Squeezing the Radius

Classic Toy Trains Forum
1

Big Boy, Spankybird, Mr. McLellan. Dave et. al. Once again HELP!!

The Little River & Hobart has hit another design snag.

We’ve tried to have 054 be our radius wherever our mainline engines must go. Now, we have a place where we’ve only got 49 inches (track center to track center) to fit in a 180 degree turn.

SO, knowing it might ban that "territory to a few of our monsters like the long Fairbanks FM, we’re thinking of "shrinking the 054 to fit the space but not going all the way down to an 042. . Perhaps by cutting short segments of 054 interspersed with short segments of 042 track . All Gargraves this time.

Have any of you guys done this “radius shrinking” trick. Are we headed for an operating problem if we do it??

Thanks as always, Joe and Joe (Jr. and III) “Building The Dream”.

P.S.

(We DId get our prevailing grade down to 4.25 % thanks to you guys). Which for the “geometry challenged” among us works out to about a half inch per foot.
For any other builders who ask, that 1/2" per foot of grade should be considered the absolute MAX for “O” Guage trains. We tested rubber tired and magnetraction engines to confirm that our full 8 car consists (heavy steel frame double stack COFC cars) could be pulled without traction loss.
You guys were SOooo right!! At. 8.5% the best ANY of them could do was 4 cars.

So the LR&H will have its own version of “The Nenanah Loop” (Alaskan RR landmark) at one location and an 054 helix (dropping 5 inches per loop at another. Thanks again to all who stepped up to help.

J & J

2

J&J. If you use the 054 as beginning, the 045 in the middle and the 054 as end, you could be able to fit it into the 49 inches and may be even don’t have to worry about the bigger engines. Most of the trains can squeeze themselves through 045 if they are guided by a bigger radius into the curve. It’s worth to try which setup will work out for your trains. the real railroads also use this to make sure every wheel follows the track in a highspeed curve.

3

Thanks Daan.
I never knew the 1:1 scale railroads did that. Pretty clever and not surprising as their engineering departments WERE amongst the most clever of their time.

Well, unless I hear something here in the next few hours to convince me otherwise, WE are going to do it here on the LR&H. Thanks for the information about using the more gentle radius FIRST in the sequence.

Have printed out your reply and will carry it upstairs to Joe III now. Then will check back to see if any more replies are posted. Thanks also to the other 9 who already took time to read our latest dilemma.
Joe (Jr)

4

Hi Joe, I think you are on the right track (alright, pun intended) with the concept of mixing radii.

How about just using a couple of sections of 054 at the beginning and end of your curve, and the 042 in the middle. You can squeeze out the few inches that you need, while not sharpening the curve that much. The result is an eliptical curve, which is very smooth and quite realistic. FM’s shouldn’t have any problems, as they are designed to go on regular 031.

You may have to do a little bit of cutting, because the different sized circles have different numbers of sections to the circle.

Thanks for playing scientist to us theorists on that grade business. I think you have made the right choice, and will be happy with the results. [swg]

5

Dang, Daan, you got me while I was typing. I guess I’ll just have to second your thoughts on Joe’s latest quandry.[swg]

6

Joes, I have been preaching spiral curves for a while now, as you can see by searching on the word. A spiral is indeed your best bet.

I may be able to help you out with the mathematics of building your curve.

The first thing that you need to know is the actual radius of the two track curvatures that you will use, presumably O42 and O54. I use 20 1/4" and 26 3/8", respectively; but that’s for O27-profile track. Whether it’s the same for the track you’re using, I don’t know. (I will put my numbers in as an example.) In any case, you can measure it by measuring the chord of one section, then using the formula

r = chord / (2 * sin(angle / 2)

where “angle” is the direction change for one section, that is, 30 degrees or 22.5 degrees, respectively. Measure the chord as accurately as you can, between the ends of the center rail at its exact center.

Then the cosine of the gentler curve, angle54, is

cos(angle54) = (r54 - 24.5) / (r54 - r42) = (26.375 - 24.5) / (26.375 - 20.25) = .306
= cos(72.174 degrees)

where 24.5 is the overall radius, that is, half of the 49" that you have, and r42 and r54 are radii that you are using for the curved track. Once you have this angle, you can measure the track by using the first formula again, but this time solved for the chord:

chord = 2 * r * sin(angle / 2)

Since angle54 is greater than three 22.5-degree sections, we need only the chord for the remainder, 72.174 - 67.5 = 4.674 degrees:

chord54 = 2 * r54 * sin(2.337 degrees) = 2.151", or about 2 1/8"

Then, of course,

angle42 = 180 degrees - 2 * angle54 = 180 - 144.349 = 35.651 degrees

Since angle 42 is greater than one 30-degree section, we need only the chord for the remainder, 35.651 - 30 = 5.651 degrees:

chord42 = 2 * r42 * sin(2.826 degrees) = 1.997, or about 2"

7

Is this curve on a grade? If it is, you may find your tractive effort reduced.

8

That’s to much math for me! [:O][:O][:O]

9

Doug, it sounds like you might be a kindred spirit to Mrs. La Touche, who said: “I do hate sums. There is no greater mistake than to call arithmetic an exact science. For instance, if you add a sum from the bottom up and then again from the top down, the result is always different.”

10

Joe,

I have done exactly the same thing on my layout where I had to use some 054 in the middle of an 072 curve. I have gotten by as long as it is just one section of the smaller radius between two larger radii curves. Once 2 pieces of the smaller radius are in series, then the smaller radius curve may be long enough to limit the ability of the equipment to get through. Some equipment (larger locos like 4-8-4s) may not get through regardless as the wheelbase between the two flanged wheels causes the flanges to climb the curve.

There are many steam locos where the curve is limited as the leading or trailing trucks do not have adequate room to swivel make the curve without climbing the rails. Some larger diesels do not have the ability for the trucks to swivel. Sometimes this is mechanical (i.e. the slots in the chassis do not allow it) or the internal wiring harness is limiting travel (in which case one can sometimes loosen it).

And just like real RRs - the speed also determines if you can make the sharper curve.

Regards,
Roy

11

Let’s go back to the beginning again. I hope I didn’t miss something, but you said

"SO, knowing it might ban that "territory to a few of our monsters like the long Fairbanks FM, we’re thinking of “shrinking the 054 to fit the space but not going all the way down to an 042. . Perhaps by cutting short segments of 054 interspersed with short segments of 042 track . All Gargraves this time.”

Why not use Gargraves flex track and just “flex it to where it fits”? Why not make a 48" or 49" curve using flex track. I use the phantom rail flex stuff and I’ve made curves from 72" down to 30" or so.

12

If using tubular, it can also easily be adjusted into any curve you like. Simply remove the ties, take the tracks out and draw a section of 049 on a piece of paper. Bend the rail to fit the lines and add the ties back. A dremer or other multitool will chop the ends to the needed proportions and voila, you have a 049 tubular railsection…

13

Well, I got the two curvatures mixed up about halfway through; so I’ve redone it. I hope it’s right this time. Notice that the sharper curvature in the middle lasts only about 36 degrees.

14

Some very good–actually great–info in this thread, esp the easement idea.

As most of you know, ad nauseum, I bend my own rails and am not stuck to any constricting track plan. In fact, I’ve been laying track all weekend and probably will finish by this long weekend.

You can see my 78" crossover that I made by bending 027 at the end of this website:

http://davidvergun.tripod.com/

I also have successfully bent solid brass rail from Realtrax, after chiseling it off the nasty plastic trackbed. Works for all types of rail. Just wear gloves.

15

Boy!! It feels SO good when I stop hitting my head!! Talk about overlooking the obvious!! We’ve got such a GREAT bunch of guys on this forum that one is teaching us trig and geometry, others are sharing their “been there and done that” , still others are sharing their “watch out for this” thoughts… and NOW, along comes the placticlizard and says WHY DON’T YOU JUST USE PHANTOM FLEX TRACK AND MAKE THE CURVE WHATEVER YOU WANT IT TO BE??

DUHHHH! wHAM, OUCH WHAM OUCH THERE I GO AGAIN.

Well, I’ve stopped for now and I’ll just go over to my favorite on-line supplier and get a couple lengths of that flex track headed to N’Hamsha.

Thanks to ALL of you for being so great EVERY time I come on in a quandry.

SOME day the LR&H will be finished in all its glory and believe me a good part of the glory will belong to you guys. Hope at least a few of you manage a vacation to Seacoast NH (good Lobstah up heah) and can stop by for an operating session once we get that far again. We usually have Summah on a Wednesday but some years it carries over to the Weekend.

Joe

16

Buckeye you have just given me a migraine!!! No, THIS curve is not on a grade but all the traction research I did (see posting on Grades and Brakes thread) was on a STRAIGHT UPHILL!!! Arrrrrrgggghhhh!! I wonder how much the traction will vary doing it on a continuous 054 helix. I’ll bet a cookie that the engineering departments of the 1:1 scale RRs KNEW just what tractive loss to factor in for climbing curves. Those old fuddy duddies, slide rules neckties and all, had figured out just about EVERYTHING to do with hauling a drag over the landscape.

IF I decide to re-run the tests using a continuous 054 I’ll publi***hose results on the Grades and Brakes thread too… Right now Il’ve gotta go beat my head on the wall some more. It feel SO good when I stop.

Gee ain’t it fun to re-invent the wheel??