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Aviation History
1911
1911 - 0058.PDF
(/JJGHI The fundamental formula linking pressure and inertia is that ;given in No. I. The expression for mass in Formula 2 is illustrated by Diagram I, and the expression for final velocity of discharge on which the acceleration of the mass is based is illustrated by three diagrams numbered 2, 3 and 4. Of these the two former show the conditions for an entry tangential to the line of flight and for a dipping front edge. The third diagram, representing Formula 6, •shows an approximate expression for the angle of deflection, which can be used when the angle is small. The acceleration is derived from the final velocity on the assumption that the camber of the plane is such as to produce uniform acceleration from entering edge to trailing edge. The chord length on which the time is calculated in Formula 7 is the effective chord length during which the camber maintains acceleration; it does not include a tangential extension of the trailing edge whether flexible or rigid. All the formulae in the list are based on the approximation to the angle of deflection .given in Formula 6. The results of applying Formula 10, which is the final expression for the lift of a plane on this basis are shown graphically in Diagram 5. It has already been explained that a numerical constant used with this formula will serve as a correction when the chord or the span or the sweep or the angle show a practical difference between their effective and measured values. It is assumed that the thrust required to propel a plane overcomes two resistances, the resistance to the support of the load and the resistance to skin friction. In this consideration, the body resistance of a practical aeroplane is ignored on the ground that it should be reckoned as an independent factor to be provided for after the planes themselves have been calculated for a given speed and •loading. In respect to the resistance to the support of the load, it is assumed that the work done in supporting the load is entirely represented by the energy in the deflected air stratum. If there is any waste elsewhere the value can be corrected by a numerical constant. It is also assumed that the energy in the deflected air stratum can be measured by the application of the fundamental Formula 12, which supposes that the mass has a uniform downward motion in space, and makes no allowance for turbulence. The rate oi communicating energy to the mass will obviously be a function of the flight speed, whence Formula 23 provides the final expression for the thrust resisted by load. The thrust resisted by skin friction is derived from an empirical formula, No. 27, which has been based, with certain assumptions, on Zahm's experiments. In order to obtain the total thrust these two factors are added together, as shown JANUARY 21, 1911. in Formula 31, which can be expressed in terms of the load, as shown in Formula 34. From this last expression it will be observed that the ratio of thrust to load is independent of flight velocity ; that is to say, the power required for maintaining the flight of the plane alone is only directly proportional to the first power of the speed. Formulae 37-39. In view of the fact, however, that the body resistance is to be considered as an independent factor, it is necessary to bear in mind that the above statement is modified for a practical aeroplane, because the bjdy resistance represents in itself a function of the square of the velocity, and consequently the power expended on forcing the body through the air becomes a function of the third power of the speed. The significance of this deduction depends on the relative numerical values of body resistance and plane resistance in a practical aeroplane ; the relationship of their respective laws indicates that it is absolutely essential to keep the body resistance down to the minimum, as, for instance, by boxing the principal objects in stream line casings, in order to obtain high speeds with economy. The relationship of loading to power for a plane of stated angle is given in Formula 40, which represents one of the most important laws in aerodynamics. The special case of minimum resistance to flight on the part of the planes alone is treated separately in Formula 41 onwards. The basic assumption underlying these deductions is that the resistance to load is strictly inversely proportional to the square of the velocity, and that the resistance to skin friction is strictly directly proportional to the square of the velocity. This second assumption is only even approximately true, according to Zahm's experiments, up to a speed of about 90 m.p.h. On the basis of the foregoing assumptions, the minimum resistance to flight obtains under conditions stated in Formula 41, from which a value for the angle of least resistance can be directly deduced. The angle in question, as given in Formula 50, is approximately 50, this being the effective angle of deflection of the air stratum, which, it is assumed, corresponds with the angle of deflection of the plane. The value 50 depends on the coefficient of skin iriction, and will change if the value of that coefficient changes. The relationship between the total thrust per unit of load for a plane flying under conditions of least resistance, and under conditions represented by any other angle, is shown graphically in Diagram 6. This diagram indicates the important advantage of designing the planes for low resistance by reducing the angle ot deflection, but also shows the danger of making them too flat. CORRESPONDENCE. The name and address of the writer (not necessarily for publication) MUST in ah cases accompany letters intended for insertion, or containing queries. PENDULUM STABILITY. Correspondents communicating with regard to letters which they have read in FLIGHT, would much facilitate ready reference by quoting the number of each such letter. NOTE.—Owing to the great mass of valuable and interesting corre spondence which we receive, immediate publication is impossible, but each letter will appear practically in sequence and at the earliest possible moment. JET PROPULSION. [1026] I have been looking through some back numbers of FLIGHT, and I came across a letter (444) from W. Le Maitre describing a new method of propulsion. His idea was this : That by ejecting into the air volumes of gas or steam he would displace •the atmosphere backwards, and so propel his aeroplane forwards. This method has been tried by the first makers of dirigible balloons, but it was not successful. But, following up this idea, we come across another method, which I think is perfectly feasible. When a bird is flying the wings move upwards, downwards and backwards, and when they come down they press close up against its body, thus displacing a certain amount of air backwards and downwards and propelling itself upwards and forwards. Therefore, if a monoplane were taken and on to the front planes were fixed another pair of planes, like this, and moved up and down, I think a certain amount •of air would be displaced backwards and downwards, thus forcing the machine upwards and forwards. Sparkhill, Birmingham. H. H. HAYES. [1027] Many thanks for kindly inserting my letter (898), re pendulum natural stability, in your popular journal. If I may be allowed to criticise your opinion, I do not consider Lilienthal or Pilcher members of the pendulum school. Lilienthal, the better example of the two (for my purpose), I gather from the illustrations and drawings published in FLIGHT, NO. 53, used his body, pivoted, as it were, from his armpits, as an equilibrator, and I've no doubt, had he by some means secured his feet rigidly at right angles to his wings, his experiments would have been more satisfactory. Thanks to Planes, Ltd., we now have a practical machine. Looking at it from a purely scientific point of view, I consider it an improvement on all machines employing the disastrous gauchisse- ment method of stability. The simplicity of control and the success already achieved with this new departure, almost convinces me that this is a working model of the "perfect flyer" expected in two or three years hence. With all due apologies, and wishing your paper every success. Audlem. THOS. KBLHAM. "ALL-BRITISH ENCOURAGEMENT." [1028] As one who has studied the problem of flight for nearly twenty years, I should like to point out that it is not obvious how the operation of placing the modest sum of ,£100,000 in the pockets of a few flying men is going to convince the foreigner that our brains are better than his. Our flying men all use foreign machines, driven by foreign propellers and engines, or else slavish copies of the same. One never hears of their inventing anything or improving anything. It is not the flying men but the science of flight that needs encourage ment, and this will be in no way advanced by a repetition of sensational performances, which only prove the skill and daring of the performer. The present type of flying man, like the racing cyclist and motorist, 60
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