University of Virginia Library

LECTURE 6 - TRANSITION CURVES

Joseph Barnett is one of my great heroes who, with Frederick W.
Cron, argued for roads of graceful curvature and the preservation
of natural features within the road corridor. They were advocates
for road spirals.

We think of Transition Curves as having three components:.

1.

• The spiral from tangent to circular curve.

2.

• The circular curve

3.

• The spiral from circular curve to tangent

If we examine the shell of the Nautilus, we find in it the
epitome of the spiral. That quality of everchanging curvature eliminates
abrupt changes in alignment and in the rhythm of movement
over the landscape.

Joseph Barnett labored over a convenient method to persuade
designers to use Transition Curves rather than Circular Curves.
The time he devoted to the mathematical tables published in his
book Transition Curves for Highways must have been endless! A man
blessed with patience and dedication to improving the beauty and
safety of highways. (Recall the discussion of physics of a moving
automobile in the lecture on Superelevation.)

The availability of the computer makes Barnett's task easier
today. The tedious calculations are things of the past so long as
we are in an office; engineering costs are reduced and the results
are more quickly available.

THE CONCENTRIC CIRCLE TEMPLATE:

The template with concentric circles which you bought from
Bailey's or Mint Printing is one I developed out of a need to convert
a 314 pencil line to geometrics. It saves time and has been reproduced
many times in the Park Service. Within the Division of
Landscape Architecture we have a set of Highway Curves for drafting
arcs of greater radius than we can draw with the compass. We'll
practice with those during the weeks ahead. My greatest concern is
that you master the geometrics so that you can draw road centerlines
with a straight-edge, a compass, and a spiral curve template. Again,
it's what you need to know.

HOWLAND'S FOURTEEN STEPS:

My purpose in spending so many hours in developing a method
for you to use in calculating Transition Curves with a pocket calculator
is that you will be more effective in the field. If you
will remember what we did together in Surveying and in Park Roads,
you will be able to lay-out roads and hold your own.

Within the capabilities of Barnett's Tables, and Howland's
Fourteen Steps, you can indeed refine the Transition Curve where
the spiral of one curve will join the adjacent spiral at the same
point:

Furthermore, you can eliminate the circular curve altogether:

Combining the two features, the Transition Curve produced would
have neither tangents nor circular curves. The curves would be
transitional throughout.

THE ENGINEER-LANDSCAPE ARCHITECT TEAM:

Dick Montgomery, Chief Engineer and Ol' Ben, Chief Landscape
Architect, agreed that our procedure should require the Landscape
Architects to draw the preliminary road centerline. Drawings were
to show tangents connecting the P.I.s, the compass points for each
curve, the tangent points perpendicular to the compass points, and
the radius of the curve shown concentric to the centerline. The
purposes of our agreement were to communicate to the Design Engineer
the controls implied in the location of the centerline, and to overcome
the time-loss in Landscape Architects doing tedious calculations
that Engineers could do faster. Once the drawing was approved by
the Chiefs, the teams worked through the construction drawings and
put the specs together. It worked. The team approach was and IS
the secret to success enjoyed by the NPS.

THE SPLINE LINE:

You will be manipulating transitions during the design of your
road at Birdwood or your project next Fall. While you are refining
"Your Road", ask what might be the next refinement in striving for
the perfect line of grace and movement. What mathematical derivation

might lead to the absence of tangents altogether? And what
might we call that line?

Let me share an experience with you:

Soon after I was called into the office from the Tree Gang in
1951, I was amazed to see a "spline and set of spline weights."
As students, we had not seen those tools much less used them during
our time in school. I was fascinated by the skill with which Mr.
VanGelder and Mr. Hanson adjusted the direction and subtle refinements
of road centerlines. This was the magic of everchanging curvature
that Prof. Albrect had described to us. To my disappointment, I
neither acquired the skill that Mr. VanGelder and Mr. Hanson had
nor was my curiosity satisfied in the potential of the "spline
line." Very soon I found myself drawing road alignment for the
Bureau Engineers in terms of tangents and circular curves onto
which they imposed their mysteries to convert my crude line to
geometrics. The fascination for the "spline line" continued through
the years and to this day I want to master that highest of park
road geometrics, "The Line Without Tangents."

I don't know the procedure for calculating the "spline line";
although Nick Annese shows me that Clarke and Rapuano uses the
method as standard procedure. Perhaps Ol' Ben could learn from
those designers who use it.

In this day of computers the calculations could be done quickly.
Programming the computer is quite another matter...and I lack the
skill to do that. To those of you who are interested and possess
the skills in programming, I would encourage you to explore the
geometrics of the "spline line". Surely the spline line geometrics
will lead to a refinement of the methods I have presented to you
in this course.