Wing beat frequency of a flier—Mass flow theory

Puranik, P. G.; Krishna, G. Vamsi; Ahmed, Adeel; Chari, N.

doi:10.1007/bf03052385

Cited by 8 publications

(4 citation statements)

References 3 publications

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“…This mean that other power-law functions discussed in Ref. [ 27 ], such as Norbergs f ∝ m 0.3 [ 14 ], Pennyquick’s f ∝ m 1/3 [ 12 ] or f ∝ m 3/8 [ 13 ], or the mass-flow theory arriving at f ∝ m [ 25 ], cannot be derived from purely physical arguments.…”

Section: A Theoretically Derived Simple Expression For the Wing-beat ...mentioning

confidence: 99%

“…Puranik et al . [ 25 ] suggested , where L is the wing span and the effective wing breath defined as wing area divided by wing length, and found a good fit to data for both insects, birds, and bats. More recently, mathematically simpler expressions, e.g., a proportionality between mass to some power and wing/stroke frequency, have been considered [ 14 , 22 , 24 , 26 ].…”

Section: Introductionmentioning

confidence: 99%

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Universal wing- and fin-beat frequency scaling

Jensen,

Dyre,

Hecksher

2024

PLoS ONE

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We derive an equation that applies for the wing-beat frequency of flying animals and to the fin-stroke frequency of diving animals like penguins and whales. The equation states that the wing/fin-beat frequency is proportional to the square root of the animal’s mass divided by the wing area. Data for birds, insects, bats, and even a robotic bird—supplemented by data for whales and penguins that must swim to stay submerged—show that the constant of proportionality is to a good approximation the same across all species; thus the equation is universal. The wing/fin-beat frequency equation is derived by dimensional analysis, which is a standard method of reasoning in physics. We finally demonstrate that a mathematically even simpler expression without the animal mass does not apply.

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Section: A Theoretically Derived Simple Expression For the Wing-beat ...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Universal wing- and fin-beat frequency scaling

Jensen,

Dyre,

Hecksher

2024

PLoS ONE

View full text Add to dashboard Cite

show abstract

“…This mean that other power-law functions discussed in Ref. [27], such as Norbergs f / m 0.3 [14], Pennyquick's f / m 1/3 [12] or f / m 3/8 [13], or the mass-flow theory arriving at f / m [25], cannot be derived from purely physical arguments.…”

Section: A Theoretically Derived Simple Expression For the Wing-beat ...mentioning

confidence: 97%

“…For instance, Pennycuick [12] arrived at f ¼ K m 1=3 g 1=2 S À 1 A À 1=4 r À 1=3 air in which K is a numerical constant by finding the best fit to a set of bird data involving the following parameters: the bird mass m, the gravitational acceleration g, the wing span S, the wing area A, and the air density ρ air . Puranik et al [25] suggested f / mL À 2 B eff , where L is the wing span and B eff the effective wing breath defined as wing area divided by wing length, and found a good fit to data for both insects, birds, and bats. More recently, mathematically simpler expressions, e.g., a proportionality between mass to some power and wing/stroke frequency, have been considered [14,22,24,26].…”

Section: Introductionmentioning

confidence: 98%