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A mechanical model of wing and theoretical estimate of taper factor for three gliding birds

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Abstract

We tested a mechanical model of wing, which was constructed using the measurements of wingspan and wing area taken from three species of gliding birds. In this model, we estimated the taper factors of the wings for jackdaw (Corrus monedula), Harris’ hawk (Parabuteo unicinctas) and Lagger falcon (Falco jugger) as 1.8, 1.5 and 1.8, respectively. Likewise, by using the data linear regression and curve estimation method, as well as estimating the taper factors and the angle between the humerus and the body, we calculated the relationship between wingspan, wing area and the speed necessary to meet the aerodynamic requirements of sustained flight. In addition, we calculated the relationship between the speed, wing area and wingspan for a specific angle between the humerus and the body over the range of stall speed to maximum speed of gliding flight. We then compared the results for these three species of gliding birds. These comparisons suggest that the aerodynamic characteristics of Harris’ hawk wings are similar to those of the falcon but different from those of the jackdaw. This paper also presents two single equations to estimate the minimum angle between the humerus and the body as well as the minimum span ratio of a bird in gliding flight.

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Abbreviations

β:

angle between humerus and body

β min :

minimum angle between humerus and body

β e :

empirical span ratio ( b obs/b max )

β min sr :

minimum span ratio

b:

wing span

bB :

body width

bmax :

maximum wing span

bobs :

observed wingspan

c:

wing chord

C l,max :

maximum lift coefficient

e:

taper factor

g:

acceleration due to gravity

k:

proportionality constant, b B = Kb max

l:

length

m:

body mass

Re:

Reynolds number

S:

wing area

S′:

wing area lost owing to flexing

r 1, r 2, r 3 :

length of wing elements

S max :

maximum wing area

Vmin :

stall speed

U ∞ :

velocity of the fluid relative to the moving object

v:

kinematic viscosity

ϑ:

angle

ρ:

air density

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Authors and Affiliations

  1. Department of Mathematics, Payame Noor University of Neyshabur, Neyshabur, Iran

    Moosarreza Shamsyeh Zahedi

  2. Department of Mathematics, University of Pune, Pune, 411007, India

    Moosarreza Shamsyeh Zahedi

  3. Department of Mathematics, Poona College of Arts Science and Commerce, Camp, Pune, 411001, India

    Mir Yaseen Ali Khan

Authors
  1. Moosarreza Shamsyeh Zahedi
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  2. Mir Yaseen Ali Khan
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Correspondence to Moosarreza Shamsyeh Zahedi.

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Zahedi, M.S., Khan, M.Y.A. A mechanical model of wing and theoretical estimate of taper factor for three gliding birds. J Biosci 32, 351–361 (2007). https://doi.org/10.1007/s12038-007-0034-z

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  • DOI: https://doi.org/10.1007/s12038-007-0034-z

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