An
**Easement** is a portion of track that connects a curve of constant radius
to a section straight track, or **Tangent** track. In the example to the
right, the easements are shown in green (animated,
131K). Each easement starts with an infinite radius at the point it connects
to the tangent track - the radius of a straight section of track is infinite, so
the blend between the two is seamless.

At
the curved end of each easement, it has a radius equal to the circle it adjoins.
Zooming into the lower easement, we can see why it is also known as a **Transition
Curve** (animated,
126K). It changes the radius from that of the curve to that of the tangent
track, and the rate of change in radius is constant along the easement. By
having the easement start farther along its length, any radius between infinity
and the radius of the curve can be found.

## Why Easements?

Easements provide two valuable purposes in railroading. The first and most
important for the prototype, is to gradually increase the side force felt as a
train moves through a curve. For example, if you were driving your car and
quickly snapped the steering wheel into the right position for a curve, you and
your passengers would be thrown to the side. What we do while driving, and what
the prototype railroads do, is "ease you into the curve". This
familiar expression helps you understand this role of the easement.

The second purpose in railroading usually applies most to the small radius
curves we use in model railroading. The two pictures below show this quite
readily. Both of these image are the same example used above, with an SD-40 and
a 60' flat car to demonstrate the second purpose of the easement. In both
pictures, the SD-40 has been highlighted to show the position of its trucks.

In
the top picture, we can see how much overhang results from track design without
an easement. The truck of the SD-40 is aligned to the curve, just before its
point of tangency with the straight track. The flat car is exactly horizontal,
still on the tangent track. The end of the SD-40 and its coupler are well to the
side of the track centerline. The resulting misalignment between the locomotive
and flat car could easily cause a derailment.

The
second example shows the same radius curve, connected to tangent track with an
easement. Here again, the SD-40's truck is aligned to the track, but this time
it is aligned to the easement. This results in a truck that has much less angle
relative to the locomotive body. The end of the SD-40 and its coupler are now
much closer to the green-colored track centerline. The flat car is no longer
horizontal, but is already eased into the curve. A train will move through this
eased curve reliably, despite the small radius of the curve itself.

One more railroading characteristic is associated with the easement, and that
is Superelevation. On the prototype and on
detailed models, the height of the outside rail is raised through the easement
on then maintained through the curve, further counteracting the effects of
centripetal force.

## The *Offset* of an Easement

In
the example, the circle has been extended and a second line has been drawn that
is directly tangent to the circle. We can see that there is an **Offset**
between track that is directly tangent to the circle, and track joined by an
easement. The Offset is present to allow the radius to gradually increase to
infinity as the easement leaves the circle. The **Radius** of the easement at
any point along its length can be found using this equation:

**
Radius = (Length * FinalRadius) / DistanceAlongEasement**

This equation states that the radius varies in proportion with distance along
the easement. The varying separation between the original tangent track that
achieves this rate of change can be found at any distance along the easement
using this equation:

**Separation = (Distance ** 3) / (6 * FinalRadius * Length)**

This is the cubic equation referenced by John Armstrong is his excellent book
__Track Planning for Realistic Operation__, and used by railroad surveyors to
lay out track on the prototype. This equation is not quite what we need as model
railroaders, as it is much easier for us to place the curve and then draw the
easement from it. We need to know the offset from the tangent line of the circle
to the tangent line from the easement. That is provided by this equation:

**Offset = (Length * Length) / (24 * FinalRadius)**

This is the distance between the two lines as shown in the diagram above.
Using this, any easement can easily be laid out on your model railroad.

## Laying out an Easement

To form an attractive, functional easement on your model railway, first
locate the centerlines of the curve and tangent track to be connected by the
easement. Mark the point of tangency with the circle as shown below. At this
point, the easement is exactly halfway between the circle and the line.

Now take a yardstick and bend it so that it follows the circle
at one end, is tangent to the tangent track at the other, and falls halfway
between the two at the point of tangency, as shown above. This will form an
excellent transition curve if you carefully align it with your eyes.
Alternatively, you can print the transition curve from a computer program and
use the output as a template.