HORIZONTAL ALIGNMENT

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HORIZONTAL ALIGNMENT

• Fall 2008

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Horizontal Alignment
Geometric Elements of Horizontal Curves
Transition or Spiral Curves
Superelevation Design
Sight Distance
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Simple Curve
Circular Curve
Tangent
PC
PT
Point of Tangency
Point of Curvature
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Curve with Spiral Transition
Circular Curve
Spiral
Tangent
CS
SC
ST
TS
Curve to Spiral
Spiral to Curve
Spiral to Tangent
Tangent to Spiral
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Design Elements of Horizontal Curves
Deflection Angle
Also known as ?
Deflection Angle
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Design Elements of Horizontal Curves
Larger D smaller Radius
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Design Elements of Horizontal Curves
EExternal Distance MLength of Middle Ordinate
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Design Elements of Horizontal Curves
LCLength of Long Cord
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Basic Formulas
Basic Formula that governs vehicle operation on a
curve
Where, e superelevation f side friction
factor V vehicle speed (mph) R radius of
curve (ft)
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Basic Formulas
Minimum radius
Where, e superelevation f side friction
factor V vehicle speed (mph) R radius of
curve (ft)
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Minimum Radius with Limiting Values of e and f
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Superelevation Design
Desirable superelevation for
R gt Rmin Where, V design speed in ft/s or
m/s g gravity (9.81 m/s2 or 32.2 ft/s2) R
radius in ft or m Various methods are available
for determining the desirable superelevation, but
the equation above offers a simple way to do it.
The other methods are presented in the next few
overheads.
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Methods for Estimating Desirable Superelevation

• Method 1
• Superelevation and side friction are directly
  proportional to the inverse of the radius
  (straight relationship between 1/R0 and 1/R
  1/Rmin)
• Method 2
• Side friction is such that a vehicle traveling at
  the design speed has all the acceleration
  sustained by side friction on curves up to those
  requiring fmax
• Superelevation is introduced only after the
  maximum side friction is used

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• Method 3
• Superelevation is such that a vehicle traveling
  at the design speed has all the lateral
  acceleration sustained by superelevation on
  curves up to those required by emax
• No side friction is provided on flat curves
• May result in negative side friction
• Method 4
• Same approach as Method 3, but use average
  running speed rather than design speed
• Uses speeds lower than design speed
• Eliminate problems with negative side friction
• Method 5
• Superelevation and side friction are in a
  curvilinear relationship with the inverse of the
  radius of the curve, with values between those of
  methods 1 and 3
• Represents a practical distribution for
  superelevation over the range of curvature
• This is the method used for computing values
  shown in Exhibits 3-25 to 3-29

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Five Methods
f
M1
M2
fmax
Side Friction Factor
e 0
emax
M5
M3
1/R
Reciprocal of Radius
M4
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Selection of fdesign and edesign (Method 5)
f
fmax (for the design speed)
Side Friction Factor
e 0
fdesign
emax (for the design speed)
1/R
Reciprocal of Radius
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Selection of fdesign and edesign
f
Rf V2/(gfmax)
Rmin V2/g(fmax emax)
fmax
Side Friction Factor
e 0
fdesign
emax
Ro V2/(gemax)
1/R
Reciprocal of Radius
R0 f 0, e emax
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Selection of fdesign and edesign
f
fdesign a(1/R)ß(1/R)2
fmax (for the design speed)
Side Friction Factor
a fmaxRmin1-Rmin/(R0-Rmin)
e 0
fdesign
ß fmaxRmin3/(R0-Rmin)
emax (for the design speed)
1/R
Reciprocal of Radius
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Superelevation Design for High Speed Rural and
Urban Highways
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Example Design Speed 100 km/h fmax 0.128 emax
0.06 Question? What should be the design
friction factor and design superelevation for a
curve with a radius of 600 m?
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1. Compute Rf, R0, and Rmin Rf V2/(gfmax)
27.782 / (9.81 x 0.128) 615 m R0 V2/(gemax)
27.782 / (9.81 x 0.06) 1311 m Rmin
V2/g(fmax emax) 27.782 / 9.81(0.1280.06)
Rmin 418 m
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Selection of fdesign and edesign (example)
f
fmax 0.128
Side Friction Factor
e 0
fdesign
emax 0.06
1 / 615
1 / 418
1 / 1311
1/R
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2. Compute a and ß a 0.128 x 418 x 1 418 /
(1311 418) 28.45 m ß 0.128 x 4183 /
(1311 418) 10502 m2 3. Compute fdesign and
edesign First, estimate the right-hand side of
equation for designing superelevation e f
V2/(gR) 27.782 / (9.81 x 600)
0.131 Then, fdesign 28.45 / 600 10502 /
6002 0.076 edesign 0.131 0.076 0.055 (lt
emax 0.06)
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Selection of fdesign and edesign (example)
f
fmax 0.128
Side Friction Factor
e 0
fdesign
emax 0.06
0.076
1 / 615
1 / 418
1 / 1311
1/R
1 / 600
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Selection of fdesign and edesign (example)
R600 ft
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Design of Horizontal Alignment

• Important considerations
• Governed by four factors
• Climate conditions
• Terrain (flat, rolling, mountainous)
• Type of area (rural vs urban)
• Frequency of slow-moving vehicles
• Design should be consistent with driver
  expectancy
• Max 8 for snow/ice conditions
• Max 12 low volume roads
• Recurrent congestion suggest lower than 6

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Method 1Centerline
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Method 2Inside Edge
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Method 3Outside Edge
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Method 4Straight Cross Slope
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Which Method?

• In overall sense, the method of rotation about
  the centerline (Method 1) is usually the most
  adaptable
• Method 2 is usually used when drainage is a
  critical component in the design
• In the end, an infinite number of profile
  arrangements are possible they depend on
  drainage, aesthetic, topography among others

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Example where pivot points are important
Bad design
Pivot points
Good design
Median width
15 ft to 60 ft
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Transition Design Control

• The superelevation transition consists of two
  components
• The superelevation runoff length needed to
  accomplish a change in outside-lane cross slope
  from zero (flat) to full superelevation
• The tangent runout The length needed to
  accomplish a change in outside-lane cross slope
  rate to zero (flat)

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Transition Design Control
Tangent Runout
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Transition Design Control
Superelevation Runoff
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Transition Design Control
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Transition Design Control
http//techalive.mtu.edu/modules/module0003/Supere
levation.htm
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Minimum Length ofSuperelevation Runoff
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Minimum Length ofSuperelevation Runoff
? relative gradient in previous overhead
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Minimum Length ofSuperelevation Runoff
Values for n1 and bw in equation
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Minimum Length ofTangent Runout
See Exhibit 3-32 for values of Lt and Lr
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Superelevation Runoff
Location 1/3 on curve
Location 2/3 on tangent
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Superelevation Runoff
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Transition Curves -Spirals

• All motor vehicles follow a transition path as it
  enters or leaves a circular horizontal curve
  (adjust for increases in lateral acceleration)
• Drivers can create their own path or highway
  engineers can use spiral transitional curves
• The radius of a spiral varies from infinity at
  the tangent end to the radius of the circular
  curve at the end that adjoins the curve

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Transition Curves -Spirals
Need to verify for maximum and minimum lengths
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Transition Curves
Superelevation runoff should be accomplished on
the entire length of the spiral curve transition
Equation for tangent runout when Spirals are used
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Sight distance on Horizontal Curve

• The sight distance is measured from the
  centerline of the inside lane
• Need to measure the middle-ordinate values
  (defined as M)
• Values of M are given in Exhibit 3-53
• Note Now M is defined as HSO or Horizontal
  sightline offset.

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