Azuma JTheoBiol 1987

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J. theo r. Biol. 1987) 129, 263-274

F l i g h t o f a S a m a r a

I somitr a macrocarpa

A K I R A A Z U M A A N D Y O S H IN O R I O K U N O

Institu te o f Interdisciplinary Research, Fa culty o f Engineering,

The U niversity o f Tokyo, Tokyo, Japa n

Received 2 December

1986)

The steady gliding flight of samples of Alsom itra macrocarpa samara was filmed

and analysed. By using the observed data, the flight performance of the samara was

made clear. The lift-to-drag ratio or the gliding ratio was about 3 ~ 4 and the rate

of descent was 0.3 - 0.7 m/sec, which was smaller than those of other rotary seeds.

The flight was so stable that samples were seen to take their optimal trimmed angle

of attack with a value between the maximum gliding ratio and the minimum rate

of descent. The aerodynamic function of the husk for the distribution of the seeds

was also revealed by making wind tunnel tests of the husk.

A C

A R

b

o

C ~

a

C G

CL

G

cm

m

center

D

d

g

L

l

M

m

rl

R e

S

U

om en c l a t u r e

aerodynamic center

aspect rat io, =b2/S

wing-span

drag coefficient, = D / ½ p V 2 S

minimum drag coefficient

two-dimensional drag coefficient, =d/½pVgc

center o f gravity

lift coefficient, =L/½pV2S

two-dimensional lift coefficient, =l/½pV2c

moment coefficient about the center of gravity,

= M / ½ p V 2 c 2

two-dimensional moment coefficient, = m/~_pVZc2

wing chord

=fb/2 c d y / b

ean wing chord ? ~-b/2

wing chord at the wing center

drag

maxi mum diameter of the husk, two-dimensional drag or spanwise drag

distribution

gravity acceleration

lift

two-dimensional lift or spanwise lift distribution

moment about the center of gravity

mass of seed, two-dimensional moment

flight number

Reynolds number, = Vcce,ter/V

wing area

wind speed

63

0 0 2 2 - 5 1 9 3 / 8 7 / 2 3 0 2 6 3 + 1 2 0 3 . 0 0 / 0 © 1 98 7 A c a d e m i c P r e ss L i m i t e d



2 6 4

V

W

X C

O~o

y

A

P

A AZ UMA AND Y. OKUNO

f li g h t s p e e d

r a t e o f d e s c e n t

l o n g it u d in a l p o s i t io n o f th e a e r o d y n a m i c c e n t e r f ro m t h e l e a d in g e d g e

ze r o l i f t an g l e

g l i d i n g a n g l e

s w e p t a n g l e o f a l in e p a s s in g t h r o u g h o n e - q u a r t e r c h o r d s a t w i n g c e n t e r

a n d 3b/8 s p a n w i s e s t a t i o n

a i r d e n s i t y

Introduct ion

I f a s e e d o r a f r u i t h a s a f i l m - l ik e w i n g w h i c h is e x t r e m e l y l i g h t w e i g h t w i t h a l a r g e

s u r f a c e , a n d i f t h e c e n t e r o f g r a v it y o f t h e s e e d i s lo c a t e d n e a r b u t i n f r o n t o f t h e

a e r o d y n a m i c c e n t e r o f th e w i n g , t h e n t h e s e e d c a n h a v e a c h a n c e t o fly b y u s in g

t h e l i f t g e n e r a t e d b y t h e w i n g i n a g l i d e r - l i k e t r a n s l a t i o n d u r i n g t h e f a l l , a n d t o

m a k e a l o n g - d i s t a n t j o u r n e y in w i n d y c o n d i t i o n s . I t is v e r y r a r e to f in d s u c h s a m a r a

w h i c h m a k e a g l id i n g fl ig h t w i t h o u t a n y a u t o - r o t a t i o n . M a n y w i n g e d s e e d s s u c h a s

m a p l e , b l a c k p i n e , sa n t a l o c e o u s , l in d e n , h o r n b e a m , p h o e n i x t r ee , a s h a n d s o o n

a u t o r o t a t e d u r i n g t h e fa ll i n t h e w i n d ( N o r b e r g , 1 9 73 ; M c C u t c h e n , 1 9 77 ; A z u m a

Y a s u d a , 1 9 8 5 ) .

T h e g l id e r - li k e fl ig h t o f s a m a r a w a s i n t r o d u c e d b y A h l b o r n ( 1 8 9 7) a n d H e r t e l

( 1 9 63 ) , a n d it s f li gh t m e c h a n i c s w e r e a n a l y s e d b y K i m u r a ( 1 94 3 ) . T h e p r e s e n t s t u d y

m a k e s f li gh t t e st s o f s a m p l e s o f Alsomitra macrocarpa s a m a r a , i n c a l m c o n d i t i o n s

t o s p e c if y th e i r p e r f o r m a n c e e x p e r i m e n t a l l y a n d t h e o re t ic a l ly . I n a d d i t i o n , w i n d

t u n n e l t e s ts o f t h e h u s k w e r e c o n d u c t e d t o f in d it s a e r o d y n a m i c f u n c t i o n i n t h e

d i s t r i b u t io n o f t h e s e e d s .

o n s t r u c t io n o f S e e d a n d W in g

A p a l e s p e c i e s f r o m J a v a , Alsomitra macrocarpa, h a s a s a i l w i n g a s s h o w n i n

F ig . 1 a n d p e r f o r m s a s t a b l e g l i d in g f l ig h t w i t h o u t a n y ta i l s u r f a c e . T h e g e o m e t r i c a l

c h a r a c te r i st ic s o f t h re e t y p i c a l s e e d s, a n d t h e m e a n a n d s t a n d a r d d e v i a t i o n o f 1 0

s e e d s a r e g i v e n i n T a b l e 1. T h e d i m e n s i o n s a r e d e f i n e d i n F ig . 2 .

T h e s e e d i t se l f is v e r y t h in , a b o u t 1 m m i n t h ic k n e s s , a n d is l o c a t e d n e a r l y a t th e

c e n t e r o f g r a v i ty , w h i c h is a s li g h tl y f o r w a r d p o s i t i o n o f t h e w i n g c e n t e r . T h e w i n g

is a l s o v e r y t h i n ( f r o m a f e w ~ m t o s o m e 1 0 p .m ) a n d h a s a s w e p t a n d t a p e r e d p l a n

f o r m , t w i s te d ( w a s h o u t ) a n g l e , re f le c te d tr a i l in g e d g e , a n d a d e q u a t e l y a r r a n g e d

p o s i t i o n o f th e c e n t e r o f g r a v i ty CG). A n e x a m p l e o f th e m e a n c a m b e r l in e is

s h o w n i n F i g . 2 ( c ) .

B y t h in w i n g t h e o r y ( A b b o t y o n D o e n h o f f , 1 9 59 ), t h e r e f le c t e d a e r o f o i l h a s

p o s i t iv e m o m e n t a t p o s i t i v e a n g l e o f a t ta c k , a s g i v e n in T a b l e 2 , a n d s h if ts t h e c e n t e r

o f p r e s s u re b a c k w a r d a s t h e a n g l e o f a t ta c k i n c re a s e s , a n d t h u s h a s a t e n d e n c y t o

s t ab i li z e th e p i t c h i n g m o t i o n o f th e s e e d .

T h e p i t c h i n g s t a b i l it y is f u r t h e r s t r e n g t h e n e d b y t h e s w e e p a n g l e o f th e w i n g i f

t h e c e n t e r o f g ra v i t y is l o c a t e d i n f r o n t o f t h e m e a n a e r o d y n a m i c c e n t e r . T h e w a s h o u t



F L I G H T O F A S A M A R A

265

FIG. I. A seed of A tsomi tr a macroearpa

T A B L E 1

eometr ica l confi guration of seeds A lsomi tr a macrocarpa)

Number of samples Typical examples Mean value

of 10

Items

1 2 3 sam p le s s .d .

Mass m (mg ) 264.0 314.1 289.1 212.1 70.9

Wing-span, b (cm ) 14,1 13,8 14.6 14.3 0.9

Wing area, S (cm z) 60-3 66,9 55.3 59.7 8.7

Aspect ratio, AR 3-3 2.8 3.9 3 5 0,4

Geometrical sweep angle, A (d eg )t 11.3 11.5 21 '6 13.7 3.1

Wing loading, mg S (N /m 2) 0 .438 0 .461 0 .512 0 .357 0.115

Center of gravity, CG

(cm ) 1.6 1.8 1.6 1.6 0.1

distance from leading edge)

Aerodynamic center, XAC (cm ) 2 3 2 1 2 4 2 2 0-1

+

Swept angle of a line passing through one-quarter chords at wing root and

3 b / 8

spanwise position.

of the wing and the dihedral , both of which result from the elastic deformation of

the wing during the flight, will prevent spiral instability (Perkins Ha ge, 1949).

Many seeds are piled up one over another in a husk, which has a human head-like

form, as shown in Fig. 3, and is hung from a vine. Under windy conditions, the

husk is able to swin g by the so-c alled Karman vortex (von Kfirmfin Ruba ck,

1912), and to scatter the seeds in regular sequence. The configuration of the lip of

a hole, which is dug underneath the husk, is such as to introduce the wind inside

the husk, and to help the separation of the flying seeds from the remainder.

After separation, the respective seeds make a gliding flight, with an individual

performance which is determined by their own geometrical configuration and the

wind conditions at that time.



266

c 3 /

A. AZUMA AND Y. OKUNO

Wing span, b

• f , ~ t . . . . , ~ ~I~-Cenferof gFavity CG

~ a n g l e ,

mic cen ter , AC

(a)

A 8 C D E F G

~ c /8 ~ c /8 ~ c /a 1 c /a ~ ' c /8 c /B 1 c /B ~ c / 8 ~

b )

~ L 0 1

:~

_ ~

0 . 0 5 / D

. o \

(e)

FiG. 2. Geometrical configuration of the seed. (a) Plan view. (b) Frontal view. (c) Profile (non-

dimensionalized by the semi-chord).

l ight Test o f P la in Seeds

By ado pti ng a meth od of Ray ner Aldridge (1985), flight tests of ma ny seeds

of A l s o m i t r a m a c r o c a r p a were, as shown in Fig. 4, conducted in a calm room, and

filmed under a series of flashed lights of a stroboscope as shown in Fig. 5. A series

of positions o f the respective gliding seeds in the space can be deter mined geometri-




67

TABLE 2

T w o d i m e n s i o n a l a e r o f o il c h a r a ct e r is t ic s

ltems

Zer o lift Mom ent coefficient

angle, a 0 abou t the center

(deg ) of gravity, cm

Aerodynamic

center, XAc/ C

A -0- 53 2-36 x 10 2

B 0-28 3-04 x 10- :

C 0-09 2-40 × 10 2

D -0 -0 5 1-48 x 10-2

E -0 .49 0-69 x 10-2

F 0 08 3 31 x 10-2

G

Mean -0. 23 2.11 x 10 2

~ ~.

I

ta )

(e)

1/4

1/4

FIG. 3. Husk of AIsomitra macrocarpa. (a) Plan view from top. (b) Plan view from bottom. (c) Side

view from left. (d) Frontal view.

c a l l y f r o m t h e i r p i c t u r e s a n d i m a g e d s c a l e s in si d e a n d r e a r vi e w s , t a k e n b y c a m e r a s

( a ) a n d ( b ) r e s p e c t i v e l y . I n t h e p r e s e n t t e s t, t h e r e l a t i v e p o s i t i o n o f c a m e r a s w i t h

r e s p e c t t o t h e s c a l e s i s f i xe d . T h e n t h e g l i d i n g s p e e d a n d r a t e o f d e s c e n t a r e c a l c u l a t e d

f o r t h e r e s p e c t i v e i n t e r v a l s . S e e d s t h a t m a d e c u r v e d f l ig h ts , i n s t e a d o f s t r a i g h t g l i d i n g ,

w e r e e x c l u d e d f r o m t h e p r e s e n t a n a l y s i s . O n l y 1 0 f l ig h t s o f t h r e e s e e d s l i s t e d i n

T a b l e 1 w e r e a v a i l a b l e f o r d a t a a n a l y s i s , b e c a u s e t h e y f le w s t r a i g h t i n f ro n t o f



2 6 8

A A Z U M A A N D Y O K U N O

Camerab)

S e e d ~ S c o

Flightpa th

FIG 4 Experimental apparatus

Scaleb)

t h e c a m e r a . T h e e f f ec t o f m e a s u r e d e r r o r in p o s i t i o n o n t h e g l i d in g p e r f o r m a n c e i s

a s fo l l o w s : a n e r r o r o f 1 c m i n d i s t a n c e w i ll b r i n g a p p r o x i m a t e l y 1 % e r r o r i n t h e

s p e e d a n d 2 % e r r o r i n t h e a e r o d y n a m i c c o e ff ic ie n ts .

T h e f l i g h t d a t a a n d t h e r e s u l t i n g a e r o d y n a m i c c o e f f i c i e n t s a r e g i v e n i n T a b l e 3 .

I n th is t a b le , m e a n v a l u e s o f t h e r e s p e c t iv e s a m p l e s w e r e n o t a s im p l e e n s e m b l e

m e a n , b u t a w e i g h t e d m e a n i n w h i c h e a r l i e r f li g ht s w e r e t r e a t e d a s m o r e i m p o r t a n t .

T h a t i s t o sa y , e a c h d a t u m w a s m u l t i p li e d b y ( 1 / 2 ) -~ a s t h e f li gh t n u m b e r ( n )

i n c r e a s ed , b e c a u s e , a s c a n b e r e c o g n i z e d f r o m T a b l e 3 , t h e p e r f o r m a n c e o f t h e

r e s p e c t i v e s e e d s d e t e r i o r a t e d s u c c e s s i v e l y w i t h t h e fl ig h t n u m b e r , b e c a u s e o f s m a l l

d e f o r m a t i o n s c a u s e d b y th e h a r d c o n t a c t w i t h e it h e r g r o u n d o r s i d e w al ls . T h e w i n g

is t h i n a n d f r a g il e , b u t o n l y o n e f li g h t o c c u r s i n n a t u r e . T h e t o t a l m e a n w a s g i v e n

b y th e e n s e m b l e m e a n o f t h e a b o v e w e i g h t e d m e a n s o f th e r e s p e c t i v e s e ed s .

I t i s c l e a r t h a t t h e f l i g h t d a t a a r e v e r y s c a t t e r e d , e v e n i n t h e s a m e s e e d . T h i s

p r o b a b l y r e s u lt e d f r o m t h e n o n l i n e a r a e r o d y n a m i c c h a r a c t e ri s t i c s o f t h e w i ng ,

b e c a u s e o f t h e lo w R e y n o l d s n u m b e r ( s u c h a s ( 4 - 5 )

x 10 3

b a s e d o n t h e m e a n w i n g

c h o r d ) , t h e n o n l i n e a r d e f o r m a t i o n b e c a u s e o f d e l ic a t e c o n s t r u c t i o n o f t h e th i n w i n g ,

a n d o f t h e su r r o u n d i n g a t m o s p h e r i c c o n d i t io n s ( s uc h a s t e m p e r a t u r e a n d h u m i d i t y ) ,

u n n o t i c e a b l e a i r c u r r e n t s i n t h e r o o m , a n d s o o n .

T h e m e a n l i ft - to - d r a g ra t io o f

L /D=3 . 7

a t t h e l i ft c o e f f i c ie n t o f C L = 0 3 4 , a n d

t h e m e a n r a t e o f d e s c en t o f w = 0 .4 1 m / s e c s h o w t h e h i g h p e r f o r m a n c e o f th e g li d in g

s e e d in c o m p a r i s o n w i th t h e p e r f o r m a n c e o f r o ta r y s e ed s , in w h i c h t h e r a t e o f

d e s c e n t i s o f t h e o r d e r o f 1 m / s e c ( A z u m a & Y a s u d a , 1 98 5).

W h e n a t y p i c a l s e e d i s, f o r e x a m p l e , r e l e a s e d a t t h e h e i g h t o f 1 0 m o n a c a l m d a y

w i t h o u t a n y w i n d , i t f li es w i t h t h e s p e e d o f 1 - 5 m / s e c f o r a d u r a t i o n o f 2 4 s e c, a n d

l a n d s a t a h o r i z o n t a l d i s t a n c e o f 37 m f r o m t h e p o i n t o f r e l e a se .



FLIGHT OF A SAMARA 269

FtG. 5. An example of flight path flashed by a series of stroboscopic flashes. a) F rontal view. b)

Side view.

I f a hor i z on ta l w ind the spe e d o f w hic h i s 10 m / se c e x i st s t he n the hor i z o n ta l

d i s t a nc e o f f l igh t is i nc re a se d fu r th e r by 10 m / se c x 24 se c = 240 m.

I t is ve ry in te res t ing to f ind tha t the f l ight i s pe rf or m ed a t a l if t coeff ic ient as smal l

a s CL = 0 34 in t he se nse o f a e ro na u t i c a l e ng ine e r ing . T he fo l low ing t e s t w a s

pe r fo r m e d to m a ke c l e a r w hy the l i ft c oe f f i c ie n t i s so sma l l.

l ight Test of Modified Seeds

In t he f l igh t t e st s o f t he p l a in se e ds i t i s impo ss ib l e t o de t e rm ine the a e ro dy na m ic

c ha ra c t e r i s t i c s o f t he w ing m ore p re c i se ly . In o rd e r t o get a po l a r c u rve o f t he w ing

t h e t r im m e d a n g l e o f a tt a c k m u s t b e c h a n g e d f o r c e d l y . T h i s w as p e r f o r m e d a s

show n in Fig. 6 by ins t a ll i ng a t h in c o lu mn a t t he w ing ce n te r a nd by sh i ft i ng the



270

A . A Z U M A A N D Y . O K U N O

TABLE

l ight test results

Fl ight Rate of Drag Li f t - to-

Sam ple Fl ight spee d , desce nt , Li f t coeff ic ien t , d rag ra te ,

No. No. , 11 V (m /sec ) w (m /se c) coeff ic ien t , C L Co L D

1 1.33 0.38 0.39 8 0.12 0 3.33

1 2 1.34 0.39 0.387 0.119 3.26

3 1-38 0.34 0.37 2 0-095 3-93

Me an 1.34 0.38 0.391 0-116 3-40

f 1 1.37 0-28 0.392 0-082 4-79

2 1.47 0.34 0.337 0.081 4.16

2 3 1-51 0.47 0.31 4 0-102 3.06

4 1-20 0 35 0 499 0-151 3-30

Me an 1-40 0.33 0-374 0.089 4-29

1 t-69 0 46 0-281 0-080 3-53

2 1,94 0.58 0,211 0.066 3-21

3 3 2.13 0 70 0 t74 0-061 2.86

Me an 1.82 0.53 0.246 0-073 3.34

Total me an 1.52 0.41 0.337 0,090 3.68

FIG. 6. Mod i f i ed seed . A n add i t i ona l w e igh t can be a t t ached unde rn ea th t he l ong i tud ina l co lumn .

p o s i t i o n o f a n a d d i t i o n a l w e i gh t o n th e c o l u m n . T h e c o l u m n a n d t h e w e i gh t w e r e

s o t h i n a n d s m a ll t h a t t h e i r a e r o d y n a m i c c h a r a c te r i st i cs e x c e p t f o r t h e t r i m m e d

a ng le o f a t t a c k a nd the re su l t e d g l id ing spe e d w e re no t a ppre c i a b ly c ha ng e d by

th i s modi f i c a t i on f rom the o r ig ina l o r p l a in se e d .

In the p re se n t t e s t s i nc e t he sa me se e ds ha d to be t e s t e d se ve ra l t ime s t he t e s te d

s e e d s w e r e c a r e f u ll y ca u g h t b y a s o f t b a s k e t m a d e o f a p a p e r w h e n e v e r th e y s e e m e d

l ike ly t o c o l l i de w i th su r rou nd i ng obs t a c l e s a nd to su f fe r f a t a l da m a ge .



I 001

~ 0.50


0 0 0 0 . 6 0

L ~ O ~

M o , i e , seeo s

0.15 0-30 0.45

Co

F I G 7 P o l a r c u r v e o f Alsornitranacrocarpa.

271

T h e d a t a o f f li gh ts t a k i n g a w e a k l y s p i r a l p a t h w e r e u t i l i z e d in t h is t e s t, b e c a u s e

t h e f l i g h t a t h i g h l i ft c o e f f i c i e n t s h o w e d a s l ig h t t e n d e n c y t o s p i r a l i n s t a b i li t y . T h e

p o l a r c u r v e o f a t y p i c a l s e e d is s h o w n i n F i g. 7 .

erodynam ic nalysis of W ing

F r o m t h e f l i gh t t e st d a t a o f t h r e e - d i m e n s i o n a l w i ng s , th e a e r o d y n a m i c c h a r a c t e r is -

t i cs o f t h e t w o - d i m e n s i o n a l w i n gs s h o u l d b e o b t a i n e d . T h i s w a s a c t u a ll y p e r f o r m e d

a s f o ll o w s : h a v i n g a s s u m e d a s e t o f a i r f o il ( o r t w o - d i m e n s i o n a l ) d a t a a r b i t r a r il y ,

w h i c h is a s s u m e d i n v a r i a n t a lo n g th e s p a n , th e t h r e e - d i m e n s i o n a l a e r o d y n a m i c

c h a r a c t e ri s ti c s o f th e w i n g o f k n o w n g e o m e t r ic a l c o n f i g u r a t io n c o u l d b e o b t a i n e d

b y a p p l y in g t he l o ca l c ir c u la t io n m e t h o d ( L C M , A z u m a e t a l . 1 9 8 1 , 1 9 8 5 ) . Th en i t

w a s e a s y t o fi nd a n a d e q u a t e s e t o f a i r fo i l d a t a b y w h i c h t h e t h r e e - d i m e n s i o n a l w i n g

c h a r a c t e r i s t i c s c o r r e s p o n d e d t o th e f l ig h t d a t a o f al l t e s t e d w i n gs . S h o w n i n F ig .

8 ( a ) a n d ( b ) a r e e s t im a t e d r e s u lt s o f p o l a r c u r v e s o f tw o - a n d t h r e e - d i m e n s i o n a l

w i n g s , a n d l i ft - to - d r a g c h a r a c t e r i s t ic s o f t h e e n s e m b l e m e a n o f th e t e s t s e e d s a t a

R e y n o ld s n u m b e r o f R e ~ 4 × 10 3. T h e m i n i m u m d r a g c o e f f ic i e n t Coo i s a b o u t t w i c e

t h e s k i n f r ic t i o n d r a g o f a fl a t s u r f a c e a t t h e s a m e R e y n o l d s n u m b e r . T h e w r i n k le s

o n b o t h s u r f a c e s o f t h e w i n g s e e m t o b e u n c o n n e c t e d t o th e d r a g r is e a t t h is s m a l l

R e y n o l d s n u m b e r .

I t m u s t b e m e n t i o n e d t h a t t h e d r a g c o e f f ic i e n t o f th e t w o - d i m e n s i o n a l w i n g is

v e r y l a rg e i n t h e r a n g e o f h i g h a n g l e - o f - a tt a c k . T h i s e x p l a i n s w h y t h e g l i d i n g f l ig h t

is p e r f o r m e d a t t h e l o w l if t c o e f f i c ie n t a s s t a t e d b e f o r e .

S h o w n i n F i g. 9 a r e t h e l i ft - to - d r a g r a t i o a n d t h e r a t e o f d e s c e n t o f t h e t h r e e -

d i m e n s i o n a l w i n g a s a f u n c t i o n o f l if t c o e f f ic i e n t, w h i c h a r e c a l c u l a t e d b y th e L C M

f r o m t h e e s t im a t e d t w o - d i m e n s i o n a l a e r o d y n a m i c c h a ra c te r is t i c s. T h e m a x i m u m

l i f t - t o - d r a g r a t i o a n d t h e m i n i m u m r a t e o f d e s c e n t a r e r e s p e c t i v e l y g i v e n a t C L ----0 2 7

a n d C L = 0 5 3 . H o w e v e r , t h e r a t e o f d e s c e n t i s a l m o s t c o n s t a n t i n t h e s p e e d r a n g e



7

A . A Z U M A A N D Y . O K U N O

. + _ -

5

u

. J

1 - 50

0 - 7 5

0 . 0 0

1 . 5 0

0 - 7 5

a)

p - 6 0

C L m a , = 1.19

2D po lor / / / CL mox 0 ' 87

0 5 7

0 -1 5 0 3 0 0 4 5

O r o g c o e f f i c i e n t C o , C d

i

b )

Ct. m a x = I '19

. . . . .

/

l e : 1 4 ( d e g )

c,~ = o.o 38 ; 5 .z a 2

5 / 0 0 I i

I 0 . 0 1 5 . 0

0 0 2 0 ' 0

A ng l e o f a t t ock , a ( deg ,)

F I G . 8 . E s t i m a t e d c h a r a c t e r i s t i c s o f

Alsomitra macrocarpa.

a ) P o l a r c u r v e . b )

Ct-a Ca-a

c u r v e o f

t h e a i r f o i l .

. _ 6 = _

D 0

5 - 0 0

2 5 0

A l som i t r o ,

c = o . 3 4

LID

/ ~ - = - - _

0 0 0 0 2 5 0 5 0 0 7 5 I ' 0 0

L i f t coe f f i c i en t , L

FIG 9 Pe r f or man c e o f t h e e s t ima t e d win g



F L I G H T O F S M R

273

of less than 1.7 m/sec. Therefore the optimal speed is considered to be the speed

of (L~D max. The ensemble mean of the lift coefficients in the flight test was CL= 0 34.

If wind is absent, the seed can get the highest distance by flying with a lift

coefficient of CL = 0 27, at which the lift-to-drag ratio and thus the gliding ratio (the

ratio of horizontal distance and the height loss) are maximum. However, if there is

a wind, then the flight is strongly dependent on the time until the seed reaches the

ground after the initiation of falling. This suggests that flight should occur at the

lift coefficient giving the minimum rate of descent. Thus, it is an interesting fact

that the actual lift coefficient of CL= 0.34 lies between two optimal lift coefficients,

the maximum lift-to-drag ratio (or the maximum gliding ratio) and the minimum

rate of descent, but is closer to the former because the minimum rate o f descent is

almost constant beyond the selected value, CL > 0 34. Here, also, as seen in many

other locomotions, the living creature acts to get the optimal performance.

o n t r ib u t io n o f t h e H u s k

The geometrical configuration of the husk appears to contribute to the dispersal

of the winged seeds. Therefore, the husk was hung in a wind tunnel which had a

circular cross section of 3 m diameter in the test area. From the observation of

smoked flow of paraffin mist around the husk it was revealed that the flow approach-

ing the mouth enters into the inside of the husk and then goes out from the rear

(downstream) part of the hole. Through this excursion of the flow, probably, the

respective seeds are removed from the husk successively.

As the wind speed increased, the husk hung in the wind tunnel was shaken by

the so-called Karman vortex series in the wake. Figure 10 shows the frequency

of the wake fluctuation, measured by a hot-wire anemometer, vs. the wind speed

U. The vertical line gives the standard deviation o f the frequency increases with the

speed almost linearly, and the slope orthe Strouhal number based on the maximum

diameter of the husk, d, is approximately given by S = nd/U ~-0-17. The husk may

therefore be shaken with its own resonant frequency, which is determined by its

p

D

o

2 0 0

I0 0

0 00

3 b o 6 b o

9 b o

W i nd s p e e d , U ( m / s )

FIG. 10. Frequencyof the Karman vortex series.

n

..0 - = o .1 7

1 2 - 0 0



274 A, AZUMA AND Y. OKUNO

pen dulu m length. The shaken m otion mu st be helpful for the dispersal of the

seed.

o n c l u s i o n

The geometrical characteristics of the wing of

A l s o r n i t r a m a c r o c a r p a ,

such as the

slightly swept and twisted wing, the reflected trailing edge of the airfoil, the lightly

loaded wing and adequately arranged

C G

position, are well fitted to assure the

good performance and stability in gliding flight of the winged seed. The thin wing

with a sharp leading edge and adequate aspect ratio ( A R =3 -- 4) produce the

appropriate lift-to-drag ratio (L/D ~ 3- 4) for the flight in small Reynolds number

( R e

~ 4 x 103). The low wing loading (m g/ S ~ 0.5 N / m 2) also guarant ees a smaller

rate of descent ( w= 0 . 3 -0 , 7 m/sec) than those of the rotary seeds. The flight is

perf orme d at a lift coefficient of CL =0. 34 , which not on ly gives the ma ximu m

gliding ratio but also guarant ees appr oxim atel y the minimum rate of descent. The

above small lift coefficient is adopted because of the large drag coefficient at high

angles of attack.

By applying the local circulation method, the two-dimensional aerodynamic

characteristics of the wing section is revealed.

It is also made clear that the dispersal of the seeds is assisted by the wind

surround ing the husk, and the resonant pen dulu m motion of the hung husk.

The authors would like to express their sincere thanks to the Botanic Gardens of Indonesia

[Lembaga Biologi National L.I.P.I., Kebum Raya Indonesia (Hortus Botanicus Bogoriensis)],

Bogor-lndonesia, for supplying a husk and winged seeds of

A l s o r n i t r a r n a c r o c a r p a

for this

study.

REFERENCES

ABBOTT I. H. VON DOENHOFF A. E. (1959). Theo O, of W ing Sections. New York: Dover.

AHLBORN, FR. (1897). In: Abhandl, aus dem Bebiete der Naturwissenschaften. Vol. XV. Hamburg: L.

Friederichsen (in German).

AZUMA, A., NASU, K. HAYASH1,T. (1981). Vertica 7, 45.

AZUMA A. YASUDA K. (I985). In: Proc. 23rd Aircra ft Syrup. Jap an So c. Aeronaut. Space Sci . , Nagoya,

21-22 October. pp. 354-357 (in Japanese).

AZUMA A. AZUMA S. WATANABE 1. • FURUTA T. (1985). J.

exp . Biol .

116, 79

HERTEL, H. (1966). In:

S t r u c t u r e - F o r m - M o v e m e n t

(translated by Katz, M.S. as editor-in-chief). New

York: Reinhold.

VON KARMAN,T. RUBACH, H. (1912).

Physik. Z.

13, 49 (in German).

K,MURA, H. (1943). K6 ku Asa hi (Aeronaut . Mag. ) November, 60 (in Japanese).

Kuo, Y. H. (1953). J. math. Phys. 32.

MCCuTCHEN, C. W. (1977). Science 197 (4304) 691.

MORIYA, T. (1942). In: Selected Scientific and Technical Papers, The Moriya Memorial Committee,

Tokyo, 1959. Translated from

J. Soc. aeronaut. Sci. Jpn

8(84), 447.

NORBERG R. ~. (1973). Biol , Rev . 48, 561.

PERKINS, C. D. HAGE, H. E. (1949). Airplane Performance, Stabit i t ) ,and Control New York: John Wiley.

RAYNER, J. M. V. ALDRIDGE,H. D. J. N. (1985). 3'. exp. Biol . 118, 247.

WEIS-FOGH, T. JENSEN, M. (1956). Phi l Trans . R. Soc . Lond. B, 239 (667), 415.

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Azuma JTheoBiol 1987