HORIZONTAL ALIGNMENT

SUPERELEVATION – TURNING AROUND THE CL

EXAMPLE :

Calculate and draw elevation running of both outer edges of pavement:

known facts: category S 9,5/80 (according to Czech standard)
radius of curve: 330 m
length of transition curve: 70 m
longitudinal slope: 2%
transversal slope: 6 %
At the beginning of superelevation there is stationing 2,000 km, altitude level
of this point is 202,50 m a.s.l. Original cross slope of the pavement is 2,5 %. The
pavement will rotate around the center line.
Calculate points every 20 m and in characteristic cross sections where p =
0,00 % and +2,50 %.

CALCULATION :

1. Set the width of traffic lanes and strip lines for category width S 9,5:
w  2  a  2  v  2  3,50  2  0,25  7,00  0,50  7,50 m
where a width of traffic lane according to Czech standard, v is width of strip line

Notice: Radius of curve is greater than 250 m so it is not necessary to design pavement
widening. The width of carriageway is 7,50 m, whic means that a´=3,75 m (w/2)

2. Determine slope of superelevation ramp s and check it against the

minimal and maximal values given by standard:
p 2  p1 2,50  6
s = . a  . 3,75  0, 4554 %
L 70
where s is slope of superelevation ramp, p2 (%) crossfall of pavement at the end of
superelevation, p1 (%) crossfall of pavement at the beginning of superelevation, Lvz (m) length of
the whole superelevation ramp and a´(m) is distance between center line (axis of the rotation) and
outer edge of strip line.
 HORIZONTAL ALIGNMENT
SUPERELEVATION – TURNING AROUND THE CL

MAXIMAL AND MINIMAM VALUES OF SLOPE OF SUPERELEVATION RAMP

Design speed max s (%) min s (%)
in km/h a´  4,25 m a´  4,25 m a´  4,25 a´  4,25 m
 50 1,2 1,4
60 až 70 1,0 1,2 0,1 a´ 0,07 a´
80 až 90 0,7 0,85 ( max s)
100 až 120 0,6 0,7

3. Calculate elevation difference between elevated outer edge of outer strip

line and unelevated outer edge of inner strip lane (m):
a + v . p
1 (2) 2 - p1  +  a . p 2
h´ =
100
where a is width of traffic lane, v is strip line width, p1 crossfall of pavement at the beginning of
superelevation, p2 is crossfall of pavement at the end of superelevation and a is with of
pavement widening
Notice: p1 is with negative sign if it is on the contrary to p2

h´ =
3,50 + 0,25 . 2,50  6,00  + 0. 6,00  0 ,3188 m
100

4. Calculate minimal length of the whole superelevation ramp Lvz min v m:

h´ . 100 0,3188 . 100

L min =   45,54m
max s 0,7

Given length of superelevation ramp is 70 m, so it is greater than Lmin

L=70 m > Lmin=45,54 m
 HORIZONTAL ALIGNMENT
SUPERELEVATION – TURNING AROUND THE CL

5. Calculations of dimensions of outer and inner edge of line strips follow from
the figure below:

Translation related to figure:

přímá - straight, přechodnice - transition curve, oblouk - circular arc or curve

w . p 0 7,5 . 2,5
h0 =   0,09375m
200 200
w . p 7,5 . 6
h=   0,45m
100 100
where w is width of carriageway (traffic lanes and strip lines) in m, p0 is crossfall of pavement in
straight in % a p is maximal value of transversal slope in curve %.

6. From the figure below follow calculations of other height dimensions:

from similarity of triangles Lz may be found:

h : L  2  h0 : LZ 
 HORIZONTAL ALIGNMENT
SUPERELEVATION – TURNING AROUND THE CL

w.p 2 7,50  6,00 45,00

h   h0   0,094   0,225  0,094  0,319 m
200 200 200
than:
2 . h0 . L 2 . 0,094 .70
Lz =   41 ,254 m
h 0,45
+ h0 + 0,094
2 2
7. For any distance x, we can calculate height dimensions h´x a h´´x as follow:

h : L  hX : X 
h
hX  X
L

hX  hX  h0
8. Height dimensions are put in the table:
+ h0

Height dimension
Longitudinal slope
Marking of point

Elevation
x
Distance x

h´´ x = h´x - h0
w * pm

h´ inner outer
w * p0
200

200

h´

Stationing
L

L edge of edge of
h´ =
h0=

h´x =

line strip line strip

vi ve

[ km ] [ %] [m] [m] [m] [m] [m] [ m] [m] [m] [m]

2,000 00 TP 202.50 0.00 0.000 -0.094 202.406 202.406

2,020 00 202.90 20.00 0.091 -0.003 202.806 202.897
0.004557

2,020 62 2 (2´) 202.91 20.62 0.093 -0.001 202.816 202.909

2.00%

0.094

0.319

2,040 00 203.30 40.00 0.182 0.088 203.206 203.338

2,041 25 3 (3´) 203.32 41.25 0.188 0.094 203.226 203.414
2,060 00 203.70 60.00 0.273 0.179 203.521 203.879
2,070 00 PK 203.90 70.00 0.319 0.225 203.675 204.125

9. Checking drainage gradient sp min:

s p min  s  s  2 ,00  0 ,456  1,544 % ,

Drainage gradient is over 0,50 % (according to standard).

 HORIZONTAL ALIGNMENT
SUPERELEVATION – TURNING AROUND THE CL

Height dimensions in cross sections