Curve Easements

[riogrande5761]

SeeYou190

The rest of this thread has made my head hurt.

I posted John Armstrongs figure from his book on the first page of this discussion.  It makes making easements fairly easy and understandable.  It really is and I try not to get too bogged down in to the technicalities.  His bent stick method works quite well.  Atlas flex track does a decent bent stick approximation however.

[SeeYou190]

Track fiddler

I think this was a great answer to the OPs original question.

The rest of this thread has made my head hurt.

rrebell

Easements are highly over rated, depending on the trackplan. They look much nicer but function wize do little unless you have a large engine. I boils down to what are you running.

I agree. I did a lot of experimentation with Kato Unitrack and my fleet of HO equipment.

My minumum radius will be 24 inches in the hidden track. I did a spiral easement into the 24 inch curve with a piece of 32 inch radius, then a piece of 28 inch radius. This revealed that these are the only advantages:

1) Smooth entrance into the curve.

2) Less diaphram seperation on full length passenger cars.

I had one engine, a 4-8-4 that did not like 24 inch curves. With easements, it still did not like them. I got rid of that locomotive.

-Kevin

[riogrande5761]

Lastspikemike

Ah yes, that magical extra half inch...which becomes one inch to get the whole train turned around. 

Now wait while I pull out my magic wand...

Your conundrum would be true if your curve ended parallel to the benchwork on each side.  But ah, I found a solution that magically fixes that problem.  My curve on both sides of the 180 turn around continues around past 180 degree's on either side, inward enough that I can avoid the half-inch requirement on both sides of the 180 turnback at benchwork sides - the easement occurs further around the curve and is natural result of the benchwork lobe bending inward as is true on many layouts.  Yes, I thought about where the easement would fall while I was making the scale drawing of the layout - they fall enough past to avoid the needed extra 1/2 inch; this ain't my first rodeo ya know.

But as pointed out by Dr. Wayne, savvy track planners can build that extra half inch on either side for the easement during planning stages.  So I give the Jedi Hand wave and don't struggle with the acadamia aspect of this.  I look at the big picture, come up with my givens and druthers, look at the room and what I can fit, come up with acceptable minimums and design away, and have enough slop that a half inch here or there isn't going to cause a problem ala Dr. Wayne.

[riogrande5761]

doctorwayne

Lastspikemike

...Geometry requires that any easement reduces (shortens) the radius of the curve that is eased....

 

 

If it's the curve that's being eased, then the easement actually increases the curve's radius at its extremities, as most modellers with any forethought would decide on their minimum-allowable radius, then add the easements as the track exits that minimum.

Wayne

 

This ^

 

Wayne has the glass half full approach rather than the glass half empty!

 

And per John Armstrong's table on Easements it only eats up about an extra half inch of benchwork on 30" curves per easement. 

[doctorwayne]

Lastspikemike

...Geometry requires that any easement reduces (shortens) the radius of the curve that is eased....

If it's the curve that's being eased, then the easement actually increases the curve's radius at its extremities, as most modellers with any forethought would decide on their minimum-allowable radius, then add the easements as the track exits that minimum.

Wayne

[rrinker]

 I think he means to add "to fit in the same space" to that. As Byron showed, a tighter radius plus easement can take up more space than a larger radius with no easement. SO if for example you have a 30" radius with no easement, but decide you want you want to add an easement to the curve, but not make the benchwork any larger, you have to use less than 30" for the middle radius of the curve.

                                              --Randy

 

[gregc]

Lastspikemike

My point was only that easements require tighter radius for some part of the curve than if no easement is used. Simple geometry.

since the easement is a transition from a straight to a curved track it is not tighter in radius than the curve.   while it replaces a portion of the curve, it requires more space.   you don't tighten the radius of the curve to create the additional space required for the easement.   the curve and easement require more space

the easement is a transition that gives the trucks a chance to slightly rotate and each car to develop an angular momentum so that the wheels remain centered between the rails and the wheel flanges don't touch the rails

[Overmod]

The tradeoff with easements is between absolute radius requirement, like rigid wheelbase or restricted truck swing or coupler engagement, and smooth lateral acceleration into and out of curves (reducing jerks between zero and curve lateral that potentially cause derailment or improper motion).

The racing line is largely determined by weight transfer and stability, with heavy braking up to the apex and high acceleration coming out of it.  Naturally you want to limit peak force on the tires to available adhesion (as brakes don't brake the car, and steering doesn't steer it) so the 'line' follows the longest smooth curve through, but you assuredly don't jerk the wheel from straight right into that curve...

All the references I have seen, specifically including the Rolls-Royce manual for chauffeurs in the late '20s, call for the wheel to be smoothly and continuously moved when entering the curve, up to the point of constant turning, and then equally smoothly and continuously unwound 'just' to where the car goes straight at exit.  In practice this is more or less exactly what a 'spiral' transition does: it increases angular rate up to a constant number of degrees per second, then decreases it smoothly again.  The human inner ear interprets this as a constant pull, like gravity and resultant with it, and consequently as a smoother ride; on the other hand, short little jerks in direction, no matter how smooth the subsequent 'turn', are annoyingly prominent.  I had to break my kids of the bad habit of cranking the wheel abruptly into turns of constant radius as if driving on snap-track; fortunately the knack of smoothly winding the wheel and then unwinding again is easily learned, just like feathering the brake as you approach a stop.

[doctorwayne]

Lastspikemike

...You need much less easing into the curve than you might think and by using less easement length you get the benefit of a longer minimum radius for more of the curve.

I don't see how having a longer minimum radius is a benefit, unless you're working with very restricted room.

I didn't have a track plan when my just barely-started benchwork was relegated to a much smaller (and oddly-shaped) room.

I decided that I needed a couple of parameters within which to work, and those turned out to be maximum radius possible wherever curves were necessary (and with 10 corners in the room, there were lots of curves), and non-confining aisle-space. 

I didn't do any calculations for easements, so simply let the Atlas flex track "relax" itself at the point where I thought that the actual curve should end.

While the minimum radius turned out to be 30" (on all three legs of a wye, and again, I think, although it may be 32", on a double track section around one of the outside corners of the room.

Everywhere else it's 34" or greater, up to 48' in a couple of areas (used simply because there happened to be enough room at that location -ya gotta have some places for nothin' but track and scenery).

All of the curves have easements, and most have superelevation, with vertical easements in and out of all superelevation, including that on S-bends.

Of course, in-truth there was more room for most of those curves, but I didn't want to sacrifice scenic areas on the limited area which was used for the actual layout - wide curves look great, but even not-so-wide ones look pretty darn good when located in an interesting setting, the latter being of more interest to me.

Oh, and as far as aisle space is concerned, I achieved my goals pretty-well throughout the layout room, with one exception.  It's fortunate that I'm a lone operator, but even that "pinch-point" would allow two of me to pass without coming in contact.  For larger folks, most could probably maneuver through, as there's nothing to catch one's clothing nor much of anything on the layout there that could be bumped or catch clothing.

Wayne

[riogrande5761]

cuyama

 

riogrande5761

Take the turnout in your diagram and flip it so the diverging route faces to the right rather than the left.   "Easement" where the curve joins the tangent through the turnout to continue to the left - the diverging route continues to the right. 

That's a completely different situation than I was describing, but OK. 

Ah, I though there was discussion of how a turnout could be the end part of an easement.  I mentioned one I used that did not require extra space.  Apologies if I missunderstood a specific application.

[cuyama]

riogrande5761

Take the turnout in your diagram and flip it so the diverging route faces to the right rather than the left.   "Easement" where the curve joins the tangent through the turnout to continue to the left - the diverging route continues to the right.   

That's a completely different situation than I was describing, but OK.

[riogrande5761]

Take the turnout in your diagram and flip it so the diverging route faces to the right rather than the left.   "Easement" where the curve joins the tangent through the turnout to continue to the left - the diverging route continues to the right.   

[cuyama]

riogrande5761

No extra length (to speak of) in the example I gave.  It might not be a "proper" easement but somewhat of the effect.  It worked.

OK, I guess I just don't understand what you are describing. If it works, it works.

[riogrande5761]

cuyama

 

Of course, but then you are back to the extra length needed for the easement itself. No free lunch. But depending on the overall track arrangement, sometimes that works.

No extra length (to speak of) in the example I gave.  It might not be a "proper" easement but somewhat of the effect.  It worked.

 

Again depending on the track arrangment, one might also consider a curved turnout. But in your case the inner curve of the PECO C100 part is right at (or just less than) 30", so it might be tighter than your minimum radius.

And that is food for thought.  My mainline minimum radius is 32 inches, but in staging I may make a compromise down to 30" on parts of the ladder.  I don't think this should cause an operation problem with the equipment I have.  However, I may want to configure the ladder so trains do not have to pass through 30 inch curves.

[cuyama]

riogrande5761

It appears you can still have an easement up to the turnout so the straight portion is after the easement is finished.  Solution no?

Of course, but then you are back to the extra length needed for the easement itself. No free lunch. But depending on the overall track arrangement, sometimes that works.

riogrande5761

Assuming the last part of the curve at the bottom of the helix is flat, I could start with a Peco large turnout there.

Again depending on the track arrangment, one might also consider a curved turnout. But in your case the inner curve of the PECO C100 part is right at (or just less than) 30", so it might be tighter than your minimum radius. Where both legs of the curved turnout are broader than the minimum radius, both routes provide some easement effect.

[riogrande5761]

cuyama

 

Yes, but only for the diverging leg – not for the straight leg.

It appears you can still have an easement up to the turnout so the straight portion is after the easement is finished.  Solution no?

Now OTOH, do a mirror image of that turnout around so the end of the turnout is the finish of the curve but bifurcating to the right....  As long as the substitution radius is much larger than the curve radius, I would think that would be provide an easement effect.  And there is no non-easement in that part.  That scenario was on my last layout - probably hard to see but in the upper left of the photo just above the green and yellow box cars.

 

The substitution radius is roughly 45”, but it’s not a perfect curve, of course, owing to the straight track at the points end and the point rails themselves.

Byron

That seems fine.  I am mulling over the other end of my staging yard and trying to efficiently allow the line coming off the bottom of the helix to split apart.  Assuming the last part of the curve at the bottom of the helix is flat, I could start with a Peco large turnout there.

[cuyama]

riogrande5761

Right, but if the radius equivelent of the curved part of the turnout is broader than the curve radius it is connected to, it can give an "effect" of an easement wouldn't it?

Yes, but only for the diverging leg – not for the straight leg.

riogrande5761

BTW, speaking of curve equivelent, do you know about what it is for a code 100 large Peco streamlined turnout?  Subsitution radius?

All of the Code 100 Streamline turnouts have about a #4½ frog. But they seem to handle larger equipment better than would be predicted, perhaps because the curved diverging leg is gentler than a straight diverging leg. The diverging radius for a PECO C100 “Large” is 60”. The substitution radius is roughly 45”, but it’s not a perfect curve, of course, owing to the straight track at the points end and the point rails themselves.

Byron

[riogrande5761]

cuyama

Generally I agree, and use easements on many of my projects for others. But not all, because occasionally the extra length and width of an eased curve, even with a tighter radius enabled by the easement, can be a deal-breaker in some situations. This is particularly true when a turnout must be fitted immediately at the end of the curve.

Right, but if the radius equivelent of the curved part of the turnout is broader than the curve radius it is connected to, it can give an "effect" of an easement wouldn't it?

BTW, speaking of curve equivelent, do you know about what it is for a code 100 large Peco streamlined turnout?  Subsitution radius?

[hon30critter]

cuyama

Generally I agree, and use easements on many of my projects for others. But not all, because occasionally the extra length and width of an eased curve, even with a tighter radius enabled by the easement, can be a deal-breaker in some situations.

Byron makes a very good point. Easements are great IF you have the space. If you don't have the space then don't beat yourself up because you don't have easements.

I also think that part of the issue is train speed. Tinplate O gauge is a prime example. If you are running trains at 150 scale mph on tight radii then the jerky movements that are a result of the lack of easements are obvious. Slow the trains down and the effect is not so pronounced.

Dave

[GP025]

Thanks Rio, that diagram does alot to clear things up. Byron, thanks for pointing out to additional room required, hadn't progressed that far to realize that. It definitely gives me pause to rethink my plans. I am constrained by a 10'6"x 10'6" room now and will need to plan for the possibility of relocation again, so initially was thinking 3'x3' corner sections so curves would not breach a joint. Food for thought to be sure, Thanks Kev

[cuyama]

Bayfield Transfer Railway

Easements are so ridiculously easy to do, and improve appearance so drastically, that there is absolutely no reason not to use them.

Generally I agree, and use easements on many of my projects for others. But not all, because occasionally the extra length and width of an eased curve, even with a tighter radius enabled by the easement, can be a deal-breaker in some situations. This is particularly true when a turnout must be fitted immediately at the end of the curve.

An example:

Byron

[riogrande5761]

This here should help:

[Overmod]

Track fiddler

You must have some kind of trick to do both at one time without the feeders wanting to come loose during the soldering process?

Now that I know the idea works ... a simple way to do this is to use two types of solder with different melting points: hard-solder the track joint, and then use additional solder and appropriate flux to add the feeder.  Would be a cinch with a temperature-controlled iron.

[selector]

Now that I think about it a bit more, I'm pretty sure it's actually a 1/3 joiner, at least in that photo. A half joiner would still be too large to fit between two tie spikehead sets, especially since they move somewhat closer on a curve...as designed.

The feeder was added later, and just happens to be co-located with that particular joiner.  Don't recall why I chose that spot...

[Track fiddler]

That's awesome selector.  I never thought of half joiners and that you stagger your joints is a great idea.  And I see you kill two birds with one stone with your feeder wires there as well  You must have some kind of trick to do both at one time without the feeders wanting to come loose during the soldering process?

 

 

TF

[selector]

I like the idea and the appearance of easements, especially since I have a twice-around folded loop with a central operating 'pit' and enjoy photography.  Rather than do the math and draw the centerline, I just let the flex track make it's own approximation of a spiral curve.  It does a passable job.  Also, I don't have problems with kinks in the middle of curves if I have to have a joint there.  I stagger the sliding rail and use half-joiners (cut with a jeweler's saw that I solder.  This allows me to leave more ties in place with those important little spikehead details that help to generate a smooth curve, kink-free.

This is a photo of tracks in my helix, last layout.  This joint had to be good and reliable as it was all inside a large 'mountain'.  I hadn't cleaned the area after soldering and filing, so it's untidy.  You can make out the half joiner leaving enough room to obviate having to remove any of the ties.  A fair bit more 'bother', but it made superb curves.

 

[Bayfield Transfer Railway]

Offset in HO scale is 1/8".  I didn't bother measuring length on my last layout.  I stopped spiking a foot and a half or so back and just bent the track into the curve.  The easement shaped itself naturally.  Also, if your offset is more than 1/8 inch that's okay.  I eyeballed everything after the first one or two.

Really, I cannot overstate how simple it is to make easements.

 

[rrebell]

Also visually an inside curve can look fine but not so much an outside curve with the same radius.

[BATMAN]

Bayfield Transfer Railway

Easements are so ridiculously easy to do, and improve appearance so drastically, that there is absolutely no reason not to use them.

 

Appearance is the operative word here. Easements do improve appearance and something else that really can improve appearance and remove some of the toy like look of a MRR is to change the radius as you go through the curve. Too many track plans just look stamped out. As an example, if you start with a 32" curve opening it up to a 40" as you go through the curve, it is very appealing to the eye.