Analytical models of avian flight have previously been used to predict mechanical and metabolic power consumption during cruise. These models are limited, in that they neglect details of wing kinematics, and model power by assuming a fixed or rotary wing (actuator disk) weight support mechanism. Theoretical methods that incorporate wing kinematics potentially offer more accurate predictions of power consumption by calculating instantaneous aerodynamic loads on the wing. However, the success of these models inherently depends on the availability and accuracy of experimental kinematic data. The predictive simulation approach offers an alternative strategy, whereby kinematics are neither neglected nor measured experimentally, but calculated as part of the solution procedure. This thesis describes the development of a predictive tool for simulating avian wingbeat kinematics and wakes. The tool is designed in a modular format, in order to be extensible for future research in the biomechanics community. The primary simulation module is an inverse dynamic avian wing model that predicts aerodynamic forces and mechanical power consumption for given wing kinematics. The model is constructed from previous experimental studies of avian wing biomechanics. Wing motion is defined through joint kinematic time histories, and aerodynamic forces are predicted using blade element momentum theory. Mechanical power consumption at the shoulder joint is derived from both aerodynamic and inertial torque components associated with the shoulder joint rotation rate. An optimisation module is developed to determine wing kinematics that generate aerodynamic loads for propulsion and weight support in given flight conditions, while minimising mechanical power consumption. For minimum power cruise, optimisation reveals numerous local minima solutions that exhibit large variations in wing kinematics. Validation of the model against wind tunnel data shows that optimised solutions capture qualitative trends in wing kinematics with varying cruise speed. Sensitivity analyses show that the model outputs are most affected by the defined maximum lift coefficient and wing length, whereby perturbations in these parameters lead to significant changes in the predicted amount of upstroke wing retraction. Optimised solutions for allometrically scaled bird models show only small differences in predicted advance ratio, which is consistent with field study observations. Accelerating and climbing flight solutions also show similar qualitative trends in wing kinematics to experimental measurements, including a reduction in stroke plane inclination for increasing acceleration or climb angle. The model predicts that both climb angle and climb speed should be greater for birds with more available instantaneous mechanical power. Simulations of the wake using a discrete vortex model capture fundamental features of the wake geometry that have been observed experimentally. Reconstruction of the velocity field shows that this method overpredicts induced velocity in retracting-wing wakes, and should therefore only be applied to extended-wing phases of an avian wingbeat.

The bell-shaped lift distribution (BSLD) wing design methodology advanced by Ludwig Prandtl in 1932 was proposed as providing the minimum induced drag. This study used this method as the basis to analyze its characteristics in two wing formation flight. Of specific interest are the potential efficiency savings and the optimal positioning for formation flight. Additional comparison is made between BSLD wings and bird flight in formation. This study utilized Computational Flow Dynamics (CFD) simulations on a geometric modeling of a BSLD wing, the Prandtl-D glider. The results were validated by modified equations published by Prandtl, by CFD modeling published by others, and by Trefftz plane analysis. For verification, the results were compared to formation flight research literature on aircraft and birds, as well as published research on non-formation BSLD flight. The significance of this research is two part. One is that the BSLD method has the potential for significant efficiency in formation flight. The optimal position for a trailing wing was determined to be partially overlapping the leading wing vortex core. For a BSLD wing these vortices are located inboard from the wingtips resulting in wingtip overlap and have a wider impact downstream than the elliptical lift distribution (ELD) wingtip vortices. A second aspect is that avian research has traditionally been studied assuming the ELD model for bird flight, whereas this study proposes that bird flight would be better informed using the BSLD.