From Studying Real Hummingbirds to Designing Hummingbird-Like Robots—A Literature Review <s> V. MORPHOLOGY OF WINGS AND GEOMETRIC SIMILARITY <s> By combining appearance and behavior in animals with physical laws, we can get an understanding of the adaptation and evolution of various structures and forms. Comparisons can be made between animal bodies and various technical constructions. Technical science and theory during the latest decades have resulted in considerable insight into biological adaptations, but studies on structures, forms, organs, systems, and processes in the living world, used in the right way, have also aided the engineer in finding wider and better solutions to various problems, among them in the design of micro-air vehicles (MAVs). In this review, I discuss the basis for flight and give some examples of where flight engineering and nature have evolved similar solutions. In most cases technology has produced more advanced structures, but sometimes animals are superior. I include how different animals have solved the problem of producing lift, how animal wings meet the requirements of strength and rigidity, how wing forms are adapted to various flight modes, and how flight kinematics are related to flight behavior and speed. The dynamics of vorticity is summarized. There are a variety of methods for the determination of flight power; it has been estimated adequately by lifting-line theory, by physiological measurements, and from mass loss and food intake. In recent years alternative methods have been used, in which the mechanical power for flight is estimated from flight muscle force used during the downstroke. Refinements of these methods may create new ways of estimating flight power more accurately. MAVs operate at the same Reynolds numbers as large insects and small birds and bats. Therefore, studies on animal flight are valuable for MAV design, which is discussed here. J. Morphol. 252:52–81, 2002. © 2002 Wiley-Liss, Inc. <s> BIB001 </s> From Studying Real Hummingbirds to Designing Hummingbird-Like Robots—A Literature Review <s> V. MORPHOLOGY OF WINGS AND GEOMETRIC SIMILARITY <s> Lift production is constantly a great challenge for flapping wing micro air vehicles (MAVs). Designing a workable wing, therefore, plays an essential role. Dimensional analysis is an effective and valuable tool in studying the biomechanics of flyers. In this paper, geometric similarity study is firstly presented. Then, the ratio is defined and employed in wing performance estimation before the lumped parameter is induced and utilized in wing design. Comprehensive scaling laws on relation of wing performances for natural flyers are next investigated and developed via statistical analysis before being utilized to examine the wing design. Through geometric similarity study and statistical analysis, the results show that the aspect ratio and lumped parameter are independent on mass, and the lumped parameter is inversely proportional to the aspect ratio. The lumped parameters and aspect ratio of flapping wing MAVs correspond to the range of wing performances of natural flyers. Also, the wing performances of existing flapping wing MAVs are examined and follow the scaling laws. Last, the manufactured wings of the flapping wing MAVs are summarized. Our results will, therefore, provide a simple but powerful guideline for biologists and engineers who study the morphology of natural flyers and design flapping wing MAVs. <s> BIB002
Hummingbird wings are relatively small, narrow and extremely thin at the leading edge. Thanks to the unique wing shape, the sharp leading edge creates a leading edge flow that produces greater lift. Recent analytical studies have shown that the wing planform of hummingbirds which has more area towards the root (i.e. wing area centroid more towards the root) is very efficient in lift generation production. There are some factors to describe the wing shape such as a lumped parameter, aspect ratio and wing loading. Wing loading and aspect ratio are widely applied to quantify the size and shape of aircraft engineering and in studies of animal flight. In certain researches, relative wing loading (RWL) is utilized to estimate the aerodynamic performance BIB001 . In this paper, a flat and rigid wing in arbitrary form is hypothesized. The wing geometry parameters are presented in Fig. 8 . In this section, wing morphology and geometric similarity are to be studied and discussed. If birds are hypothesized to be a geometric similarity, then weight and lift can be expressed a characteristic length l during the steady-state flight. The entire wing surface A including two wings in vertebrate flyers with projected body area and volume V varies with characteristic length, that is,A ∼ l 2 , V∼ l 3 . In hovering or steady forward flight, it is reasonable to assume that the weight is proportional to lift forceF L . where, C L is the lift coefficient, ρ is the density, v t is the forward flight velocity. where , W is the weight, m is the mass of flyer, g is the gravitational acceleration. Total surface can be written as BIB002 A ∼ l 2 ≈ (m (3)