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Aviation History
1915
1915 - 0322.PDF
fOcsg MAY 7, 1915. THE SCREW PROPELLER. By F. Of) reference to Fig. 7 it will be at once evident that the so- called chord angle, as measured from an actual aerofoil (or propeller blade), ia a quantity entirely without meaning ; the leading edge may be curtailed to a greater or less degree, or the trailing edge may be pushed out further or less far along the lines of flow in the wake, without aftectin^ thir dynamic value of the aerofoil in any measurable degree, but with a* many different so-called chord angles as the variations made. The chord angle of hypothesis, which is equal to TJ/2, has no real relation to the go-called chord angle, and is a quantity which must either be given by the designer, or calculated from the dynamic properties ot the actual foil on the lines laid down in the author's " Aerodynamics," or in accordance with the newer rtgime discussed in his recent paper. II. We may now revert to the main subject. We may allow that in view of all the conditions, the rotor efficiency cannot be as high as theory indicates as its maximum ; probably, if we take it that efficiencies of the order of 85 per cent, are possible, we shall not be far from the mark. It must be recalled that the term efficiency in the present connection is an altogether different matter from that with which we have to deal in the general theory of the screw pro- propeller ; it does not represent any ultimate work done, except in the form of the kinetic energy represented in the downward wake, so that there is nothing contrary to established experience, even though the full theoretical efficiency of over 90 per cent, should be attainable. In the case of the aerofoil of a flying machine, we know that after all other considerations have been taken into account there remains the factor of aerofoil weight as tending to curtail the area which should in practice be found most advantageous; now in the case of the helicopter it ia this aclf-samc question of the aerofoil weight, or rather the rotor weight, which almost entirely determines the best diameter to use ; were it not for this factor the power required could l>e reduced indefinitely by progressively increasing the diameter ; this is clear from equation (1). If, for the purpose of illustration, we suppose the total weight it is required to lift to be one ton, there should be no great difficulty in designing • roto of 50 or bo ft. diameter within the permissible weight which could be assigned to that part of the machine. Tne conditions would indicate a " monoplane " structure of, say, 56 ft. length, about b fi. wide in the central portion, tapering to about 3 ft. at the extremities, the two blades thus being embodied in a single structural member. Calculating on the basis of equation (1), the weight sustained per h.p. expended in the downward motion imparted to the air is approximately 40 pounds, and if we allow for an energy loss as due to a value of (» = 1 -5, a reasonable allowance to make, the weight per h.p. will be 40 divided by J '\ or approxi mately 12 pounds, or 70 h.p., for the one ton weight total. If, now, we take the rotor efficiency, to lie on the safe side, as 75 per cent., we tind the total required to I* between 90 and 100 b.h.p. The author is firmly of the belief that a machine designed to the dimensions given, and in accordance with the requirements of theory as herein laid down, would lift satisfactorily if driven by reasonably efficient gearing and a power expenditure of 100 b.h.p. There are, we know, several problems in connection with the direct lift machine beyond that of sustentation which need to be solved before any such machine can be deemed even an engineerirg success, but these fall rather outside the scope of the present paper. There is, for example, the question of rotational anchorage : evi dently some provision is needed in any actual design to prevent the car rotating instead of the rotor ; obviously two rotors having reverse rotation offer a simple solution, and here there appears to be a possibility of an actual improvement. Thus, if two rotors of opposite hand be arranged on concentric shafts a large portion of the energy otherwise b*l in rotational wake may be recovered. The author has not pursued the matter further ; an investigation to cover the condition in question would be an affair of some length. 12. On looking into the various schemes for direct lift which have been proposed from time to time, it is quite clear that owing to a want of appreciation of the principles involved, the conditions of least power expenditure have not been complied with. Thus, we are familiar with designs in which are embodied members fashioned after the manner of an American windmill, with an incredible multiplicity of blades, also with machines with fundamentally in adequate rotor area, and others with other defects of an equally detrimental kind. One of the standard methods of miscalculating a helicopter is to figure the lifting value of the blades on the assumption that they are full v arml'iiTniK fit f h*» rt + mf?\il .it" a £«>,'_„ ... i_: * . • W. LANCHESTER, M.InstC.E. (Continuedfrom page 306). that ultimately the lifting reaction is tied down by the Newtonian principle, that is to say, as due to the downward momentum of the air passing through the circular area swept by the rotor blades, in accordance with the teaching of Rankine and Froude. All question of blade interference is thus ignored. Summarising the position, we may take it that there is no present prospect of making a direct lift machine without a considerably greater expenditure of power than that required for a flying machine of ordinary type of equal weight, or in the alternative, should this be achieved, it can only be done by the adopiion of a diameter far greater than the span of a flying machine of equal weight, the diameter of rotor required being in the region of twice the span of the machine of ordinary type. At the same time, unless there are unaccounted losses of efficiency of unsuspected magnitude, it is equally clear that the direct lift machine is, as a problem in engineering, capable of present-day solution ; whether the problem, when solved, will result in a machine of any possible value, military or otherwise, is quite another and in itself a very debatable question. PART II. — The Screw Propeller under tne Conditions of Maximum Efficiency. 13. The screw propeller under the conditions of maximum effici ency may be considered and treated as a special case. In the general treatment it is necessary to take account separately of the loss due to the axial or direct (rearward) velocity component and that due to the circumferential or rotational component, in addition to the skin-frictional or direct blade loss. So long as we confine ourselves to the condition of maximum efficiency, the whole problem is vastly simplified • it is demonstrated in the author's "Aero dynamics " that for this particular condition the whole of the losses may be lumped into one as expressed by the least gliding angle, or least resistance/lift coefficient of the blade, considered as an aerofoil adapted to move in the helical path. The method of treating the blade of a propeller as a number of annular elements is originally due to the late Mr. W. Froude, whose paper of 1878 is summarised in White's " Naval Architec ture," p. 606 (3rd Ed.). The present author, working on a similar basis (" Aerial Flight," Vol. i, Chap. IX), has obtained values for the pressurejvelocity'1 relation of least resistance for the different annular elements of the blade, and has worked out a rational method of blade design in accordance with this relation ; curves of efficiency also are obtained based on the proved constancy of the minimum gliding angle, the whole of the real complexity of the problem being by these means evaded ; it has, however, to be frankly acknowledged that the treatment as such is that of the special case, and can only be applied with a certain amount of " interpretation " when the essential conditions of maximum efficiency are departed from or are rendered impossible by the limitations imposed. One of the most interesting of the actual results reached by Mr. Froude is that the condition of maximum efficiency, that is to say, the most efficient annular element of a blade whose efficiency is everywhere maximum, has an angle of 450. The author in his investigation obtained a very similar result, namely, that the most efficient element of the best possible blade will have an effective pitch of 45° less half the least gliding angle. Now these two results in any case are in close accord, for the least gliding angle is probably between 0-05 and 010 (radians), or, say, between 30 and 6°; hence the author's result is in fact that the best effective pitch angle is between 42° and 43!°. In order that the matter shall be quite clear, plottings of the curve of efficiency are given in Figs. S to 13 for values of 7 the gliding angle being (in radians) from C05 to o-io inclusive ; in the figures the radius of the propeller in terms of pitch is given by abscissae and the efficiency corresponding to these radius values is given by ordinatcs ; the angles corresponding to the abscissae values of pitch ratio are given as an irregular scale. It is to be pointed out that both the radiusjpitch values and the corre sponding $ values relate to the effective pitch and the effective pitch angle, in other words they represent the motion of the propeller as if the fluid were a solid and the gliding angle a certain constant angle of friction. This analogy is, for the purpose of quantitative deduction, complete, and the diagrams may be applied (and have l»een so applied by the author) to the representation of the efficiency of screw gear or worm gear ; the analogy is due to the fact (which the author believes he was the first to demonstrate) that the least gliding angle as a function of velocity is approximately constant. Now the probability is that Mr. Froude was not dealing with the effective pitch angle, but rather with what is sometimes termed the true pitch angle, so that there is no reason to suppose that the fully analogous to the aerofoil of a flying machine, usinr the "- *~*.T»"» s". laar ,lnere, 1SL o 7eason to suppose tnat me established aerofoil data for the purpose ; thegfac is entireWignored ,^T« £ S2U V>A that °f the author «Presents "* K F«» , u«iacn» entirety ignored real discrepancy; the difficulty is to satisfactorily define the true 322
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