Horizontal Alignment

1
Horizontal Alignment
2
Horizontal Curves

• Provide transition of a roadway between two
  straight sections
• Two key factors
• Superelevation ? number of vertical feet of
  rise per 100 feet of horizontal distance
• Coefficient of side friction fs - function of
  design speed

3
(No Transcript)
4
Centripetal or Centrifugal?

• As a vehicle moves in a circular path
• Centripetal acceleration acts on the vehicle in
  the direction of the center of the curve
• The acceleration is sustained by
• Component of the vehicles weight related to the
  roadway superelevation
• Side friction developed between the vehicles
  tires and the pavement surface
• Or a combination of the two

5
Centrifugal Force

• Imaginary force that drivers believe is pushing
  them outward while maneuvering a curve
• In fact, the force they feel is the vehicle being
  accelerated inward towards the center of the curve

6
Centripetal Acceleration

• Is counter-balanced by two factors
• Superelevation
• Side Friction Factor
• Research has been conducted (dated) that has
  established limiting values for superelevation
  rate (e max) and side friction demand (f max)
• Applying the limiting values results in the
  minimum curve radius for various design speeds

7
Superelevation

• Limits of the rate superelevation are related to
• Climate
• Ice and snow can slow vehicles. Should not
  create a situation where these vehicles slide
  into the center of the curve when traveling
  slowly or standing still.
• Constructability (cost)
• Adjacent land use
• Frequency of slow moving vehicles

8
Superelevation

• Too much super
• When traveling slowly, must steer up the slope or
  against the horizontal curve to maintain proper
  path
• Undesirable to have such situations when slow
  traveling traffic can occur often (urban areas
  with congestion)
• Considerations for SUV traffic, high center of
  gravity, can cause roll-overs on such designs

9
Side Friction Factor

• The vehicles need for side friction to maintain
  path on curve
• Upper limit of side friction is the point at
  which a tire would begin to skid, point of
  impending skid
• We design for safety, so f values substantially
  less than this

10
Side Friction Factor

• How do we choose maximum side friction factors
  for use in design?
• We measure the level of centripetal or lateral
  acceleration that causes drivers to react
  instinctively to choose a lower speed.
• We set this as the maximum side friction factor.

11
Maximum Rates of Superelevation

• Controlled by four factors
• Climate conditions (snow/ice regions)
• Terrain conditions (flat, rolling, mountainous)
• Type of area (rural, urban, suburban)
• Frequency of very slow-moving vehicles
• Conclusion no universal e max can be set
• However, for similar areas, a consistent maximum
  superelevation should be selected

12
Recommended Practice

• 12 percent superelevation should not be exceeded
• 4 or 6 percent superelevation is applicable for
  urban design with little constraints
• Superelevation may be omitted on low-speed urban
  streets where severe constraints exist

13
Minimum Radius

• Controls design speed
• Can be determined from the max superelevation and
  the max side friction factor
• Can be calculated from equation 3.34 or
  determined from Table 3.5

14
Example Minimum Radius

• 70 mph design speed e 8 fs 0.10
• Determine the minimum radius of curve (measured
  to the traveled path).

15
Example Continued
16
Elements of a Simple Circular Horizontal Curve
17
Important Relationships
18
Example

• horizontal curve with 2000 radius 400 tangent
  length PI is at station 10300
• Determine the stationing of the PT

19
Example continued

• Determine the central angle, ?. Next determine
  the Length of Curve, L.

20
Example continued

• Knowing tangent length is 400 and PI is at
  10300
• stationing PC10300 minus 4009900
• Horizontal curve stationing is measured along the
  alignment of the road
• stationing of PT stationing of PCL
• 9900 plus 789.58 10689.58

21
In-Class Problems

• Calculate the maximum degree of curve and minimum
  radius of a simple circular curve with an
  external angle of 100º. Design speed of 50mph
  fmax 0.14 max e 0.10.

22
Stopping Sight Distance Horizontal Curve Design

• Adequate sight distance must be provided in the
  design of horizontal curves
• Cost of right of way or the cost of moving
  earthen materials often restrict design options
• When such obstructions exist, stopping sight
  distance is checked and measured along the
  horizontal curve from the center of the traveled
  lane

23
(No Transcript)
24
Sight Distance Relationships
25
Sight Distance Example

• Horizontal curve with 2000 radius 12lanes
  60mph design speed. Determine the distance that
  must be cleared from the inside edge of the
  inside lane to provide sufficient stopping sight
  distance.

26
Sight Distance Example Continued
SSD is determined from Table 3.1 for 60mph
design speed
27
Vertical Alignment

• Specifies the elevation of points along a roadway
• Provides a transition between two grades
• Sag curves and crest curves
• Equal-tangent curves - half the curve length
  positioned before the PVI half after

28
(No Transcript)
29
(No Transcript)
30
Vertical Curves

• Controlling factor sight distance
• Stopping sight distance should be provided as a
  minimum
• Rate of change of grade should be kept within
  tolerable limits
• Drainage of sag curves is important
  consideration, grades not less than 0.5 needed
  for drainage to outer edge of roadway

31
Vertical Alignment Relationships
32
Example Problem Vertical Curve

• A vertical curve crosses a 4 diameter pipe at
  right angles. Pipe at sta 11085 with centerline
  elevation of 1091.60. PVI at sta 11000
  elevation 1098.4. Equal tangent curve, 600
  long with initial and final grades of 1.2 and
  -1.08. Using offsets determine the depth below
  the surface of the curve the top of the pipe and
  determine the station of the highest point of the
  curve.

33
Sight Distance

• Equations 3-43 and 3-44 describe the required
  sight distance for crest vertical curves
• Stopping sight distance equations for crest
  vertical curves given in equations 3-45 and 3-46
• Passing sight distance equations for crest
  vertical curves given in equations 3-47 and 3-48
  (7-10 times longer than stopping sight distance)

34
Stopping Sight Distance and Crest Vertical Curves
35
SSD Crest Curve Relationships
H13.5 H22.0 Assume SSSD
36
Example Problem

• 70mph design speed equal tangent vertical curve
  needed to connect 1.0 with -2.0.
• Determine min length of curve to meet SSD
  requirements.

37
Sag Vertical Curves

• Four criteria for establishing length of sag
  curves
• Headlight sight distance
• Passenger comfort
• Drainage control
• General appearance

38
Headlight Sight Distance

• At night, the portion of highway that is visible
  to the driver is dependent on the position of the
  headlights and the direction of the light beam
• Headlights are assumed to be 2 ft (600 mm) and
  1-degree upward divergence of the light beam from
  the longitudinal axis of the vehicle
• Equations 3-19 through 3-23 describe the required
  sight distance for sag curves

39
Sag Vertical Curve Length

• The most controlling factor is headlight sight
  distance
• If for economic reasons such lengths cannot be
  provided, fixed source lighting should be
  provided to assist the driver.

40
(No Transcript)
41
Passing Sight Distance Crest Vertical Curve
Design

• Only a factor for vertical curves
• A consideration for two-lane highways
• Sag curves have unobstructed sight distance
• Assume driver eye height and height of object on
  roadway surface both 3.5