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
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
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.
[2c]
Dave
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?
Yes, but only for the diverging leg – not for the straight leg.
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
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.
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.
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.
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.
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.
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.
OK, I guess I just don’t understand what you are describing. If it works, it works.
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.
That’s the trade off. For every inch of easement, necessarily at a larger radius than the main part of the curve, you have an inch of tighter than necessary radius in your main curve. So whether you use them at all, or use shorter than ideal easements or use the prototypically correct long easements you will find you make compromises with tighter minimum radii as a consequence.
Actually, the same problem arises when driving. The racing line is rarely suitable to use when road driving. There is a myth about that smooth road driving requires that you trace a racing line as closely as possible. In reality you want to drive a curve with the largest possible radius which is one of constant radius more often than not. Reason is the racing line is designed to let you exit the curve at the highest possible speed which you can almost never safely reach in ordinary road driving. The most com
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 th
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.
My point was only that easements require tighter radius for some part of the curve than if no easement is used. Simple geometry. Note that MRR provides the minimum radius number for almost all the layouts for which they run articles. Minimum radius is the most important limitation of any model railroad. If you use easements your minimum radius will be tighter than if you do not.
As for the physics of the racing line I am happy to compare lap times…
My point there was the same: maximum tire grip and therefore maximum achievable speed in the actual corner is at the point of maximum radius of the path of travel for the car. That will not be on the racing line where the maximum speed desired is at the exit of the corner just as the car straightens up for the ensuing straight. “In fast out slow” is the admonition faster drivers give to the slowpokes who cannot understand this reversal of common sense. Racing lines require slower speeds in the actual corner than the car is capable of in that corner, in order to maximize entry speed to the following straight which is the fastest way around a circuit. This is not the fastest way to drive on the road because: speed limits. And just btw weight transfer isn’t what you might think it is. To understand how vehicle springing and non linear pneumatic rubber tires are affected by inertial loads induced (hopefully) by the driver you need to realize that there is no such thing as weight transfer, from the point of view of physics. What’s going on is leverage exerted around the CG by momentum effects. Nothing at all to do with weight which remains more or less constant lap after lap and all around the lap, apart from fuel consumption. Indeed, railroad vehicles experience the same “weight transfer” forces until they fall off the track. They don’t roll much in corners and exhibit next to no dive or squat. Watch a Pendelino for the physics of all that.
If you doubt this check out the raci
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
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
I mean exactly that. And only that. Got that problem myself right now. Minimum radius is 24". Except the easements made many of those curves actually 22" minimum. Next time minimum radius will be 26" with easement.
Interesting way to express the physics. Maybe a more straightforward explanation is that an easement eliminates an abrupt change in direction. Geometry requires that any easement reduces (shortens) the radius of the curve that is eased. Put another way: a four foot wide piece of plywood accommodates a 24" radius ( in theory and not allowing for track width or any space outside the curve ) but if you include any easement it will not.