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AE-705 Introduction to Flight Lecture No. 19 Capsule 10

Flapping Wing Aerodynamics

Some Lessons from Natural Flyers

• Prof. Rajkumar S. Pant

AE-705 Introduction to Flight Lecture No. 19 Capsule 10

Aeronautical Technology v/s Natural Evolution

AERONAUTICAL TECHNOLOGY

 Fastest Aircraft: (SR-71 Blackbird)

• 900 m/s = 32 body-lengths/s

 Fastest Roll Rate: A4 Skyhawk

• 720 o/s

 Aircraft Highest g-rates = 7 – 9

WHY ?

~ 100 years old

NATURAL EVOLUTION

 Fastest Bird: Spine Tailed Swift

• 47.5 m/s = 150 body-lengths/s

 Fastest Roll Rate: Barn Swallow

• 5000 o/s

 Bird Highest g-rates 20 – 25

~ 150 Million Years old

Humans fly commercially or recreationally, but birds fly professionally

• J. H. McMasters and M. J. Henderson, “Low speed single element airfoil synthesis,” Technical Soaring, vol. 6, pp. 1–21, 1980.

AE-705 Introduction to Flight Lecture No. 19 Capsule 10

 Usually a Figure of Eight motion

• Downward stroke, wing pronated, AoA ↓
• Upward stroke, wing supinated, AoA ↑

 Three desirable features of bird’s wing

• Camber change and Twisting
• Area expansion and contraction
• Transverse bending

 Similarities with Humans

• Bone Structure
• Muscle Structure

Flapping Flight in Birds

Source: http://www.cambridge.org/9781107037267 pp. 17 The Dove by Ed Braverman

AE-705 Introduction to Flight Lecture No. 19 Capsule 10

Wings: Aircraft v/s Birds

AIRCRAFT WING PIGEON WING Pigeon wings exhibit much higher change in Camber and Thickness along Span

Source: http://www.cambridge.org/9781107037267 pp. 18

Nachtigall, H. v. W. and J. Wieser (1966). "Profilmessungen am Taubenflugel." Zeit.

• Vergl. Physiol. 52: 333-346

AE-705 Introduction to Flight Lecture No. 19 Capsule 10

 The Great Flight Diagram

• W/S v/s W v/s V
• 𝑋

𝑇 = 1 2 𝜍𝐷𝑀𝑊2, hence when 𝑋 𝑇 ↑, V ↑

• 𝑋

𝑇 = 𝑙1

3 𝑋

• k1 = 53 (Aircraft)
• k1 = 30.5 (Birds)

Scaling Laws of Flying Bodies

INSECTS AIRCRAFT BIRDS

Source: Tennekes H, The Simple Science of Flight from Insects to Jumbo Jets, Cambridge, MA, The MIT Press, 1996

Source: T. Liu, “Comparative scaling of flapping- and fixed- wing flyers,” AIAA Journal, vol. 44, pp. 24–33, 2006.

AE-705 Introduction to Flight Lecture No. 19 Capsule 10

 Wingspan (b)

• b ~ 1.654 m1/3 (aircraft) b ~ 1.704 m1/3 (birds)

 Wing Area (s)

• Large variations seen

s ~ m0.78 (most birds); s ~ m1.04 (HB)

 Wing Flapping Frequency (fwing)

• Max. fwing~ m(-1/3)
• Min. fwing~ m(-1/6)
• Larger Birds Flap slowly !

 Wing Aspect Ratio (AR)

• Large soaring birds:

AR ~ 15  L/Dmax ~ 20

• Large Sailplanes:

AR ~ 30  L/Dmax ~ 60

Scaling of parameters with Mass m

AE-705 Introduction to Flight Lecture No. 19 Capsule 10

PARAMETER UNITS SCALING Wingspan m W1/3 Wing Area m2 W2/3 Wing Loading N/m2 W1/3

• Min. Power

W W1/6 Speed for min. Power m/s W1/6

• Max. Wing beat frequency /s

W (-1/3)

• Min. Wing beat frequency

/s W (-1/6)

Summary: Scaling of bird parameters with mass W

AE-705 Introduction to Flight Lecture No. 19 Capsule 10

Fastest Flying Birds

Level Flight (~ 171 kmph) Dive (~ 389 kmph)

Spine Tailed Swift Peregrine Falcon

AE-705 Introduction to Flight Lecture No. 19 Capsule 10

 Gliding = Flights without Flapping

• Thrust comes from Gravity

 Glide Angle θ =

1 (

𝑀 𝐸)

• As

𝑀 𝐸↑, θ↓, Glide Range↑

• As Size ↑ , Re ↑,

𝑀 𝐸↑

• Albatross:

bw = 3000 mm, L/D = 19

• Fruit Fly:

bw = 6 mm, L/D = 1.8

 Even Snakes can Glide !

 Soaring

• Gaining height due to thermals/updrafts

Mechanics of Gliding & Soaring

Gliding Snakes

AE-705 Introduction to Flight Lecture No. 19 Capsule 10

 L =

1 2 𝜍𝑇𝐷𝑀𝑊2 = 𝑛𝑕 𝑑𝑝𝑡𝜄 ≈ 𝑛𝑕 ∴ 𝑊 ≈

2𝑛𝑕 𝜍𝑇𝐷𝑀

𝑊 ≈

2𝑋 𝜍𝑇𝐷𝑀

 Assume CL = 0.65 and ρ = 1.2256 kg/m2  V ∝

𝑋 𝑇 ∝

𝑛0.28 ∝ 𝑛0.14

• Heavier birds glide at higher speeds

Improving glide characteristics by wing morphing

Bird W/S N/m2 Vglide (Estim) m/s Vglide (Quoted) m/s % Error Mute Swan 170 20.66 21 1.62 Albatross 140 18.75 19 1.33 Ultralight 133 18.27 18

• 1.50

Graylag Goose 115 16.99 17 0.05 Common Gull 32 8.96 9 0.41

Source: Tennekes H, The Simple Science of Flight from Insects to Jumbo Jets, Cambridge, MA, The MIT Press, 1996

Birds ↑ S as Vglide ↓

AE-705 Introduction to Flight Lecture No. 19 Capsule 10

Rotary Wing Aircraft & Natural Flyers : Similarities

Rotary Wing Aircraft

 Lift

• Relative flow around rotors created by

rotating continuously along central shaft

 Thrust

• Tilting the rotational plane of the rotor

forward

 During Forward Flight

• Change the angle of the rotors

Natural Flyers

 Lift

• Flapping wing about shoulder in an arc,

and reversing every half cycle

 Thrust

• Tilting the flapping stroke plane
• down and forward on the downstroke
• up and backward on the upstroke

 During Forward Flight

• Make the stroke more vertical by

increasing the up-and-down amplitude

AE-705 Introduction to Flight Lecture No. 19 Capsule 10

Wingtip paths relative to the body

 Smaller flyers flap in a more complex pattern

ALBATROSS HORSESHOE BAT PIGEON BOW FLY LOCUST BEETLE FRUITFLY

AE-705 Introduction to Flight Lecture No. 19 Capsule 10

Flapping Patterns of some Natural Flyers

Canada Goose Fruit Bat Hawk Moth Dragon Fly Hummingbird

Source: http://www.coolinfographics.com/blog/2015/4/27/flight-patterns-deconstructed.html

AE-705 Introduction to Flight Lecture No. 19 Capsule 10

Flapping in Slow Motion

PIGOENS FRUIT BATS DRAGON FLY

AE-705 Introduction to Flight Lecture No. 19 Capsule 10

Hovering Flight

Humming Birds in slow motion

AE-705 Introduction to Flight Lecture No. 19 Capsule 10

Principal Sources

1. Shyy et al., An Introduction to Flapping Wing Aerodynamics, Cambridge Aerospace Series, ISBN 9781107037267, 2013. 2. Tennekes H., The Simple Science of Flight from Insects to Jumbo Jets, Cambridge, MA, The MIT Press, 1996.