Sharon M. Swartz

THE ‘LAW OF BONE TRANSFORMATION’: A CASE OF CRYING WOLFF?

Transformation der Knochen, describing in full his understanding of the link between mechanical loading and bone form, developed from many years of investigation (Wolff, 1868, 1869, 1870, 1874, 1884a, b, 1891, 1892). T h e basis of the work was Wolffs general theory of bone transformation : Every change in the.. . function of a bone.. . is followed by certain definite changes in.. . internal structure and external conformation in accordance with mathematical laws. (Treharne, 198 I ) .

Bone modeling during growth: dynamic strain equilibrium in the chick tibiotarsus.

SummaryBone loading was quantified, usingin vivo strain recordings, in the tibiotarsus of growing chicks at 4,8, 12, and 17 weeks of age. The animals were exercised on a treadmil at 35% of their maximum running speed for 15 minutes/day.In vivo bone strains were recorded at six sites on the tibiotarsus. Percentages of the bones length and a percentage of top running speed were used to define functionally equivalent sites on the bone, and a consistent exercise level over the period of growth was studied. The pattern of bone strain defined in terms of strain magnitude, sign, and orientation remained unchanged from 4–17 weeks of age, a period when bone mass and length increased 10-fold and threefold, respectively. Our findings support the hypothesis that bones model (and remodel) during growth to achieve and maintain a similar distribution of dynamic strains at functionally equivalent sites. Because strain magnitude and sign (tensile versus compressive) differed among recording sites, these data also suggest that cellular responses to strain-mediated stimuli differ from site to site within a bone.

Aeromechanics of Membrane Wings with Implications for Animal Flight

5. The lift and drag coefficients were measured for wings of varying aspect ratio, compliancy, and prestrain values. In addition, the static and dynamic deformations of compliant membrane wings were measured using stereo photogrammetry. A theoretical model for membrane camber due to aerodynamic loading is presented, indicating that the appropriate nondimensional parameter describing the problem is a Weber number that compares the aerodynamic load to the membrane elasticity. Excellent agreement between the theory and experiments is found. Measurements of aerodynamic performance show that, in comparison with rigid wings, compliant wings have a higher lift slope, maximum lift coefficients, and a delayed stall to higher angles of attack. In addition, they exhibit a strong hysteresis botharoundazeroangleofattackaswellasaroundthestallangle.Unsteadymembranemotionswerealsomeasured, anditisobservedthatthe membranevibrateswithaspatialstructure thatisclosely relatedto thefreeeigenmodesof themembraneundertensionandthattheStrouhalnumberatwhichthemembranevibratesriseswiththefreestream velocity, coinciding with increasing multiples of the natural frequency of the membrane.

Quantifying the complexity of bat wing kinematics

Body motions (kinematics) of animals can be dimensionally complex, especially when flexible parts of the body interact with a surrounding fluid. In these systems, tracking motion completely can be difficult, and result in a large number of correlated measurements, with unclear contributions of each parameter to performance. Workers typically get around this by deciding a priori which variables are important (wing camber, stroke amplitude, etc.), and focusing only on those variables, but this constrains the ability of a study to uncover variables of influence. Here, we describe an application of proper orthogonal decomposition (POD) for assigning importances to kinematic variables, using dimensional complexity as a metric. We apply this method to bat flight kinematics, addressing three questions: (1) Does dimensional complexity of motion change with speed? (2) What body markers are optimal for capturing dimensional complexity? (3) What variables should a simplified reconstruction of bat flight include in order to maximally reconstruct actual dimensional complexity? We measured the motions of 17 kinematic markers (20 joint angles) on a bat (Cynopterus brachyotis) flying in a wind tunnel at nine speeds. Dimensional complexity did not change with flight speed, despite changes in the kinematics themselves, suggesting that the relative efficacy of a given number of dimensions for reconstructing kinematics is conserved across speeds. By looking at subsets of the full 17-marker set, we found that using more markers improved resolution of kinematic dimensional complexity, but that the benefit of adding markers diminished as the total number of markers increased. Dimensional complexity was highest when the hindlimb and several points along digits III and IV were tracked. Also, we uncovered three groups of joints that move together during flight by using POD to quantify correlations of motion. These groups describe 14/20 joint angles, and provide a framework for models of bat flight for experimental and modeling purposes.

Wake structure and wing kinematics: the flight of the lesser dog-faced fruit bat, Cynopterus brachyotis

SUMMARY We investigated the detailed kinematics and wake structure of lesser dog-faced fruit bats (Cynopterus brachyotis) flying in a wind tunnel. High speed recordings of the kinematics were conducted to obtain three-dimensional reconstructions of wing movements. Simultaneously, the flow structure in the spanwise plane perpendicular to the flow stream was visualized using time-resolved particle image velocimetry. The flight of four individuals was investigated to reveal patterns in kinematics and wake structure typical for lower and higher speeds. The wake structure identified as typical for both speed categories was a closed-loop ring vortex consisting of the tip vortex and the limited appearance of a counter-rotating vortex near the body, as well as a small distally located vortex system at the end of the upstroke that generated negative lift. We also investigated the degree of consistency within trials and looked at individual variation in flight parameters, and found distinct differences between individuals as well as within individuals.

Allometric patterning in the limb skeleton of bats: Implications for the mechanics and energetics of powered flight

Allometric analysis was employed to compare linear dimensions of forelimb and hindlimb bones (humeri, radii, third and fifth metacarpals, third and fifth manual phalanges, femora, and tibiae) of 227 species of bats and 105 species of nonvolant mammals of varying degrees of phylogenetic affinity to bats. After accounting for body size, all forelimb bones are longer in bats than in nonvolant species, with the exception of humeri and radii of a few highly arboreal primates. Hindlimb bones are generally, but not uniformly, shorter in bats than in other mammals. For the humerus, radius, and metacarpals, midshaft diameters are greater in bats than in their comparably sized relatives. Proximal phalangeal midshaft diameters are statistically indistinguishable from those of other mammals, and distal phalanges show significantly reduced outer diameters. The pattern of relative reduction in wing bone diameters along the wings proximodistal axis parallels the reduction in bone mineralization along the same axis, and a similar pattern of change in cortical thickness from the smallest wall thicknesses among mammals in the humerus and radius to the greatest wall thicknesses among mammals in the phalanges. The combination of altered cross‐sectional geometry and mineralization appears significantly to reduce the mass moment of inertia of the bat wing relative to a theoretical condition in which elongated bones preserve primitive mammalian mineralization levels and patterns of scaling of long bone diameters. This intercorrelated suite of skeletal specializations may significantly reduce the inertial power of flight, contributing significant energetic savings to the total energy budgets of the only flying mammals. J. Morphol. 234: 277–294, 1997.

Kinematics of slow turn maneuvering in the fruit bat Cynopterus brachyotis

SUMMARY Maneuvering abilities have long been considered key factors that influence habitat selection and foraging strategies in bats. To date, however, very little experimental work has been carried out to understand the mechanisms that bats use to perform maneuvers. In the present study, we examined the kinematics of slow-speed turning flight in the lesser short-nosed fruit bat, Cynopterus brachyotis, to understand the basic mechanics employed to perform maneuvers and to compare them with previous findings in bats and other flying organisms. Four individuals were trained to fly in L-shaped flight enclosure that required them to make a 90 deg. turn midway through each flight. Flights were recorded with three low-light, high-speed videocameras, allowing the three-dimensional reconstruction of the body and wing kinematics. For any flying organisms, turning requires changes of the direction of travel and the reorientation of the body around the center of mass to maintain the alignment with the flight direction. In C. brachyotis, changes in body orientation (i.e. heading) took place during upstroke and preceded the changes in flight direction, which were restricted to the downstroke portion of the wingbeat cycle. Mean change in flight direction was significantly correlated to the mean heading angular velocity at the beginning of the downstroke and to the mean bank angle during downstroke, although only heading velocity was significant when both variables were considered. Body reorientation prior to changes in direction might be a mechanism to maintain the head and body aligned with the direction of travel and, thus, maximizing spatial accuracy in three-dimensionally complex environments.

Wing structure and the aerodynamic basis of flight in bats

Powered, flapping flight has evolved at least four times in the Animal Kingdom: in insects, birds, pterosaurs, and bats. Although some aspects of flight mechanics are probably common to all of these lineages, each of the four represents a unique solution to the challenges of maneuverable flapping flight at animal length scales. Flight is less well documented and understood for bats than birds and insects, and may provide novel inspiration for vehicle design. In particular, bat wings are made of quite flexible bones supporting very compliant and anisotropic wing membranes, and possess many more independently controllable joints than those of other animals. We show that the mechanical characteristics of wing skin play an important role in determining aerodynamic characteristics of the wing, and that motions at the many hand joints are integrated to produce complex and functionally versatile dynamic wing conformations.

Biomechanics of the Bat Limb Skeleton: Scaling, Material Properties and Mechanics

Background/Aims: Wing skeletons of bats are uniquely specialized for flight, reflecting both evolutionary history and the need to maintain structural integrity while generating aerodynamic forces. Methods: We analyzed the anatomical structure of bat wing skeletons in the context of scaling patterns relative to other mammals, material properties and the mechanical function of the wing bones during flight. Results: Compared with nonvolant mammals, the bones of the bat forelimb are elongated, even after correcting for shared phylogenetic history. Bats have consistently larger-diameter bones in the forelimb than do nonvolant mammals but significantly narrower hindlimb bones. Mineralization in the cortical bone of wings is lower than in the long bones of other adult mammals, with a proximodistal gradient of decreasing mineralization. The distal phalanges have only a small amount of mineralized tissue underlying the articular cartilage. Loads required to elicit a 10% length deflection in the wing bones of Glossophaga soricina varied approximately 50-fold along the wing and flexural stiffness nearly 200-fold. Commensurate with low mineralization and flexural stiffness, bat bones experience extraordinarily high bending strains during flight. Conclusion: Bat limb skeletons share features with other mammals and possess specialized characteristics, mostly related to the mechanical demands of flight.

Design and characterization of a multi-articulated robotic bat wing

There are many challenges to measuring power input and force output from a flapping vertebrate. Animals can vary a multitude of kinematic parameters simultaneously, and methods for measuring power and force are either not possible in a flying vertebrate or are very time and equipment intensive. To circumvent these challenges, we constructed a robotic, multi-articulated bat wing that allows us to measure power input and force output simultaneously, across a range of kinematic parameters. The robot is modeled after the lesser dog-faced fruit bat, Cynopterus brachyotis, and contains seven joints powered by three servo motors. Collectively, this joint and motor arrangement allows the robot to vary wingbeat frequency, wingbeat amplitude, stroke plane, downstroke ratio, and wing folding. We describe the design, construction, programing, instrumentation, characterization, and analysis of the robot. We show that the kinematics, inputs, and outputs demonstrate good repeatability both within and among trials. Finally, we describe lessons about the structure of living bats learned from trying to mimic their flight in a robotic wing.