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Flight of Seeds, Flying Fish, Squid, Mammals, Amphibians and Reptiles 89

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Flight of Seeds, Flying Fish, Squid, Mammals, Amphibians and Reptiles 89 Flight of seeds, flying fish, squid, mammals, amphibians and reptiles A. Azuma University of Tokyo, Tokyo, Japan. Abstract There are four ways for dispersing flying seeds: parachuting flight with fine filaments or pappi and gliding, rocking and spinning (or autorotational) flights with a wing or wings. A bundle of pappi applied to small seeds of flowering plants enables the seed to drift in a wind at a low rate of descent less than 0.5 m/s, whereas the wing utilized widely for flowering trees makes the seed flyable at the rate of descent less 0.5 m/s for gliding seeds and near 1.0 m/s for spinning seeds. These values are not irrelevant to their environmental condition and season of dispersion. Flying fish and squid make gliding flight with a pair of pectoral fins and membraned legs, respectively. The aspect ratio of their wing is so large (more than 5) that they are high performance flyers without beating their wings. The flying fish obtains its take-off speed by the violent fanning of the lower part of caudal fin immersed in the water and by exposing other parts of body in the air to reduce the drag. On the other hand, the flying squid attains its take-off speed by the water jet expelled from a nozzle of mantle where the water is stored. During the flight, in responding to the speed reduction due to the drag, the squid increases the trimmed angle of attack or the lift coefficient and keeps the flying height constant. Flying mammals, amphibians and reptiles have a membranous wing, the aspect ratio of which is less than 2, and make the gliding flight with a poor gliding ratio. However, the low aspect ratio wing enables them to perform highly maneuverable flights and to land either on the horizontal ground surface without over-running or on the vertical tree surface. 1 Flying seeds 1.1 Pappose seeds Fundamentally, in a calm atmosphere, pappose seeds make vertical descending flights by utilizing the drag force acting on the pappi as shown in Fig. 1a and b. The aerodynamic characteristics of a circular cylinder, which can simulate not only a pappus but also a flagellum of small swimming organisms in low Reynolds number, are given by Lamb [1], Gray and Hancock [2], Holwill and Burge [3], Cox [4], Chwang and Wu [5], Lighthill [6] and Azuma [7]. By conducting falling tests WIT Transactions on State of the Art in Science and Engineering, Vol 3, © 2006 WIT Press www.witpress.com, ISSN 1755-8336 (on-line) doi:10.2495/1-84564-001-2/2b Flight of Seeds, Flying Fish, Squid, Mammals, Amphibians and Reptiles 89 Figure 1: Parachuting flight and the aerodynamic forces acting on a pappose seed. of pappose seeds in calm air, Minami and Azuma [8] evaluated the well-fitted equation describing the drag force. As shown in Fig. 1b, under the assumption of no lateral (or side slipping) translation, the longitudinal and normal components of inflow velocity caused by the vertical descent w are, respectively, given by w sin β and w cos β. Then the longitudinal and normal components of the aerodynamic force acting on a pappus, which is assumed to be a fine circular cylinder with length of lp and located at azimuth angle ψ and coning angle β are, respectively, given by ft = µlpw sin β Kt, (1) fn = µlpw cos β Kn, where, according to Chwang and Wu [5] and Jones et al. [9], the coefficients Kt and Kn are selected to be = π − Kt 2 / loge 2lp/dp 0.5 , (2) = π + Kn 2 / loge 2lp/dp 0.5 . The lift and drag components of a pappus are given by l = f cos ϕ, (3) d = f sin ϕ, = 2 + 2 where f ft fn . Then, the drag force acting on all pappi and directing vertically upward is given by Dp = [( ft sin β) + ( fn cos β)], (4) n where the summation must be extended over every pappus arranged with respective azimuth angle ψ and the coning angle β. WIT Transactions on State of the Art in Science and Engineering, Vol 3, © 2006 WIT Press www.witpress.com, ISSN 1755-8336 (on-line) 90 Flow Phenomena in Nature This parachuting force must be balanced with the weight of the whole seed and the drag force of the seed and stalk. The seed and stalk are also assumed to be an ellipsoidal body and a circular cylinder, respectively. Their drag force is directed upward and is given by 1 D = ρw2S C + µl wK , (5) s 2 c D,s s t = 1 π 2 where Sc is the cross-sectional area of the seed body Sc 4 d and CD,s is given by Hoerner [10] as follows: 1/2 CD,s = 0.44(d/l) + 4Cf (l/d) + 4Cf (d/l) , (6) where the Reynolds number is based on the length of the seed. Then the vertical force is given by W = D = Dp + Ds. (7) This equation can be solved for the rate of descent for a given configuration of the seed. A dashed line designated ③ in Fig. 2 shows a relation of w = 7.0 ×(W/A), which represents approximately the above relation. In Fig. 2, results obtained from other numerical analyses, which are based on different expres- sions of the drag coefficient for the circular cylinder [8], are also presented by designations ①, ② and ④ as a function of either wing loading W/S or disc loading W/A. For comparison, many statistical data obtained from the flight tests of various species of pappose seeds are also presented in Fig. 2. Since their rate of descent is very low, less than 0.4 m/s, a slight wind can scatter them widely from the top of stem, the length of which varies in proportion to the height of surrounding grasses in order to be well ventilated. Figure 2: Statistical data and numerical analyses of flying seeds observed in the rate of descent versus disc loading (redrawn from [8]). WIT Transactions on State of the Art in Science and Engineering, Vol 3, © 2006 WIT Press www.witpress.com, ISSN 1755-8336 (on-line) Flight of Seeds, Flying Fish, Squid, Mammals, Amphibians and Reptiles 91 1.2 Winged seeds Winged seeds are further classified into three groups, making such flights as gliding, straying or rocking accompanied with some fluctuations of the center of gravity location, and spinning or autorotational flights, each of which utilizes the lift as well as the drag acting on a flattened wing. 1.2.1 Steady gliding If the lift and drag coefficients are under a well-known relation = + 2 π CD CD0 CL/ AR, (8) the maximum lift-to-drag ratio can be given by 1 (L/D) = (C /C ) = πAR/C (9) max L D max 2 D0 at = π CL,(L/D)max ARCD0 . (10) Then, under the assumption of large L/D, in the steady gliding flight, the maximum range Rmax,s and the flight velocity V(L/D)max from a given height H can be obtained approximately as follows: = · Rmax,s (L/D)max H, (11) = π V(L/D)max 2(W/S)/ρ ARCD0 . (12) Similarly, under the same approximation, the minimum rate of descent wmin and other related equations can be given by w = 4 2/ρ W/SC1/4/(3πAR)3/4 = (4/3) (2/ρ)(W/S)C /πAR, (13) min D0 L,wmin = π 1/4 = 1/4 Vwmin (2/ρ)(W/S)/ 3CD0 AR V(L/D)max /3 , (14) at √ = π = CL,wmin 3CD0 AR 3CL,(L/D)max . (15) A species of winged seeds in Java, Alsomitra macrocarpa, shown in Fig. 3, makes an extremely high-performance gliding among other species. This is accomplished by its large aspect ratio wing, AR = 3 ∼ 4. The lift-to-drag ratio or gliding ratio is about L/D = 3 ∼ 4 and the rate of descent is w = 0.3 ∼ 0.7 m/s [11]. The stability of flight is guaranteed by having the following configuration [11]. The seed itself is very thin, about 1 mm in thickness, and core of the seed is located nearly at the center of gravity, which is a slightly forward position of the wing center. The wing is also very thin (from a few micrometers to some 10 µm) and has a swept and tapered plan form, twisted (washout) angle, reflected trailing edge, and adequately arranged position of the center of gravity. The reflected trailing edge must be essential for keeping longitudinal stability of tailless gliders [7]. Furthermore, when the seed is laterally slipped, the restoring force and moment can be generated by bending up the leading tip of flexible wing. It is interesting to know that the center of gravity of the winged seeds is located at an optimal position at which the respective seed can fly at the lowest rate of descent or the highest duration of flight [11]. WIT Transactions on State of the Art in Science and Engineering, Vol 3, © 2006 WIT Press www.witpress.com, ISSN 1755-8336 (on-line) 92 Flow Phenomena in Nature Figure 3: A gliding seed with large aspect ratio wing, Alsomitra macrocarpa. This species of flying seed is a parasitic plant. It inhabits forests of the southeastern tropical area. Just before the rainy season in this area, many seeds take-off from a husk hanging from the tree which tangles with any branch of the parent tree. The winds surrounding the husk are not strong but include an upcurrent.
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