Objective

The object of this project is to design, build, and operate a catapult that can launch a squash ball so that it passes through a given horizontal and vertical location in space. The catapult is to be built from a kit of parts (Erector Set) which will be provided to your team. We will also provide the squash ball.

Tasks

• Designing the catapult from the parts in the Erector Set. You may have to supplement the kit with some type of basket to hold the squash ball, and some elastic material or spring of some sort to provide the energy source for the catapult. The total cost of any additional parts shall not exceed $5.50. The design must be such that the squash ball can be launched reproducibly. The device you design must be mountable on top of a cart. The "pull" of the catapult and the angle of the catapult launch are important variables - your team must address how to vary or how to fix these quantities. The release procedure should allow the ball to be shot in a smooth and reproducible manner.
• Constructing the catapult.
• Taking data on the trajectory of the ball being launched as a function of either the pull or the take-off angle.
• Determining the "performance map" of the launcher/ball combination from this data. That is, your team must establish the relationship between the horizontal and vertical distances of the trajectory as a function of the pull and/or the angle so that the data can be used to select the values of these quantities to launch the ball through a 0.35m by 0.35m target a specified vertical and horizontal distance from the launcher. This performance map must be constructed by empirical means (i.e., experimental measurements) and not from any modeling based on theory from physics. You may use calculus to perform curve-fitting to the data you obtain.
• Demonstrating that your catapult and performance map work by either:
  • Successfully launching the ball through the target placed arbitrarily in the range of the device, or
  • Adequately explaining why your device would not launch the ball through the target and how you would improve the second generation launch device.

The final design and the design process must be documented by the team. The process should be documented in a "design notebook," and the final design in a succinct report that also includes the testing and final outcome of the project.

Further Information

The data collection for launch performance will take place on Tuesday. At that time you will be asked to launch squash balls over a range of pulls and/or angles. The location for the practice will be announced on Monday. Each team will be given ten minutes to carry out their experimentation. The time period when your team will do the practice shots will also be given out on Monday.

There have been several questions about the nature of the launch, such as, Is there a minimum launch distance? Is there a maximum launch distance? What is the most significant factor - accuracy of shots, or precision of shots, or length of shots? The answers are roughly the following:

• The minimum and maximum distances are not really fixed in advance. As each team is using a different elastic energy source (spring, rubber band, what-not), each team's design will have different operating characteristics. However, you might "shoot" for a minimum of 10 feet and a maximum of 30 feet. But these are only guidelines, because...
• The most important factor is reproducibility, which is related to accuracy and precision, which are not synonymous. This we will discuss in class. So obviously...
• The catapult that achieves the longest (or shortest) throw is not necessarily the best. The one that hits the target, in this particular project, is the "best."

The data collection will consist of videotaping the launches over a range of pulls and/or release angles. The tape of each launch will be digitized so that you will have sets of data points (x,y pairs) that represent each launch trajectory. You should begin to think about how you might use this data to establish a performance map of your catapult and how to use the map as a predictor to hit a target given it's (x,y) location.

Performance Map

Consider the data of Team 21 (Roedel, Wigner, Cronin, and Schwinger) - two of their squash ball launches looked very much like parabolas. One represents the minimum, the other the maximum distance that their brilliantly designed catapult can reproducibly achieve. They are plotted on this graph. The equations for these two parabolas are given by:

• y = -0.1*x^2 + x
• y = -0.08*x^2 + x

The launch point was chosen to be (0,0) and the floor had the y-coordinate of -4 ft. The one launch, which was produced by a certain pull, goes around 13 feet and the other, which was produced by a longer pull, around 16 feet. Lovely looking shots. Now, on the day of the shoot-out, Team 21 is certain that Professor Evans will put the target at some coordinates that fall between the two parabolas. The question is, how does Team 21 prepare for this eventuality? What can the equations tell you?

Writing Assignments

You will be asked to submit several types of write-ups on this project.