Calculating Drag Forces on Arcs for Engineering Project

[SkydiverChris]

I'm currently working on an engineering project for my high school engineering course, and the knowledge of physics I should have for this project is more than I actually know. I want to build a catapult that can shoot a tennis ball at an 8” target on the ground from 30 feet away. I want to take into account wind resistance in the building of my catapult, but I’m having trouble finding the right equation for drag forces on arcs. Is there anyone who can help me with this? I’m working on my general blueprints for the project, so I’ll be able to give you exact dimensions and measurements before long, but as of now I don’t have any. I can tell you that there will be no angle on the plain of the catapult and the target, so it’ll be level, and I can vary the weight on the arm of my catapult launching the tennis ball. Does anyone know what kind of equation I should be using?

 

[drpizza]

I thought about this for a bit. If you were shooting a tennis ball several hundred yards, what you want to do might be worth the effort, and it would be a lot of effort. You'd need to consider the spin of the ball (think of a golf ball - with just the right amount of spin, it travels much farther than if it had no spin, and certainly much much much farther than a ball hit with top spin as is often the case when I play.) And, as important as the spin would be, how fuzzy is it? And, how pronounced are the seams? (edit: and the math will not be as trivial as plugging numbers into an equation.)

However, as you're only building your catapult to toss the ball 30 feet, my hunch is that the effects of drag are going to be smaller than the effects of an imperfect catapult. You might be better off with making a design change to allow you to calibrate your catapult.

Having watched several people (who knew what they were doing) build trebuchets (an advanced catapult), there was always a lot of fine tuning after their device was built. Those "minor" adjustments often resulted in several hundred percent change in the range. That is, they may calculate that ideally, their trebuchet will fire a golf ball 200 feet. But, their first shot only travels 50 feet. A little adjustment here and there, and they hit 120 feet. A little more adjustment and they get 180 feet, which they're satisfied with, as no device is perfect and getting 90% of what would be perfect is pretty darn good. Now consider these numbers and question if a difference of 10 or 15 feet was something they needed to bother with. If their goal was to hit a target 150 feet away, it would seem like a waste of time to have bothered worrying about drag which might affect their range by 10 feet, while an extra half inch of rope might affect their range by 30 feet.

 

[SkydiverChris]

alright, so since the air resistance is too insignificant to be calculated into my equation, what formula would I use to find the weight I would want on the sling end of the catapult if I have a fixed angle for my catapult?