Need Help With Curve Calculations

Trying to visualize what you are asking. Are you creating an outside trim? Just a stab based on my guess, here is my calculation. A half circle is 180 degrees. If you wanted to cut 6 pieces of 2x4 the angle at each intersection would be 180/6 or 30 degrees.

@BigAl56 posted:

Trying to visualize what you are asking. Are you creating an outside trim? Just a stab based on my guess, here is my calculation. A half circle is 180 degrees. If you wanted to cut 6 pieces of 2x4 the angle at each intersection would be 180/6 or 30 degrees.

...for which you would make a 15º cut at each end of the 2x4 segments...yes?  The two 15º cuts would marry to form a 30º bend at that intersection.  And, BTW, if each end of the semicircle end up in tangents (straightaways), you'd want to make that 15º cut at the ends of the adjoining straights, too.

(And then your teenager asks why you have to learn all this geometry stuff!..what's the practical use of it!??)

Don't quite understand the 2x4's for roadbed, but TEHO.

...for which you would make a 15º cut at each end of the 2x4 segments...yes?

Ummm, yes. Math, who knew?

Its an ambitious plan. Its a 7'x11' open helix that will rise 4 or 5 levels with an inner return track. I'm using 2x4's as a kick plate because of the narrow pathway in the basement. On top of the base I'm using 1x4's as the roadbed. On top of the helix will be another layout with plywood placed on top of the supports.

Just an observation, all wood, including roadbed will be pretty noisy, regardless of the track type.  I'd suggest using some sound absorbing material as the roadbed.  My layout has 1/2" Homasote over 1/2" Baltic Birch, and I use 1/4" foam roadbed.  Nice quiet running with Gargraves track and Ross switches.

Thanks for the reply. I had inquired before and was told no matter what, because I'm using tubular track there wasn't much I could do to mitigate  the noise. Weren't you the person who was using rolls of beveled foam roadbed?

I don't know who you're talking to, but there's always ways to mitigate track noise, some track is easier than other track to deal with.

Yes, I used the foam roadbed.  For tubular track, I'd be tempted to use cork roadbed as it's more "solid", and you don't have all the ties to provide support on tubular track, so it would likely sink into the foam.  I can assure you that tubular track directly on plywood is MUCH noisier than tubular track on plywood topped with Homasote, I've seen that difference personally.  The extra roadbed would likely help, and it would also enhance the appearance.

Which ever way I tried the math I could never get the right answer. Trail and trail I settled on a 5 1/4 angle. Not perfect but very close. I looked at many sites giving information on making bowls with segmented 2x4's. You also have to know what lenght you want each segment. Knowing the 72 curves are 14 inches I went with two 7+ inch pieces per track.

Twenty half circles needed.  320+ 7 inch pieces all with slots cut with a biscuit cutter. That's another 640 cuts! Glued and clamped with a tourniquet. Four done.

You got it.. Silver'... That will work'.. good luck and keep going'...... 👍✔

It was a thought at the beginning. The quantity  needed, the price of plywood and space to cut had me think differently. Plus I had purchased the lumber awhile back when on sale and cheaper to begin with compared today. Because the helix is meant to be a feature and seen I wanted to avoid as many supports as possible. This has turned out to be very strong. The worst is over as far as cutting goes. BTW after the fact I found a formula to calculate angle -  "You can't figure this out without knowing how many boards your circle will have; once you choose the number of boards, just divide 360 by the number of bevels (one for each end of each board) and that's how far from 90° each end should be.

So, if you have 4 boards (a square):

4 * 2 = 8 beveled ends
360° / 8 = 45°"

In my case I would have chosen 5.6%. Not a big difference from my guess of 5.25%.

@SilverChief posted:

Twenty half circles needed.  320+ 7 inch pieces all with slots cut with a biscuit cutter. That's another 640 cuts! Glued and clamped with a tourniquet. Four done.

Excuse my confusion, but are you making a helix?  What else could you be using ten complete circles for?

I am. Oval in shape. 10 circles make 20 arcs that I need for the 5 levels. Five feet added to each outer ring, inner ring is shorten by one 10 inch track. Inner curve has two 54% tracks replacing two 72% all to fit within the outer shape. Its easier to clamp a full circle. I'm not gluing the ends where they met so I'll have two arcs.

OK, just curious.

Why did you go with small pieces that you had to glue together?  Wouldn't it have been easier to to do 90 degree curves?  I guess you can save a little wood with the small pieces, but the larger curves would certainly be more structurally sound I would think.  It would also be a ton easier to cut far fewer pieces.

Confusion on my part then. I don't see how a fixed track of 72% would fit on boards cut to a 90% angle? The arcs are the roadbed. The tracks fit evenly between the boards as cut.

@SilverChief posted:

Confusion on my part then. I don't see how a fixed track of 72% would fit on boards cut to a 90% angle? The arcs are the roadbed. The tracks fit evenly between the boards as cut.

What's the 72%?

Well, if you think you're confused, imagine me!  Any curve configuration you can build using small pieces of wood can surely be cut out of a single piece of wood!  I'm seeing a 360 degree circle that could be made using a few curves cut from wood.  It can obviously be made from many little pieces, that just seems to me to be a ton more work.

The master speaks.  @Tom Tee  thanks for the insight on curve building.  Whether for a helix or elevated curves the idea of sandwiching the 1/4 multiply together is not something I considered. Having built my first decent layout with nominal 1/2 plywood (5ply) there were inherent problems with that method including warping tendencies and adequately addressing the butt joints. Screwing them into an underlying 1/2 pieces works but then requires an extra 1/2 rise for any underpassing track. 

Tom recommended Baltic Birch multi-ply for my layout and I couldn't be more pleased.  It was a pleasure to work with, and it goes without saying that 11 plies makes it very resistant to warping!

No turning back for me. Wood is cut. Gallon of glue.

This was my inspiration for having an open helix as a main feature - https://www.therailwire.net/fo...ex.php?topic=46896.0 - and this for an inner return track - https://www.youtube.com/watch?v=-hPuNFjRTZA

I have wiggle room for clearance to adjust grade. When I attempted a software design I was getting 1.5 grade at the most. The guy from Lloyd's Train was  going to create something for me but was too involved in projects to follow through. He did say the concept would work and be interesting. I'm not a modeler looking for authenticity. I don't get into operations. Lighted passenger cars going round and round in the dark is fine for me

IF I can get a decent grade the next challenge is wiring. Lots of wire. Another reason for using thicker boards was to be able to router channels in the wood so I can recess  and hide wire.

The correct answer WAS use a trammel.....

@Ron H posted:

The correct answer WAS use a trammel.....

Difficult on a 8 foot board. I needed to know setting on a miter saw. You would have to explain how that would work for my situation.

Here's one of many videos on a trammel.

It's not important, but I don't understand the problem. No need to respond.

Best of luck putting every thing together.

Ron H

Once the pieces are all glued up and cured, the half circle will be very rigid. I think that may be an issue. I’ll try to explain. If you want to maintain 5” clear from top of rail to underside of the 2x4 you will need to raise 6.5” going around the half circle. The arc length along the half circle is 113”, (pi x 36”). The grade would then be 100 X 6.5” / 113” = 5.75%. The grade across from one end of arc to the other end of arc would be 100 x 6.5” / 72” = 9.03%. This will have the result of having one rail of the track almost an eight of an inch higher than the other rail at the arc ends. At the mid-point of the arc the rails will be level. A train entering the half circle will be tilted to the right while twisting to vertical at the mid-point and then again twisting to being tilted to the left as it exits the half circle. An engine that is 4” tall will be a little over 3/8” out of being truly vertical at the arc ends.

I don’t know if any of this will prove to be an operational problem or not, but I wanted to point it out. It probably will not be a problem at slow speeds.

@Jack L posted:

Once the pieces are all glued up and cured, the half circle will be very rigid. I think that may be an issue. I’ll try to explain. If you want to maintain 5” clear from top of rail to underside of the 2x4 you will need to raise 6.5” going around the half circle. The arc length along the half circle is 113”, (pi x 36”). The grade would then be 100 X 6.5” / 113” = 5.75%. The grade across from one end of arc to the other end of arc would be 100 x 6.5” / 72” = 9.03%. This will have the result of having one rail of the track almost an eight of an inch higher than the other rail at the arc ends. At the mid-point of the arc the rails will be level. A train entering the half circle will be tilted to the right while twisting to vertical at the mid-point and then again twisting to being tilted to the left as it exits the half circle. An engine that is 4” tall will be a little over 3/8” out of being truly vertical at the arc ends.

I don’t know if any of this will prove to be an operational problem or not, but I wanted to point it out. It probably will not be a problem at slow speeds.

Thanks for the reply.  Time will tell.... I'm testing grade tomorrow with what I've made already. The 2x4's are supports for the 1x4 boards I'm using for the roadbed. I get 344 inches on the outer tracks. Using an online grade calculator I get a grade of 1.75 using 6 inch rise. I measured that with a 1/4 inch foam road that I'm using to mitigate the noise.

I've certainly seen videos of much shorter and steeper setups on YouTube that are capable of running. I've seen others glue, screw and add metal plates for rigidity so I guess I'll just have to experience and adapt. I realize other issues are possible such as derailments.

I'm using L shaped metal hangers on the 2x4's to hold  the roadbed. I can adjust height and pivot the angle before adding the second screw. Not sure if I'll screw roadbed into the other half of hanger. It can float.  Using the 6 inch clearance my understanding on how to measure the location and height of the hangers is to start with the halfway point of the ring which is 3 inch's, directly across from the starting point. So that would give me 1.5 inches at the apex of the first arc and 4.5 and the second arc before rising to  6 inches above first level. No?

I dare say I'm going to experiment with adding slight super elevation.

I get 346" for one loop but 344" is close enough and the grade will be 1.75% which is great. Even with 1x4 roadbed, I still think there may be some twisting like I mentioned, but you can correct that if needed when you assemble it.

So… did it work?  

I ended up in a back brace for six weeks. Put everything on hold until after Christmas.