Quick estimates of flight fitness in hovering animals
Quick estimates of flight fitness in hovering animals
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发表时间：
1973-08
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通讯作者：
T. Weis-Fogh
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作者：
T. Weis-Fogh
1. 在采用稳态空气动力学的假设下，导出了动物水平拍打翅膀正常悬停时的平均升力系数、雷诺数、气动功率、翼质量转动惯量和动力效率的简单解析表达式。2. 大多数悬停动物，包括大型板叶虫和鞘蛾，主要依靠正常的翼型作用。然而，在一些翼载荷小于10 N m -2 （1 kgf m -2）的群体中，非稳态空气动力学必须起主要作用，即在低雷诺数的非常小的昆虫中，在真正的盘旋蝇（Syrphinae）中，在大型蜻蜓（Odonata）中，在许多蝴蝶（鳞翅目Rhopalocera）中。3. 具体的气动功率范围在1.3到4.7 WN -1 （11-40 cal h -1 gf -1）之间，但功率输出并不随尺寸系统地变化，特别是因为升阻比在低雷诺数时恶化。4. 代谢率、空气动力和动力效率的比较表明，大多数昆虫需要并依赖于胸部有效的弹性系统来抵消翅膀惯性引起的弯矩。5. 用慢动作电影的方法分析了一种非常小的黄斑小黄蜂的自由飞行。在如此低的雷诺数（10-20）下，稳定的空气动力学条件下，2或3的高升力系数是不可能的，黄蜂必须几乎完全依赖于非稳定的流动模式。6. 在悬停时，Encarsia的翅膀几乎是水平移动的，身体是垂直的，在翅膀的划动中有三个不同寻常的阶段：拍击，投掷和翻转。在拍击中，翅膀在形态上划的顶部聚集在一起。在腾空中，这是形态下划开始时的旋前动作，相对的翅膀像一本书一样张开，在它们的后缘上盘旋。在翻转中，这是在形态上划的开始时的旋后，翅膀迅速扭曲约180°。7. 投掷是迄今为止未描述的一种机制，用于产生升力，并在预期下击时在机翼上建立适当的循环。在Encarsia的情况下，计算和观察到的机翼速度在升力等于体重的情况下是一致的，升力几乎是瞬间产生的，从下冲程开始，没有任何瓦格纳效应。这种飞行机制似乎与蝴蝶的正常飞行有关，可能也与果蝇和其他小型昆虫有关。尺寸和其他方面的考虑表明，在鸟类和蝙蝠起飞和紧急情况下，它可能是一个有用的机制。8. 翻转也被认为是在机翼周围建立适当循环的一种手段，迄今为止还没有引起人们的注意；但人们对它的运作却知之甚少。它不仅局限于Encarsia，也适用于其他昆虫，不仅在向上划水的开始（旋后），而且在向下划水的开始，翻转（旋前）取代了Encarsia的拍击和投掷。一项对自由飞行的飞蝇的研究有力地表明，食蚜蝇科（和食蚜蝇科）在悬停时几乎完全依赖于翻转机制。在这些昆虫的情况下，假定在翅膀通过空气平移之前，通过快速的旋前（或旋后），在翅膀柔软的后部之前影响坚硬的前缘，建立了一个短暂的循环。在翻转机制中，相反意义的旋涡必须脱落，并且必须存在瓦格纳效应。9. 在一些悬停昆虫中，翅膀扭曲发生得如此之快，以至于弹性扭转波从底部到尖端的传播速度起了重要作用，似乎带来了有益的影响。10. 非稳定时期，特别是翻转效应，存在于所有拍打的动物中，它们会改变并叠加在这里给出的数学模型所描述的稳态模式上。然而，积累的证据表明，大多数悬停动物都相当符合这个模型。11. 许多新的分析类型在文本中指出，现在开放给未来的理论和实验研究。
1. On the assumption that steady-state aerodynamics applies, simple analytical expressions are derived for the average lift coefficient, Reynolds number, the aerodynamic power, the moment of inertia of the wing mass and the dynamic efficiency in animals which perform normal hovering with horizontally beating wings. 2. The majority of hovering animals, including large lamellicorn beetles and sphingid moths, depend mainly on normal aerofoil action. However, in some groups with wing loading less than 10 N m -2 (1 kgf m -2 ), non-steady aerodynamics must play a major role, namely in very small insects at low Reynolds number, in true hover-flies (Syrphinae), in large dragonflies (Odonata) and in many butterflies (Lepidoptera Rhopalocera). 3. The specific aerodynamic power ranges between 1.3 and 4.7 WN -1 (11-40 cal h -1 gf -1 ) but power output does not vary systematically with size, inter alia because the lift/drag ratio deteriorates at low Reynolds number. 4. Comparisons between metabolic rate, aerodynamic power and dynamic efficiency show that the majority of insects require and depend upon an effective elastic system in the thorax which counteracts the bending moments caused by wing inertia. 5. The free flight of a very small chalcid wasp Encarsia formosa has been analysed by means of slow-motion films. At this low Reynolds number (10-20), the high lift co-efficient of 2 or 3 is not possible with steady-state aerodynamics and the wasp must depend almost entirely on non-steady flow patterns. 6. The wings of Encarsia are moved almost horizontally during hovering, the body being vertical, and there are three unusual phases in the wing stroke: the clap , the fling and the flip . In the clap the wings are brought together at the top of the morphological upstroke. In the fling, which is a pronation at the beginning of the morphological downstroke, the opposed wings are flung open like a book, hinging about their posterior margins. In the flip, which is a supination at the beginning of the morphological upstroke, the wings are rapidly twisted through about 180°. 7. The fling is a hitherto undescribed mechanism for creating lift and for setting up the appropriate circulation over the wing in anticipation of the downstroke. In the case of Encarsia the calculated and observed wing velocities at which lift equals body weight are in agreement, and lift is produced almost instantaneously from the beginning of the downstroke and without any Wagner effect. The fling mechanism seems to be involved in the normal flight of butterflies and possibly of Drosophila and other small insects. Dimensional and other considerations show that it could be a useful mechanism in birds and bats during take-off and in emergencies. 8. The flip is also believed to be a means of setting up an appropriate circulation around the wing, which has hitherto escaped attention; but its operation is less well understood. It is not confined to Encarsia but operates in other insects, not only at the beginning of the upstroke (supination) but also at the beginning of the downstroke where a flip (pronation) replaces the clap and fling of Encarsia . A study of freely flying hover-flies strongly indicates that the Syrphinae (and Odonata) depend almost entirely upon the flip mechanism when hovering. In the case of these insects a transient circulation is presumed to be set up before the translation of the wing through the air, by the rapid pronation (or supination) which affects the stiff anterior margin before the soft posterior portions of the wing. In the flip mechanism vortices of opposite sense must be shed, and a Wagner effect must be present. 9. In some hovering insects the wing twistings occur so rapidly that the speed of propagation of the elastic torsional wave from base to tip plays a significant role and appears to introduce beneficial effects. 10. Non-steady periods, particularly flip effects, are present in all flapping animals and they will modify and become superimposed upon the steady-state pattern as described by the mathematical model presented here. However, the accumulated evidence indicates that the majority of hovering animals conform reasonably well with that model. 11. Many new types of analysis are indicated in the text and are now open for future theoretical and experimental research.