The (American) football shape is a special case of ellipsoid called
a prolate spheroid, which is an ellipse rotated about it's major
Draw the football shape (ellipse), to scale, with the long axis
Draw the long and short axis diameters to divide the shape into 4
equal parts, or quadrants.
Choose one of the quadrants to work with - you can ignore the other
three. I'll assume you chose the top right-hand quadrant.
Divide the quadrant into vertical strips by drawing vertical lines
from the horizontal axis to the circumference of the ellipse. They
don't have to be equal distances apart, but the more you have the
more accurate will be the final result. I would suggest 6 or 7. The
narrowest strips should correspond with the part of the ellipse that
curves the most, ie. the right hand end.
Each of the (vertical) lines represents the radius of a circle on
the football shape.
From the left, measure the length of each line, starting with the
left edge of the quadrant - the last one is, of course, length zero.
Then (here's the hard part) measure the length of the ellipse
circumference between each line. Try using a pair of dividers to
"walk along" each section. Be as accurate as you can 'cos this
determines the length of each panel.
You should now have three measurements for each strip: the length of
each vertical side, and the length of the section of the ellipse
For each vertical line, calculate a C_Length equal to 1/10 of the
circumference of the corresponding circle - ie. half the part of the
circle that crosses one of your 5 panels. If the length of a
vertical line is L, the C_Length will be 2*PI*L/10 = 0.628*L
(approx). You are now ready to start drawing one of you 5 panels. You
start by drawing one quadrant of a panel, as follows.
Draw a horizontal line with a length equal to the sum of the ellipse
circumference lengths of the strips you drew. Starting at the left
end of the line, draw a vertical line upwards equal to the first
C_length. Then space along the horizontal line a distance equal to
the ellipse length of the first strip, then draw another vertical
line equal to the second C_Length. Space along by the length of the
ellipse circumference of the second strip, then draw another vertical
line equal to the length of the next C_Length.
Continue to the end of the horizontal line. The last C_Length is, of
Now draw a nice curve through the tips of each of the vertical
lines. Make sure the curve is horizontal at the top of the first
C_Line, and vertical at the last (zero length) one. That curve, plus
the horizontal line and the first C_Length line is the outline of one
quadrant of one of your 5 panels. Mirror copy it to make one half of
a panel, then mirror copy again to make the entire panel.
I hope this helps. Email me off-line if you need better
instructions. Regards, Gary Wooding