# Ball Density Distance Calculations

After finally getting some balls, we were able to test the variance in density, and how it effects the balls. Many people have pointed out the variance in the balls. In our fly wheel system test, the less dense balls flew considerably farther than the denser balls.

I tried to squish these two balls to the same amount:

http://puu.sh/i6n2v/191ea38f08.jpg

Using balls of varying densities, we tested how far they flew. we marked where they first impacted. We ran he balls again to see if they landed in a similar location.

http://puu.sh/i6n6U/348b28b51d.jpg

While the balls were consistent with themselves (each ball landed in a similar location to the previous launch of that ball). There was much variance between the different densities of balls. (ranging almost 2 meters in distance)

http://puu.sh/i6n3J/7c3dd2cfa2.jpg

We then tested how high each ball was at 4 meters in distance. These were not as spread out with the exception of the densest ball.

http://puu.sh/i6nuR/83ed6ac057.jpg

Collecting data from many balls in varying densities. We used the the three points we now had in a quadratic regression model. We got a parabolic equation, that can be used to demonstrate the ball’s flight pattern and where the ball is likely to be at a given distance or height.

http://puu.sh/i6nb4/fbbf8d1de8.png

Obviously the distance and trajectory will vary between launchers, but this is mathematical evidence on just how much the balls this year vary.

*This graph was made using demos (mobile version)https://www.desmos.com/calculator

Very very interesting. I am assuming you launched all of these at the same flywheel RPM (or at least just maxed them out with your joystick). I can’t tell if your launcher has encoders or IMEs on it. If so, could you tell us what RPM the wheels where spinning at before and after launching the less dense and more dense balls?

This is very, very interesting.

I’m just wondering: when you talk about the densities of the balls, are you talking about actual densities that you measured or are you talking about differences only in weight while presuming that the actual volume of each ball is identical? I know that from a practical standpoint (hitting the target) my question is irrelevant, but I’m just curious, and I know some of the people of the forum have been working diligently to create computer models of ball trajectories and they would probably like to know, too.

Also wondering: how many flywheels did you use? Vamfun, et al, have indicated that adding more flywheels should help reduce errors of this sort. I was also wondering if you had any kind of speed control and/or monitoring on your shooter.

I hope other teams will post their results of these kinds of tests. A larger question is whether ball properties (and behaviors) will vary greatly throughout the season as different manufacturing batches are released into the wild.

Thanks again for providing such detailed info.

I don’t think the actual mass of the ball is the major issue here. They are seeing deviations around 20% which is far larger than what Vamfum and all had predicted.
Instead, I think it is the “squishiness” of the ball that is dominating here. The softer balls are compressing more through the shooter. This would give a better contact surface and overall improve the shot performance by closely representing our theoretical no-slip condition. I think the harder, more dense balls are not compressing as much. As it passes through the wheels a few things will happen. Firstly, since the balls are not going to deform as much, some part of the shooter will have to (either the flywheels or the axels will bend out momentarily). This probably causes a lot of additional friction that eats up flywheel energy during the shot. Also, I would guess that the harder balls are slipping more through the shooter because they will have less contact area. This divergence from the no-slip condition would also reduce performance.
If we can get an idea of what the flywheels are doing before and after these shots we may be able to understand exactly what the root of the problem is and design around it. Adding weight like you said would also be interesting. I wonder exactly how much of this range deviation could be reduced in real practice.

We plan to add encoders later, the current theoretical RPM is 1866.666 before launching. The RPM doesn’t decrease too much after the ball, and quickly recovers to full power. We will run more tests on this later, this was our first major field test, with many more to come.

Yes this just involves running our motors at power 127 and launching the balls.

The “denser” balls are harder and heavier. So the hardness implies there is more foam in the same space. I don’t know if they are any larger, but they all appear to be within similar size constraints, but I am not positive. I will test this as soon as I can.

Just 2 5" wheels with 6 holes between the treads (3" spacing) to give the balls compress the ball. This gives sightly longer distances.

Yes, I know they are redesigning the goals right now. We will have to see if the balls get a reboot as well.

This is a good observation. It probably plays a role in the performance of the launch. But if the mass is greater it will have a larger inertia as well. there fore it will not launch as far. Although you make a very good point, That must be playing a role in the launch.

We did observe some similar things when testing various spacing between the wheels of the launcher.

Nice work folks,

As others have mentioned, my post on range variation with ball mass predicts about 2 to 3% range error for a 10% ball weight variation for your two wheel launcher configuration. So, it is likely, that the large variation you are seeing is due to other sources. I think you are experiencing the contact issues that are attendant to the two wheel shooter.

Perhaps you can run a few more tests to help isolate the causes.

I would suggest multiple shots (maybe 10 +) with the same ball. One squishy and one dense.
Hold speed at 127 and measure the steady state speed before each launch with an encoder or better yet adjust the speed to be the same before each launch. If you know the speed, you can adjust your data for that variation.

If you can try a 3.5 inch wheel separation and still get the balls to launch, this might be worth another data set.

Perhaps you could also do a mass variation delta by picking one ball and using a balance scale to measure the mass difference with respect to other balls.

Keep up the good work!

Thank you. Yes, more tests are definitely going to be taking place soon once we are done with finals.

we originally had a 3.5" spacing between the wheels and we were experiencing about half the range in the shots, which is why I was thinking the compression of the ball caused the inconsistency. Less compression = less range. So a ball that compresses less with not fly as far.

How will this impact the Programming and Driver ranking for Worlds qualifications?

Since the top 30 scores qualify for Worlds, what happens if the ‘variation’ in density of the balls is reduced for a skills field in a way that is advantageous for a flywheels or other mechanisms? Potentially, that field could have higher scores simply based on sorting what balls go to which field.