04-02-2013, 12:17 PM
Mechanics of Train Movement
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Equations of train motion
In the basic equations, d and t are given. In the train motion, however, only the
total distance d and total time T of the three sections are given; da, dc, db, ta, tc
and tb are all unknown. (da, dc and db are areas under the curves at time zones ta,
tc and tb.)
Traction Tutorial 1
Train mechanics
1. Distinguish the two terms: schedule speed and average speed. Hence
comment on the effect of stop time on (i) city service (e.g. MTR) and (ii)
main line service (e.g. KCR). Furthermore, what are the effects of other train
characteristics such as acceleration and braking retardation?
2. A train has an acceleration of 3 km/hr/s and a braking retardation 4 km/hr/s.
Determine the total distance travelled if the train accelerates from zero speed,
decelerates once it reaches the crest speed of 120km/hr. If this train is
arranged to travel between the two stations with distance apart being (i) 1km
(ii) 3 km, and (iii) 10km, estimate the change in the average speed, when the
allowable crest speed is increased to 180 km/hr. Assuming a trapezoidal
speed-time curve for simplicity. Hence comment on the crest speed
requirement with respect to MTR and KCR.
(1.167km; 0, 96-86.4=9.6km/hr, 142.6-107.5=35.1km/hr)
3. A train has an average speed of 80 km/hr between two stops of 10 km apart.
The acceleration is 4 km/hr/s, and the retardation is 0.1 km/hr/s for coasting
and 3 km/hr/s for braking. Determine the (i) crest speed, (ii) the time and
distance travelled during acceleration, braking and coasting.
(104 km/hr; 26s, 21.4s, 402.5s; 0.38km, 0.19km 9.43km)