Hemisphere Parachute Design (for parafauna)

Contents

Introduction
Calculation Method (the rules)
Gore Pattern Construction
Parachute Construction
Parachute Use and Deployment
Other Things To Try
Windsocks and more complex shapes
Responses
up Back to Anthony's Kite Workshop

up Back to Tuffy's Parachuting Adventure

[photo]

Introduction

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 "Parachute Backpack". However the complete process is described including how the pattern, called a "gore" is designed and created.

The same basic principles layed out below is also used to create a multitude of "Line Laundary" or "Sky Junk" commonly seen 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....

[photo] [photo] [photo] [photo] [photo]

See Wind Socks and more complex shapes below.

To create a simple parachute, you need a sewing pattern called a "gore". This pattern is typically 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, and 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 points...
Width
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.

Angle
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 centerline 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.

[diagram] 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 will 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 the hemisphere gore pattern below).

[diagram] 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 way 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 plenty 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 length 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 values 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 suggestion 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 his 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.

[diagram] 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 suitable 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 (height) 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 are 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 still 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 way the gores will nicely line up for easy flat sewing.

Parachute Construction

For 'Tuffy' I use a stretchy and soft nylon fabric called 'tafetta', whcih is also the same material used for umbrellas) for the parachute (red and white alternating colors). Basically because I had it handy. Ripstop should do as well but I think a much softer 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.

Basically 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 mark 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, but 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 stop 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.

[diagram] 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 knot. The third line descended further and was tied to the backpack harness on each side 6cm along (down) from these group knots.

[photo] 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 number 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 setting 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), which really looks horrid. OR just leave the chute catch the wind to help pull a very simple messager up the kite line.

Other Things To Do

[photo] 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.

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-by-side without any wastage, and makes for a very interesting looking parachute.

Windsocks and 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 same hemisphere plan above. The rules above were also applied to find the connection point between the tube and gore pieces.

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.

The 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 the 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 created 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 don'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.

Responses

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 skins collected from around the streets of Belfast. I presently have around 100 skins and am still collecting.

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

DO NOT DO IT!!!!

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.

At 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 facts).

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.

Anthony

Peter Simons <peter.simons@goudsmit-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 material 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 aeroplane, 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 to 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 any 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
Updated: 8 November 2000
Author: Anthony Thyssen, <anthony@cit.gu.edu.au>
WWW URL: http://www.cit.gu.edu.au/~anthony/kites/parafauna/chute_design/