Sigh.
As you rightly point out, I do not have definitive answers, we can get those only from the Lego engineers involved, and I doubt we can get in contact with them...
However, I’ll try to give some more comments, taking your original questions one by one:
(1) the radius used for curved tracks must have some reasons behind it. I don’t know which and I would very much like to know.
My answer to that one is a guess, but I think it was mainly the need to make the figure-eight with rails (you call them tracks, but neither is a good word really, but we know what we mean: the track “unit” piece).
As you can see from what I did with the plates under the connections, for some strange reason the curved track actually spans 30.3 degrees! And it is also slightly wider than the straight one.
(2) Ever tried to connect the ends of such right angle with Duplo bricks?
I suppose what you mean here is this: suppose there is an infinite grid of studs (knobs) that are “virtual”. Place the half-sleeper of one end of the right-angle set of three rails exactly on those studs, then the half-sleeper at the other end does NOT fit the studs. That is true indeed, and I have no clue why, other than that the curved rail is some compromise that allows building the figure-eight and also fits several other layouts that cannot be made exactly, but can be made because there is enough play.
As the engineer that I am, I would probably make a number of “popular” layouts, calculate the curved track dimensions to do each of them, and then design a piece that, with some play, would work in all those layouts.
Take a look at http://www.cailliau.org/Alphabetical/M/Mathematics/APR/Description/
The layout in the photo can probably not be made "rigidly", and relies on the play. The diagonal, projected on the other sides woud involve a cosine of 30 degrees, and that is not a rational number.
What I do know is that the older rails, black (still for sale as used items on eBay), are the same width but have many disadvantages: they divided the circle in 8 instead of 12, and the sleepers could not fit on plates because the tabs were not raised above the studs. Their surfaces are also a little lower than the new ones.
(3) a whole circle of 12 curved tracks you would not get a circle but an ellipse with short radius of 17 Duplo studs and long radius of 18 Duplo studs
Using the method of forcing the half-sleepers to unite over a plate or brick, I come to 36.5 for the outer diameter. If you do not use that method, then the play in the connections (we really lack a vocabulary for naming the different parts of rails we are talking about!) will allow for a diameter of 2x18=36.
(4) Another failed example is when you connect two curved tracks in opposite direction. That way the lines entering and leaving the two tracks are parallel. Its tempting to see if you can mount it on a plate. But as it shows again it is not possible.
Indeed. I have a drawing that shows it, for ideal alignments. The play in the connections lets one align straight and snaky tracks, but not if alignment is forced by plates under sleepers. And so maybe that was another important consideration: a snaky track should be able to replace a straight one. For, I suppose you have noticed, most sets have far more curved than straight rails. (a good source of straight rails, used, is eBay)
(5) a train having two or three railcars significantly slows down on longer curves. The cars are long and wheels don’t turn around in no way which means that the do no align well with curved track and cause some friction
This problem occurs also in real trains. Over the length of a long car it is alleviated by the bogies on each end of the car that can turn around a vertical axis, but within the (very short) bogies the problem remains. The other kind of friction is caused by the fact that the wheels are fixed to the axles, and the outer wheel must go further than the inner wheel. That is the reason for supressing the ridges on the inner surface (point 5 on my page, traction) which unfortunately also leads to the locomotive slowing down somewhat and having less traction. In real trains the wheels are slightly conical, and there is 12.7 mm play between the rails and the wheel flanges (see point 2.). This play allows the car to shift slightly towards the outer rail in a bend, so that the outer wheel rolls on a larger diameter of its conical shape than the inner wheel which rolls on a smaller diameter. This is just sufficient to compensate the difference in distance travelled. In fact, original railways in mines had a rail distance of 4’8” (don’t ask where that silly number came from...) and this was no good for higher speed locomotive pulled trains for people, hence the addition of 0.5” and the standard rail gauge of 4’8.5”. Human silliness has no bounds. And even so, many trains screech when going through a bend because of the slipping of steel on steel (do not buy a house close to a railway bend).
But Lego rails of course do not have this possibility of the conical wheels, so the inner wheel slips and causes friction.
(6) Now knowing the drawbacks of current curved track design we might wonder what are its advantages so that the trade off goes well. Anyone?
There I think I did give several answers: it had to be child-proof, withstand pressure on the wheel rims, be easy to put the cars on the rails, allow for use without rails, and so on.
(7) Why current locomotives do move in only one direction?
The older ones do have reverse, and can be programmed. I don’t know why this was stopped.
(8) Or would it be much more difficult for kids?
You touch a delicate point. I would say it would be too difficult for the parents. Sadly, we seem to be in a dumbing-down phase of everything, including Lego. I remember that when IKEA became popular, it was mainly because it was so EASY to assemble, and all I hear now is that people find it difficult! Yet IKEA has not changed its , so it must be people’s attitudes that did.
(9) Current sets with locomotives are from 2 years. How it was with the old “smart locomotive”? As I think it was far more “difficult” and “complex”.
I agree. Kids figure this out quickly, but parents are too impatient and dislike figuring things out. See also (7) and (8).
(10) I find it rather odd that (current) Duplo locomotives don’t have anchors on both sides as all railcars do.
I agree completely. However, going over a bridge might become more difficult if the train is pushed, as the rack-and-pinion design of hte locomotive’s driving wheels would not engage with the bridge (page about that to come). But that is a minor point.
(11) Tracks and the engine wheels of the locomotive are corrugated. Why is this needed? As it seems LEGO trains don’t use it. So why Duplo trains need it?
Because of the flat wheel rims, see also point 5. The other trains are designed like real ones and run with conical wheels on top of rails. I will soon put up a page on locomotive design.
(12) Does LEGO provide precise specification of their “bricks”?
I do not know, as I have been in direct contact with Lego only once, almost 30 years ago. In this day and age of companies making a wall between themselves and their customers, it will be difficult to get those specs. On the other hand, Lego must have filed patents on everything, and so perhaps I should try to find out what the European Patent Office has. This is hard work though... I have a lot of dimensions, from reverse engineering, and my info about it was/is on my old site. I’m converting it (slowly...) to the renovated site, but it will take some time.
Have you got access to Adobe Illustrator, or to a good SVG editor? I could send you some of my drawings of parts. Otherwise, watch the Lego section, more will come over the next months.
Robert.
Perhaps one more thing: I have not yet finished a page on switches. They are different in dimensions from a superposed pair of curved rails. Maybe they have the original curvature. Writing to you has brought this up as a possibility, I will explore it.
Also: the older switches had "memory": if you set one to fork to the left, say, it would stay that way. If a train came from the other direction on the right side of the fork, then it would push the point to the right, but that would bounce back after the train left the switch. The new switches no longer have a spring in them. If you set one to fork to the left, and then a train passed over it in the other direction from the right side, the switch will then be set to fork to the right...
Things are being dumbed down.
