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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. Quiz Answers. Increase clear zone Improve horizontal and vertical alignment Assure adequate surface drainage

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quiz answers
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
quiz answers1
Quiz Answers
  • Increase clear zone
  • Improve horizontal and vertical alignment
  • Assure adequate surface drainage
  • Increase skid resistance on downgrade curves
some of your answers
Some of Your Answers
  • Decrease posted speed
  • Add rumble strips
  • Bigger or better signs
  • Guardrail
  • Better lane markers
  • Sight distance
  • Decrease radius
objectives
Objectives
  • Define superelevation runoff length and methods of attainment (for simple and spiral curves)
  • Calculate spiral curve length
other issues relating to horizontal curves
Other Issues Relating to Horizontal Curves
  • Need to coordinate with vertical and topography
  • Not always needed
attainment of superelevation general
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
superelevation transition section
Superelevation Transition Section
  • Tangent Runout Section + Superelevation Runoff Section
tangent runout section
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

superelevation runoff section
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
slide11

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.

slide12

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.

slide14

Source: CalTrans Design Manual online, http://www.dot.ca.gov/hq/oppd/hdm/pdf/chp0200.pdf

slide15

Same as point E of GB

Source: Iowa DOT Standard Road Plans

attainment location where
Attainment Location - WHERE
  • Superelevation must be attained over a length that includes the tangent and the curve (why)
  • 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)
minimum length of runoff for curve
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)
minimum length of tangent runout
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)

length of superelevation runoff
Length of Superelevation Runoff

r

α = multilane adjustment factor

Adjusts for total width

relative gradient g
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
maximum relative gradient g
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.

multilane adjustment
Multilane Adjustment
  • Runout and runoff must be adjusted for multilane rotation.
  • See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
length of superelevation runoff example
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 = 12eα

G

slide24
Lr = 12eα = (12) (0.04) (1.5)

G 0.5

Lr = 144 feet

tangent runout length example continued
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

slide26
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.

spiral curve transitions1
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
spirals
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
minimum length of spiral
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)

minimum length of spiral1
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)

maximum length of spiral
Maximum Length of Spiral
  • Safety problems may occur when spiral curves are too long – drivers underestimate sharpness of approaching curve (driver expectancy)
maximum length of spiral1
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)

length of spiral
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.

slide38

SPIRAL TERMINOLOGY

Source: Iowa DOT Design Manual

attainment of superelevation on spiral curves
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.
slide40

Same as point E of GB

With Spirals

Source: Iowa DOT Standard Road Plans RP-2

slide41

With Spirals

Tangent runout (A to B)

slide42

With Spirals

Removal of crown

slide43

With Spirals

Transition of superelevation

Full superelevation

transition example
Transition Example

Given:

  • PI @ station 245+74.24
  • D = 4º (R = 1,432.4 ft)
  •  = 55.417º
  • L = 1385.42 ft
with no spiral
With no spiral …
  • T = 752.30 ft
  • PC = PI – T = 238 +21.94
slide47
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.

slide48
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’ = 238+21.94 - 168.00 =

Station = 236+ 53.94

location example with spiral
Location Example – with spiral
  • Speed, e and NC as before and
  •  = 55.417º
  • PI @ Station 245+74.24
  • R = 1,432.4’
  • Lr was 144’, so set Ls = 150’
location example with spiral1
Location Example – with spiral

See Iowa DOT design manual for more equations:

http://www.dot.state.ia.us/design/00_toc.htm#Chapter_2

  • Spiral angle Θs = Ls * D /200 = 3 degrees
  • P = 0.65 (calculated)
  • Ts = (R + p ) tan (delta /2) + k = 827.63 ft
location example with spiral2
Location Example – with spiral
  • TS station = PI – Ts

= 245+74.24 – 8 + 27.63

= 237+46.61

Runoff length = length of spiral

Tangent runout length = Lt = (eNC / ed ) x Lr

= 2% / 4% * 150’ = 75’

Therefore: Transition from Normal crown begins at (237+46.61) – (0+75.00) = 236+71.61

slide52

Location Example – with spiral

With spirals, the central angle for the circular curve is reduced by 2 * Θs

Lc = ((delta – 2 * Θs) / D) * 100

Lc = (55.417-2*3)/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)

slide53

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???)

notes iowa dot
Notes – Iowa DOT

Source: Iowa DOT Standard Road Plans

Note: Draw a sketch and think about what the last para is saying