Horizontal Alignment

1
Horizontal Alignment

• CE 453 Lecture 16

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Objectives

• Identify curve types and curve components
• Learn basics of curve design
• See http//www.fhwa.dot.gov/environment/flex/ch05
  .htm (Chapter 5 from FHWAs Flexibility in
  Highway Design)

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Horizontal Alignment

• Design based on appropriate relationship between
  design speed and curvature and their relationship
  with side friction and superelevation
• Along circular path, vehicle attempts to maintain
  its direction (via inertia)
• Turning the front wheels, side friction and
  superelevation generate an acceleration to
  offset inertia

4
Horizontal Alignment

• Tangents
• Curves
• Transitions
• Curves require superelevation (next lecture)
• Reason for super banking of curve, retard
  sliding, allow more uniform speed, also allow use
  of smaller radius curves (less land)

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Radius Calculation

• Rmin ___V2______
• 15(e f)
• Where
• Rmin is the minimum radius in feet
• V velocity (mph)
• e superelevation
• f friction (15 gravity and unit conversion)
  

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Radius Calculation

• Rmin uses max e and max f (defined by AASHTO,
  DOT, and graphed in Green Book) and design speed
• f is a function of speed, roadway surface,
  weather condition, tire condition, and based on
  comfort drivers brake, make sudden lane
  changes, and change position within a lane when
  acceleration around a curve becomes
  uncomfortable
• AASHTO f is from 0.5 _at_ 20 mph with new tires
  and wet pavement to 0.35 _at_ 60 mph
• f decreases as speed increases (less
  tire/pavement contact)

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Max e

• Controlled by 4 factors
• Climate conditions (amount of ice and snow)
• Terrain (flat, rolling, mountainous)
• Type of area (rural or urban)
• Frequency of slow moving vehicles who might be
  influenced by high superelevation rates

8
Max e

• Highest in common use 10, 12 with no ice and
  snow on low volume gravel-surfaced roads
• 8 is logical maximum to minimize slipping by
  stopped vehicles, considering snow and ice
• Iowa uses a maximum of 6 on new projects
• For consistency use a single rate within a
  project or on a highway

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Source A Policy on Geometric Design of Highways
and Streets (The Green Book). Washington, DC.
American Association of State Highway and
Transportation Officials, 2001 4th Ed.
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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? (urban situation)
• Rmin _____602________________
• 15(0.04 0.12)
• Rmin 1,500 feet

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Radius Calculation (Example)

• For emax 2? (rotated crown)
• Rmin _____602________________
• 15(0.02 0.12)
• Rmin 1,714 feet

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Radius Calculation (Example)

• For emax -2? (normal crown, adverse direction)
• Rmin _____602________________
• 15(-0.02 0.12)
• Rmin 2,400 feet

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Curve Types

• Simple curves with spirals (why spirals)
• Broken Back two curves same direction (avoid)
• 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)
• Reverse curves two curves, opposite direction
  (require separation typically for superelevation
  attainment)

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Important Components of Simple Circular Curve

• See ftp//165.206.254.150/dotmain/design/dmanual/
  English/e02a-01.pdf
•  
• 1.     See handout
• 2.     PC, PI, PT, E, MO, and ?
• 3.     L 2(?)R(?)/360
• 4.     T R tan (?/2)

Direction of stationing
Source Iowa DOT Design Manual
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Sight Distance for Horizontal Curves

• Location of object along chord length that blocks
  line of sight around the curve
• m R(1 cos 28.65 S/R)
• Where
• m line of sight
• S stopping sight distance
• R radius

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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 p/r 2.5 and a 11.2
  ft/sec2
• SSD 1.47vt _________v2____
• 30(__a___ ? G)
• 32.2

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Sight Distance Example

• SSD 1.47(35 mph)(2.5 sec)
• _____(35 mph)2____ 246 feet
• 30(__11.2___ ? 0)
• 32.2

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Sight Distance Example

• m R(1 cos 28.65S/R)
• m 800 (1 cos 28.65246/800) 9.43 feet

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Horizontal Curve Example

• Deflection angle of a 4º curve is 55º25, PI at
  station 24597.04. Find length of curve,T, and
  station of PT.
• 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? First
calculate the station of the PC PI
24597.04 PC PI T PC 24597.04 752.29
23844.75
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Stationing Example (cont)
PC 23844.75 L 1385.42 ft Station at PT PC
L PT 23844.75 1385.42 25230.17
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Suggested Steps in Horizontal Design

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

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HOMEWORK

• Your team is responsible for the design of a
  small roadway project in Iowa. Your individual
  task is to design a horizontal curve to the right
  using an even value radius slightly larger than
  the minimum radius curve. Use a design speed of
  55 mph and a superelevation rate of 4. Assume
  the PI has a station of 35244.97 the ? (delta)
  of the curve is 35 24 55.

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HOMEWORK

• Assignment Summary
• Reading carefully the design guidance with
  special attention to the items to be included on
  the plans, calculate all of the values to be
  shown on a plan set for this curve. Be sure to
  calculate the stations of the PC and PT in
  addition to the values listed.

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HOMEWORK

• At this time do not concern yourself with
  superelevation runoff just use the design speed
  and superelevation rate to determine the minimum
  radius curve allowable. It may help you to
  create a list of the items to be included before
  doing your calculations.

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HOMEWORK

• Repeat your calculations, using a design speed of
  60 mph and the same 4 superelevation rate. Your
  PI station and ? will remain unchanged.
• Assignment due Friday.

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HOMEWORK

• Assignment Summary
• Assignment handout
• DOT horizontal curve handout

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HOMEWORK

• Refer to the Iowa DOT Design Manual to find
  guidance on the design of horizontal curves at
  ftp//165.206.203.34/design/dmanual/02a-01.pdf .