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Aviation History
1909
1909 - 0294.PDF
MAY 22, 1909. If the ratio of the transverse to the fore and aft dimen- sion of a pterygoid aeroplane is increased, the weight sustained for a given area is increased also. It follows, therefore, that it is necessary among other things to know the value of this ratio, n, before it is possible to either analyse or design an aeroplane for a given load. Constancy of the Skin-Friction Co-efficient. It has further been assumed in previous arguments that the co-efficient of skin-friction is constant. This assumption is justified by the investigations of Allen,* the conditions of such constancy being that the product of some linear dimension, denning the area, into the velocity shall remain unchanged. And in the case of an aeroplane, it has just been shown in a previous paragraph relating to the effect of area that this condition applies, hence the co-efficient of skin-friction depends on the weight alone. Taking a certain range of skin-friction values, such as have already been indicated, and a certain range for the values of the aspect ratio, it is possible to draw up a table giving the value of the load in lbs. per sq. ft. which will be supported at any given velocity by an aeroplane which is designed for least resistance. This last factor is essential, and must not be overlooked. Such values would not apply to a machine which did not fit the minimum point of its resistance curve, as already explained, in spite of the fact that the skin-friction and aspect ratio co-efficient might have been accurately represented. , The Cyclic-Up Current. At this point it is necessary to branch off from direct sequence in order to refer to a phenomenon which is of immense importance to design, as it leads to the adoption of a cambered surface instead of a flat plane. And here it may be convenient to adopt the use of the term " aerofoil " to denote a surface of indeterminate contour as distinct from a plane which implies, in fact specifies, flatness. When a plane falls normally through a vertical path, there is set up around the edges an up-current of air The effect of the horizontal component of motion is to cause a plane to be continually running into its own cyclic up-current, and in consequence it is like flying in a wind with an upward trend. The Arched Section. Such being the case, a simple oblique plane is obviously inadequate, for it is incapable of taking advantage of the upward flow, which everywhere precedes it in flight. In order to --adapt the plane to the condi- tions it produces, it is obviously neces - sary to turn down or dip the front edge, from which it at once follows that the front and rear edges would be connected by a curved surface in order to avoid sharp corners ; hence the cambered section In order to take advantage of thecyclic up-current the aeroplane needs a dipping front edge, whichevolves into the arched section of practice in order to avoid sharp- angles. that is always used for aerofoils in prac- tice. Nature, too, affords a proof of the correctness of this principle, for the dipping front edge is a characteristic feature of the bird's wing. Moreover, the well-known inaccuracy of the ordinary formula connecting pressure and velocity by means of air density in the inclined plane are eliminated in the cambered aerofoil when the angle of entry is reckoned with the angle of trail. Proof of Cyclic Motion in a Propeller. There is a great deal that is of immense interest in the study of cyclic disturbance, and one of the objects that may be investigated to advantage is the propeller. A propeller is in effect a series of aerofoils flying in a helical path : each blade is itself a complete aerofoil, GROUND When a plane falls normally,i.e., face on, a cyclic disturbance takes place round its edges. GROUND If the same plane falls along anoblique path the cvclic disturbance will still prevail. If the oblique fall is changed forhorizontal flight, there is still the cyclic up-current preceding the frontedge of the plane. which flows in to make good the space previously occupied by the falling body. If the downward fall is compounded with a horizontal velocity, so that the net result is a sloping glide, it will not change this essential up-current or cyclic disturbance. The imposing of a horizontal component in this way is equivalent, it will be evident, to replacing the ground line by another in some other position according to the slope of fall. Or, if the horizontal component is sufficient, it will give horizontal flight still without having changed the cyclic disturbance. * See Lanchester's Aerodynamics, Chapter II. having one extremity terminating at the boss. Hydro- dynamic theory demands that cyclic motion can only exist in a " doubly-connected " region—a term which it is not easy to exactly define in simple language—and from this it follows that if, as is assumed from the foregoing theory, cyclic motion exists round the blades, it will be demonstrated in the wake. Photographs which have been taken of a propeller in water, have de- monstrated that such is the case, the cyclic motion manifesting in the form of vortex cords paying off from the blade tips and from the propeller-boss. It will be noticed that the latter phenomenon is manifested at the 296
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