10 Geometric Design of Railway Track [Horizontal Alignment] (Railway Engineering Lectures هندسة السكك الحديدية & Dr. Walied A. Elsaigh)

1. Dr. Walied A. Elsaigh
welsaigh@ksu.edu.sa
Asst. Prof. of Civil Engineering
CE 435
Railway Engineering
Geometric Design
of Railway Track
Horizontal
Alignment

2. Text Book
Railway Engineering,
Satish and Agarwal,
2nd edition, 2013
Chapter 13
Page 208-258

3. Textbook
HSR Technical Specification for interoperability (INF-TSI)

4. CIRCULAR CURVE
A curve of constant radius !

5. Transition Curve
A curve of varying curvature. It is normally provided between two
circular curves, each of different radius, or between a circular curve
and a straight. R @ straight = ∞ & R of circular at curve.
TS (Tangent to Spiral)
SC (Spiral to Curve)

6. Cant (Super-elevation)
CANT
The amount by which one running rail is raised above the other
running rail; measured at the centre of the rail head (It may be
expressed as a difference in height or in terms of an angle).
POSITIVE CANT: Cant is positive when the outer rail on a curve
is raised above the inner rail
NEGATIVE CANT: Cant is negative when the inner rail is raised
above the outer rail.

7. Cont. Cant
Negative Cant

8. Cont. Cant
CANT GRADIENT: The amount by which Cant is increased
or decreased in a given length of track, e.g. 1 in 1200 means
that a Cant of 1mm is gained or lost in every 1200mm of track.
TRACK TWIST: The variation in cross level over a given
distance along the track. It has the same value as Cant Gradient,
except the term Track Twist is normally associated with higher
values which are considered to be faults.
Cant excess Cant excess (Ce) occurs when a train travels
around a curve at a
speed lower than the equilibrium speed. It is the difference
between the actual cant provided and the theoretical cant required
for such a low speed.

9. Cont. Cant
RATE OF CHANGE OF CANT OR RATE OF CHANGE
OF CANT DEFICIENCY
The rate at which Cant or Cant Deficiency is increased or
reduced relative to the maximum speed of a vehicle passing
over the Transition Curve, e.g. 35mm per second means that a
vehicle when travelling at the maximum speed permitted will
experience a change in Cant or Cant Deficiency of 35mm in
each second while travelling over the length of transition.

10. Speed
EQUILIBRIUM SPEED: The speed of a vehicle following a
curved path is such that the resultant of the weight of the vehicle
and the effect of centrifugal force is perpendicular to the plane of
the rails.
EQUILIBRIUM CANT: The amount that it is necessary to
raise one running rail above the level of the other running rail
to obtain Equilibrium at a nominated speed.
CANT DEFICIENCY: The difference between actual Cant and
the theoretical Cant that would have to be applied to maintain
Equilibrium at a nominated speed (Cant deficiency is expressed
in the same terms as cant).

11. Cont. Speed

12. Cont. Speed
PERMISSIBLE SPEED : The speed which may be permitted
on a curve with associated transitions when radius, Cant, Cant
Deficiency, and Cant gradient (rates of change of Cant) have all
been taken into consideration together with the characteristics of
the trains. When the Permissible Speed of the curve or part of
the curve is less than the route speed limit for the particular type
of train it will be necessary to impose a lower Permanent Speed
Restriction at that location.

13. Cont. Speed

14. Unbalance Elevation
• Different maximum
allowed speeds for
different trains on the
same track:
• passenger, express
freight, general
freight
• Actual elevation on
track to balance head
and flange wear of both
rails
UNDERBALANCE
Superelevation
Centrifugal
Force
Gravity
Resultant
Center of
Gravity
EQUILIBRIUM
Superelevation
Centrifugal
Force
Gravity Resultant
Center of
Gravity
OVERBALANCE
Superelevation
Gravity
Resultant
Centrifugal
ForceCenter of
Gravity
D
E
V a
0007.0
3
max


= Maximum allowable operating speed (mph).
= Average elevation of the outside rail (inches).
= Degree of curvature (degrees).D
E
V
a
max
Amount of
Underbalance

15. Cant Limits
The maximum Cant on sharp radius curves shall not be greater
than shown in the following table.

16. Super-elevation – Cant
Highway Railroad
Expressed
by…
“e” expressed as cross-slope
in percent
“E” is inches of elevation difference
between “high rail” (outside) and “low
rail” (inside)
Function of… Vehicle speed, curve radius
and tire side friction
(0.01e + f) / (1 – 0.01ef) =
V2/15R
Function of design speed, degree of
curve
E = 0.0007V2D – Eu
Where Eu is unbalance (1-2” typical)
Max. values 6-8% Freight: 6-7”
Light Rail: 6”
Rotation point Centerline “Inside rail”
Transition Runoff (2/3 on tangent, 1/3 in
curve)
Spiral

17. Radius Limits
Highway Railroad
Criteria - Design speed -Design speed
-Allowable superelevation
Typical values Freeway:
- 60 mph, R=1,340, D=4.28
- 70 mph, R=2,050, D=2.79
Main lines:
-High speed: R > 5,729, D<1
-Typical: R >2,865, D<2
-Low speed: R>1,433, D<4
Industrial facilities:
- R>764, D<7.5

18. Equilibrium Cant

19. Degree of Curvature

20. Why Straight Railway Track?

21. Calculate the superelevation (Cant) and the maximum
permissible speed for a 2° standard gauge transitioned curve on a
high-speed route with a maximum sanctioned speed of 110 km/h.
The speed for calculating the equilibrium superelevation as decided
by the chief engineer is 80 km/h and the booked speed of goods
trains is 50 km/h.
Example
R = mm, Equilibrium Cant = mm, cant for sanctioned speed = mm,
cant deficiency = mm, Cant for freight train = mm,
cant excess = mm < excess limit =75 mm OK

22. Geometry Cars

23. Thank You

24. Transition Curves

25. Role of Transition Curves

26. Transition Curves
Several Types of transition curves exist, Cubic Parabola and
cubic spiral are widely used
(Cubic Parabola) (Cubic Spiral)

27. Shift
S= Shift (m)
L=Length of transition curve (m)
R= Radius of circular curve (m)

28. Shift
y

29. Cont. Shift

30. Length Of Transition Curve
Task: Find the formula according to AREMA

31. Example
standard gage

32. Cont. Example
AREMA

33. Cont. Example

34. Cont. Example

35. Laying Transition Curve

36. Laying Transition Curve

37. Laying Transition Curve

38. Laying Transition Curve

39. Example
Draw the offsets of a cubic parabola transition curve.
Given: the design speed of the train on curve is 90km/hr, circular
curve radius of 573m, gauge of 1435 mm, Transition curve
length (cubic parabola) = 105m

40. Transition needed?
AREMA: Spiral transition curves can be omitted where the
length of spiral (Ls) divided by the radius (R) is less than 0.01
For example: If the required spiral length is calculated
as 40 m for a curve radius of 500 m, Can the spiral
curve be omitted?
Ls/R = 40/500 = 0.08> 0.01 (spiral can not be omitted)
What would be the curve radius that would allow for
design with no spiral? R > 40/0.01 = 4000 m or greater

41. Widening of Gauge on Curves

42. Widening of Gauge on Curves
Watch out for the units:
h (cm), D (cm), L (m), B (m), R (m), and w (cm)

43. Example
The Wheel base of a vehicle moving on a standard gauge track is 6
m. The diameter of the wheel is 1542 mm and the flanges project
32mm below the top of the rail. Calculate the extra width of the
gauge required on a circular curve having a radius of 168 m
Lap of flange (L) = 0.446 m
Extra width (w) = 3.21cm (32.1 mm) – Too large allowable is in the
range of 5 to 10 mm
Note: Larger curve radius requires less widening ! Can you
explain why?

44. Cont.
Widening
of Gauge

45. Thank You