Model & prototype curves

It's interesting that on the prototype, they measure curves by degrees, while in model form, they measure it in radius, I guess they couldn't buy 300' foot yard sticks back in those days.....

Alan

"Alan Gilchrist"

Depends on your prototype.

In the UK, they measure radius. They used to measure in chains. Dunno what they do now.

Why the difference? Because the U.S. of A always seems to name things and do many things differently from the UK just as a matter of course. Something to do with a little disagreement around 200 years ago I believe.

-- Cheers

Roger T.

Home of the Great Eastern Railway

For the information of all: A one degree railway curve has a radius of 5,729' 6-15/16" or 1736.375 meters This is 36000/pi X 1/2 An HO scale one degree curve has a radius of 65' 9-1/2" or 20.053 meters. The circumference of a prototype one degree circle is 36000 feet. One degree of deviation per 100' linear distance. 360º X 1º/100' = 36000'

With that data you should be able to calculate any equivalent model degree of curvature. If you do that, you will see that model railway equipment operates on curves that are exceedingly sharp by prototype standards. Prohibitively sharp in many cases.

Charles Crocker

Curves on the model can easily be measured by radius because that center of the curve is available to work with. On the prototype, that center of the curve may be inside a mountain and thus be quite inaccessable. Thus the prototype needed a method of measuring a curve from the track itself. In came the chain for a fixed length and the Dumpy Level or a transit instrument to measure the angle that the curve is making as it goes along from one length of the chain to the next. Thus it is naturally listed in degrees curvature. Just imaging drawing fixed length chords around a curve and measuring each angle and dividing them by two to get the correct offset for the curve. This is the only way to accurately measure a curve in the surveying stage and also is the basis for checking the rail for the correct curve. I'll note that trolley curves are also measured this way often (buildings do get in the way!) although in many cases, the curved rails can be setup beforehand in a yard and then taken to the site and installed. The chain in those cases is usually a much shorter one than the mainline roads use. I've helped lay out curves for a large scale model railroad with a 20' chain and it was an interesting job that really went pretty fast. We later had to go back and redo more stakes as 20' ended up being a bit long to hit and just took the chain and marked the center link and measured off from that for the mark at the 10' point.

-- Yeppie, Bush is such an idiot that He usually outwits everybody else. How dumb!

Here is how I understand the problem:

From a straight line run of track, hold one end of a chain at the point to begin the curve. Stretch the chain and swing it some angle from the previous straight line. The track will now curve to go through the other end of the chain. The curve is also tangent to the straight run.

If this is correct, then this is not a linear problem, and the above is just an approximation. The formula is:

Radius = Chain/(2*sin(Angle))

Where:

Radius - The radius of the resulting curve Chain - The length of the chain Angle - The angle between the previous straight run and the chain

I have confirmed this on my CAD program and it yields results which are about half of the above. So for a 100 unit chain:

Angle(°) Radius

1 2864.934425 2 1432.685417 3 955.3661305 4 716.7793513 5 573.6856623 6 478.3386117 7 410.2754524 8 359.2648267 9 319.6226611 10 287.9385242 11 262.0421532 12 240.4867172 13 222.2705741 14 206.6782747 15 193.1851653 16 181.3977639 17 171.015181 18 161.8033989 19 153.5776743 20 146.19022

Here is a link to the CAD layout:

I would invite you to confirm this in your own favorite CAD program or with pencil and paper.

Bill MacIndoe

Prototype curves tend to be laid out geometrically due to the inherent difficulties with the nail and string or wooden trammel methods. The British stated theirs as if they had used the nail and string (well, nail and chains) whereas the yanks stated theirs relating to the manner in which they achieved the theoretical radius. (specific length of track and it's divergence)