I’ve been trying to learn how to calculate the trajectory of a ball for the upcoming season, but have some question I was hoping the community could answer.

The initial velocity will (ideally) be the same as the flywheel when the ball separates from it. If you were to track the velocity of the flywheel, the minimum flywheel velocity should be the same as the ball’s velocity when it leaves.

As for the differences, the forum link takes into account the significant air resistance of the NBN balls. The first link presents the idealized zero-friction trajectory. This year’s balls will probably be somewhere in between the two.

Like most things with engineering, there’s only so far theory can take you. Perfect information on how a thing works really only comes from building it and collecting data. If you have V5 motors, data collection is easy, otherwise you’re going to need an optical shaft encoder. What you’re interested in is mapping initial flywheel velocity versus trajectory. Use the information you can get from theory to come up with some idea about what your first device might need to do, then build one and see if you were right.

Only conditionally. You’re talking about a double flywheel. If it’s a single flywheel with a backing the ball rolls against, it works differently. The edge of the ball touching the flywheel will move as fast as the outer part of the flywheel, while the edge of the ball touching the backing will not be moving. This is known as rolling without slipping. (It’s actually rolling without slipping on two surfaces.) The center of the ball will be traveling at half the tangential speed of the outer part of the flywheel.

There are 2 “speeds” that we are referring to in the flywheel setup.
One is the angular speed/velocity, and the other is the linear velocity.

The rpm of the flywheel is closely related to the angular speed.
As for the speed of the ball, it is actually the linear velocity (making a big assumption that everything is transferred from the flywheel to the ball).
But in actual situation, only part of the momentum of the flywheel is transferred to the ball (and that is also the reason why the flywheel will always slow down after shooting a ball). So if you are able to track the angular speed of the flywheel before and after the ball exited, then you will be able to figure out the linear speed of the ball.

And if you are looking for formula, then linear velocity, v = radius x angular velocity

Edit: as @callen has pointed out… there is a difference between double or single flywheel. Mine is for single flywheel.

Yes, depending on the units you want. What you have will give you a tangential speed for the outer part of the flywheel in (circumference units) per minute.

Oh, and as for finding initial velocities, something that can work really well is launching close to and in a plane parallel to a grid while taking video. You can then take data frame-by-frame to figure out the speed of the projectile (algebra, best-fits, etc.). You’ll also be able to determine your launch angle from this. At the same time, read values for the flywheel’s angular speed. This should allow you to get a realistic comparison between the flywheel’s angular speed and the ball’s launch speed, especially if you do this a bunch of times with different flywheel angular speeds. You could choose to use initial flywheel angular speeds so you know what you’re setting and what it will result in. Essentially, you’re finding the ball’s launch speed as a function of the wheel’s angular speed experimentally this way.

Angular speed is how quickly the wheel is spinning, measured in things like rpm, rad/s, degrees/s, etc. Angular velocity is essentially the same thing with direction included. You can probably always interpret them interchangeably when someone states them here.

Tangential speed is the translational speed around the center of rotation at which a point on the object is moving.

So for a rigid wheel rotating around its axis, every point will have the same angular speed while points at different radii will have different tangential speeds following the formula vt = r * w, where vt is the tangential speed, r is the radius, and w is the angular speed. Be careful with units.

Keep in mind these are ideal … single flywheels change the angle they shoot at based on variances in ball width, traction between the ball wheel and back plate, and projectile spin rate. Also if your back plate is too slick, and your launch angle too steep, the Corvallis effect is very much applicable… in NBN i saw a bot at comp that could only score high when up against the bar and the had a fly wheel such that the ball shot nearly straight up, the ball went about 3 inches out of the 12’X12’ field and then via aerodynamics spun the ball backward and into the high goal… with slicker and less squishy balls we will need to be even more careful to make sure this doen’t happen to your shots. But the flatter the shooting angle the less it applies.

I’m not familiar with the Corvallis effect. It sounds like you’re describing the Magnus effect, which, yes, could potentially be made quite significant. What is the Corvallis effect?

YES after some refreshers yes, magnus is correct for this situation … Covallis was what spell check suggested when i attempted to spell Coriolis effect which is a somewhat related aero phenomenon involving spinning bodies. What can I say I’m not the best at engrish. Thanks Callen for fact checking cause honestly I don’t intend to mislead people. Yes flywheels are awkward but never underestimate the value of perfect compression and friction on the wheel. Too much grip you loose power to squishing the ball, not enough and you loose energy to the wheel skidding across the ball. Ideally you want as little friction as possible in the gear box … in practice if you have a magic witch building your robot you might have to deliberately add a tiny amount of friction so the flywheel slows down fast enough for shorter shots ( this is probably more relevant to nbn though since less of this game is focused on shooting while moving).

That makes more sense. For those who don’t know, the Magnus effect is what governs things like how a ball with top spin, bottom spin, or side spin will curve as it travels through the air. In this particular game, the Magnus effect will be more limited because the balls are relatively slick, lacking a golf ball’s dimples or a table-tennis ball’s roughness and lacking a spongy surface like a tennis ball’s fibers or a foam ball’s pores. But it will show up, generally as bottom spin from single flywheels. And as @theone1728 said, more so if the back plate is slick so that the ball can spin a lot more.

For clarity, the Coriolis effect has nothing to do with aerodynamics. The Coriolis force is a fictitious force (non-existent, only perceived) akin to centrifugal force. The Coriolis effect can be experienced when position is changed on a rotating object. For example, if you shoot a gun or cannon horizontally in the northern hemisphere on earth, the bullet or shell can be seen to curve off to the right. A simplified way of seeing this is that if the bullet is fired toward the equator then it does not have enough tangential speed to keep up with the earth and so falls behind, and if it’s fired away from the equator it has too much tangential speed and moves ahead. While this has nothing to do with aerodynamics, it does come in to play significantly with air as it helps govern the motion of air on our rotating earth and is the reason hurricanes spin in the directions they spin.