The efficiency and mechanical power output of insect flight muscle have been estimated from a study of hovering flight. The maximum power output, calculated from the muscle properties, is adequate for the aerodynamic power requirements. However, the power output is insufficient to oscillate the wing mass as well unless there is good elastic storage of the inertial energy, and this is consistent with reports of elastic components in the flight system. A comparison of the mechanical power output with the metabolic power input to the flight muscles suggests that the muscle efficiency is quite low : less than 10%.

In recent years the mechanical analysis of animal locomotion has become increasingly sophisticated, resulting in accurate estimates of the sustained, aerobic mechanical power output required of the locomotor muscles. These estimates have been compared with the metabolic power input, as measured by the rate of oxygen consumption, to determine the muscle efficiency. Two major studies, one on running birds and mammals (Heglund, Fedak, Taylor & Cavagna, 1982) and the other on hovering insects (Ellington, 1984), have both concluded that the muscle efficiency can be much lower than the commonly expected 20–30%. The results for terrestrial locomotion are discussed elsewhere in this volume (Heglund, 1985), and I shall review the power and efficiency of insect flight muscle during hovering, a type of flight so energetically demanding that only hummingbirds and insects can sustain it aerobically.

We begin with the estimates of the mechanical power output required of the flight muscles. My estimates were obtained in a study that extended Weis-Fogh’s (1972, 1973) pioneering work on hovering flight. This study involved determining the wing motion from high-speed ciné films of a variety of insects in free hovering flight, and combining this data with morphological measurements in a new aerodynamic analysis. The oxygen consumption during hovering has been measured for only three of these insects, so I shall just present the results for them : a bumblebee, Bombus sp., a honey-bee, Apis mellifera, and a drone-fly, Eristalis tenax. For these insects, the aerodynamic power required to move the wings through the air ranged between 167 and 186Wkg-1 (muscle mass): all mass-specific powers will refer to the power per unit muscle mass.

Inertial power is needed to oscillate the wing mass during each wingbeat, but its net value will depend on the amount of elastic storage that is present. Perfect elastic storage will require no inertial power from the muscles, and the total mechanical power output will just be the mean aerodynamic power over the cycle: 167–186 Wkg-1. If there is no elastic storage, then the inertial power requirement raises the total power output to 441–568 Wkg-1. Elastic storage, and hence the muscle power output, will lie somewhere between these two extreme cases.

These power outputs can be compared with the metabolic power input for hovering insects to determine the overall mechanochemical muscle efficiency. The oxygen consumption of hovering insects has been reported many times in the last decade, and the metabolic power input can be estimated using a standard conversion factor : 20 J of chemical energy per ml O2 consumed. From the published data, the metabolic power for my three insects is 3·2 kW kg-1for Bombus (Heinrich, 1975), 3·7kWkg-1 for Apis (Withers, 1981) and 2·0 kWkg-1 for Eristalis (Gilbert, 1983).

The metabolic rates during insect flight are often 50–100 times the resting level, and it is commonly assumed that the metabolic cost of physiological support systems is negligible in flight. Despite Casey’s (1981a) warning that the cost of ventilation may be significant, it is customary to assume that virtually all of the O2 uptake is used by the flight muscles for mechanical (i.e. aerodynamic plus inertial) work. Dividing this mechanical power output by the metabolic power input gives the following efficiencies for the flight muscles: 5–8% assuming perfect elastic storage, and 12–29% assuming no elastic storage. These values are in close agreement with measurements of the metabolic power input and estimates of the mechanical power output presented by Casey (1981b) for hovering sphinx moths: his data yield mean efficiencies of 6% and 17% for perfect and zero elastic storage, respectively (Ellington, 1984).

We are thus left with an unpleasant choice. If there is good elastic storage then the muscle efficiency is much lower than the common expectation of 20–30 %, based on measurements from vertebrate striated muscle. To obtain more palatable values of efficiency we must stipulate negligible elastic storage, but this grates against an optimistic belief that locomotor systems are sensibly designed. It also denies the existence of three elastic elements that have previously been discovered in the insect flight system (Buchthal & Weis-Fogh, 1956; Machin & Pringle, 1959; Weis-Fogh, 1959, 1972; Jensen & Weis-Fogh, 1962; Alexander & Bennet-Clark, 1977): (i) the hard skeletal cuticle, (ii) elastomers such as the protein resilin, and (iii) an elastic component present in the flight muscle.

The evidence for elastic storage makes it likely that the muscle efficiency is indeed low. This tentative conclusion is also supported by Weis-Fogh’s & Alexander’s (1977) estimate of the maximum power output from striated muscle (about 250 Wkg-1 for insect non-fibrillar and vertebrate striated muscle) and there seems little reason to suspect that the value for insect fibrillar muscle should be any greater. If their estimate is correct, the insects mentioned above would be unable to hover unless they had very good elastic storage ; otherwise, the power output required from the muscles would be about twice the maximum available.

Pennycuick & Rezende (1984) have just published new estimates of the power output of muscle, based on a simplified form of the model of Weis-Fogh & Alexander (1977). They suggest that the power output asymptotically approaches a limit of 860 Wkg-1 as wingbeat frequency increases; for the frequencies of my three insects mentioned above the value would be 340–400 W kg-1. If their estimates are true, then only a moderate amount of elastic storage would be required, and the muscle efficiency could increase to 11–17%. These values are more acceptable than the earlier estimates of 5–8 %, but would still conflict with the experimental evidence for good elastic storage. In this paper I shall look at the characteristics of insect flight muscle to obtain new estimates of the power output, and show that the conclusion of low muscle efficiency is probably still with us.

Pennycuick & Rezende (1984) use a very simple expression for the mean power output of a muscle performing cyclic contractions. Let the muscle exert a force F over its cross-sectional area A while contracting through a length Δ L. We define the stress, σ, as F/A and the strain ϵ as Δ L/L, where L is the initial length of the muscle. The work done per unit mass of muscle is then σ ϵ / ρ, where the mass density of muscle ρ is about 1060 kgm-3 (Méndez & Keys, 1960). If the frequency of contractions is f, the mean power output per unit mass of muscle is just
formula
For a given skeletal lever system, the product of strain and frequency determines the flapping velocity of the wings. Aerodynamic requirements fix the flapping velocity within narrow limits for any particular flying insect, so the estimation of mean power output depends only on the choice of a suitable value for the muscle stress.

In choosing a value for stress, we must distinguish between two quite different types of insect flight muscle. In many respects, the main power-producing flight muscles of all insects are similar to vertebrate striated muscle. There is a comparable pattern of cross-striation from the actin- and myosin-containing filaments, the sarcoplasmic reticulum mediates calcium activation of the myofibrillar ATPase, and vesicles of the sarcoplasmic reticulum are closely associated with the transverse, or T, system that is formed by invaginations of the plasma membrane. Indeed, the only anomaly readily apparent under the light microscope is the tracheal system with its terminal tracheoles that supply the muscles with oxygen.

In the more primitive synchronous insect flight muscles there is direct nervous stimulation of each muscle contraction. Limitations on the speed of muscle relaxation are believed to impose an upper frequency limit of about 100 Hz on these muscles (Pringle, 1981). Insects achieved even higher wingbeat frequencies with the evolution of a special type of flight muscle, called asynchronous flight muscle. This name arises from the physiological peculiarity that muscle contractions proceed at a rate which is not coupled to the rate of nervous stimulation. General reviews of both types of flight muscle are plentiful (e.g. Pringle, 1967, 1972, 1981; Elder, 1975; Cullen, 1974; Usherwood, 1975; Tregear, 1977); I shall discuss only those aspects directly concerned with force and power production.

Synchronous muscle

Synchronous flight muscle occurs in relatively primitive insects like the Odonata (dragonflies and damselflies), Orthoptera (grasshoppers and locusts) and Lepidoptera (butterflies and moths). Many of the structural characteristics of synchronous muscle suggest high rates of contraction and high rates of energy utilization. The sarcoplasmic reticulum (SR) is well developed, and forms a fenestrated curtain around the fibrils. The distance from the SR to the myofibrils is generally less than 0·5 μm, facilitating rapid movement of Ca2+, and this extensive SR system occupies 5–20 % of the fibre volume. Large and numerous mitochondria fill some 30–40 % of the fibre, a proportion that is found in only the most aerobically active vertebrate muscles. Oxygen is supplied by tracheoles which, for most synchronous muscle, indent the plasma membrane and ramify throughout the fibres, reducing diffusion distances to the mitochondria to about 5 μm.

We now turn to the flight muscle of the locust, which is the only synchronous muscle that has been studied extensively. It is a typical twitch muscle that is stimulated once per wingbeat in normal flight, and twice in more strenuous flight (Wilson & Weis-Fogh, 1962). Its intrinsic speed is not very impressive, 6–9s-1 at 30 °C (Buchthal, Weis-Fogh & Rosenfalck, 1957), so the strain during contraction is only about 5 % (Weis-Fogh, 1956a) at the wingbeat frequency of 17 Hz (Weis-Fogh, 1956b). This strain is much less than that characteristic of vertebrate muscle and, as in all insects, the movement must be greatly amplified by the lever-like articulation of the wing base to produce the required wing motion. The mitochondria and SR occupy about 30% and 20% of the fibre volume, respectively, (Bûcher, 1965; Elder, 1975), leaving only half of the volume for myofibrils. The fibres constitute about 80 % of the muscle volume, with haemolymph and the tracheal system filling the rest (Buchthal & Weis-Fogh, 1956).

The maximum isometric stress σo exerted by the muscle is 160 kN m-2 at 11 °C (Weis-Fogh, 1956a). From his isotonic experiments Weis-Fogh suggested that σ0 might be 400 kN m-2 at 35 °C, which is close to the thoracic temperature during flight, but this would require a stress of 1000 kN m-2 (myofibril), more than twice the values for vertebrate striated muscle (Close, 1972; Weis-Fogh & Alexander, 1977). Buchthal et al. (1957) measured a maximum isometric twitch stress of 196 kN m-2 at 30 °C, which would give a more reasonable myofibrillar stress of 490 kN m-2 (myofibril). We may also note that σ0 for the flight muscle of a katydid, Neoconocephalus robustus, is 137 kN m-2 at 35 °C; the myofibrils of this muscle occupy 57 % of the fibres, and the intrinsic speed is about 11s-1 (Josephson, 1984). Taking all of these values into account, I would thus be surprised if σ0 for the locust muscle was much greater than about 200 kN m-2 at flight temperatures.

Isotonic contractions of synchronous muscle exhibit a typical force-velocity curve, so the operating stress must be considerably less than σo. Pennycuick & Rezende (1984) suggest that a stress of 0·5σo might be appropriate, assuming that the muscle is working near maximum efficiency. From the force-velocity curves of the locust (Buchthal et al. 1957) and the katydid (Josephson, 1984), a strain of 5 % at the respective wingbeat frequencies would indeed correspond to stresses close to 0·5σo. Taking an operating stress of 100 kN m-2, the maximum power output would then be 80 Wkg-1 for the locust, and 94 Wkg-1 for the katydid. The value for the locust agrees very well with two independent measures: Jensen’s (1956) aerodynamic analysis predicted 67–100 W kg-1, depending on assumptions about elastic storage and negative work, and Buchthal et al. (1957) measured a maximum of 81 Wkg-1 for isotonic twitch contractions.

Why is my estimate of 80 Wkg-1 so much less than the 250 Wkg-1 predicted by Weis-Fogh & Alexander ( 1977) and the 284 W kg-1 for the locust from Pennycuick & Rezende (1984)? Both previous studies ignored the relatively large volume occupied by the SR, and hence overestimated the myofibrillar content. Furthermore, Pennycuick & Rezende assumed that the locust muscle contracts 15 % of its length instead of the observed 5 %, and this factor of 3 largely accounts for the difference between our estimates. The estimate of maximum power output by Weis-Fogh & Alexander is based on an intrinsic speed of 25 s-1 and an optimum strain rate derived from Hill’s equation and the isometric tension-length curve. For an intrinsic speed of 9 s-1 and the observed strain rate, their model would, in fact, predict a power output close to 80 Wkg-1. Weis-Fogh & Alexander also quote a value of 170 Wkg-1 for the maximum power output that has been determined experimentally for the locust, which is about twice the value predicted here. However, that value results from a measured metabolic power input (Weis-Fogh, 1964) multiplied by an assumed muscle efficiency of 20 % ; since we are presently questioning the efficiency of flight muscle, that estimate should be regarded as dubious, if not misleading. Indeed, Weis-Fogh (1976) derived the efficiency of locust flight muscle as only 11%, which would reduce the estimate to 94Wkg-1.

In general, a maximum power output of about 80 Wkg-1 agrees fairly well with the scanty experimental data for the locust, and the discrepancies with other estimates are readily explained. It is quite likely that the maximum power output scales with wingbeat frequency, so estimates for all other synchronous fliers will have to be extrapolated from this one value pieced together for the locust ! These estimates are discussed in the section on scaling.

Asynchronous muscle

Asynchronous flight muscle is found in the Diptera (flies), Coleoptera (beetles), Hymenoptera (bees), Thysanoptera (thrips), Psocoptera (booklice) and Hemiptera (true bugs). Much of the research has concentrated on a glycerol-extracted flight muscle preparation from the giant waterbug Lethocerus, and Tregear (1977) provides a convenient review of this work.

Even though asynchronous muscle evolved independently many times from synchronous muscle (Cullen, 1974), it always shows the same basic structure. The myofibrils tend to have large diameters, and so it is often known as fibrillar flight muscle; synchronous muscle is then referred to as non-fibrillar muscle, but this classification is not very reliable (Josephson & Young, 1981). In asynchronous muscle, large mitochondria occupy 30–40 % of the fibre volume, and the T-system is well developed, although the location of the transverse tubules differs from that in synchronous muscle. The SR is greatly reduced, consisting of little more than isolated vesicles in association with the T-system. Such a degenerate system is incapable of releasing and sequestering Ca2+ during each contraction, and indeed these muscles contract rhythmically under constant Ca2+ concentrations. The muscles contract through strains of less than 5 %, and this near isometric specialization is reflected in an almost complete overlap of the thick and thin filaments.

The most interesting feature of asynchronous muscle is that its contractile activity is maintained by a self-oscillatory mechanism that is under mechanical, not nervous, control. This is shown in Fig. 1 by the loop in the stress/strain diagram for the intact flight muscle of a coconut beetle Oryctes rhinoceros. Machin & Pringle (1959) replaced the natural load on that muscle with an artificial inertia, stiffness and damping. They discovered that the muscle would not contract rhythmically if it was highly damped or if an inertial load was absent; under those conditions the muscle simply exhibited a high stiffness, even when unstimulated. This stiffness is considerably greater than locust synchronous flight muscle (Buchthal et al. 1957), which in turn is much higher than vertebrate striated muscle (Pringle, 1977). All insect flight muscle is extremely stiff; even at the small operating strains it can store elastically much, if not all, of the inertial energy of the oscillating wings (Weis-Fogh, 1959; Alexander & Bennet-Clark, 1977; Ellington, 1984).

Fig. 1.

Typical stress/strain curve for intact asynchronous flight muscle of Oryctes rhinoceros under non-oscillatory (stimulated and unstimulated) and oscillatory (the loop) conditions. Adapted from Machin & Pringle (1959).

Fig. 1.

Typical stress/strain curve for intact asynchronous flight muscle of Oryctes rhinoceros under non-oscillatory (stimulated and unstimulated) and oscillatory (the loop) conditions. Adapted from Machin & Pringle (1959).

For oscillatory operation the asynchronous muscle must be under static tension, and it must also be stretched dynamically by an inertial load (the lower half of the loop in Fig. 1) before it will contract (the upper half). To produce rhythmic contractions, all that is required is a mechanism which will produce a delayed tension after the muscle is stretched. Wray (1979) has proposed a plausible answer, which involves a periodic matching of myosin heads with the preferred attachment sites on the actin filaments. Oscillatory contraction and/or delayed tension after stretch is also widespread in vertebrate muscle (Goodall, 1956; Lorand & Moos, 1956; Armstrong, Huxley & Julian, 1966; Rüegg, Steiger & Schädler, 1970; Steiger, 1977; Kawai & Brandt, 1980), and can even be found in the anterior byssus retractor muscle of the mussel Mytilus edulis (Gagelmann, Gäth & Rüegg, 1984), although the underlying mechanism has not been established for these examples.

We now return to the main problem: what is the power output of asynchronous flight muscle? Hill’s relation is clearly not applicable to this muscle and cannot be used to estimate the operating stress. From Fig. 1 it is evident that the net work per cycle is equal to the loop area, and it is substantially smaller than the inertial energy absorbed and returned each cycle (the shaded area). The effective operating stress can therefore be defined as the maximum difference between the stress during the shortening and lengthening half-loops (Pennycuick & Rezende, 1984). When multiplied by the operating strain, this stress will somewhat overestimate the work done since the average stress difference must be less than the maximum.

The maximum stress difference that has been measured is 200 kN m 2 (myofibril) for glycerol-extracted Lethocerus muscle oscillating at a strain of 7 · 8 % at 2 Hz at 20 °C (Pringle & Tregear, 1969) ; this agrees with the maximum delayed stress developed in response to a stretch (Schädler, Steiger & Rüegg, 1971). Allowing for mitochondria and extracellular spaces, the operating muscle stress would be close to 100 kN m-2, the same as the locust. If the same stress could be achieved at the normal wingbeat frequency of 30Hz and strain of 4%, the power would be 113Wkg-1. For the maximum power output of intact asynchronous muscle we must go back to Machin & Pringle (1959), who measured 29Wkg-1 for Oryctes and 88Wkg-1 for the bumblebee Bombus terrestris. These values are less than the power output of Lethocerus extrapolated to 30 Hz, but Machin & Pringle pointed out that their values were probably lower than those achieved during flight because they could not mimic the special loading conditions produced by the natural wing articulation.

The data required to estimate the maximum aerobic power output of insect flight muscle are extremely scarce. In the preceding sections we obtained (with difficulty) estimates for just two cases, synchronous locust muscle and asynchronous Lethocerus muscle. Do these values apply to all synchronous and asynchronous insects, or does the power output scale with body size? Perhaps it would be more appropriate to ask whether power scales with wingbeat frequency, since the power equation (page 295) suggests a linear dependence on f. The frequency increases for smaller insects, so the power equation may indicate that their power outputs are greater than the two relatively large insects considered so far.

Pennycuick & Rezende (1984) have investigated the effect of frequency on power output in an elegantly simple model. They assume that the muscle strain and myofibrillar stress are relatively constant muscle properties, leaving the contraction frequency as the primary determinant of power. They further assume that the rate of ATP production per unit volume of mitochondria is a constant, and that the mitochondrial fraction is just sufficient to balance the maximum power of the myofibrils. Thus a frequency increase allows a greater power output, but this requires a greater mitochondrial fraction; the myofibrillar fraction must therefore be reduced, decreasing the muscle stress and yielding a lower power output than predicted by the linear dependence on frequency alone. The net result is that the power increases with frequency, but at a progressively lower rate as the mitochondria occupy more of the fibres, and eventually a limit is reached when the muscle is almost entirely filled by mitochondria.

Fig. 2 shows the results of Pennycuick & Rezende for insect synchronous and vertebrate striated muscle (curve A) and for asynchronous muscle (curve B). However, their results for synchronous muscle are marred by incorrect data for the locust, as described above; at 17Hz the power should be 80 Wkg-1, as indicated by the square, which is less than one-third the value from their curve A. I have not drawn a corrected curve for synchronous muscle in Fig. 2, even though one is desirable, because of a failing of the Pennycuick & Rezende model : they neglect the relatively large volume fraction of the SR, and without knowing how this fraction scales with frequency it cannot be corrected for. We can consider two extreme cases, though: (i) the fraction remains a constant 20 % and (ii) the fraction increases in proportion to the mitochondrial fraction. The power output at the 100 Hz upper limit for synchronous muscle would then be 168 and 137 Wkg-1 for these two assumptions, respectively, as shown by the circles in Fig. 2. Thus the curve for synchronous muscle should be below Pennycuick’s & Rezende’s curve B for asynchronous muscle, but the exact shape of the curve cannot be established without more information. These power estimates are of the right magnitude to account for the aerodynamic power expended by synchronous fliers (Casey, 19816; Ellington, 1984), but little would be left over for inertial power, indicating that elastic storage would have to be quite effective.

Fig. 2.

The mass-specific power output, predicted by Pennycuick & Rezende, as a function of contraction frequency for (A) insect synchronous and vertebrate striated muscle, and (B) asynchronous muscle. Symbols explained in text. Adapted from Pennycuick & Rezende (1984).

Fig. 2.

The mass-specific power output, predicted by Pennycuick & Rezende, as a function of contraction frequency for (A) insect synchronous and vertebrate striated muscle, and (B) asynchronous muscle. Symbols explained in text. Adapted from Pennycuick & Rezende (1984).

Pennycuick’s & Rezende’s results for vertebrate striated muscle (curve A) indicate that it is more powerful than synchronous insect muscle, based on our new estimates. The myofibrillar stress of both muscle types is similar, suggesting that the lower power of synchronous muscle is attributable mainly to its smaller operating strains. Why should the strain be lower? Perhaps because it is limited by the maximum strain rate. Josephson ( 1984) noted that the twitch rise time (6–7 ms) and duration (6 ms) of the katydid are comparable with the fastest known vertebrate muscles, even though the intrinsic speeds of katydid and locust muscles are not very impressive. If the intrinsic speeds of synchronous muscles are seriously limited, then a small operating strain would necessarily result from the high contraction frequencies.

Pennycuick’s & Rezende’s model is much more appropriate for asynchronous muscle (Fig. 2, curve B), where the myofibrils and mitochondria do account for nearly all of the fibre volume. Their analysis predicts a power output of 340–400 Wkg-1 for the three insects I studied, but they did not allow for the extracellular volume of the muscles, which would reduce the power to about 300Wkg-1. Furthermore, their power must be overestimated because the maximum stress difference of 200 kN m-2 (myofibril) was used instead of an average difference, so the power output is probably very close to Weis-Fogh’s & Alexander’s (1977) value of 250Wkg-1.

This evaluation of Pennycuick’s & Rezende’s analysis of asynchronous muscle confirms that the maximum power output for my three insects is sufficient for aerodynamic requirements, but that little power is available for inertial work. Extensive elastic storage is therefore implied, which is consistent with other results, and we are led to the conclusion that the efficiency of asynchronous flight muscle is indeed low - less than 10%. The maximum power output of synchronous muscle is even smaller, and again it is just adequate for aerodynamic needs, indicating good elastic storage and similarly low efficiencies. This evidence for the low efficiency of insect flight muscles is persuasive but indirect, and future research must aim for more conclusive results and a rigorous examination of the scaling of maximum power output.

It is a pleasure to thank Dr K. E. Machin for stimulating discussions and comments on the manuscript.

I have recently learned of a very relevant paper in press by R. K. Josephson (7- exp. Biol. 114). He measured the mechanical power output of a flight muscle of the katydid Neoconocephalus triops while it was subjected to sinusoidal length oscillations and stimulated at selected phases of the cycle. The experiments deliberately searched for the conditions giving maximum power output, and were performed at normal flight frequency (25 Hz) and temperature (30°C). A maximum power output of 76 Wkg-1 was obtained with a strain of 6-0 % and three stimuli per cycle. Using that strain and frequency with the data from the closely related N. robustus on maximum isometric stress (137 kN m-2 at 35°C), the power equation (page 295) would predict a maximum power output of 97Wkg-1. The agreement between prediction and observation is satisfactory given the limitations on both, and it provides support for the conclusions above.

Alexander
,
R. Mcn.
&
Bennet-Clark
,
H. C.
(
1977
).
Storage of elastic strain energy in muscle and other tissues
.
Nature, Lond
.
265
,
114
117
.
Armstrong
,
C. F.
,
Huxley
,
A. F.
&
Juuan
,
F. J.
(
1966
).
Oscillatory responses in frog skeletal muscle fibres
.
J. Physiol., Lond
.
186
,
26P
.
Bocher
,
T.
(
1965
).
Formation of the specific structural and enzymic pattern of the insect flight muscle
.
In Aspects of Insect Biochemistry, Biochem. Soc. Symp. No
.
25
, pp.
15
28
.
Buchthal
,
F.
&
Weis-Fogh
,
T.
(
1956
).
Contribution of the sarcolemma to the force exerted by resting muscle of insects
.
Acta physiol, scand
.
35
,
345
364
.
Buchthal
,
F.
,
Weis-Fogh
,
T.
&
Rosenfalck
,
P.
(
1957
).
Twitch contractions of isolated flight muscle of locusts
.
Acta physiol, scand
.
39
,
246
276
.
Casey
,
T. M.
(
1981a
).
Insect flight energetics
.
In Locomotion and Energetics in Arthropods
, (eds
C. F.
Herreid
II
&
C. R.
Fourtner
), pp.
419
452
.
New York
:
Plenum Press
.
Casey
,
T. M.
(
1981b
).
A comparison of mechanical and energetic estimates of flight cost for hovering sphinx moths
.
J. exp. Biol
.
91
,
117
129
.
Close
,
R. I.
(
1972
).
Dynamic properties of mammalian skeletal muscle
.
Physiol. Rev
.
52
,
129
197
.
Cullen
,
M. J.
(
1974
).
The distribution of asynchronous muscle in insects with special reference to the Hemiptera: an electron microscope study
.
J. Ent
.
49A
,
17
41
.
Elder
,
H. Y.
(
1975
).
Muscle structure
.
In Insect Muscle
, (ed.
P. N. R.
Usherwood
), pp.
1
74
.
London
:
Academic Press
.
Elungton
,
C. P.
(
1984
).
The aerodynamics of hovering insect flight. VI. Lift and power requirements
.
Phil. Trans. R. Soc. Ser. B
305
,
145
181
.
Gagelmann
,
M.
,
Goth
,
K.
&
Roegg
,
J. C.
(
1984
).
Stretch induced tension rise in a molluscan smooth muscle skinned by freeze drying
.
J. comp. Physiol
.
154B
,
187
189
.
Gilbert
,
F. S.
(
1983
).
The foraging ecology of hoverflies (Diptera, Syrphidae): circular movements on composite flowers
.
Behav. Ecol. Sociobiol
.
13
,
253
257
.
Goodall
,
M. C.
(
1956
).
Auto-oscillations in extracted muscle systems
.
Nature, Lond
.
177
,
1238
1239
.
Heglund
,
N. C.
,
Fedak
,
M. A.
,
Taylor
,
C. R.
&
Cavagna
,
G. A.
(
1982
).
Energetics and mechanics of terrestrial locomotion. IV. Total mechanical energy changes as a function of speed and body size in birds and mammals
.
J. exp. Biol
.
79
,
57
66
.
Heglund
,
N. C.
(
1985
).
Efficiency of vertebrate locomotory muscles
.
J. exp. Biol
.
115
,
283
292
.
Heinrich
,
B.
(
1975
).
Thermoregulation in bumblebees. II. Energetics of warm-up and free-flight
.
J. comp. Physiol
.
96
,
155
166
.
Jensen
,
M.
(
1956
).
Biology and physics of locust flight. III. The aerodynamics of locust flight
.
Phil. Trans. R. Soc. Ser. B
239
,
511
552
.
Jensen
,
M.
&
Weis-Fogh
,
T.
(
1962
).
Biology and physics of locust flight. V. Strength and elasticity of locust cuticle
.
Phil. Trans. R. Soc. Ser. B
245
,
137
169
.
Josephson
,
R. K.
(
1984
).
Contraction dynamics of flight and stridulatory muscles of tettigonid insects
.
J. exp. Biol
.
108
,
77
96
.
Josephson
,
R. K.
&
Young
,
D.
(
1981
).
Synchronous and asynchronous muscles in cicadas
.
J. exp. Biol
.
91
,
219
237
.
Kawai
,
M.
&
Brandt
,
P. W.
(
1980
).
Sinusoidal analysis: a high resolution method for correlating biochemical reactions with physiological processes in activated skeletal muscles of rabbit, frog and crayfish
.
J. Muscle Res. Cell. Motility
1
,
305
320
.
Lorand
,
L.
&
Moos
,
C.
(
1956
).
Auto-oscillations in extracted muscle systems
.
Nature, Lond
.
177
,
1239
.
Machin
,
K. E.
&
Pringle
,
J. W. S.
(
1959
).
The physiology of insect fibrillar muscle. II. Mechanical properties of a beetle flight muscle
.
Pmc. R. Soc. Ser. B
151
,
204
225
.
Méndez
,
J.
&
Keys
,
A.
(
1960
).
Density and composition of mammalian muscle
.
Metabolism
9
,
184
188
.
Pennycuick
,
C. J.
&
Rezende
,
M. A.
(
1984
).
The specific power output of aerobic muscle, related to the power density of mitochondria
.
J. exp. Biol
.
108
,
377
392
.
Pringle
,
J. W. S.
(
1967
).
The contractile mechanism of insect fibrillar muscle
.
Prog. Biophys. molec. Biol
.
17
,
3
60
.
Pringle
,
J. W. S.
(
1972
).
Arthropod muscle
.
In The Structure and Function of Muscle
, Vol.
1
, (ed.
G. H.
Bourne
), pp.
491
541
.
New York
:
Academic Press
.
Pringle
,
J. W. S.
(
1977
).
The mechanical characteristics of insect fibrillar muscle
.
In Insect Flight Muscle
, (ed.
R. T.
Tregear
), pp.
177
196
.
Amsterdam
:
North-Holland
.
Pringle
,
J. W. S.
(
1981
).
The evolution of fibrillar muscle in insects
.
J. exp. Biol
.
94
,
1
14
.
Pringle
,
J. W. S.
Tregear
,
R. T.
(
1969
).
Mechanical properties of insect fibrillar muscle at large amplitudes of oscillation
.
Proc. R. Soc. Ser. B
174
,
33
50
.
Rüegg
,
J. C.
,
Steiger
,
G. J.
&
Schâdler
,
M.
(
1970
).
Mechanical activation of the contractile system in skeletal muscle
.
Pflügers Arch. ges. Physiol
.
319
,
139
145
.
Schâdler
,
M.
,
Steiger
,
G. J.
&
Rüegg
,
J. C.
(
1971
).
Mechanical activation and isometric oscillation of insect fibrillar muscle
.
Pflügers Arch. ges. Physiol
.
330
,
217
229
.
Steiger
,
G. J.
(
1977
).
Stretch activation and tension transients in cardiac, skeletal and insect flight muscle
.
In Insect Flight Muscle
, (ed.
R. T.
Tregear
), pp.
221
268
.
Amsterdam
:
North-Holland
.
Tregear
,
R. T.
(
1977
).
(ed.) Insect Flight Muscle
.
Amsterdam
:
North-Holland
.
Usherwood
,
P. N. R.
(
1975
). (ed.)
Insect Muscle
.
London
:
Academic Press
.
Weis-Fogh
,
T.
(
1956a
).
Tetanic force and shortening in locust flight muscle
.
J. exp. Biol
.
33
,
668
684
.
Weis-Fogh
,
T.
(
1956b
).
Biology and physics of locust flight. II. Flight performance of the desert locust (Schistocerca gregaria)
.
Phil. Trans. R. Soc. Ser. B
239
,
459
510
.
Weis-Fogh
,
T.
(
1959
).
Elasticity in arthropod locomotion : a neglected subject, illustrated by the wing system of insects
.
XVth int. Congr. Zool
., Vol.
4
, pp.
393
395
.
Weis-Fogh
,
T.
(
1964
).
Biology and physics of locust flight. VIII. Lift and metabolic rate of flying locusts
.
J. exp. Biol
.
41
,
257
271
.
Weis-Fogh
,
T.
(
1972
).
Energetics of hovering flight in hummingbirds and in Drosophila
.
J. exp. Biol
.
56
,
79
104
.
Weis-Fogh
,
T.
(
1973
).
Quick estimates of flight fitness in hovering animals, including novel mechanisms for lift production
.
J. exp. Biol
.
59
,
169
230
.
Weis-Fogh
,
T.
(
1976
).
Energetics and aerodynamics of flapping flight: a synthesis
.
In Intect Flight
, (ed.
R. C.
Rainey
), pp.
48
72
.
New York
:
Wiley
.
Weis-Fogh
,
T.
&
Alexander
,
R. Mcn.
(
1977
).
The sustained power output from striated muscle
.
In Scale Effects in Animal Locomotion
, (ed.
T. J.
Pedley
), pp.
511
525
.
London
:
Academic Press
.
Wilson
,
D. M.
&
Weis-Fogh
,
T.
(
1962
).
Patterned activity of co-ordinated motor units, studied in flying locusts
.
J, exp. Biol
.
39
,
643
667
.
Withers
,
P. C.
(
1981
).
The effects of ambient air pressure on oxygen consumption of resting and hovering honeybees
.
J, comp. Physiol
.
141
,
433
437
.
Wray
,
J. S.
(
1979
).
Filament geometry and the activation of insect flight muscles
.
Nature, Lond
.
280
,
325
326
.