Weapon energy & gyro effects
A kinetic weapon is a flywheel. Its effectiveness comes from the energy stored in that flywheel and how fast it can be delivered through a small contact patch.
Stored energy
Section titled “Stored energy”KE = ½ · I · ω²- I — moment of inertia of the weapon about its spin axis (kg·m²).
- ω — angular velocity (rad/s) =
2π · rpm / 60.
Because energy scales with ω², rpm matters more than mass. A light bar spun fast can out-hit a heavy drum spun slow.1
Moment of inertia (common weapon shapes)
Section titled “Moment of inertia (common weapon shapes)”| Shape | I about spin axis |
|---|---|
| Thin bar, length L, mass m, centered | m·L² / 12 |
| Solid disc, radius R, mass m | ½·m·R² |
| Ring / shell, radius R, mass m | m·R² |
| Two masses m at radius r (asymmetric bar) | 2·m·r² |
Mass concentrated at the tips (bar, ring shell) stores more energy per gram than a solid disc, at the cost of a less rigid structure.1
Tip speed
Section titled “Tip speed”v_tip = ω · RA common design target is a tip speed around 250 mph (~110 m/s), and competitive beetleweights rarely design past 300 mph (~135 m/s). Higher tip speed raises per-hit energy but also stress on the weapon shaft and bearings, gyro effects, and — by reducing bite — the fraction of that energy that actually transfers. Many drivers deliberately run below full speed for most of a match because consistent bite beats raw power.2 Check tip speed with the Bristol Bot Builders or Ember calculator.
Spin-up time
Section titled “Spin-up time”t_spinup ≈ I · ω_target / τ_motor_avgThe motor’s average accelerating torque τ_motor_avg falls as the weapon
approaches free speed. Practically:
- A beetle bar/disc reaching full speed in 1.5–4 s is normal.
- Too much
Ifor the motor → slow spin-up, weapon never recovers between hits. - Too little
I→ fast spin-up but low stored energy; the weapon bounces off.
Match I to the weapon motor so spin-up is fast enough
to re-arm between exchanges.
Gyroscopic precession
Section titled “Gyroscopic precession”A spinning weapon is a gyroscope. When the robot yaws (turns), the weapon’s angular momentum L = I·ω produces a torque at right angles:
τ_precession = L × ω_yawEffects on a horizontal spinner (vertical weapon axis): turning the robot makes it tip / lift a corner. Effects on a vertical spinner (horizontal weapon axis): turning makes the nose pitch up or down.1 Consequences:
- Fast, high-
Iweapons make the robot “walk” or hop when driving. - Mitigations: lower
I, lower rpm, 4WD for a wider stability base, a heavier chassis, or accepting it and driving around it. - A vertical disc’s gyro can help self-righting and keeps the front down.
Energy vs. the opponent
Section titled “Energy vs. the opponent”Delivered energy goes into denting armor, breaking fasteners, and — usefully — throwing the opponent (and often yourself). Newton’s third law: a big hit accelerates both robots. Structure both to survive your own weapon’s reaction.
References
Section titled “References”Footnotes
Section titled “Footnotes”-
Meggiolaro, M. A. RioBotz Combat Robot Tutorial, v2.0, PUC-Rio, 2009 (CC BY-NC-ND) — spinner kinetic energy, moment-of-inertia formulas, spin-up, and gyroscopic effects. ↩ ↩2 ↩3
-
Ping, L., with L. Skotiniotis, I. Talbert & D. Tran. Beetleweights for Dummies (Fall 2025 revision) — builder-maintained beginner guide distributed via the NHRL Discord. Section: Spinning Weapon Design → Maximizing Bite. ↩