Hi Keith,

Thanks for your message

This is  the type of design issue that a second year engineering design
student would be expected to model and solve. That may be first year now as
things are moving so fast! My daughter's school does time-series analysis
and that was PhD stuff some years ago.

Back to the train.

Imagine each wagon on the train being represented by one large mass with a
connection to the wagon in front. (we'll ignore the rotational inertias of
the wheels for the moment as well as the slip-stick behaviour of the
bearings and the slightly springy resistive interaction between the wheels
and the rail). We'll assume the train is on a level track.

The connection between the wagons is special. We'll model it as a spring
with a damper and a bit of slack. 

The picture of the train overall is of a lot of individual masses all
connected together in a line with a springy link with a bit of slack in
each.

So as one wagon starts to move to pull on the next, first nothing happens
while the slack is taken up. Then the first wagon starts to stretch the
spring which starts to pull on the second wagon which follows with a slight
delay, pulling backwards on the wagon in front

That delay is important,  as  is the pulling backwards on the wagon in
front. 

The next wagon  follows a similar process. 

Imagine the middle wagon in a group of three. It first gets tugged from in
front and then a short time later after a delay  it gets tugged from the
back as it starts to pull the wagon behind it.

As a limiting slow start case, imagine all the wagons closed up together
with all the connections slack. The engine at the front starts moving
forward at an very very  slow speed. If it is slow enough,  the train will
simply become 'stretched out' to its full length with each wagon moving
after the one in front until all the slack in the connections is removed
before the last wagon starts to move.

If, instead, the first wagon starts with a bit of a jerk (i.e faster than
the above very slow version), then it will have achieved some speed before
the slack is taken up and the effect of its inertia moving forward (remember
each wagon is a large mass)  will act to jerk the wagon behind it forward.
The front wagon will also have the same force acting backwards on it, acting
to slow it slightly.  

After that slight delay, the second wagon is tugged from the front, and then
from behind, with a slight but  different delay.

Each of the tugs extends and contracts each connection between the wagons
each delayed slightly.

The effect is of a wave of movement passing down the train.

At the other end, the last wagon does not have another wagon behind it. Its
behaviour is to be jerked forward and then be bounced backwards on its
spring connection. This gives a jerk backwards on the next wagon - the
equivalent of the whole process starting from the other end of the train.
 
The effect is of a second  wave of movement passing down the train
originating at the other end. This in turn also bounces off the front end of
the train and starts another wave going backwards.

As the waves propagate up and down the train they do so through the
couplings and in each coupling the energy in the springs is slightly
dissipated through damping effects. Eventually the waves decay and disappear
- until the next jerk  

With a bit of mental 3D juggling, one can see that the model is similar-ish
to a vibrating string or air vibrating in an organ pipe. 

It is different mechanical process, however, to the Doppler effect.

Best wishes,
Terry


-----Original Message-----
From: PhD-Design - This list is for discussion of PhD studies and related
research in Design [mailto:[log in to unmask]] On Behalf Of Keith
Russell
Sent: Thursday, 19 November 2009 7:43 AM
To: [log in to unmask]
Subject: concatenation - trains and shunting

Dear Listers

Perhaps there is someone out there who can relieve me of my morning puzzle.
It is stopping my normal activities.

While walking to work, I pass by a train line that carries the coal trains
that deliver the largest amount of export coal in the world.

This morning, an empty coal train came to a stop nearby. It then started to
move again.

When it stopped, I noticed the usual ripple of sound that accompanies the
concatenation of carriages as they shunt into each other.

When it started up again, the auditory ripples were much more pronounced and
they repeated in both directions for some time.

What I noticed was that the speed of the ripple event was vastly greater
than the speed of travel of the train. That is, the wave event was its own
event.

Does anyone know of a technical account of what is going on to account for
these speed differences? Does the ripple speed up as it goes down the train?
It certainly seems to.

Anyway, I pose my problem in order to free my brain up, a little.

cheers

keith russell

newcastle OZ