Lec 23, Ch'16, pp'692708: Horizontal alignment objectives

1
Lec 23, Ch.16, pp.692-708 Horizontal alignment
(objectives)

• Understand how sight distance requirements are
  met in a horizontal curve section of an highway
• Be familiar with the characteristics of simple,
  compound, and reversed curves (Spiral curves will
  be covered in CE561)
• Understand some combinations of vertical and
  horizontal curves may result in favorable or
  unfavorable appearances due to optical
  foreshortening effect (Details will be covered in
  CE561. Here just get a feel of it.)

2
What we cover in class today

• How to determine appropriate horizontal curve
  radii when sight obstructions exist
• Curve equations for simple horizontal curves
• Curve equations for compound horizontal curves
• Curve equations for reverse horizontal curves
• A few examples of the combination of horizontal
  and vertical curves

3
Deriving the formula for determining the middle
ordinate
?
?
You can determine m, R, or S using this formula,
depending on the information known.
This is the correct form. The one in page 707 has
a typo.
(Review Example 16-6)
4
Range of lower values for stopping sight
distances on horizontal curves
D (degree of curvature) Central angle subtended
by the 100ft arc length
5
Formulas for simple circular curves that you want
to know
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Setting out of a simple horizontal curve

• Usually PI is given
• First find the station of PC ? Subtract T from
  the station of PI
• Then find the next whole station from PC. Compute
  l1 to find ?1.
• Then find D for L 100 ft
• Then find the left over of the curve length l2
  to determine the station of PT

T
(Review Example 16-7)
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Compound curves
R1 and R2 are usually known.
Eq. 16-39 and Eq. 16-40 on page 715 are missing a
bar above VG and VH.
8
Reverse curves
Reverse curves are seldom recommended. They are
absolutely NOT recommended for high-speed roads.
For high-speed roads, we must provide a tangent
section that will allow full development of
superelevation at both ends.
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Reverse curves (2)
Reverse curves usually consist of two simple
curves with equal radii turning in opposite
directions with a common tangent.
Remember that the deflection angle is one-half of
the central angle?
Hence,
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Visual effect of having a spiral curve before a
simple horizontal curve
The sharp corners at the juncture of curve and
tangent section may become obvious to from the
drivers seat especially when the radius is small.
Smooth transition from tangent to curve
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Visual effect caused by the combination of
horizontal and vertical curves (1)
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Visual effect caused by the combination of
horizontal and vertical curves (1a)
13
Visual effect caused by the combination of
horizontal and vertical curves (2)
14
Visual effect caused by the combination of
horizontal and vertical curves (3)
15
Visual effect caused by the combination of
horizontal and vertical curves (4)
16
Visual effect caused by the combination of
horizontal and vertical curves (5)
17
Video Cow Turn
A mix of low skid resistance, probably inadequate
superelevation for the posted speed, and wet
pavement causes
It is an entrance (on-ramp) to the Cross Bronx
Expressway (I-95 in Bronx) from another
expressway (off-ramp). I forgot the exact
location it is one of the circled ones