O O

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4.5~5 cm(AR) 1.71 0.12 0.06 0.02 g 0.0012 0.0003 m2(R2=0.9586)(R2=0.5559R2=0.4726)23 1.010.24 m/s(51623)(y=0.07x0.7733R2=0.6967)(45 )() 60(2.20.1cm)

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Abridgement TOPICThe pilot of Mother Nature-butterflys flying ability

This research approaches the flying ability of butterflies. Our research mainly discusses the weight,

aspect ratio of butterflies, frequency of flapping, and the shape, surface area of butterflies wings, and the connection between temperature and flying velocity. More over, we use the wind tunnel which was made by us to observe the movement of butterflies wings and analyzed the direction of airflow and aero-elastic which pass through the wind tunnel. Our research shows that Pieris canidias length of wings is about 4.5 to 5 cm. The average of aspect ratio (AR) is 1.710.12 . Its weight is about 0.060.02 . And its surface area is about 0.00120.0003 m 2 . The heavier Pieris canidia is, the bigger its surface area will be (R 2 =0.9586). In addition, the heavier it is, the smaller its aspect ratio will be (R 2 =0.5559, R 2 =0.4726), and the swifter its flying velocity will be. When it is 23C, the flying velocity of Pieris canidia is 1.010.24m/s. The hotter temperature is (5,16,23C), the swifter it flies (y=0.07x+0.7733,R=0.6967).

Accroding to the detect of the wind tunnels experiment , the butterflies will fly on luff. When the stronger the wind of the wind tunnel is, the larger the angles of wings flap are. And they are fast and lasting, the elevation also becomes larger (45). The butterflies trochoids of wings mimic the word eight, and the movement of wingspan includes parallel movement of linearity and wheel. When butterflies flap, it will amount depression upon and in front of the wings, amounting the high pressure on the back so that butterflies can fly antrorsely. Furthermore, the larger the curvy angle of marginal wings (Dihedral) is, the higher the ascending height of model butterfly will be. When dihedral is 60, the ascending height of model butterfly is the highest(2.20.1 ).

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() --- () ---

1.

( ) ( )22

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2

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1

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1 VPVP +=+

2.1A1V12A2V2 (MAV)

1996 (DARPA)(Micro Air VehiclesMAV) 15 8.33~16.67 m/s (Fixed- Wing)(Rotary-Wing)(Flapping-Wing)(2002) 1.

() 15cm (Aspect-RatioAR)(AR~1) 2.

MAV( IMM 19mm MAV)MAV(Michigan HoverBot Stanford Mesicopters )()(Thrust-Wing)

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In gliding flight, a bird's wingsdeflect air downward, causing a liftforce that holds the bird up in the air.

By tilting forward and goinginto a slight dive, the bird canmaintain forward speed.

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8 8 8 ( 68)

1.

(venation) 2 3 2 ( 92)(Comstock-Needham)(Hampson) 1a 12 ()

A.(Longitudinal veins) B.(Cross veins) 1.(Pc) 1.(r) 2.(C) 2.(s) 3.(Sc) 3.(r-m) 4.(R) 4.(m-m) 5.(M) 5.(m-cu) 6.(Cu) 7.(Pcu) 8.(A) 9.(J)

2.

(Rm)(Vn)( Pcu 1V )( 68)

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(220x)

3. ()

()( 81)( 88)

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(Olympus NO.100) 1 2 1 (200cm100cm150cm) 1 (FUJIFILM FinePix 6900) 1 (15cm10cm15cm) 1 (Nikon FM2) 1 (MnO2)(H2O2) (Lutron LM-81AM) 1 1 (112cm38cm38cm) 1

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1.

a. (112cm38cm38cm)()

b. 1.5 7 () (1)A() (2)B()( 10 )() (3)C() 0.5 (

) (4)D() 25cm20cm20cm (5)E() (6)F() (7)G()

(A)(B) (C)(D)

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2.

a. b. 0.4cm c. 1/2 (

) 03060 90()

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1.()

2. 3.

1. 2.

1.(g)

2.

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)()(4)(4)(

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= 4. L1(

) L2() R()(m)(AS)

)()(212

2

mmLL

=

12

1.(23)

(cm/s)

2. T2 16 T3 5

3. T2 60 T2 30 (cm/s)

4. T3 3(cm/s)

1. a.

b. 3m/s c.(H2O2)(MnO2)

()

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2.() a.

b.

c.

3m/s d.

(0306090) 5

e.(H2O2)(MnO2)()

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(Pieris rapae crucivora boisduval)(Lepidoptera)(Pieridae)() 1. 4.5~5 cm

(Pieris canidia)()

2.

() (Sc)(R)

(R1~R5)(M)(M1~M3)(Cu)(Cu1Cu2)(A)(2A3A)

(ScR1)(RS)(M)(M1~M3)(Cu)(Cu1Cu2)(A)(2A3A)

(Pieris canidia) (Pieris rapae crucivora)

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()(

)()(L1)(L2)(=3.37)(R)(=8.9 cm)-- 4.95 0.41 cm 4.10 0.55 cm 4.84 0.49 cm

(cm) (cm) / (cm)

11.0 12.5 0.9 15.2 10.1 7.2 1.4 11.7 10.4 4.0 2.6 12.0

7.4 7.3 1.0 10.2 8.0 7.1 1.1 9.5 8.0 6.9 1.2 9.6 8.8 5.1 1.7 9.9

6.0 5.1 1.2 8.1 5.9 5.1 1.2 7.2

5.9 4.1 1.4 7.2 6.0 3.4 1.8 7.5 5.5 4.1 1.3 7.1 6.4 3.2 2.0 7.0

4.6 5.0 0.9 7.0 5.1 4.7 1.1 6.2 5.8 3.2 1.8 6.6

6.8 5.5 1.4 8.9

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(cm) (cm) / (cm)

6.0 1.5 4.00 5.3 5.0 1.7 2.94 6.8 8.3 4.6 1.79 10.2

7.7 4.8 1.62 9.2 4.8 1.9 2.53 5.3

5.5 2.0 2.75 6.5 4.3 1.3 3.31 4.6

4.6 1.5 3.07 4.6 5.8 2.0 2.90 6.6

5.2 1.6 3.25 6.4 5.2 2.2 2.32 9.1

5.6 2.2 2.50 8.5 4.7 1.9 2.47 5.5 5.5 2.5 2.20 6.0 6.0 2.0 3.00 6.6 5.9 2.3 2.54 6.7 6.4 1.4 4.54 7.2 6.0 1.9 3.16 6.5 5.0 0.5 10.00 4.2

5.2 2.0 2.67 6.1 4.9 1.5 3.27 5.0

5.7 3.0 1.90 6.2 3.9 1.5 2.60 5.0 5.0 1.1 4.55 4.9

7.2 2.6 2.77 7.7 6.2 2.1 2.92 6.8 4.7 2.0 2.35 5.1

5.5 2.0 2.75 5.6 5.2 1.5 3.47 5.6

4.7 1.6 2.94 5.0 6.5 0.9 7.22 5.6

5.5 1.0 5.45 4.5 8.3 1.5 5.51 8.2

5.7 2.0 3.37 6.5

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y = 0.0125x + 0.0005R2 = 0.9586

0.0000

0.0005

0.0010

0.0015

0.0020

0.00 0.02 0.04 0.06 0.08 0.10Body mass (g)

Wing

area

(m2)

(cm) (cm) / (cm)

5.1 3.9 1.30 5.2 3.5 3.1 1.13 4.3

5 4.4 1.14 5.6 5.5 4.2 1.30 6

5.5 3.5 1.57 5.9 5 4 1.25 5.3

4.7 3.7 1.27 5.4 4.1 3.5 1.17 4.6 4.6 5 0.92 6.4

6.2 5.4 1.14 7 4.5 2.2 2.05 3.8

5 3 1.67 2.6

4.9 3.8 1.29 5.18

(g)(m2)0.06 0.02 g 0.0012 0.0003 m2(R2=0.9586)

(g)(m2)

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y = 0.3884x + 0.481R2 = 0.5559

-0.3

-0.2

-0.1

0.0

0.1

0.2

-1.8 -1.6 -1.4 -1.2 -1.0 -0.8log mass

log ve

locity

y = 0.629x + 1.8335R2 = 0.3955

-0.3

-0.2

-0.1

0.0

0.1

0.2

-3.2 -3.1 -3.0 -2.9 -2.8 -2.7log wing area

log ve

locity

(g)(m/s)( 23)

(R2=0.5559)

(g)(m/s)( 23)

(m2)(m/s)( 23)

(R2=0.3955)

(m2)(m/s)( 23)

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0.4

0.6

0.8

1.0

1.2

1.4

5 16 23temperature

veloc

ity(m

/s)

y = -2.3202x - 1.7925R2 = 0.4726

-0.3

-0.2

-0.1

0.0

0.1

0.2

-0.90 -0.85 -0.80 -0.75 -0.70log aspect ratio

log ve

locity

(AS)(m/s)( 23)

(Aspect-RatioAR) 1.71 0.12(AR)(R2=0.4726)

(AR)(m/s)( 23)

(m/s)5 0.870.26 m/s16 0.860.22 m/s 23 1.010.24 m/s(y=0.07x0.7733R2=0.6967)

(51623)(m/s)

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()(45 )()

()( a)

()()

( 3m/s)

21

() (3m/s)()

(cm)()()60(2.20.1cm)

()( 3m/s)

0.0

0.5

1.0

1.5

2.0

2.5

0 30 60 90

(cm)

22

(venation)(Sc)(R1)(R)( 92)

5~7 (AR) 1.71 0.12(AR)(R2=0.4726)

(R2=0.5559)(R2=0.9586)(68)

(9 s1)(1.010.24 m/s)( 91)

(m/s) (s1) Ref 1.010.24 9 In this study (Tabanus bovinus) 14 68 (Libellula depressa) 4~10 280 68 2~2.3 180~197 68 (Bumble bee) 3~5 220~240 68 2.5~3.7 180~203 68

(51623)(y=0.07x0.7733R2=0.6967)

(45 )

23

()

()

() (0306090)() 0

()()()()

(flapping fly)

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4.5~5 cm

(Pieris canidia) (Sc)

(R)(R1~R5)(M)(M1~M3)(Cu)(Cu1Cu2)(A)(2A3A)(ScR1)(RS)(M)(M1~M3)(Cu)(Cu1Cu2)(A)(2A3A)

(AR) 1.71 0.12 0.06 0.02 g 0.0012 0.0003 m2

23 1.010.24 m/s(51623)

60(2.20.1cm)

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1. ( 92) ()22(1)28-41 2. ( 91) 1002-5 3. ( 90) 4. ( 90)

615-29 5. ( 91)

1.http://www.ornithopter.org/store/teacherguide.pdf 2. ( 92) 3. ( 68) 4. ( 88) 5. ( 81)

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