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Pushing vs Pulling on Cog Railway
Name: Steven J.
Status: student
Age: 20s
Location: N/A
Country: N/A
Date: 10/2/2004
Question:
I read today about the Mount Washington Cog Railway in
New Hampshire, which unlike the typical railroad with a grade of about
2-4%, has a grade of 37%. Because of this, it is necessary for
locomotives to PUSH single cars up the track. My question is this: why
must it push, rather than pull, the car up? Is there a difference in
force exerted between these two methods? If so, is that why sports cars
are so often rear-wheel drive? Thanks for any help with figuring this out.
Replies:
It is not absolutely necessary for the locomotive to push; the same force
and energy is required for pulling as pushing. A principal reason for
pushing instead of pulling is that if the connection between the cars
breaks, the cars cannot roll down the hill.
The goal of sports car racing is to travel around a track in the minimum
amount of time, and it is found that rear wheel drive is often best, for
complicated reasons involving braking, acceleration, and steering.
Bob Erck
Dear Steven,
I do not believe there is any difference in the force exerted by a pushing
locomotive as compared to a pulling locomotive. The only disadvantage in
pulling that I can think of is that if the coupling breaks, the locomotive
is not in the way to stop the passenger car; the locomotive might also block
some of the view when it is in front.
I believe the reason that racing cars are rear wheel drive is that it is
easier to control them when skidding around corners. If the rear wheels are
skidding, the car tends to turn too much, which can be corrected by turning
the front wheels, which are in good contact with the road since they are not
skidding.
In a front wheel drive car, when the engine causes the front wheels to spin,
they lose the ability to steer and the car tends to continue in the
direction it was going. This is not good if you are trying to get around a
curve. I was raised in northern Wisconsin and had many opportunities to do
experiments on icy and snowy roads.
Best, Dick Plano, Professor of Physics emeritus, Rutgers University
Climbing a slope that steep on frictionless wheels and rails is scary.
It is of paramount importance that every force pushes the locomotive's
gear down onto the teeth in the track below it.
(I do not yet see that it has much to do with automobile design. Maybe you
will.)
With the rail car behind and below the locomotive, there is a tensile
force in the coupling linking them.
In combination with the locomotive's rear wheels, this tries to make the
loco do a "wheely", i.e. tilt backwards.
This takes away some of the weight which holds the engine's gear in
contact with the track's teeth. Not good.
With the car in front, on the other hand, the compressive force in the
coupling might be re-directable to push the gear down onto the track instead.
At such a steep slope, building a new machine with serious responsibility
for engineering safety, the difference is night and day.
Also compressive stresses tend to be safer and more predictable than
tensile stresses, anywhere near the breaking point.
I would feel safer sliding up in chair pushed up from underneath, than in
a chair slung from a cable, wouldn't you?
Going through it again,
suppose whether front or rear, you are determined design the coupling
to push/pull slightly upwards on the rail car (rather than purely
parallel to the track).
Because, that way it pushes/pulls down on the engine, improving security
of gear contact.
The two cases are still not equivalent:
.............................................................
. Engine behind:
. +-----------+ +-----------+
. | engine | _o railcar |
. | |_/ | |
. | Gear _/| | |
. |_____v__/__| |_^_________|
._____O___*___O_______O_______O_____ --> 37% grade uphill ->
.............................................................
Railcar pushes down on gear and on all engine wheels -- This is OK.
The compressive line of force in the sketch above goes right through the
center of the gear.
Torque = (Force x Offset), and the offset here is zero.
So this arrangement won't feel like the rail car is trying to tip over the
engine.
In fact, going between the two wheels, it's in the right direction to push
the engine flat onto the tracks.
The gear teeth are then very securely engaged.
If the upwards force lifts the rear wheel of the rail car off the rails a
little, that does not hurt anything.
These trains climb slowly, and do not do fast turns.
If this diagonal force is in the rear, it must hit the engine at a point
well above the wheels,
and must place a torque on the engine.
Of course the coupling can be shifted downwards a bit, but not enough to
get near zero offset.
.............................................................
. Engine ahead:
. +-----------+ +-----------+
. | railcar | | engine |
. | | | |
. | | _o Gear ^ |
. |_________^_|_/ |_____^___|_|
._____O_______O_______O___*___O_____ --> 37% grade uphill ->
.............................................................
Rail car pulls down on engine rear wheel, levering up the
gear and engine's front wheel - That's bad.
The tensile line of force here has a large offset from the first fulcrum,
which is the engine's rear wheel.
So this design will always feel like it is trying to flip the engine
backwards.
Even with the car empty.
The first design above works even if the rail car is loaded heavier than
the engine.
The second design absolutely requires the engine to be heavier than the
rail car.
You do not want that economic limitation or that fool's danger when
running a railroad.
cordially-
Jim Swenson
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