Halloween is here! And I want to build a pumpkin from 2cm foam and t-shirt material glued on to it.
The maths is in the diameter and circumferance. I can calculate both. I cannot work out how to calculate the total area of cloth I need.
Given a sphere of, say, 1m in diameter, and given that the surface is “pumpkin-like” - that is ( _ ).( _ ).( _ )( _ ).( _ ) going around a circle, and I choose something like 30cm for the underscores, how do calculate for the curves?
Trial and error will probably win out here, but I feel I should know the math.
Not sure I understand the question. Is there any reason SA = 4πr^2 won’t work?
I am not good at descriptions or math.
The problem is that the circle each group of more or less U shaped hoops needs to the hoops foot distance to be equal to the total number of “hoops”/circumferance at the equator of the sphere.
God, re-reading that made even me confused, I will give this subject more thought and try to produce a rational, answerable question.
I feel like I’m having a stroke while reading that.
Lets see if I can help draw the problem out.
What is the difference between what you’re trying to calculate and the surface area of a sphere? That the surface has ridges on it?
If that’s the case we would need to know how deep the grooves are.
And with a diameter of 3.142m and ridges of 0.3m, are there 10 or 11 ridges?
Ok. Despite my completely terrible wording, I think you got me.
Consider an air balloon. It has multiple “folds” that become a )()()()_ sort of pleated design
Og, well, Discorse fucked that up.
Its not a big deal, I will just give up the subject.
Not before I thank you for trying to make sense of my madness.
Personally I’d just call it a sphere and assume the stretch in the fabric is enough for the grooves. Should be fine unless the grooves are very deep.
I’ve never seen one of the US orange pumpkins, so I am basing all my creative output on my imagination, movies, and our own white - but much flatter - pumpkins.
I don’t think we can give you a better answer than what you’ve already come up with (doubtless something a bit more than the surface area of a sphere of comparable diameter, but trial and error will tell exactly how much more).
Because while I can begin to think of how to describe the problem, that’s only in theory, and not in practice, because you have not provided, and perhaps do not expect to know, certain critical dimensions that would be necessary to provide a mathematical solution.
Namely, can you describe, in mathematical terms, the “segments” that will actually be making up the surface of the pumpkin? Because that’s what you really need to do: you need to figure out how many (presumably identical) segments you’re going to have (like, think of orange slices) and how to describe the curvature of those segments mathematically, so that you may then decide the surface area of an individual segment, and then multiply by however many segments you have. But you haven’t told us—and are unlikely to know yourself—just how “curved” those segments are going to be, along either axis. More or less pronounced segments will require more or less fabric to cover more or less surface area.
So my advice is to calculate it for a sphere, throw in some fudge factor (an extra 20% to be safe?) and then cut away/discard the excess when you’re done.
ETA: Honestly, the bigger conceptual problem for me is how you’re going to convert these materials into a spherical shape, segmented or otherwise. Like the reverse problem of trying to convert a spherical-ish earth into a paper chart that lays flat. It’s not trivial.
I think you are right.
If I was carving the thing out of a solid block, say, of polystyrene.
But I am building it from foam, with a hollow centre and relying on the structural integrity of the foam to keep a reasonably rigid lightweight shape. Like an onion if you could magically remove the center. The flexibility of the foam gives it some structural integrity, as long as I design for that, with internal trusses etc.
Here is an early prototype
I build both using conduit and garden hose piping, covered by hessian sack.
I may be misunderstanding, but if you want to have a pumpkin-like form, you may search for “hot air balloon” pattern.
How much pieces do you need? take circumference (2PiR so 3,14 m in your case) and divide by that much. If 20 pieces that’s 16 cm. Give 1 cm more on each side and it’s 18 cm at the wider part.
For the length, that’s half circumference, so 1,6 m. you will have to cut 20 () shaped pieces of this dimensions.
Glue or sew on the inner face, letting the bottom part free to reverse it at the end.
The shape is roughly a barrel so if you seek a formula it is of parabole.
Oh, perfect.
I was trying a bunch of math where I knew I was going down a black hole.
Thank you.
Welcome.
If you want a human-sized-pumpkin-shaped thing, you need to estimate the circumference at the top and bottom so your pieces will not be in acute angle at the top and bottom but rather flat.
The barrel shape indeed: Barrel Volume Calculator
Wow. Thank you. Seriously. That is astoundingly cool.
If you don’t have a sphere at hand you can always use an idealized cow.
I can locate a cow, nearby. I’m just not sure she would be the ideal cow.
Just assume it is and strike a nice torero pose just in case. Torera, in this case.
