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Horizontal Alignment
Highway Design Project
Horizontal Alignment
Amir Samimi
Civil Engineering Department
Sharif University of Technology
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Curve Types Types of Circular Curves
1..S p e curves
Simple cu ves with
w t spirals
sp a s Si l Curve
Simple C Compound Curves Broken-Back Curves
2. Broken Back – two curves same direction (avoid)
3. Compound curves: multiple curves connected directly
together (use with caution) go from large radii to smaller
radii and have R(large) < 1.5 R(small)
4. Reverse curves – two curves, opposite direction (require
Broken-Back
B k B kC Curves should
h ld beb avoided
id d if
separation typically for superelevation attainment) possible. It is better to replace the Curves with a
Reverse Curves
larger radius circular curve.
A tangent should be placed between reverse
Curves.
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Typical Configurations of Curves Horizontal Alignment
Spirals are typically placed Objective:
between tangents and circular Geometry of directional transition to ensure:
curves to provide a transition Safety
from a normal crown section Comfort Δ
to a superelevated one. Primary challenge
Transition between two directions
Spirals are typically used at Horizontal
H i t l curves
intersections to increase the Fundamentals
room for large trucks to make Circular curves
turning movements. Superelevation
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Horizontal Alignment Horizontal Curve Fundamentals
1..Tangents
a ge ts
2. Curves
3. Transitions T R tan
2
Curves require superelevation
100
Retard sliding,
g, L R
Allow more uniform speed, 180 D
Allow use of smaller radii curves (less land)
180
100
18 ,000
D D = degree of curvature
R R (Delta / L = D / 100)
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Horizontal Curve Fundamentals Example
A horizontal curve is designed with a 1500 ft. radius. The
tangent length is 400 ft. and the PT station is 20+00. What are
the PI and PT stations?
1
E R 1
cos 2
M R 1 cos
2
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Superelevation Superelevation
Rv
W p F f Fcp
≈
WV 2 WV 2
W sin f s W cos sin cos
Fc
gR v gR v
V2
e
tan f s 1 f s tan
gR v
W 1 ft
V2
e fs 1 f s e
gR v
α
V2
WV 2 WV 2 Rv
W sin f s W cos sin cos g fs e
gR v gR v
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Radius Calculation Selection of e and fs
Rmin related to max. f and max. e allowed Practical limits on superelevation (e)
Rmin use max e and max f and design speed Climate
f is a function of speed, roadway surface, weather condition, Constructability
tire condition, and based on comfort Adjacent land use
AASHTO: 0.5 @ 20 mph with new tires and wet pavement to Side friction factor (fs) variations
0.35 @ 60 mph Vehicle speed
f decreases as speed increases (less tire/pavement contact) Pavement texture
Tire condition
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Maximum e Side Friction Factor
Co
Controlled
t o ed by 4 factors:
acto s:
Climate conditions (amount of ice and snow)
Terrain (flat, rolling, mountainous)
Frequency of slow moving vehicles who might be influenced by
high superelevation rates
Highest in common use = 10%, 12% with no ice and snow on low
volume gravel-surfaced
gravel surfaced roads
8% is logical maximum to minimized slipping by stopped vehicles
from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004
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Minimum Radius Tables WSDOT Design Side Friction Factors
For Open Highways and Ramps
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WSDOT Design Side Friction Factors Design Superelevation Rates - AASHTO
For Low-Speed Urban Managed Access Highways
from AASHTO’s A Policy on Geometric Design of Highways and Streets 2004
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Design Superelevation Rates - WSDOT Radius Calculation (Example)
Assume a maximum e of 8% and design speed of 60 mph, what
emax = 8% is the minimum radius?
fmax = 0.12 (from Green Book)
V2 60 2
.R min
15 ( e f ) 15 ( 0 .08 0 .12 )
Rmin = 1200 feet
from the 2005 WSDOT Design Manual, M 22-01
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Radius Calculation (Example) Stopping Sight Distance
SSD
Assume
ssu e a maximum
a u e of
o 4%
% SSD Rv s
180
fmax = 0.12 (from Green Book) 180 SSD Ms
s
V2 60 2 Rv
.R min
15 ( e f ) 15 ( 0 .04 0 .12 ) 90 SSD Obstruction
M s Rv 1 cos
Rv
Rmin = 1500 feet
Rv
Rv 1 R v M s
SSD cos Δs
90 Rv
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Sight Distance Example Sight Distance Example
A horizontal curve with R = 800 ft is part of a 2
2-lane
lane highway Now estimate the minimum distance that the billboard can be
with a posted speed limit of 35 mph. What is the minimum placed :
distance that a large billboard can be placed from the centerline
of the inside lane of the curve without reducing required SSD? 90 SSD
m Rv 1 cos
Assume p/r =2.5 sec and a = 11.2 ft/sec2 Rv
V2 28 .65 ( 246 )
SS 1 .47
SSD 4 Vt R 1 COS 9 .43 feet
f t
(800 )
30 G
a
32 . 2
(35 mph ) 2 in radians not degrees
1 .47 (35 mph )( 2 .5 sec) 246 feet
30
11 .2
0
32 .2
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Horizontal Curve Example Horizontal Curve Example
Deflection
e ect o angle
a g e of
o a 4º cu
curve
ve iss 55
55º25’,
5 , PC
C at station
stat o 238
38 + Stat
Stationing
o g goes around
a ou d horizontal
o o ta curve.
cu ve.
44.75. Find length of curve, T, and station of PT. What is station of PT?
D = 4º
= 55º25’ = 55.417º
PC = 238 + 44.75
100 180 5729 .58 L = 1385.42 ft = 13 + 85.42
.D R 1432 .4 ft
R R Station at PT = (238 + 44.75) + (13 + 85.42) = 252 + 30.17
2R 2 (1432 .4 ft )( 55 .417 )
L 1385 .4 ft
360 360
55 .417
T R tan 1432 .4 tan 752 .3 ft
2 2
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Superelevation Transition Superelevation Transition
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Superelevation Runoff/Runout Superelevation Runoff - WSDOT
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Purpose of Transition Curves Characteristics of Transition Curve
Provides path for vehicle to move from straight to a circular Should have constant rate of change of radius of curvature
curve Transition should be equal to zero at start of straight and equal
Improved appearance of curve to driver to radius of curvature at circular curve
Allows introduction of superelevation and pavement widening Allows passengers to adjust to change in rate of curvature
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Types of Transition Curve Geometry of Clothoid
C
Clothoid
ot o d K = Lp..R
Most commonly used Lp = Length of plan transition
Will be examined in more detail R = Radius of circular curve
Lemniscate K = constant
Used for large deflection
angles on high speed roads Coordinates can be represented by
Cubic Parabola x = l – l5/40(RLp)2 - …
Unsuitable for large y = l3/6RLp – l7/336(RLp)3 +…
deflection angles
x and y are measured along the tangent and at right angles from
the tangent respectively.
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Shift of Curve for Transition Shift of Curve for Transition
To accommodate the transition curve the circular curve is The shift can be calculated by:
normally shifted inwards towards the centre of the curve. Shift = S =Lp2/24R
Lp is the length of transition
If S <0.25m then the transition
is usually ignored or not required
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Terminology Tangent Length
W
When
e a ttransition
a s t o curve
cu ve iss used :
Tangent Length = (R +S) tan (/2)
The distance from the IP to the TS = (R+S) tan (/2) + Lp/2
The circular arc length from SC – CS is reduced by Lp:
Arc = R* - Lp
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Transition Length Transition Length
Radial Acceleration Method: Rate of Rotation of Pavement Method:
Lp = V3/46.73Ra Most calculations for plan transition are done in conjunction with
Lp = length of plan transition the superelevation development length (Le).
V = design speed (km/hr) Usually relies on design speed and rate of rotation of pavement:
R = radius of circular curve
a = radial acceleration
Lp = Le – 0.4V
a varies with design
g speed
p and design
g authority.
y
Typical values: Le = (e1 - e2) V / 0.09
Rotations of 2.5%/sec – this is most common, where e1 = 0
Le = (e1 - e2) V / 0.126
Rotation rates of 3.5%/sec
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Tables
