Approximate ballistics formulas for spherical pellets in free flight

The ballistics equations for spherical pellets in free flight are simplified through appropriate scaling of the pellet velocity and pellet distance. Two different drag coefficient curves are averaged to yield a single curve applicable to shot pellets and round balls. The resulting S-shaped drag coefficient curve is approximated by three straight-line segments. The scaled ballistics equations are then solved exactly and simple formulas are found for the velocity and flight time with respect to trajectory distance. The formulas are applicable to spherical shot pellets and round balls of any composition under any atmospheric conditions. The formulas are amenable to quick and easy computation and may also serve as an aid in understanding and comparing black-box ballistics calculators. For shotshell ballistics, an important assumption in the present investigation is that the pellets are moving as single, free spheres and not as a dense cloud or in a shot column, in particular, the pellets are not interacting during flight. Therefore, the formulas are most appropriate for single round balls, for large shot sizes, and for pellets of small shot size fired from open chokes. The formulas are clear and accessible, and can be implemented by military or law enforcement personnel as well as hunters and shooters. This work differs from previous investigations in that accurate ballistics formulas are derived for spherical projectiles of shotguns and muzzleloaders using realistic drag coefficients.

IMPROVEMENT TO THE EVAPORATION DUCT MODEL BY INTRODUCING NONLINEAR SIMILARITY FUNCTIONS IN STABLE CONDITIONS

Modified refractivity (M) profile is an important parameter to describe the atmospheric refraction environment,as well as a key factor in uniquely evaluating electromagnetic propagation effects.In order to improve the model-derived M profile in stable (especially very stable) conditions,three nonlinear similarity functions,namely BH91,CB05,SHEBA07,are introduced in this paper to improve the original Babin_V25 model,and the performances of these modified models are verified based on the hydrometeorological observations from tower platforms,which are finally compared with the original Babin_V25 model and Local_HYQ92 model.Results show that introducing nonlinear similarity functions can significantly improve the model-derived M profile;especially,the newly developed SHEBA07 functions manage to reduce the predicted root mean square (rms) differences of M and M slope (for both 0-5m and 5-40m) by 64.5%,16.6%,and 60.4%,respectively in stable conditions.Unfortunately,this improved method reacts little on the evaporation duct height;in contrast,Local_HYQ92 model is capable of reducing the predicted rms differences of M,M slope (for both 0-5m and 5-40m),and evaporation duct height by 76.7%,40.2%,83.7%,and 58.0% respectively.Finally,a new recommendation is made to apply Local_HYQ92 and Babin_SHEBA07 in very stable conditions considering that M slope is more important than evaporation duct height and absolute M value in uniquely determining electromagnetic propagation effects.

Closed-loop flow control of an ultra-compact serpentine inlet based on nondimensional model

Ultra-compact serpentine inlet faces serve inlet-engine compatibility issues due to flow distortion.To ensure inlet-engine compatibility over a wide range of Mach number,novel active flow control techniques with the ability of being opened or adjusted as needed draw many attentions in recent years.In this paper,a feedback control system was developed based on the method of microjet blowing.The proposed system includes a pressure adjusting valve to adjust the control effort,a dynamic pressure sensor to sense the inlet distortion intensity,a signal processing instrument to calculate the Root-Mean-Squared(RMS)pressure,and a controller to implement feedback control.To achieve high quality closed-loop controls at dynamic conditions,a novel nondimensional feedback method was developed.The advantage of this nondimensional method was validated at both off-design and arbitrarily changing Mach number conditions.With a sectional PI control law,the RMS control error reduced more than 56%at arbitrary changing conditions.Works in this paper also showed that the dynamics of this nondimensional system can be simplified as a stable second-order overdamped system.