Torkel Weis-Fogh

Bio: Torkel Weis-Fogh is an academic researcher from University of Copenhagen. The author has contributed to research in topics: Resilin & Wing. The author has an hindex of 30, co-authored 36 publications receiving 5539 citations. Previous affiliations of Torkel Weis-Fogh include University of Cambridge & Medical Research Council.

Quick Estimates of Flight Fitness in Hovering Animals, Including Novel Mechanisms for Lift Production

Abstract: 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.

A Rubber-Like Protein in Insect Cuticle

Abstract: 1. A new type of hyaline, colourless cuticle, called rubber-like cuticle, is described and analysed qualitatively with respect to mechanical behaviour, structure and composition. Externally it is covered by ordinary thin epicuticle, but otherwise it represents the simplest type of cuticle known and consists only of thin continuous lamellae of chitin (0-2 µ) separated and glued together by an elastic protein, resilin , not hitherto described. There are only traces of water-soluble substances present and resilin sometimes occurs as pure, hyaline patches more than 100 µ thick and suitable for macroscopic experiments. 2. In all physical respects, resilin behaves like a swollen isotropic rubber but the rigid experimental proof is given elsewhere (Weis-Fogh, 1961). An outstanding feature is the complete lack of flow not paralleled by other natural or synthetic rubbers. 3. Resilin resembles elastin but it is devoid of colour and has a different and characteristic amino-acid composition (Bailey & Weis-Fogh, 1961). The nature of the cross-linkages is unknown at present but they are extremely stable, of a co-valent type and different from other known cross-linkages in proteins. This accounts for its insolubility and resistance to all agents which do not break the peptide backbone. 4. Resilin is a structure protein in which the primary chains show little or no tendency to form secondary structures; they are bound together in a uniform three-dimensional network (the tertiary structure) with no potential limits as to size.

Energetics of Hovering Flight in Hummingbirds and in Drosophila

Abstract: 1. Expressions have been derived for an estimate of the average coefficient of lift, for the variation in bending moment or torque caused by wind forces and by inertia forces, and for the power output during hovering flight on one spot when the wings move according to a horizontal figure-of-eight. 2. In both hummingbirds and Drosophila the flight is consistent with steady-state aerodynamics, the average lift coefficient being 1.8 in the hummingbird and 0.8 in Drosophila. 3. The aerodynamic or hydraulic efficiency is 0.5 in the hummingbird and 0.3 in Drosophila, and in both types the aerodynamic power output is 22-24 cal/g body weight/h. 4. The total mechanical power output is 39 cal g-1 h-1 in the hummingbird because of the extra energy needed to accelerate the wing-mass. It is 24 cal g-1 h-1 in Drosophila in which the inertia term is negligible because the wing-stroke frequency is reduced to the lowest possible value for sustained flight. 5. In both animals the mechanical efficiency of the flight muscles is 0.2. 6. It is argued that the tilt of the stroke plane relative to the horizontal is an adaptation to the geometrically unfavourable induced wind and to the relatively large lift/drag ratio seen in many insects. The vertical movements at the extreme ends may serve to reduce the interaction between the shed ‘stopping’ vortex and the new bound vortex of opposite sense which has to be built up during the early part of the return stroke. 7. Two additional non-steady flow situations may exist at either end of the stroke, delayed stall and delayed build-up of circulation (Wagner effect), but since they have opposite effects it is probable that the resultant force is of about the same magnitude as that estimated for a steady-state situation. 8. Most insects have an effective elastic system to counteract the adverse effect of wing-inertia, but small fast-moving vertebrates have not. It is argued that the only material available for this purpose in this group is elastin and that it is unsuited at the rates of deformation required because recent measurements have shown that the damping is relatively high, probably due to molecular factors.

Fat combustion and metabolic rate of flying locusts (Schistocerca gregaria Forskål)

Abstract: The nature and the amount of fuel used by flying Schistocerca gregaria Forskal have been estimated from direct analyses of the total content of fat and glycogen in control groups and in the corresponding flying groups, i.e. groups which had flown continuously for several hours. The locusts were cage-bred and resembled phase gregaria or phase transiens. Each batch was so homogeneous that it was possible to select two groups, consisting of six to fifteen individuals, which did not differ by more than 2% from one another. Because of this uniformity and because of the high rate of metabolism during flight, this rate could be estimated within about $\pm $ 15% (in one case $\pm $ 30%). For flight, the locusts were suspended at the periphery of a special roundabout (Krogh & Weis-Fogh 1952). The groups could choose the flying speed that they would naturally adopt. The speeds and durations of flight were of the same order of magnitude as observed in swarms in nature, so that some of the results could be applied to natural swarms. Analyses of the geometric similarity and of the distribution and nature of dry matter made possible an estimation of average size and gross composition of fully developed but sexually immature S. gregaria. Such standard individuals were found to contain large amounts of lipids (an average of 10% of the fresh weight), and about 85% of the stored energy was in the depot fat. The cuticle and the wing muscles of newly emerged adults (fledglings) contained only one-third of the dry matter that was found in fully developed individuals, and the accumulation of dry matter lasted 2 or 3 weeks. Fledglings were unable to fly or disinclined to fly for long. In spite of differences in age, sex, training and food, in all flight experiments fat constituted the principal source of energy, the remainder being glycogen. An average of 80 to 85% of the total energy expenditure was derived from fats or fatty acids during the first 5 h of flight. All the available glycogen was utilized during the first few hours, most of it probably within the first hour. Flight was nevertheless maintained for several hours without reduction of speed. The metabolic rate on the roundabout increased approximately with the second power of the flying speed. The speed was almost independent of temperature and varied between 2 $\cdot $ 3 and 3 $\cdot $ 7 m/s, but the speeds recorded from a large number of experiments were equally distributed around 3 m/s; the average metabolic rate of flying Schistocerca was about 75 kcal/kg/h. This corresponded to an oxygen uptake of 161. O $_{2}$ /kg/h. The values deduced for the first few minutes after the start were three times higher, and cruising rates twice as high were sometimes maintained for several hours. An average flight performance of 5 h at 3 m/s required twice as much energy as was contained in the constituent proteins of the wing muscles. Sustained flight therefore depends on large-scale transport of fuel from the stores to the muscles. The fat body delivered 85 to 90% of the energy, and the remainder was mobilized from wing muscles, legs and wings. Since even the remote cells of the wings provided stores of fuel, the mobilization was of a general nature and the transport of fuel took place via the blood. Concerning migrating swarms the following was suggested: in the morning, milling and surging of groups of locusts before mass departure tends to empty the stores of glycogen; the proper migratory flight therefore takes place at the expense of fat and, under suitable climatic conditions, the endurance of flight is proportional to the amount of fat in storage before the start. Standard individuals with 10% of fat (by fresh weight) should be able to fly continuously for about 12 h, 20 h being the upper limit (15 to 16% of fat). The amount of vegetation daily consumed by a migrating swarm probably weighs as much, and possibly three times as much, as the weight of the swarm. Sufficient time and opportunity for feeding will therefore be essential for migrations. A large migrating swarm (say 15000 tons) was estimated to require as many calories per day as do 1 $\cdot $ 5 million men. The rate at which the wing muscles of locusts converted energy was between 400 and 800 kcal/kg muscle/h; i.e. the same rates as found in hovering humming birds and flying Drosophila. Even for very intense muscular work, fat cannot therefore be regarded as inferior fuel in well-oxygenated muscles. An increasing amount of evidence from the literature favours the view that fat can be utilized directly. A possible cause for the lowered mechanical efficiency of man when fat is oxidized is the formation of ketone bodies parallel to the direct combustion of fat. On the other hand, initial mobilization seems to be slower for fat than for glycogen. When flight starts, this gives glycogen an advantage over fat, whereas the weight economy, and thus the endurance, is decisively improved by the ability to utilize stored fat; this will be further discussed elsewhere.

Biology and Physics of locust flight II. Flight performance of the desert locust (Schistocerca gregaria)

Abstract: The main purpose is to analyze how a number of wing-stroke parameters are related to the lift (average vertical force) and thrust (average horizontal force) produced by the insect under well defined aerodynamic conditions. The locust was suspended from a complicated balance and flew against a uniform horizontal wind from an open-jet wind tunnel. The wind speed was automatically adjusted to the preferred flying speed (air speed), i.e. the speed at which the thrust equals the extra-to-wing drag . The lift was measured as the apparent reduction in weight; it is given as a percentage of the weight which the individual would have if it had flown for about one hour, was full-grown and well fed but, if a female, with undeveloped eggs ( = basic weight). This figure is the relative lift, and it is used because the actual weight changes much with age, feeding, sexual development, etc., while the dimensions of the flight motor remain constant. The angle between the wind and the long body axis is the body angle and was chosen by the observer or by the insect itself. Most experiments took place at 30° C (constant temperature room), but series were run at the upper and lower limits for flight, including experiments with small flocks of locusts suspended from a roundabout. The rate of evaporation of water from the thorax was kept constant. In a large number of individuals sustained steady-state flight was studied; at regular intervals a set of simultaneous readings were taken consisting of the lift, the speed, the body angle, the stroke frequency, the extreme angular positions of the wings, and of the inclination to the vertical of the stroke planes. In addition, the angular movements of the entire wings relative to the body were estimated from slow-motion films. The results are seen in §§4 to 7. The frequency distribution of the relative lift has its maximum about 100 %, showing that, in this respect, the flight comes near to free flight. It varied from 35 to 175 %, i.e. about five times. During continuous horizontal flight the flying speed was 3•5+ 0•1 m/s and may increase to 4•2 m/s in free flight. At larger lifts (climbing) the steady-state speed could reach 4•5 m/s. During the first minutes the speed was often 4•5 to 5•0 m/s, the maximum observed being 5•5 m/s. No locust lifted its own weight at speeds less than 2•5 m/s. The power necessary to overcome the extra-to-wing drag only corresponds to 1 to 3 % of the total metabolic rate. The effect of altering the body angle is fundamentally different from that of altering the pitch of an aircraft; the lift is controlled and kept constant by the locust and proved to be independent of alterations in the body angle amounting to as much as 20°. This is the basis for the technique and for the treatment of the results. In spite of the large variations in lift, the following stroke parameters varied little or not at all: the stroke angles , the stroke-plane angles , the middle position of the wings , and the time course of the angular movement of the entire wing, y = y(t). The latter function deviates considerably from a simple harmonic oscillation. According to figure II, 20, the average points are determined with an accuracy of better than + 1 %, permitting graphical differentiation. The stroke frequency was rather constant but increased with the reflexly controlled lift, contrary to Chadwick’s experiments on Drosophila , and decreased with increasing size, according to Sotavalta’s findings in other insects. The maximal changes were small, however, amounting to 8 % (lift) and 15 % (size) respectively. The flight performance and the stroke parameters were independent of changes in air temperature (no radiant heat) within 25 to 35° G, although the pterothorax is subjected to similar changes. Sustained flight does not take place below 25° C and above 35° G, but short performances were observed between 22 and 24° C as well as above 37° C. The great variation in lift could not be explained by changes in the measured stroke parameters, and by analogy with a variable-pitch propeller, it must be caused by differences in wing twisting 0(r,t). It was also found that lift and thrust varied in a more intricate way than in a simple actuator disk. The regularity of the stroke and its independence of temperature makes it possible to define a standard stroke , making it easy to compare a given performance with the normal.

The insects: structure and function.

Abstract: The Insects has been the standard textbook in the field since the first edition published over forty years ago. Building on the strengths of Chapman's original text, this long-awaited 5th edition has been revised and expanded by a team of eminent insect physiologists, bringing it fully up-to-date for the molecular era. The chapters retain the successful structure of the earlier editions, focusing on particular functional systems rather than taxonomic groups and making it easy for students to delve into topics without extensive knowledge of taxonomy. The focus is on form and function, bringing together basic anatomy and physiology and examining how these relate to behaviour. This, combined with nearly 600 clear illustrations, provides a comprehensive understanding of how insects work. Now also featuring a richly illustrated prologue by George McGavin, this is an essential text for students, researchers and applied entomologists alike.

Wing rotation and the aerodynamic basis of insect flight.

Abstract: The enhanced aerodynamic performance of insects results from an interaction of three distinct yet interactive mechanisms: delayed stall, rotational circulation, and wake capture. Delayed stall functions during the translational portions of the stroke, when the wings sweep through the air with a large angle of attack. In contrast, rotational circulation and wake capture generate aerodynamic forces during stroke reversals, when the wings rapidly rotate and change direction. In addition to contributing to the lift required to keep an insect aloft, these two rotational mechanisms provide a potent means by which the animal can modulate the direction and magnitude of flight forces during steering maneuvers. A comprehensive theory incorporating both translational and rotational mechanisms may explain the diverse patterns of wing motion displayed by different species of insects.

Cryo-electron microscopy of vitrified specimens.

Abstract: Water is the most abundant component of biological material, but it is systematically excluded from conventional electron microscopy. This is because water evaporates rapidly under the vacuum conditions of an electron microscope. Cryoelectron microscopy has long been seen as a possible avenue to overcome this limitation, but until recently the direct observation of frozen-hydrated specimens was relatively unsuccessful because of a number of serious difficulties. These were, in particular, due to the absence of a good cryospecimen holder, the inherently low contrast of hydrated specimens and the structural damage due to ice crystals formed during freezing. As a consequence, the cryomethods which have flourished in electron microscopy during the last 20 years were not aimed at preserving the hydration of the specimen in the electron microscope. Freezing was only used as an aid to preparation. The objects ultimately observed in the electron microscope were dry and at room temperature. Such cryomethods have recently been reviewed in detail (Robards and Sleytr 1985).

Leading-edge vortices in insect flight

Abstract: INSECTS cannot fly, according to the conventional laws of aerodynamics: during flapping flight, their wings produce more lift than during steady motion at the same velocities and angles of attack1–5. Measured instantaneous lift forces also show qualitative and quantitative disagreement with the forces predicted by conventional aerodynamic theories6–9. The importance of high-life aerodynamic mechanisms is now widely recognized but, except for the specialized fling mechanism used by some insect species1,10–13, the source of extra lift remains unknown. We have now visualized the airflow around the wings of the hawkmoth Manduca sexta and a 'hovering' large mechanical model—the flapper. An intense leading-edge vortex was found on the down-stroke, of sufficient strength to explain the high-lift forces. The vortex is created by dynamic stall, and not by the rotational lift mechanisms that have been postulated for insect flight14–16. The vortex spirals out towards the wingtip with a spanwise velocity comparable to the flapping velocity. The three-dimensional flow is similar to the conical leading-edge vortex found on delta wings, with the spanwise flow stabilizing the vortex.

Quick Estimates of Flight Fitness in Hovering Animals, Including Novel Mechanisms for Lift Production

Abstract: 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.