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THERE is, however, one method of considering the problem theoretically which is given tentatively here. Assuming the helicopter has its blade angle reduced so that it will auto‐rotate, the power required to sustain the screw is given by equation (10). This power must be precisely the same as that expended in dropping at its normal velocity Vv because, considering an interval of time t, there is a certain difference of potential energy between the two machines—one hovering, the other descending. In the same time t, therefore, there must be an equivalent input of energy to sustain the helicopter to balance the difference in potential energy. We are considering now only airscrew horse‐power, not engine horse‐power. The power expended in dropping at Vv is WVv. Therefore we have or Put in another form by means of the previous equations:

Thus, consider an unstaggered biplane at, say, 40 dug. incidence. At values of rotational speed likely to be expected in a spin it will have a iairly large positive value of rolling moment, which means, as we have seen, an inward sideslip. This means in turn less sideslip at the tail leading to difficulty in preserving the spin at a low incidence. ? monoplane spinning at the same incidence would do so with outward sideslip, thereby augmenting the sideslip due to rotation. Inertia moments enter into the question as well, and, in fact, the aerodynamic and inertia moments and the eitects of sideslip are so interwoven as to make any simple separation of cause and effect extremely difficult. An opinion has been expressed that the ordinaiy autorotation experiment has no bearing on the fully developed spin at all but may be important as regards the incipient spin. In the wind tunnel spins have been observed on monoplanes at incidences quite outside the autorotation range.

There are several methods available for either preventing autorotation or reducing the autorotation speeds. There are special devices available such as slots or Schrenk slits, or the ailerons themselves may be used for this purpose. Once the designer has selected his plan form, etc., he can have a variety of aids to hinder the rotation of the machine about the longitudinal axis. The tendency to‐day is to eliminate such extraneous devices since the designer is loath to fit any arrangement which involves any complication such as moving parts or any increase in weight. He is content to rely for the most part on his experience in assessing the relative merits of various degrees of taper and tip sections, etc., and to assume that if he can dispose of wing dropping the autorotational characteristics of his wing will be satisfactory. This is not by any means a reliable guide at the coarser angles of incidence of a spin.

The rolling inertia moment can be obtained by substitution of liquation (1) in liquation (9). Thus:

THE fundamental problem of aerofoil theory is to predict accurately the characteristics of wings of various sections and plan form when the former may be any function of the latter. The vortex theory of aerofoils enables us to predict the chief properties of aerofoils below the stall. We are, however, interested also in the conditions obtaining at and above the stall. In the present state of the art we are obliged to rely on wind tunnel tests. The number and variety of wings that would have to be tested in order to give us at all a comprehensive survey of the possibilities of taper, aerodynamic twist and varying section are so great that wind tunnel tests can so far only be said to have touched the fringe of the problem.

IT is shown that the down gust requirement is open to the objection that heavier loads may be taken by the front spar at lightly loaded weight than those for which the spar was designed. This is normally covered by the factor of safety of 2, but the method of calculating the loads on a basis of all up weight is not very rational. Some available data concerning the magnitudes of down gusts are reviewed and the sharp‐edged gust hypothesis briefly examined. The British requirement is compared with those of the I.C.A.N. and the U.S.A. The conclusions are that there are no very practical alternatives to sharp edged theory and while the estimate of the magnitudes of normal down gusts at 25 f.p.s. appears satisfactory and British standards of strength in this respect need not be tightened up, a modification to the requirement to meet the above objection is desirable. A suggested alternative is put forward.

In this paper a comprehensive survey of spinning phenomena is attempted. The presentation is elementary in character, starting with the simple geometry of the spin, then dealing with autorotation, including wing‐dropping tendencies, passing on then to a consideration of aerodynamic pitching and yawing moments, and finally some attention is given in turn to the incipient spin, the steady spin and recovery. The arguments are in the main qualitative so that a student of the subject may first familiarise himself with the fundamental principles. A bibliography is given which includes all the important papers published on the subject within the last few years, together with a few which are now more of historical interest. Most of these reports emanate from the A.R.C. and N.A.C.A. and due acknowledgment is made of the source of some of the experiments which have been taken in illustration of the points made. Although not the urgent problem that it once was, the subject of the spinning of aeroplanes continues to occupy a prominent place in the programmes of various research establishments, both here and abroad. Because both of the complexity of the phenomena involved and of the great importance that an ultimate solution should be found it has continued to be since the war one of the most difficult and protracted problems in aeronautics. Owing to the body of experimental data which has been gradually built up, model and full scale, designers now know what peculiar properties in an aeroplane are liable to prove dangerous as far as recovery is concerned. There is unfortunately no mathematical precision about this process and the fact that machines can still be built which, unless they are tested in the spinning tunnel and the necessary modifications made, might become uncontrollable in a spin should be sufficient to indicate that a final solution is far front having been achieved. It seems exceedingly unlikely that there will ever be sufficient experimental evidence to enable a designer to predict confidently that his machine, if it be perfectly orthodox, will not have some vicious spinning tendency. On the other hand, any designer could build a perfectly safe aeroplane from the point of view of spinning if due regard had not to be paid to other items of performance and safety. The necessity for compromise in design becomes a major problem when spinning is one of the factors that have to be taken into account. There is ample evidence that this problem is being resolutely tackled by designers. All the same, the present position cannot be regarded as satisfactory and, unless some new device is produced which will remove autorotation from the possible regimes of an aeroplane, we must continue to progress along already well‐tried lines.

ONE of the most puzzling problems of aviation at the present time is to come to any sort of conclusion as to the precise place in the future scheme of things of the type of gyroplane so aptly named “Autogiro” by its inventor.

In recent years little has been published on the mathematical theory of vertical flight, though more intelligent work is being done on the subject by various engineers than, probably, at any previous time. In this and a following article, to be published next month, one of the leading exponents of the helicopter, in a specialised and highly ingenious form, covers the whole field of sustentation, ascent, descent and the thorny problem of stability more completely than has ever hitherto been attempted