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CHAPTER 4
Transit Vehicle Flange Climb
Derailment Simulation
Flange climb derailment can occur due to excessive lateral and 7.5 in. cant deficiency overbalance speeds on main-line
forces acting on the wheel as a vehicle negotiates a curve. tracks for different radius curves (see Table 5).
A common remedy for flange climb derailment in curves The wheel/rail friction coefficient has a large effect on the
is to install guard rails on curves to provide additional potential for derailment; therefore, all simulation cases were
resistance to flange climbing. The fundamental flange climb carried out for W/R friction coefficients of 0.3, 0.4, 0.5 and 0.6.
derailment mechanism was investigated in TCRP Report 71,
Volume 5 (2).
4.2 Transit Rail Cars
In this Chapter, dynamic curving simulations were con-
ducted on four types of transit vehicles by using the NUCARS Figure 22 shows the steady-state curving results for a transit
program. The L/V ratio and flange climb distance criteria rail car (Type 1) on a yard track without perturbations. The
proposed in the previous TCRP project (2) were applied to wheel L/V ratio on tight curves with a radius less than 500 ft
the simulation results. Guidelines for guard rail installation increases when the W/R friction coefficient increases. The
were produced based on these analyses. vehicle derailed on curves with a radius less than or equal to
250 ft at a friction coefficient of 0.6, which indicates that a guard
rail is needed even on a perfect track without perturbations.
4.1 Simulation Cases
As expected, the dynamic curving L/V ratios on a perturbed
The track geometries were represented both as smooth track without a guard rail increase with the W/R friction coeffi-
track without track irregularities (as designed) and also with cient and the amplitude of the perturbations (See Figures 23
a "down and out" perturbation in the middle of the curve. and 24). The L/V ratios are generally higher than those in the
The "down and out" perturbations consisted of a combination steady curving conditions. The dynamic L/V ratios approach
of track geometry irregularities that were of a magnitude at or exceed the Nadal limit (shown as a solid line) at a friction
the limit generated based on the track standards from several coefficient of 0.5. The vehicle derailed for all simulated cases
transit systems. This consisted of a downward vertical cusp (100 to 3,000 ft radii curves) with a friction coefficient of 0.6
on the high rail combined with an outward lateral alignment and Level 3 perturbations.
cusp on the high rail and an inward cusp on the low rail of a There are many factors that lead to flange climb derailment.
magnitude sufficient to ensure that the maximum permitted Three of them have the most critical effects: wheel flange angle,
gage was not exceeded. These irregularities had a 31-ft wave- friction coefficient, and perturbation amplitude. As Figure 22
length with a cosine shape, with three levels of severity of shows, even without perturbations, wheel flange climbing can
perturbations, as displayed in Figures 19 through 21. Table 4 still occur because of a lower (63°) flange angle and a higher
lists the amplitudes of the track perturbations. friction coefficient (0.6).
The most severe perturbation (Level 3) is typical of the Tests and simulations show that the friction coefficient plays
maintenance limit for low-speed operation in rail yards. The a critical role for derailment. If the W/R friction coefficient
Level 1 perturbation represents a typical limit for a high speed can be controlled to remain under 0.4 with reliable lubrication
on a main line. These perturbations were placed in the middle devices, guard rails are not needed for this type of vehicle
of a number of left hand curves with curve radii from 100 ft (Figures 22 through 24). However, many factors lead to the
to 3,000 ft, and 1-in. superelevation. The vehicle running speed variation of the friction coefficient such as weather conditions,
was 15 mph on yard track, and speeds corresponding to 4.0 in. unreliable rail lubrication, new trued wheel surface roughness,
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Level 1 Level 3
0.00 0.00
-0.50 -0.50
Perturbation (in.)
Perturbation (in.)
-1.00 -1.00
-1.50 Lat Right -1.50 Lat Right
Lat Left Lat Left
-2.00 Vert Right
-2.00
Vert Right
-2.50 -2.50
360 380 400 420 440 460 360 380 400 420 440 460
Distance (ft) Distance (ft)
Figure 19. Track perturbation, Level 1. Figure 21. Track perturbation, Level 3.
and W/R wear conditions; all of these factors are hard to The likelihood of flange climb derailment is rare if the
control. wheel climbs on the rail with distance less than 3 ft.
Table 6 lists the W/R friction coefficients measured on · For curves with radii greater than 755 ft:
TTCI's track. The measured rail friction coefficient at normal The L/V ratio limit equals the Nadal limit; and
conditions can be higher than 0.55 but are seldom above 0.6. Flange climb distance limit equals 5 ft.
To ensure a reasonable safety margin, the simulation results
with a friction coefficient of 0.6 are used in this study to make The reasons for using a longer flange climb distance criteria
judgments about whether guard rail installations are needed. for curves with radii larger than 755 ft are the following:
The simulation results with a friction coefficient of 0.55 were
also conducted for a less conservative application. · The steady-state axle AOA on curves with radii larger than
Based on the conclusions and findings in TCRP Report 71 755 ft is normally less than 5 milliradians (mrad);
(2), the following criteria were used for making judgments · The L/V ratio limit decreases with the increase of AOA and
about whether a guard rail is needed: converges to the Nadal value as the AOA becomes larger
than 10 mrad (2); and
· For curves with radii less than or equal to 755 ft or for · The flange climb distance decreases when the AOA increases,
vehicles with independent rotating wheel: and converges to a value (2).
The L/V ratio limit equals the Nadal limit. There is no
flange climb derailment risk if the L/V ratio is less than Based on these criteria, for the Type 1 transit rail car with
the Nadal limit; and a 63° flange angle running on yard track with Level 3 pertur-
The flange climb distance limit equals 3 ft. This criterion bation, the guard rail should be installed on curves with radii
is less conservative than the above L/V ratio criterion. less than 3,000 ft to prevent flange climb derailment because
the L/V ratios with a 3-ft window (for curves with radii less than
or equal to 755 ft) or a 5-ft window exceeded the Nadal value.
However, if the track perturbation maintenance improves to
Level 2 the Level 2 standard on yard tracks, only curves with radii less
0.00
than or equal to 755 ft need to be guarded, as Figure 25 shows.
-0.50 Maintenance on a main-line track is normally better than
Perturbation (in.)
maintenance on a yard track. Correspondingly, the allowable
-1.00 running speed on a main-line track is higher than the allowable
running speed on a yard track. The Type 1 transit rail car either
-1.50 Lat Right derailed or the L/V ratio and flange climb distance exceeded
Lat Left the criteria values on all simulated curves at speeds of 4 or
-2.00 Vert Right
7.5 in. cant deficiency on Level 3 perturbed tracks, which
-2.50 indicates such maintenance levels cannot be tolerated on
360 380 400 420 440 460 main-line track for this vehicle. The situation was a little better
Distance (ft) for Level 2 perturbations where the L/V ratio had less than a
Figure 20. Track perturbation, Level 2. limit of 4 in. cant deficiency speed on curves with radii larger
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Table 4. Track perturbation amplitude.
Perturbation Left (Low) Rail Lateral Left (Low) Rail Right (High) Rail Right (High) Rail
Level Perturbation Vertical Lateral Vertical
Amplitude (in.) Perturbation Perturbation Perturbation
Amplitude (in.) Amplitude (in.) Amplitude (in.)
1 0.13 0 0.50 0.50
2 0.63 0 1.00 1.25
3 1.25 0 2.00 1.25
Table 5. Overbalance running speed on curves.
Curve Radius Superelevation 4.0 in. Cant Deficiency Speed 7.5 in. Cant Deficiency
(ft) (in.) (mph) Speed (mph)
100 1.0 11.14 14.52
250 1.0 17.62 22.96
320 1.0 19.93 25.97
500 1.0 24.92 32.46
755 1.0 30.62 39.89
955 1.0 34.43 44.87
1,145 1.0 37.70 49.13
2,000 1.0 49.83 64.93
3,000 1.0 61.03 79.52
R=100 ft R=250 ft
1.2
R=320 ft R=500 ft
Nadal--63°
R=755 ft R=955 ft
Lead Axle High Rail Wheel L/V
1
R=1145 ft
0.8
0.6
0.4
0.2
0
0.3 0.4 0.5 0.6
Friction Coefficient
Figure 22. Wheel L/V ratio of a Type 1 transit rail car with
steady-state curving 15 mph, no guard rail.
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R=100 ft R=250 ft
1.2 R=320 ft R=500 ft
Nadal--63°
Lead Axle High Rail Wheel L/V
R=755 ft R=955 ft
1 R=1145 ft
0.8
0.6
0.4
0.2
0
0.3 0.4 0.5 0.6
Friction Coefficient
Figure 23. Wheel L/V ratio, Type 1 transit rail car, Level 2
perturbations 15 mph, no guard rail.
R=100 ft R=250 ft
1.2
R=320 ft R=500 ft
Nadal--63°
Lead Axle High Rail Wheel L/V
R=755 ft R=955 ft
1
R=1145 ft
0.8
0.6
0.4
0.2
0
0.3 0.4 0.5 0.6
Friction Coefficient
Figure 24. Wheel L/V ratio, Type 1 transit rail car, Level 3
perturbations 15 mph, no guard rail.
Table 6. Measured W/R friction coefficients (tribometer readings)
on TTCI track.
Track Location Inside Outside Weather Condition Date Time
R36 Post Marker 0.43 0.52 Sunny 2/25/2007 10:30 AM
R36 Post Marker 0.41 0.46 Cloudy 3/08/2007 9:00 AM
RTT
R36 Post Marker 0.40 0.44 Sunny 3/15/2007 9:10 AM
R36 Post Marker 0.46 0.45 Sunny 3/16/2007 8:40 AM
R165 Post
0.50 0.56 Sunny 2/23/2007 10:00 AM
Marker
TDT Sunny, Soap and
R165 Post
0.32 0.37 Water Spray on 2/23/2007 11:00 AM
Marker
Track
7.5° curve 0.48 0.46
WRM 12° curve 0.43 0.43 Sunny 2/19/2007 12:20 PM
10° curve 0.49 0.47
WRM 10° bypass curve 0.44 0.45 Sunny 3/20/2007 1:30 PM
7.5° curve 0.48 0.5
WRM 7.5° curve 0.43 0.44 Cloudy 3/21/2007 10:20 AM
12° curve 0.46 0.5
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Friction Coefficient 0.6
0.8
Lead Axle High Rail Wheel L/V
0.7
0.6
0.5
NADAL Limit
0.4
7.5 inch CD, no pert
0.3 7.5 inch CD, pert1
0.2 7.5 inch CD, pert2
4.0 inch CD, pert2
0.1
15 mph, pert2
0
100 300 500 700 900 1100
Curve Radius (ft)
Figure 25. The wheel L/V ratio of a Type 1 transit rail car
with a 0.6 friction coefficient and a 63° flange angle.*
*Refer to Table 5 for the different speeds corresponding to 7.5-in. cant deficiency (CD).
than 2,000 ft. For Level 1 track perturbations, the L/V ratio A measured worn rail profile was used in the simulation to
exceeded the Nadal value on curves with radii less than or investigate the effect of worn rails on flange climb derailment.
equal to 500 ft at 7.5 in. cant deficiency speed, as Figure 25 Figures 27 through 29 show that the L/V ratio for the worn rail
shows. Under such conditions, no guard rails are needed for case is less than that of the new rail case shown in Figures 22
curves with radii larger than 500 ft for the Type 1 transit to 24. These results imply that simulations using new W/R
rail car. profiles will lead to conservative conclusions. An investigation
Another way to decrease the flange climb derailment risk is to of worn W/R profiles on freight car flange climb derailment (5)
decrease the W/R friction coefficient. As Figure 26 shows, if the also showed a similar phenomena because most wheels and
friction coefficient is 0.5, for the Type 1 transit rail car, the guard rails wore into a steeper flange contact angle.
rail should be installed on yard curves with radii less than or Another common practice to decrease flange climb derail-
equal to 300 ft, and main-line curves with radii less than or equal ment risk in transit systems is to increase the wheel flange angle.
to 500 ft at a 7.5 in. cant deficiency speed. However, controlling As discussed in the previous TCRP Report 71, Volume 5 (2),
the friction coefficient to less than 0.5 on curves in a consistent increasing the flange angle increases the Nadal flange climb
and reliable way may be difficult during actual service. limit. Case studies were conducted for the Type 1 transit rail car
Friction Coefficient 0.5
0.8
Lead Axle High Rail Wheel L/V
0.7
0.6
0.5
NADAL Limit
0.4
7.5 inch CD, no pert
0.3 7.5 inch CD, pert1
0.2 7.5 inch CD, pert2
4.0 inch CD, pert2
0.1
15 mph, pert2
0
100 300 500 700 900 1100
Curve Radius (ft)
Figure 26. The wheel L/V ratio of a Type 1 transit rail car with
a 0.5 Friction Coefficient and a 63° Flange Angle.*
*Refer to Table 5 for the different speeds corresponding to 7.5-in. cant deficiency (CD).
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R=100 ft R=250 ft
1.2
R=320 ft R=500 ft
Nadal--63°
R=755 ft R=955 ft
Lead Axle High Rail Wheel L/V
1
R=1145 ft
0.8
0.6
0.4
0.2
0
0.3 0.4 0.5 0.6
Friction Coefficient
Figure 27. Wheel L/V ratio, Type 1 transit rail car, steady-state
curving, 15 mph, worn rail.
R=100 ft R=250 ft
1.2 R=320 ft R=500 ft
R=755 ft R=955 ft
Lead Axle High Rail Wheel L/V
1 R=1145 ft
0.8
0.6
0.4
0.2
0
0.3 0.4 0.5 0.6
Friction Coefficient
Figure 28. The wheel L/V ratio, Type 1 transit rail car,
perturbation Level 1, 15 mph, worn rail.
R=100 ft R=250 ft
1.2
R=320 ft R=500 ft
Nadal--63° R=755 ft R=955 ft
Lead Axle High Rail Wheel L/V
1
R=1145 ft
0.8
0.6
0.4
0.2
0
0.3 0.4 0.5 0.6
Friction Coefficient
Figure 29. Wheel L/V ratio, Type 1 transit rail car, perturbation
Level 3, 15 mph, worn rail.
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R=100 ft R=250 ft
1.8
R=320 ft R=500 ft
1.6 R=755 ft R=955 ft
Lead Axle High Rail Wheel L/V
Nadal--75°
1.4 R=1145 ft
1.2
1
0.8
0.6
0.4
0.2
0
0.3 0.4 0.5 0.6
Friction Coefficient
Figure 30. Wheel L/V ratio, Type 1 transit rail car, 15 mph,
75° flange angle, steady-state curving.
using the same modeling parameters except for the wheelset rail is needed on yard curves with radii larger than 100 ft for
dimensions and the 75° angle wheel profiles. Figure 30 shows the a vehicle with a 75° flange angle wheel running at a speed of
significant safety improvements made by using the 75° flange 15 mph. However, the risk of derailment still exists under
angle wheel compared with the 63° flange wheel (Figure 22), conditions of higher speeds and a poorly maintained track. As
with all simulated steady-state curving L/V ratios far below Figure 33 shows, the vehicle with a 75° flange angle wheel still
the Nadal values. derailed on curves with radii larger than or equal to 1,145 ft at a
Figures 31 and 32 show that the dynamic curving L/V ratios 7.5 in. cant deficiency speed because of excessive lateral impacts.
of the Type 1 transit rail car with 75° flange angle wheels also The track has to be maintained with at least a Level 2 standard
increase as the perturbation increases. As Figure 30 shows, a to allow a 7.5 in. cant deficiency running speed.
steeper flange angle wheel increases the L/V ratio slightly com- The following conclusions for the Type 1 transit rail car can
pared with the 63° flange angle wheel. The improvement is be drawn from the above analyses:
because the NADAL value for the 75° flange angle is consid-
erably higher than for the 63° flange angle. · The flange climb derailment risk is very high for the
The use of a steep flange angle wheel reduces the flange climb Type 1 transit rail car with a 63° flange angle wheel. Guard/
derailment potential. Figure 33 shows that the L/V ratios for restraining rails should be installed on the following:
all the simulated cases at a speed of 15 mph and with Level 3 Yard curves with radii less than 755 ft; the speed limit is
perturbations are less than the Nadal value. Therefore, no guard 15 mph under Level 2 perturbations.
R=100 ft R=250 ft
1.8 R=320 ft R=500 ft
1.6 R=755 ft R=955 ft
Lead Axle High Rail Wheel L/V
1.4 R=1145 ft
1.2
1
0.8
0.6
0.4
0.2
0
0.3 0.4 0.5 0.6
Friction Coefficient
Figure 31. Wheel L/V ratio, Type 1 transit rail car, 15 mph,
75° flange angle, perturbation Level 2.
