Fun with Catapults

Round 1: Over interim of our senior year, my roommate Sam, Robert, and I built a small trebuchet to throw caf apples, as part of the First Annual Society of Physics Students Catapult Contest. The contest was sponsored by us (Sam being SPS "President" after usurping power due to member apathy and failure to hold elections), as a thinly veiled excuse to build a catapult-type device. The first version was adequate, but Robert and I beefed it up the day before the contest, so that it had a rather Frankenstein appearance. Here are some pictures and movies of the fun we had. Click on the images for full sized versions.

Round 2: Finding himself in the difficult position of having no real classes the second semester of his senior year, and constantly complaining that he had no homework, Robert decided to pursue construction of a larger device which the three of us had discussed while building the first. Catapults are similar to boats, in that you always want one that is just a few feet bigger. I participated in the early planning and a tiny bit of construction, but Robert soon brought together the Ballistic Engineers to realize his dream. The team consisted of Robert, Peter Pearson (of radar group fame), Josh Braun, and Evan Frodermann; some of whom actually knew something about using power tools and building with wood (an improvement over my ignorant enthusiam in the face of power tools while building the previous trebuchet, which had led to a few scares for Sam and Robert). Limited only by the size of the doors to the woodshop, this larger trebuchet had dimenions of 6.5' high by 8' wide by 8' long, a massive contraption. Anytime I mention building a trebuchet now, Robert is quick to dismiss our first project as a mere prototype, and point out that his trebuchet was much bigger. As we all graduated at the end of the year, the Saint Olaf physics department became the lucky recipients of a generous donation by the Ballistic Engineers for future class demonstrations.

Math Mess: All this catapult mania inspired a Problem of the Week in the Math Mess. See below for problem and solution.

Pictures of the First Trebuchet and Catapult Contest

 A picturesque shot of the catapult behind Old Main. Bernt Julius Muus would have been proud. Sam in the Gulag style work camp where we built the catapult. He's holding the 35lb lead brick we used as part of our counterweight. A collection of fruit that I took out of the caf in one evening to use as amunition. Notice the decorative gourd.(Update: Sam's Aunt Anne informs us that it is in fact an acorn squash.) The weather on the day of the contest was quite a bit nastier than on our previous outing. It may not look it in the picture, but that wind is blowing at about 20mph and taking a lot of dry snow with it. In spite of the weather a good crowd showed up to watch. We were definitely cold after an hour outside. But neither rain, nor snow, nor common sense will stop the catapult enthusiast from launching caf apples. An action shot of all three teams examining their various devices and preparing for the next launch. The girl's team went a different route than the other two teams and built an onager, which uses incredibly twisted rope to power the throwing arm rather than counterweights. Peter preparing to launch. In addition to the 35lb lead brick, he used a few heavy-duty bungie cords for that added oomph. Sam, Robert, and I standing triumphantly with our trebuchet after a good day's launching. That's quite the throwing arm, no?

The First Trebuchet in Action!
Click on the pictures below to download .avi movies of the trebuchet.
Warning: Both of these movies are over 1 MB large. Unless you have a highspeed internet connection, you'll have to wait a long time for them to download.

One of our more successfully launches with the original trebuchet, as seen from atop Old Main hill.

Our first trebuchet in action after our additions. With the longer throwing arm it has a very stately throwing motion.

Pictures of the Second Trebuchet

 Just getting the massive trebuchet to the launch site took quite a bit of work. Fortunately, the Science Center janitors are great and let us borrow one of the janitorial carts. Loading the trebuchet with 210lbs of counterweight was a potentially life threatening experience. There's Robert gamely preparing another cantalope for launch. Robert, Peter, and Evan standing proudly next to their 14' baby.

Second Trebuchet Movies

Click on the pictures below to download .avi movies of the trebuchet.
Warning: All of these movies are over 1 MB large. Unless you have a highspeed internet connection, you'll have to wait a long time for them to download.
 Exploding cantalope! Look at that huge throwing arm. Another great movie of flying fruit. When we ran out of moldy cantalopes, grapefruits worked just as well.

 As seen in the MathMess... (Professor Molnar is the Problem Guy) Problem: "Here is another immensely practical problem which I was reminded of watching trebuchet videos on Tom Engle's homepage. It is well known that the best angle at which to launch a projectile in order to maximize distance traveled across a flat field is 45 degrees. (This is math class; we ignore air resistance, etc.) That's all well and good, but what if you are launching apples down Old Main hill? I don't know how much of a slope that is, so let's call the angle of inclination X. Assuming a fixed initial velocity, what launch angle (as a function of X) will maximize distance traveled down the hill?" Solution: "I[, the Problem Guy,] received a solution from Craig Williams which seems to work. The simplest statement of the result is that the optimal angle for firing objects down a hill is halfway between the angle of the hill and the vertical. Note that this agrees with the well-known result for X=0."