Accurate Measurements of Free Flight Drag Coefficients with Amateur Doppler Radar

📝 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.

💡 Analysis

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.

📄 Content

Accurate Measurements of Free Flight Drag Coefficients with Amateur Doppler Radar ELYA COURTNEY, COLLIN MORRIS, AND MICHAEL COURTNEY Michael_Courtney@alum.mit.edu 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.

Keywords: drag coefficient, ballistic coefficient, free flight, wind tunnel, optical chronograph, Doppler radar, physics labs Introduction Drag coefficients and/or the equivalent ballistic coefficients are used to predict projectile trajectories, wind drift, and kinetic energy retained downrange. They are often of academic interest in undergraduate laboratories as students learn more accurate methods to account for air resistance. However, there are few simple and inexpensive experimental approaches to measuring drag coefficients with accuracy of better than 5-10%. Ballistic coefficients provided by the manufacturers are often inaccurate or apply only under ideal conditions. (Courtney and Courtney, 2007; Litz, 2009a; Halloran et al., 2012; Bohnenkamp et al., 2012). Air drag may also depend on the bore from which a projectile is launched (Bohnenkamp et al., 2011). Further, drag coefficients can depend on gyroscopic stability and velocity of a projectile (Courtney and Miller, 2012a, 2012b; McDonald and Algren, 2003). An accurate measurement technique is needed to measure drag coefficients with an accuracy better than 5-10%. For a given instrumental uncertainty, the most accurate approach to measuring drag coefficients is by measuring a near and a far velocity over a specified distance (Courtney et al., 2015; Bailey and Hiatt, 1972). Simple calculations using classical mechanics and the definition of drag coefficients yield the experimental values. Ballistic calculators may be used to yield ballistic coefficients with a given near and far velocity (www.jbmballistics.com ). It has previously been shown that with adequate experimental care and calibration, drag coefficients can be determined to an accuracy of 1- 2% using optical chronographs designed for the sporting market (Courtney et al., 2015). While accurate and inexpensive, this method has disadvantages, including the requirements to place the projectile in a small area passing over the chronographs, to carefully measure the chronograph separation, to calibrate the chronographs daily, and to pay constant attention to other details like skyscreen angles. A new amateur Doppler radar based chronograph has recently come onto the sporting market (www.mylabradar.com ). An early review suggested the feature of recording velocity as a function of distance might prove useful for accurately determining

ballistic

coefficients (https://www.shootingsoftware.com/doppler.htm) . The purpose of this paper is to explore accuracy potential and ease of use in using amateur ballistic radar to experimentally determine projectile drag coefficients.
The method section describes basic use of the radar system, but also focuses on two main analysis options for determining drag and ballistic coefficients: 1) using the velocity at two ranges as Page 1 of 12 Accurate Measurements of Free Flight Drag Coeffici

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