WOOFWATT

The physics of a bark

Sound is alternating pressure. An energy harvester must intercept part of the wave, turn diaphragm motion into electrical charge, rectify that alternating signal, and store more energy than the circuit leaks. The logarithmic decibel scale makes loud sound feel impressive while still representing surprisingly little total power.

Core equations

A useful upper-bound check

If 95 dB SPL were measured 1 m from a roughly spherical source, the inferred acoustic power would be P = 4πr²I, or about 0.040 W while the bark is occurring. A 0.5 s bark would contain about 0.020 J of radiated sound. A 100 cm² collector at that distance geometrically intercepts only about 0.08% of the sphere before conversion losses. That leaves roughly 1.6 µJ at 10% conversion efficiency.

Why measured SPL must be local

• Specify dB SPL at the mouth of the collector, not somewhere else in the room.
• Record A-weighted level for human exposure context, but also capture unweighted or Z-weighted spectral data for engineering.
• Use the peak and time-integrated waveform; a single maximum dB number cannot determine energy.
• Measure orientation and distance. A dog is neither an isotropic speaker nor a calibrated signal generator.

Literal acoustic harvester

The most credible build is a passive acoustic front end feeding piezoelectric diaphragms, followed by a low-leakage rectifier, storage capacitor, voltage monitor, and threshold-switched load. A separately powered measurement channel proves what the harvester itself contributes.

4.1 Acoustic front end

• Use a flared horn or shallow parabolic mouth with 200–400 cm² physical aperture. Its purpose is pressure concentration and directionality, not magic amplification of total energy.
• Split the horn into three interchangeable Helmholtz cavities targeting roughly 350, 700, and 1,400 Hz. Final frequencies should come from an actual bark spectrum.
• Mount a flexible diaphragm at each cavity's high-pressure region. Candidate transducers: PVDF film for sensitivity, piezo bimorphs for strain, or metal-backed piezo discs for low cost.
• Isolate the enclosure from floor vibration during acoustic tests. Otherwise footsteps can masquerade as harvested sound.

Helmholtz starting point

For a cavity with neck area A_n, effective neck length L_eff, cavity volume V, and sound speed c, start with f_H = c/(2π) · √(A_n / (V · L_eff)). Treat this as an initial geometry estimate; the diaphragm compliance, losses, end correction, and enclosure walls shift the real resonance.

4.2 Transducer and rectifier

The Texas Instruments BQ25570 is designed for high-impedance energy-harvesting sources, with a 600 mV cold-start requirement and continued harvesting from inputs as low as 100 mV under specified conditions. A piezo source still needs rectification, adequate open-circuit voltage, and an impedance match. The IC is a candidate, not a guarantee.

Buildable prototype: BarkSpark Mark I

The first prototype should prove energy transfer with controlled speaker tests, then passively observe naturally occurring barks. Its target is not continuous operation; its target is a defensible capacitor-voltage rise attributable to acoustic excitation.

Mechanical specification

Electrical specification

Illustrative bill of materials

Control system and data model

The bark detector is a user-interface channel, not an energy meter. Run it on a separate low-voltage supply. Its job is to classify events, avoid false triggers, and coordinate a calm-reward sequence.

State machine

Bark-event record

Pseudocode

on_bark(event):
  if event.confidence < 0.85: return
  if daily_bark_rate > welfare_limit: enter_lockout()
  E = 0.5 * C * (V_after^2 - V_before^2) - leakage_baseline
  acoustic_joules += max(E, 0)
  show_invitation_only_if_cooldown_complete()

on_motion(sample):
  kinetic_wh += sample.volts * sample.amps * sample.dt / 3600
  stop_if_guard_open_or_temperature_high()

on_motion_end():
  wait_for_quiet(15 seconds)
  release_one_reward_event()

Safety, welfare, and failure modes

Non-negotiable design constraints

• Nothing attaches to the dog's muzzle, throat, collar, or body for acoustic collection.
• No shock, ultrasonic feedback, startling spray, punishment, restraint, forced treadmill use, or closed-loop sound amplification.
• The dog controls participation and can leave immediately. Human supervision is required for kinetic machinery.
• Rewards occur after quiet behavior, not immediately after barking. Apply rate limits and cooldowns.
• Guard all pinch points, gears, belts, electrical conductors, hot parts, and stored-energy components.

Failure mode and effects analysis

Behavior note

The ASPCA recommends first identifying the function of the bark; different causes require different responses. Persistent barking when alone can accompany separation anxiety, particularly when combined with pacing, destruction, elimination, depression, or escape behavior. The engineering project should never displace that assessment.

Worked calculations

A.1 Reference acoustic scenario

Inputs: L_p = 95 dB; effective area A = 0.010 m²; end-to-end efficiency η = 0.10; bark duration t = 0.50 s.

A.2 Close/resonant scenario

Inputs: L_p = 105 dB; A = 0.020 m²; η = 0.20; t = 0.70 s.

A.3 Capacitor threshold

For C = 0.010 F charged from 0 to 3.3 V, E = 0.5 × 0.010 × 3.3² = 0.05445 J. If 70% of the close/resonant 88.54 µJ reaches storage, net energy is 61.98 µJ per bark. Ideal count = 0.05445 / 0.00006198 = 879 barks. Real count will be higher because leakage grows with time and because real barks vary.

A.4 Kinetic scenario

For F = 5 N, v = 1.5 m/s, η = 0.50: P = F · v · η = 3.75 W. For 20 minutes: E = 3.75 × 20/60 = 1.25 Wh. This scenario is illustrative and must be adjusted to the dog's size, condition, interest, and veterinary guidance.

A.5 Measurement uncertainty

Capacitor energy depends on V squared, so voltage uncertainty matters more at low voltage. Propagating first-order uncertainty for E = 0.5 C(V₂² − V₁²) gives contributions from capacitance tolerance, ADC gain, divider tolerance, noise, and timing of before/after samples. Calibrate C directly, use precision resistors, record temperature, and calculate a blank-trial distribution.