# Scale power and weight

Discussion in 'FAQs' started by LoudMusic, Sep 5, 2006.

1. ### LoudMusicMember

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I'm curious what formulas are used to calculate scale power and weight, and if they're even necessary in modeling.

1:87(.1) is HO scale, so an SD40-2 which is 68'10" in length is about 9.5" in HO scale. But that's only one dimension. To say that it is 1:87 the size of the real thing is not including all thre dimensions. It's also 1:87 the width, and 1:87 the height. An HO model is in fact 1:658,503 the size of the real thing, meaning it would take 659,503 SD40-2 models to occupy the same space as 1 of the real thing. Does that mean that power and weight are the same ratio? They're definitely not 1:87 - that would mean an HO scale SD40-2 would have a miraculous 34.5HP ... shazzam! But it would also weigh 4230 pounds - not likely to be supported by ... anything.

So should weight and power be divided by the cube of 1:87, or 659,503? That would mean the HO version of an SD40-2 would be .004556HP. Though rediculously small, it actually sounds right to me. And what about weight? The 184 ton SD40-2 would be a wopping 8.9 ounces.

Or am I just way off base? Does it even matter? Without proper testing it seems like one of my Athearn F7s could pull literally hundreds of HO rolling stock, which is completely unrealistic. And probably do it up a 4% grade.

Any thoughts or advice? Mathmaticians who can educate me?
2. ### tverskayaMember

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You're correct, Power and weight should also be divided by 87³.

But the mechanics of model railroad rolling stock (friction!) are again different from the real thing (how often do you see a train made largely out of plastic, for instance?) And a real engine is steel and lots of it.
3. ### ThoroughbreedMember

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But theoritically, the weight should be the same whether plastic or steel, 1 ton of feathers = 1 ton of lead, hence why there is an nmra weight rule http://www.nmra.org/beginner/weight.html to help keep things as a constant.
4. ### tverskayaMember

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Theoretically, yes, but if you would miniaturize a 1:1 engine to 1:87, the mass per unit of volume would also be reduced by 1:87³. However, as plastic has a lower mass per unit of volume (=weighs less!), the 1:87 engine with plastic parts would weigh less than 1:87³ of the prototype. Model trains, however, are made to weigh to get realistic running properties instead of having correctly scaled down mass. (Someone correct me here if I'm wrong!) Same applies to the engine power. The appearance is the primary objective.
5. ### LoudMusicMember

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The following is not likely for anything run on a table top ...

What about a 1/12 or 1/8 scale built out of the same materials (blue prints even!) as the real thing? They should then be theoretically 1/12^3 or 1/8^3 the power and weight of the 1:1 unit, correct?

Anyway, I was mostly just curious what people do about correct weight and engine power. I assume most HO locos are wildly over powered, and most cars are wildly underweight.
6. ### Jim KrauseActive Member

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I don't even concern myself with such things. When you take material strength into consideration, there's no real, useful, reason to bother with it. If you are into mathmatics and structural engineering, you could completely redesign a scale locomotive but it wouldn't look like the prototype. Isn't making the model look like the real thing the basic premise of modeling? Having said this, I know I'm going to get all sorts of replies, so have at me. Isn't that what forums are for?
7. ### LoudMusicMember

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Oh yes, primary goal is physical representation. I'm with you 100%. However, a realistic operation is very important as well. I don't want to have to add locomotives to a train just because "that's the way the real ones do". I want to add them because they are needed to pull the cars in the consist. Additionally I was curious if my math was right
8. ### shaygetzActive Member

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Cool line of thought...any more of this, though, and my few brain cells leftover from the 70s are gonna be singin' "Innagaddadavida" at 78 rpm:thumb:
9. ### Herc DriverActive Member

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Wow...what an impressive question, and (showing my ignorance here) something I didn't give thought to before in prototypical operations. How does a railroad decide how many engines to lash together to pull a train over certain terrain? Weight? Braking requirements? Scheduling constraints?

But as a side note...I can see I was waaaaay off in my thinking. I thought the cost of the engine had to exceed the combined cost of the cars for the train to move.
10. ### tverskayaMember

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Just a wild guess: speed required taking in account the weight pulled and the track used with all terrains, curves and whatnots included plus a little bit to be on the safe side but no more than the regulations as to not to waste resources. Don't ask for the maths.

By the way, does anyone here know how much extra fuel is carried on locomotives? Of course they are no aircraft where every pound counts, but railroads are still businesses which would probably want to save every cent they could.

Herc Driver - I think your final note applies to model railroads mainly! ;-)
11. ### LongIslandTomMember

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Yep, typical HO plastic engines like the Athearn SD40-2 do indeed weigh under 10 ounces. They usually have a drawbar pull of around 2 ounces (I'll let someone else convert that to horsepower, heh).

Well... You gotta remember that an Athearn F7 and one of their C44-9Ws share essentially the same drive mechanism, the only real difference being the C44-9W has two extra axles. If you want a "realistic" HO F7, then you need to swap out that Athearn motor for a weaker one or something.
12. ### 60103Pooh Bah

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Some random comments:
a 1:8 scale loco would have a volume proportion of 512.
This means that a 150 ton loco would come down to about 586 pounds. Any live steamers out there?
Someone once complained about having a train come in pulled by a heavy locomotive and then having a little yard engine pull the same string of cars off to be switched. Not mentioned was that the yard engine was taking them off a 10 mph instead of 70.
I read that the pulling power of a loco should be about 4 times its own weight (or weight on drivers).
Model railway dynamics are quite different than real railways. The movies find this when they film trains falling off bridges. As an exercise for the student, calculate the time for a train to fall 170 feet from a trestle, and for a train to fall 170 HO feet (about 2 prototype feet, it'll calculate easier). Remember that the first 16 feet take one second, and it gets faster.
13. ### Herc DriverActive Member

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Tverskaya you are correct! That was a model train comment and should not be construed to resemble any intelligent real-world train operations comment. Personnally, I really do find the actual physics of railway operation interesting - it is quite opposite to my world of moving heavy weight with the lightest yet strongest aircraft possible. Seems like in railroading, heavier is better and for many reasons absolutely opposite to moving aircraft.
14. ### doctorwayneActive Member

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I don't think that there's any point in trying to scale down weight when there are so many other things that we don't really scale down properly, like our curve radii, or our grades, or in many cases, even the speed at which we run trains.
As for how the prototype selects power for a train: each locomotive type is assigned a tonnage rating for each division or subdivision on which it is allowed to operate. This can sometimes vary depending on the season (for instance, wet leaves on the rails can play havoc with tonnage ratings). Steep grades (up or down), curvature (sharp or otherwise) and weather conditions can all have a negative effect on tonnage ratings. A locomotive rated for 5500 tons on straight and level track will not have that same tonnage rating on a mountainous division. I'm not sure how the prototype arrives at their tonnage ratings, but as modellers, it's fairly simple.
On my layout, the Erie Northshore sub is either level or downhill going west, and level and uphill going east. A modified Athearn Mikado, travelling west, can pull probably a couple dozen cars (funny, I've never done the tests for west-bound trains), although such a train would be too long for the passing sidings). East-bound, the same loco will handle 12 randomly selected freight cars (some roll freely, others less so, and sometimes, there'll be a real brick in the consist - car weights are approximately around the NMRA recommendations). I know this because I've tested these locos upgrade, starting with a train that the loco can move on level track, but not up the grade. I simply remove cars until the loco can consistently make the grade. If one loco in the same class cannot pull as many cars as the others, then the whole class is assigned the lower rating. If the train that needs to be moved exceeds, even by one car, the tonnage rating for the loco available, then a second loco is added to the consist. These same locos, when working on a different subdivision, may or may not have the same tonnage rating: that will be determined by on-site tests. I have two Moguls, one from IHC and the other a re-motored brass import. The smaller brass loco will outpull the IHC, but both are rated for the lower tonnage rating of the IHC.
I also do another tonnage rating test, this one because I run trains of hoppers with "live" loads. Each of the cars weigh 8 ounces, quite a bit more than the NMRA recommendations, and enough to severely tax just about any loco. The power plant requires three trains of twelve cars each, per week. To move a 12 car train of the loaded hoppers, plus a caboose, requires two Athearn Mikados, or two Bachmann Consolidations, or one of each: all have the same tonnage rating for coal trains. (One of these loaded hoppers in a train of mixed freight doesn't affect the tonnage rating, as there's a bit of a built-in "cushion". Two or more can be enough to push a train over the tonnage rating of a single locomotive).
My locomotives were modified to achieve these tonnage ratings because that was the heaviest train that will be regularly operated. In actual practice, most trains are usually overpowered, as my passing sidings limit train length.
As a general rule-of-thumb, the maximum pulling power of any locomotive is approximately 25% of the locomotive's weight, so the heavier the locomotive, the more it will pull. I have three modified Athearn U-boats (A bit out-of-place on a 1930s-era layout ) that each have two can motors and weigh just over 33 ounces: their measured drawbar pull is 8.3 ounces, about 25% of their weight. Traction tires can increase this percentage, but I don't use them. Most locomotives can stand to have some weight added to them: those Athearn Mikes, when I was trying to determine how much weight I could safely add, were still able to slip their drivers with a 20 oz. saddle of sheet lead draped over the boiler. Unfortunately, I couldn't find room inside the boiler shell to hide that much weight.:cry: If you're going to add weight to a locomotive, it is important that the loco, when pulling a train that exceeds its pulling power, is still able to slip its wheels when the weight of the train overwhelms it. An easy way to ensure that this will happen is to place the desired amount of weight atop the loco (like my experience with the lead saddle, you may not be able to fit all of it into the shell when you actually set about modifying your loco), then couple one car behind the loco. While you hold the single car in place on the track, open the throttle: the loco will try to move the car, but because your hand prevents this, the loco's wheel will start to slip (spin). If this occurs, you can safely add that weight to the loco. If the loco's wheels do not slip when you open the throttle, you have used too much weight, and you should remove some, in increments, until the wheels do slip. Wheel slippage is like a safety valve: it lets you know that the train is too heavy for the locomotive. When the train stops moving, but the wheels don't slip, all of that power that you're applying through the throttle is still trying to make the motor run: when it can't, it produces heat, which will, sooner or later, destroy the motor. If you're running a train, and the wheels slip somewhat on a grade or curve, you might want to add another locomotive, or remove a couple of cars from the train, as excessive slipping will, over time, remove the conductive plating from the wheel treads.
As usual, I've blathered on well past my two cents worth, but I hope this adds something useful to the discussion.

Wayne
15. ### jim currieActive Member

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[
By the way, does anyone here know how much extra fuel is carried on locomotives? Of course they are no aircraft where every pound counts, but railroads are still businesses which would probably want to save every cent they could.

on a quick check i found fuel capacity of two the SD40-2 has a 4000 gal. cap. and the dash8 has a 5000 gal. cap. and from the looks of them that would be about as much as they could carry.
16. ### LoudMusicMember

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Wow, that's a mountain of information. And I read every word

I still contend that HO scale locos are overpowered, but until I have 60' of track that I can adjust the grade on on-the-fly I can't really prove it.

So to elaborate on trains and power, continuing with the SD40-2 topic, I've found a few sources talking about the tonnage rates of these locos. Also I found that in some cases the SD50 was derated to an SD40-2 and renamed SD50-2. Anyway ...

Looks like wolfboy works for Conrail. He says their rule of thumb is to keep the tonnage lower than the horse power. Using Conrail's r.o.t. the UP east bound 3 loco 99 hopper train I waited on on my way home Monday must have had something like the following figures.

SD70: 4000HPx3 = 12000HP
Within 9000 tons and 12000 tons (low number specified otherwise there would be fewer locos in the lashup)
Individual hopper car weight between 90 tons and 120 tons

Grantid I could have counted wrong, and I'm no expert on loco spotting, but I think I'm close enough to play with numbers.

That seems high. I thought cars usually rode full between 70 and 100. But I guess those figures allow it to be the high end, and being that they were grain cars at the end of growing season I bet they had them crammed full.

A lot of you are probably thinking "What the hell does it even matter, kid?!?" I'll tell you. I'm BORED. My current layout is a 10' 1x6 that I tacked three pieces of flex track to last night on the floor of my garage so I could dig out my dusty old engines and run them back and forth for half an hour. You know what I learned? I need to clean the wheels.
17. ### Russ BellinisActive Member

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In the case of BNSF at least all or some of the above. For coming down Cajon Pass they have a requirement of a certain number of dynamic brakes per ton. They also require a minimum of wheels with brakes per a tonnage figure. Their fastest trains are the Q-LANY & Q-NYLA, & in both cases they have delivery guarrantees with penalties for late arrival. In the case of those two trains at least, they put enough engines on to maintain the speed they need to meet the schedule. They also have formulas to determine whether helpers can go in the front of the train, rear of the train, or if they have to go in the middle. It isn't enough to have enough power to lift the train over Cajon Pass if they pull a coupler in two and loose the train in a run away back down the mountain.
18. ### Herc DriverActive Member

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Very interesting information...thanks Russ. The physics of simply moving a train is quite amazing.

BTW...my side note was just a small joke. Ok...a really small joke.
19. ### Jim KrauseActive Member

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jim c: Our club just purchased two of Atherns latest SD40's. The instruction sheet lists four different fuel tank capacities depending on the railroad.
20. ### jim currieActive Member

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intetresting as the info i got was from a EDM and a GE web site.4000 gal might be the maxium cap.