scaling, wing geometry and kinematics of bird flight...scaling, wing geometry and kinematics of bird...

Scaling, Wing Geometry and Kinematics

of Bird Flight

Tianshu Liu

Department of Mechanical and Aerospace Engineering

Western Michigan University

Kalamazoo, MI 49008

Human’s Dream of Flight:

Fly like Birds

Wright Brothers’ Flyer

A Good Idea of George Cayley:

Separating Lift and Propulsion

Modern Jets

Recent Interests on Flapping Flight:

Micro Air Vehicles

Scaling Questions

• Similarity and Difference in Scaling

of Geometry, Velocity and Power ?

• Aerodynamic Implications of Scaling ?

Two Long-Standing Problems

• Relative Efficiency of Flapping Flight against

Fixed-Wing Flight

• Maximum Weight for Feasible and Sustainable

Flapping Flight

Scaling

3/1W~S/W,L,b

Wing Span, Overall Length, Wing Loading:

3/2W~S

Wing Area:

6/1W~U

Velocity:

6/7W~P

Power:

Maximum Take-Off Weight vs. Empty Weight

W786.1WMTO

Upper Bound of Weight vs. Mean Weight for Birds

Wing Span vs. Weight

Wing Area vs. Weight

Overall Body Length vs. Weight

Maximum Body Diameter vs. Weight

Wing Loading vs. Weight

Cruising Velocity vs. Weight

Birds:

Heavier!

More lift?

Weight vs. Reynolds Number

Cruise Power vs. Weight

Engine and Muscle Power Available

Engine Power Available vs. Engine Weight

Engine Weight vs. Total Weight

Specific Power of Aero-Engine and Muscles

Scaling Laws

85.0prop Scaling Laws:

Unsteady Lifting-Line: 75.0prop

Optimum Wake Model: 85.0prop

Derived Results from the Scaling Laws

Bird Muscle Power Available:

Cruise Power Required:

Flying Bird Weight Limit:

Deduction: Flying Bird Weight Limit

6/7

bird,mr W23.1P

9675.0

muscle,A W4.3P

kg4.108.16

Mute Swan: < 15 kg

Further Deduction: Pterosauers

W =126-292 N

Deduction:

Sustainable Flapping Flight Take-off from ground???

More Deduction: Archaeopteryx

W= 2.5 N

Muscle Power < 50% Deduction:

Sustainable Flapping Flight

Take-off from ground???

• Birds are geometrically similar to aircraft.

Conclusions Based on Comparative Scaling

• Birds and aircraft have comparable flight efficiency

in cruising flight.

No Comparison:

Agility and Maneuverability of Birds

Avian Wing Geometry and Kinematics

3D Laser Scanner

on FARO Arm Data Cloud of Seagull

Wing Surface

Geometry Data Processing

3

1n

1nn

max)c()c()12(S)1(

c

z

c

z

The camber line:

The thickness distribution:

4

1n

1nn

max)t()t()(A

c

z

c

z

The wing planform:

)(F)(F2/b

c

2/b

ccorrOK

0

Seagull Wing Geometry

The camber line and thickness

distribution

Seagull Wing Planform Seagull Wing Chord

Distribution

Reconstructed Seagull Wing Surface

Merganser Teal

Owl

Merganser, Teal and Owl Wings

Owl

Teal Merganser

Avian Airfoil Comparison

Avian Wing Kinematics (Crane, Seagull & Goose)

2

4/12

4/11

4/1

2/b

y)t(A

2/b

y)t(A

2/b

z

The front-projected 1/4-chord line:

2

1n

n1n1101 )tncos(B)tnsin(CC)t(A ,

2

1n

n2n2202 )tncos(B)tnsin(CC)t(A ,

2

1n

bnbn0b )tncos(B)tnsin(CC)2/bmax(

2/)t(b

.

Two-Jointed Arm Model

3D View

Projected Views

X-Ray

Reconstruction of the Flapping Seagull Wing

0t 4/

2/

4/3

f =1.0 Hz

f =2.0 Hz

Aerodynamics of Flapping Flying Seagull

Cheolheui Han (2009)

Aerodynamics of Flapping Flying Bat

Wang et al. (2010)

Aerodynamics of Microraptor

-- The Origin of Bird Flight

Xu et al. (2000)