Design of Horizontal
Alignment : Curve
Degree of Curve Why Degree of Curve is
used in railway design?
• Railway curves are
designed to be
circular or part of a
30.5 m
circular arc.
Few Books use
• Simplicity and
30 m
Standardization
• A 100-foot length is
practical for field
measurements and
surveying
• The 100-foot chord
Degree of Curve
Degree of curve (D)
Angle subtended at the center of
curve by a chord of 30.5 m or 100
feet length.
Where:
•D is the degree of the curve.
•R is the radius of the circular curve (in
meters).
Maximum degree and minimum
radius as per Indian Railways
Plain Track Turnout
Max Deg, Min Radius Max Deg, Min Radius
BG 10o, 175m 8o, 218m
MG 16o, 109m 15o, 116m
NG 40o , 44m 17o, 103m
Relationship b/w R , Versine(v) and
Chord length(C)
In Indian Railways, the versine is an essential
measurement used in the maintenance and alignment of
railway tracks
The versine (or mid- It helps ensure that the curvature of the track is
ordinate) is the consistent and follows the designed radius, which is
perpendicular distance from critical for safe train operations.
the midpoint of a chord to
the arc of a circle. During the design phase of new railway lines or when
upgrading existing lines, versine is calculated to
design curves
Relationship b/w R , Versine(v) and
Chord length(C)
Property of circle, two intersect
chords
The versine (or mid-
ordinate) is the
perpendicular distance from
the midpoint of a chord to
the arc of a circle.
(C,R & V in
Superelevation or Cant
The outer rail of the curve is elevated
compared to the inner rail, and the
difference in height is called the cant or
superelevation.
Objectives
1. Counteract the centrifugal force
2. Improve Safety: By providing
superelevation, the risk of derailment
is minimized
3. Enhance Comfort: Superelevation reduces
the discomfort felt by passengers due to
the lateral forces experienced in
curves.
4. Minimize Wear and Tear on Tracks and
Wheels: By reducing lateral forces,
superelevation helps in minimizing the
wear and tear on both the railway tracks
and the train wheels.
Relationship b/w e , Gauge(G),
Speed (V) and R
Relationship b/w e , Gauge(G),
Speed (V) and R
Chandra’s Book
Dynamic Gauge
BG=1750mm
Equilibri
Arora’s Book BG is1676
um Cant
Limit of superelevation or cant
Normally, the max SE as per Indian Railway Board is approximately
1/10 of the gauge
Maximum S.E. when V ≤ 100 Maximum S.E. for high speeds (V >
km/h 120 km/h)
Under Under special
Gauge ordinary permission of
120kmph 160kmph 200 kmph
conditions chief engineer
(cms) (cms)
BG 14 16.5 16.5 18.5 18.5
Not Not
Not
MG 9 10 specified specified
specified
NG 6.5 7.6 - do- - do- -do-
Provision of superelevation
Constant superelevation should be maintained on circular curve and
varied at uniform rate on transition curve.
Gauge Max cant gradient
BG 1 in 360
MG and NG 1 in 72
Equilibri
um Cant
Cant Deficiency
The difference between the actual cant and the theoretical cant required for a train to travel
around a curve at a certain speed
The Indian Railways limits the cant deficiency for two reasons:
i) Higher Cant deficiency gives rise to discomfort
ii) Higher cant deficiency means higher would be the centrifugal
forces and high lateral forces on the outer rail.
Maximum Permissible Speed on the
Curve
i) Maximum sanctioned speed on the section
ii)Safe speed over the curve
iii)Speed based on the consideration of
superelevation
iv)Speed from the length of the Transition Curve
i) Maximum sanctioned speed on the section
The Maximum Sanctioned Speed (MSS) in railways refers to the highest speed that a
particular section of the railway track is authorized for trains to operate, based
on safety, track conditions, and infrastructure capabilities. This speed limit is
determined by railway authorities after thorough inspection and testing of the
track and related infrastructure, such as signaling, bridges, and curves.
Factors influencing MSS include:
•Track Quality: The condition and maintenance of the
tracks.
•Train Type: Different trains (freight vs. passenger,
regular vs. high-speed) have different speed
capabilities.
•Curvature and Gradient: Sections with tight curves or
steep gradients typically have lower speed limits.
•Signaling and Safety Systems: The quality and type of
signaling systems (manual, automatic, etc.) also play
a role.
•Environmental Conditions: Weather and other
environmental factors may impose further speed
restrictions.
ii) Safe speed on the curve
Martin’s
ii) Safe speed on the curve
iii) Speed based on consideration
of super elevation
Formula considering
dynamic gauge
iv) Speed from the length of the
Transition Curve
L is length of transition curve
D is Cant deficiency in mm
Formula based on the
rate of change of cant
in mm/sec
