cant deficiency

Cant Deficiency/TiltMarquis / US DOT Volpe Center

Federal Railroad Administration

Cant Deficiency, Curving Speeds Cant Deficiency, Curving Speeds and Tiltand Tilt

Brian Marquis Brian Marquis –– Mechanical EngineerMechanical EngineerVolpe National Transportation Systems CenterVolpe National Transportation Systems Center

Cambridge, MassachusettsCambridge, Massachusetts



TopicsTopicsCant DeficiencyCant Deficiency

•• Definition of Cant DeficiencyDefinition of Cant Deficiency

•• Benefits of Operating at Cant DeficiencyBenefits of Operating at Cant Deficiency

•• Effect of Cant Deficiency on Rail Vehicle PerformanceEffect of Cant Deficiency on Rail Vehicle Performance

•• Use of Tilt at High Cant DeficiencyUse of Tilt at High Cant Deficiency



Steady State Forces on Trains in Curves Steady State Forces on Trains in Curves



•• Trains operating in curves experience net lateral force (centrifTrains operating in curves experience net lateral force (centrifugal ugal force) to the outside of the curve that is a function of the velforce) to the outside of the curve that is a function of the velocity.ocity.

•• With superelevation (cant), the centrifugal force acting on the With superelevation (cant), the centrifugal force acting on the passengers is reduced, or eliminated, by a component of the passengers is reduced, or eliminated, by a component of the gravitational force (weight).gravitational force (weight).

•• Balance speed for any given curve is the speed at which the lateBalance speed for any given curve is the speed at which the lateral ral component of centrifugal force will be exactly compensated (or component of centrifugal force will be exactly compensated (or balanced). balanced).

•• Cant deficiency involves traveling through a curve faster than tCant deficiency involves traveling through a curve faster than the he balance speed and produces a net lateral force to the outside ofbalance speed and produces a net lateral force to the outside of the the curve.curve.

•• Cant deficiency is measured in inches and is the amount of Cant deficiency is measured in inches and is the amount of superelevation that would need to be added to achieve balance superelevation that would need to be added to achieve balance speed.speed.

Definition of Cant Deficiency Definition of Cant Deficiency



Increasing SpeedIncreasing Speed

Superelevation Superelevation Superelevation

Stopped

Superelevation

Center ofGravity

Resultant

Increase superelevation to create balance

condition

Superelevation counteracts centripetal acceleration

Decrease superelevation to create balance

condition

Remove superelevation to create balance

condition

Lateral acceleration=0

UnderbalanceUnderbalance(Cant Deficiency)(Cant Deficiency)BalanceBalanceOverbalanceOverbalance

(Cant Excess)(Cant Excess)OverbalanceOverbalance(Cant Excess)(Cant Excess)

Lateral acceleration<0 Lateral acceleration<0 Lateral acceleration>0

Definition of Cant Deficiency Definition of Cant Deficiency

Center ofGravity

Resultant

Center ofGravity

Resultant

Center ofGravity

Resultant



Benefits of Operating at CDBenefits of Operating at CD

•• Higher curving speeds Higher curving speeds VVmaxmax

–– Depends on curve Depends on curve characteristics characteristics –– curvature curvature and superelevation (cant)and superelevation (cant)

•• Reduce trip time without Reduce trip time without reconfiguring existing route reconfiguring existing route layoutlayout

–– Strongly dependent on Strongly dependent on route makeuproute makeup

–– Can improve speed on Can improve speed on tangents as welltangents as well

•• Can reduce need for braking Can reduce need for braking or accelerating when or accelerating when entering or exiting curvesentering or exiting curves

D.EEV ua

0070

max

49 CFR 213.57 and 213.32949 CFR 213.57 and 213.329Curves; Elevation and Speed LimitationsCurves; Elevation and Speed Limitations

Eu = Cant Deficiency (inches)



Vehicle Speed (3" Superelevation)

0

20

40

60

80

100

120

140

0 1 2 3 4 5 6

Curvature (deg)

Spee

d (m

ph)

0" CD1" CD2" CD3" CD4" CD5" CD6" CD7" CD8" CD9" CD


D.EEV ua

0070

max

Higher Speed with Increasing CD



Time per Mile (3" Superelevation)

0.0

0.5

1.0

1.5

2.0

2.5

0 1 2 3 4 5 6

Curvature (deg)

Tim

e pe

r Mile

(min

)

0" CD1" CD2" CD3" CD4" CD5" CD6" CD7" CD8" CD9" CD


Lower Trip Time with Increasing CD



Time Savings per Mile Over Balance Speed (3" Superelevation)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 1 2 3 4 5 6

Curvature (deg)

Tim

e Sa

ving

s pe

r Mile

(min

)

1" CD2" CD3" CD4" CD5" CD6" CD7" CD8" CD9" CD


Larger Time Savings with Increasing CD

Greater Time Savings in Higher Degree Curves




•• Example Trip Time Comparison for 2 routesExample Trip Time Comparison for 2 routes

–– Route 1: NEC Boston to Washington DCRoute 1: NEC Boston to Washington DC

–– Route 2: Seattle to PortlandRoute 2: Seattle to Portland

•• This analysis does not include tangent miles This analysis does not include tangent miles and assumes speed in curve is constant at and assumes speed in curve is constant at either either VmaxVmax or the maximum operating or the maximum operating speed (the lesser of the two)speed (the lesser of the two)



Benefits of Operating at CDBenefits of Operating at CDPercentage of Track Length Below Curvature

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5 6 7 8 9 10

Curvature (deg)

Perc

ent o

f Tra

ck L

engt

h (%

)

Curves on NEC (129.3 miles)

Curves Seattle to Portland (71.0 miles)

* 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)



NEC: 129.3 miles, 125mph maximum speedSeattle-Portland: 71.0 miles, 80mph maximum speed

0

10

20

30

40

50

60

70

80

90

100

3 4 5 6 7 8 9

Cant Deficiency (in)

Trip

Tim

e (m

in)

NECSeattle - 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)

90

7368

53




•• Estimate of reduction in trip time in previous example Estimate of reduction in trip time in previous example does not account for all factors that affect actual tripdoes not account for all factors that affect actual trip–– Time strongly dependent on route makeup Time strongly dependent on route makeup –– order of curves, etc.order of curves, etc.

–– Although equipment qualified for higher CD, Although equipment qualified for higher CD, VmaxVmax in a particular in a particular curve may not be achievable due to constraints of neighboring curve may not be achievable due to constraints of neighboring curves, etc.curves, etc.

–– May not want to maintain to higher track class corresponding to May not want to maintain to higher track class corresponding to higher speedhigher speed

–– Higher CD may permit higher speed on tangents as wellHigher CD may permit higher speed on tangents as well

–– Reduces need for slowing down when entering a curveReduces need for slowing down when entering a curve

–– Reduces need for accelerating when exiting a curveReduces need for accelerating when exiting a curve

–– Etc.Etc.




0

25

50

75

100

125

150

175

200

225

250

275

300

325

0102030405060708090100110120130140150Curve Number

Spee

d (m

ph)

7" CD speed for curve

9" CD speed for curve

7" Line Speed

9" Line Speed

New HavenMP 75

BostonMP 225

MP155

MP170

10 Short Curves

ProvidenceMP 185

Interlockings

Xing

Bridge

Xing

0

5

10

Class 9

Class 8

Class 7

Class 6

Class 5

Class 4

Class 3

Class 2

Class 1



•• Increase in lateral force exerted on track during curvingIncrease in lateral force exerted on track during curving–– Increased deterioration of track, lower safety margin for curvinIncreased deterioration of track, lower safety margin for curving, g,

and may result in unsafe wheel force conditionsand may result in unsafe wheel force conditions

•• Decrease in load on wheels on inside railDecrease in load on wheels on inside rail–– Increased risk of vehicle overturn, especially if high winds preIncreased risk of vehicle overturn, especially if high winds presentsent

•• Reduction in margin of safety associated with vehicle Reduction in margin of safety associated with vehicle response to track geometry variationsresponse to track geometry variations–– Suspension elements operating at performance limitsSuspension elements operating at performance limits

•• Increase in net steady stated carbody lateral accelerationIncrease in net steady stated carbody lateral acceleration–– Decreased passenger ride comfortDecreased passenger ride comfort–– Tilt can be used at high cant deficiency to reduce the net laterTilt can be used at high cant deficiency to reduce the net lateral al

acceleration acting on the passengers acceleration acting on the passengers

Effect of CD on Vehicle PerformanceEffect of CD on Vehicle Performance



Increasing SpeedIncreasing Speed

Superelevation Superelevation Superelevation

Stopped

Superelevation

Center ofGravity

Resultant

Increase superelevation to create balance

condition

Superelevation counteracts centripetal acceleration

Decrease superelevation to create balance

condition

Remove superelevation to create balance

condition

Lateral acceleration=0

UnderbalanceUnderbalance(Cant Deficiency)(Cant Deficiency)BalanceBalanceOverbalanceOverbalance

(Cant Excess)(Cant Excess)OverbalanceOverbalance(Cant Excess)(Cant Excess)

Lateral acceleration<0 Lateral acceleration<0 Lateral acceleration>0

Center ofGravity

Resultant

Center ofGravity

Resultant

Center ofGravity

Resultant

Effect of CD on Vehicle PerformanceEffect of CD on Vehicle Performance



Use of Tilt at High Cant DeficiencyUse of Tilt at High Cant Deficiency

Lateral acceleration>0.12 Lateral acceleration<0.12

Operating at High CD Operating at High CD withoutwithout TiltTilt

Operating at High CD Operating at High CD withwith TiltTilt



Cant Deficiency at which Tilt-body Compensation Becomes Necessary

0

1

2

3

4

5

6

7

8

9

10

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Suspension flexibility (S)

Can

t Def

icie

ncy

(inch

)

Limit of 0.1gLimit of 0.15gLimit of 0.12g


Suspension with No

Carbody Roll Typical Roll Suspension

Soft Roll Suspension

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.




plane) track to relative (measured tionsupereleva to due roll

ation)(superelev horizontal and plane track between angle

Rstatic

track

track

Rstatic

where

S




Benefits Benefits –– not a complete listnot a complete list

•• Addresses ride comfort at higher cant deficiencyAddresses ride comfort at higher cant deficiency–– Reduces steady state lateral acceleration felt by passengersReduces steady state lateral acceleration felt by passengers

•• Allows operation at higher cant deficiency by meeting Allows operation at higher cant deficiency by meeting regulatory requirements on steady state lateral accelerationregulatory requirements on steady state lateral acceleration

•• Has little to no effect on wheel rail forces or derailment safetHas little to no effect on wheel rail forces or derailment safetyy

Drawbacks Drawbacks –– not a complete listnot a complete list

•• Compatibility with clearance envelopes for existing lines and Compatibility with clearance envelopes for existing lines and equipmentequipment

•• Increased suspension complexity and maintenanceIncreased suspension complexity and maintenance

•• Motion sicknessMotion sickness

cant deficiency

Documents

balance superelevation

deficiency effect

tcant deficiency

gravitational force

given curve

latebalance speed

outside ofbalance speed

curves steady state