Scale & Gauge

People often ask me what is the difference between scale and gauge. They do so because people talk about HO-gauge or HO-scale trains, or O-Scale or O-gauge trains, etc. The situation gets more complex when referring to the Narrow Gauge models, such as On30 or HOn30, which run different scales on different gauges. So, these notes try to explain all that for you. I've also added some notes on the oddities of scaling.


Track Gauge

Track Gauge or Gauge is the distance between the rails. In the United States and many parts of the world the prototype Track Gauge is 4' 8-1/2". Four feet, eight and one-half inches. Fifty Six and one-half inches. That is not a metric conversion -- that is the gauge of standard gauge railroads around the world. The history of that gauge dates back to horse carts, roman chariots, and how two horses fit on a road. There are some cool articles you can find describing the history, look for them.

Given that we know what standard gauge is, Narrow Gauge is simply defined as tracks narrower than standard gauge. There are some standard Narrow-Gauge tracks, such as 30 inch. Broad Gauge is defined as tracks wider apart than standard gauge. The choice of gauge is an engineering and compatability and interchange decision. Narrow Gauge rolling stock and locomotives are typically smaller and lighter than Standard Gauge. This makes it possible to build a railroad in conditions where a standard gauge railroad couldn't exist. Broad Gauge rolling stock might be able to hold more, or be slightly more stable.


Scale

OK, so what is Scale? Scale is something you see with model railroads, it is the proportion or fraction of size of the real or prototype. For example with a 1:4 scale or 1/4 scale, the model would be 25% of the prototype. A 40 foot boxcar would now be 10 feet long.

How or why do you choose a particular scale? Space, money, time, train length, train count, track mileage, ease of handling, .. are all reasons. You choose a scale because you want to do something with a train that large, or because of the environment it will operate in.

Grandeur of Operation -- O Scale

I thought of O Scale as Lionel for many years. Then I met some Scale O Scale modellers, and watched and listened to their trains run.

Wow!

For years the Museum of Science & Industry in Chicago had a beautiful O-Scale layout. It was quite old, but had been modernized through the years. It had working CTC and Interlocking, and could also run on automatic. O-Scale was a good choice for the layout. It let you see the trains across the large layout, yet it also allowed for larger sweeping vistas, separation of scenes, and also let you have reliable operation versus dust, wind, and being disturbed slightly by visitors. It is gone now, which is a great shame, it was one of the nicest layouts I'd ever been able to enjoy. A lot of that is due to the Scale.

Massive Modelling -- N Scale

One of the most impressive (though dimunitive layouts) I've seen as been in N Scale. I hadn't thought much about N before, except to purchase N gauge track for out HOn30 trains. This layout changed my mind. By going to a smaller scale it allows for many trains. Each train can have a prototype number of cars. The space allows for industry, terminals, and main-line. It is a layout that feels so busy and rail-road-like! The possibilities for operation due to the overall large railroad in a a small space were amazing.

Dad's Trains -- HO Scale

HO lets you do everything.

HO is a nice scale, it lets you do many things. You can build things with detail that people can appreciate. You can run larger trains (though not as large as most N, unless you have a huge space). You need to engineer things. You can work on making good operating cars and engines, they are large enough to work on without being a jeweler. Prices are reasonable because things aren't pushing the limits of miniaturization as with N Scale, nor the 8x larger cost of materials for O Scale.


Scale Notes & Oddities

One interesting thing to note is that because you are scaling in 3 dimensions, that some odd effects that you might not expect occur... Lengths do change in linear proportion, as I mention above. However, overall size changes are more drastic. Referring back to the 40 foot boxcar in 1/4 scale ... For example, say that the boxcar is 40 feet long by 10 foot wide by 10 foot tall. OK, lets scale the side of the car again:

if you look at two dimensions, such as the 40x10 side of the boxcar, and then scale it by 1/4, its size is now 10x2.5. But if you look at the area of the side of the car, it has shrunk more! Wait a minute, how come the area is 1/16th that of the original? Well, that is because the boxcar side is being shrunk in two dimensions. Each Dimension is Scaled by 1/4, so the area is reduced twice by the scaling factor, so now the area is 1/4 x 1/4 == 1/16. If you look at the volume of the scaling, the results are even more dramatic Now the size is 1/64th of the original. That is because it is shrunk in three dimensions by 1/4, so the volume is now 1/4 x 1/4 x 1/4 == 1/64.

OK you say, so the scaled object is way smaller. Thanks, big deal. I mention all that above so you can see what happens if you are going to work in a larger scale which is closer to prototype. If you move from HO scale (1:87) to O Scale (1:48) your dimensions individually only increase by a factor of 2x. However, the total space occupied by that car's box will be 8x as much (2 x 2 x 2 == 8). So, say you have your boxes for your train cars -- in the same amount of space you store 8 HO scale cars, you will only be able to store 1 O scale car.

The good news is that other items don't scale so drastically. For example, curve radii. In HO, a common curve radius is 22 inches, and 30 is quite generous, at least for 4x8 layouts! In O, the radius will only increase x2, since it is a dimensionless constant. So, you will only need 44 inches or 60 inches curve radii in O Scale to duplicate the same effects as you have been having on a HO layout. But, lets look at the area effect again -- to have the same layout in O Scale as you fit on your 4x8 HO Layout -- How much space is needed to make it fit. how much extra space to make everything fit -- twice as much?? Hmmm, how about 4x as much -- for area 2 x 2, so now you need 8x16, or 4 times as much area. However, what if you only have the space for a 4x8 layout? Well, in O-Scale your radii will still be 22 inches, but now the turn is twice as tight. Actually I think it is too tight -- you are down below the turn radii for industrial trackage in O-Scale! However, don't despair -- there is still from for the operation of Trolley Equipment which has to squeeze around much tighter bends than railroad equipment! But so much for your scale length 87' passenger cars as anything more than a non-moving piece.

Then comes something really funny -- lets look at your track requirements for the 4x8 HO layout scaled up to an 8x16 O-Scale layout. Say you have 100 feet of straight track on the HO-Scale layout;

How much straight track will you have on the O-Scale layout?
How about 200 feet (100 x 2 == 200).
OK, now say you have 100 feet of curved track on the HO Scale layout;
how much curved track will you hae on the O-Scale layout?
How about 200 feet (100 x 2 == 200).
Why isn't there a difference? Straight track is linear, so it scales linearly with only one multiplier But curved track, it encompasses an area carves out a shape of a box (think of a square box enclosing a circle of track), or a circle. So it seems like it is an area effect, that would scale in two dimensions, and need two multipliers (2 x 2). Fortunately that isn't the case; the circumference of a circle varies linearly with respect to the radius. Refer to geometry -- the circumference of a circle is 2 x π x radius. So, even though a the O-Scale curved track encompasses a much larger (2x2 == 4x) area, the track amount only doubles. Whew! Saved a bunch of money there -- O Scale track is already quite expensive before needing 4x instead of 2x as much!

Scale & Gauge

So that is gauge and scale, but that isn't the end, I promised to explain this stuff a bit.

By default the gauge of a particular scale model railroad is just the (standard) gauge for the prototype scaled by the scaling factor for that scale. They then refer to that gauge by the scale factor, for example, HO Gauge. Many people use the Terms HO Scale and HO Gauge as synonyms -- but be careful, they actually aren't the same. One is the 1:87 scaling factor, while the other is the prototype 4' 8-1/2" scaled by 1:87. One is a measurement, the other is a dimensionless scale.

Now that distinction is made, lets look at at a scale of On30. The overall scale is O Scale 1:48; the n30 designator means narrow gauge 30 inches. That just means that it is running a prototype track gauge of 30 inches. But what gauge is that really? Well, it turns out that the gauge of On30 is HO gauge track. It is quite convenient actually, HO track is easy to get! But now the scale and the gauge are no longer the same; if you purchases a On30 train and "O Gauge" track, your locomotive would sit between the rails on the ties most unhappily. That is why the difference between scale and gauge is so important. By the way, there is HOn30 -- HO Scale modelling 30 inch gauge. It turns out that N Gauge track is the equivalent of 30 inch gauge in HO scale -- again the track is easy to find instead of having to hand-lay it.

But now, just when you thought it was over, it gets weirder. Some Scales, the most common is G Scale, do not use scale track. They do this to get different operating qualities from a non-standard gauge in that scale. The reason all the vendors give is that the wider gauge they use makes the rolling stock more stable. Which basically means it is less likely to tip over, whether from bad track work or outside forces -- such as cats.

O Scale / O Gauge trains are also a bit of an oddity. If I recall correctly some of the things are not exactly to scale, probably due to reliability issues as mentioned with G Scale above. There is a movement afoot for Prototype 1:48 modelling, which is also called Scale O-Scale, because they want to run actual Scale O-Scale railroads!


Model Railroad Scales

The Wikipedia Page on Model Railway Scales has a nice table of scales. Unfortunately they are metric oriented in an inch world. Another Wikipedia page has a good reference to the History of Model Railway Scales.


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Last Modified: Wed Jan 14 09:32:28 CST 2009
Bolo (Josef Burger) <bolo@cs.wisc.edu>