Hemisphere Parachute Design (for parafauna)

hundredcarriageSoftware and s/w Development

Nov 3, 2013 (3 years and 9 months ago)


Hemisphere Parachute Design (for parafauna)



Calculation Method (the rules)

Gore Pattern Construction

Parachute Construction

Parachute Use and Deployment

Other Things To Try

Windsocks and more complex shapes


Back to Anthony's Kite Workshop

Back to Tuffy's Parachuting Adventure


This page details the design of a hemisphere parachute, suitable for use by "parafauna", such as
Tuffy Koala, Not People!. Particularly in conjunction with the ``Parac
hute Backpack''. However
the complete process is described including how the pattern, called a ``gore'' is designed and

The same basic principles layed out below is also used to create a multitude of ``Line Laundary''
or ``Sky Junk'' commonly s
een at kite sestivals. These include: spheres, oblongs (football), bols,
ring bols, windsocks, and inflated eyes. A slight variation to add a flap also makes these things
spin, forming spin socks, spinning rings, etc..

The follow photos are all objects
made by a friend of mine Baz and Gill Thrower and are all
basied on the same basic principles....

See Wind Socks and more complex shapes below.

To create a simple parachute, you need a sewing pattern called a ``gore''. This pattern is
y 1/ 6th of the final parachute. More than 6 gore patterns can used but the gore pattern
becomes very long and thin, the more you have. The final shape however be lot thinner.

For example a 20 piece hemisphere parachute gore is used to create a ``large
4 foot bol'', which
is a spining paracute used as link lanudary . This pattern has been slightly distorted though to
create flaps, givening the shute a spin. (last segments from "g" to "i" in that plan).

UPDATE: This page plus the parachute backpack, an
d various dropinng devices have all been
collected together and translated to Dutch by Peter en Marleen Simons on his Parachuteren van
beren Pgae.

Calculation Method

The design of a gore, even very odd shaped ones is easy. All you have to remember is few


The radius at a point is proportional to the width of the gore.

That is if the width of a gore is half that of the maximum width, then the radius
or diameter at
that point in the final chute/windsock/whatever, will also be half of the maximum.


If the end of the chute comes to a point which is `flat' at the end, then all the angles at that end
must add up to 360 degrees. As such for a 6 piece

gore pattern, the top of the gore must equal a
60 degree angle. EG: 6 gores × 60 degrees => 360 degree flat at top of chute.

Similarly if the mouth of the parachute is vertical (or cylindical) then the edge of the gore must
be parallel to the centerlin
e of the pattern, or 90 degrees to the mouth edge of the gore pattern.

Ok them's the rules! So lets study a hemisphere a little more closely!

Remember these rules also apply to Windsocks too.

First the maximum diameter of the parachute is the mouth
opening, the radius of which is r. The
circumference of the opening is, from your high school mathematics (it had to be good for
something didn't it) is 2 PI r. As we are making 6 gores to create a parachute, the width of the
gore at the mouth (which I wil
l call l) is 1/ 6th of this length or PI r/ 3.

Here we can take a liberty, as the value of PI is close to 3 we can basically make the gores
maximum width l equal to r. This roughness will make the resulting parachute only 3% smaller
in size which is too

small to be of real concern. The parachute will still form a proper hemisphere
as all gore pattern measurements will be based on the value of l. Also setting l equal to r we
simplify all the calculations, and don't have to deal with PI (apple or otherwise


OK the width of the gore is 1/ 6th of the circumference of the parachute radus. The height is also
1/ 4 of the circumference, which you should be able to easily verify. As such the height of the
gore will be 1.5 times its maximum width (l). (see t
he hemisphere gore pattern below).

On your gore plan you can now lay out the angles the gore has to have at the mouth (parallel to
the center line) and the top (a 60 degree angled end) as per the second design point above. The
edge of your gore should
curve to match these lines as the edge approaches the top and bottom.

Now we come to the tricky part. The radius of the parachute is proportional to the width of the
gore. As such, studying the hemisphere, we can look at the radus of the hemisphere half

between the top and the bottom of the fabric. This is at 45 degree angle to the center point of the
hemisphere and thus radius from the centerline at this point is 1/ sqr(2) (you knew math would
have to come in somewhere didn't you :
) or about .71 of

the radus of the sphere.

This means that the width of the gore half way along must also be .71 of the width of the
parachute mouth. (See pattern).

The two angles and the center point would probably be enough for you to now sketch out the
curved edge

of the gore. I have however also worked out the points for the 1/ 3 (.86l) and 2/ 3
positions (.5l) on the gore, to produce a better result.

Even more measurements could also be calculated, and for large chutes may be nessary to refine
the curve of the gore side. Other angles however will involve trigonometry, and its sine and
cosine calculations (yuck). I found the above three measurements pl
enty for the small chute
Tuffy required.

If you want to make more than 6 gores for your hemisheric chute, the only changes is that ALL
the widths of the gore pattern will be proportionally smaller. For example an 8 gore parachute
will have a smaller len
gth of l approximatly equal to 2/ 3r while the gore height will remain as it
was (approximately 1.5r). The only other change is that the angle of the tip of the gore will be 45
degress instead of 60. You may however like to calculate more gore width ratios

just to set the
curve better.

ASIDE: Also Alex Cresswell <UKajc@aol.com> has created Hemisphere Parachute Calculator
Spreedsheet for you to download. Just type in the diameter and number of gores, and it will
generate a table and diagram showing the val
ues you need to create a gore template.

Also Arthur Dibble has put up a Java Script Page which will generate the parachute
measurments using the above principles. The program also generates a suggested 'bear' weight,
though does not say how this suggesti
on was derived.

And finally another website with a more mathematically rigorious detail of parachute design is
Richard Nakka's Parachute Design and Construction page. This is well worth a loot in you are
interested in making more parachutes. Also from h
is pages I found this like that tries to explain
how big should the chute be, a difficult question that even this page can not answer, as it depends
on how far you want your para
jumper to drift.

Gore Pattern Construction

To create your gore pattern from

the calculations take a sheet of paper and fold it in half. This
way, both sides of the gore will be the same, when you cut it out. This is important or you will
find they don't match properly when sewing the pieces together.

Pick out the approximately

radius of your final parachute, for example in the case of `Tuffy',
who in terms of typical parafauna, isn't that big, I chose 20cm (Aside later I made a larger 30cm
paracute for him, so he had more 'hang
time'). It is difficult to say just what size is s
uitable for a
particular bear. My best suggestion is that the radius should be about twice the height of the
typical "bear" parachutist (four times for the diameter). After a few trials you should then know
what size it should be.

Measure the length (he
ight) of the gore along the fold of your template paper (1.5 l = 30cm) and
the half the width across the folded pattern (see diagram left) from the fold (1/ 2l = 10 cm). The
three other points are also marked out 10cm, 15cm and 20cm from bottom to top and
respectively 8.6cm, 7.1cm and 5 cm distant from the center fold.

If you used that Java script above (or other program), mark out those points as well from the
center fold.

Also mark out the angles at the two ends of the gores curve. These I feel
are more important that
the above pints as they make the final shape look correct. That is if you don't want to give your
parachute a pointy top.

Now get a flexi ruler, or a length of 2mm fibreglass rod, anything which bends easily, and curve
it around
the points marked and the angle lines. Drawing along the curved rod will then give you
a nice smooth curve to the gore edge. I find using a pin board and pins to hold the rod in place
makes the job a lot easier.

Cut out the gore pattern while it is stil
l folded, or just half a pattern if it is made of cardboard.
And you have your parachute gore pattern. It is important that the curve is the same for both
sides of the gore, and thus the fabric you mark out with the gore pattern will be the same. That
the gores will nicely line up for easy flat sewing.

Parachute Construction

For `Tuffy' I use a stretchy and soft nylon fabric called `tafetta' for the parachute (red and white
alternating colors). Basically because I had it handy. Ripstop should do as w
ell but I think a soft
fabric works better as it tends to `spring' out from the backpack, when released, on its own. It
also not as crinkly as some ripstops can be. I have also used old broken umbrellas, which I find
in trash bins after a recent rain.

asically any fabric should work for the parachute as long as you don't mix and match different
fabrics types.

All that is now necessary is to lay the pattern down on your parachute fabric, (iron the material
if it is all crinkled up) and trace around the pattern. Cut out the 6 peices leaving a 6 to 12 mm
hem allowance around all the borders of your gore.

To ma
rk out a hem line I use a small plastic wheel I found, I put the pen in the center of the
wheel and then run it around the edge of the cardboard pattern. Some people use a soldering iron
in a teflon wheel to hot cut the pieces directly from the material, b
ut that isn't required.

To sew the pieces with the curved edge I found the simplest way is to put two gores front
(outside) to front and pin together. Then sew with a straight stich along the gore boundary (the
gore pattern mark sould be visible on the
back (inside of chute) of the fabric). Then go back with
a zig zag along the hem space to prevent fraying, or hem it properly by folding the hem material
over before using using zigzag (difficult with a curved edge).

Do not worry about the tip (top) of
the gore as you would cut this out later to create a hole there.
Also don't worry about the hem sticking out and not sewn flat as you normally would with a kite,
as this will be inside the parachute and will not be visible or effect the result.

When all

the gores have been sewn together hem along the outside rim of the parachute folding
the hem over, once or twice, and using a zigzag stich.

Now cut a small hole at the top and use a zigzag button hole type stitch to hem around the edge
of the hole to s
top it fraying. The size of the hole is not critical, but allows the chute release line
to be inserted and stops the chute swing around to much when descending. 2 to 3 centimeters (1
inch) accross should be plenty.

Add the chute lines the same length as

the gores (1.5l) zigzag stiched at the places where the
gores were sewn together. The 6 lines were then tied together in 2 groups of 3, l distant from the
parachute. Two of the lines in each group three was then cut, and heat sealed, just below the
The third line descended further and was tied to the backpack harness on each side 6cm
along (down) from these group knots.

This gave tuffy's parachute lines a look like a real parachute, (see photo left) especially when I
added a small strip of fabric
between the two group knots above Tuffys ears. Take a look at a
photo or video of a real parachute to see what I mean. That link strap, also prevents a lot of line
tangles when tuffy lands and rolls on the ground.

Parachute Use and Deployment

Quite a nu
mber of people have asked how I use the parachute, which is not really the scope of
this plan. However as I mentioned in ``Tuffy's Parachuting Adventure'', I use a ``Parachute
Backpack'' as described in the dutch plan.

On that same plan are details of s
etting up a static chute line to un
pin and pull the chute out of
the backpack when the parafauna (or other object) is dropped. Another technique is to stuff the
parachute loosly into a open downward pointing tube. When the parafauna drops, the chute will
be pulled out of the tube and open even faster. But I think it looks ugly.

The last two methods is to just hang the parafauna by the top of the chute (from a loop sewen in
the shut hole) to the lifting device (EG: messager or other drop
nik dropper), whi
ch really looks
horrid. OR just leave the chute catch the wind to help pull a very simple messager up the kite

Other Things To Do

This method of working out the gore pattern, is very versitile. For example a have a look at the
Carochute which is a

parachute basied on a vaguely carrot shape (see photo right). The parafauna
using the parachute is actually a rabbit, thus the carrot chute. Here are a few other simple things
you could try using this plan.

Flatten the height of the chute to make it mo
re ovoid in shape

Extend the gore slighty below the maximum width l, curving inward just a little bit to make it
look more spherical.

Sew strips of different colored fabric together before cutting out the gores to create a interesting

Cut go
res out of a patchwork fabric to make the chute look like a patchwork quilt.

Add mickey mouse ears to the parachute :

Add a fish head and tail to the parachute.

You may also like to look at the "Lara" chute in which the top curve matches the inverse of the
lower part of the gore curve. This allows 2 gores to be cut side
side without any wastage, and
makes for a very interesting looking parachute.

Windsocks a
nd more complex shapes

This section was added in response to a email from Dan Shipsides <hipsides@hotmail.coml> on
November 8th, 2000.

The principles I give above work for lots of different line laundary and tail designed you find on
the net. Windsocks

are basically just more tubular. Have a look at the spaceball tails I use on my
Giant Panflute. The spaceball tails are basically just a long tapering tube with sphere inserted in
the middle. Each sphere (7 in total in 3 sizes) is 12 pieces and used the s
ame hemisphere plan
above. The rules above were also applied to find the connection point between the tube and gore

Actually I could have even made a gradual change from tube to spherical forms in the tube if I
so wish. Just curve the gore edges

back into a stright edge parellel to the center line instead of
toward a point. The tails would then look like a snake that had just swollowed a large meal (IE:
bugle in his belly), instead of a ball in the middle of a tube, which is what I wanted.

Melon Queue (french plan) is basically streched sphere gore to form oblongs (footballs),
joined end to end, to each other instead of a intervening tube.

If you look at the Twisty Tube Tail Plan you will find that it also follows the same rules, though
he gore pieces fit together so they spiral around the tube, instead of separate `cylindrical' parts
joined together. More complex but not overly so.

You can even hide the gore structure with extra attached pieces as is done with the Duck
Windsock plan c
reated by Ken Friis Hansen. Or use the structure as part of a kites design, such
as the body of Graeme Poole's Dragon Fly Kites.

Only when you really start changing each gore piece separately that some sort of computer aided
design, CAD, is needed. (I d
on't). Then you can start creating helical tubes, or other shapes like
dinosaurs, kangaroos, and spiny ant eaters that you see at many of the larger kite festivals.


Name Withheld wrote on 6 November, 2000...

Dear Anthony,

I came across your

response on the site about Hemisphere parachute design. I was so excited by
the site and by Peter Simon's response. I'm proposing to make a chute and need your advice.

I am intending to manufacture ( or have manufactured ) a parachute out of umbrella s
collected from around the streets of Belfast. I presently have around 100 skins and am still

It may ( optimistically ) be possible to produce a parachute using these materials which could be
used to jump with ( subjecty to safety backup

if not then the parachute could possibly be able
to descend a weight and video camera.

Anthony's Empathic Response...

Yes I have some advise...


This plan is for ``parafauna'', such as soft cuddly koalas, bears, and other robust little children's
friends. I would never use this for anything that is breakable, especially when you consider a
sudden stop from just 3 meters could be disasterious.

t no point do I claim any real knowledge of real parachute design or construction. I have not
even looked up a book on the subject. And reject any such suggestion that this should be used for
anything other than stuffed toys (sorry Tuffy, but them's the fa

Also I do know that `base jumps' only did become practical when the modern controlable chute
was created. Allowing the chutist to steer themselves away from the wall, and even then they are
not always successfull. Anything else adds greatly to the

already high risk of the sport. I suggest
you search for web pages on this subject for more definitive information.

PS: I have never used a parachute myself. And don't plan too!!!! I like terrafirma just fine.


Peter Simons <peter.simons@gouds
magnetics.nl> on 25 March 1999, wrote...

After collecting several articles about parachuting bears, I decided to build the parachute
described in your web
page. I used an old umbrella for the chute material and backpack and
realise now that this mater
ial is very, very suitable for this purpose. It is flexible, so it really pops
out of the backpack. Also the releasing systems is very realistic and works proper.

Thanks a lot for publishing!

My bear is called Freddy, is about 18cm height. He has got

a leather coat, motor glasses and a
white scarf. He looks really cute with its new backpack. I use a home
made ferry with 0.5m2
surface. He has flow before too: I have made a down scaled hang glider (2m) wich goes op like a
kite and goes down like an aero
plane, he was the pilot. I dont know wether he liked it or not;
landings were not always lucky......

PS: Freddy has been flying yesterday and noticed a small landing place at the other side of a
small river. He managed to land there, but I was not able t
o cross that river by jumping. After
walking a half a mile for the first bridge etc. etc.. He's back now and promised to do this never
ever again.

Peter Simons

If like this plan, and/or build one, please mail and let me know what you think. Including an
ideas, suggestions or other experiences. That way I can add them to the above so others can read
and benifit from your results. :
) Photos especially welcome!

Anthony Thyssen

ADDENDUM: Someone at NASA obviously found and liked the above plan. After a search I
found a reference to this page from a The Gore of Math and Parachutes, a fun school
trigonometry project for high school students.

Created: 2 November 1997

8 November 2000

Author: Anthony Thyssen, <anthony@cit.gu.edu.au>

WWW URL: http://www.cit.gu.edu.au/~anthony/kites/parafauna/chute_design/