Federal Railroad Administration Cant Deficiency, Curving Speeds Cant Deficiency, Curving Speeds and Tilt and Tilt Brian Marquis – – Mechanical Engineer Mechanical Engineer Brian Marquis Volpe National Transportation Systems Center Volpe National Transportation Systems Center Cambridge, Massachusetts Cambridge, Massachusetts Cant Deficiency/Tilt US DOT Volpe Center Marquis / Page 1
Federal Railroad Administration Topics Topics Cant Deficiency Cant Deficiency • Definition of Cant Deficiency • Definition of Cant Deficiency • Benefits of Operating at Cant Deficiency • Benefits of Operating at Cant Deficiency • Effect of Cant Deficiency on Rail Vehicle Performance • Effect of Cant Deficiency on Rail Vehicle Performance • Use of Tilt at High Cant Deficiency • Use of Tilt at High Cant Deficiency Cant Deficiency/Tilt US DOT Volpe Center Marquis / Page 2
Federal Railroad Administration Steady State Forces on Trains in Curves Steady State Forces on Trains in Curves Cant Deficiency/Tilt US DOT Volpe Center Marquis / Page 3
Federal Railroad Administration Definition of Cant Deficiency Definition of Cant Deficiency • Trains operating in curves experience net lateral force (centrif ugal ugal • Trains operating in curves experience net lateral force (centrif force) to the outside of the curve that is a function of the velocity. ocity. force) to the outside of the curve that is a function of the vel • 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 lateral ral • Balance speed for any given curve is the speed at which the late 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 t he he • Cant deficiency involves traveling through a curve faster than t balance speed and produces a net lateral force to the outside of the the balance speed and produces a net lateral force to the outside of 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. Cant Deficiency/Tilt US DOT Volpe Center Marquis / Page 4
Federal Railroad Administration Definition of Cant Deficiency Definition of Cant Deficiency Increasing Speed Stopped Increasing Speed Overbalance Overbalance Underbalance Overbalance Overbalance Underbalance Balance Balance (Cant Excess) (Cant Excess) (Cant Deficiency) (Cant Excess) (Cant Excess) (Cant Deficiency) Lateral acceleration<0 Lateral acceleration<0 Lateral acceleration=0 Lateral acceleration>0 Center of Center of Center of Center of Gravity Gravity Gravity Gravity Resultant Resultant Resultant Resultant Superelevation Superelevation Superelevation Superelevation Remove Decrease Superelevation Increase superelevation to superelevation to counteracts superelevation to create balance create balance centripetal create balance condition condition acceleration Cant Deficiency/Tilt condition US DOT Volpe Center Marquis / Page 5
Federal Railroad Administration Benefits of Operating at CD Benefits of Operating at CD • Higher curving speeds V V max • Higher curving speeds max – Depends on curve – Depends on curve characteristics – characteristics – curvature curvature 49 CFR 213.57 and 213.329 49 CFR 213.57 and 213.329 and superelevation (cant) and superelevation (cant) Curves; Elevation and Speed Limitations Curves; Elevation and Speed Limitations • Reduce trip time without • Reduce trip time without reconfiguring existing route reconfiguring existing route E E a u V max layout layout 0 007 . D – – S S trongly dependent on trongly dependent on route makeup route makeup – – Can improve speed on Can improve speed on E u = Cant Deficiency (inches) tangents as well tangents as well • Can reduce need for braking • Can reduce need for braking or accelerating when or accelerating when entering or exiting curves entering or exiting curves Cant Deficiency/Tilt US DOT Volpe Center Marquis / Page 6
Federal Railroad Administration Benefits of Operating at CD Benefits of Operating at CD Vehicle Speed (3" Superelevation) 140 120 Higher Speed with 0" CD 100 Increasing CD 1" CD Speed (mph) 2" CD 80 3" CD 4" CD 5" CD 60 6" CD 7" CD 40 8" CD 9" CD E E a u V max 20 0 007 . D 0 0 1 2 3 4 5 6 Cant Deficiency/Tilt Curvature (deg) US DOT Volpe Center Marquis / Page 7
Federal Railroad Administration Benefits of Operating at CD Benefits of Operating at CD Time per Mile (3" Superelevation) 2.5 2.0 0" CD Time per Mile (min) 1" CD 2" CD 1.5 3" CD 4" CD 5" CD 1.0 6" CD 7" CD 8" CD 9" CD 0.5 Lower Trip Time with Increasing CD 0.0 0 1 2 3 4 5 6 Cant Deficiency/Tilt Curvature (deg) US DOT Volpe Center Marquis / Page 8
Federal Railroad Administration Benefits of Operating at CD Benefits of Operating at CD Time Savings per Mile Over Balance Speed (3" Superelevation) 1.2 Larger Time Savings 1.0 with Increasing CD Time Savings per Mile (min) 1" CD 0.8 2" CD 3" CD 4" CD 0.6 5" CD 6" CD 7" CD 0.4 8" CD 9" CD 0.2 Greater Time Savings in Higher Degree Curves 0.0 0 1 2 3 4 5 6 Cant Deficiency/Tilt Curvature (deg) US DOT Volpe Center Marquis / Page 9
Federal Railroad Administration Benefits of Operating at CD Benefits of Operating at CD • Example Trip Time Comparison for 2 routes Example Trip Time Comparison for 2 routes • – Route 1: NEC Boston to Washington DC Route 1: NEC Boston to Washington DC – – Route 2: S Route 2: S eattle to Portland – eattle 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 Vmax Vmax or the maximum operating or the maximum operating either speed (the lesser of the two) speed (the lesser of the two) Cant Deficiency/Tilt US DOT Volpe Center Marquis / Page 10
Federal Railroad Administration Benefits of Operating at CD Benefits of Operating at CD Percentage of Track Length Below Curvature 100 90 Percent of Track Length (%) 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 20 either Vmax or the maximum operating speed (the lesser of the two) 10 0 0 1 2 3 4 5 6 7 8 9 10 Curvature (deg) Cant Deficiency/Tilt US DOT Volpe Center Marquis / Page 11
Federal Railroad Administration Benefits of Operating at CD Benefits of Operating at CD NEC: 129.3 miles, 125mph maximum speed Seattle-Portland: 71.0 miles, 80mph maximum speed 100 NEC 90 90 Seattle - Portland 80 73 68 70 Trip Time (min) 60 53 50 40 * This analysis does not include tangent miles and assumes speed in curve is constant at 30 either Vmax or the maximum operating 20 speed (the lesser of the two) 10 0 3 4 5 6 7 8 9 Cant Deficiency/Tilt Cant Deficiency (in) US DOT Volpe Center Marquis / Page 12
Federal Railroad Administration Benefits of Operating at CD Benefits of Operating at CD • 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 trip does 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, Vmax Vmax 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 speed higher speed – Higher CD may permit higher speed on tangents as well Higher CD may permit higher speed on tangents as well – – Reduces need for slowing down when entering a curve – Reduces need for slowing down when entering a curve – Reduces need for accelerating when exiting a curve Reduces need for accelerating when exiting a curve – – Etc. Etc. – Cant Deficiency/Tilt US DOT Volpe Center Marquis / Page 13
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