*
The following exchange on the Burning Man email list prompted Argyre to
make a further post concerning the construction of a home from a parachute:*

>>| Here is a representative example where I worked backwards from the materials >>| - figure 4 x 20 foot lengths of PVC for hoop = 80'. Divide by 2pi to get >>| radius=12.5 feet. Using this hoop on the edge of your 33' chute, you can >>| shade a 25 foot circle, and it will need a 17 foot mast to support the hoop, >>| if you want the edge to float at 6 foot height. This difference in the >>| diameters of the hoop and the chute is what allows the hoop to hang flat. >>| I used a hoop approximately equal to the chute circumference, and that is >>| why I got the nice flippy trilobal thing. This had it's pluses and >>| minuses. If you try this with the 33' chute, you'll need a the hundred foot >>| hoop. > > The chute I have is stamped as being a "35 foot" parachute, though I >found this to the half-circumference over the top of the chute. The edge >circumference was about 67 feet (if I remember correctly, the diameter >across the bottom of the chute was 20'). Don't know how most chutes are >measured, it one might want to check how the chute was measured when it >was labeled in the store.... >

Here is *WAY* too much information about parachute cuts and measurements...

Of course it is the half circumference over the top of the chute...it is the diameter of the circle of fabric. A circle (flat) of 35-foot diameter is 35 x pi= almost 110 feet of circumference. If you have this draped over anything that makes the base circle smaller, the circumference drops a lot.

This is based on the chute being able to lay flat. One of mine does this quite nicely.

Another way to check the circumference is to multiply the number of panels by the width of the panel at the edge...

This is when you discover that your chute is NOT the diameter you expected it would be when flat...

Note that the 'chutes people have been buying from Bonanza have a panel width, at the edge, of 28" (2.33 feet). {NOTE: There is a bit of elasticity in this edge, and so, if you stretch it quite taut, you can get at least another inch out of this. That means a total of 2.5 feet more circumference or about 2/3 of a foot diameter increase. Not much...} They have a total of 30 panels, for a total edge circumference of 70 feet. So the diameter of the base of the chute is 22.3 feet (roughly). Taking into account the edge to edge diameter of the fabric, of 33 feet, and assuming the chute would, in normal use, form a hemisphere (approx.), the diameter of that hemisphere would be about 21 feet (which is close enough to the 22.3 number above for work use). If this went over a dome running from ground level, the peak would be about 10 to 11 feet tall.

If you set this chute up in any mode which places the fabric flat (teepee, parasol, flat circle, etc.) over a planar structure, there will be terrible sag in the fabric (quite capable of catching lots o' wind. A curved surface will do a better job with this, if the sag bothers you.

By way of comparison, my other chute, which is only 28' in fabric diameter, also has 30 panels, but they measure at least 35" per panel at the edge. this yields a circumference of 87.5 feet, and a diameter of 27.86 feet (which sounds like 28 feet to me...). Clearly this parachute lays just about perfectly flat.

>DOME MATH QUESTION #1: > >I have a 7-foot high dome... >14 feet in diameter... > >what's the surface area of this size dome? >what's the circumference of this size dome? >DOME MATH QUESTION #2: > >I have a 4-foot high dome... >8 feet in diameter... > >what's the surface area of this size dome? >what's the circumference of this size dome?

Circumference is pi * diameter of circle, so the circumferences are:

pi * 14 feet diameter = 43.974 feet (44 feet in the real world)
and

pi * 8 feet diameter = 25.128 feet (25 feet...)

pi, of course, is 3.141 (and anyone who gives me trouble, I want to know if you think that more accuracy than this is an issue for any BM playa structure?)

Surface area of a sphere is calculated via pi * diameter squared, so

pi * (14 * 14) = 615.636 sq. feet for the sphere.

Divide this in half to get the half dome that we are measuring and get: 307.818 sq. feet

and, similarly,

pi * (8 * 8) = 201.024 sq. feet/2 = 100.512 sq. feet for the area of 8' dome.

Note that while the diameter of the larger dome is not quite twice the small dome, it's surface area is more than triple. And if you look at volume:

Volume of a sphere is (pi/6)*(diameter cubed). Divide this in half to get the volume of the hemisphere.

((pi/6) * (14 * 14 * 14))/2 = 718.242 cubic feet

((pi/6) * (8 * 8 * 8))/2 = 134.016 cubic feet

So the interior volume of a sphere or hemisphere differs by a factor of 5 and a third for this jump from 8 to 14 foot diameter. So, as diameter increases 75%, circumference also increases by 75%, surface area increases approximately 206% and included volume increases by 436%.

Hope this helps.

If you want to be pickier, I also have the equations for the simplest dome geometry, the icosahedron, and the dodecahedron, if you need them. All the equations above are made assuming that the beast we are measuring is the proverbial "spherical chicken"...

--

Argyre Patras

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