From: Simo Salanne
Message-Id: <199308060707.AA06952@csc.fi>
Subject: contribution to rec.kites archive
Date: Thu, 5 Aug 1993 21:07:35 -1000
Soccer Ball - Line Toy
======================
Based on articles posted to rec.kites June...August 1993.
General Instructions (by Jeff Burka)
------------------------------------
There's a rather easy way to build a line toy which is
basically a ripstop soccer ball. After the methodology was
explained to me yesterday, I built one this evening out of
scraps. Start to finish construction, (creating pattern
pieces, hot-cutting, sewing, and bridling) took maybe 2
hours (well, okay, 3, but I also ate dinner in that time
period...;-)
The toy is constructed of a combination of hexagons and
pentagons. Both geometric figures have the same edge
length. Use a protractor to construct the shapes (inside
angles of 120 and 72 degrees for the hexagon and pentagon
respectively). Because I was unsure of the size of my scrap
material, I chose an edge length of just 3". Because that
3" also included a seam allowance, the finished product was
a sphere just slightly larger than a real soccer ball. This
line toy will work quite well in significantly larger sizes.
You will need 19 hexagons and 12 pentagons.
There is a simple pattern to follow in sewing the pieces
together. All hexagons are surrouned by 3 hexagons and 3
pentagons. All pentagons are surrounded by 5 hexagons.
It's very easy to build up based on these 2 major
relationships, and the ball shape quickly forms. As you get
toward the far end of the ball, you'll be mostly working
with the object inside out. Eventually, you'll be left with
a sphere that has a hexagonal face missing. Hem the edges
around this hole and attach 6 bridle points, one in each
corner of the missing hexagon. Bridle lines are a bit
longer than the diameter of the sphere.
I've seen these toys at a number of events, usually made by
Scott Spencer. I was suprised to learn how quick and easy
they are to make. There is, however, a fair amount of
sewing. Each sphere will have over 100 seams. But they're
all short, and it's neat to watch the sphere forming under
your needle.
As usual, if I've not been clear on something here, drop me
a letter complaining about my lack of expository writing
skills and asking for clarification. ;-)
Dimensioning (by Simo Salanne)
------------------------------
If you want to make a ball with predictable size, instead
of letting your scrap bag to determine what you get, proceed
as follows:
1. Select the diameter (D) of the ball you want to make.
2. Divide D by 4.8 giving the lenght of the hexagon/pentagon
edge (E).
3. Draw a circle with radius E on your favourite template
material. Draw the hexagon inside of the circle. Add
allowance for seams.
4. Draw a circle with radius 0.85*E and a pentagon inside
of it. Add allowance for seams.
5. Cut the templates.
6. Cut your rip-stop pieces; 19 hexagons, 12 pentagons.
7. Sew. Hexagons are surrouned by 3 hexagons and 3
pentagons. Pentagons are surrounded by 5 hexagons.
8. Flyplay.
Derivation of the magic number: 4.8 (by Simo Salanne & Ed Sarlls)
------------------------------------------------------------
>From CRC Standard Math Tables, 25th ed., Geometry Mensuration Formulas
>From p. 142: REGULAR POLYGONS
s = length of side, K = area
Polygon K
Pentagon 1.72048 (s^2)
Hexagon 2.59808 (s^2)
So area of 20 hexagons + 12 pentagons is:
A = 20 * 2.59808 (s^2) + 12 * 1.72048 (s^2)
A = 72.60736 (s^2)
>From p. 148: SPHERICAL FIGURES
D = diameter of sphere, S = surface area
S = pi * (D^2)
So to get the diameter of a soccer ball:
pi * (D^2) = 72.60736 (s^2)
(D^2) = (s^2) * 23.11164
D = s * 4.80746
Sanity Check (by Marty Akerman & Andrew Beattie)
------------------------------------------------
Well, my 3" faces made a ball about 14" in diameter, so the
ratio 14/3 is what I use to determine resulting ball size
>From face size. Andrew Beattie mentions that he uses a
ratio of 5, which is pretty close too. I'm not enough of a
math wizard to figure out precisely what the ratio is, so 5
works good enough for back of a napkin types of estimating.
3" * 4.8 = 14.4" about 14" as above!