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Several weeks ago I received an email from Joe L. asking some questions about measuring spring constants for a catapult he and his daughter, Alexis, were building for her high school Physics class. These folks live on an island in the Mississippi River where it cuts through Illinois. How cool is that!
They used our DFF Catapult Simulator for the design phase. I wrote the simulator at the request of an old engineering buddy of mine, Jim Corley, who sponsors an annual Physics competition down in his home town of Lucedale, MS. Here's a link to Jim's web page with results of 10 year's worth of projects.
The catapult that Joe and Alexis built turned out well so that I asked him to provide some information for others who may be undertaking the same sort of project. It is built largely from 1/2" PVC pipe and weighs about 4 3/4 lbs.
Here are links to the parts list and images of the project (including one of a previous project, a working model of a 7 cylinder Radial Air Compressor made from Lego parts!)
The rest of the Catapult story is best told in Joe's words in these three emails:
Attached are photos of the completed catapult. As I explained to my daughter, function many times dictates design. This design is wrapped around the principles illustrated in your catapult simulator.
When we were working on the design, we separated the elements that would remain constant from the ones we could choose to be variable. Even though the spring strength can be changed, we assume that it is a constant. Another design point was that we wanted to be able to quickly alter the initial arm angle and the stop so we could zero in on our target. The firing pin sets the initial arm angle while the rope through the aluminum tube can be easily untied and the arm stop relocated, The tube acts as a spacer while the rope pulls the top of the frame tightly together reinforcing the frame. The aluminum tube withstands the force of the arm well.
The holes for the arm stop are five degrees apart and go from 30 to 70 degrees. Unfortunately, the 30 degree hole is blocked by the payload cup. But, I didn't figure we'd be using that one much anyway unless we were trying to hit ourselves. ;-] So, the effective arm stop range is from 35 to 70 degrees of the arm pivot.
I have included a detail of the pivot. Using the 1/2" threaded adapters with a smooth T, it rotated with very little resistance. Using the threaded adapters also allowed me to adjust the gap to ensure free movement. I opted to connect the joints with a metal screws so it could be taken apart and stored in a small area.
The only major surprise after assembly was the arm stop interfering with the spring location at the top of the arm's swing. We had to wrap the latex tubing so that it was all behind the arm. That moved the spring down the arm a bit and allowed the spring not to lose strength by hitting the arm stop.
I hope you like our catapult design. Thanks again for your help.
Today was exhibition day in Alexis' Physics class. Everyone was supposed to bring their catapult designs and try to hit the target. I stopped by to check them out. I was impressed by the variety of approaches. Many looked like a lot of thought was put into them, but others looked like they were thrown together at the last minute.The students in the class were randomly paired up and were supposed to build the catapult together. My daughter's partner told her that, if she designed it, he would build it. To properly design it, we had to build one for testing. We spent the first two weeks of the month long project perfecting the design that I sent you. Her partner was given the plan with the parts list I sent to you along with the photos. He waited until last night to attempt to build it, couldn't understand the design, didn't call with questions and built one after a photo he found on the Internet. It was a square of tubing as a base with the front edge holding the pivot for the arm and a handle like center piece to tie off the latex tubing and act as the arm stop. The only allowance for adjusting for distance was the spring strength.
Alexis was not pleased. We even gave him some of the parts he needed for her design and loaned him the fish scale to measure the spring tension. So much for depending on a partner to come through. The balloons flung from his catapult didn't hit the target. The final trials will be held on Thursday when their grade depends on accuracy.
I'm trying to let Alexis work out this problem with her partner, but, if necessary, I'm going to have a talk with her Physics teacher. Too much of her grade depends on this project to let someone else screw it up.
I'm emailing your simulator program the Physics teacher, by the way. Thanks again for your simulator program. It help us a lot. I hope the results will benefit my daughter.Sincerely, Joe L.
Gary, All came out well in the end. My daughter's lab partner's day-before-thrown-together catapult was replaced with the one I helped her build during our design process. On exhibition day, his catapult wouldn't throw the one half pound water balloon more than one foot. He decided the grade was more important than his pride. The final testing day showed that designs based on solid scientific principles and mathematics, such as shown in your simulator program, get results. One chaotic factor that was hard to control was the shape of the balloons. Until the balloons were filled with water, it was impossible to tell if they were egg shaped or pear shaped. The closer to round the balloon was, the truer it's path of flight. The first three trial shots hit right in the center of the bull's eye, but when the balloons were catapulted for grade credit, they just missed the bull's eye on the target. Hitting the bull's eye would have meant five points of extra credit for each of the three balloons fired. That would have meant a total of 115 possible credit points. But still, 100 points wasn't too bad. If they would have been more careful to save the egg shaped water balloons for the credit shots, it might have given better results. They had fun and learned a lot, so it was an all around success.
Alexis' design was the only one with a moveable arm stop on exhibition day. The students had three days to change and perfect their designs. After some of the other students observed the benefits of the movable stop, they used it on their designs too. Personally, I think the movable stop is one of the most critical parts that helps with accuracy.
Something that I noticed when I looked at all the designs on exhibition day was the tendency of the students to design based on how they thought a catapult worked rather than on the actual physics of it. Also, many of them made the mistake of not designing for the requirements of the assignment. Some built catapults that would throw a water balloon 100 feet or more, but couldn't hit the target 20 feet away and had no accuracy even at long distances. That may be more a listening problem rather than an inability to build a good design.
Now that the assignment is done, we're going to see how much spring we can add to the design and find the limits to how far it will throw. It's a sturdy design and I think it will hold together. My only concern is bending the arm stop when it shoots, but I have more tubing, so it's worth a try.
I think I misinformed you about the weight of the water balloons earlier. I think that comes from metric to US weight measurement conversion confusion at the time. The water balloon weight we used was about one half pound. The most successful setting for hitting the target was 45 degrees for the arm stop and 2.5 degrees up from level for the arm start angle. The spring tension was a consistent 10 pounds on the fish scale.
If you have any questions, please let me know and thanks again for your simulator program.
Feedback like this makes DFF a worthwhile exercise. I thank Joe for taking the time to keep me informed about the project and congratulate him for the principles he is instilling in his daughter. If you have similar tales, please let me know.
Also, if you have specific questions about this project, or Jim Corley's competitions, use the feedback link below to send me a message and I will be happy to pass it along to them.
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