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Superelevation is the banking of the roadway along a
horizontal curve so that the drivers can negotiate the
curve at safe and comfortable speed.
Normal crown
Dr. Rizwan Memon Fully superelevated 2
Superelevation “e” and side friction coefficient “f” on horizontal curves
Dr. Rizwan Memon 3
From the laws of mechanics, the basic formula that governs vehicle
Operation on a curve is:
0.01e + f v2
=
1 − 0.01ef gR
In practice: 1 − 0.01ef 1
v2
0.01e + f =
gR
v : vehicle speed, (m/s or ft/s)
R: radius of curve, (m or ft)
e: rate of superelevation, percent
f: side friction factor (lateral ratio, cornering ratio, unbalanced
Dr. Rizwan Memon centrifugal ratio) 4
Minimum Radius (Rmin)
It is minimum value of curvature for a given design speed and is
determined from emax and fmax
V2
Rmin =
127(0.01emax + f max )
v : vehicle speed, km/h
R: radius of curve, m V2
Rmin =
e: rate of superelevation, percent 15(0.01emax + f max )
f: side friction factor (lateral ratio)
v : vehicle speed, mph
R: radius of curve, ft
e: rate of superelevation, percent
Dr. Rizwan Memon f: side friction factor (lateral ratio)
5
Get familiar with GB tables
Minimum radius with design speed
Dr. Rizwan Memon 6
Dr. Rizwan Memon 7
For a given design speed v, there are multiple combinations of e and f
for sustaining centripetal acceleration on curves. Green book
recommends 5 methods.
Method 1: Superelevation and side friction are directly proportional to
the inverse of the radius
Method 2: Start with using side friction f up to fmax, then f remains
fmax, then e is used until emax
Method 3: start with using e, until emax, then e remains emax, and f is
used until fmax
Method 4: same as method 3, but using average running speed instead
of design speed
Method 5: e and f are in a curvilinear relation with 1/R
Dr. Rizwan Memon 8
Dr. Rizwan Memon 9
Tangent runout (crown runoff) section :
Length of roadway needed to accomplish a change in out-
side cross slope from normal cross slope rate to zero
Runoff section :
Length of roadway needed to accomplish a change in
out-side cross slope from zero to full superelevation
Dr. Rizwan Memon 10
Tangent Run-out Profile
0%
Normal crown
Dr. Rizwan Memon 11
Supperelevation runoff
0%
Normal crown Relative gradient
Dr. Rizwan Memon 12
Dr. Rizwan Memon 13
Minimum Length of Tangent Runout
eNC Lr
Lt =
ed
where
◼ Lt = minimum length of tangent
runout (ft or m)
◼ eNC = normal cross slope rate (%)
◼ ed = design superelevation rate
◼ Lr = minimum length of superelevation
runoff (ft or m)
Dr. Rizwan Memon 14
Minimum Length of Superelevation Runoff
( wn1 )ed 12 e
Lr = (bw ) Lr =
where G
◼ Lr = minimum length of superelevation
runoff (ft)
◼ Δ or G = maximum relative gradient(%)
◼ n1 = number of lanes rotated
◼ bw or α= adjustment factor for number
of lanes
◼ w = width of one traffic lane
eRizwan
◼ Dr. d = design
Memon superelevation rate 15
Keep water drainage in mind while considering all of the
available cross-section options
Dr. Rizwan Memon 16
Axis of rotation:
Undivided highways are usually superelevated with the axis of rotation
at the roadways centerline
Axis of rotation
Superelevated section
Normal cross section
Dr. Rizwan Memon 17
Muti-lane highways with depressed medians are usually superelevated with the axis of
Rotation at the median edges of the traveled way.
Axis of rotation
Median width
Dr. Rizwan Memon 18
Transition Curves
◼ Gradually changing the curvature from tangents to circular
curves
Without Transition Curves
With Transition Curves
Dr. Rizwan Memon 19
Spiral Curve:
Spiral curves are curves with a continuously
changing radii, they are sometimes used on
high-speed roadways with sharp horizontal
curves and are sometimes used to gradually
introduce the superelevation of an upcoming
horizontal curve
Dr. Rizwan Memon 20
Spiral Transition:
1. Spiral transition tends to promote uniformity in speed as a
vehicles enters and leaves a circular curve
2. The transition curve length provides a suitable location for
the superelevation runoff.
3. Use of spiral transition provides flexibility in accomplishing
the widening of sharp curves
4. The appearance of the highway or street is enhanced by
the application of spiral transition curves
Dr. Rizwan Memon 21
Dr. Rizwan Memon 22
length of spiral – should be larger of 1, 2
V 3 V3
Ls ,min = 0.0214 OR Ls ,min = 3.15 (1)
RC RC
Ls ,min = 24( pmin ) R (2)
Maximum length of spiral: Ls ,max = 24( Pmax ) R (3)
Where,
Ls,min = minimum length of spiral, (m or ft)
Ls,max = maximum length of spiral, m
Pmin = minimum lateral shift that occurs as a result of the natural steering
behavior of most drivers (0.20m or 0.66ft)
Pmax = maximum lateral shift that occurs as a result of the natural steering
behavior of most drivers (1.0 m or 3.3 ft)
R = radius of circular curve, m
V = design speed, (kmph or mph)
C = maximum rate Memon
Dr. Rizwan of change in lateral acceleration, (1.2 m/s3 or 4 ft/s3) 23
