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Aviation History
1909
1909 - 0552.PDF
SEPTEMBER II, 1909. determine the correct value for the pitch, by substituting the numerical values for the corresponding symbols in the equation. No value has yet been assigned to the symbol W\ in the equation, but as we are dealing with air in units of cubic feer, the value of W\ is therefore, the weight of one cubic foot of air, which can be taken approximately as -073 pound, although in practice this may vary con- siderably, depending on barometric and thermometric differences, and the velocity with which the air is being handled. The numerical value of g is, as usual, 32-16. Now having numerical values for all of the variants involved except the pitch, the equation can be stated . „ , 50 x P3 x8ooo x -07-? arithmetically thus : -. , which solved 3 64-32 x 11000 ' for Ps= 24-2, makes P = 2*893 ano- completes the full set of correct proportional values for the elements of the standard propellers thus : H.P. = 20, R.P.S. = 20, P. = 2-893, A. = 50. To get complete data for comparison, let the thrust be calculated in actual quantity also, and, remembering that the propeller can be designed to give the effect of air blowing against a normal disc, the formula P = SV2-oc>3 can be used by altering the co-efficient to correspond with V in feet per second, and substituting the symbols we are using here for the sake of uniformity, and using T as the symbol for thrust, it becomes T = Az>2*ooi39. Applying this formula to the standard propeller gives Sox (2*893 x 2o)3x "00139 = 232-67 lbs., or 116 lbs. per h.p. As the proposition under consideration requires two propellers of varying thrusts per h.p., another propeller having a decreased thrust per h.p. can now be prepared for comparison. Noting from the table (Variation 7 in our issue of July 3rd) that an increase of pitch reduces the thrust per unit of power, let the same h.p. and speed of revolution be maintained and it is evident that the area will have to be reduced. As doubling the pitch without altering the power or speed of revolution would reduce the area to one-eighth of its previous size (this effect is not stated in just this way in the table, but can be deduced from Variation 7), it will do as well to increase the pitch any amount that will not vary the working conditions too greatly, and accordingly let the pitch be made 3 ft. and solve the Ax 27 x 8000x-073 , . . , equation for A, thus —7 and A is found H ' 11000x64-32 to be 44-87 sq. ft., or a diameter of approximately and calculating for thrust 44*87 x (3 X 2o)2x-00139 = 224-18, or II*2 lbs. per h.p. With theoretically perfect efficiency, we now have the equivalent of two normal surfaces, one having an area of 50 sq. ft. and being moved at a velocity of 5 7 "86 ft. per second with an expenditure of 20 h.p, and one having an area of 44-87 sq. ft. and being moved at a velocity of 60 ft. per second utilizing the same h.p. Now, presuming that the total head resistance of the machine (whether composed of area and drift in a dynamically sustained machine or area alone in a buoyancy-sustained machine) to which the propeller is attached, is equal to the resistance caused by a surface of 20 sq. ft. area, normally presented, this resistance is proportional to the square of the velocity of flight v2 and produces slip in the propeller. Representing the factors of the initial propulsive force in the propeller by the symbols A for the area against which the force is exerted, and v for the velocity at which A is being moved, it is apparent that this velocity will be decreased by any additional area moved in pro- portion to the added resistance, which, as we know, varies with 7>-, consequently symbolising the added area by a, the resultant velocity of the combined resistance is expressed by the formula :rw in which A represents the surface against which the pro- pulsive force is exerted, and A + a the surfaces presenting resistance to propulsion. Stating arithmetically the resultant velocity of the machine with the standard propeller attached, thus: r5ox(2~893X2o)2_^ ••,.•;•-,••..- 50 x 20 we find it to be approximately 49 ft. per second, and for the same machine with the second propeller 744-87 x (3 X2o)3_/.[ ••••..: \ / •£, = 1' , .---..••.:.• V 44.-87 + 2O -..••-- :.:•• a velocity of approximately 50 ft per second, thus show- ing that it is possible for a propeller having a lower thrust per h.p. than another when the machine to which it is attached is held stationary, to drive the machine faster through the air in flight, than the propeller having the higher thrust per h.p. I wish to specially comment on the common error of using the wind pressure coefficient in propeller thrust calculations. I have ,only used it so far for the sake of simplicity in laying down comparative effects. Before closing this series of lessons I will give it differentiating values under varying conditions. As noted above, its value not only changes materially with barometric and thermometric differences and the velocity with which the air is being handled by the propeller, but also with the speed of the machine, to which the propeller is attached, through the air, its greatest variation being most notice- able in propellers designed for sustentation only, due to the increase in its value caused by the inertia of the air on the intake side of the propeller, and again in the opposite condition, of full flight, decreasing its value. This is true only of propellers revolving at constant speed, different values obtaining again when propeller and motor are so designed as to permit of the rotating speed increasing as the machine containing them acquires velocity up to the full flight maximum. ; ft.; THE "DAILY MAIL" AIRSHIP GARAGE. THE last day of August saw the garage which has been built at Wormwood Scrubbs to house the Clement- Bayard airship, when it flies from Paris to London, com- pleted. Building operations commenced on July 15th, and although the weather has considerably interfered with the work, every available moment has been taken advantage of. On an average 150 men have been kept at work and the wages bill amounted to ^2,000. The building is 365 ft. long—more than half as long again as the nave of St. Paul's Cathedral—65 ft. broad, and 98 ft. high, while the wind-resisting capacity of the structure is 40 lbs. per sq. ft. According to the Daily Mail, the following materials were used in its construction :— 17,000 pieces of iron sheeting, 6 ft. or 10 ft. by 2 ft. ; total weight, 85 tons. 500 tons of steel girders. Thirty-eight windows, 13 ft. by 7 ft., containing 266 sheets of frosted glass, 7 ft. by 2 ft. ; total weight, 30 tons. Sailcloth curtain at entrance, 100 ft. by 75 ft. ; weight, 2 tons. Ashes to the depth of 6 ins. are laid on the 23,725 sq. ft. of floor. 156
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