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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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