The effect of body size on the wing movements of pteropodid bats, with insights into thrust and lift production

In this study we compared the wing kinematics of 27 bats representing six pteropodid species ranging more than 40 times in body mass ( M b=0.0278–1.152 kg), to determine whether wing posture and overall wing kinematics scaled as predicted according to theory. The smallest species flew in a wind tunnel and the other five species in a flight corridor. Seventeen kinematic markers on the midline and left side of the body were tracked in three dimensions. We used phylogenetically informed reduced major axis regression to test for allometry. We found that maximum wingspan ( b max) and maximum wing area ( S max) scaled with more positive allometry, and wing loading ( Q s) with more negative allometry ( b max∝ M b0.423; S max∝ M b0.768; Q s∝ M b0.233) than has been reported in previous studies that were based on measurements from specimens stretched out flat on a horizontal surface. Our results suggest that larger bats open their wings more fully than small bats do in flight, and that for bats, body measurements alone cannot be used to predict the conformation of the wings in flight. Several kinematic variables, including downstroke ratio, wing stroke amplitude, stroke plane angle, wing camber and Strouhal number, did not change significantly with body size, demonstrating that many aspects of wing kinematics are similar across this range of body sizes. Whereas aerodynamic theory suggests that preferred flight speed should increase with mass, we did not observe an increase in preferred flight speed with mass. Instead, larger bats had higher lift coefficients ( C L) than did small bats ( C L∝ M b0.170). Also, the slope of the wingbeat period ( T ) to body mass regression was significantly more shallow than expected under isometry ( T ∝ M b0.180), and angle of attack (α) increased significantly with body mass [α∝log( M b)7.738]. None of the bats in our study flew at constant speed, so we used multiple regression to isolate the changes in wing kinematics that correlated with changes in flight speed, horizontal acceleration and vertical acceleration. We uncovered several significant trends that were consistent among species. Our results demonstrate that for medium- to large-sized bats, the ways that bats modulate their wing kinematics to produce thrust and lift over the course of a wingbeat cycle are independent of body size. * A hori z : net forward acceleration for the wingbeat cycle (m s–2) AR : aspect ratio (dimensionless) A vert : net vertical acceleration for the wingbeat cycle (m s–2) b max : maximum wingspan (m) b min : minimum wingspan (m) C L : coefficient of lift (dimensionless) c max : maximum wing chord (m) COM : center of mass d.f. : degrees of freedom DLT : direct linear transformation g : acceleration of gravity (9.81 m s–2) GLM : generalized linear model M b : body mass (kg) Q s : wing loading (N m–2) RMA : reduced major axis S : wing area (m2) S max : maximum wing area (m2) St : Strouhal number T : wingbeat period (s) T down : downstroke duration (s) V horiz : forward velocity (m s–1) V vert : vertical velocity (m s–1) V wrist : velocity of the wrist in the x g– z g plane at the time of max wingspan (m s–1) x b : body-centered x dimension x g : global x dimension y b : body-centered y dimension y g : global y dimension z b : body-centered z dimension z g : global z dimension α : angle of attack at mid-downstroke (deg; α=α1+α2) α1 : angle of wing chord to horizontal at mid-downstroke (deg) α2 : angle of wrist trajectory to oncoming flow at mid-downstroke (deg) β : stroke plane angle (deg) ρ : density of air (1.204 kg m–3) τ : downstroke ratio (dimensionless) φ : stroke amplitude (deg)