Federal Railroad Administration
Cant Deficiency, Curving Speeds
and Tilt
Brian Marquis – Mechanical Engineer
Volpe National Transportation Systems Center
Cambridge, Massachusetts
US DOT Volpe Center
Cant Deficiency/Tilt
Marquis / Page 1
Federal Railroad Administration
Topics
Cant Deficiency
• Definition of Cant Deficiency
• Benefits of Operating at Cant Deficiency
• Effect of Cant Deficiency on Rail Vehicle Performance
• Use of Tilt at High Cant Deficiency
US DOT Volpe Center
Cant Deficiency/Tilt
Marquis / Page 2
Federal Railroad Administration
Steady State Forces on Trains in Curves
US DOT Volpe Center
Cant Deficiency/Tilt
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Federal Railroad Administration
Definition of Cant Deficiency
• Trains operating in curves experience net lateral force (centrifugal
force) to the outside of the curve that is a function of the velocity.
• With superelevation (cant), the centrifugal force acting on the
passengers is reduced, or eliminated, by a component of the
gravitational force (weight).
• Balance speed for any given curve is the speed at which the lateral
component of centrifugal force will be exactly compensated (or
balanced).
• Cant deficiency involves traveling through a curve faster than the
balance speed and produces a net lateral force to the outside of the
curve.
• Cant deficiency is measured in inches and is the amount of
superelevation that would need to be added to achieve balance
speed.
US DOT Volpe Center
Cant Deficiency/Tilt
Marquis / Page 4
Federal Railroad Administration
Definition of Cant Deficiency
Increasing Speed
Stopped
Overbalance
(Cant Excess)
Overbalance
(Cant Excess)
Balance
Underbalance
(Cant Deficiency)
Lateral acceleration<0
Lateral acceleration<0
Lateral acceleration=0
Lateral acceleration>0
Center of
Gravity
Center of
Gravity
Center of
Gravity
Resultant
Resultant
Superelevation
Remove
superelevation to
create balance
US DOT condition
Volpe Center
Center of
Gravity
Resultant
Superelevation
Decrease
superelevation to
create balance
condition
Resultant
Superelevation
Superelevation
counteracts
centripetal
acceleration
Superelevation
Increase
superelevation to
create balance
Cant Deficiency/Tilt
condition
Marquis / Page
5
Federal Railroad Administration
Benefits of Operating at CD
• Higher curving speeds Vmax
– Depends on curve
characteristics – curvature
and superelevation (cant)
• Reduce trip time without
reconfiguring existing route
layout
– Strongly dependent on
route makeup
– Can improve speed on
tangents as well
49 CFR 213.57 and 213.329
Curves; Elevation and Speed Limitations
V
max
E a  Eu

0.007D
Eu = Cant Deficiency (inches)
• Can reduce need for braking
or accelerating when
entering or exiting curves
US DOT Volpe Center
Cant Deficiency/Tilt
Marquis / Page 6
Federal Railroad Administration
Benefits of Operating at CD
Vehicle Speed (3" Superelevation)
140
120
Higher Speed with
Increasing CD
Speed (mph)
100
0" CD
1" CD
2" CD
3" CD
4" CD
5" CD
6" CD
7" CD
8" CD
9" CD
80
60
40
V
20
E a  Eu

0.007D
max
0
0
US DOT Volpe Center
1
2
3
Curvature (deg)
4
5
6
Cant Deficiency/Tilt
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Federal Railroad Administration
Benefits of Operating at CD
Time per Mile (3" Superelevation)
2.5
Time per Mile (min)
2.0
0" CD
1" CD
2" CD
3" CD
4" CD
5" CD
6" CD
7" CD
8" CD
9" CD
1.5
1.0
0.5
Lower Trip Time
with Increasing CD
0.0
0
US DOT Volpe Center
1
2
3
Curvature (deg)
4
5
6
Cant Deficiency/Tilt
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Federal Railroad Administration
Benefits of Operating at CD
Time Savings per Mile Over Balance Speed (3" Superelevation)
1.2
Larger Time Savings
with Increasing CD
Time Savings per Mile (min)
1.0
1" CD
2" CD
3" CD
4" CD
5" CD
6" CD
7" CD
8" CD
9" CD
0.8
0.6
0.4
0.2
Greater Time Savings in Higher Degree Curves
0.0
0
US DOT Volpe Center
1
2
3
Curvature (deg)
4
5
6
Cant Deficiency/Tilt
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Federal Railroad Administration
Benefits of Operating at CD
• Example Trip Time Comparison for 2 routes
– Route 1: NEC Boston to Washington DC
– Route 2: Seattle to Portland
• This analysis does not include tangent miles
and assumes speed in curve is constant at
either Vmax or the maximum operating
speed (the lesser of the two)
US DOT Volpe Center
Cant Deficiency/Tilt
Marquis / Page 10
Federal Railroad Administration
Benefits of Operating at CD
Percentage of Track Length Below Curvature
100
Percent of Track Length (%)
90
80
70
60
50
Curves on NEC (129.3 miles)
40
Curves Seattle to Portland (71.0 miles)
30
* This analysis does not include tangent miles
and assumes speed in curve is constant at
either Vmax or the maximum operating
speed (the lesser of the two)
20
10
0
0
1
2
3
4
5
6
7
8
9
Curvature (deg)
US DOT Volpe Center
Cant Deficiency/Tilt
Marquis / Page 11
10
Federal Railroad Administration
Benefits of Operating at CD
NEC: 129.3 miles, 125mph maximum speed
Seattle-Portland: 71.0 miles, 80mph maximum speed
100
90
90
NEC
Seattle - Portland
80
70
Trip Time (min)
73
68
60
53
50
40
* This analysis does not include tangent miles
and assumes speed in curve is constant at
either Vmax or the maximum operating
speed (the lesser of the two)
30
20
10
0
3
US DOT Volpe Center
4
5
6
Cant Deficiency (in)
7
8
9
Cant Deficiency/Tilt
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Federal Railroad Administration
Benefits of Operating at CD
• Estimate of reduction in trip time in previous example
does not account for all factors that affect actual trip
– Time strongly dependent on route makeup – order of curves, etc.
– Although equipment qualified for higher CD, Vmax in a particular
curve may not be achievable due to constraints of neighboring
curves, etc.
– May not want to maintain to higher track class corresponding to
higher speed
– Higher CD may permit higher speed on tangents as well
– Reduces need for slowing down when entering a curve
– Reduces need for accelerating when exiting a curve
– Etc.
US DOT Volpe Center
Cant Deficiency/Tilt
Marquis / Page 13
Federal Railroad Administration
Benefits of Operating at CD
325
10
300
5
275
250
New Haven
MP 75
7" CD speed for curve
0
9" CD speed for curve
7" Line Speed
225
Speed (mph)
Boston
MP 225
9" Line Speed
200
Class 9
175
MP
155
MP
170
150
10 Short Curves
Class 8
Xing
125
Class 7
Class 6
100
Class 5
75
50
Class 4
Xing
Interlockings
Class 3
Bridge
Providence
MP 185
25
Class 2
Class 1
0
150 140
US DOT Volpe Center
130 120
110 100
90
80
70
60
Curve Number
50
40
30
20
10
Cant Deficiency/Tilt
Marquis / Page 14
0
Federal Railroad Administration
Effect of CD on Vehicle Performance
• Increase in lateral force exerted on track during curving
– Increased deterioration of track, lower safety margin for curving,
and may result in unsafe wheel force conditions
• Decrease in load on wheels on inside rail
– Increased risk of vehicle overturn, especially if high winds present
• Reduction in margin of safety associated with vehicle
response to track geometry variations
– Suspension elements operating at performance limits
• Increase in net steady stated carbody lateral acceleration
– Decreased passenger ride comfort
– Tilt can be used at high cant deficiency to reduce the net lateral
acceleration acting on the passengers
US DOT Volpe Center
Cant Deficiency/Tilt
Marquis / Page 15
Federal Railroad Administration
Effect of CD on Vehicle Performance
Increasing Speed
Stopped
Overbalance
(Cant Excess)
Overbalance
(Cant Excess)
Balance
Underbalance
(Cant Deficiency)
Lateral acceleration<0
Lateral acceleration<0
Lateral acceleration=0
Lateral acceleration>0
Center of
Gravity
Center of
Gravity
Center of
Gravity
Resultant
Resultant
Superelevation
Remove
superelevation to
create balance
US DOT condition
Volpe Center
Center of
Gravity
Resultant
Superelevation
Decrease
superelevation to
create balance
condition
Resultant
Superelevation
Superelevation
counteracts
centripetal
acceleration
Superelevation
Increase
superelevation to
create balance
Cant Deficiency/Tilt
condition
Marquis / Page
16
Federal Railroad Administration
Use of Tilt at High Cant Deficiency
Operating at High CD
without Tilt
Lateral acceleration>0.12
US DOT Volpe Center
Operating at High CD
with Tilt
Lateral acceleration<0.12
Cant Deficiency/Tilt
Marquis / Page 17
Federal Railroad Administration
Use of Tilt at High Cant Deficiency
Cant Deficiency at which Tilt-body Compensation Becomes Necessary
10
The choice of tilt is dependent on the
criterion for lateral acceleration, the
roll suspension of the vehicle, and the
desired level of CD to make trip time.
9
Cant Deficiency (inch)
8
7
6
5
4
3
Suspension
with No
Carbody Roll
2
Limit of 0.1g
Limit of 0.15g
Limit of 0.12g
Typical Roll
Suspension
1
Soft Roll Suspension
0
0
US DOT Volpe Center
0.1
0.2
0.3
0.4
0.5
0.6
Suspension flexibility (S)
0.7
0.8
0.9
Cant Deficiency/Tilt
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1
Federal Railroad Administration
Use of Tilt at High Cant Deficiency
S
Rstatic
 track
where
 track  angle between track plane and horizontal (superelevation)
Rstatic  roll due to superelevation (measured relative to track plane)
US DOT Volpe Center
Cant Deficiency/Tilt
Marquis / Page 19
Federal Railroad Administration
Use of Tilt at High Cant Deficiency
Benefits – not a complete list
• Addresses ride comfort at higher cant deficiency
– Reduces steady state lateral acceleration felt by passengers
• Allows operation at higher cant deficiency by meeting
regulatory requirements on steady state lateral acceleration
• Has little to no effect on wheel rail forces or derailment safety
Drawbacks – not a complete list
• Compatibility with clearance envelopes for existing lines and
equipment
• Increased suspension complexity and maintenance
• Motion sickness
US DOT Volpe Center
Cant Deficiency/Tilt
Marquis / Page 20