Accurate Measurements of Free Flight Drag Coefficients with Amateur Doppler Radar

TL;DR

This paper demonstrates that inexpensive amateur Doppler radar can accurately measure free flight drag coefficients of projectiles, offering advantages over optical chronographs in ease of use, accuracy, and safety, with applications in physics and ballistics.

Contribution

It introduces a cost-effective Doppler radar system for precise drag coefficient measurements, expanding accessibility and capabilities beyond traditional optical methods.

Findings

Drag coefficients determined with 1% accuracy in many cases

Radar system detects projectile tumbling and instability

Method is safer and easier than optical chronographs

Abstract

In earlier papers, techniques have been described using optical chronographs to determine free flight drag coefficients with an accuracy of 1-2%, accomplished by measuring near and far velocities of projectiles in flight over a known distance. Until recently, Doppler radar has been prohibitively expensive for many users. This paper reports results of exploring potential applications and accuracy using a recently available, inexpensive (< $600 US) amateur Doppler radar system to determine drag coefficients for projectiles of various sizes (4.4 mm to 9 mm diameter) and speeds (M0.3 to M3.0). In many cases, drag coefficients can be determined with an accuracy of 1% or better if signal-to-noise ratio is sufficient and projectiles vary little between trials. It is also straightforward to design experiments for determining drag over a wide range of velocities. Experimental approaches and limitations are described. Overall, the amateur radar system shows greater accuracy, ease of use, and simplicity compared with optical chronographs. Doppler radar has advantages of working well with less accurate projectiles without putting equipment at risk of projectile impact downrange. The system can also detect phenomena that optical chronographs cannot, such as projectile instability resulting in tumbling in flight. This technology may be useful in introductory physics labs, aerodynamics labs, and for accurately determining drag and ballistic coefficients of projectiles used in military, law enforcement, and sporting applications. The most significant limitations are reduced signal-to-noise with smaller projectiles (< 5 mm diameter) and inability to detect projectiles more than 100 m down range.