Methods for Accurate Free Flight Measurement of Drag Coefficients

TL;DR

This paper presents experimental methods for measuring drag coefficients during free flight with approximately 1% accuracy, analyzing tradeoffs, practical considerations, and error sources affecting measurement precision.

Contribution

It introduces and compares two main experimental approaches for accurate free flight drag coefficient measurement, highlighting their tradeoffs and error sensitivities.

Findings

Using near and far velocities yields about half the uncertainty compared to time-of-flight methods.

Proper experimental design minimizes errors from atmospheric conditions and measurement uncertainties.

Tradeoffs involve balancing flight distance to optimize velocity change and measurement accuracy.

Abstract

This paper describes experimental methods for free flight measurement of drag coefficients to an accuracy of approximately 1%. There are two main methods of determining free flight drag coefficients, or equivalent ballistic coefficients: 1) measuring near and far velocities over a known distance and 2) measuring a near velocity and time of flight over a known distance. Atmospheric conditions must also be known and nearly constant over the flight path. A number of tradeoffs are important when designing experiments to accurately determine drag coefficients. The flight distance must be large enough so that the projectile's loss of velocity is significant compared with its initial velocity and much larger than the uncertainty in the near and/or far velocity measurements. On the other hand, since drag coefficients and ballistic coefficients both depend on velocity, the change in velocity over the flight path should be small enough that the average drag coefficient over the path (which is what is really determined) is a reasonable approximation to the value of drag coefficient at the near and far velocity. This paper considers these tradeoffs as well as practical considerations for obtaining accurate near and far velocity measurements and the impact of different sources of error (velocity, distance, time, atmospheric conditions, etc.) on the resulting accuracy of drag coefficients and ballistic coefficients. For a given level of accuracy of various quantities, the method of using near and far velocities usually produces drag coefficients with about half the uncertainty of the method using a near velocity and time of flight.