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G e o m e t r i c D e s i g n o f R a i l w a y T r a c k
The geometric design of railway tracks plays a crucial role in ensuring the efficient and
safe movement of trains. It encompasses various factors, including alignment, gradients,
curves, super elevation, and transitions. Railway engineers employ advanced techniques
and mathematical principles to optimize track geometry, aiming to strike a balance
between speed, comfort, and safety.
D i f f e r e n t g a u g e s
S a f e s p e e d o n c u r v e s B a s e d o n M a r t i n s F o r m u l a
(a) For Transition curve
(i) For B, G & M.G
V=4.35v5-67 where, V is in kmph.
(ii) For N,G V = 3.65vR-6 For V is km/hr.
(b) For non-Transition curve
V=0.80 × speed calculated in (a)
(c) For high speed Trains V=4.58vR
S a f e s p e e d B a s e d o n S u p e r el e v a t i o n
( a ) For Transition curves
The above two formula based on the assumption that G = 1750 mm for B.G
G = 1057 mm for N.G
Page 2


G e o m e t r i c D e s i g n o f R a i l w a y T r a c k
The geometric design of railway tracks plays a crucial role in ensuring the efficient and
safe movement of trains. It encompasses various factors, including alignment, gradients,
curves, super elevation, and transitions. Railway engineers employ advanced techniques
and mathematical principles to optimize track geometry, aiming to strike a balance
between speed, comfort, and safety.
D i f f e r e n t g a u g e s
S a f e s p e e d o n c u r v e s B a s e d o n M a r t i n s F o r m u l a
(a) For Transition curve
(i) For B, G & M.G
V=4.35v5-67 where, V is in kmph.
(ii) For N,G V = 3.65vR-6 For V is km/hr.
(b) For non-Transition curve
V=0.80 × speed calculated in (a)
(c) For high speed Trains V=4.58vR
S a f e s p e e d B a s e d o n S u p e r el e v a t i o n
( a ) For Transition curves
The above two formula based on the assumption that G = 1750 mm for B.G
G = 1057 mm for N.G
And Where, e = super elevation.
Where, v= speed in km/hr
R = Radius of curve in ‘mm’
C
a
= Actual cant in ‘mm’
C
d
= Cant deficiency in ‘mm’
S p e e d f r o m t h e L e n g t h o f T r a n s i t i o n C u r v e
( a ) For speed upto 100 km/hr .
(min. of two is adopted)
Where, L = Length of transition curve based on rate of change of cant as 38 mm/sec. for
speed upto 100 km/hr & 55 mm/sec for speed upto 100 km/hr & 55 mm/sec for high
speeds.
C
a
= Actual cant in ‘mm’
C
d
= Cant deficiency in ‘mm’
(b) For high speed trains (speed>100km/hr)
Either ,
Minimum of the two is adopted.
R a d i u s & D e g r e e o f c u r v e
if one chain length = 30 m.
if one chain length = 20 m
Where, R = Radius
Page 3


G e o m e t r i c D e s i g n o f R a i l w a y T r a c k
The geometric design of railway tracks plays a crucial role in ensuring the efficient and
safe movement of trains. It encompasses various factors, including alignment, gradients,
curves, super elevation, and transitions. Railway engineers employ advanced techniques
and mathematical principles to optimize track geometry, aiming to strike a balance
between speed, comfort, and safety.
D i f f e r e n t g a u g e s
S a f e s p e e d o n c u r v e s B a s e d o n M a r t i n s F o r m u l a
(a) For Transition curve
(i) For B, G & M.G
V=4.35v5-67 where, V is in kmph.
(ii) For N,G V = 3.65vR-6 For V is km/hr.
(b) For non-Transition curve
V=0.80 × speed calculated in (a)
(c) For high speed Trains V=4.58vR
S a f e s p e e d B a s e d o n S u p e r el e v a t i o n
( a ) For Transition curves
The above two formula based on the assumption that G = 1750 mm for B.G
G = 1057 mm for N.G
And Where, e = super elevation.
Where, v= speed in km/hr
R = Radius of curve in ‘mm’
C
a
= Actual cant in ‘mm’
C
d
= Cant deficiency in ‘mm’
S p e e d f r o m t h e L e n g t h o f T r a n s i t i o n C u r v e
( a ) For speed upto 100 km/hr .
(min. of two is adopted)
Where, L = Length of transition curve based on rate of change of cant as 38 mm/sec. for
speed upto 100 km/hr & 55 mm/sec for speed upto 100 km/hr & 55 mm/sec for high
speeds.
C
a
= Actual cant in ‘mm’
C
d
= Cant deficiency in ‘mm’
(b) For high speed trains (speed>100km/hr)
Either ,
Minimum of the two is adopted.
R a d i u s & D e g r e e o f c u r v e
if one chain length = 30 m.
if one chain length = 20 m
Where, R = Radius
D = Degree of curve
V i r s i n e o f C u r v e ( V )
G r a d e c o m p e n s a t i o n
For B.G ? 0.04% per degree of curve
M.G ? 0.03% per degree of curve
M.G ? 0.02% per degree of curve
S u p e r E l e v a t i o n ( c a n t ) ( e )
Where, V
a v
= Average speed or equilibrium speed.
E q u i l i b r i u m s p e e d o r A v e r a g e S p e e d ( V a v )
(a) when maximum sanctioned speed>50km/hr .
(b) When sanctioned speed <50 km/hr
Page 4


G e o m e t r i c D e s i g n o f R a i l w a y T r a c k
The geometric design of railway tracks plays a crucial role in ensuring the efficient and
safe movement of trains. It encompasses various factors, including alignment, gradients,
curves, super elevation, and transitions. Railway engineers employ advanced techniques
and mathematical principles to optimize track geometry, aiming to strike a balance
between speed, comfort, and safety.
D i f f e r e n t g a u g e s
S a f e s p e e d o n c u r v e s B a s e d o n M a r t i n s F o r m u l a
(a) For Transition curve
(i) For B, G & M.G
V=4.35v5-67 where, V is in kmph.
(ii) For N,G V = 3.65vR-6 For V is km/hr.
(b) For non-Transition curve
V=0.80 × speed calculated in (a)
(c) For high speed Trains V=4.58vR
S a f e s p e e d B a s e d o n S u p e r el e v a t i o n
( a ) For Transition curves
The above two formula based on the assumption that G = 1750 mm for B.G
G = 1057 mm for N.G
And Where, e = super elevation.
Where, v= speed in km/hr
R = Radius of curve in ‘mm’
C
a
= Actual cant in ‘mm’
C
d
= Cant deficiency in ‘mm’
S p e e d f r o m t h e L e n g t h o f T r a n s i t i o n C u r v e
( a ) For speed upto 100 km/hr .
(min. of two is adopted)
Where, L = Length of transition curve based on rate of change of cant as 38 mm/sec. for
speed upto 100 km/hr & 55 mm/sec for speed upto 100 km/hr & 55 mm/sec for high
speeds.
C
a
= Actual cant in ‘mm’
C
d
= Cant deficiency in ‘mm’
(b) For high speed trains (speed>100km/hr)
Either ,
Minimum of the two is adopted.
R a d i u s & D e g r e e o f c u r v e
if one chain length = 30 m.
if one chain length = 20 m
Where, R = Radius
D = Degree of curve
V i r s i n e o f C u r v e ( V )
G r a d e c o m p e n s a t i o n
For B.G ? 0.04% per degree of curve
M.G ? 0.03% per degree of curve
M.G ? 0.02% per degree of curve
S u p e r E l e v a t i o n ( c a n t ) ( e )
Where, V
a v
= Average speed or equilibrium speed.
E q u i l i b r i u m s p e e d o r A v e r a g e S p e e d ( V a v )
(a) when maximum sanctioned speed>50km/hr .
(b) When sanctioned speed <50 km/hr
(c) W eighted A verage Method
Where, n
1
,n
2
,n
3
… etc. are the number of trains running at speeds
v
1
,v
2
,v
3
… etc.
M a x i m u m v a l u e o f C a n t e m a x
C a n t D e f i c i e n c y ( D )
C a n t d e f i c i e n c y = x
1
-x
A
Where,
x
A
= Actual cant provided as per average speed
x
1
= Cant required for a higher speed train.
e
t h
= e
a c t
+ D
Page 5


G e o m e t r i c D e s i g n o f R a i l w a y T r a c k
The geometric design of railway tracks plays a crucial role in ensuring the efficient and
safe movement of trains. It encompasses various factors, including alignment, gradients,
curves, super elevation, and transitions. Railway engineers employ advanced techniques
and mathematical principles to optimize track geometry, aiming to strike a balance
between speed, comfort, and safety.
D i f f e r e n t g a u g e s
S a f e s p e e d o n c u r v e s B a s e d o n M a r t i n s F o r m u l a
(a) For Transition curve
(i) For B, G & M.G
V=4.35v5-67 where, V is in kmph.
(ii) For N,G V = 3.65vR-6 For V is km/hr.
(b) For non-Transition curve
V=0.80 × speed calculated in (a)
(c) For high speed Trains V=4.58vR
S a f e s p e e d B a s e d o n S u p e r el e v a t i o n
( a ) For Transition curves
The above two formula based on the assumption that G = 1750 mm for B.G
G = 1057 mm for N.G
And Where, e = super elevation.
Where, v= speed in km/hr
R = Radius of curve in ‘mm’
C
a
= Actual cant in ‘mm’
C
d
= Cant deficiency in ‘mm’
S p e e d f r o m t h e L e n g t h o f T r a n s i t i o n C u r v e
( a ) For speed upto 100 km/hr .
(min. of two is adopted)
Where, L = Length of transition curve based on rate of change of cant as 38 mm/sec. for
speed upto 100 km/hr & 55 mm/sec for speed upto 100 km/hr & 55 mm/sec for high
speeds.
C
a
= Actual cant in ‘mm’
C
d
= Cant deficiency in ‘mm’
(b) For high speed trains (speed>100km/hr)
Either ,
Minimum of the two is adopted.
R a d i u s & D e g r e e o f c u r v e
if one chain length = 30 m.
if one chain length = 20 m
Where, R = Radius
D = Degree of curve
V i r s i n e o f C u r v e ( V )
G r a d e c o m p e n s a t i o n
For B.G ? 0.04% per degree of curve
M.G ? 0.03% per degree of curve
M.G ? 0.02% per degree of curve
S u p e r E l e v a t i o n ( c a n t ) ( e )
Where, V
a v
= Average speed or equilibrium speed.
E q u i l i b r i u m s p e e d o r A v e r a g e S p e e d ( V a v )
(a) when maximum sanctioned speed>50km/hr .
(b) When sanctioned speed <50 km/hr
(c) W eighted A verage Method
Where, n
1
,n
2
,n
3
… etc. are the number of trains running at speeds
v
1
,v
2
,v
3
… etc.
M a x i m u m v a l u e o f C a n t e m a x
C a n t D e f i c i e n c y ( D )
C a n t d e f i c i e n c y = x
1
-x
A
Where,
x
A
= Actual cant provided as per average speed
x
1
= Cant required for a higher speed train.
e
t h
= e
a c t
+ D
Where, e
t h
= theoretical cant
e
act
= Actual cant
D = Cant deficiency.
T r a n s i t i o n C u r v e ( C u b i c p a r a b o l a )
Equation of T ransition curve:
(a) shift (s)
Where, S = shift in ‘m’
L = Length of transition carve in ‘m’
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