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Aerodynamic power and mechanical efficiency of bat airframes using a quasi-steady model

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Abstract

Previous bat aerodynamic power models are refined by (1) varying the value of wing profile drag with lift coefficient, which varies with both flight speed and Reynolds number, (2) allowing for the aerodynamic cleanliness of head, body, ears and tail in calculating parasitic drag values at various speeds and according to airframe type, (3) incorporating models of wingbeat amplitude and frequency in the power calculations, and, (4) upgrading the allometric, phylogenetically corrected relationship between basal metabolic rate and body mass using data from 98 bat species. The fidelity of the aerodynamic power model is assessed using published wind tunnel data on a bat in steady glide. By comparing empirical published metabolic power (P met) values with values derived using the new aerodynamic model, we update estimates of in-flight musculoskeletal mechanical efficiency (η) for the airframes of eight bat species at steady level flight speeds. Furthermore, we calculate the increase in η at high speeds. The bats assessed range in body mass from 0.01 to 1 kg, and the comparison covers the speed range normally used by free-flying bats during their excursions. At their best endurance flight speeds (V end), η = 1.52 Ln (m bat) + 11.44 (%). At speeds > V end, η = η@ Vend + 1.3 (V−V end) (%). These equations yield accurate P met estimates for flight speeds within the range used for the steady level flight.

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Abbreviations

AR :

Aspect ratio

B :

Span (m)

C D :

Three-dimensional lifting surface drag coefficient = 2 D/ρ/S ref/V 2

C d :

Two-dimensional airfoil section drag coefficient

C L :

Three-dimensional lifting surface lift coefficient = 2 L/ρ/S ref/V 2

C l :

Two-dimensional airfoil lift coefficient

D :

Drag (N)

f w :

Wingbeat frequency (Hz)

g :

Acceleration due to gravity = 9.81 m s−2

L :

Lift (N)

m :

Bat mass (kg)

P :

Power (W)

q :

Dynamic pressure = ½ ρV 2 (N m−2)

Re :

Reynolds number

R :

Pearson’s correlation coefficient

S :

Area of a lift or drag generating surface of body (m2)

T :

Time (s)

t :

Thickness, e.g. body thickness (m)

V :

Bat flight speed (m s−1)

v :

Local airflow velocity (m s−1)

w :

Width, e.g. body width

η :

Mechanical efficiency (%)

θ:

Wingbeat amplitude—empirical above or below the body axis reference dorsal plane (degrees)

ρ:

Air density = 1.2256 kg m−3 at sea level and 15 °C

ω:

Wingbeat angular velocity (rad s−1)

(1 + δ):

Induced drag factor accounting for effect of non-elliptical wing spanwise lift distribution

body:

Body

dot:

Acceleration

ear:

Ear

head:

Head

h/t:

Tail membrane (uropatagium)

ind:

Indicated

max:

Maximum condition

mech:

Mechanical

pro:

Profile

para:

Parasitic

ref:

Reference condition

sh:

Shoulder

true:

True airspeed

w:

Wing

wd:

Wing disk (area)

wr:

Wrist

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Acknowledgments

We wish to thank the Western Australian Department of Parks and Wildlife for providing laboratory facilities used during the preparation of this manuscript. Information on branch lengths used to calculate the distance matrix for the phylogenetic correction of BMR data was provided by Kate Jones (Institute of Zoology, UK).

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Authors and Affiliations

  1. 43 Murray Drive, Hillarys, 6025, Australia

    R. D. Bullen

  2. Department of Parks and Wildlife, Government of Western Australia, PO Box 51, Wanneroo, 6946, Australia

    N. L. McKenzie

  3. Department of Zoology, Universidade Estadual Paulista, Rio Claro, CP199, Sao Paulo, Brazil

    A. P. Cruz-Neto

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  1. R. D. Bullen
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  2. N. L. McKenzie
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  3. A. P. Cruz-Neto
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Correspondence to R. D. Bullen.

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Bullen, R.D., McKenzie, N.L. & Cruz-Neto, A.P. Aerodynamic power and mechanical efficiency of bat airframes using a quasi-steady model. CEAS Aeronaut J 5, 253–264 (2014). https://doi.org/10.1007/s13272-014-0104-5

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