Archery Ballistics Study | Sound Testing

Overview and Test Facility

Accurate measurement of arrow fly-by noise requires strict control of environmental variables. Testing was conducted in the Arrow Sound Testing Chamber (ASTC), a custom shoot-through facility designed to isolate the arrow's in-flight noise from external sounds (wind, wildlife, traffic, aircraft) and from noises generated by the bow or arrow impact.

The ASTC achieves an average noise floor of 22 dB(Z) across 500 Hz–31,500 Hz, with validated free-field acoustic conditions down to 250 Hz (per ISO 26101:2017). Reverberation times are low (0.03 s RT60, T20) from 500 Hz to 8 kHz (ISO 3382-1).

To confirm the chamber does not affect measurement accuracy, a control test was run both outdoors and within the ASTC. After adjusting for ground reflections, measurements matched within ±0.5 dB, confirming the reliability of the facility.

Arrow Fly-By Measurement Setup

Arrows were shot through the ASTC so they passed a calibrated measurement microphone at a fixed distance of 1 meter. Stringlines, forming a 50 mm-wide window, ensured a consistent flight path. Any contact with the stringlines was visually detected and that shot was repeated, resulting in all valid measurements occurring between 975 mm and 1025 mm from the microphone. This constrains theoretical sound level variation to ±0.2 dB (inverse-square law).

Equipment

• Microphone: Earthworks M30 Measurement Microphone (Class 1)
• Audio Interface: RME Babyface Pro FS
• Software: Audio and Acoustical Response Analysis Environment (AARAE) in MATLAB
• Calibration: ¼″ microphone calibrator (94 dB @ 1 kHz)
• Velocity: Garmin C1 Pro Chronograph

Arrow Testing Procedure

• 38 arrow configurations tested over three days
• Each configuration shot repeatedly until two valid, stringline-cleared measurements were obtained
• All arrows initially shot from a Hoyt Nitrum (74 lbs, 28.5″ draw)
• Average test velocity: 280.0 fps across all configs
• Additional velocities gathered using 60 lb Elite Ritual 35 and 80 lb Hoyt Alpha (all at 28.5″ draw)
• Each bow tuned to produce a bullet hole through paper with standard reference arrow

Audio Processing and Loudness Calculation

1. Calibrate microphone input using the ¼″ calibrator
2. Trim audio to a 0.2 second window to exclude bow noise and target impact
3. Apply a Tukey window (tapered cosine, ratio 0.2) for smooth fade-in and fade-out
4. Screen each recording by ear and omit any with audible background noise
5. Apply 1/3-octave band FFT with IEC Class 0 filter slopes
6. Compute L(Z)max values (Fast, 125 ms time weighting) from 500 Hz–31,500 Hz
7. Log-average valid shots per arrow configuration in each 1/3-octave band
8. Apply Deer-Weighting and Human-Weighting: Each band adjusted per white-tailed deer auditory threshold (Heffner, 2010) to reflect perceived “loudness” for deer, whose hearing is centered one octave higher than humans. In addition, A-Weighting was applied to each band to reflect perceived loudness for humans.
9. 95% confidence intervals were calculated for each band's SPL for each arrow configuration using the t-distribution with degrees of freedom equal to the sample size minus one, to appropriately reflect the increased uncertainty associated with small sample sizes.
10. For bands where the lower 95% confidence interval was not defined (i.e., negative in the linear domain), a value of –120 dB SPL was substituted for the purposes of weighted summation. These cases are marked as 'N/A' in band-specific CI reporting.
11. Sum the weighted bands logarithmically to yield a single-number perceived loudness metric