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For Layout Planners Who Like Math

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Posted by Doughless on Thursday, August 4, 2022 2:04 PM

ROBERT PETRICK

 

 
Doughless

But, if I were to draw lines on the bench first, what tool do I use to make sure the angle is 7.15 and not 7.0 or 7.25?

 

 

Here's how I would do it:

Measure horizontally 8 inches and then vertically 1 inch and put a small mark. Or 16 inches horizontally and 2 inches vertically. Or 24 inches and 3 inches. And so forth. This is the analog solution to a trigonometric calculation. You would be marking out the sine and cosine of 7.15 degrees. This could also be done easily using a 24" framing square.

Sheldon started out life as a draftsman. So did I.

Hope this helps.

Robert 

 

Duh, ok.  It goes back to the basis of the #8 frog.  1 for every 8, another way to think of it.

- Douglas

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Posted by ROBERT PETRICK on Thursday, August 4, 2022 1:50 PM

Doughless

But, if I were to draw lines on the bench first, what tool do I use to make sure the angle is 7.15 and not 7.0 or 7.25?

Here's how I would do it:

Measure horizontally 8 inches and then vertically 1 inch and put a small mark. Or 16 inches horizontally and 2 inches vertically. Or 24 inches and 3 inches. And so forth. This is the analog solution to a trigonometric calculation. You would be marking out the sine and cosine of 7.15 degrees. This could also be done easily using a 24" framing square.

Sheldon started out life as a draftsman. So did I.

Hope this helps.

Robert 

LINK to SNSR Blog


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Posted by Doughless on Thursday, August 4, 2022 12:58 PM

ROBERT PETRICK
My question is why a rhombus?

I guess you knew the term was wrong back then but said nothing.  Thanks.

ROBERT PETRICK
You suggested this simple solution a few posts earlier where this could be solved to a pretty close tolerance by carefully laying out two parallel lines 9" apart and slicing another line across at a 7.15 degree angle and then measuring the results

As revealed in my post to Dave, there is existing track in the way preventing any sort of straight lines being drawn.  I did not reveal this early because I know the habit of members to devise alternative plans or alternative methods...like iterating lines or downloading software ...and just wanted to stick with the mathematical answer to the question because that answer was all that I needed before I started.

 But, if I were to draw lines on the bench first, what tool do I use to make sure the angle is 7.15 and not 7.0 or 7.25?

- Douglas

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Posted by ROBERT PETRICK on Thursday, August 4, 2022 11:37 AM

DrW

Much of the confusion arose because the OP called it a rhombus. A rhombus has four sides of equal length. What he wanted was a parallelogram, as has been figured out by now.

JW

Yes, exactly.

LINK to SNSR Blog


DrW
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Posted by DrW on Thursday, August 4, 2022 11:23 AM

Much of the confusion arose because the OP called it a rhombus. A rhombus has four sides of equal length. What he wanted was a parallelogram, as has been figured out by now.

JW

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Posted by Doughless on Thursday, August 4, 2022 11:09 AM

dehusman

 

 
Doughless
The exercise was to understand what the lengths of the pair of sides would be before I started laying out lines or track.

 

Draw a center line for one ladder, draw the diverging center line.  Then just draw the centerline for the other ladder wherever you want it.  I guess I'm not seeing why it needs to be so precise or one needs all the math.  Laying it out should be fairly straight forward.

 

This is getting into personal layout situations which I avoided to limit confusion, but i already have the layout built and I wanted to know the runaround length there would be by reconfiguring the runaround.  I wanted to reconfigure to have more straight tracks towards the backdrop over any thing else, but wanted to see if it also increased the runaround lengths.  It does, as expected, but not by very much.

I called it a yard because that's where most folks do the angles and straight line thingy so I thought that it would help them relate.  It appears to have added to the confusion rather than subtracted.  I actually don't care about the placement of the yard tracks, in that they will fill in wherever later.  There is only a need for one or two on each side and they can originate off of any track, frankly.

I can't lay it out and measure accurately because there is already roadbed, track, and caulked and wired.  I want more straight tracks towards the back of the layout than what I have now.  That is the reason for this entire project.

So I'm redesigning on paper before I plunge into making lines that I can't make anyway, especially useful because this situation is dictated by geometric angles and absolutely no curves anywhere to adjust any errors.

Also, I am impressed by the number of comments on this forum that appear to design layouts by understanding the angles and the math of it all, where I never had much need to ever do that.  I thought there would be plenty of responses eager to use calculations.  Frankly, I'm a bit surprised by the number of comments that suggest to just lay it out with templates or draw out lines on the bench before even fashioning a diagram.  Oh well.

- Douglas

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Posted by Lee 1234 on Thursday, August 4, 2022 9:28 AM

Peco #8

If you lay out 4 of these in a row that's more than 4 feet long.  I did a quick lay out in XTrackCAD and 4 lefts are like 15 inches wide with a diverging angle on the last track 4 times the frog angle.  

Lee

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Posted by dehusman on Thursday, August 4, 2022 9:17 AM

Doughless
The exercise was to understand what the lengths of the pair of sides would be before I started laying out lines or track.

Draw a center line for one ladder, draw the diverging center line.  Then just draw the centerline for the other ladder wherever you want it.  I guess I'm not seeing why it needs to be so precise or one needs all the math.  Laying it out should be fairly straight forward.

Dave H. Painted side goes up. My website : wnbranch.com

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Posted by Doughless on Thursday, August 4, 2022 9:09 AM

ROBERT PETRICK

 

 
Doughless

Now we can adjust the height a bit to see what it does to the length.  If anybody wanted to play along.  I understand if people have better things to do.

 

 

For every inch you increase the "height", you increase the length 8 inches. That's kinda where the No 8 turnout designation comes from. Exactly fits the 7.15 degree angle offset.

 

Ah, yes, of course.  Thanks Robert.

- Douglas

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Posted by Doughless on Thursday, August 4, 2022 5:49 AM

ATLANTIC CENTRAL

  So I am assuming the storage tracks run the long dimension? That may seem obvious to you, but not out here with us.

Once you get the first one right, the rest are parellel lines.

A chalk line is not eaxpensive, can I send you one?

Sheldon

 

Having a chalk line for this purpose would expand my layout building tools from 3 to 4, and that would be overkill for the hobby. Big Smile

And I want to make sure I get the lengths correct before I fill the benchwork with lines.  I'm not a carpenter by trade so laying lines is usually an iterative process for me, resulting in a lot of lines being laid. 

BTW, I was quick to see the diagram last night. 

Ray's diagram has the long and short sides flipped from the final plan and shows two long ladder tracks, where as the short sides will run from SW to NE and the long sides will run from E to W.  Geometry tells me that swapping the long sides with the short sides will change the shape of the runaround, but won't change the mathematically determined lengths. 

So the short sides will run from SW to NE and will be the ladders.  Only two storage tracks per ladder resulting in shorter storage tracks, but they will abutt the backdrops on the E and W, to give the impression they are long and go into the horizon.  Storage capacity is minimal because of this shape, but, its plenty for the 20 to 25 cars I need to hold in the yard.  About 10 to 12 on each side, each side will make up one or two (about) 68 inch trains that will fit on the runaround.

- Douglas

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Posted by Doughless on Thursday, August 4, 2022 5:35 AM

dehusman

I'm not sure how this is at all useful because he's asking about FROG to FROG and any measurements for the track are taken from the centerline of the track and point of intersection of the centerlines of the track.

So even if you calculate the distance from the PI on the SW switch to the PI on the NE switch, its not going to give you the distance between the frogs and it's not going to give you the length of the run around and it's not going to give you the capacity or length of a yard track, it just gives you a dimension that is not really useful for any design purpose.

 

Yes Dave, I originally asked frog to frog thinking it would help know the exact distance but it isn't needed.  

Better than having the PECO templates, I already have PECO #8s to play with.

The exercise was to understand what the lengths of the pair of sides would be before I started laying out lines or track.

- Douglas

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Posted by dehusman on Wednesday, August 3, 2022 10:07 PM

You do realize that PECO offeres free downloadable switch templates.  You can print them off, put two pair of switches together, and then position them exactly as you want them and measure the clearance with actual cars.

Dave H. Painted side goes up. My website : wnbranch.com

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Posted by dehusman on Wednesday, August 3, 2022 10:01 PM

I'm not sure how this is at all useful because he's asking about FROG to FROG and any measurements for the track are taken from the centerline of the track and point of intersection of the centerlines of the track.

So even if you calculate the distance from the PI on the SW switch to the PI on the NE switch, its not going to give you the distance between the frogs and it's not going to give you the length of the run around and it's not going to give you the capacity or length of a yard track, it just gives you a dimension that is not really useful for any design purpose.

Dave H. Painted side goes up. My website : wnbranch.com

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Posted by ROBERT PETRICK on Wednesday, August 3, 2022 9:17 PM

Doughless

Now we can adjust the height a bit to see what it does to the length.  If anybody wanted to play along.  I understand if people have better things to do.

For every inch you increase the "height", you increase the length 8 inches. That's kinda where the No 8 turnout designation comes from. Exactly fits the 7.15 degree angle offset.

LINK to SNSR Blog


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Posted by ATLANTIC CENTRAL on Wednesday, August 3, 2022 8:42 PM

So I am assuming the storage tracks run the long dimension? That may seem obvious to you, but not out here with us.

Once you get the first one right, the rest are parellel lines.

A chalk line is not eaxpensive, can I send you one?

Sheldon

    

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Posted by Doughless on Wednesday, August 3, 2022 8:14 PM

ATLANTIC CENTRAL

And it would still be so much simpler to see the proposed track diagram.

I have used track arrangements similar to this which take advantage of the specific angle of a turnout for decades now.

And the prototype does the same thing all the time.

Still not sure what the point of all this?

Sheldon

 

You have the diagram in Ray's post, Edit: just swap out the short sides and the long sides to make a really short ladders and room for only two yard tracks off each ladder.  If I could have drawn it and posted it, it would have saved a lot of confusion.  I admit that.

I could explain further as to how much total space I have for everything, but this runaround section is the critical place.

Now we can adjust the height a bit to see what it does to the length.  If anybody wanted to play along.  I understand if people have better things to do.

The point is that I usually plan by laying the track by eyeball with some straight pencil lines writtne on the benchwork.  But this seciton I want perfect from all corners, so knowing that the length of a short side is 26.25 inches and not 26.5 inches, for example, matters to keep things "square" so to speak.

I don't trust myself to lay out the lines at 7.1 degree angles, not having a chalk line to snap, and keeping everything perfect.  Knowing the lengths of the 4 sides beforehand helps to know that the turnouts are being placed perfectly.

I knew you'd come through though, thanks.

- Douglas

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Posted by ATLANTIC CENTRAL on Wednesday, August 3, 2022 8:03 PM

And it would still be so much simpler to see the proposed track diagram.

I have used track arrangements similar to this which take advantage of the specific angle of a turnout for decades now.

And the prototype does the same thing all the time.

Still not sure what the point of all this?

Sheldon

    

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Posted by Doughless on Wednesday, August 3, 2022 7:33 PM

Colorado Ray

 

 
ATLANTIC CENTRAL

 

 
ROBERT PETRICK

Based on the angles you gave (7.15 degrees and 172.85 degrees) and the length projected onto the x-axis (98"), there would be four sides, each 49.19" long. The 9" height does not fit. (actually 6.12")

Holding the 98" projected length and the 9" offset, then the angles become 10.49 degrees and 169.51 degrees and the four sides become 49.41" long.

 

 

 

Robert, I know you did what it sounded like he was explaining, but that is not what he is looking for.

He does not mean the x-axis thru the rhombus. 

He means draw a rhombus using the angles he indicated, a long skinny rhombus where the two horizontal sides are 9" apart.

The left and right sides of the rhombus will become the "C" side of a right triangle scribed inside or outside the tip of the rhombus. 

That triangle "A" side, plus length of the horizontal side of the rhombus = 98"

How long is horizontal side of the rhombus? How long is the left/right side of the rhombus?

What I want to know is why 9"?

If I was laying out track I would be using center lines on 2" centers so the width would be an even number. OR, if I wanted to map the space that would be used it would sill be an even number, 2" "spsce" for each track.

But to answer the question, the horizontal sides would be 26.2542" long, the angled sides sloping up from horizontal at 7.15 degrees would be 72.3080" long.

I would draw a picture, but I don't really know how to do that quickly on here.

Sheldon

 

 

 

Sheldon's right.  Here's a scaled sketch based on what was told.

Each track would hold about two 73' cars.

Ray

 

Thanks for the sketch.  Actully the long sides and short sides are flipped, making the runaround having a less diagnal look to it, but the 4 lengths, but the 4 sides comprise the runaround tracks not the storage tracks.  The sorage tracks will come off the two long sides, which will serve as ladders.

Including what Sheldon calculated, 72.30 inches for the long sides, the runaround length adds up to just over 98 inches...then deducting clearance needed for the loco to runaround the cars, which is considerable given the 7.15 angle of the #8s, give me a functional runaround/train length of probably around 76 inches? (we...er...you..could use math to tell me how much length I lose to provide clearance  for a standard width HO car on a track angled at 7.15 degrees...at both ends of course).  

The yard tracks would come off of the longer sides of the runaraound at each direction.  Coming off the bottom of the long side on the right would be longer than 26 inches, especially given that I have more space available to the right beyond the diagram.

However, if we increase the height (or depth as laying on the bench) to 9.5 or 10 inches, that extends the length of the long sides and moves the NE corner to the right (the SW corner is a fixed point), and then I may run out of room for a proper tail track/ lead track at the NE.

Why am I doing this?   As you can see, the diagonal shape puts the runaround more towards the back drop as the train moves from left to right. 

With #8s, its tough to have a conventional runaround that runs parallel to the bench work edge, and still have enough room to swing any track to be close to the backdrop for any amount of distance.  Now I've got 4 tracks coming off the corners of the runaround to maximize the amount of straight trackage in the space, which is important to me for modern open space railroading with long centerbeam flats.

- Douglas

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Posted by Colorado Ray on Wednesday, August 3, 2022 7:08 PM

ATLANTIC CENTRAL

 

 
ROBERT PETRICK

Based on the angles you gave (7.15 degrees and 172.85 degrees) and the length projected onto the x-axis (98"), there would be four sides, each 49.19" long. The 9" height does not fit. (actually 6.12")

Holding the 98" projected length and the 9" offset, then the angles become 10.49 degrees and 169.51 degrees and the four sides become 49.41" long.

 

 

 

Robert, I know you did what it sounded like he was explaining, but that is not what he is looking for.

He does not mean the x-axis thru the rhombus. 

He means draw a rhombus using the angles he indicated, a long skinny rhombus where the two horizontal sides are 9" apart.

The left and right sides of the rhombus will become the "C" side of a right triangle scribed inside or outside the tip of the rhombus. 

That triangle "A" side, plus length of the horizontal side of the rhombus = 98"

How long is horizontal side of the rhombus? How long is the left/right side of the rhombus?

What I want to know is why 9"?

If I was laying out track I would be using center lines on 2" centers so the width would be an even number. OR, if I wanted to map the space that would be used it would sill be an even number, 2" "spsce" for each track.

But to answer the question, the horizontal sides would be 26.2542" long, the angled sides sloping up from horizontal at 7.15 degrees would be 72.3080" long.

I would draw a picture, but I don't really know how to do that quickly on here.

Sheldon

 

Sheldon's right.  Here's a scaled sketch based on what was told.

Each track would hold about two 73' cars.

Ray

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Posted by Doughless on Wednesday, August 3, 2022 7:06 PM

ROBERT PETRICK

Based on the angles you gave (7.15 degrees and 172.85 degrees) and the length projected onto the x-axis (98"), there would be four sides, each 49.19" long. The 9" height does not fit. (actually 6.12")

Holding the 98" projected length and the 9" offset, then the angles become 10.49 degrees and 169.51 degrees and the four sides become 49.41" long.

 

Thank you Robert.  But the length is the variable in my case and not the height. 

At a 9 inch height, what length would fit?  And then what would each leg length be.

NVM, see below.

Thanks for your help.

- Douglas

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Posted by ROBERT PETRICK on Wednesday, August 3, 2022 6:38 PM

ATLANTIC CENTRAL

Robert, I know you did what it sounded like he was explaining, but that is not what he is looking for.

I agree. This is why I try to keep my nose out of these sort of threads. But I can't seem to help myself . . . . kinda like watching a car wreck . . . 

ATLANTIC CENTRAL

What I want to know is why 9"?

My question is why a rhombus?

ATLANTIC CENTRAL

But to answer the question, the horizontal sides would be 26.2542" long, the angled sides sloping up from horizontal at 7.15 degrees would be 72.3080" long.

Yes, exactly. I calculated the same. You suggested this simple solution a few posts earlier where this could be solved to a pretty close tolerance by carefully laying out two parallel lines 9" apart and slicing another line across at a 7.15 degree angle and then measuring the results. No need to fidget with rhombuses (rhombii ??).

ATLANTIC CENTRAL

I would draw a picture, but I don't really know how to do that quickly on here.

I know how to draw one quickly, but it is a pain in the neck to get the image up on this forum.

Robert

LINK to SNSR Blog


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Posted by ATLANTIC CENTRAL on Wednesday, August 3, 2022 6:05 PM

ROBERT PETRICK

Based on the angles you gave (7.15 degrees and 172.85 degrees) and the length projected onto the x-axis (98"), there would be four sides, each 49.19" long. The 9" height does not fit. (actually 6.12")

Holding the 98" projected length and the 9" offset, then the angles become 10.49 degrees and 169.51 degrees and the four sides become 49.41" long.

 

Robert, I know you did what it sounded like he was explaining, but that is not what he is looking for.

He does not mean the x-axis thru the rhombus. 

He means draw a rhombus using the angles he indicated, a long skinny rhombus where the two horizontal sides are 9" apart.

The left and right sides of the rhombus will become the "C" side of a right triangle scribed inside or outside the tip of the rhombus. 

That triangle "A" side, plus length of the horizontal side of the rhombus = 98"

How long is horizontal side of the rhombus? How long is the left/right side of the rhombus?

What I want to know is why 9"?

If I was laying out track I would be using center lines on 2" centers so the width would be an even number. OR, if I wanted to map the space that would be used it would sill be an even number, 2" "spsce" for each track.

But to answer the question, the horizontal sides would be 26.2542" long, the angled sides sloping up from horizontal at 7.15 degrees would be 72.3080" long.

I would draw a picture, but I don't really know how to do that quickly on here.

Sheldon

    

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Posted by ROBERT PETRICK on Wednesday, August 3, 2022 4:17 PM

Based on the angles you gave (7.15 degrees and 172.85 degrees) and the length projected onto the x-axis (98"), there would be four sides, each 49.19" long. The 9" height does not fit. (actually 6.12")

Holding the 98" projected length and the 9" offset, then the angles become 10.49 degrees and 169.51 degrees and the four sides become 49.41" long.

LINK to SNSR Blog


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Posted by Doughless on Wednesday, August 3, 2022 2:46 PM

If anybody wants to try, I'll skip the track planning part and focus strictly on the geometry and math.  Here is the picture (albeit taller and not as long as actual..this is a "wracked square" and I'm describing a "wracked rectangle")

Ceramic Tile Symmetry Series Flat Rhombus - Carbon by Flooringsupplyshop.comYou can draw this at home if you like:  Assuming 2 sets of angles at 7.15 and 172.85, and the total height of the figure is 9 inches, and its length from SW point to NE point along a horizonatal axis is (about) 98 inches ( if we dropped a plumb off the NE tip to extend the bottom line to that point) ..What is the length of each of the four sides?  (of course, 2 sets of 2 equal length sides).

I think this is enough information for a geometry mathmetician to calculate.  

 

 

 

- Douglas

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Posted by ATLANTIC CENTRAL on Wednesday, August 3, 2022 11:43 AM

I would still like a sketch of the whole area.

Sheldon

    

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Posted by Doughless on Wednesday, August 3, 2022 10:26 AM

Yes, laying it out on grid paper is the way to do this, then measuring the different lengths according to scale, AFTER its laid out.  

It dawned on me that since I will be laying out a perfectly symetrical geometric shape, we can know the exact dimensions and runaround length we will have BEFORE I start laying out lines on the benchwork or grid paper.

Its really no different than forming a siding with tracks 2 inches apart, but where using two LH turnouts to do that makes the mainline shift to flow through a diverging path of a turnout(most sidings are built with a LH and a RH turnout).  I'm essentially extending the crossover length to make 9 inch center spacing between the "main" and the siding/runaround, which pushes total length of the siding to be longer (the distance between the two frogs).  (I just happen to be using two more turnouts to return each track back to parallel).  In this case, the crossover portions are becoming a functional part of the runaround since its becoming longer.  (They will also serves as the ladders)

I think that when making the crossovers taller, I'm gaining some functional length to the runaround compared to how much the total horizontal length of the siding also has to grow.  But I'm not sure about that. 

Its just something that we could know before we start laying anything out on paper.

- Douglas

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Posted by ATLANTIC CENTRAL on Wednesday, August 3, 2022 9:21 AM

I always build yards, or passing sidings with perfectly parallel tracks, never willy nilly. 

Again, on paper or on the bench work, if you lay out the parallel tracks, the leads will cross them at the frog angle 

Sheldon

    

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Posted by Doughless on Wednesday, August 3, 2022 7:27 AM

Thanks y'all for indulging my question, its amittedly sort of academic.  And my questions are poorly described. The questions are:

What is the distance between the SW and NE frogs...as the crow flies?

What is the total distance of the two legs that connect the SW and NE frogs ...that will be the linear length of the runaround track (s)?

I neglected to give some dimensions (but that's okay because nobody really asked about the math) .  I edited my comments above to give a veritcal height of 9 inches and a horizontal length of (about) 98 inches from left to right (if it were a rectangle), and the angles are 7.15 degrees (and 172.85 degrees for the other two angles).

I laid this out on the benchwork and realized that fussing around trying to get things "square" would be a lot easier if I had some precise measurments to use.  Since all tracks in this rhombus are suppossed to be perfectly straight (with no kinks, small curves, or bows; unlike a traditional runaround) and the angles are precise, geometry formulas and math should give me the precise answers to shoot for.  It also tells me runaround length (not including the narrow portions that approach the frogs)

Its a way of knowing the answers without employing any type of track planning process.  Its really a geometry question.  It may not be answerable on this forum.

- Douglas

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Posted by ATLANTIC CENTRAL on Wednesday, August 3, 2022 5:37 AM

And this is the short coming of the PECO turnout, with its "compact" footprint.

With Atlas turnouts you just join the turnouts to each other on the straight route and you get diverging routes spaced at 2" track centers.

And I still don't understand which direction the yard leads enter and leave? Not that it matters that much.

And I'm still not sure I understand the question? Or did I cover it in my second sentance - you need to know how big of a spacer to add between the turnouts?

With Atlas it would be zero for 2" track centers.

Just another reason I don't like PECO turnouts, short spacers on yard leads.

As a professional draftsman, who has done my share of track planning, the easy answer to this question is to draw the parallel yard tracks and then cross them with a line at the frog angle.

Yes, the prototype uses turnouts larger than #6 in yards, more like #8 or #10 or even bigger.

Sheldon 

    

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