where do you account for the additional (flange) friction of the wheels on the curve?
Crr increases on curves, by 1% on a 32" radius, from 2 to 3%
Way too many variables to set up rules for car moving capability. The only way to truly determine is to load up a train until it no longer can manage the load. And yet, that determination is only correct for those locos combined with those cars, on that section of trackage, etc., etc.
I agree its fun for some to play with stats and math formulas and matrixes, but it is not going to be an exact science in this situation.
Remember, “one size truly fits nothing” - as in “gimme caps” and other personal items…
Gotta agree with mobilman on this issue. This is all great in a classroom setting, but on a model railroad not so much. For one thing, most layouts are too small for this to matter. On my layout, it is totally irrelevant because as large as my layout is, it is perfectly flat and my longest reversing section is 12’. So, a 4-loco diesel consist pulling 7 passenger cars or a single steam locomotive pulling 24 coal cars is about as long as it gets.
Rich
of course it’s not an exact science. but you’re suggesting building the layout and then finding out the grade is too much for the loco and cars you planned to use? (of course you can shorten the train, add another loco, improve the rollability of the cars or add weight to the loco)
it’s obvious that many modelers don’t understand this. but it doesn’t mean that a reasonable estimate can’t be made by some
this is yet another aspect of the hobby.
huh?
I revised the formular slightly. For each loco, the force to next car is
(F-GW-CrrW)*A
This added to each car calculation. I also set Crr=0.02 to compare with your table.
This is all very interesting and not terribly complicated to follow. The maths references are nice but you don’t need to completely follow the maths to find the discussion of interest.
We all intuitively understand vectors which is what this discussion is all about. Vector analysis is also very easy and need not involve the precision of maths. Just draw the three lines and measure the proportions with an ordinary ruler. That delivers the concepts nicely. The maths is just interesting, not necessary.
Pulling a train on straight and level track is the baseline.
Add a curve and we add wasted effort dragging wheel flanges sideways against the rails. Add a grade and you add a different type of resistance to the drawbar force available from the locomotive. The effective weight on the drivers is reduced and the effective weight of the train is increased. Gravity pulls the train backwards even though the force is exerted only vertically. Load on the rails decreases (that is a little counterintuitive).
This thread explains how you might estimate these effects. It also enables a better understanding of the variables which may help you solve derailments, binding, stringlining and uncoupling events.
Also of interest is the fact that prototype railroading must deal with the same stuff.
Coincendently i’m in the middle of planning an elevated radius for my expansion of my 3’ x 14’ grade level switching layout. My concept plan is for a 24 inch curve at a max 2% incline, my 6 axel diesel engines will be (double headed) and mostly be pulling 6-12 hopper or intermodel well cars at a time out to a single main track leading to a staging yard. All of the cars are weighted in accordence with NMRA standards and have metal wheel sets with kadee couplers. Based on these discussions and mathmatical analysys i think there will be little or no flange resistance and there should not be any power issues while traveling up and through the curved the incline (unless i’m wrong with my assumption) ?
Bayway Terminal NJ
Me too. We built a layout to that spec and had no practical limits to train length (weight). We did need two or more locomotives for long trains but then that’s why we put in the grades…it’s a mountain railway and we say nobody can have too much motive power.
the values in the original post didn’t include flange resistance
the conventional estimate for effective grade on curve is 32/rad, posted by Byron for HO model railroads
if you have a 32" curve, the effective grade is 1%.
32" curve and 2% grade, the effective grade is 3%
24" curve and 2% grade, the effective grade is 3.3%
considering that at least one measurement found rolling resistance to be approximately 2% on relatively straight and level track, ~5.3% of the total car weight is needed to pull a train up a 24" curve and 2% grade.
10 4oz cars requires 2.12 and a loco weighing ~8.5 oz
As long as you have one curving to the right, right before you have one curving to the left. It balances itself out and you’ll be OK.
Curves are utterly delightful and should not be confused with trains.
When in doubt, just add another diesel!
TF
Exactly!!
I tried to pull 60 cars on my layout, which is spiral with a continous grade 2-3%. I used 3 locos at the front. I had some 89’ auto carrier cars near the front. They could not go through some of my curves (36"). These cars simply fell off my track because of the large side force… That made me wonder what was happening and tried to make these calculations…
Huh!
That string line effect always sucks doesn’t it eh?
TF
Actually as many suggested, there will be flange resistance and they could be relatively large. 24" is kind of sharp. So following the suggestions from others, the frictional resistence or the rolling resistence could be large. I meaured my 3-stall hopper cars and they are about 8" long (depending on the model), and 4.2-4.5oz. If you loco have a pulling force of 4.5oz, and car weigt of 4.2oz, here is the estimate of the cars you can pull
Crr #cars
0.02 15
0.03 13
0.04 11
0.05 10
If you want to pull cars that are longer, such as intermodal cars, the number will drop quite a bit. If I take the length of 10",
Crr #cars
0.02 12
0.03 11
0.04 9
0.05 8
Jerry
I checked again. According gregc, the effective Crr due to curve is 32/R%. So 24" curve would give you 1.33%. If I use this number
Car length #car
8" 17
10" 13
Try not to pull long cars, you might be ok.
Yes! I really felt that…[:)]
Sometimes a pusher can unbind the slack!
If you just so happen to be that lucky with your push-a-me-pull-you calculations[oX)]
[;)]TF
not sure how your accounting for this
shouldn’t longer cars be heavier and won’t that help offset tipping?
There’s a really good-looking almost naked lady on their advertisement here slightly dressed in red.
After I looked at her a little bit[:P]
I think I remember it was either Ed or Wayne that said. “If radius re-versus, it cancels itself out”.
With either Ed or Wayne saying that, I will take that one to the bank.
I think it was Wayne with a long train wrapping all the way continuously through both reversed curves and he found reversed radius canceled itself out[Y]
I don’t do any math when I see it’s unnecessary.
TF
Long cars have more side force because the angle between them is large. On his 24" curve, the angle between two 8" car is t=19 degree, the force transfer coefficient is A=cos(t)=0.94. If the cars are 10" long, the angle is t=23.8, A=0.91; for 12" long car, t=28.6, and A=0.88. Also, I feel if the car is long, you would have more side force, thus the effective friction coefficient might also be higher.
I feel once the track is built, no more math is needed. And all I have is some of kind regret. I wish I could have done more math when I planed my track [:)][:)]
Must have been Wayne, TF, I don’t recall saying that. I cant imagine that two reverse curves “cancel” each other out.
Still, I like to run long trains and I do have lots of curves. It is a necessary evil in our layout designs.
One thing I’ll mention about long cars is a design technique some manufacturers adopt and that is to place the truck bolster pivot closer to the center of the car. This has the effect of “shifting” the car centerline outward which helps prevent binding and excessive overhang of the center of the car under the inside rail. It may aid in reducing the “stringlining” effect as well.
Train resistance:
Alco_data_hilite by Edmund, on Flickr
Alco_data_0001 by Edmund, on Flickr
Alco_data_0002 by Edmund, on Flickr
Alco_data_0003 by Edmund, on Flickr
More than you wanted to know…
Cheers, Ed