REG NASA-TN-636-1938 The estimation of the rate of change of yawing moment with sideslip.pdf

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1、e TECHNICAL NOTES -.- - NATIONAL ADVISORY COKl!ITTZE FOR AERONAWTICS . No, 636 _. =- TEE ESTIMATIOX OF THjj! RATZ OF CRANGE OF YATPIEG XOMEBT iVITH SIDESEIP . , _. : I _ By Zreaerick H. Inlay Langley Memorial Aeronautical LaboratoSy Trrsshin,-t cn Fcbrua?y 1938 Provided by IHSNot for ResaleNo reprod

2、uction or networking permitted without license from IHS-,-,-NATIONAL ADVISORYC:MMI%TEE FOR AERONAUTICS -I- TECHNICAL NOTE NO. 636 - THE ESTIMATION OF THE RATE OF CHANGE OF YAi7ING MOhlENT SMITH SIDESLIP By Frederick H. Imlay SUMMARY .XL -. _ mind-tunnel data are presented on the rate of change of ya

3、wing moment with sideslip for tests of 9 complete airplane models, 20 fuselage shapes, and 3 nfng models rrith various combinations of dihedral, srreepback, and tnist. The data wore collected during a survey of exist- ing information, which was made to find a reliable rnethod , of computing the yawp

4、ing moment due to sidoslip. Impor- tant errors common to methods of computation used at D-ros- ent appear to be due to large interference effects, the investigation of which rrill undoubtedly.require an exten- sive program of systematic aind-tunnel tests. At present it is necessary to place consider

5、able reliance on past - _L design experience in proportioning an airplane so as to obtain a reasonable degree of directional stdbility. L- .- .- INTRODUCTION .- Theoretical studies of later.4 stability (reference 1) have sho-sn that the rate of chnnge of yawing-moment coefficient with angle of sides

6、lip dCn/d 9 is one of the more important factors influencing the lateral-stabfltty characteristics of an airplane. At present there exists no depondsble method of computing this factor-from the di- mensions of an airplane. Several methods of estimating its agproximate value are in use but they have

7、proved to be inaccurate rrhen the results are compare-d with those fron mind-tunnel tests. In an attempt to devise arelia- blo method of determining the value of the derrvative for -. an nirplano in tho course of dosign, a study has bcon made of all avaflable wind-tunnel data on the subject. During

8、tho survey, the rosults of aind-tunnel tests of 127 airplane models mere analyzed. The models embraced Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2 N;A.C.A. Technical Note No. 636 . a wide variety of designs, including such diverse types as raci

9、ng seaplanes and troop and cargo carriers. In 1 spite of the large number of test results available, no satisfactory method of estimating dcn/dP was developed .3 because. the data offered little apportunity for the study of interference effects. Indications.are that the inter- ference effects betwee

10、n comFonents of-the airplane may change the yarning moment for bination by an amount equal to the sum of the yarning moments obtained when the components are tested separately An extonsivo program of correlated mind-tunnel tests mill probably be required to pormit the isolation and c?.nalysis of the

11、se interfor- - ence effects. In thb absence of an accurate method of estimation, certain of the more useful data collected during the study are presented as an aid to the designer in judging the value of dc,/dP for complete airplanes or component parts. . . . PRESENTATION OF DATA As theoretical cons

12、iderations indicate that the value of dCn/ d B should be only slightly dependent onthe an- glo of attack, the groator portion of .the test data pro- sentod is only for low angles of attack, Figure 1 has beon included to show the variation of dcn/dB with *angle of attack CL, for eight completaiairpla

13、ne models. From the figuro it can bo seen that, although the variation of dC,/dS with a is appreciable in the normal-flight range, the magnitude of the cffcct is not large except at anglos of attack above the stall. The yarning momenta were meas- ured about an axis normal.to the relative mind. The d

14、ata of figure 1, and also therest of the aerodynamic data _nresent,ed, were obtained from wsnd-tunnel tests made at Reynolds Numbers fn the neighborhood of 200,000. s - Table I presents yarning-moment data obtained from mind-tunnel tests of nine-airplane designs (fig. 2). Two of the types mere teste

15、d, each with two tail arrangements, All the models mere tested both complete and with the em- pennage removed. The table gives the value of dCn/dB B where S is measured in radians, for the complete models and also the increment of den/d8 contributed by the ver- tical tail surfaces dcnt/dS9 as determ

16、ined from the dff- ,- . + Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-3.A.C .A. Technic%1 Note No. 636 3 fercnce bctncon, the results of the toats of the complete models and the tests of the models without empennage. The proportions of the models

17、 listed in the table may be de- ternined fram the given values of wing span b, TPing as- pect ratio b%, ratio of vertical tail area to ;Ping area St/S, ratio of fuselage side area to ning area - Sf/s, ratio of the distance between the rudder hinge and the airplane center of gravity toning spzn Wb ra

18、tio of over-all fuselago length to ving span If/b, aspect - ratio of vertical tail surfaces ht/St, ratio of over- all fuselage length to maximum depth of fuselage Jfldf, . and ratio of-distance between the airplane center of grcv- ity end the fuselage nose to over-all fuselage length XJZf 0 The heig

19、ht of the vertical tailsurfacos -htS used in the calculation of aspect ratio; doesnot include the fuselage. The results of tests of a ITide variety of fuselage shaaes (fig. 3) are givon.in table II. The values of the rate of change of later.al-force coEf.fEient Vith angle 03 sideslip, dcy/dP, nnd of

20、 dcn/dB r given in table II, are of necessity based on the side area and ovor-all length of the fuselage rather than on ning area and span. For all the fuselage shapes, the yanfng-moment d.zta are given nbou,t an axis located a distance 0.30 -Zf back of the fuselage nose. On the basis of average air

21、plane pro- portions, the coefficients used in this table are about five times as largo as corresponding coefficients based on ning area znd span. Tho fact that till. the fuselage shales -.- tested, cxcopt Hull No. 10, dcn/dB have unstablo (negative) vnl- .-. ues of is predicted by the theory of yarn

22、ed st-roam- . . lined bodies (reforonco 4). Hull Bo. 10 had donsidorable vertic,?l fin nrea built in at tho roar. (Soo fig. 3.,) .- Tho dstj obtnfncd from nind-tunnel yan tests of se-+ ornl types of airfoils are given in table III. UC6 of dcn/dP The uCl- . -i listed are b,ascd on a yaning-moment axi

23、s passing through tho quartor-chord saint at the canter sec- tion of thd n-ing. For the tests of afng tmfst, the-air- foils had a uniform rato of tnist along. tho semispan such that tho ning-tip incidorco differs from the coqtor-sedf$on - incidence by an amount dofincd as the nn2le. of .twist,L-me -

24、1 angle of tnist eras such that tho rring tips had my and the increment- contributed by the wing - -z : cellule, dCnw/dB- - I Factors Affecting dC,/dP For all practical purposes, if the angle of-sideslip f3, is limited to small values, the value of dC,/dp is . dC *t St tt %t -e-e.- = - - - dB s,b aB

25、 I rvhero St .is the area of the vorfical tail surfaces, It is the distance. from the rudder hinge ix-the airplgng.cbn ter ,of gravity, and %t. is the cross-mind forcecoeffi- cient for the tail, based on St, Since dCct/d6 -is bnal- T-m ogousto the rate of change of lif-t with angle of attack, d%/ aa

26、 I for an airfoil, the problem of determining dCnt/de, becomes oneof determining the slope of the lift curve for the vertical tail surfaces. Data presented in references 7 and 8 indicate that the value of %Jd8 mill not be affected by airfoil section for airfoils of the symnetrical typo normally used

27、 for tail surfaces. Refcrenco 9 indicates that the effect of tail upper con- tour (corresponding to wing-tip shase) milLbe_. s.mall_.a,nd -. _ may be noglectad for aspect ratios usually encountered in t vertical tail surfaces. . . ._ , I -A- , L * The determination of the effective aspect ratio of t

28、he vertical taii surfaces is difficult, -primarily because Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-N.A.C.A. Technical.Note No. 636 s C 5 of the flqw interference caused by other portions of the airplane. The location, size, and shape of the h

29、orizontal surfaces appear to have a marked influence on the.magni- - tude of this interference effect. An analysis of %e data given in table I indicates that the most efficient arrange- ment is the one in which the vertical surfaces are placed as high as possible above the hprizontal surfaces. Un- d

30、oubtedly, the location of the vertical tail area below- the horizontal surfaces would be equally effective. C!Ihe poorest arrangement appears to be the one in which the horizontal surfaces are located in a median position. - In addition to the change in effective aspect ratio caused by interference

31、effects, various parts of fhe air- plane may also cause a reduction in dynamic pressure at the vertical tail surfaces. These two interference cf- fects are naturally difficult to separate, but together they may change the effectiveness of the vertical tail _. surfaces as much as 65 percent. Factors

32、Affecting dCnf/dP Values of dC,/dP are plotted against the ratio t f/ .The.pertinent. data for dihedral-and sweepback.are platted-.in .figure.5. l?or both the rectangu- lar and the Army tips, the .effect,of:-dihedral is approxi- mated by I - , where I is the- dihedral angle in d.egrees and B is the

33、angle of sideslip in radians. Additional data given-in reference 5 shorn that this relationship should vary slight- ly with lift coefficient, as is predictep by theory. For sweepback with rectangular tips : c . - where .A is the angle af sweepback in degrees., The in- crements of dC,/d due to dihedr

34、al or saveepback are to - - , be added algebraicslly to the value of dCnw/dB for the Wing mith no dihedral or swoopback. The- test data indi- cate that wing twist has a negligible effect on Gl,pa* Theory indicates that the value of is de- pendent on the lift coefficienti-In addition,the effect of sm

35、ec?back may be considerably difpoint of the center section, if so desired. Insufficient data are available to study the effect of other factors of probable impor,tance in. determining the value of d%-ection, bi?le!ne .arrango- ments, etc; Also, no conclusions.c.an be drawn as to. the0 influence of o

36、ne factor on the eff.ect.of another. Gompar- ison of test results given in table III for one ming with combineddihodral, smccpback, and twist with data for the - a . Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-H.A.-CA. Technical Note- Uo. 686 7 s

37、ame wing without dihedral, saeepback, or twist indicates that the effects are not additive. . -_ The effect of the interference between the wing and fuselage ic another factor that cannot be determined from tho data available at present* Unpublished results of vind-tunnel tests mado by the N.A.C.A.

38、of a flyingliboat - model, for the rringand hull sesarateky and in combination, indicate that this effect may equal the summation of the . momonts.of the ning and of tho fuselage tested separately. - Effect of Flaps .- Study of the data listed in table IV gives conflict- 1 indications but, in genera

39、l, deflecting the flaps in- creases tho value of dCn/dP* It should be noted that, nhcn flaps are doflocted, of den/a8 they not only affect the -qA.C.A., 1935. -. Blenk, Herman: Gattingen Six- Coraponont Measurements on Wings with Dihedral, Swecpback,.and Warp. h.C.T.R*, Translation No. 230, Matii; d

40、C zq - Lngle 0 attack b b2 ht2 11 (deg.) (ft.1 G 2 ; G- TF -L - A 1.00 2.6% 3.225 LO644 I.301 1305 3.301 I.0530 B -.75 2.875 5.719 .1365 .652 1.589 .377 .1210 C .75 2.011 3.442 .0451 -223 1.753 .255 .0229 3 1.00 2.125 3.790 .0647 .211 1.496 .278 .0239 E 1.00 2.-i25 3.790 .0646 .2l2 1.402 .274 .0220

41、F 1.00 2.125 3.790 .0679 .211 1.602 .27F .0430 G .oc 3.562 7.998 .0825 .39 1.373 .353 .0696 H -.50 2.436 5.E95 A876 -378 1.118 .296 I -2.00 2.260 3.377 .0513 225 1.660 .294 .0322 f 1.75 2.562 4.132 .0776 .338 2.174 .279 p.0046 K 1.75 2.5o Uo. 5 Fuselrp Bo. 6 Hull lao. 7 Hull No: 8 Hull No. 9 Hull no

42、. 10 - - sf (sq.ft.) %f (ft. 1 d.3 a$ - dc, a$ - 52 df - ,0.413 1:958 5.88 -0.308 -0.129 .416 1,862 5.57 -.204 -,134 .416 1,932 5?79 -.301 -!133 .326 1,694 6.23 -.300 -.083 .429 11957 5.97 -.076 -.175 .413 1,759 6.07 -.159 -,125 ,425 1.834 6.32 -.179 -.131 ,409 1,849 5.62 -.153 -,151 .282 1,513 5.67

43、 -.083 -,139 ,316 1.590 5.44 -.171 -,132 .453 1,908 5.93 -.130 -.162 .446 1.792 5.56 -.115 -.173 .532 1.670 5.92 -.109 -.114 1*219 1,468 1,182 1,268 1.2.93, 17300 832 :7er .474 .783 2;995 6.33 -.176 -.137 3,373 5,61 -,160 -,116 3,197 6.85 -.157 -.lOO 3,281 6.66 -.452 -.058 31544 7,70 -,278 -.108 2,9

44、53 4,94 1.560 -,188 2.625 5:93 -.244 -to86 2,953 7.79 -,253 -.105 2.205 8.72 -.292 -.078 2.748 7.61 -.530 .170 .I. . . Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-N.A.C.A. Technical Note Wo. 636 TABLE III Values of + for Airfoils Wing shape -w-P_

45、 Rectangular plan form and tip; 0.93 2 dihedral; Clark2P soctipn; aspect ratio 6 (from reference 5) Do. but with Army tip Rectangular glen form and tis; 1.00 $ dihedral; G%ttingen 387 section; 2,sect ratio 5 (from reference 6) . -_- -_ Angle of attack (d:g. - 1,8 1,8 1,8 4,2 4?2 47 2. 4.3 4.3 - Dihe

46、- dral angle (d:g:) se- 0. 5,O 10.0 0. 2.0 520 10.0 15.0 0. 3.0 6.0 0 0 0 0 3.0 Smeep- Angle back of angle hi 33 0 0 0 0 0 0 0 0 0 0 0 15,o 30.0 0 0. 30.0 - (deg. 0 0 0 0 0 0 0 0 0 0 0 0 0. 3.0 577 3.0 - den dS 3.0046 0.020 .oooo -.049 .oooo -.120 ,0048 -.020 ,0017 -:020 -.0046 -qo49 -.0014 -,092 -.

47、0077 -.192 .0102 -.0464 .0064 -.0590 .0053 -.0728 .0265 -.0573 ,0436 -.0665 .OlOl -.0482 .0109 -.0499 .0328 -.0797 11 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NiA.C.h, Technical Hate Nob 636 12 TABLE IV Effect of Flaps on i+ for Complete Airpl

48、ane -e-e, Model m-m_, 1 2 3 4 5 6 7 8 9 9 ( Ting only v-B-, T Angle of attack (dl -m-w Plaps up -p-m 999 11.8 13,5 999 1191 IO,9 lo,9 995 8*0 10.0 - :* Flaps.donn 1093 12,2 13.6 1090 12,2 9,3 11.3 .8,0 8.0 8.0 T - dC, dB - Flaps up - OF0433 .0335 Flaps down - 0.0622 .0312 io972 TO816 .0579 .0685 .0149 ,0257 ,0026 .0086 ? 0923 .1126 .0539 .lOll .0550 TO492 .0063 .0046 - Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-. . . . . . . :I - . k I- _-_ dC dB f -. 5 -. 1