HiveCaster

1 · Wheel to ball (impulse model)

The ball is squeezed between two surfaces: the spinning wheel and the hood (or a second wheel). Friction impulses at both contacts act until neither contact slips. Solving the impulse equations together with the wheel's angular momentum gives exit speed, spin and the wheel's RPM drop in one step:

• Wheel: I·(ω₀ − ω₁) = r_w·J₁ − τ_motor·t_contact
• Ball: m·v = J₁ + J₂, k·m·r·ω_b = J₁ − J₂
• No slip at the end: v ± r·ω_b = contact surface speed

A heavy wheel on a hood gives v ≈ ½ of wheel surface speed. A light wheel gives less because it slows down during contact. A slick hood lets the ball slide, so it leaves slower with more spin.

2 · Compression

Compression sets grip and losses. Too little and the ball slips on the wheel (grip falls off fast below about 5% of ball diameter). Too much and energy goes into squashing the ball and the wheel, the contact force climbs and the flywheel stalls. Ball and wheel materials set both curves. The efficiency readout shows the combined effect.

3 · Flight

RK4 integration at 2 ms steps with gravity, quadratic drag ½ρC_dAv² and Magnus lift ½ρC_LAv², where C_L = 1/(2 + 1/S) and S = rω/v. Backspin lifts, topspin dives. Spin decays with time constant τ. Perforated balls have weaker, less predictable Magnus lift, so the default strength is reduced.

4 · HIVE geometry

From the BIOBUZZ manual (V1, Fig. 9-8 to 9-11): pivot 43.95 in above the tiles, upward CELL opening from 53.5 in to 65.6 in, HIVE tilted 30°, CELL opening 14 in tall in this view and 12 in deep. The opening faces away from the pivot, up and out at 30°. A shot scores when the ball's center crosses the opening with a full ball radius of clearance from both lips while moving into the CELL. Manual dimensions are ±1 in.

5 · Getting to 1:1

The physics is first-principles, but real wheels, worn balls and printed hoods vary. Fire one test shot onto flat floor, measure the landing distance, and use Calibrate to a real shot. That one number lines the sim up with your robot. Re-check if you change wheels, compression or the hood.

Defaults

The tool opens on an example shooter: 72 mm wheel, two goBILDA 5203 6000 RPM motors (1.47 kg·cm stall each) at 1:1, pollen, overhand hood. Wheel mass and hood details are typical values, not measurements. Enter your own robot's numbers, then calibrate with one real shot. Your settings are saved in your browser only.