Flywheels and launchers

A flywheel launcher transfers energy from a rotating wheel to an object through contact. Repeatable output requires controlled wheel speed, contact geometry, feed timing, and object behavior.

Energy and surface speed

Stored rotational energy is $E = \tfrac12 I\omega^2$, where $I$ is rotational inertia and $\omega$ is angular speed in radians per second. Increasing inertia reduces the speed change caused by a given energy transfer, but also increases spin-up demand and stored energy.

Wheel surface speed is $v = r\omega$. It is not automatically the launch speed: object slip, compression, a second wheel or stationary hood, and energy losses affect the result. Match the contact path to the object instead of deriving a launch prediction from RPM alone.

For an illustrative wheel with $I = 0.0003$ kg·m² at 300 rad/s, stored energy is 13.5 J. If 3 J leaves that rotating assembly during a feed, the remaining idealized speed is:

$$\begin{aligned} \omega_2 &= \sqrt{\omega_1^2-\frac{2\Delta E}{I}} \\ &= \sqrt{300^2-\frac{2(3)}{0.0003}} \\ &\approx 265\ \mathrm{rad/s} \end{aligned}$$

This example isolates the energy change; it does not model the motor adding energy during contact or predict a particular game object's trajectory.

Contact geometry

Set wheel diameter, compliant material, compression, hood shape, and object entry pose as a system. Too little contact can slip; too much can damage the object, stall the feed, or produce large wheel-speed drop.

A feed mechanism should release a consistent number of objects with a repeatable entry orientation. Keep an accessible recovery path for a jam. Archived Ultimate Goal flywheel experiments compare contact arrangements for that season's rings; their geometry is not a recipe for a different game object.

Speed recovery

Measure wheel speed before, during, and after a feed. Use a defined readiness band and settling time if speed feedback is available. A fixed delay may work under tested conditions, but battery change and repeated shots can alter recovery.

PID control provides background for speed regulation. Verify archived flywheel-control examples against your SDK and hardware instead of copying season-specific setpoints.

Repeated shots

Tune the launcher and transfer as one system. The feeder controls when an object arrives; the wheel and contact geometry must still produce an acceptable shot at that interval.

Start with enough time between shots for repeatable output, then reduce the interval in measured steps. Compare shot spread, wheel-speed drop, missed feeds, and double feeds. If the first shot works but later shots fall short, check both recovery and changes in the objects' arrival conditions.

Define readiness from the range that passed your shooting tests. A wheel crossing the target speed for one reading is different from holding it steadily. Where needed, require the speed to remain in range briefly, with a timeout and a way to cancel. Include the aim and object-staging conditions too.

Software cannot replace missing motor power or inconsistent contact. Check the actual control update timing, but do not assume that a faster loop alone fixes a feed path that changes the ball's position or spin. Test repeated shots while other mechanisms are running and at representative battery states.

For trajectory and calibration, continue with Projectile mathematics and Shooting on the move.

Testing and guards

Use a controlled test area, an appropriate backstop, and a clear procedure for stopping motion. Keep hands and loose items away from the wheel and feed path. Remove power and wait for rotation to stop before clearing a jam.

At a fixed measured setup, record entry pose, wheel speed, post-feed speed, recovery time, landing position, and failed feeds. Compare the spread of outcomes as well as the average. Include worn contact surfaces and representative object variation before claiming a reliable operating range.