Quiz Answers

1
Quiz Answers

• What can be done to improve the safety of a
  horizontal curve?
• Make it less sharp
• Widen lanes and shoulders on curve
• Add spiral transitions
• Increase superelevation

2
Quiz Answers

• Increase clear zone
• Improve horizontal and vertical alignment
• Assure adequate surface drainage
• Increase skid resistance on downgrade curves

3
Some of Your Answers

• Decrease posted speed
• Add rumble strips
• Bigger or better signs
• Guardrail
• Better lane markers
• Sight distance
• Decrease radius

4
Superelevation and Spiral Curves

• CE 453 Lecture 18

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Objectives

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

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Other Issues Relating to Horizontal Curves

1. Need to coordinate with vertical and topography
2. Not always needed

MAXIMUM CENTERLINE DEFLECTION MAXIMUM CENTERLINE DEFLECTION
NOT REQUIRING HORIZONTAL CURVE NOT REQUIRING HORIZONTAL CURVE
Design Speed, mph Maximum Deflection
25 530'
30 345'
35 245'
40 215'
45 115'
50 115'
55 100'
60 100'
65 045'
70 045'

Source Ohio DOT Design Manual, Figure 202-1E Source Ohio DOT Design Manual, Figure 202-1E
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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 3-37 p. 186)
• 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, 2001 4th Ed.
12
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.
13
(No Transcript)
14
Source CalTrans Design Manual online,
http//www.dot.ca.gov/hq/oppd/hdm/pdf/chp0200.pdf
15
Same as point E of GB
Source Iowa DOT Standard Road Plans
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Attainment Location - WHERE

1. Superelevation must be attained over a length
   that includes the tangent and the curve (why)
2. Typical 66 on tangent and 33 on curve of
   length of runoff if no spiral
3. Iowa uses 70 and 30 if no spiral
4. 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)
• (Result is the edge slope is same as for Runoff
  segment)

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Length of Superelevation Runoff
r
a multilane adjustment factor Adjusts for total
width
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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.
22
Multilane Adjustment

• Runout and runoff must be adjusted for multilane
  rotation.
• See Iowa DOT 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 0.5
• 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.
27
Spiral Curve Transitions
28
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 recommended spiral lengths
  based on driver behavior rather than a specific
  equation. 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
36
Source Iowa DOT Design Manual
37
Source Iowa DOT Design Manual
38
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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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)
42
With Spirals
Removal of crown
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With Spirals
Transition of superelevation
Full superelevation
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(No Transcript)
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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 (delta /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 ((delta 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 who can tell 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