FreeHand Easements

[Xiong]

I seem to have stumbled on a method for generating custom cubic easements, using Macromedia FreeHand, without calculations or templates. At the risk of making a total ass of myself, I've put together a demonstration:

http://arms.x10hosting.com/wiki/FreeHand_Easements

In short, the method is to generate the entire easement as a piece using cubic Bezier curves. This capacity is built in to FreeHand and frankly, I don't know why I didn't try it before.

If this is idiotic or I've overlooked something, please let me know.

 

[cidchase]

ni hao xiong,
I think most easements in model railroading are quite informally structured. I used a method out of MRR which simply used a flexible stick to conform from the straight section to the curve. It worked quite well. The offset from the straight section to the true tangent only needs less than half an inch for good results. What the easement achieves is reduction of the "O-effect", which is the sudden change in direction of a car or loco as it makes the transition into a curve which is so pronounced in the larger scales with tight radii. It's one of the things that makes the model appear toy-like but is easily mitigated with a moderate easement, making a train operating on a small diameter curve look much more realistic. :thumb: It seems that excessive easement like is shown in the example takes up scarce real estate on your layout. Really you only need to lose about 6 inches of straight track and about 3/8" of radius to get a good easement. (IMO)

 

[Russ Bellinis]

As Cid says, you don't need an extreme easement for your model railroad. What I have done is to layout my curves with flex track and at the beginning of a curve I just off set the track about 1/2 the width of the track to the outside of the curve.

 

[Xiong]

Nihao, Cid.

The easement shown in the example is exaggerated to better demonstrate the method. The result is only so-so. Using smaller offsets, the results are pretty good -- but it's very hard to see what exactly is going on in a single look.

I don't doubt there are many ways of making an easement -- and my gut instinct is that the exact shape may not matter too much. However, I can't bend any physical stick and transfer that curve to the computer screen -- not unless I hook up my flatbed scanner. .

 

[60103]

Xiong: 30 years ago (or so) Model Railoader printed a set of easement templates on a large foldout in their magazine. They used a cubic curve to lay them out. Part of the formula involves the size of equipment. I noticed that for actual layout work, going from tangent to circle, the circular curve was offset by about 1/4" (in HO) and the easement took about a coach length (or boxcar length) each side of the point where the circular curve would meet the tangent.
If your program does something like this, you're probably on the right track.
The templates also allowed for easing between two radii.

 

[Xiong]

Clothoid or ten-chord easements seem to be typical of modern or old-time prototypes but there seems to be plenty of support for cubic easements, too. I think in the end, I'll build what I can build reliably.

Yes, when I use a smaller offset, I get very good results. I haven't tried easements from one radius to another but I suppose it will be possible. It helps that I have considerable experience with this particular drawing tool; I get a lot of mileage from it.

 

[Santa Fe Jack]

Bezier curves seem to me to be the computational equivalent of the bent stick. There are the same constraints on continuity of at least a couple of derivatives, the matching of position and angle and radius (more derivatives) at the ends. Very cool. And it makes for a natural and pleasing curve.

So, sure - use bezier curves to lay it out on the computer, then actual rails to work out the same thing on the layout. I expect that they will follow the same curve.