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272
Coupler Force, kN
Coupler Force, kN
400
0
- 400
- 800
400
- 400
- 800
0 20 40 60 80 100
Time,s
FIGURE 9.45 Power to dynamic brake transition without pausing.
0
0 20 40 60 80 100
Time,s
FIGURE 9.46 Power to dynamic brake transition with 20 second pause.
from stretched to bunchedor vice versa ,preventing large impact forces. Examples are simulated in
Figure 9.45 and Figure 9.46.
4. Energy Considerations
Minimisation of energy usage is often apopular emphasis in train management. It is helpful to
examine the way energy is utilised before innovations or changes topractice are adopted. Air
resistance, for example, is often over-stated. Abreakdown of the Davis equation 14 shows the
significance of air resistance compared to curving resistance and rolling resistance factors and
grades, Figure9.47.Itwill be noticed that on a1in 400 grade,0.25% is approximately equal to the
propulsion resistance at80km/h.
The minimum energy required for atrip can be estimated by assuming an average train speed
and computing the sum of the resistances to motion, not forgetting the potential energy effects of
changes inaltitude. The work carried out to get the train up to running speed once must also be
added. As the train must stop at least once, this energy islost at least once. Any further energy
consumed will be due to signalling conditions, braking, stop–starts, and the design of grades.
Minimum trip energy can be estimated as:
E min ¼ 1
2 m t v 2 þ m t gh þ Xq
i ¼ 1
0
@
X
m i
r
j ¼ 1
1
�ðx¼l �
cj
X
F crjd x A þ q � ð x ¼ L �
F prjd x
0
i ¼ 1
m i
0
ð 9 : 25Þ
where E min is the minimum energy consumed, J; g is gravitational acceleration in m/sec 2 ; h is the
net altitude change, m; L is the track route length, m; l cj is the track length of curve j, m; m i is
© 2006 by Taylor & Francis Group, LLC
Wagon Accelerations, m/s/s
Wagon Accelerations, m/s/s
- 4
- 8
8
4
0
- 4
- 8
8
4
0
Handbook of Railway Vehicle Dynamics
0 20 40 60 80 100
Time,s
0 20 40 60 80 100
Time,s