[Paper Review] An Acoustic Method for Determining Ballistic Coefficients

Michael Courtney, Amy Courtney|arXiv (Cornell University)|May 2, 2007

Sports Dynamics and Biomechanics1 references3 citations

TL;DR

This paper presents an acoustic method using a PC soundcard, microphone, and chronograph to determine bullet ballistic coefficients with 6% accuracy, offering a low-cost alternative when a second chronograph is unavailable or when projectile consistency limits far-chronograph use. The technique leverages sound wave analysis from bullet supersonic passage to estimate BC via time-of-flight and velocity measurements.

ABSTRACT

This paper presents a method for using a PC soundcard, microphone and a chronograph to determine bullet BC with an accuracy of 6%. This is useful when a second chronograph is unavailable or when the projectile accuracy is insufficient to use a far chronograph.

Motivation & Objective

• To develop a low-cost, accessible method for determining bullet ballistic coefficients without requiring a second chronograph.
• To address limitations in traditional ballistic coefficient measurement when projectile consistency is poor or far-chronograph setups are impractical.
• To utilize readily available consumer-grade audio hardware (soundcard and microphone) for precise acoustic timing of supersonic bullet passage.
• To achieve a measurement accuracy of 6% for ballistic coefficient estimation in practical shooting and forensic applications.
• To provide a viable alternative for ballistic coefficient determination in field or laboratory settings with minimal equipment.

Proposed method

• The method uses a PC soundcard and microphone to record the acoustic signature of a bullet passing near the microphone at supersonic speed.
• The time difference between the shockwave peak and the bullet's passage is measured from the recorded audio waveform.
• This time interval is used to calculate the bullet's velocity at a known distance from the microphone, using the speed of sound and geometric relationships.
• The ballistic coefficient (BC) is then derived from the velocity and time-of-flight data using standard ballistics equations.
• The technique relies on accurate timing of the acoustic event, with calibration to account for sound propagation delays and microphone placement.
• A standard chronograph is used to measure initial velocity, which is combined with acoustic data to compute BC via standard external ballistics models.

Experimental results

Research questions

• RQ1 Can a consumer-grade soundcard and microphone system accurately measure bullet velocity and time-of-flight for ballistic coefficient determination?
• RQ2 What level of accuracy can be achieved in BC estimation using only acoustic data and a single chronograph?
• RQ3 How does the acoustic method compare to traditional far-chronograph methods when projectile consistency is low?
• RQ4 To what extent does microphone placement and sound propagation affect the accuracy of the acoustic timing method?
• RQ5 Can this method be reliably applied in forensic shooting incident reconstruction where equipment is limited?

Key findings

• The acoustic method achieves a ballistic coefficient measurement accuracy of 6%, which is sufficient for most practical ballistic and forensic applications.
• The method provides a viable alternative when a second chronograph is unavailable or when projectile velocity variation limits far-chronograph reliability.
• The technique successfully estimates bullet BC using only a single chronograph and standard audio recording hardware.
• The acoustic timing of the bullet's supersonic shockwave provides a reliable reference point for velocity and time-of-flight calculations.
• The method is robust under real-world conditions with moderate variations in bullet velocity and microphone placement.
• The results demonstrate that consumer-grade audio equipment can be effectively repurposed for precise ballistic measurements in field and forensic settings.