# How to Make a Tower Out of One Piece of Paper

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The paper tower challenge is an important exercise for students beginning their study of structural engineering because it teaches about load distribution, kinematics, Newton's laws of motion and other important principles. In a simple version of the challenge, students build a stable tower out of a single piece of 8 1/2 -by-11-inch paper. Most strategies call for cutting the paper into strips and forming them into girders. When more than one team competes against one another, the winning team is the one that builds the highest tower that can withstand a predetermined amount of force, such as the breeze from a fan, without falling over.

## A Winning Strategy

The most important part of the tower is the base, and although there are several approaches to constructing it, the most stable structure is an equilateral tripod. Because it distributes the load symmetrically, the tripod resists tipping better than a flat piece of paper. The tripod also adds height to the tower.

After you constructed the base, use the rest of the paper you have for the tower itself. If you're going for maximum height, you'll want to create the smallest possible base, but don't sacrifice stability for economy or the tower may not be able to withstand even a gentle breeze.

## Building Paper Girders

Every solution to this challenge involves cutting the paper into thin strips and forming them into girders. You want to maximize the number of girders you get from the paper. To do that, you should cut thin strips, but if you cut the strips too thin, they are difficult to form. A good compromise between economy and stability is to cut the entire sheet of paper into 1-inch strips along its width.

You can form the strips into girders in two ways. One is to wrap them around a pencil to make cylinders and the other is to fold them into tubes with triangular cross sections. A piece of tape at either end of each girder should be enough to hold it together, but you may want to add a third piece of tape in the middle. Leave at least an inch at both ends of each girder untaped. This will allow you to fit the girders together lengthwise.

## Build the Base

You need a minimum of three girders to build a tripod for the base. They should splay out from a central apex, and the distance between each of the feet should be equal to the length of a girder. To join the girders at the apex, wrap a single piece of tape around the ends of the girders to form a cylinder that can fit inside one of the girders. If you find this too difficult to do, squeeze the ends together and give them a twist before taping.

If you're constructing the tower on a slippery surface, you may have trouble stabilizing the base. One solution is to connect the feet with three more girders to create a triangle. This gives you fewer girders to construct the tower, so it won't be as high, but it will be more resistant to falling.

## Erect the Tower

You form the tower by fitting the remaining girders together to form a long tube. Insert the end of one girder into the end of another one and push them together until the tape prevents you from pushing them any farther. This gives you a single tube that is somewhere between 40 and 60 inches long, depending on how many girders you used for the base. Erect the tower by pushing one end of the long tube onto the apex formed by the three base girders.

Because you have cut the paper along its width, you have shorter girders than you would if you cut the paper lengthwise, which means the tower has more joints. This is a good thing, because the joints are stronger than the spans of the girders. However, if you're someone who likes to experiment, try building a tower with the identical procedure, but this time cutting the girders along the length of the paper and compare the stability of the two finished towers.

## An Extra Challenge

Some competitions don't allow the use of tape. You can still use this strategy to build the tower, but you'll have to find a way to make the girders stay together by making small cuts in the ends of the paper and folding them together. Be sure your hands are clean when doing this and use sharp scissors.

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