehicles which
  influenced by high superelevation rates
• Highest in common use 10, 12 with no ice and
  snow on low volume gravel-surfaced roads
• 8 is logical maximum to minimized slipping by
  stopped vehicles

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Example
A curving roadway has a design speed of 110
km/hr. At one horizontal curve, the Super
elevation has been set at 6.0 and the
coefficient of side friction is found to be 0.10.
Determine the minimum radius of the curve that
will provide safe R 1102/9.8(0.100.06) 595
meters
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Radius Calculation (Example)

• Design radius example assume a maximum e of 8
  and design speed of 60 mph, what is the minimum
  radius?
• fmax 0.12 (from Green Book)
• Rmin _____602________________
• 15(0.08 0.12)
• Rmin 1200 feet

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Radius Calculation (Example)

• For emax 4?
• Rmin _____602_________ 15(0.04
  0.12)
• Rmin 1,500 feet

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Sight Distance Example

• A horizontal curve with R 800 ft is part of a
  2-lane highway with a posted speed limit of 35
  mph. What is the minimum distance that a large
  billboard can be placed from the centerline of
  the inside lane of the curve without reducing
  required SSD? Assume b/r 2.5 sec and a 11.2
  ft/sec2
• SSD is given as
• SSD 1.47vt _________v2____
• 30(__a___ ? G)
• 32.2
• SSD 1.47(35 mph)(2.5 sec) _____(35
  mph)2____ 30(__11.2___ ? 0)
• 
  32.2
• 246 feet

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Sight Distance Example

• m R(1 cos 28.65 S)
• R
• m 800 (1 cos 28.65 246) 9.43 feet 800
• (in radians not degrees)

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Horizontal Curve Example

• Deflection angle of a 4º curve is 55º25, PC at
  station 238 44.75. Find length of curve,T, and
  station of PC.
• D 4º
• ? 55º25 55.417º
• D _5729.58_ R _5729.58_ 1,432.4 ft
• R 4

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Horizontal Curve Example

• D 4º
• ? 55.417º
• R 1,432.4 ft
• L 2?R? 2?(1,432.4 ft)(55.417º) 1385.42ft
• 360 360

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Horizontal Curve Example

• D 4º
• ? 55.417º
• R 1,432.4 ft
• L 1385.42 ft
• T R tan ? 1,432.4 ft tan (55.417) 752.29 ft
• 2 2

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Stationing Example
Stationing goes around horizontal curve. For
previous example, what is station of PT? PC 238
44.75 L 1385.42 ft 13 85.42 Station at PT
(238 44.75) (13 85.42) 252 30.17
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Suggested Steps on Horizontal Design

1. Select tangents, PIs, and general curves make
   sure you meet minimum radii
2. Select specific curve radii/spiral and calculate
   important points (see lab) using formula or table
   (those needed for design, plans, and lab
   requirements)
3. Station alignment (as curves are encountered)
4. Determine super and runoff for curves and put in
   table (see next lecture for def.)
5. Add information to plans

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Geometric Design Horizontal Alignment (1)

• Horizontal curve
• Plan view, profile, staking, stationing
• type of horizontal curves
• Characteristics of simple circular curve
• Stopping sight distance on horizontal curves
• Spiral curve

Lecture 8
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Plan view and profile
plan
profile
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Surveying and Stationing

• Staking route surveyors define the geometry of a
  highway by staking out the horizontal and
  vertical position of the route and by marking of
  the cross-section at intervals of 100 ft.
• Station Start from an origin by stationing 0,
  regular stations are established every 100 ft.,
  and numbered 000, 12 00 (1200 ft), 20 45
  (2000 ft 45) etc.

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Horizontal Curve Types
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Curve Types

1. Simple curves with spirals
2. Broken Back two curves same direction (avoid)
3. Compound curves multiple curves connected
   directly together (use with caution) go from
   large radii to smaller radii and have R(large) lt
   1.5 R(small)
4. Reverse curves two curves, opposite direction
   (require separation typically for superelevation
   attainment)

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1. Simple Curve
Straight road sections
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2. Compound Curve
Straight road sections
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3. Broken Back Curve
Straight road sections
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4. Reverse Curve
Straight road sections
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5. Spiral
Straight road section
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Angle measurement
(a) degree
(b) Radian
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As the subtended arc is proportional to the
radius of the circle, then the radian measure of
the angle Is the ratio of the length of the
subtended arc to the radius of the circle
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• Define horizontal Curve
• Circular Horizontal Curve Definitions
• Radius, usually measured to the centerline of the
  road, in ft.
• Central angle of the curve in degrees
• PC point of curve (the beginning point of the
  horizontal curve)
• PI point of tangent intersection
• PT Point of tangent (the ending point of the
  horizontal curve)
• T tangent length in ft.
• M middle ordinate from middle point of cord to
  middle point of curve in ft.
• E External distance in ft.
• L length of curve
• D Degree of curvature (the angle subtended by a
  100-ft arc along the horizontal curve)
• C chord length from PC to PT

Note use chord in practice
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Key measures of the curve
Note converts from radians to
degrees
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Example A horizontal curve is designed with a
2000-ft radius, the curve has a tangent length of
400 ft and The PI is at station 103 00,
determine the stationing of the PT. Solution
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Sight Distance on Horizontal Curve Minimum sight
distance (for safety) should be equal to the safe
stopping distance
Sight Distance
Highway Centerline
M
PC
PT
Line of sight
Sight Obstruction
Centerline of inside lane
R
R
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To provide minimum sight distance
Or, by the degree of curvature, D
Try yourself
Where, ds safe stopping distance, ft.
and, v design speed, mi/h t
reaction time, secs G grade,
ds stopping distance, in ft.
a deceleration rate, 11.2 ft/s2,
recommended by Green Book
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Example A 6 degree curve (measured at the
centerline of the inside lane) is being designed
for a highway with a design speed of 70 mi/hr.,
the grade is level, the driver reaction time is
taken as 2.5 s (ASSHTOs standard value). What
is the closest place that a roadside object
(trees etc) can be Placed? Solution
The closest place of a object is given by
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Spiral Curve
Spiral curves are curves with a continuously
changing radii, they are sometimes used on
high-speed roadways with sharp horizontal curves
and are sometimes used to gradually introduce the
super elevation of an upcoming horizontal curve
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