Physics Problem :D

Okay so my team is trying to keep our bot stupid simple to drive and control. What we decided is that the arm that controls our claw and shooter will be controlled by pneumatic’s. This would give us two positions: Pick Up and Shoot. We want to shoot on the edge of the Red (or blue) division line. Then the ball would be put into firing position and shot. This is similar to The Holy Cows strategy last year but they used the pyramid as their aimer. Okay now to my question what angle will the arm have to be at if it is being shot by a surgical tubing punch that has 100lbs of pull back force when pulled all they way back. Sorry for the kind of lack of details but that is all the real information I have. Thanks for any help you can provide.

Unfortunately, you don’t have enough details specified. For a spring-like mechanism the tension is: kx where x is the distance it’s pulled back, but the energy stored is kx^2. So for a given force you don’t always have the same energy, even in the ideal case.

Yeah I have tried to find a graph of surgical tubing’s “force” compared to inches stretched but I have had no luck or else I would of provided that to you now. As for the distance pulled back I simply forgot to put that in there. The puncher will be pulled back 7in and the loops of tubing un-stretched are 6in long, so when loaded the tubing will be 13in.

A rough idea of how far that kind of energy will take you is attached. Note that it makes assumptions like the surgical tubing behaving like an ideal spring, there being no air resitance, and 100% of the energy is imparted to the ball. It says that if you fired straight up it would go about 10 feet, which seems a little far to me so you may want to double check my math.

This suggests that there should be a pretty wide range of angles that would work.

launch_calc.xls (7.5 KB)

launch_calc.xls (7.5 KB)

WOW okay that is interesting so what exactly do you mean by a variety of angles because I just want to shoot on the line and that should have an “ideal” trajectory right? Thanks for your help so far.

Just drew a simple triangle over our CAD model and if your data is anywhere near correct our shooter should launch the ball in a close linear while it flys through the 18ft to the goal. With that being said the “sweet spot” angle seems to be between 30 degrees and 35 degrees. What do you think?

How high is your release point?

When the arm is at 35 degrees the shooter is at about 25in off the ground.

Just take a length of surgical tubing and find a spring scale. If you line it up with a meter stick or ruler, you can experimentally find the curve for surgical tubing’s force per distance stretched.

It shouldn’t take much time, and can probably be extrapolated to different lengths pretty simply.

This spreadsheet will be useful to you. You can determine your initial velocity using energy (as others were saying).

.5 * k * x^2 = .5 * m * v^2

I recommend getting your surgical tubing spring constant experimentally by loading your mechanism with weights so mg = kx if you know k and you know how far you’re pulling it back then you can calculate velocity. Be sure to include the weight of your launching mechanism when calculating velocity, it is being accelerated too.

In most catapults and kickers, a large portion of the spring energy is not imparted as kinetic energy to the ball. Thus this equation will give a substantially over-optimistic estimate of ball speed if “x” is the total amount the tubing is stretched (including pre-tensioning stretching).

You can increase the available spring energy by adding more strands or tubing and/or pre-tensioning the spring (or surgical tubing) with the launcher (or kicker) against the hard stop in the “fired” position.

That is true for catapults, but I was under the impression that a linear launcher (like I imagined they were using if they were asking about angle from an arm) would be more efficient at energy transfer. With the exception of friction what would prevent it from imparting energy? Deformation of the ball?

Friction, deformation, and…

When the catapult/kicker/punch hits its hard stop, all its kinetic energy at that point is lost and not transferred to the ball.

Don’t forget the issues related to momentum transfer and impulse in a VERY inelastic collision. Then add the time-domain issues of the rebound of the ball off your shooter…

There’s many, many variables that COULD be added to the problem. I have strongly encouraged our programming team to consider the law of diminishing returns with regard to how much they try to analyze.

We are only shooting a ball 20’ into a goal. We’re not putting a hypersonic dart through a tank turret a mile away while the gun platform is bounding over terrain :yikes:

Lots of physics going on, but we only need to know the parts that contribute to the shot within the limits of the robot’s own tolerances.