![]() I bought it at a train show, probably in the early '90s, with the idea that it was 45 degrees, but when I got it home I realized that it didn't look quite right and then measured it at 40 degrees.Check out the pizza size calculator!, the newer version of the pizza comparison calculator □ He also said that for a while, as part of this fiddling, they even produced 40-degree crossings rather than 45-degrees. ![]() ![]() (I have the magazines around somewhere, but can't lay my hands on them right now.) This changing went on for years from the start of Lionel O in 1915, finally settling down by about 1930, IIRC. In one of the articles on the earlier years of O gauge, he said that Lionel fiddled repeatedly with the exact lengths of the sections - straight and curved - and the exact geometry of the track, trying to get everything to fit together right. He documented the different lengths, etc., though I don't remember any of the specifics. Some years ago (probably more than 20 by now) the late Max Knocklein - train collector & historian extraordinaire - wrote a series of articles published in the TCA's Train Collector Quarterly on the history of Lionel track. The more careful you are measuring to the exact center of the end of the center rail, the more accurate your result will be. (For 8 sections in a circle, multiply by 1.306563 and for 16 sections, by 2.562915.) Therefore you multiply by half the cosecant of 15 degrees, or 1.931852. The result is the radius to the center rail.įor example, O42 has 12 sections in a complete circle so each section turns through 30 degrees. Multiply that number by half the cosecant of half the angle that the section turns. Measure the chord of a curved section, in a straight line from one end to the other of the center rail. I have posted it several times before here it is again: It is also fairly insensitive to whether the section measured may have been bent a little straighter or more curved than it should be. It has the useful feature of working better, the more sections are needed for a circle. It is essential to make at least two measurements, at right angles, to have any hope of accuracy.īecause of the difficulty of making a full-circle measurement, even if you are lucky enough to have enough sections for that, I devised the following method that requires only a single section and knowledge of how many sections a circle comprises. As Rob pointed out, the joints can vary in tightness and the track itself is quite flexible (one of its virtues, actually). Marx was particularly inconsistent.Īs Fred suggested, it is quite tedious to get a good measurement, particularly by the obvious method of putting together a full circle and measuring it directly. I think that track manufacturers have not generally understood where this number may come from, because straight O27 sections vary quite a bit around this length. Then, dividing by the square-root of 2, we can back into the "correct" length for the straight section, which comes to an awkward 8.838835 inches. So, subtracting the somewhat shorter 2-inch tie and dividing by 2 gives a radius of 12.5 inches. It seems to have been designed with a round number for the overall diameter. O27, which I believe Lionel got from Ives, is the other way around. (I think we're using the same reasoning.) When you double this to get the diameter, and add a tie length of 2.25 inches, the overall diameter comes to 30.534271, which is where we get the modern nominal diameter of O31 (but occasionally O30 for the same track). It's pretty clear that Lionel intended their straight section to be exactly 10 inches, with the result that the radius is 14.142136 inches, the value that Rob and I agree on. With 8 curved sections in a circle, this scheme effectively requires that the radius be the length of a straight section multiplied by the square-root of 2. This assures that a passing siding can be made using only standard sections. I am convinced that the original scheme for O27 and (so-called) O31 tubular track was to coordinate the curved and straight sections so that the joints in a siding alongside a straight main line would match those of the main line.
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