Water Balloon Trebuchet/catapolt Physics Problems

[Ransom7D]

Hello,

This is my first post and I hope it's not incorrectly placed...

Recently I made the naive decission to design a water balloon trebuchet as a pet project. Furthermore, I wanted to calculate the exact specifications of the design ( counterweight, arm lengths, ect.) using only the knowledge that the desired distance was to be 50m, the release point was to be at 45 degrees, and that the avg. water balloon would weigh around 1kg.

Determining the necessary velocity at the point of release was reletivly easy. I used the formulas, x=t(v)cos() and y=t(v)sin()-(.5)(g)t^2 , pluged in the release angle of 45 and the distance of 50m, then solved the horizontal formula for t and substituted it into the vertical formula when y is 0. this resulted in a velocity of 11.07m/s. I was excited, but little did i know what was to come.

So next i drew a simple desing and determined that I needed to find the mass of the weight, and the two arm lengths. furthermore I determined that the total force of the counterweight minus the total force of gravity on the projectile arm would have to equal a force whose velocity was 11.o7m/s. So I sought the neccsary formulas, and from there I realized my folly. At first i began with a simple F=ma style approch, but remembered that this was a curcular trajectory problem. I then began using F=mv^2/r for a bit until i remembered that was for centripital force and would be of no use.

I have tried a miriad of other approches ranging from determining angular velocity and acceleration to formulas in inertia, to even turning the whole thing sideways and attempting to turn it into a modified trajectrory problem with gravity as wind resistance and centripital force as gravity! I have yet to get any consistant results. So now I've decided to give in and ask for help.

Can someone please point me in the proper direction on how to figure this out?

(note: I'm a rising senior in high school with only a knowledge of precal and basic physics guiding me... i fear I am over my head but am obsessed!)

 

[Cleonis]

Recently I made the naive decission to design a water balloon trebuchet as a pet project.

Well, I suggest you first try a simplified version of the problem. Lessons learned will help you follow the discussion by Franco on his http://www.real-world-physics-problems.com/trebuchet-physics.html" page.

A true trebuchet has the rigid swingarm, and then there is the sling with the pouch. As a simplification you can:
- Leave out the sling
- Attach the counterweight directly to the short end.

For the simplified case let's say the swingarm hits a cross member, just like the swingarm of an Onager hits a cross member, releasing the payload. Let's say that initially the swingarm is at a 45 degrees angle, with the long end pointing down, and that at the instant of launch the the swingarm is pointing up at a 45 degrees angle.

Then you can divide the setup in four contributing elements:
- The counterweight
- The payload
- The long end of the swingarm (holding the payload)
- The short end of the swingarm (holding the counterweight)

Each of the contributing elements has its own moment of inertia with respect to the pivot point. For each of the elements gravity contributes a torque. You have to evaluate the resultant torque that is acting relative to the pivot point. Once you have the resultant torque and the combined moment of inertia you can compute the angular acceleration of the payload. That should enable you to home in on an angular acceleration that leads up to the needed launch velocity.

You may have to simplify even more. The torque from gravity depends on the angle of the swingarm. When the swingarm is level the torque is largest, when the swing arm is at an angle the torque is correspondingly smaller. You can opt to take a guessed average for that torque, and then you treat the torque as constant throughout.

If you manage such a simplified setup then maybe you'll be equipped to handle a less simplified version. Good luck.

 

[Ketman]

Will you put your trebuchet on wheels or will it be fixed in position?