Found something interesting cleaning up my files, wonder if these numbers work well for G (they came from a smaller scale).
Rough rule of thumb:
Load up a given loco with cars on the flat and level until its wheel slip.
Count the cars.
Then, for running that combination on grades you might expect:
1% - 80% of that number
2% - 60% of that number
3% - 30% of that number
4% - 15% of that number
5% - Just the loco itself
If the grade is on a curve, take off another 10% from that number
Greg, I am not sure, but it would be a good place to start.
Well, I have a 3.4% and a 5.5% so I might try it out.
Be interesting if these worked out in our scale, but it’s interesting how the train length drops rapidly.
Greg
Greg yes it is. I wonder if the length would not drop as rapidly if the cars had ball bearing journals.
The frictional losses are there, but they are constant, irrespective of the grade.
There’s no advantage level vs. up a grade with ball bearings, they give less rolling friction at all times.
(clearly you can pull a longer train with bb wheelsets)
Greg
Dave and Greg,
I beg the question - Are we talking prototype or model?
The following link provides the ‘actual’ numbers used by the D&RGW for rating both the K27 and K36 from an official timetable. If we are comparing prototype numbers to Greg’s table above, the 4% grade at 15% is almost spot on to the numbers provided by D&RGW on the time table. The numbers in between I can’t prove, but will ‘assume’ they are relative and within reason, accurate.
http://ngdiscussion.net/phorum/read.php?1,101241,101243#msg-101243
BTW, for all the narrow gaugers here, there is a wealth of information on that site. It is predominantly D&RGW, but there are other NGs and some SG stuff as well. Usually some fantastic pics posted there as well.
As for our models, we tend to run trains that are for the most part enormous relative to prototype (maybe not some of the modern SG guys). At traveling shows and open house weekends at the club I have run 30 + car trains behind my K27. Most small children only want to see trains, and most adults, if they see it, have never made comment.
For myself, after learning how small the NG trains really were, I tend to not be so concerned about ‘how many cars can my loco pull?’. When I see a video on Youtube of a USA Big Boy with 152 cars, again, not concerned. Most folks don’t have the space to run half that. A fellow club member who owned a Big Boy had 62 Aristo covered hoppers and a hack at a show we did in Dalton, GA. That is the longest I have personally seen. And that train at the club would have been ‘chasing the caboose’.
Just my thoughts…
In terms of the prototype, I’ve got an early Baldwin locomotive catalog (c. late 1870s) that lists tonnage for locomotives on various grades up to just under 2% (100 feet per mile). An example from the catalog, a Baldwin 10-22 E (in layman’s terms, a 2-8-0 with a tractive effort of 9,600 pounds)
Level - 1060 tons
20’ per mile - 490 tons (46%)
40’ per mile - 310 tons (29%)
60’ per mile - 220 tons (20%)
80’ per mile - 175 tons (16%)
100’ per mile - 140 tons (13%)
The percentages in terms of how the load is decreased with respect to grade are fairly consistent from locomotive to locomotive. It stops at 100’ per mile (1.8% grade). You could probably extrapolate these data points to get a rough estimate at higher percentages. My guess would be that by the time you get up towards 4%, you’re looking at numbers somewhere in the neighborhood of 5% - 8% or so.
That matches the numbers Bob linked to from the D&RGW when you take into consideration the fact that the D&RGW has the tonnage rating of their K-27 at 1180 tons on the level, where Baldwin has the tonnage rating of their Consolidation–with 1/3 the tractive effort–at 1060 tons! Baldwin’s numbers are in all likelihood heavily weighted heavily towards the theoretical, since in the 1870s there wasn’t a whole lot of experience running locos in “real world” conditions. The timetable Bob references lists the K-36s which didn’t arrive until 1925. That’s 50 years of railroading in between to give railroaders a proper sense of what a loco could or could not do.
Having said all that, it’s almost a universal truth that our model locos can out-pull their prototypes by a comfortable margin.
Later,
K
Good info, now I need to look for similar stuff applying to the RhB.
The Bernina line has up to 7% grades. The line between Landquart and Davos tops out at 4.5 %.
So, at 20 ft per mile, or 0.4% grade, the tonnage that can be hauled is cut by more than half? Wow!
And that is why grades are such a big deal on the prototype… QED…
Greg
As for loading our locomotives with more cars then the prototype, I would say some photos of say the EBT, or some logging railroads, shows some pretty long trains on NG lines. Since I have a small railroad, if I can run a 5 to 7 car train then I am happy. That size fits well with my small railroad. Since I have grades of about 2.58%, those may be long trains for that grade.
However my Bachmann 2-4-2 can barely haul 3 hoppers and a caboose, so she is going to be replaced.
This is why I caution folks about grades on their railroads. The effect of grade, especially with curves, can be dramatic. Mainlines try and keep below 2%, preferably 1% or less if they can. Us narrow gaugers will go as high as 4%, but prefer to be well below that if possible. Logging railroads and traction lines can approach %10. When Pittsburgh went shopping for its LRV cars, they solicited bids for cars that can handle 10% grades. One company inquired if that was a typo on the bid specifications, because 10% is rather steep. No, it wasn’t a typo.
Pittsburgh ain’t flat.
Bob, no kidding. Even downtown isn’t flat, I know, I get to walk around down there 5 days a week, dragging a cart of copier parts and tools. And I can vouch for my performance degrading when I am pulling that thing up a grade.