Hemisphere Parachute Design

Well, Tuffy Koala wanted to know how to make a simple hemisphere parachute, and seeing as at this time the only parachute patterns available on the WWW is a Spinning Parachute and a java-aided parachute design program (which is nice to work from), I thought I would explain how a hemisphere parachute is designed. With this knowledge you can not only make parachutes of this and other shapes but also window socks and other `line junk', as they both follow the same principles.

To create a parachute you create 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 is a lot thinner.

For example a 20 piece hemisphere parachute gore is used to create a ``bol'', for use as line junk, sky junk, laundry. This pattern has been slightly distorted though to create flaps, to produce a spin in the chute.

Gore Calculations

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

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 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!

[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 hemishereic 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.

Gore Pattern Construction

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

[diagram] Pick out the approximately radus of your final parachute, for example in the case of `Tuffy' I chose 20 cm. For a larger `bear' I would suggest maybe 25cm, or for a very slow descent, 30cm. The pattern I will create as an example however will be approximatly 20 cm radius or about 40cm diameter. Its your choice.

Measure the length (height) of the gore along the fold (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.

Also mark out the angles at the two end of the gores curved. These are important get the parachutes final shape looking correct. That if you don't want to give you 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 so cut gores will nicely line up.

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 well 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. 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, 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 sew them together 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 decending.

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 decended further and was tied to the backpack harness on each side 6cm along (down) from the group knots.

This gave tuffy's parachute lines a look like a real parachute, especially went I added a small strip of fabric between the two group knots above Tuffys ears. Take a look at a photo of a real parachute.

That is it, mail me if you have any questions and I will answer them and expand on the above as needed.

-- Anthony Thyssen
Up with kites, down with Parafauna!

Other Things To Do

Here are a few other things you could try using this plan.

  • Flatten the height of the chute to make it more ovoid in shape
  • Extend the gore slight 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 pattern.
  • Cut gores 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.


Sorry, no one has yet responded to this plan. Please mail me your finding, problems and experiences for inclusion here, and expandsion of the above plan as required.

Thanks to all who have built this messenger and responded -- Anthony Thyssen.

Created: 2 November 1997
Updated: 25 November 1997
Author: Anthony Thyssen, <anthony@cit.gu.edu.au>
WWW URL: http://www.sct.gu.edu.au/~anthony/kites/parafauna/chute_design/