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### Easements

Easements (or spiral transition curves) can be used to connect tracks with differing radii. This ensures a smooth transition from one track to another and helps prevent jerky motion.

Easements can be created every time you Join tracks, Extend a track or create a Tangent track. It is best to turn Easements off when using sectional track.

When using easements, an error message will be generated if the tracks have a radius that is too small or are too short for the transition curve.

The Easement dialog is invoked from the Options menu.

- Value - allows fine tuning of the easement parameters (restricted to values >= 0.5).
- R - minimum radius of the curved track.
- X - offset between a straight and curved track.
- L - length of the transition track.
- Radio button group with None, Sharp, Normal and Broad - corresponding to Values of 0, 0.5, 1.0 and 2.0. Select None to turn off easements.

R, X and L values are read-only.

These values indicate the worst case of joining a straight track with a curve of radius R. The two tracks are separated by the offset X, and the easement curve extends for L/2 inches or centimeters to each side.

The formula used to draw easements is:

    	x = l*l*l / (6*R*L)
    	r = L*R/l

where

- l is the distance along the tangent to the easement.
- R is the final radius of the easement.
- L is the total length of the easement along the tangent.
- x is the offset from the tangent at l.
- r is the radius of easement curve at l.

The Easement Button on the Main Window changes its label to indicate the current Easement value. The following diagrams illustrates the R, X and L values and the resulting easement curve.

If you use curves with radius larger than R or are connecting two curves (that bend in the same direction) then the easement curve will be shorter and the offset smaller. If the computed offset is small then no easement is generated.

A curved track that bends in one direction and then bends in the opposite direction is an S-curve. This will generate the worst case easement which is two easement curves placed end to end.

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