Post by: Geezer on 12/05/2012 07:01:34
Here's the thing:
In the US, and most of Europe, a common model scale is HO, and the scale ratio from the real thing is 1:87. Due to a lot of history, the UK (mostly) landed on OO, which has a ratio of 1:76
Now, 1:76 against 1:87 does not seem like that much of a difference, but when you compare the same original modeled in both scales side by side, the difference seems to be far greater.
Is our perception of scale based on volume? If so, should we cube the difference in ratios?
Post by: CliffordK on 12/05/2012 08:22:34
All you need to find is 1/76 scale models of the 4'1" or 4'0" gauge railways, and they should come out just about right. [;)]
http://en.wikipedia.org/wiki/List_of_rail_gauges#Medium_gauge
| Metric | Std | Country | RR | 1/87 width | 1/76 width |
| 1,435 mm | 4 ft 8 ½ in | About 60% of Worlds Railways | Standard Guage | 16.49mm | 18.88mm |
| 1,245 mm | 4 ft 1 in | England | Middleton Railway, pre 1881 | 14.31mm | 16.38mm |
| 1,219 mm | 4 ft 0 in | Wales | Padarn Railway (1842–1961) | 14.01mm | 16.04mm |
| 1,219 mm | 4 ft 0 in | Wales | Saundersfoot Railway (1829–1939) | 14.01mm | 16.04mm |
| 1,219 mm | 4 ft 0 in | Scotland | Glasgow Subway, Falkirk (1905–1936) | 14.01mm | 16.04mm |
| 1,219 mm | 4 ft 0 in | England | Furzebrook Railway (c.1830–1957) | 14.01mm | 16.04mm |
| 1,219 mm | 4 ft 0 in | England | Redruth and Chasewater Railway (1826–1915) | 14.01mm | 16.04mm |
| 1,219 mm | 4 ft 0 in | New Zealand | Wellington tramway system: electric trams, system closed 1964. | 14.01mm | 16.04mm |
Post by: Geezer on 12/05/2012 17:23:21
It's been that way for about sixty years, and it wasn't really a problem, because the UK railway system was isolated from Europe, so there were very few instances of mixed equipment operating on both sides of the channel. However, that situation is rapidly changing.
I have proposed to the UK community that it adopt a "sliding scale" based on the age of the prototypes so that OO would, over time, merge into HO. It's already half way there because of the track.
My proposal was not appreciated!
Post by: Geezer on 14/05/2012 01:20:27
It's really intended to be a (sort of) serious question about how we perceive things. Does using a one-dimensional ratio really give a true sense of what we perceive, or do we in fact perceive "scale" as more of a three dimensional ratio?
Post by: CliffordK on 16/05/2012 07:24:55
You may be right, for a space filling model, perhaps one should judge it by volume.
Consider a 50% model of a 10x10x10 cube (very exciting, I know), with a total volume of 1000 units.
If you go by length, then the resulting 50% model would result in a 5x5x5 cube, with a total volume of 125 units, or 1/8 of the above, or (½×½×½).
If you tried to make it half the volume, then the length of side would be
x LOr, about 0.7937 x L, or nearly 80% of the original length.
So, setting three proportional cars next to each other. The one that is 50% of the volume would be 80% of the length of the original. The one that is 50% of the length of the original would be only about 12.5% of the original volume.
Which is best?
Apparently it gets much more complicated when making model aircraft, because lift is a function of Wing area (square), Cord Length (linear), and Velocity (Should velocity be reduced?).
Volume, and in many senses, mass, of course, is a cubic measurement.
Is drag proportional to the fontal area (a square)?
Anyway, to calculate the aerodynamics of the scale model, you have to incorporate linear measurements, square measurements, and cubic measurements.
Large ships, of course, have a "hull speed" which is a linear measurement. Yet displacement, and most other quantities are cubics.
Post by: JP on 16/05/2012 16:46:38
I guess what this means is that people (at least somewhat) extrapolate volumes from linear dimensions.
Post by: Geezer on 16/05/2012 17:31:28
For example, a 10% increase in scale (linear) does not sound like very much, but when you compare a two 3-D models, the difference seems much greater, which probably is not surprising because the volume has actually increased by 33%
As Clifford points out, dimensional scaling is only one aspect of the problem. Physical effects can't really be scaled.
Post by: JP on 17/05/2012 03:39:12
Post by: CliffordK on 17/05/2012 04:13:12
Yikes! If the physics scaled linearly you'd be in trouble. To run your model train, you'd have to use ~1/87th of the power needed to drive an actual train! From a back of the envelope calculation (~1000 horsepower full sized train, 1/100th scale locomotive, and google conversion from hp to watts) you'd be running at ~7500 watts!Ahhh...
All you need is Tim the Toolman Taylor (http://en.wikipedia.org/wiki/Tim_Taylor_%28character%29)... to build you a super powered 7.5 KW micro bullet train ;)
Post by: Geezer on 17/05/2012 04:29:09
Yikes! If the physics scaled linearly you'd be in trouble. To run your model train, you'd have to use ~1/87th of the power needed to drive an actual train! From a back of the envelope calculation (~1000 horsepower full sized train, 1/100th scale locomotive, and google conversion from hp to watts) you'd be running at ~7500 watts!
I think the rails would glow red hot and fuse! And 1000HP is a conservative estimate. The real things can produce several thousand kW. Scaling 3000kW by the cube of the 87 ratio gives about 4.5W which is actually pretty close to the power output of the electric motor in the model.
Post by: Geezer on 17/05/2012 04:35:25
Post by: SeanB on 20/05/2012 14:49:40
Post by: evan_au on 02/06/2012 10:42:18