Easements on the real thing?

[electrolove]

I wonder how the real thing works? Do they make the easement out of 2 different radius, 1 radius for the curve and a bigger one when they enter and leaves the curve or is it a continuous spiral that is smaller and smaller?

Are you guys using easements on your layouts and how do you construct them?

[richhotrain]

As a general rule, I don't think that the real railroads have the same issues as we do on model railroads with small radius tight curves.  Of course, there are always exceptions to the general rule.

The link that follows does a good job of discussing easements and how to construct them:

http://www.trackplanning.com/easements.htm

[dehusman]

Easements are a spiral curve on real railroads.

I ease curves by offsetting the curve from the tangent at the PT (point of tangency)  by 1/2" and then connecting the two with a smooth curve (either by eye or bending a wooden yardstick).

[dknelson]

Easements on the prototype are a gradual spirals ending up in the final radius, or degree of curvature.  Three are also compound curves

The math (trig?) behind all of this is explained in various engineering texts, oif which perhaps the best known is Allen's Railroad Curves and Earthworks.  I happen to have an old copy in my collection but as it happens portions are avaialbe on Google books:

http://books.google.com/books?id=LwdKAAAAIAAJ&printsec=frontcover&dq=allen's+railroad+curves&source=bl&ots=bq_9Iuqgg6&sig=458PxnC1Fi92GddKvV7zkqHdDV4&hl=en&ei=nsjKTLyXCsurnQfOneTGDw&sa=X&oi=book_result&ct=result&resnum=1&ved=0CBMQ6AEwAA#v=onepage&q&f=false

There is no need for a model railroad to follow the strict math, but there are definite and real benefits to having easement curves on a layout, as explained in John Armstrong's Track Planning For Realistic Operation -- his discussion of the "co-efficient of lurch" demonstrates how equipment can be used with 24" radius curves if there are easement curves into that radius, where the same equipment would derail if tangent track led directly into the 24" radius curve. 

From time to time MR has published tempates for easement curves.  One old method is called the bent stick method.  A long wood stick nailed into wood with paper below it -- bend the stick with your finger and trace the curve that results with a pencil.  That curve is not a single radius curve but is a gradual spiral.

There are other mechanical and math simulations of prototype easement curves.  There are benefits in appearance and operation to using them if you have the space.

Dave Nelson

 

[cv_acr]

Easements are smooth transitions. A large radius curve with no transition will cause a bit(!) of a jerk.

Curves on the real thing will be engineered to be smooth, and as broad as possible given the geography. They don't build curves out of sectional track pieces of a fixed radius like some of us modellers do.

[tomikawaTT]

An honest easement is a logarithmic spiral, radius expanding from that of the true curve to infinity (the 'radius' of tangent track.)  The earlier posters have pretty well covered how this is generated.

The 'faked with lengths of constant radius' easement was developed in the 1940s by Ed Ravenscroft.  His technique was to go from R (actual curve radius) to 1.5R, to 3R, to tangent.  Each arc was approximately the length of his longest car.  Ed modeled in HO, and his arcs had 12 inch (305mm) chords.  For a 24 inch (610mm) radius true curve, the expanded curves would have been 36 inch (915mm) radius and 72 inch (1830mm) radius.  Part of the reason he did it that way was his use of Tru-Scale milled roadbed with integral ties.

My own method is to offset the tangent line outside the circumference of the curve, then measure 25 times the offset to find the points of tangency and true curvature (the latter being measured on the chord, not the arc, of the curve.)  A length of fairly stiff thin wood and a few nails are then used to establish the actual easement.  I did my work over a piece of card stock, then cut it and now use that for a template.  Actually, multiple templates, for several different radii and offsets - I go from 50mm tangent track spacing to 60mm spacing on concentric curves by using a 20mm offset on the inner track and a 10mm offset on the outer track.

Yes, I am an American - but I use metric measurements because all of my prototype/model dimensions are metric.  Besides, it's INFINITELY easier to think in base-10.

Chuck (Modeling Central Japan in September, 1964)

[edkowal]

richhotrain

As a general rule, I don't think that the real railroads have the same issues as we do on model railroads with small radius tight curves.  Of course, there are always exceptions to the general rule.

Hi fellow writers:

(Betcha thought you were modelers?
  Well, that's true as far as it goes; but you're also writers.)

The prototype _does_ have the same issues as we do, but their definition of tight radius is very different than ours.  There's also gravity and inertial forces to deal with.  Those are the major reasons for transition spirals.  What you ( and they ) are trying to do is minimize injury to passengers, freight and equipment by changing the radius of curvature suddenly.  So...., you don't !!!

For how to construct them, follow the link that's in richhotrain's post, to wit:

http://www.trackplanning.com/easements.htm