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Aviation History
1946
1946 - 0535.PDF
MARCH 14TH, 1940 FLIGHT 273 expressed as multiples of our " Master " thickness at E-E.Bear in mind what was said beforehand anent centrifugal stress; since the areas of all sections will be increased (ordiminished) proportionately, and in the same proportion as those of our " Standard" .airscrew, the centrifugalstress will remain constant, although the total centrifugal pull will vary very considerably. By now the reader—if he or she has had the patienceto get so far—has in all likelihood become rather .perturbed, and has begun to think, " Good Heavens, have I got towork all this stuff out for myself before I can get the answer i want?" -No, indeed; and to show how simple thewhole thing is, I suggest that we take, here and now, another hypothetical airscrew and work it out by meansof the charts given in this article. It would add a slight spice of fun and excitement to time oneself, and see howlong (or rather, how short!) a time one takes over the business. We will suppose, then, that the airscrew has the followingcharacteristics :— Diameter = 12ft R.p.m. = 1,200. " Activity Factor' Air load per blade Weight of material 130 120 TIVII Y FACTO R i S 8 c 70 21-5V \ ,,2 \ ACT AC VITY RViTY IK) ACTC RATIC "•? [l-OR !o-2R 2«CMA\ j ^^69-43 0-75 = 81. = 950 lb.= 80 lb/ft3. Permissible compressive stress = 7,000 lb/in2.We have to find the thicknesses ofthe various sec- tions such that thecompressive stress on each one is themaximum permis- sible. First of all,a word or two about the " Acti-vity Factor." This is a parameterthat has fairly re- cently come intogeneral use. It can be defined asa non-dimensional function of the plan form, designed to express the integrated capacity ofthe blade elements for absorbing power. In many ways it conveys a much better idea of an airscrew's capabilities inthis line than the old-fashioned " Aspect Ratio," though for our own particular needs we shall want this latter. Soanother chart, Fig. 15, has been made to show how "Activity Factor" corresponds to "Aspect Ratio." Offwe go, then :— From Fig. 15. A.F. of 81 = A.R. of 6. 144.-. C max. (or Cc) = = 12.0m. , • •"• From Fig. 1. CE = CC X 0.785 = 9.42m. From Fig. 4. BME= 0.04753 X 95» X 72 = 3,256 lb/in. ASPECT RATO 5*0" Fig. 15. Curve of Activity Factoragainst Aspect Ratio. From Fig. 8. SPE = I,45O X (72) 2 X (l,2OO)2 X 80 IO1 \ Then And = 865 lb/in2. = 3,256 ~~ 7,000 -f S65 0.414 = 0.414 / = / °-4r4 \4 E \9-42 X O.O8 ) Stress Ratio " = 42 = 0.7411 in. 865 = o.i 2367,000 We now, without any further bother, write down theLord and thicknesses of the remaining sections. Section A-A B-B C-C D-D E-E F-F G-G Chords 10.80 11.52 12.00 11.40 9.426.00 4.50 V Fig. I. Thickness 2.095 Fig. 9. 1.830 Fig. 10. 1.453 1.100 0.7411 0.3280 Fig. II. Fig. 12. 0.1622 Fig. 13. Fig. 14. that all is straight and above board, the detailed stressesare given below : (I) Section A-A . B-B . C-C . D-D . E-E . F-F G-G . (2; Zc 3.792 3.087 2.027 1.104 0.4140.05165 O.U0947 (3) BM (Ib in 33,810 27, M0 17.340 9,095 3,256 382 67.6 (4) Ib in(comp:) 8.915 8,792 8.555 8,241 7.86S7,395 7,141 . (M Sp. 1,92: 1.795 1,560 1,250 865 395 149 16) Ult. .'resi lb-nJ '*! IK= v4) — [51 6,9926,997 6,995 6.991 7,000 7.000 6.992 3-Ol'j 24 2-5 0?A/AEi 15 K> 6 '120 T oU PROPORTIONAL AREASi-A/AE PROBABLE VALUES OF t/C c REQUIRED BY CONSIDERATIONS Of MANUFACTURE Fig. Looking at the final figures, I think that the most carpingcritic will admit that the accuracy is quite reasonably close to the desired answer, allowing for the fallibility of thehuman factor in reading charts. At any rate, every pre- caution has been taken to make it so, as a faulty tool isno good whatever, however " slick " in operation. So there we are. In a very few minutes, and at a mini-mum expenditure of time, trouble, and temper, we have fixed the scantlings of an airscrew blade stressed mosteconomically up to just on 7,000 lb/in2, the permissible limit for the material. Furthermore, we know from prac-tical experience that such a blade will run under load sweetly, smoothly and without flutter. Everything in thegarden is, in fact, lovely, and Bob shows every sign of being our uncle. Stop ! But does he, though ? Listen to the critics." You have failed lamentably in 3'5 ••what you set out to do. You havemade no mention whatsoever of re-storing moments due to centrifugalforce when the blade deflectsunder load ; you have said nothingabout feasibility of introducing acentrifugal bend- ing moment ofopposite sign to the air bendingmoment by tilting the blade forward in elevation. Your answer, please ? " Dash these critics ! They are, of course, as always, quiteright. I am guilty of both these glaring omissions, but for reasons that seem to me, at any rate, fairly sound. Dealingfirst with centrifugal restoring moments : if pushed to its logical conclusion, the admission of this factor would leadto scantlings so absurdly slender that the blade would whip and twist horribly under load." Some early Frenchwooden airscrews were notorious offenders in this respect, and even to watch them " revving-up " on the groundgave one a queer feeling in the pit of the " tummy," whilst everybody took very good care to avoid standingin the plane of rotation ! However, as some wit aptly remarked, they were usually " too weak to break "•*Again, we must bear in mind that all engineering is of necessity more or less a compromise. Considerations ofstiffness, rigidity, and limitations of manipulative and manufacturing possibilities all combine to render impossibleof attainment that beautiful ideal which theory dangles so enticingly before our eyes. It is believed that, for non-metallic airscrews, the dimensions arrived at in this article are as small as are desirable. At any rate, they work wellin practice, and, ultimately the proof of the pudding is in the eating thereof ! Now for the second objection :—The introduction of aforward tilt to the blade, in order to provide a relief to the compressive bending stresses, is a trick that has often beenused, especially in ordinary wooden airscrews, but I believe, personally, that it is one of those things which are betterdone without, if possible. For one thing, the amount of tilt can only be right for one particular set of operating AIRSCREW RADIUS 16. Characteristic curves ior an hypothetical airscrew. ] USt to show that there is IIO " Catch " anywhere and * The late E.V.B. FUher of early Brooklaud-- memory.
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