MacGuyers of the world; unite!

October 9, 2006 12:50 AM

So, I have 13"x21" of paper, two metres of sticky tape and a paperclip. What is the strongest free-standing structure that I can make?

It needs to support as much weight as possible! One can cut or fold it up however he or she wants.

posted by PuGZ to grab bag (20 comments total)

Schoolwork, right? Is there a minimum height?

If there's no mimimum height I'd use the tape to bind the paper into a pair of solid blocks. (273 square inches of paper, assuming a sheet thickenss of 0.1mm, gives us two blocks about 1inchx1inchx~0.5inches). Then I'd position the blocks a couple of inches apart and just stack kilo weights on them. Be prepared for accusations of cheating, even if you're technically within the rules.

If there's a minimum height, cut paper to minimum height, roll into tube, bind with tape. If you have enough paper, one cylinder inside another can help spread the load, as long as they're exactly the same height. Place the load directly on top of the cylinder. Experiment with the direction of the grain in the paper (I forget which is better).
posted by Leon at 1:24 AM on October 9, 2006

I'd go for cones.
posted by b33j at 1:32 AM on October 9, 2006

If the minimum height is a couple inches, but the weights don't have to be above said height, unfold the paperclip and tape it to the side of one of Leon's blocks. Maybe use a little piece of paper to make it a flagpole.
posted by TheOnlyCoolTim at 1:41 AM on October 9, 2006

Scrunch up with paper with the paperclip in the middle. Make the smallest ball you can. Wind the tape around the outside of the ball.
posted by rongorongo at 1:46 AM on October 9, 2006

Leon: Yeah, it's for a project we did a while ago and my teacher said there were better ways of going about it than we did. For what it's worth, I used the cylinder idea and it worked reasonably well, but I am curious to know what I could have improved upon!

Thanks for most of the answers thus far. ;-)
posted by PuGZ at 2:29 AM on October 9, 2006

You want a laminate structure (one made up of multiple layers) and possibly corrugated. Like a cardboard box. (Usually, these contests forbid laminating, precisly because it works.)

Fan fold the paper, using the tape to stick the layers together. Make two shorter layers and one longer layer. Then fan-fold the longer layer(a right angle to the original folds) to corrugate it, and use the tape to sandwich the longer later between the shorter layers. Finally, fold or bend the whole thing into a cylinder or triangular wedge shape.

Asciii Art

|\|\|\|\| < -- layer make up of fan folded laminatebr>
|||||\ < -layer stuck together, side viewbr>

Fan fold laminated later two, stick between layer 1 and layer 3:

|Z|
|Z|
|Z|
...
posted by orthogonality at 2:51 AM on October 9, 2006

Are arches not pretty strong (was thinking aquaducts, and an eggbox) ?
posted by twistedonion at 3:55 AM on October 9, 2006

twistedonion- exactly correct. An arch is the way to go.
posted by horsemuth at 4:12 AM on October 9, 2006

An arch made out of something that buckles or folds easily — like, uh, paper — is going to be pretty weak, no? You'd need a material that stands up well under compression.
posted by nebulawindphone at 4:15 AM on October 9, 2006

No, it's all about the shape as opposed to the material. I could have sworn that I saw something on the PBS show Nova about it. I believe that they used paper in their example as well. I'll see if I can come up with a little more supporting evidence, though.
posted by horsemuth at 4:59 AM on October 9, 2006

On the first series of the UK tv show Scrapheap Challange there was an engineering student called Chen(?) who'd won a competition for designing the highest tower from a single sheet of A4 paper (and tape) that could support the weight of a full can of Coke. His was over 6 foot tall! - Can't remember anything about the design (sorry) but it took advantage of papers excellent tensile strength rather than its week compression strength
posted by handybitesize at 5:33 AM on October 9, 2006

I used to teach a long unit for a 7^th grade class in structural engineering which was done in a set of challenges. I gave pairs of students tightly constrained resources and a specific goal. The first challenge was to build the tallest free-standing structure out of a single sheet of paper and a mailing label, done within one class period. The second was the same thing, but it had to hold a paperclip the highest height off a durface.

Here's the deal - paper holds up really well under tension, but is really lousy under compression and shear. Any structure you design needs to keep that in mind.

Corrugation is a nice idea in theory, but fails pretty badly with the resources provided. Most students (and most adults) don't have the time or dexterity to make corrugated paper without glue.

For this particular problem, you need a wide stable base and the ability to grow as tall as possible.

Sacrifice a strip of paper about 1 3/4" wide and 8 inches long. Fold quarter inch lips top and bottom and tape the strip into a cylinder. This is your base. The lips are to help keep the paper from buckling in on itself.

With the rest of the paper, you want to make a series of long spiral cylinders. You'll need a form to help you, like a 1/8" dowel. Spiral strips of paper around the dowel, taping it to itself as you go. When you get close to one end, slide the paper most of the way off and start spiraling on more paper. You want to be sparing with your tape, but honestly, 2 meters of tape is a luxury. Do not be tempted to make cylindrical sections and pressure fit (jam) them together.

Take your resulting cylinder and tape it to the inside of your base very carefully. It might help to snip the bottom of your thin clyinder with scissors to get as flat a bottom as possible. You basically want it to stand on its own (which it won't), with the base to hold it up.

Using this design, you can easily get a meter tall structure.

Now for fun, take a single sheet of paper and very carefully tape it into a cylinder and neatly as you can. You will only need 1 piece of tape in the center. Set the cylinder up on end and it will hold the weight of one typical school dictionary. What happens is that the compression force gets distributed and turned into tension and paper likes tension more than compression. Give the cylinder a poke with a pencil and it will come crashing down as you disrupt the transfer of force. Compression wins and the paper loses.

I usually escalate my students up to a structure made from two pieces of paper and three mailing labels that needs to hold 20g at a height of 50cm for a minute. This is straightforward, but in pairs, students need to be able to cooperate and be on task to finish it in the time constraints.
posted by plinth at 5:34 AM on October 9, 2006 [1 favorite]

Have you ever made a paper football? Fold a bunch of those and tape several together to form a tetrahedron. Use tetrahedrons as your base for the structure.
posted by JJ86 at 6:12 AM on October 9, 2006

One ambiguity is that you have not been told anything about the desired shape of the final structure. If you had a problem of the type that handybitesize describes (ie build the tallest tower to support a weight X) or if you were told what exactly the definition of "Strong" was in this context then your task would be easier. How are they going to test the strengh of your design?
posted by rongorongo at 7:04 AM on October 9, 2006

rongorongo, typically these contests are "last man standing" with no other design constraints other than free-standing.
posted by JJ86 at 8:11 AM on October 9, 2006

rongorongo, typically these contests are "last man standing" with no other design constraints other than free-standing.

In that case, I'd lie the paper flat and call that my structure.
posted by malp at 8:40 AM on October 9, 2006 [1 favorite]

Make something long and skinny and non-freestanding; use th paperclip to hang it, and it becomes freestanding. Problem solved.
posted by DenOfSizer at 8:43 AM on October 9, 2006

Said objective being about strong, not tall, I'd think you could do pretty well bonding thin strips of paper as straw-sized cylinders and make yourself a brick-shitter stable cube reinforced across the diagonals to keep it from shearing.

I now feel a compulsion to start building one of these to see if I'm full of shit or not. Man, offices just don't have as much day to day excitement as high school.
posted by Ogre Lawless at 12:25 PM on October 9, 2006

Assuming that just lying the paper flat would not be legal, I have to go with cutting up the paper, and making as many very short cylinders as possible, bound by the tape. Throw the paperclip away.

The shorter the cylinders the better, to prevent buckling.
posted by tadellin at 12:40 PM on October 9, 2006

the absolute strongest shape is a triangle. therefore two triangles crossed together in the shape of a pyramid are very strong! if you want to make something tall, i'd go with the corrugated look, of making lots of smaller triangles between two upright sheets of paper/other material.
posted by alona at 6:35 PM on October 13, 2006