Projectile linear theory for aerodynamically asymmetric projectiles
Dykes, John William
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Currently, there are few analytical tools within the ballistics community to aid in the design and performance evaluation of aerodynamically asymmetric projectiles. The scope of this thesis is to (1) create analytical tools that are capable of quantifying aerodynamically asymmetric projectile performance, (2) demonstrate the ability of these models to accurately account for aerodynamic asymmetries, and (3) gain insight into the flight mechanics of several aerodynamically asymmetric projectiles. First, a six-degree-of-freedom (6 DOF) flight dynamic model, which uses a point-force lifting-surface aerodynamic model, was developed to replicate flight characteristics observed from measured results of common projectiles. A quasi-linear flight dynamic model was then created using the machinery of Projectile Linear Theory (PLT). From this, flight dynamic stability models were developed for linear time-invariant (LTI) and linear time-periodic (LTP) systems. Dynamic simulation and stability trade studies were then conducted on asymmetric variants of 4-finned, 3-finned, 2-finned, and hybrid projectile configurations. First, stability of symmetric projectiles are validated and show that the classical and extended PLT model yielded identical results. Results show that aerodynamic asymmetries can sometimes cause instabilities and other times cause significant increase in dynamic mode damping and increase/decrease in mode frequency. Partially asymmetric (single plane) configurations were shown to cause epicyclic instabilities as the asymmetries became severe, while fully asymmetric (two plane) can grow unstable in either the epicyclic modes or the roll/yaw mode. Another significant result showed that the LTP stability model is able to capture aerodynamic lifting-surface periodic affects to evaluate dynamic stability requirements for asymmetric projectiles.