Phase II Final Report - NASA's Institute for Advanced Concepts

Chapter 3.0 Vehicle Design
3.3 Wing Aerodynamics
unsteady phenomenon, and the forces will vary at every point in a flapping cycle. The thrust and
lift values will vary all along the flapping cycle, and time dependant results must be calculated.
Furthermore, these results of past research can only act as a guideline, but in no way can be used
to predict the result for Entomopter due to its peculiar design and environment.
3.3.3.2.2 Experimental/Computational Results
Since the historical data cannot be used directly for the Entomopter, the best approach for prediction
of results could be obtained from CFD simulations or physical experiments for different
configurations within the design space, and then extrapolate these results for Mars Environment.
For this approach, complete design space exploration would require a huge array of experiments
or CFD runs. A "design-of-experiments" could be performed within the reasonable ranges of
design characteristics/variables to limit the number of experiments/runs required, but this would
still require many experiments in wind tunnel or an enormous CFD effort which was not achievable
within the scope of this NIAC Phase II study. However, a limited amount of CFD effort was
used for this project which can only serve to validate the analytical model, but in no way was
sufficient to help create an empirical model by itself.
3.3.3.2.3 Physics-based Model
Lifting line theory by Prandtl and boundary layer theory explain the physics of conventional
fixed wing flight, and Navier Stokes equations explain the balance of aerodynamic forces. But
these models cannot be directly applied to flapping wing flight, due to the peculiarities of flapping
aerodynamics which remain unaccounted for in fixed wing models. It is pertinent to note
that when relying only upon the principles of conventional fixed wing aerodynamics, an insect
cannot produce sufficient lift to support its weight in Earth's atmosphere, despite using three
degrees of freedom in flight. Hence, an endeavor was made to comprehend the peculiarities of
low Reynolds number flapping wing flight. The following flapping wing peculiarities have been
observed by many researchers, notably C.P Ellington of Cambridge University (who was part of
the original GTRI-DARPA Entomopter team) [77]:
• Formation of a Leading Edge Vortex (LEV)
• Unsteady flow
• Deviation from normal boundary layer theory at much lower angles of attack
• Separation and Wake deformations
Mainly, the leading edge vortex is responsible for much higher lift values and cannot be accommodated
in the domain of conventional aerodynamics. No parametric definition for these leading
edge vortices exists and just the flow visualizations and experimental data by research for
different point solutions is available- but that does not provide any deep insight to these lift generating
phenomenon. Figures 3-115 and 3-116 given below illustrates the formation of leading
edge vortices for flapping wings.
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