U.S. patent application number 12/703959 was filed with the patent office on 2010-09-23 for system and method for controlling braking of a train.
This patent application is currently assigned to Ansaldo STS USA, Inc.. Invention is credited to Chinnarao Mokkapati, Brian Michael Nypaver, Robert D. Pascoe, William Stover Rhea, JR..
Application Number | 20100241296 12/703959 |
Document ID | / |
Family ID | 42562053 |
Filed Date | 2010-09-23 |
United States Patent
Application |
20100241296 |
Kind Code |
A1 |
Rhea, JR.; William Stover ;
et al. |
September 23, 2010 |
System and Method for Controlling Braking of a Train
Abstract
A method of controlling braking of a train that includes
obtaining in an on-board computer of the train a brake propagation
delay time (T.sub.d), a brake build-up time (T) and a maximum brake
rate (.alpha..sub.max) for the train, and controlling braking of
the train in the on-board computer by generating one or more
braking signals for the train using T.sub.d, T and .alpha..sub.max.
Also, a methods of determining for a train a profile velocity to a
target position of a selected target, selecting a most restrictive
target from among a plurality of targets for a train, and
determining a plurality of braking parameters for a train having a
train consist, wherein the parameters include a brake propagation
delay time (T.sub.d), a brake build-up time (T) and a maximum brake
rate (.alpha..sub.max).
Inventors: |
Rhea, JR.; William Stover;
(Lower Burrell, PA) ; Mokkapati; Chinnarao;
(Export, PA) ; Pascoe; Robert D.; (Pittsburgh,
PA) ; Nypaver; Brian Michael; (Pittsburgh,
PA) |
Correspondence
Address: |
ECKERT SEAMANS CHERIN & MELLOTT
600 GRANT STREET, 44TH FLOOR
PITTSBURGH
PA
15219
US
|
Assignee: |
Ansaldo STS USA, Inc.
Pittsburgh
PA
|
Family ID: |
42562053 |
Appl. No.: |
12/703959 |
Filed: |
February 11, 2010 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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61152098 |
Feb 12, 2009 |
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61152083 |
Feb 12, 2009 |
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61152040 |
Feb 12, 2009 |
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61152101 |
Feb 12, 2009 |
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Current U.S.
Class: |
701/20 |
Current CPC
Class: |
B61L 27/04 20130101;
B61L 3/008 20130101; B60T 13/665 20130101; B60T 17/228
20130101 |
Class at
Publication: |
701/20 |
International
Class: |
G05D 1/00 20060101
G05D001/00 |
Goverment Interests
GOVERNMENT CONTRACT
[0002] Inventors' Assignee has a contract with the Alaska Railroad
Corporation, an Alaskan corporation (ARRC Contract No. 25329).
Funding for this contract is provided, in part, by the Federal
Railroad Administration, a United States government agency. The
United States government may have certain rights in the invention
described herein.
Claims
1. A method of controlling braking of a train, comprising:
obtaining in an on-board computer of the train a brake propagation
delay time (T.sub.d), a brake build-up time (T) and a maximum brake
rate (.alpha..sub.max) for the train; and controlling braking of
the train in the on-board computer by generating one or more
braking profiles for the train using T.sub.d, T and
.alpha..sub.max.
2. The method according to claim 1, wherein the controlling further
comprises calculating in the on-board computer a profile velocity
to a particular target using T.sub.d, T and .alpha..sub.max and
generating one or more braking signals for the train in the
on-board computer using the profile velocity.
3. The method according to claim 1, wherein the controlling further
comprises calculating in the on-board computer a profile velocity
to a particular target using T.sub.d, T and .alpha..sub.max and
determining in the on-board computer whether to request a penalty
brake application for the train based on the profile velocity.
4. The method according to claim 3, wherein the obtaining comprises
calculating T.sub.d, T and .alpha..sub.max in the on-board
computer.
5. The method according to claim 4, wherein the train comprises a
train consist defined by a plurality of consist parameters, and
wherein the calculating comprises calculating T.sub.d, T and
.alpha..sub.max using the consist parameters.
6. The method according to claim 5, wherein the consist parameters
include a length (L) of the train consist, a ratio (w) of a weight
(W) of the train consist to a total number (V) of brake valves in
the train consist excluding any brake valves on any locomotives in
the train consist, a total number (N) of cars in the train consist
excluding the any locomotives, and a number (n.sub.i) of each type
of car in the train consist excluding the any locomotives.
7. The method according to claim 6, wherein T.sub.d is calculated
based on L, N and n.sub.i, wherein T is calculated based on L, N
and wherein .alpha..sub.max is calculated based on L, N, n.sub.i
and w.
8. The method according to claim 3, wherein the obtaining further
comprises obtaining an average grade from a current position of the
train to a position of the particular target, and wherein the
profile velocity is also calculated using the average grade.
9. The method according to claim 8, wherein the average grade is
calculated from a rear of the train to the position of the
particular target.
10. The method according to claim 3, further comprising obtaining
target data for a plurality of targets within a predetermined
distance ahead of a current position of the train, and determining
a most restrictive target from among the plurality of targets, the
particular target being the most restrictive target.
11. The method according to claim 3, wherein if it is determined
that the penalty brake application should be requested, the method
further comprises sending a signal from the on-board computer to a
braking system of the train causing the braking system to bring the
train to a stop.
12. A train-borne component of a positive train control system
comprising an on-board computer for a train, the on-board computer
being programmed to control braking of the train by: obtaining a
brake propagation delay time (T.sub.d), a brake build-up time (T)
and a maximum brake rate (.alpha..sub.max) for the train; and
controlling braking of the train by generating one or more braking
profiles for the train using T.sub.d, T and .alpha..sub.max.
13. The train-borne component according to claim 12, wherein the
controlling further comprises calculating a profile velocity to a
particular target using T.sub.d, T and .alpha..sub.max, and
generating one or more braking signals for the train using the
profile velocity.
14. The train-borne component according to claim 12, wherein the
controlling further comprises calculating in the on-board computer
a profile velocity to a particular target using T.sub.d, T and
.alpha..sub.max and determining whether to request a penalty brake
application for the train based on the profile velocity.
15. The train-borne component according to claim 14, wherein the
obtaining comprises calculating T.sub.d, T and .alpha..sub.max.
16. The train-borne component according to claim 15, wherein the
train comprises a train consist defined by a plurality of consist
parameters, and wherein the calculating comprises calculating
T.sub.d, T and .alpha..sub.max using the consist parameters.
17. The train-borne component according to claim 16, wherein the
consist parameters include a length (L) of the train consist, a
ratio (w) of a weight (W) of the train consist to a total number
(V) of brake valves in the train consist excluding any brake valves
on any locomotives in the train consist, a total number (N) of cars
in the train consist excluding the any locomotives, and a number
(n.sub.i) of each type of car in the train consist excluding the
any locomotives.
18. The train-borne component according to claim 17, wherein
T.sub.d is calculated based on L, N and n.sub.i, wherein T is
calculated based on L, N and n.sub.i, and wherein .alpha..sub.max
is calculated based on L, N, n.sub.i and w.
19. The train-borne component according to claim 14, wherein the
obtaining further comprises obtaining an average grade from a
current position of the train to a position of the particular
target, and wherein the profile velocity is also calculated using
the average grade.
20. The train-borne component according to claim 19, wherein the
average grade is calculated from a rear of the train to the
position of the particular target.
21. The train-borne component according to claim 14, wherein the
on-board computer is further programmed to control the braking by
obtaining target data for a plurality of targets within a
predetermined distance ahead of a current position of the train,
and determining a most restrictive target from among the plurality
of targets, the particular target being the most restrictive
target.
22. A method of determining for a train a profile velocity to a
target position of a selected target having a target speed, the
train having a current position located a first distance from the
target position, comprising: determining in an on-board computer of
the train a second distance, the second distance being a distance
from the current position that would be required by the train to
reach the target speed at the instant brake build-up in the train
is complete; determining in the on-board computer whether the first
distance is greater than or equal to the second distance; if the
first distance is greater than or equal to the second distance,
determining in the on-board computer the profile velocity using one
or more first equations, wherein the one or more first equations
assume that steady state braking by the train is needed to achieve
the target speed from the current position; if the first distance
is not greater than or equal to the second distance: (i)
determining in the on-board computer a third distance, the third
distance being a distance from the current position that would be
required by the train to reach the target speed at the instant
brake propagation delay is complete; (ii) determining in the
on-board computer whether the third distance is greater than or
equal to the first distance; and (iii) (a) if the third distance is
greater than or equal to the first distance, determining in the
on-board computer the profile velocity using one or more second
equations, wherein the one or more second equations assume that
steady state braking by the train is not needed to achieve the
target speed from the current position but that transient braking
is needed to achieve the target speed from the current position,
and (b) if the third distance is not greater than or equal to the
first distance, determining in the on-board computer the profile
velocity using one or more third equations, wherein the one or more
third equations assume that neither steady state braking nor
transient braking by the train is needed to achieve the target
speed from the current position.
23. The method according to claim 22, wherein the determining in
the on-board computer the profile velocity using the one or more
second equations comprises determining an amount of brake build-up
time (t) that would be required to reach the target speed from the
current position and using t while determining the profile
velocity, and wherein the determining in the on-board computer the
profile velocity using the one or more third equations comprises
determining an amount of propagation delay time (t.sub.d) that
would be required to reach the target speed from the current
position and using t.sub.d while determining the profile
velocity.
24. The method according to claim 22, wherein the second distance
is determined using the following equation: S = [ v T + ( kg avg +
.alpha. max 2 ) T + kg avg T d ] T d - 1 2 kg avg T d 2 + [ v T + (
kg avg + .alpha. max 2 ) T ] T - ( 1 2 kg avg + .alpha. max 6 ) T 2
, ##EQU00019## wherein V.sub.T is the target speed, k is a
conversion factor needed to determine the effect of gravity on
stopping distance, g.sub.avg is an average grade between the
current position and the target position, .alpha..sub.max is a
maximum brake rate of the train, T is a brake build-up time of the
train, and T.sub.d is a brake propagation delay time of the
train.
25. The method according to claim 22, wherein the one or more first
equations include the following equation: v P 2 + ( 2 .alpha. max T
d + .alpha. max T ) v P - [ .alpha. max ( .alpha. max + 4 kg avg 12
) T 2 + kg avg .alpha. max T d ( T + T d ) + v T 2 + 2 ( .alpha.
max + kg avg ) S DTT ] = 0 , ##EQU00020## wherein V.sub.P is the
profile velocity, S.sub.DTT is the first distance, V.sub.T is the
target speed, k is a conversion factor needed to determine the
effect of gravity on stopping distance, g.sub.avg is an average
grade between the current position and the target position,
.alpha..sub.max is a maximum brake rate of the train, T is a brake
build-up time of the train, and T.sub.d is a brake propagation
delay time of the train.
26. The method according to claim 23, wherein the one or more
second equations include the following equation: v p = v T + kg avg
T d + kg avg t + .alpha. max 2 T t 2 , ##EQU00021## wherein V.sub.P
is the profile velocity, V.sub.T is the target speed, k is a
conversion factor needed to determine the effect of gravity on
stopping distance, g.sub.avg is an average grade between the
current position and the target position, .alpha..sub.max is a
maximum brake rate of the train, T is a brake build-up time of the
train, and T.sub.d is a brake propagation delay time of the
train.
27. The method according to claim 23, wherein the one or more third
equations include the following equation:
v.sub.p=v.sub.T+kg.sub.avgt.sub.d, wherein V.sub.p is the profile
velocity, V.sub.T is the target speed, k is a conversion factor
needed to determine the effect of gravity on stopping distance, and
g.sub.avg is an average grade between the current position and the
target position.
28. The method according to claim 22, wherein the third distance is
determined using the following equation: S = v T T d + 1 2 kg avg T
d 2 , ##EQU00022## wherein V.sub.T is the target speed, K is a
conversion factor needed to determine the effect of gravity on
stopping distance, g.sub.avg is an average grade between the
current position and the target position, and T.sub.d is a brake
propagation delay time of the train.
29. The method according to claim 22, further comprising obtaining
a brake propagation delay time (T.sub.d) for the train, a brake
build-up time (T) for the train, a maximum brake rate
(.alpha..sub.max) for the train, and an average grade (g.sub.avg)
from the current position to the target position, wherein the
determining in the on-board computer the profile velocity using the
one or more first equations uses T.sub.d, T, .alpha..sub.max, and
g.sub.avg, wherein the determining in the on-board computer the
profile velocity using the one or more second equations uses
T.sub.d, T, .alpha..sub.max, and g.sub.avg, and wherein the
determining in the on-board computer the profile velocity using the
one or more third equations uses g.sub.avg.
30. The method according to claim 29, wherein the obtaining
comprises calculating T.sub.d, T and .alpha..sub.max in the
on-board computer.
31. The method according to claim 30, wherein the train comprises a
train consist defined by a plurality of consist parameters, and
wherein the calculating comprises calculating T.sub.d, T and
.alpha..sub.max using the consist parameters.
32. The method according to claim 27, wherein the consist
parameters include a length (L) of the train consist, a ratio (w)
of a weight (W) of the train consist to a total number (V) of brake
valves in the train consist excluding any brake valves on any
locomotives in the train consist, a total number (N) of cars in the
train consist excluding the any locomotives, and a number (n.sub.i)
of each type of car in the train consist excluding the any
locomotives.
33. The method according to claim 32, wherein T.sub.d is calculated
based on L, N and n.sub.i, wherein T is calculated based on L, N
and n.sub.i, and wherein .alpha..sub.max is calculated based on L,
N, n.sub.i and w.
34. A train-borne component of a positive train control system
comprising an on-board computer for a train, the on-board computer
being programmed to determine for the train a profile velocity to a
target position of a selected target having a target speed when the
train has a current position located a first distance from the
target position by: determining a second distance, the second
distance being a distance from the current position that would be
required by the train to reach the target speed at the instant
brake build-up in the train is complete; determining whether the
first distance is greater than or equal to the second distance; if
the first distance is greater than or equal to the second distance,
determining the profile velocity using one or more first equations,
wherein the one or more first equations assume that steady state
braking by the train is needed to achieve the target speed from the
current position; if the first distance is not greater than or
equal to the second distance: (i) determining a third distance, the
third distance being a distance from the current position that
would be required by the train to reach the target speed at the
instant brake propagation delay is complete; (ii) determining
whether the third distance is greater than or equal to the first
distance; and (iii) (a) if the third distance is greater than or
equal to the first distance, determining the profile velocity using
one or more second equations, wherein the one or more second
equations assume that steady state braking by the train is not
needed to achieve the target speed from the current position but
that transient braking is needed to achieve the target speed from
the current position, and (b) if the third distance is not greater
than or equal to the first distance, determining the profile
velocity using one or more third equations, wherein the one or more
third equations assume that neither steady state braking nor
transient braking by the train is needed to achieve the target
speed from the current position.
35. The train-borne component according to claim 34, wherein the
determining the profile velocity using the one or more second
equations comprises determining an amount of brake build-up time
(t) that would be required to reach the target speed from the
current position and using t while determining the profile
velocity, and wherein the determining the profile velocity using
the one or more third equations comprises determining an amount of
propagation delay time (t.sub.d) that would be required to reach
the target speed from the current position and using t.sub.d while
determining the profile velocity.
36. The train-borne according to claim 34, wherein the second
distance is determined using the following equation: S = [ v T + (
kg avg + .alpha. max 2 ) T + kg avg T d ] T d - 1 2 kg avg T d 2 +
[ v T + ( kg avg + .alpha. max 2 ) T ] T - ( 1 2 kg avg + .alpha.
max 6 ) T 2 , ##EQU00023## wherein V.sub.T is the target speed, k
is a conversion factor needed to determine the effect of gravity on
stopping distance, g.sub.avg is an average grade between the
current position and the target position, .alpha..sub.max is a
maximum brake rate of the train, T is a brake build-up time of the
train, and T.sub.d is a brake propagation delay time of the
train.
37. The train-borne according to claim 34, wherein the one or more
first equations include the following equation: v P 2 + ( 2 .alpha.
max T d + .alpha. max T ) v P - [ .alpha. max ( .alpha. max + 4 kg
avg 12 ) T 2 + kg avg .alpha. max T d ( T + T d ) + v T 2 + 2 (
.alpha. max + kg avg ) S DTT ] = 0 , ##EQU00024## wherein V.sub.p
is the profile velocity, S.sub.DTT is the first distance, V.sub.T
is the target speed, k is a conversion factor needed to determine
the effect of gravity on stopping distance, g.sub.avg is an average
grade between the current position and the target position,
.alpha..sub.max is a maximum brake rate of the train, T is a brake
build-up time of the train, and T.sub.d is a brake propagation
delay time of the train.
38. The train-borne according to claim 35, wherein the one or more
second equations include the following equation: v p = v T + kg avg
T d + kg avg t + .alpha. max 2 T t 2 , ##EQU00025## wherein V.sub.p
is the profile velocity, V.sub.T is the target speed, k is a
conversion factor needed to determine the effect of gravity on
stopping distance, g.sub.avg is an average grade between the
current position and the target position, .alpha..sub.max is a
maximum brake rate of the train, T is a brake build-up time of the
train, and T.sub.d is a brake propagation delay time of the
train.
39. The train-borne component according to claim 35, wherein the
one or more third equations include the following equation:
v.sub.P=v.sub.T+kg.sub.avgt.sub.d, wherein V.sub.p is the profile
velocity, V.sub.T is the target speed, k is a conversion factor
needed to determine the effect of gravity on stopping distance, and
g.sub.avg is an average grade between the current position and the
target position.
40. The train-borne component according to claim 34, wherein the
third distance is determined using the following equation: S = v T
T d + 1 2 kg avg T d 2 , ##EQU00026## wherein V.sub.T is the target
speed, k is a conversion factor needed to determine the effect of
gravity on stopping distance, g.sub.avg is an average grade between
the current position and the target position, and T.sub.d is a
brake propagation delay time of the train.
41. The train borne component according to claim 34, wherein the
on-board computer is further programmed to obtain a brake
propagation delay time (T.sub.d) for the train, a brake build-up
time (T) for the train, a maximum brake rate (.alpha..sub.max) for
the train, and an average grade (g.sub.avg) from the current
position to the target position, wherein the determining the
profile velocity using the one or more first equations uses
T.sub.d, T, .alpha..sub.max, and g.sub.avg, wherein the determining
the profile velocity using the one or more second equations uses
T.sub.d, T, .alpha..sub.max, and g.sub.avg, and wherein the
determining the profile velocity using the one or more third
equations uses g.sub.avg.
42. The train-borne component according to claim 41, wherein the on
board computer is programmed to obtain T.sub.d, T and
.alpha..sub.max by calculating T.sub.d, T and .alpha..sub.max.
43. The train-borne component according to claim 42, wherein the
train comprises a train consist defined by a plurality of consist
parameters, and wherein the calculating comprises calculating
T.sub.d, T and .alpha..sub.max using the consist parameters.
44. The train-borne component according to claim 43, wherein the
consist parameters include a length (L) of the train consist, a
ratio (w) of a weight (W) of the train consist to a total number
(V) of brake valves in the train consist excluding any brake valves
on any locomotives in the train consist, a total number (N) of cars
in the train consist excluding the any locomotives, and a number
(n.sub.i) of each type of car in the train consist excluding the
any locomotives.
45. The train borne component according to claim 44, wherein
T.sub.d is calculated based on L, N and wherein T is calculated
based on L, N and n.sub.i, and wherein .alpha..sub.max is
calculated based on L, N, n.sub.i and w.
46. A method of selecting a most restrictive target from among a
plurality of targets for a train having an on-board computer, the
train being located at a current position, the method comprising
performing each of the following steps in the on-board computer:
(a) initially including all of the plurality of targets in a group
of targets to be evaluated; and (b) performing a series of
evaluations on selected pairs of the targets in the group until
only one of the targets remains in the group, wherein in each of
the evaluations a first one of the targets remaining in the group
and a second one of the targets remaining in the group are
evaluated together to determine which one of them is a more
restrictive target based on a profile velocity to the first one of
the targets and the target speed associated with the second one of
the targets, wherein in each of the evaluations the first one of
the targets is the target remaining in the group that is furthest
from the current position of the train and the second one of the
targets is the target remaining in the group that is second
furthest from the current position of the train, and wherein
following each of the evaluations the one of the first one of the
targets and the second one of the targets not determined to be more
restrictive is removed from the group, and wherein when all of the
evaluations are completed the one of the targets that remains in
the group is identified as the most restrictive target.
47. The method according to claim 46, wherein each of the
evaluations is also based on a time to penalty brake application
for the second one of the targets.
48. The method according to claim 47, wherein in each of the
evaluations, the first one of the targets is determined to be more
restrictive if the profile velocity to the first one of the targets
is not greater than the target speed associated with the second one
of the targets and if the time to penalty brake application for the
second one of the targets is not less than a predetermined time,
and wherein the second one of the targets is determined to be more
restrictive if the profile velocity to the first one of the targets
is greater than the target speed associated with the second one of
the targets or if the time to penalty brake application for the
second one of the targets is less than the predetermined time.
49. A train-borne component of a positive train control system
comprising an on-board computer for a train, the on-board computer
being programmed to select a most restrictive target from among a
plurality of targets when the train is located at a current
position by: (a) initially including all of the plurality of
targets in a group of targets to be evaluated; and (b) performing a
series of evaluations on selected pairs of the targets in the group
until only one of the targets remains in the group, wherein in each
of the evaluations a first one of the targets remaining in the
group and a second one of the targets remaining in the group are
evaluated together to determine which one of them is a more
restrictive target based on a profile velocity to the first one of
the targets and the target speed associated with the second one of
the targets, wherein in each of the evaluations the first one of
the targets is the target remaining in the group that is furthest
from the current position of the train and the second one of the
targets is the target remaining in the group that is second
furthest from the current position of the train, and wherein
following each of the evaluations the one of the first one of the
targets and the second one of the targets not determined to be more
restrictive is removed from the group, and wherein when all of the
evaluations are completed the one of the targets that remains in
the group is identified as the most restrictive target.
50. The train-borne component according to claim 49, wherein each
of the evaluations is also based on a time to penalty brake
application for the second one of the targets.
51. The train-borne component according to claim 50, wherein in
each of the evaluations, the first one of the targets is determined
to be more restrictive if the profile velocity to the first one of
the targets is not greater than the target speed associated with
the second one of the targets and if the time to penalty brake
application for the second one of the targets is not less than a
predetermined time, and wherein the second one of the targets is
determined to be more restrictive if the profile velocity to the
first one of the targets is greater than the target speed
associated with the second one of the targets or if the time to
penalty brake application for the second one of the targets is less
than the predetermined time.
52. A method of selecting a most restrictive target from among a
plurality of targets for a train having an on-board computer, each
of the targets having an associated target speed, the train being
located at a current position, the method comprising performing the
following steps in the on-board computer: (a) including all of the
plurality targets in a group of targets to be evaluated; (b)
indentifying as a first target the one of the targets that is
located furthest from the current position and as a second target
the one of the targets that is located second furthest from the
current position, and eliminating the first target and the second
target from the group; (c) determining a profile velocity to the
first target; and (d) (1) if the profile velocity to the first
target is greater than the target speed associated with the second
target or if a time to penalty brake application for the second
target is less than a predetermined amount: (i) determining whether
any targets remain in the group, and (ii) if no targets remain in
the group, setting the most restrictive target to be the second
target and ending the method, and (iii) if targets do remain in the
group, identifying as the first target the second target,
identifying as the second target the target remaining in the group
that is furthest from the current position, removing from the group
the target remaining in the group that is furthest from the current
position, determining the profile velocity to the first target, and
repeating step (d) one or more times until the method ends; (2) if
the profile velocity to the first target is not greater than the
target speed associated with the first target and if the time to
penalty brake application for the second target is not less than
the predetermined amount: (i) determining whether any targets
remain in the group, and (ii) if no targets remain in the group,
setting the most restrictive target to be the first target and
ending the method, and (iii) if targets do remain in the group,
identifying as the second target the target remaining in the group
that is furthest from the current position, removing from the group
the target remaining in the group that is furthest from the current
position, and repeating step (d) one or more times until the method
ends.
53. A train-borne component of a positive train control system
comprising an on-board computer for a train, the on-board computer
being programmed to select a most restrictive target from among a
plurality of targets when the train is located at a current
position by performing a method including the following steps: (a)
including all of the plurality targets in a group of targets to be
evaluated; (b) indentifying as a first target the one of the
targets that is located furthest from the current position and as a
second target the one of the targets that is located second
furthest from the current position, and eliminating the first
target and the second target from the group; (c) determining a
profile velocity to the first target; and (d) (1) if the profile
velocity to the first target is greater than the target speed
associated with the second target or if a time to penalty brake
application for the second target is less than a predetermined
amount: (i) determining whether any targets remain in the group,
and (ii) if no targets remain in the group, setting the most
restrictive target to be the second target and ending the method,
and (iii) if targets do remain in the group, identifying as the
first target the second target, identifying as the second target
the target remaining in the group that is furthest from the current
position, removing from the group the target remaining in the group
that is furthest from the current position, determining the profile
velocity to the first target, and repeating step (d) one or more
times until the method ends; (2) if the profile velocity to the
first target is not greater than the target speed associated with
the first target and if the time to penalty brake application for
the second target is not less than the predetermined amount: (i)
determining whether any targets remain in the group, and (ii) if no
targets remain in the group, setting the most restrictive target to
be the first target and ending the method, and (iii) if targets do
remain in the group, identifying as the second target the target
remaining in the group that is furthest from the current position,
removing from the group the target remaining in the group that is
furthest from the current position, and repeating step (d) one or
more times until the method ends.
54. A method of determining a plurality of braking parameters for a
train having a train consist, comprising: obtaining train consist
parameters for the train consist, wherein the consist parameters
include a length (L) of the train consist, a ratio (w) of a weight
(W) of the train consist to a total number (V) of brake valves in
the train consist excluding any brake valves on any locomotives in
the train consist, a total number (N) of cars in the train consist
excluding the any locomotives, and a number (n.sub.i) of each type
of car in the train consist excluding the any locomotives;
determining a brake propagation delay time (T.sub.d) for the train
based on L, N and n.sub.i; determining a brake build-up time (T)
for the train based on L, N and n.sub.i; and determining a maximum
brake rate (.alpha..sub.max) for the train based on L, N, n.sub.i
and w.
55. The method according to claim 54, wherein the step of
determining T.sub.d is based on the following equation: T d = a 0 +
( a 1 .times. L ) + i = 1 N b i .times. n i , ##EQU00027## wherein
the train consist is of a certain train consist type and wherein
.alpha..sub.0, .alpha..sub.1, and b.sub.i are constants associated
with the train consist type.
56. The method according to claim 54, wherein the step of
determining T is based on the follow equation: T = c 0 + ( c 1
.times. L ) + i = 1 N d i .times. n i , ##EQU00028## wherein the
train consist is of a certain train consist type and wherein
c.sub.0, c.sub.1 and d.sub.i are constants associated with the
train consist type.
57. The method according to claim 54, wherein the step of
determining .alpha..sub.max is based on the following equation:
.alpha. max = e 0 + ( e 1 .times. w - e 2 ) + ( e 3 .times. L ) + i
= 1 N f i .times. n i , ##EQU00029## wherein the train consist is
of a certain train consist type and wherein e.sub.0, e.sub.1,
e.sub.2, e.sub.3 and f.sub.i are constants associated with the
train consist type.
58. A train-borne component of a positive train control system
comprising an on-board computer for a train having a train consist,
the on-board computer being programmed to determine a plurality of
braking parameters for the train by: obtaining train consist
parameters for the train consist, wherein the consist parameters
include a length (L) of the train consist, a ratio (w) of a weight
(W) of the train consist to a total number (V) of brake valves in
the train consist excluding any brake valves on any locomotives in
the train consist, a total number (N) of cars in the train consist
excluding the any locomotives, and a number (n.sub.i) of each type
of car in the train consist excluding the any locomotives.
determining a brake propagation delay time (T.sub.d) for the train
based on L, N and n.sub.i; determining a brake build-up time (T)
for the train based on L, N and n.sub.i; and determining a maximum
brake rate (.alpha..sub.max) for the train based on L, N, n.sub.i
and w.
59. The train-borne component according to claim 58, wherein the
determining T.sub.d is based on the following equation: T d = a 0 +
( a 1 .times. L ) + i = 1 N b i .times. n i , ##EQU00030## wherein
the train consist is of a certain train consist type and wherein
.alpha..sub.0, .alpha..sub.1, and b.sub.i are constants associated
with the train consist type.
60. The train-borne component according to claim 58, wherein the
determining T is based on the follow equation: T = c 0 + ( c 1
.times. L ) + i = 1 N d i .times. n i , ##EQU00031## wherein the
train consist is of a certain train consist type and wherein
c.sub.0, c.sub.1 and d.sub.i are constants associated with the
train consist type.
61. The train-borne component according to claim 58, wherein the
step of determining .alpha..sub.max is based on the following
equation: .alpha. max = e 0 + ( e 1 .times. w - e 2 ) + ( e 3
.times. L ) + i = 1 N f i .times. n i , ##EQU00032## wherein the
train consist is of a certain train consist type and wherein
e.sub.0, e.sub.1, e.sub.2, e.sub.3 and f.sub.i; are constants
associated with the train consist type.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application claims priority under 35 U.S.C.
.sctn.119(e) from U.S. Provisional Application No. 61/152,098,
entitled "Method to Determine Time to Penalty Full Service Brake
Application to Assure Safe Braking Occurs", filed on Feb. 12, 2009,
U.S. Provisional Application No. 61/152,083, entitled "Method of
Braking a Train Utilizing Speed Profile and Time to Penalty
Processes", filed on Feb. 12, 2009, U.S. Provisional Application
No. 61/152,040, entitled "Method for Braking a Train for a Given
Train Configuration to reduce Train Speed to a Target Speed Over a
Specific Distance and Grade Scenario to a Target Position", filed
on Feb. 12, 2009, and U.S. Provisional Application No. 61/152,101,
entitled "Method to Determine the Maximum Velocity that a Given
Train Configuration Can be Travelling at Any Instant in Time to
Assure a Speed Reduction Resulting from a Full Service Brake
Application that Will Result in a Target Speed Over a Specific
Distance and Grade Scenario to a Target Position", filed on Feb.
12, 2009, the disclosures of which are incorporated herein by
reference.
BACKGROUND OF THE INVENTION
[0003] 1. Field of the Invention
[0004] The present invention relates to the automatic control of
trains, and in particular to positive train control systems and
methodologies that provide enhanced safety by controlling the
braking of a train including generating braking signals or requests
that are provided to a train engineer and/or that automatically
cause a brake application to occur.
[0005] 2. Description of the Related Art
[0006] Positive train control (PTC) refers to various technologies
that are used to monitor and control the movements of trains, such
as passenger and freight trains, to provide increased safety. In
PTC systems, the train receives information about its location,
including maximum speed limits, and where it is allowed to safely
travel. Equipment on-board the train then enforces these limits to
prevent unsafe movement. In particular, PTC systems employ
sophisticated braking algorithms designed to reviews speeds, track
conditions, and vehicle locations and automatically slow a train or
bring a train to a safe stop (by alerting the crew and/or
automatically causing an emergency stop of the train) if the train
encounters a condition (such as the engineer not paying attention
to a signal or a switch not being fully engaged) that could lead to
an accident. A typical PTC system consists of equipment provided on
the train, equipment provided in a centralized control center,
equipment provided on the rail wayside, and a wireless
communication system that allows for wireless communications
between the elements just identified.
[0007] While many known PTC systems and technologies have proven to
be effective in certain situations, there is room for improvement
in the field of positive train control, and in particular braking
algorithms and related control functions.
SUMMARY OF THE INVENTION
[0008] In one embodiment, the invention provides a method of
controlling braking of a train that includes obtaining in an
on-board computer of the train a brake propagation delay time
(T.sub.d), a brake build-up time (T) and a maximum brake rate
(.alpha..sub.max) for the train, and controlling braking of the
train in the on-board computer by generating one or more braking
profiles for the train using T.sub.d, T and .alpha..sub.max, which
may then be displayed to the driver of the train for controlling
the train.
[0009] In another embodiment, the invention provides a train-borne
component of a positive train central system that includes an
on-board computer for a train, wherein the on-board computer is
programmed to control braking of the train by obtaining a brake
propagation delay time (T.sub.d), a brake build-up time (T) and a
maximum brake rate (.alpha..sub.max) for the train, and controlling
braking of the train by generating one or more braking profiles for
the train using T.sub.d, T and .alpha..sub.max, which may then be
displayed to the driver of the train for controlling the train.
[0010] In still another embodiment, the invention provides a method
of determining for a train a profile velocity to a target position
of a selected target having a target speed, wherein the train has a
current position located a first distance from the target position.
The method includes determining in an on-board computer of the
train a second distance, the second distance being a distance from
the current position that would be required by the train to reach
the target speed at the instant brake build-up in the train is
complete, and determining in the on-board computer whether the
first distance is greater than or equal to the second distance. If
the first distance is greater than or equal to the second distance,
the method includes determining in the on-board computer the
profile velocity using one or more first equations, wherein the one
or more first equations assume that steady state braking by the
train is needed to achieve the target speed from the current
position. If the first distance is not greater than or equal to the
second distance, the method includes (i) determining in the
on-board computer a third distance, the third distance being a
distance from the current position that would be required by the
train to reach the target speed at the instant brake propagation
delay is complete, (ii) determining in the on-board computer
whether the third distance is greater than or equal to the first
distance, and (iii) (a) if the third distance is greater than or
equal to the first distance, determining in the on-board computer
the profile velocity using one or more second equations, wherein
the one or more second equations assume that steady state braking
by the train is not needed to achieve the target speed from the
current position but that transient braking is needed to achieve
the target speed from the current position, and (b) if the third
distance is not greater than or equal to the first distance,
determining in the on-board computer the profile velocity using one
or more third equations, wherein the one or more third equations
assume that neither steady state braking nor transient braking by
the train is needed to achieve the target speed from the current
position.
[0011] In yet another embodiment, the invention provides a
train-borne component of a positive train control system that
includes an on-board computer for a train, wherein the on-board
computer is programmed to determine for the train a profile
velocity to a target position of a selected target having a target
speed when the train has a current position located a first
distance from the target position using the method just
described.
[0012] In still another embodiment, the invention provides a method
of selecting a most restrictive target from among a plurality of
targets for a train having an on-board computer, wherein the train
is located at a current position. The method includes performing
each of the following steps in the on-board computer: (a) initially
including all of the plurality of targets in a group of targets to
be evaluated, and (b) performing a series of evaluations on
selected pairs of the targets in the group until only one of the
targets remains in the group, wherein in each of the evaluations a
first one of the targets remaining in the group and a second one of
the targets remaining in the group are evaluated together to
determine which one of them is a more restrictive target based on a
profile velocity to the first one of the targets and the target
speed associated with the second one of the targets, wherein in
each of the evaluations the first one of the targets is the target
remaining in the group that is furthest from the current position
of the train and the second one of the targets is the target
remaining in the group that is second furthest from the current
position of the train, and wherein following each of the
evaluations the one of the first one of the targets and the second
one of the targets not determined to be more restrictive is removed
from the group, and wherein when all of the evaluations are
completed the one of the targets that remains in the group is
identified as the most restrictive target.
[0013] In yet another embodiment, the invention provides a
train-borne component of a positive train control system that
includes an on-board computer for a train, wherein the on-board
computer is programmed to select a most restrictive target from
among a plurality of targets when the train is located at a current
position using the method just described.
[0014] In another embodiment, a method of selecting a most
restrictive target from among a plurality of targets for a train
having an on-board computer is provided, wherein each of the
targets has an associated target speed and wherein the train is
located at a current position. The method includes performing the
following steps in the on-board computer: (a) including all of the
plurality targets in a group of targets to be evaluated, (b)
indentifying as a first target the one of the targets that is
located furthest from the current position and as a second target
the one of the targets that is located second furthest from the
current position, and eliminating the first target and the second
target from the group, (c) determining a profile velocity to the
first target; and (d) (1) if the profile velocity to the first
target is greater than the target speed associated with the second
target or if a time to penalty brake application for the second
target is less than a predetermined amount: (i) determining whether
any targets remain in the group, and (ii) if no targets remain in
the group, setting the most restrictive target to be the second
target and ending the method, and (iii) if targets do remain in the
group, identifying as the first target the second target,
identifying as the second target the target remaining in the group
that is furthest from the current position, removing from the group
the target remaining in the group that is furthest from the current
position, determining the profile velocity to the first target, and
repeating step (d) one or more times until the method ends, (2) if
the profile velocity to the first target is not greater than the
target speed associated with the first target and if the time to
penalty brake application for the second target is not less than
the predetermined amount: (i) determining whether any targets
remain in the group, and (ii) if no targets remain in the group,
setting the most restrictive target to be the first target and
ending the method, and (iii) if targets do remain in the group,
identifying as the second target the target remaining in the group
that is furthest from the current position, removing from the group
the target remaining in the group that is furthest from the current
position, and repeating step (d) one or more times until the method
ends.
[0015] In still another embodiment, the invention provides a
train-borne component of a positive train control system that
includes an on-board computer for a train, wherein the on-board
computer is programmed to select a most restrictive target from
among a plurality of targets when the train is located at a current
position by performing the method just described.
[0016] In another embodiment, the invention provides a method of
determining a plurality of braking parameters for a train having a
train consist, wherein the method includes obtaining train consist
parameters for the train consist, wherein the consist parameters
include a length (L) of the train consist, a ratio (w) of a weight
(W) of the train consist to a total number (V) of brake valves in
the train consist excluding any brake valves on any locomotives in
the train consist, a total number (N) of cars in the train consist
excluding the any locomotives, and a number (n.sub.i) of each type
of car in the train consist excluding the any locomotives,
determining a brake propagation delay time (T.sub.d) for the train
based on L, N and n.sub.i, determining a brake build-up time (T)
for the train based on L, N and determining a maximum brake rate
(.alpha..sub.max) for the train based on L, N, n.sub.i and w.
[0017] In another embodiment, the invention provides a train-borne
component of a positive train control system that includes an
on-board computer for a train having a train consist, wherein the
on-board computer is programmed to determine a plurality of braking
parameters for the train using the method just described.
[0018] Therefore, it should now be apparent that the invention
substantially achieves all the above aspects and advantages.
Additional aspects and advantages of the invention will be set
forth in the description that follows, and in part will be obvious
from the description, or may be learned by practice of the
invention. Moreover, the aspects and advantages of the invention
may be realized and obtained by means of the instrumentalities and
combinations particularly pointed out in the appended claims.
BRIEF DESCRIPTION OF THE DRAWINGS
[0019] The accompanying drawings illustrate presently preferred
embodiments of the invention, and together with the general
description given above and the detailed description given below,
serve to explain the principles of the invention. As shown
throughout the drawings, like reference numerals designate like or
corresponding parts.
[0020] FIG. 1 is a block diagram of a high-level architecture of a
railroad Positive Train Control (PTC) system according to one
particular embodiment which implements the principles of the
present invention;
[0021] FIG. 2 is a block diagram of certain components of the
train-borne component of the PTC system of FIG. 1 according to an
exemplary embodiment of the invention;
[0022] FIGS. 3A and 3B are a flowchart of one particular, exemplary
embodiment of the braking function methodology of the present
invention;
[0023] FIG. 4 is a flowchart showing a method for determining the
most restrictive target (MRT) from among multiple targets in the
local target table maintained and used by the train-borne component
of the PTC system of FIG. 1 according to one particular,
non-limiting embodiment;
[0024] FIG. 5 is a profile velocity v. distance curve that shows
the equations that describe the velocity and distance traveled for
each of the free run, transient and steady state braking segments
that were used in the development of the profile velocity and time
to penalty determination methodologies described herein; and
[0025] FIGS. 6A and 6B are a flowchart showing one particular
embodiment of a profile velocity determination methodology that may
be employed by the PTC system of FIG. 1.
DETAILED DESCRIPTION OF THE EXEMPLARY EMBODIMENTS
[0026] Directional phrases used herein, such as, for example and
without limitation, top, bottom, left, right, upper, lower, front,
back, and derivatives thereof, relate to the orientation of the
elements shown in the drawings and are not limiting upon the claims
unless expressly recited therein.
[0027] As employed herein, the statement that two or more parts or
components are "coupled" together shall mean that the parts are
joined or operate together either directly or through one or more
intermediate parts or components.
[0028] As employed herein, the statement that two or more parts or
components "engage" one another shall mean that the parts exert a
force against one another either directly or through one or more
intermediate parts or components.
[0029] As employed herein, the term "number" shall mean one or an
integer greater than one (i.e., a plurality).
[0030] FIG. 1 is a block diagram of a high-level architecture of a
railroad Positive Train Control (PTC) system 2 according to one
particular embodiment which implements the principles of the
present invention as described in greater detail herein. As seen in
FIG. 1, the PTC system 2 includes an office component 4, including
a safety server, a train-borne component 6, and a wayside component
8. The three components of the PTC System 2 just described exchange
information with each other using a secure communications network
10, which is typically a wireless data radio network. The office
component 4 of the PTC system 2 provides a central command and
control facility for management of the train traffic and work crews
on the railroad. As noted above, the office component 4 also
contains a safety server that adds the required safety level to the
command and control functions of the PTC system 2 by knowing where
all of the trains are located in the railroad system associated
with the PTC system 2. As described in greater detail elsewhere
herein, the train-borne component 6 includes an on-board computer
12 (FIG. 2) that performs all train-borne control functions of the
PTC system 2, including safe speed control. The train-borne
component 6 also includes a number of human-machine interfaces in
the faun of locomotive display units 14 (FIG. 2) for the train crew
to interact with the PTC system 2. The wayside component 8 provides
vital information to the office component 4 and the train-borne
component 6 regarding the status of wayside devices such as
switches, signals, track circuits (used for rail integrity
monitoring), highway-rail grade crossing warning devices, and
hazard detectors, etc., in order to maintain safe train movement on
the railroad.
[0031] FIG. 2 is a block diagram of certain components of the
train-borne component 6 provided on a train 16 according to an
exemplary embodiment of the invention. As noted above, the
train-borne component 6 includes an on-board computer 12 that
performs all train-borne control functions of the PTC system 2. In
the exemplary embodiment, the on-board computer 12 consists of one
or more processing units that are programmed to perform all the
functions necessary for safe train control. In addition, the train
braking function of the present invention that is described in
greater detail elsewhere herein is implemented in the on-board
computer 12. More specifically, as seen in FIG. 2, the on-board
computer 12 includes a Location Determination (LD) function 18, an
Automatic Train Protection (ATP) function 20, a communications
interface 22, and an on-board database 24. The communications
interface 22 allows for communications with the office component 4
and the wayside component 8.
[0032] The on-board database 24 is preloaded with and stores
certain information needed by the train-borne component 6
including, without limitation, an ATP target table which includes
information relating to a number of targets in the railroad system.
In the exemplary embodiment, the ATP target table includes the
following data for each target: (i) the location of the target
(from which a current distance to the target may be determined),
(ii) the target speed limit (V.sub.T), and (iii) the distance
between the target and the previous target.
[0033] The ATP target table that is stored in the on-board database
24 may be for the entire railroad system, or for a portion of the
railroad system that is relevant to the train 16 for its current
journey. Also, the ATP target table that is stored in the on-board
database 24 may be updated periodically by the office component 4
through the communications interface 22.
[0034] In operation, the locations of the leading end and trailing
end of the train 16 are determined by the LD function 18 and the
ATP function 20 using inputs such as train speed, GPS coordinates,
train deceleration (under slip/slide conditions) and the track
segment information stored in the on-board database 24. According
to an aspect of the present invention, the ATP function 20
continuously receives other safety-critical information from the
office component 4 and the wayside component 8 via the
communications interface 22, looks three miles ahead of the current
location of the train 16 for any speed restrictions to be met
(based on information from the ATP target table stored in the
on-board database 24), and determines the safe speed limit at its
current location. It also determines the time to a penalty brake
application in the event the train exceeds the safe speed limit. As
used herein, the term "time to penalty" shall mean the time (in
seconds) that a train can travel at its current speed before a
penalty brake request will occur in response to a penalty curve
violation, and the term "penalty brake request" shall mean a full
service brake request in response to a penalty condition. The ATP
function 20 computes these safety-critical outputs using the
braking function methodology of the present invention, an exemplary
embodiment of which is described in greater detail below in
connection with FIGS. 3A and 3B. The ATP function 20 also conveys
certain information, such as distance to target and time to
penalty, to the train crew via the locomotive display units 14
forming a part of the train-borne component 6. If the speed of the
train 16 exceeds the safe limit at any point, the ATP function 20
issues a penalty brake request to reduce the speed of the train 16
to a safe speed (e.g., a complete stop). More specifically, in the
case of a penalty brake request, the ATP function 20 sends a brake
request to the train braking system 26 of the train 16 which causes
the brakes of the train 16 to be applied. The ATP function 20
simply performs overspeed protection at the current civil speed
limit when there are no other speed restrictions within three miles
of the current location of the train 16.
[0035] FIGS. 3A and 3B are a flowchart of one particular, exemplary
embodiment of the braking function methodology of the present
invention. Preferably, the braking function methodology of FIGS. 3A
and 3B is implemented as a number of software routines in the
on-board computer 12 of the train-borne component 6. As described
in detail below, the braking function methodology of the present
invention is able to provide safe braking functionality to the
train 16 as it moves along its route on an area of mapped track.
Prior to execution of the braking function methodology, the train
16 must be initialized, which, in the exemplary embodiment,
includes at least the following steps: (i) the on-board computer 12
receives train consist parameters (described elsewhere herein) for
the train 16 from the computer aided dispatching (CAD) system of
the office component 4, (ii) the braking parameters T.sub.d (brake
propagation delay time), T (brake build-up time), and .alpha..sub.m
(maximum brake rate, also referred to as .alpha..sub.max) (which
are used to determine braking profiles and profile velocities
according to a further aspect of the present invention as described
in detail elsewhere herein) for the train 16 are calculated by the
on-board computer 12 (one particular method of calculating each of
these braking parameters is described elsewhere herein), and (iii)
the initial location of the train 16 and the direction of travel of
the train 16 on the mapped track are determined by the LD function
18 of the on-board computer 12. As used herein, the term "brake
propagation delay time" shall mean the time duration between a
brake application request (by the on-board computer 12) and the
time that the braking effort begins, the term "brake build-up time"
shall mean the time duration between braking effort initiation and
the achievement of the full braking effort, and the term "maximum
brake rate" shall mean the constant brake rate achieved during
steady-state braking.
[0036] Referring to FIGS. 3A and 3B, the steps of the exemplary
embodiment of the braking function methodology of the present
invention that are performed as the train 16 moves on the mapped
track will now be described. The methodology begins at step 50,
wherein the LD function 18 of the on-board computer 12 determines
the current location and the current speed (preferably corrected
for spin/slide as needed) of the train 16. Next, at step 52, the
target data (described elsewhere herein) for all targets in the ATP
target table stored in the on-board database 24 that are within a
specified distance (three miles in the exemplary embodiment) ahead
of the current location of the train 16 are loaded into a local
target table maintained by the ATP function 20 (preferably, this
data replaces any data that may have previously been loaded into
the local target table such that the local target table will, at
any time, only have target data for the target(s) that are
currently within a specified distance). In addition, the following
information is obtained/determined (e.g., calculated) and added the
local target table: (i) the previous target's speed limit, and (ii)
the average grade between the tail end of the train 16 and the
target (the average grade is based on the actual grade of the grade
segments between the previous target and the target). This grade
information allows the braking function to calculate the average
grade from the current position of the train (the rear end of the
train in the exemplary embodiment) to a specific target location.
As described in greater detail elsewhere herein, the calculated
average grade is then used for determining profile velocities
(V.sub.P) and selecting targets. As used herein, the term "profile
velocity" shall mean the maximum train speed from which an
instantaneous full service brake request and subsequent application
will result in a train speed reduction to the target speed
threshold over the actual distance to target.
[0037] Thus, in summary, the local target table will contain the
following information for each target: (i) the location of the
target (from which a current distance to the target may be
determined), (ii) the target speed limit (V.sub.T), (iii) the
distance between the target and the previous target, (iv) the
previous target's speed limit, and (v) the average grade between
the tail end of the train 16 and the target.
[0038] At step 54, a determination is then made as to whether there
is more than one target in the local target table.
[0039] If the answer at step 54 is yes, then, at step 56, the only
target in the local target table is established as the most
restrictive target (MRT). The significance of the MRT is discussed
below. If, however, the answer at step 54 is no, then, at step 58,
the MRT is determined from among the multiple targets in the local
target table (i.e., one of the targets currently in the local
target table is selected as the MRT). One particular method for
determining the MRT from among the multiple targets in the local
target table is shown in FIG. 4 and described elsewhere herein. As
described in greater detail elsewhere herein, the method shown in
FIG. 4 includes calculating a profile velocity (V.sub.P) to each of
the targets in the local target table. In the preferred embodiment,
such profile velocities are calculated using the braking profile
determination methodology shown in FIGS. 6A and 6B. As described
elsewhere herein, that methodology establishes the profile velocity
(V.sub.P) at each position approaching a target and profiles the
train along the curve. Following either step 56 or step 58, the
method proceeds to step 60.
[0040] At step 60, the profile velocity to MRT (V.sub.P-MRT) is
determined. If step 60 is reached following step 56, that
determination will be made by calculating the profile velocity
(V.sub.P) to the only target in the local target table, preferably
using the method of FIGS. 6A and 6B. If step 60 is reached
following step 58, the profile velocity to MRT (V.sub.P-MRT) may be
determined from the profile velocities that were previously
calculated during the determination of the MRT in step 58. Next, at
step 62, the enforceable speed limit (ESL) is determined from the
profile velocity to MRT (V.sub.P-MRT) and the current most
restrictive speed (which could be, for example and without
limitation, a civil speed limit or a Form A restriction), and in
particular is set equal to the lower of the profile velocity to MRT
(V.sub.P-MRT) and the current most restrictive speed. At step 64,
time to penalty (TTP) and distance to target (S.sub.DTT) are
calculated and displayed to the crew of the train 16 using one of
the locomotive display units 14. Time to penalty (TTP) is, in the
exemplary embodiment, calculated as follows:
Distance to Penalty = ( v P - v a ) Delta S v P - v T feet
##EQU00001## Time To Penalty = Distance to Penalty 1.467 v a
seconds ##EQU00001.2##
where V.sub.a is the train's current speed in miles/hour, V.sub.P
is the current profile velocity in miles/hour, V.sub.T is the
target speed in miles/hour, and Delta S is the train's actual
distance to the target from its current position in feet.
[0041] Following step 64, the method proceeds to step 66 of FIG.
3B. At step 66, a determination is made as to whether the current
speed of the train 16 is less than or equal to the ESL plus some
buffer value, discussed in greater detail below. If the answer at
step 66 is no, then, at step 68, the ATP function 20 of the
on-board computer 12 calls for a penalty brake application (a
penalty brake request is issued and sent to the train braking
system 26) and brings the train 16 to a stop. If, however, the
answer at step 66 is yes, then, at step 70, the train engineer
controls the speed of the train 16 and the method returns to step
52 of FIG. 3A. In the exemplary embodiment, the buffer value
concept of step 66 works as follows: (i) buffer value is 3 mph
(i.e., add 3 mph to the ESL) if the ESL is not 0 mph and is less
than or equal to 20 mph; (ii) buffer value is 3 mph (i.e., add 3
mph to the ESL) if the ESL is greater than 20 mph; (iii) buffer
value is 3 mph (i.e., add 3 mph to the ESL) if the ESL is
Restricted, but ESL may not exceed 20 mph, and (iv) 0 mph if ESL is
0 mph (i.e., a Stop). In an alternate embodiment, the buffer value
may be eliminated from step 66 entirely, in which case a
determination is simply made as to whether the current speed of the
train 16 is less than or equal to the ESL.
[0042] FIG. 4 is a flowchart showing a method for determining the
MRT from among multiple targets in the local target table according
to one particular, non-limiting embodiment. As noted above, this
method may be employed in step 58 of FIG. 3A. In determining the
MRT, the method of FIG. 4 considers the targets in the local target
table in pairs, starting with the two targets that are furthest
from the current position of the train 16. Thus, as described
below, the method of FIG. 4 employs the variables "Target 1" and
"Target 2" in the steps thereof.
[0043] The method begins at step 80, wherein Target 1 is set to the
target in the local target table that is furthest from the current
position of the train 16, and Target 2 is set to the target in the
local target table that is second furthest from the current
position of the train 16. Next, at step 82, the profile velocity
(V.sub.P) to Target 1 is determined. In the exemplary embodiment,
the profile velocity (V.sub.P) to Target 1 is determined using the
braking profile determination methodology shown in FIG. 6A and 6B
and described elsewhere herein. Then, at step 84, a determination
is made as to whether the profile velocity (V.sub.P) to Target 1 is
greater than the speed limit of Target 2. If the answer at step 84
is yes, then, at step 86, a determination is made as to whether
there are any more targets (other than those that have been
considered) left in the local target table. If the answer at step
86 is no, then, at step 88, Target 2 is determined to be the MRT.
If, however, the answer at step 86 is yes, meaning there are
targets remaining in the local target table that have not yet been
considered, then, at step 90, Target 1 is set to Target 2 (in other
words, the target that was formerly Target 2 is now Target 1) and
Target 2 is set to the one of the remaining targets that is next
furthest from the current position of the train 16. The method then
returns to step 82 for further processing as described above.
[0044] If the answer at step 84 is no, then the method proceeds to
94, wherein a determination is made as to whether there are any
more targets (other than those that have been considered) left in
the local target table. If the answer at step 94 is no, then, at
step 96, Target 1 is determined to be the MRT. If, however, the
answer at step 94 is yes, meaning there are targets remaining in
the local target table that have not yet been considered, then, at
step 98, Target 2 is set to the one of the remaining targets that
is next furthest from the current position of the train 16. The
method then returns to step 84 for further processing as described
above.
[0045] As will be appreciated, the method of FIG. 4 will proceed as
described until one of the targets in the local target table is
selected as the MRT (either step 88 or step 96).
[0046] As noted elsewhere herein, an aspect of the present
invention relates to a braking profile determination methodology
that is able to establish the profile velocity (V.sub.P) for a
train, such as the train 16, at each position approaching a target
and profile the train along the curve. More specifically, one
general philosophy of the protection and braking methodology
implemented in the on-board computer 12 as described in detail
elsewhere herein is for the on-board computer 12 to periodically
(e.g., each software cycle) determine the maximum speed that the
train 16 can be traveling at its current position (a particular
distance away from a particular target over a specific grade
scenario) and protect the train 16 against exceeding that speed.
This maximum speed is the profile velocity (V.sub.P) that has been
discussed elsewhere herein. In order to calculate profile velocity
(V.sub.P) to a particular target position using the braking profile
determination methodology of this aspect of the present invention,
it is necessary to determine the following parameters: (i) the
average grade between the current position of the train 16 and the
target position; (ii) the braking parameters T.sub.d (brake
propagation delay time), T (brake build-up time), and .alpha..sub.m
(maximum brake rate) of the configuration of train 16 (a specific
methodology for determining these braking parameters is described
elsewhere herein); and (iii) the center of gravity of the
configuration of train 16 (the braking calculations described
herein are valid only when grade is referenced from the center of
gravity).
[0047] In addition, in order to fully appreciate the development of
the methods associated with determination of profile velocity
(V.sub.P) and time to penalty (TTP) of this aspect of the
invention, some fundamentals associated with train braking must be
established. Braking consists of three segments as follows: (1) the
free run segment, which occurs during the propagation delay portion
(i.e., from the time the brake application is requested by the
on-board computer 12 until the time that the actual braking effort
begins), (2) the transient segment, which occurs during the brake
build-up (i.e., from the time that the actual braking effort begins
until the full braking effort is achieved), and (3) the steady
state segment, which occurs during the constant braking portion at
the full braking effort. As used herein, the term "transient
braking" shall mean the increasing deceleration to the maximum
brake rate that occurs during the brake build-up time and the term
"steady-state braking" shall mean the constant deceleration that
occurs at the full braking effort after transient braking is
complete. The equations that describe the velocity and distance
traveled for each of these braking segments were used in the
development of the profile velocity and time to penalty
determination methodologies described herein and are defined in
FIG. 5. In those equations, .alpha..sub.m (also referred to herein
as .alpha..sub.max) is the maximum brake rate (brake
capacity)(mph/s), g.sub.avg is the average grade of the track
between the train's current position and the target position (%
grade), k is the conversion factor needed to determine the effect
of gravity on the stopping distance and is equal to 0.219 mph/s per
% grade, S.sub.DTT is the train's distance to target (feet),
S.sub.P is the distance that the train travels during the
propagation delay (feet), S.sub.SS is the distance that the train
travels during constant braking (feet), S.sub.t is the distance
that the train travels during the transient brake build-up (feet),
T is the brake build-up time (seconds), T.sub.d is the brake
propagation delay time (seconds), V.sub.i is the train velocity
after the brake propagation delay (mph), V.sub.P is the profile
velocity (mph), V.sub.SS is the train velocity after the transient
brake build-up (mph), and V.sub.T is the target velocity (mph).
[0048] In order to solve for the desired profile velocity
(V.sub.P), each velocity and distance equation is converted to a
function of the profile velocity (V.sub.P) as presented in FIG. 5.
A summary of relevant equations is presented below.
[0049] The equation that defines the train's velocity after the
brake propagation delay time is complete as a function of the
profile velocity (V.sub.P) is:
v.sub.i=v.sub.P-kg.sub.avgT.sub.d (1)
[0050] The equation that defines the train's velocity after the
brake build-up time is complete as a function of the profile
velocity (V.sub.P) is:
v SS = v i - ( kg avg + .alpha. max 2 ) T = v p - kg avg T d - ( kg
avg + .alpha. max 2 ) T = v p - [ kg avg T d + ( kg avg + .alpha.
max 2 ) T ] ( 2 ) ##EQU00002##
[0051] The equation that defines the distance traveled after the
brake propagation delay time is complete as a function of the
profile velocity (V.sub.P) is:
S P = v P T d - 1 2 k g avg T d 2 ( 3 ) ##EQU00003##
[0052] The equation that defines the distance traveled after the
brake build-up time is complete as a function of the profile
velocity (V.sub.P) is:
S T = v i T - ( 1 2 kg avg + .alpha. max 6 ) T 2 = ( v P - kg avg T
d ) T - ( 1 2 kg avg + .alpha. max 6 ) T 2 ( 4 ) ##EQU00004##
[0053] The equation that defines the distance traveled during
steady state braking as a function of the profile velocity
(V.sub.P) is:
S SS = v SS 2 - v T 2 2 ( .alpha. max + kg avg ) = ( v P - [ kg avg
T d + ( kg avg + .alpha. max 2 ) T ] ) 2 - v T 2 2 ( .alpha. max +
kg avg ) ( 5 ) ##EQU00005##
[0054] The general equations as a function of time for velocities
and distances associated with the brake propagation delay and brake
build-up segments are as follows:
v i ( t ) = v P - kg avg t 0 .ltoreq. t .ltoreq. T d ( 1 a ) S P (
t ) = v P t - 1 2 kg avg t 2 0 .ltoreq. t .ltoreq. T d ( 3 a ) v SS
( t ) = v i - kg avg t - .alpha. max 2 T t 2 0 .ltoreq. t .ltoreq.
T ( 2 a ) S T ( t ) = v i t - 1 2 kg avg t 2 - .alpha. max 6 T t 3
0 .ltoreq. t .ltoreq. T ( 4 a ) ##EQU00006##
[0055] With these fundamental braking concepts and
velocity/distance equations established, the methodologies
associated with determination of the profile velocity and time to
penalty will now be described.
[0056] The development of the profile velocity determination
methodology begins with the fundamental assertion that, for any
position with known distance to target, there exists a velocity for
which the braking distance between that velocity and the target
velocity is equal to the actual distance to the target. As
discussed elsewhere herein, this velocity is referred to as the
profile velocity (V.sub.P). The initial problem that is encountered
when attempting to establish the profile velocity (V.sub.P) at any
given location (a particular distance away from a particular target
over a specific grade scenario) is that one does know which of the
available equations to solve given a specific target velocity and
distance to target. In other words, the train 16 may be able to
reach the target velocity (e.g., the speed limit of the particular
target) over the associated distance to the target during the brake
propagation time due to grade, or during the brake build-up time,
or after the propagation and brake build-up times are complete and
steady state braking is in effect. Each of these scenarios presents
a different set of equations to solve and there is nothing inherent
in the known data to differentiate. Therefore, the profile velocity
determination methodology described herein performs a series of
tests in order to identify the correct braking scenario and
associated equations. This presents an additional problem in that
the profile velocity (V.sub.P) that needs to be identified is not
yet known, and therefore an approach for which it is not required
must be utilized. The approach used by the profile velocity
determination methodology described herein is to consider the
distance necessary to achieve the target velocity from some unknown
speed at the exact instant that the brake build-up is complete and
compare that distance to the actual distance of the train 16 to the
target. The equation that is used evaluates this distance from the
target position backwards, since the initial velocity is not known.
FIGS. 6A and 6B are a flowchart showing one particular embodiment
of the profile velocity determination methodology. The steps shown
in FIGS. 6A and 6B are described in detail below.
[0057] The method begins at step 100, wherein the braking
parameters T.sub.d (brake propagation delay time), T (brake
build-up time), and .alpha..sub.m (maximum brake rate) of the train
16 are obtained. In the exemplary embodiment, these braking
parameters are calculated by the ATP function 20 of the on-board
computer 12. In addition, one specific methodology for determining
these braking parameters is described elsewhere herein. Next, at
step 102, the average grade form the rear end of the train 16 to
the selected target position is calculated. In the exemplary
embodiment, this average is calculated by the ATP function 20 of
the on-board computer 12 based on the target data received from the
ATP target table.
[0058] As noted above, the approach used by the profile velocity
determination methodology described herein is to consider the
distance necessary to achieve the target velocity from some unknown
speed at the exact instant that the brake build-up is complete and
compare that distance to the actual distance of the train 16 to the
target. Thus, at step 104, the ATP function 20 of the on-board
computer 12 calculates the distance S that would be required to
reach the speed limit of the selected target at the instant brake
build-up is complete (i.e., within the time of T.sub.d+T). In the
exemplary embodiment, the fundamental distance equation developed
and used by the on-board computer 12 for the distance S traveled
after the brake build-up is complete is as follows (also see FIG.
5):
S = S P + S T = ( v P T d - 1 2 kg avg T d 2 ) + [ v i T - ( 1 2 kg
avg + .alpha. max 6 ) T 2 ] then , for v i = v T + ( kg avg +
.alpha. max 2 ) T and v P = v i + kg avg T d = v T + ( kg avg +
.alpha. max 2 ) T + kg avg T d S = [ v T + ( kg avg + .alpha. max 2
) T + kg avg T d ] T d - 1 2 kg avg T d 2 + [ v T + ( kg avg +
.alpha. max 2 ) T ] T - ( 1 2 kg avg + .alpha. max 6 ) T 2 ( 6 )
##EQU00007##
[0059] If the solution S to equation (6) is less than the actual
distance to the target S.sub.DTT, braking will progress through the
brake propagation and build-up segments and steady state braking is
necessary to achieve the target speed. Thus, at step 106, a
determination is made as to whether S.sub.DTT is greater than or
equal to S. If the answer is yes, than, as noted above, steady
state braking is necessary to achieve the target speed and the
method proceeds to step 108. At step 108, the ATP function 20 of
the on-board computer 12 determines the profile velocity (V.sub.P)
to the selected target using an equation that defines the sum of
the three braking distances, i.e., the distance traveled during
brake propagation delay time, the distance traveled during brake
build-up time (transient braking), and the distance traveled during
steady state braking. In the exemplary embodiment, that equation is
as follows:
S = S P + S T + S SS = { v P - 1 2 kg avg T d 2 } + { ( v P - kg
avg T d ) T - ( 1 2 kg avg + .alpha. max 6 ) T 2 } + { ( v P - [ kg
avg T d + ( kg avg + .alpha. max 2 ) T ] ) 2 - v T 2 2 ( .alpha.
max + kg avg ) } and reduces to the quadratic equation in v .rho.
as follows : v P 2 + ( 2 .alpha. max T d + .alpha. max T ) v P - [
.alpha. max ( .alpha. max + 4 kg avg 12 ) T 2 + kg avg .alpha. max
T d ( T + T d ) + v T 2 + 2 ( .alpha. max + kg avg ) S DTT ] = 0 (
7 ) ##EQU00008##
[0060] Solving this quadratic equation (7) results in the profile
velocity (V.sub.P).
[0061] If the solution S to equation (6) is not less than the
actual distance to the target, i.e., if the answer at step 106 is
no, then steady state braking is not necessary for the train 16 to
achieve the target speed from the unknown profile velocity. It must
then determined if transient braking would be necessary to achieve
the target speed. To accomplish this, the distance necessary for
the train 16 to achieve the target velocity from some unknown speed
at the exact instant that the brake propagation delay time is
complete is evaluated and this distance is compared to the actual
distance of the train 16 to the target. Thus, at step 110, the ATP
function 20 of the on-board computer 12 calculates the distance S
required to reach the speed limit of the selected target at the
instant brake propagation delay is complete (i.e., within T.sub.d).
In the exemplary embodiment, the fundamental distance equation
developed and used by the on-board computer 12 for the distance S
traveled after the brake build-up is complete as follows (also see
FIG. 5):
S = S P = v P T d - 1 2 kg avg T d 2 then , for v P = v T + kg avg
T d S = v T T d + 1 2 kg avg T d 2 ( 8 ) ##EQU00009##
[0062] If the solution S to equation (8) is less than the actual
distance to the target S.sub.DTT, braking will progress through the
brake propagation segment and transient braking is necessary for
the train 16 to achieve the target speed from the unknown profile
velocity. Thus, at step 112, a determination is made as to whether
S.sub.DTT is greater than or equal to S calculated in step 110. If
the answer is yes, then, as noted above, transient braking is
necessary to achieve the target speed. In other words, braking has
to progress through T.sub.d and target speed will be achieved at
some time t during the brake build-up interval T. At this stage, it
is necessary to determine how much of the brake build-up time will
be expired when the train 16 reaches the target velocity. In other
words, the train 16 may reach the target velocity over the
particular distance to target at some time during the brake
build-up and not require the full brake build-up time. Therefore,
it is necessary to solve for the amount of brake build-up time t
required for the train 16 to reach the target velocity before the
method can proceed with the solution of the profile velocity
(V.sub.P). Thus, following a yes answer at step 112, the method
proceeds to step 114, wherein the amount of brake build-up time t
required for the train 16 to reach the target velocity is
calculated. In the exemplary embodiment, the on-board computer 12
bases that calculation on the following:
S = S P + S T = v P T d - 1 2 kg avg T d 2 + [ v i T - ( 1 2 kg avg
+ .alpha. max 6 ) T 2 ] ; ##EQU00010##
however, for partial brake build-up time t, S=S.sub.P+S.sub.t
S = S p + S t = ( v P T d - 1 2 kg avg T d 2 ) + ( v i t - 1 2 kg
avg t 2 - .alpha. max 6 T t 3 ) ##EQU00011## and for ##EQU00011.2##
v i = v T + kg avg t + .alpha. max 2 T t 2 ##EQU00011.3## and
##EQU00011.4## v p = v i + kg avg T d = ( v T + kg avg t + .alpha.
max 2 T t 2 ) + kg avg T d ##EQU00011.5## S = S P + S t = [ ( v T +
kg avg t + .alpha. max 2 T t 2 + kg avg T d ) T d - 1 2 kg avg T d
2 ] + [ ( v T + kg avg t + .alpha. max 2 T t 2 ) t - 1 2 kg avg t 2
- .alpha. max 6 T t 3 ] ; ##EQU00011.6##
setting S=the actual distance to target S.sub.DTT, the equation
reduces to the cubic equation in t as follows:
( .alpha. max 6 T - .alpha. max 2 T ) t 3 - ( .alpha. max 2 T T d +
1 2 kg avg ) t 2 - ( v T + kg avg T d ) t + [ S DDT - ( v T T d + 1
2 kg avg T d 2 ) ] = 0 ( 9 ) ##EQU00012##
The brake build-up time t is then solved for recursively. Next, at
step 116, the solution for t is used to calculate the profile
velocity (V.sub.P) based on the following:
v T = v i - kg avg t - .alpha. max 2 T t 2 for v i = v P - kg avg T
d v T = ( v P - kg avg T d ) - kg avg t - .alpha. max 2 T t 2
.thrfore. v P = v T + kg avg T d + kg avg t + .alpha. max 2 T t 2 (
10 ) ##EQU00013##
[0063] If the solution S to equation (8) is not less than the
actual distance to the target S.sub.DTT (i.e., if the answer at
step 112 is no), then that means that transient braking is not
necessary for the train 16 to achieve the target speed from the
unknown profile velocity (i.e., the target speed will be achieved
within the propagation delay time). In such a circumstance, it is
necessary to determine how much (i.e., what fraction or portion) of
the propagation delay time (T.sub.d) is required for the train 16
to achieve the target speed. In other words, the train 16 may reach
the target speed over the particular distance to target at some
time during the propagation delay and not require the full
propagation delay time (T.sub.d). Therefore, the amount of
propagation delay time required for the train 16 to achieve the
target speed (referred to herein as t.sub.d) must be solved for
before the method can proceed with the solution of the profile
velocity (V.sub.P). Thus, at step 118, the on-board computer 12
calculates that delay time t.sub.d. In the exemplary embodiment,
the on-board computer 12 bases that calculation on the
following:
S = S P = v P T d - 1 2 kg avg T d 2 ; ##EQU00014##
however, for partial propagation delay time t.sub.d, S=S.sub.P;
S = S p = v P t d - 1 2 kg avg t d 2 ##EQU00015## for
##EQU00015.2## v p = v T + kg avg t d ##EQU00015.3## S = S P = ( v
T + kg avg t d ) t d - 1 2 kg avg t d ##EQU00015.4##
setting S=the actual distance to target S.sub.DTT, the equation
reduces to the quadratic equation in t.sub.d as follows:
( 1 2 kg avg ) t d 2 + ( v T ) t d - S DTT = 0 ( 11 )
##EQU00016##
The partial delay time t.sub.d is then solved for recursively.
Next, at step 120, the solution for t.sub.d is used to calculate
the profile velocity V.sub.P based on the following:
v.sub.P=v.sub.T+kg.sub.avgt.sub.d (12)
[0064] In short, the methodology shown in FIGS. 6A and 6B may be
summarized as follows. First, evaluate the distance required to
achieve the target speed at the instant that transient braking is
complete by solving equation (6) for S. If the distance to target
is greater than or equal to the calculated distance S (braking will
progress through the full brake build-up and steady state braking
will be necessary to achieve the target velocity during the braking
process), then solve quadratic equation (7) for V.sub.P. If the
distance to target is not greater than or equal to the calculated
distance S, then evaluate the distance required to achieve the
target speed at the instant that the brake propagation delay is
complete by solving equation (8) for S. If the distance to target
is greater than or equal to the calculated distance S (braking will
progress through the brake propagation delay and the target
velocity will be achieved during transient braking), then solve
cubic equation (9) for t and solve equation (10) for V.sub.P using
the solution t. If the distance to target is not greater than or
equal to the calculated distance S (the target velocity will be
achieved during the brake propagation delay), then solve quadratic
equation (11) for t.sub.d and solve equation (12) for V.sub.P using
the solution t.sub.d.
[0065] In one particular embodiment, the braking parameters T.sub.d
(brake propagation delay time), T (brake build-up time), and
.alpha..sub.max (maximum brake rate, also referred to as
.alpha..sub.m) for a given type of train consist are computed in
the on-board computer 12 using the following general expressions,
called braking parameter expressions:
T d = a 0 + ( a 1 .times. L ) + i = 1 N b i .times. n i
##EQU00017## T = c 0 + ( c 1 .times. L ) + i = 1 N d i .times. n i
##EQU00017.2## .alpha. max = e 0 + ( e 1 .times. w - e 2 ) + ( e 3
.times. L ) + i = 1 N f i .times. n i ##EQU00017.3##
As noted elsewhere herein, these braking parameters are used to
determine braking profiles and profile velocities according to a
further aspect of the present invention (See FIGS. 6A and 6B).
[0066] In the above braking parameter expressions, a.sub.0,
a.sub.1, b.sub.i, c.sub.0, c.sub.1, d.sub.i, e.sub.0, e.sub.1,
e.sub.2, e.sub.3, and f.sub.i are all constants for a given train
consist type. In addition, in the above braking parameter
expressions, L is the length of the train consist,
w = W V , ##EQU00018##
where W is the total weight of the train consist and V is the total
number of brake valves in the train consist, excluding those on the
locomotives in the train consist, N is the total number of cars in
the train consist, excluding the locomotives, and n.sub.i is the
number of each type of car in the train consist, excluding the
locomotives. The parameters L, W, V, N, and n.sub.i are, for a
given train consist type, referred to herein as consist parameters,
and the constants a.sub.0, a.sub.1, b.sub.i, c.sub.0, c.sub.1,
d.sub.i, e.sub.0, e.sub.1, e.sub.2, e.sub.3, and f.sub.i are, for a
given train consist type, referred to herein as braking parameter
expression coefficients.
[0067] Train consists typically used on a railroad can be
classified into the following main types: (i) freight train
consists made up with different freight cars such as hoppers, flat
cars, tank cars, box cars, gondolas, air dump cars, etc., (ii)
passenger train consists made up with different types of passenger
cars, and (iii) mixed train consists for trains with a mix of
passenger and freight cars. In addition, the major freight train
consist types can be further divided into sub-types such as unit
hopper trains, unit tank car trains, unit flat car trains, and
mixed freight trains.
[0068] Typically, the characteristics of each passenger and freight
car in a railroad's fleet are known. These characteristics include,
without limitation, empty and maximum loaded weight, empty/load
sensors, length, number and type of brake valves, brake cylinder
piston stroke length, brake pipe length and pressure, and braking
force per shoe. When a railroad configures a specific train consist
type for a specific journey, the consist parameters {L, W, V, N,
and n.sub.i} will be known. Then, if the braking parameter
expression coefficients {a.sub.0, a.sub.1, b.sub.i, c.sub.0,
c.sub.1, d.sub.i, e.sub.0, e.sub.1, e.sub.2, e.sub.3, and f.sub.i}
are known, the braking parameters {T.sub.d, T, and .alpha..sub.max}
for a given train consist type can be computed by the on-board
computer 12 using the braking parameter expressions identified
above.
[0069] In the exemplary embodiment, the braking parameter
expression coefficients {a.sub.0, a.sub.1, b.sub.i, c.sub.0,
c.sub.1, d.sub.i, e.sub.0, e.sub.1, e.sub.2, e.sub.3, and f.sub.i}
for a given train consist type for train 16 are determined using
the following procedure. First, speed vs. distance and deceleration
vs. time plots, with braking applied to bring the train 16 to a
stop from a known initial speed over a known territory of constant
grade, are obtained either from field runs or from simulations of a
large sample of train consist configurations of a given type. Next,
the deceleration vs. time plot in each run or simulation is
approximated into three segments represented by the three braking
parameters {T.sub.d, T, and .alpha..sub.max}. That is, sample data
points of {T.sub.d, T, and .alpha..sub.max}are obtained as
functions of consist parameters {L, W, V, N, and n.sub.i}. Then,
using a non-linear regression curve-fitting process that minimizes
the sum of the squares of the residual error, the braking parameter
expressions are obtained for the given train consist type. The
obtained braking parameter expressions are then stored in the
on-board computer 12 for each train consist type (freight,
passenger and mixed), to be used to calculate the braking
parameters {T.sub.d, T, and .alpha..sub.max} for the given train
consist type at the beginning its journey and at any intermediate
point when the particulars of the consist change due to car
set-outs and pick-ups.
[0070] While preferred embodiments of the invention have been
described and illustrated above, it should be understood that these
are exemplary of the invention and are not to be considered as
limiting. Additions, deletions, substitutions, and other
modifications can be made without departing from the spirit or
scope of the present invention. Accordingly, the invention is not
to be considered as limited by the foregoing description but is
only limited by the scope of the appended claims.
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