Perhaps this is as much a physics question as one about railroading:
Is there a quick way or formula to determine how many cars a given locomotive can pull on level track?
I do realize the answer is contingent on the following parameters:
Am I missing anything important?
I'm interested in calculating how many cars a prototypical steam switcher might have been expected to shuttle in a yard. Here are the three types of steam switchers that I have in my roster, along with their individual wheel configuration, weight, tractive force, and driver OD:
Is there anything else that should be included?
Below are also the typical freight cars that I would be shuttling in my yard:
As noted earlier, the numbers will obviously vary on whether the cars are empty or full. Is that enough information for making the calucations?
Thanks for your time and effort in this discussion. I really appreciate it.
Tom
https://tstage9.wixsite.com/nyc-modeling
Time...It marches on...without ever turning around to see if anyone is even keeping in step.
Oh, I'll bet there's a formula for everything
Alco_data_hilite by Edmund, on Flickr
Alco_data_0001 by Edmund, on Flickr
There was a discussion here a while back on train resistance and I copied these pages to contribute to the study.
Alco_data_0002 by Edmund, on Flickr
I've heard railroaders talk about coupling on to a cut of cars and having a difficult time moving them when the weather was colder (i.e. Friction, or solid bearings). It takes a while to get the film of oil around the journal surface.
Roller bearings helped alleviate that immensely.
Alco_data_0003 by Edmund, on Flickr
Alco_data_0004 by Edmund, on Flickr
Alco_data_0005 by Edmund, on Flickr
Good Luck, Ed
Using the data provided by Ed, and some similar data I have, but without showing all my work:
Your 0-8-0 should be able to handle 45 to 50 average "steam era" 50 ton cars.
A little more if the yard is truely flat and has few curves.
Your 0-6-0, likely about 30 cars, and the 0-10-0, 65-70 cars.
Using the 0-8-0 as an example, it would typically be able to start and pull any string of cars a similar weight Mikado can, but at much slower max speeds.
You may or may not find you models able to match these numbers.
Few model steam locos I have tested can equal their prototypes in number of cars (scale tonnage) pulled.
Sheldon
Ed & Sheldon - Thanks!
Sheldon - I'm presuming the quantities you've given are for empties rather than full cars? If so, what would those numbers look like given full loads?
And I do realize that our scale models generally fall short of matching the actual pulling capability of the prototype. However, this does give me a good general idea of what is believable for a yard switcher and what isn't.
tstage Ed & Sheldon - Thanks! Sheldon - I'm presuming the quantities you've given are for empties rather than full cars? If so, what would those numbers look like given full loads? And I do realize that our scale models generally fall short of matching the actual pulling capability of the prototype. However, this does give me a good general idea of what is believable for a yard switcher and what isn't. Tom
No, that would be loaded 50 ton cars, your average 40' box car or 35' two bay hopper.
Obviously in real life not every car is loaded to the max, except maybe hoppers.
But based on research and math I have done for my 1954 time period, these would be average or typical cut lengths for switchers of these wheel arrangements.
To use a mainline example from history, the B&O typically used two Mikados on 3500 ton trains (70 to 100 cars, depending on actual weight) leaving Batimore and heading west.
On level straight track, one Mikado of this type could handle that much or more. But the ruling grade from Baltimore to Brunswick is .9% and line is curvy. So two Mikados were necessary.
At Brunswick that same train would get two EM1's or EL's for the trip over the mountains.......easily double the power, for the 2.6% grades ahead.
Move or switch? An 0-6-0 could probably move a cut that a 2-8-2 brought into the yard. It would just move it very slowly on level ground.
Switching is a different matter. While a switch engine could probably move 50-75 cars, it would only switch with 25-30 cars at a time because it has to be able to rapidly stop and start to switch cars.
Dave H. Painted side goes up. My website : wnbranch.com
Thanks, Sheldon. Those are impressive quantities and waaaay more than I was originally expecting. I was expecting the 0-6-0 to be in the 8-10 car range, max.
Good point, Dave. Realistically, I would be doing both, although my yard will not be anywhere as long as the length of cars you've cited above.
I anticipate a yard that will hold no more than 12 cars per track. So, using the figures that you and Sheldon have provided, I will be well within the limits for either the 0-6-0, 0-8-0, or the 0-10-0.
One final note: Apparently the NYC 0-10-0 was used in hump yard service. Even though I will never model a hump yard on my layout, I still thought it was a handsome-looking switcher and plan to use it in regular service in my yard.
I appreciate everyone's input on this topic. There's always something interesting to learn about a prototype.
Years back there was an article on adhesion and maximum grade in MR years ago. The theoretical limit is a 25% grade but if I recall right only a locomotive with all drivers powered, and pulling no cars, could do it or at least come close. So an 0-6-0T could take a steeper grade than an 0-6-0 with tender. But in terms of flat level track, it also means that those pilot and trailing wheels on road power, while essential to good tracking and balance and support of the firebox, are likely decreasing "pure" tractive effort.
Second, a switcher spends so much time being idle and thus is more likely to have boiler pressure close to its maximum when called upon to move a cut of cars. This would also explain how an 0-6-0 in a yard could move a cut of cars that taxed a 2-8-2 out on the main.
Slightly OT but the Pennsylvania Railroad had an 0-8-8-0 that must have been something to see and hear when worked to the max.
Dave Nelson
tstageSheldon - I'm presuming the quantities you've given are for empties rather than full cars? If so, what would those numbers look like given full loads?
based on John Armstrong's Chart the rolling resistance is more for an MT car, but of course an MT weight less
I come up with different numbers than Sheldon. If it's ~2 lbs/ton for a loaded car @ 5mph, that's 100 lbs. And if the loco has a tractive effort of 34,000 lbs, that's a 100 cars.
of course grades make a big difference
170000 LocoWt 20% Adhesion 34000 TE 100000 CarWt cars Res/car Gr Wt mph load gr 340 100 0 5 Loaded 0.00 % 161 210 0 5 Empty 0.00 % 226 150 0 20 Loaded 0.00 % 130 260 0 20 Empty 0.00 % 56 100 500 5 Loaded 0.50 % 47 210 500 5 Empty 0.50 % 30 100 1000 5 Loaded 1.00 % 28 210 1000 5 Empty 1.00 % 21 100 1500 5 Loaded 1.50 % 19 210 1500 5 Empty 1.50 % 16 100 2000 5 Loaded 2.00 % 15 210 2000 5 Empty 2.00 %
greg - Philadelphia & Reading / Reading
Not OT at all, Dave. Like the Pennsy, the NYC had an 0-8-8-0 (Class NU-1), which was used strickly for hump yard service:
Would love to take a time machine back 90-100 years to see one of those in action.
In regards to yard switchers, I'm guessing that a 0-8-0 was designed with a smaller firebox than it's cousin, the 2-8-2 Mike, so that more of the locomotive's weight was balanced over the drivers for better adhesion.