Open Access

Olavi Sotavalta

• The present work deals with the problem of the essential factor regulating the wing-stroke frequency in some insects in wing mutilation and loading experiments and in subatmospheric air pressure experiments. The diverse opinions concerning this factor, appearing in the literature, are reviewed. As appears in this review, one of two factors, the inertia of the wings or the resistance of the gas medium, is claimed to be the main regulator of the wingstroke frequency. Therefore two series of experiments have been performed. In the first series the correlation between the moment oi inertia of the wings and the wing-stroke frequency is examined. The wings are mutilated by cutting them transversely, longitudinally or obliquely or loaded with a drop of collodion. It is found that (1) the wing-stroke frequency is proportional to the -0.35th power of the moment of inertia of the wings, that (2) this applies to both mutilation and loading experiments, that (3) it makes no difference whether the procedures are equal or unequal on both sides or only one-sided, and that (4) the frequency tends not to rise above a certain lirnit in mutilation experiments. In the second series of experiments the correlation between the pressure of the gas medium and the wing-stroke frequency is examined. It is found that the effect of pressure varies greatly in different insects and may even be totally absent. The wing-stroke frequency is proportional to (pressure) exp 0 to (pressure) exp -0.25. The degree of the effect is found to depend on the size and the wing-stroke frequency of the insect; the effect is absent in big insects with a medium or high frequency, and more or less present in insects with a small size or with a low frequency. The results are discussed. A theory is constructed using well established physical concepts by considering the wings as acting simultaneously as bodies performing simple harmonic rotary motion and as paddles working against the air. It is assumed that the kinetic energy is destroyed after each single stroke. By making this assumption, the frequency in the energy equation is found to be, within a constant rate of energy output, proportional to the -0.33rd power of the moment of inertia of the wings, and thus agrees very well with the correlation between these factors found experimentally. Further it is found that the aerodynamic work of the wings is in most cases very much smaller than the work done in overcoming the effect of the inertia of the wings. It is negligible in big insects with, a medium or high frequency, but more or less significant in insects with a small size or a low frequency. The magnitude of this effect thus depends, in theory, on the size and the wing-stroke frequency, which entirely agrees with the effect of atmospheric pressure found experirnentally. The inferences drawn from this theory show that (1) the energy economy in a big insect is very wasteful, that (2) the rate of energy output is not greatly varied, that (3) it is profitable for the insect to vary the aerodynamic work of the wings by altering the amplitude rather than the frequency of the stroke, that (4) the distribution of energy in flight is delicately balanced, and that (5) the frequency must be low and the amplitude large in insects of great size and weight, and that a very high frequency and a small amplitude can be afforded only by small insects. Many such observations as have been made in nature agree with these inferences. Furthermore, (6) attempts are made to calculate the muscle efficiency in some insects on the basis of the theory. In Appendix I, the technique used to check and eliminate some sources of error in the methods is described, in Appendix II, an application of tlie theory to derive a law between the wing-stroke frequency and the morphological properties of insects is attempted, and in Appendix III, some laws relating different morphological properties of the wings of insects are described.