Superelevation and Spiral Curves

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Superelevation and Spiral Curves

• CE 453 Lecture 17

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Objectives

• Define superelevation runoff length and methods
  of attainment (for simple and spiral curves)
• Calculate spiral curve length

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Issues Relating to Horizontal Curves

• Need to coordinate with vertical and topography
• Not always needed

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Attainment of Superelevation - General

• Tangent to superelevation
• Must be done gradually over a distance without
  appreciable reduction in speed or safety and with
  comfort
• Change in pavement slope should be consistent
  over a distance
• Methods (Exhibit 3-40 pgs. 194 195)
• Rotate pavement about centerline
• Rotate about inner edge of pavement
• Rotate about outside edge of pavement

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Superelevation Transition Section

• Tangent Runout Section Superelevation Runoff
  Section

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Tangent Runout Section

• Length of roadway needed to accomplish a change
  in outside-lane cross slope from normal cross
  slope rate to zero

For rotation about centerline
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Superelevation Runoff Section

• Length of roadway needed to accomplish a change
  in outside-lane cross slope from 0 to full
  superelevation or vice versa
• For undivided highways with cross-section rotated
  about centerline

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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, 2004 5th Ed.
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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, 2004 5th Ed.
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(No Transcript)
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Source CalTrans Design Manual online,
http//www.dot.ca.gov/hq/oppd/hdm/pdf/chp0200.pdf
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Same as point E of GB
Source Iowa DOT Standard Road Plans
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Attainment Location - WHERE

• Superelevation must be attained over a length
  that includes the tangent and the curve
• Typical 66 on tangent and 33 on curve of
  length of runoff if no spiral
• Iowa uses 70 and 30 if no spiral
• Super runoff is all attained in spiral if used
  (see lab manual (Iowa spiral length runoff
  length))

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Minimum Length of Runofffor curve

• Lr based on drainage and aesthetics
• rate of transition of edge line from NC to full
  superelevation traditionally taken at 0.5 ( 1
  foot rise per 200 feet along the road)
• current recommendation varies from 0.35 at 80
  mph to 0.80 for 15mph (with further adjustments
  for number of lanes)

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Minimum Length of Tangent Runout

• Lt eNC x Lr
• ed
• where
• eNC normal cross slope rate ()
• ed design superelevation rate
• Lr minimum length of superelevation runoff (ft)

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Length of Superelevation Runoff
r
a multilane adjustment factor Adjusts for total
width Also note that e and G can be decimals or
percents, as long as consistent
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Relative Gradient (G)

• Maximum longitudinal slope
• Depends on design speed, higher speed gentler
  slope. For example
• For 15 mph, G 0.78
• For 80 mph, G 0.35
• See table, next page

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Maximum Relative Gradient (G)
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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Multilane Adjustment

• Runout and runoff must be adjusted for multilane
  rotation.
• See Iowa DOT Design Manual section 2A-2 and
  Standard Road Plan RP-2

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Length of Superelevation Runoff Example

• For a 4-lane divided highway with cross-section
  rotated about centerline, design superelevation
  rate 4. Design speed is 50 mph. What is the
  minimum length of superelevation runoff (ft)
• Lr 12ea
• G

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• Lr 12ea (12) (0.04) (1.5)
• G 0.005
• Lr 144 feet

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Tangent runout length Example continued

• LT (eNC / ed ) x Lr
• as defined previously, if NC 2
• Tangent runout for the example is
• LT 2 / 4 144 72 feet

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• From previous example, speed 50 mph, e 4
• From chart runoff 144 feet, same as from
  calculation

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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Spiral Curve Transitions
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Spiral Curve Transitions

• Vehicles follow a transition path as they enter
  or leave a horizontal curve
• Combination of high speed and sharp curvature can
  result in lateral shifts in position and
  encroachment on adjoining lanes

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Spirals

• Advantages
• Provides natural, easy-to-follow path for drivers
  (less encroachment, promotes more uniform
  speeds), lateral force increases and decreases
  gradually
• Provides location for superelevation runoff (not
  part on tangent/curve)
• Provides transition in width when horizontal
  curve is widened
• Aesthetic

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Minimum Length of Spiral

• Possible Equations
• Larger of (1) L 3.15 V3
• RC
• Where
• L minimum length of spiral (ft)
• V speed (mph)
• R curve radius (ft)
• C rate of increase in centripetal acceleration
  (ft/s3) use 1-3 ft/s3 for highway)

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Minimum Length of Spiral

• Or (2) L (24pminR)1/2
• Where
• L minimum length of spiral (ft)
• R curve radius (ft)
• pmin minimum lateral offset between the
  tangent and circular curve (0.66 feet)

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Maximum Length of Spiral

• Safety problems may occur when spiral curves are
  too long drivers underestimate sharpness of
  approaching curve (driver expectancy)

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Maximum Length of Spiral

• L (24pmaxR)1/2
• Where
• L maximum length of spiral (ft)
• R curve radius (ft)
• pmax maximum lateral offset between the
  tangent and circular curve (3.3 feet)

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Length of Spiral

• AASHTO also provides desirable spiral lengths
  based on driver behavior rather than a specific
  equation (Exhibit 3-37). See Table 16.12 of
  text and the associated tangent runout lengths in
  Table 16.13.
• Superelevation runoff length is set equal to the
  spiral curve length when spirals are used.
• Design Note For construction purposes, round
  your designs to a reasonable values e.g.
• Ls 147 feet, round it to
• Ls 150 feet.

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Source Iowa DOT Design Manual
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Source Iowa DOT Design Manual
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Source Iowa DOT Design Manual
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SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
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Attainment of superelevation on spiral curves

• See sketches that follow
• Normal Crown (DOT pt A)
• Tangent Runout (sometimes known as crown runoff)
  removal of adverse crown (DOT A to B) B TS
• Point of reversal of crown (DOT C) note A to B
  B to C
• Length of Runoff length from adverse crown
  removed to full superelevated (DOT B to D), D
  SC
• Fully superelevate remainder of curve and then
  reverse the process at the CS.

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Image

• http//techalive.mtu.edu/modules/module0003/Supere
  levation.htm

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Same as point E of GB
With Spirals
Source Iowa DOT Standard Road Plans RP-2
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With Spirals
Tangent runout (A to B)
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With Spirals
Removal of crown
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With Spirals
Transition of superelevation
Full superelevation
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Transition Example

• Given
• PI _at_ station 24574.24
• D 4º (R 1,432.4 ft)
• ? 55.417º
• L 1385.42 ft

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With no spiral

• T 752.30 ft
• PC PI T 238 21.94

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• For
• Design Speed 50 mph
• superelevation 0.04
• normal crown 0.02
• Runoff length was found to be 144
• Tangent runout length
• 0.02/ 0.04 144 72 ft.

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• Where to start transition for superelevation?
• Using 2/3 of Lr on tangent, 1/3 on curve for
  superelevation runoff
• Distance before PC Lt 2/3 Lr
• 72 2/3 (144)
  168
• Start removing crown at
• PC station 168 23821.94 - 168.00
• Station 236 53.94

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Location Example with spiral

• Speed, e and NC as before and
• ? 55.417º
• PI _at_ Station 24574.24
• R 1,432.4
• Lr was 144, so set Ls 150

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Location Example with spiral

• See Iowa DOT design manual for more equations
• http//www.dot.state.ia.us/design/00_toc.htmChapt
  er_2
• Spiral angle Ts Ls D /200 3 degrees
• P 0.65 (calculated)
• Ts (R p ) tan (? /2) k 827.63 ft

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Location Example with spiral

• TS station PI Ts
• 24574.24 8 27.63
• 23746.61
• Runoff length length of spiral
• Tangent runout length Lt (eNC / ed ) x Lr
• 2 / 4 150 75
• Therefore Transition from normal crown begins
  at (23746.61) (075.00) 23671.61

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Location Example with spiral

• With spirals, the central angle for the
  circular curve is reduced by 2 Ts
• Lc ((? 2 Ts) / D) 100
• Lc (55.417-23)/4)100 1235.42 ft
• Total length of curves Lc 2 Ls 1535.42
• Verify that this is exactly 1 spiral length
  longer than when spirals are not used (extra
  credit for anyone who shows me why provide a
  one-page memo by Monday)

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Location Example with spiral

• Also note that the tangent length with a spiral
  should be longer than the non-spiraled curve by
  approximately ½ of the spiral length used. (good
  check but why???)

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Notes Iowa DOT
Source Iowa DOT Standard Road Plans
Note Draw a sketch and think about what the last
para is saying