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## Geometric Design (II)

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### Geometric Design (II) ... and the side-friction factor. The minimum radius serves not only as a constraint on the geometric design of the roadway, ... – PowerPoint PPT presentation

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Title: Geometric Design (II)

1
Geometric Design (II)
2
Learning Objectives
• To calculate minimum radius of horizontal curve
• To understand design concepts for transition
curves and compute min length
• To understand the role of SSD in horizontal and
vertical design
• To define and apply grade considerations
• To develop vertical curves
• (Chapter 6.1 6.4)

3
Horizontal Curve
• Curve requiring the most centripetal force for
the given speed
• Given emax, umax, Vdesign

R
4
Horizontal Curve Properties
• Based on circular curve
• D degree of curve
• ? central angle
• T length of tangent
• L length of curve
• LC long chord
• M middle ordinate dist
• E external dist

5
Horizontal Design Iterations
• Design baseline
• Curve radius above the minimum
• Superelevation and side-friction factor not
exceeding the maximum values
• Design is revised to consider
• cost, environmental impacts, sight distances,
aesthetic consequences, etc.

6
Horizontal Curve Sight Distance
• Sight line is a chord of the circular curve
• Sight Distance is curve length measured along
centerline of inside lane

7
Horizontal Curve Sight Distance
• Figure 6-10

8
Transition Curves
• Gradually changing the curvature from tangents to
circular curves

Without Transition Curves
With Transition Curves
9
Transition Curves
• Gradually changing the curvature from tangents to
circular curves
• Use a spiral curve
• L min length of spiral (ft)
• V speed (mph)
• C rate of increase of centrifugal accel
(ft/sec3), 13

10
Transitional Curves
• Gradually changing the cross-section of the
roadway from normal to superelevated (Figure 6-9)

Keep water drainage in mind while considering all
of the available cross-section options
11
Vertical Alignment
Reduced Speed
Increased Speed
12
Vertical Alignment
• measure of inclination or slope, rise over the
run
• Cars negotiate 4-5 grades without significant
speed reduction
• Trucks significant speed changes
• 5 increase on short descending grades
• 7 decrease on short ascending grades

13
functional class, and design speed

Rural Arterials
Terrain 60mph 70mph
Level 3 3
Rolling 4 4
Mountainous 6 5
14
• Maximum length which a loaded truck can travel
without unreasonable speed reduction
• Based on accident involvement rates with 10mph
speed reduction as threshold

15
General Design Speed Reduction
16
Vertical Curves
• To provide transition between two grades
• Consider
• Drainage (rainfall)
• Driver safety (SSD)
• Driver comfort
• Use parabolic curves
• Crest vs Sag curves

17
Vertical Curves
18
Vertical Curves
• Given
• G1, G2 initial final grades in percent
• L curve length (horizontal distance)
• ? Develop the actual shape of the vertical curve

point of vertical intersection
PVI
point of verticaltangency
point of vertical curvature
G1
G2
19
Vertical Curves
• Define curve so that PVI is at a horizontal
distance of L/2 from PVC and PVT
• Provides constant rate of change of grade

A
G1
G2
20
Example
• G1 2
• G2 -4
• Design speed 70 mph
• Is this a crest or sag curve?
• What is A?

21
Vertical Curves
• Major control for safe operation is sight
distance
• MSSD should be provided in all cases (use larger
sight distance where economically and physically
feasible)
• For sag curves, also concerned with driver
comfort (large accelerations due to both
gravitational and centrifugal forces)

22
Crest Vertical Curves
• Critical length of curve, L, is where sight line
is tangent to the crest
• Assume driver eye height (H1) 3.5 ft and object
height (H2) 2.0 ft and SMSSD

23
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28
Sag VC - Design Criteria