US2010241296A1PendingUtilityA1
System and Method for Controlling Braking of a Train
Est. expiryFeb 12, 2029(~2.6 yrs left)· nominal 20-yr term from priority
B61L 27/04B60T 13/665B60T 17/228B61L 15/0062
33
PatentIndex Score
0
Cited by
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0
Claims
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 d ), a brake build-up time (T) and a maximum brake rate (α 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 d , T and α 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 d ), a brake build-up time (T) and a maximum brake rate (α max ).
Claims
exact text as granted — not AI-modified1 . A method of controlling braking of a train, comprising:
obtaining in an on-board computer of the train a brake propagation delay time (T d ), a brake build-up time (T) and a maximum brake rate (α 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 d , T and α 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 d , T and α 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 d , T and α 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 d , T and α 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 d , T and α 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 i ) of each type of car in the train consist excluding the any locomotives.
7 . The method according to claim 6 , wherein T d is calculated based on L, N and n i , wherein T is calculated based on L, N and wherein α max is calculated based on L, N, n 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 d ), a brake build-up time (T) and a maximum brake rate (α max ) for the train; and controlling braking of the train by generating one or more braking profiles for the train using T d , T and α 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 d , T and α 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 d , T and α 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 d , T and α 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 d , T and α 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 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 d is calculated based on L, N and n i , wherein T is calculated based on L, N and n i , and wherein α max is calculated based on L, N, n 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 d ) that would be required to reach the target speed from the current position and using t 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
+
α
max
2
)
T
+
kg
avg
T
d
]
T
d
-
1
2
kg
avg
T
d
2
+
[
v
T
+
(
kg
avg
+
α
max
2
)
T
]
T
-
(
1
2
kg
avg
+
α
max
6
)
T
2
,
wherein V T is the target speed, k is a conversion factor needed to determine the effect of gravity on stopping distance, g avg is an average grade between the current position and the target position, α max is a maximum brake rate of the train, T is a brake build-up time of the train, and T 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
α
max
T
d
+
α
max
T
)
v
P
-
[
α
max
(
α
max
+
4
kg
avg
12
)
T
2
+
kg
avg
α
max
T
d
(
T
+
T
d
)
+
v
T
2
+
2
(
α
max
+
kg
avg
)
S
DTT
]
=
0
,
wherein V P is the profile velocity, S DTT is the first distance, V T is the target speed, k is a conversion factor needed to determine the effect of gravity on stopping distance, g avg is an average grade between the current position and the target position, α max is a maximum brake rate of the train, T is a brake build-up time of the train, and T 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
+
α
max
2
T
t
2
,
wherein V P is the profile velocity, V T is the target speed, k is a conversion factor needed to determine the effect of gravity on stopping distance, g avg is an average grade between the current position and the target position, α max is a maximum brake rate of the train, T is a brake build-up time of the train, and T 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 p =v T +kg avg t d , wherein V p is the profile velocity, V T is the target speed, k is a conversion factor needed to determine the effect of gravity on stopping distance, and g 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
,
wherein V T is the target speed, K is a conversion factor needed to determine the effect of gravity on stopping distance, g avg is an average grade between the current position and the target position, and T 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 d ) for the train, a brake build-up time (T) for the train, a maximum brake rate (α max ) for the train, and an average grade (g 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 d , T, α max , and g avg , wherein the determining in the on-board computer the profile velocity using the one or more second equations uses T d , T, α max , and g avg , and wherein the determining in the on-board computer the profile velocity using the one or more third equations uses g avg .
30 . The method according to claim 29 , wherein the obtaining comprises calculating T d , T and α 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 d , T and α 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 i ) of each type of car in the train consist excluding the any locomotives.
33 . The method according to claim 32 , wherein T d is calculated based on L, N and n i , wherein T is calculated based on L, N and n i , and wherein α max is calculated based on L, N, n 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 d ) that would be required to reach the target speed from the current position and using t 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
+
α
max
2
)
T
+
kg
avg
T
d
]
T
d
-
1
2
kg
avg
T
d
2
+
[
v
T
+
(
kg
avg
+
α
max
2
)
T
]
T
-
(
1
2
kg
avg
+
α
max
6
)
T
2
,
wherein V T is the target speed, k is a conversion factor needed to determine the effect of gravity on stopping distance, g avg is an average grade between the current position and the target position, α max is a maximum brake rate of the train, T is a brake build-up time of the train, and T 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
α
max
T
d
+
α
max
T
)
v
P
-
[
α
max
(
α
max
+
4
kg
avg
12
)
T
2
+
kg
avg
α
max
T
d
(
T
+
T
d
)
+
v
T
2
+
2
(
α
max
+
kg
avg
)
S
DTT
]
=
0
,
wherein V p is the profile velocity, S DTT is the first distance, V T is the target speed, k is a conversion factor needed to determine the effect of gravity on stopping distance, g avg is an average grade between the current position and the target position, α max is a maximum brake rate of the train, T is a brake build-up time of the train, and T 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
+
α
max
2
T
t
2
,
wherein V p is the profile velocity, V T is the target speed, k is a conversion factor needed to determine the effect of gravity on stopping distance, g avg is an average grade between the current position and the target position, α max is a maximum brake rate of the train, T is a brake build-up time of the train, and T 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 P =v T +kg avg t d , wherein V p is the profile velocity, V T is the target speed, k is a conversion factor needed to determine the effect of gravity on stopping distance, and g 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
,
wherein V T is the target speed, k is a conversion factor needed to determine the effect of gravity on stopping distance, g avg is an average grade between the current position and the target position, and T 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 d ) for the train, a brake build-up time (T) for the train, a maximum brake rate (α max ) for the train, and an average grade (g avg ) from the current position to the target position, wherein the determining the profile velocity using the one or more first equations uses T d , T, α max , and g avg , wherein the determining the profile velocity using the one or more second equations uses T d , T, α max , and g avg , and wherein the determining the profile velocity using the one or more third equations uses g avg .
42 . The train-borne component according to claim 41 , wherein the on board computer is programmed to obtain T d , T and α max by calculating T d , T and α 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 d , T and α 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 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 d is calculated based on L, N and wherein T is calculated based on L, N and n i , and wherein α max is calculated based on L, N, n 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 i ) of each type of car in the train consist excluding the any locomotives; determining a brake propagation delay time (T d ) for the train based on L, N and n i ; determining a brake build-up time (T) for the train based on L, N and n i ; and determining a maximum brake rate (α max ) for the train based on L, N, n i and w.
55 . The method according to claim 54 , wherein the step of determining T d is based on the following equation:
T
d
=
a
0
+
(
a
1
×
L
)
+
∑
i
=
1
N
b
i
×
n
i
,
wherein the train consist is of a certain train consist type and wherein α 0 , α 1 , and b 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
×
L
)
+
∑
i
=
1
N
d
i
×
n
i
,
wherein the train consist is of a certain train consist type and wherein c 0 , c 1 and d i are constants associated with the train consist type.
57 . The method according to claim 54 , wherein the step of determining α max is based on the following equation:
α
max
=
e
0
+
(
e
1
×
w
-
e
2
)
+
(
e
3
×
L
)
+
∑
i
=
1
N
f
i
×
n
i
,
wherein the train consist is of a certain train consist type and wherein e 0 , e 1 , e 2 , e 3 and f 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 i ) of each type of car in the train consist excluding the any locomotives. determining a brake propagation delay time (T d ) for the train based on L, N and n i ; determining a brake build-up time (T) for the train based on L, N and n i ; and determining a maximum brake rate (α max ) for the train based on L, N, n i and w.
59 . The train-borne component according to claim 58 , wherein the determining T d is based on the following equation:
T
d
=
a
0
+
(
a
1
×
L
)
+
∑
i
=
1
N
b
i
×
n
i
,
wherein the train consist is of a certain train consist type and wherein α 0 , α 1 , and b 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
×
L
)
+
∑
i
=
1
N
d
i
×
n
i
,
wherein the train consist is of a certain train consist type and wherein c 0 , c 1 and d i are constants associated with the train consist type.
61 . The train-borne component according to claim 58 , wherein the step of determining α max is based on the following equation:
α
max
=
e
0
+
(
e
1
×
w
-
e
2
)
+
(
e
3
×
L
)
+
∑
i
=
1
N
f
i
×
n
i
,
wherein the train consist is of a certain train consist type and wherein e 0 , e 1 , e 2 , e 3 and f i ; are constants associated with the train consist type.Join the waitlist — get patent alerts
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