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Aviation History
1951
1951 - 2374.PDF
November 1951 FORCES AND MOMENTS ON HINGED ROTOR BLADE WITH TIP ENGINE • •» m,Jo I |n/.dV. Centrifugal Force of _, o>2 fR w.r.dr. UftonBlade L=]o Blade Weight 1=7Jo BL.eW.ightigh «,,„=£ Centrifugal^ of Cf2=- x _ Blade Weight Mb = ft? w.r.dr. Centrifugal Moment of M . _ftu2 NWi'R*Moment J o Engine Weight ncr2- — X — _- Engine Weight N.Wy'/n Coning Angle (Considered small) /3 Radians t N-WJR/n Angular Velocity u> Radians/seconds N.W/, V 3" 'w-(1 673 engines as compared with blades of conventional weight dis- tribution. They also indicated how the ratio of blade weight to gross weight might be controlled by small increases in coning angle with increasing size, so as to remain, even for very large helicopters, within the limits to which we were now accustomed on small helicopters. These graphs, more- over, related to a family of rotors of constant tip speed and disc loading, whereas in the larger sizes, the rotational speeds were so low, and the ground effect so powerful, that both tip speed and disc loading would probably be increased in the event, so providing additional means of blade weight control effective well beyond the range of foreseeable size require- ments. Whereas there appeared to be no significant upper limit to the size of this family of rotors, Fig. 5 A, B and C suggested that there was a lower size limit below which this type of rotor ceased to be attractive. This was shown by the dotted and chain-dotted lines superimposed on the main curves. These lines gave a rough indication of the weight of blade material likely in any case to be necessary to provide sufficient strength and stiffness, but it was obvious from Fig. 5A (point B) that even gross errors in the estimates would hardly alter the indicated radius of about 50ft, below which the advantages of a tip-mounted turbojet installation began to be lost. The lecturer stated that in his examples the blade weight was assumed to be 5 per cent of the gross weight for values of rotor radius from 50ft up to approximately 90ft, indicating a gradual increase in coning angle with size. Beyond 90ft Fig. 3. Blade coning equilibrium. stant for the entire family, the variation of gross weight could conveniently be plotted for the family as a function of rotor radius. It had been assumed that all helicopters of the family were fitted with jet engines having a sea level static thrust given by the equation:— Static Thrust= loading lb.55O \ 2p 0This variation of static thrust gave a reasonable level of performance, and was convenient in that it expressed power requirements in terms of gross weight and hence in terms of rotor radius. In estimating the weight of the rotor blades, it had been assumed that they were freely hinged at the rotor centre line. The forces and moments acting on such a blade were shown in Fig. 3, and using the notation of this figure, it could be shown that the ratio of blade weight to aircraft gross weight was:— ^Rg~/ W k, where W was the weight of the jet engine attached to each blade tip. Mr. FitzwilUams had also assumed that the modifications needed to render a normal turbojet suitable for operation at the tip of a rotor blade would not add materially to the weight of the engine. In any case, quite large errors in this assump- tion would have little effect on the analysis. A plot of the relationship between static thrust and weight for various existing turbojets was given in Fig. 4, and indicated that a suitable assumption was represented by the equation:— 1^=250+0.3 (Static Thrust),lb (5) Since the static engine thrust was taken to be a function of gross weight and, therefore, of rotor radius so, by means of equation (5) the engine weight could also be determined as a function of rotor radius. The engine weights could then be substituted in the blade weight equation (4) from which it was possible to plot the ratio of blade weight to gross weight as in Fig, 5A, B and C, these showing the variation of this ratio with rotor radius for constant coning angles of 4, 6 and 8deg. These figures showed the large reduction in total blade weight which could be achieved by the addition of tip jet 10000 sooo 6000 4OOO 2OOO V Wj-25OK>3 (STATIC THRUST)—^6^(5) jf-\ DERWENT ADDER / "» A =s L NEN \ V VON* A sAov GOBLIN A ^y/DERWENT I \ y ^APW r\ .:—• IRE IOOO 2OOO 3OOO Wj- Fig. 4. Plot of static thrust against weight for various existing turbojets. radius, he had assumed that the ratio of blade weight to gross weight increased as indicated by the lower line of Fig. 5C, since a coning angle of 8 deg corresponded roughly with the upper limit of present experience. Having accounted for the weight of blades and engines, it was necessary to assume certain percentages of the gross weight as representing the fuselage structure, undercarriage, etc., and the percentages chosen corresponded to the average achieved in present conventional helicopters. On this basis, the fuselage of a jet-driven helicopter might reasonably be expected to be lighter than assumed here, since it would be proportionately much shorter and also free from the large tail rotor thrust moments of the conventional type. The percentages assumed were as shown in Table I. TABLE 1 Structure-weight Breakdown) per cent Rotor head i 3.80 Tail rotors 0.40 Fuselage 13.00 Landing gear 4.00 Flight controls 1.50 Fuel system 2.00 Transmission (tail rotors) ... ... ... ... 0.20 Hydraulics 0.40 Electrics 1-20 Miscellaneous (radio, instruments, etc.) 1.50 Total structure (less blades and power units) ... 28.00
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