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Drawing an Ellipse
for Relief Carving
by W.F. Judt
Saskatoon, Saskatchewan, Canada
ne of the tasks I disliked early on in my carving career was trying
to draw an accurate ellipse. I read up on the subject, of course,
and remembered some of my geometry classes in high school, but
I was still ill-equipped to draw an ellipse the EXACT dimensions
I required for a particular project. I found this task frustrating
and annoying. Maybe you have had a similar experience.
The worst part was trying to manage the pins, paper,
axes, string and pencil required to draw an accurate ellipse
according to one particular method I call the "How-To-Drive-Yourself-Crazy"
method. Even worse was the "mathematical approach"
which required a person to grasp the principles of mathematics
in order to "plot out" an accurate ellipse.
For your information, I had the MOST consistent
math marks in my entire high school of 1500 kids. My marks were
51%, 51%, 51% every term of every year that I took math. Now,
that's not an easy accomplishment, eh?
One evening, while teaching a class of carving
students, I was trying to draw an ellipse, with the usual frustration
that accompanies such a task, when a student of mine, Ron Bush
(bless his
:-)
showed me what he termed the "trammel method". This
method involves only a piece of paper, a clear plastic ruler
and a pencil. Oh, and one more thing you have to poke your tongue
out of the side of your mouth
just a little bit, to help with concentration.
<grin>
he Trammel
Method
Start
with a piece of paper,
8.5" X 11" (standard letter size), since you will first
draw a small ellipse to see how it works. You can move to a larger
size of paper later when you wish to draw an ellipse large enough
for a relief carving design.
Get a
clear plastic ruler,
a pencil, and two small pieces of masking tape. The ellipse you
are going to draw will be 8" wide and 10" tall. Fasten
the paper with masking tape, to a flat surface so that the length
of the paper is vertical. Then draw a vertical line up the middle
of the paper. Be accurate. The line should be dead center on
the width, and parallel to the edges of the paper. This will
form the "X" axis of your ellipse.
Now draw a horizontal line across the middle
of the paper, equal distance from both top edges of the paper
and at right angles to the vertical line. This line will be your
"Y" axis, and where it intersects with the "X"
axis, you will have the center of your ellipse.
From the
center of the ellipse,
and measuring up the "X" axis 5" and make a mark.
Measure down from center of the ellipse 5" and make another
mark. These two marks are the outside limits of the "X"
axis. For the "Y" axis, measure 4" to either side
of center and mark the points. These two marks are the outside
limits of the "Y" axis.
Cut two small pieces of masking tape, and place
these at the edge of the ruler, right over the 4" mark and
the 5" marks (see the drawing). Hold the ruler up to the
light so you can see the 4" mark, and draw a short line
on the tape to show where the 4" mark is underneath. Do
the same for the 5" mark. This step is needed in order for
you to easily and quickly identify the two marks on your ruler.
You'll make less mistakes with these marks in place. The 5"
and 4" marks represent 1/2 of the "X" and "Y"
axes respectively.
Now you are ready to draw the ellipse onto
the paper. Use a sharp pencil, for the sake of accuracy, OK?
Place the ruler so that the Zero (0) mark is at the
top-most point of the "X" axis (*see note on proper
English usage, below
)
You will notice that the 5" mark is resting,
logically, on the center of the ellipse, which is also on the
"Y" axis. As the ruler is positioned to plot the perimeter
of the ellipse, the 5" mark will "slide" along
the "Y" axis, just as the 4" mark will slide along
the "X" axis. The "O" (zero) mark will plot
the perimeter of the ellipse for you. All you have to do is plot
with a pencil the location of the "0" mark in 1/2"
increments as the 4" mark and the 5" mark "slide"
along their respective axes. Simple, eh?
Plot one quarter (one quadrant) of the ellipse.
No need to plot the others. If you have accurately drawn your
axes, you will be able to fold the paper along the vertical axis
and using a light table or a window, you can trace the first
quadrant onto the opposite side of the axis. Then, with the two
upper quadrants drawn, you can fold the paper along the horizontal
axis and trace the bottom two quadrants from their counterparts
in the upper half.
Unfold your paper, and you will see a perfect
ellipse sitting in front of you, and you will understand how
to draw any ellipse of any size. All you need to do is decide
how wide and tall you want your ellipse to be!
n Oval is
NOT an Ellipse
Many people mistake ovals for ellipses. Ovals
are made up of two circles connected on their sides by parallel
lines. Ovals are what they use for race tracks. That way you
can have "straight-aways". Ellipses have no straight
sides. Their perimeters are constantly curved according to a
mathematical formula. The earth travels an elliptical orbit around
the sun, one of the interesting natural facts that we can enjoy.
The cause of this is gravitational, of course.
Nor is an Ellipse an "egg-shape".
Eggs have a shape of their own, even more wonderful than the
ellipse. These are created by the Creator through the humble
bird.
I hope this short article will be of help to
you as you prepare patterns for your relief carving. Let me know
if this article has helped, OK?
Bill Judt
[Note
on proper English usage <big grin>: This is where Canadians
get the idea that the letter "Z" should be pronounced
"Zee" instead of "Zed". Consider the words
"Zero, Zebra, Zenith", etc. They are not pronounced
"Zedro, Zedbra, or Zednith, are they? Sorry to draw this
to the attention of our American readers, but after all those
years having Americans giggle when I pronounced "Z"
as "Zee", this is my opportunity to straighten the
record.]
I love to
hear from fellow carvers, even if they pronounce the letter "Z"
as "Zed". Contact me by e-mail. My email address is:
bjudt@sk.sympatico.ca.
My home page
on the World Wide Web is: wwwoodcarver.com/AssortedWebPages/myhome.html
I live in
Grande Prairie, Alberta, Canada.
Phone: (403) 539-6949
Fax: (403) 538-4359
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