ImageVerifierCode 换一换
格式:PDF , 页数:12 ,大小:413.53KB ,
资源ID:1017553      下载积分:10000 积分
快捷下载
登录下载
邮箱/手机:
温馨提示:
如需开发票,请勿充值!快捷下载时,用户名和密码都是您填写的邮箱或者手机号,方便查询和重复下载(系统自动生成)。
如填写123,账号就是123,密码也是123。
特别说明:
请自助下载,系统不会自动发送文件的哦; 如果您已付费,想二次下载,请登录后访问:我的下载记录
支付方式: 支付宝扫码支付 微信扫码支付   
注意:如需开发票,请勿充值!
验证码:   换一换

加入VIP,免费下载
 

温馨提示:由于个人手机设置不同,如果发现不能下载,请复制以下地址【http://www.mydoc123.com/d-1017553.html】到电脑端继续下载(重复下载不扣费)。

已注册用户请登录:
账号:
密码:
验证码:   换一换
  忘记密码?
三方登录: 微信登录  

下载须知

1: 本站所有资源如无特殊说明,都需要本地电脑安装OFFICE2007和PDF阅读器。
2: 试题试卷类文档,如果标题没有明确说明有答案则都视为没有答案,请知晓。
3: 文件的所有权益归上传用户所有。
4. 未经权益所有人同意不得将文件中的内容挪作商业或盈利用途。
5. 本站仅提供交流平台,并不能对任何下载内容负责。
6. 下载文件中如有侵权或不适当内容,请与我们联系,我们立即纠正。
7. 本站不保证下载资源的准确性、安全性和完整性, 同时也不承担用户因使用这些下载资源对自己和他人造成任何形式的伤害或损失。

版权提示 | 免责声明

本文(REG NACA-TN-667-1938 Operational treatment of the nonuniform-lift theory in airplane dynamics.pdf)为本站会员(terrorscript155)主动上传,麦多课文库仅提供信息存储空间,仅对用户上传内容的表现方式做保护处理,对上载内容本身不做任何修改或编辑。 若此文所含内容侵犯了您的版权或隐私,请立即通知麦多课文库(发送邮件至master@mydoc123.com或直接QQ联系客服),我们立即给予删除!

REG NACA-TN-667-1938 Operational treatment of the nonuniform-lift theory in airplane dynamics.pdf

1、i TECXBICAL UOTXS NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS .-_- . _- - -. . - NO . 667 OFERETIONAL TRldTtiENT OF TZE NONUNIFORH-LIFT TKEORY iN AIRPLAXE DYBIMICS Sy Robert T. Jones Langley demorisl. Aeronautical Laboratory t . gashington October I.938 . ; -.- . Provided by IHSNot for ResaleNo repr

2、oduction or networking permitted without license from IHS-,-,-J I. . J NATIONAL AL)VISORY COMXITTES: FOR AEROBAUTICS TECHNICAL NOTE NO. 667 i OFERATIO2?AL TREATXEXT OF THE NONUNIBORM-LIFT T3XORY IN AIRPLAYE DYNAMICS By Robert T. Jones The method of operators is used in the application of . ._ nonuni

3、form-lift theory to problerils of airplane dynamics. The nethod is adapted to the determination of the lift under prescribed conditions of motion or to the detorafnation of tho motions with prescribed disturbing forces. - 11TRODUCTION : Problems in airplane dynamics are usually treated on the assump

4、tion that the air forces are instantly adjusted to each motion of the airplane. Since the developmsnt of recent theories for the nonuniform motion of airfoils, it - has become possible to consider more exact laws for the ad- justucnt of the lift. The nonuniform-lift theory has already been applied t

5、o certain dynamical problems, notably to the problen of flut- .- ter. These applications have, however, been confined either to approxinate solutions or to case-s in which the-type of - ;uotion is prescribed beforehand. The Eore usual problem, in which the resulting xnotion is unknown, roauircs the

6、so- lution of integral equations. .-. - *The present papsr shows ho:w ; solutions of these equations may be obtained fairly simply by operational nethods. SUPERPOSITION OF LIFTS In nearly every aerodynamic problen, the approximations that Llust be made to effect solutions are such as to lead to- .-

7、_ linear relations. Thus, in the case of the unsteady lift of a wing, Laplaces equation cotibined with the assumption of - Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2 X.A.C.A. Technical Wote 370. 667 . an undistorted wake leads to a linear rela

8、tion between the lift and the angle of attack. Such a relation means that the lift due to the ,sum of ttio variable motione is equal to the sum of the lifts for the two motions taken lndepend- ently. 1 .- In particular, if the lift following a sudden unit I jump of angle of attack 1-s known (see rof

9、eronco l), then the lift for any variable motion is easily obtainol by breaking the given motion down into a. succession of small. jumps or steps and adding the lifts incident to each one. A The case treated by Wagner thus becomes the key to the calculation of lift for any variable motion. IPagnerIs

10、 function (reference 1) gi.ving the lift after a sudden unit jump of angle of attack (two:-lmcnsiona.1 - case) may be denotod by c 1Js) l The superposition of lifts for any variablemotiin CL(S) 9 as previously exa plained, is accomplished by the integration of Duhnmalls integral L - - a I I 0 ci, (s

11、 - so cL(so -so . (1) ci (See reference 2.) OPERATIONAL SOLUTION OF IXTEGRAL ;IlQUATIONS It is evident that, in order to take account oLun- 1 steady air-flow Phenomena in the theory of airplane dynam- *I= I.- its (including,stability and related problems) the custom- ary instantaneous equations of.

12、mot.ion_mu.gt be reglaced.by 1: equations involving the integral (l), The equati,ons of_ -, ;gotion then become linear integral e.quations, Solutions of these equations may be convoniontly obtained by opera- tional mothods. Lot D reprosent tho.operator d/da and let 1 = l(s) ro-orosent the unit jump

13、fuction, thaeis, a function of having the value 1 at .- 0 ix- s 0 .%iYd having the -velue s 1: (s) Equation (6) becomes F(1/2) Jr X(s) - 2x(s) = (9. - 2) D2 1 (s) r(i/2) 2 w-L or D ,31” + C2ehzs where co = .2-l-r $ = 1 -0.330,rr c, = -0.670 l-r K, = -0.0455 .- A, Z -0.300 and where s refers to the h

14、alf-chord as unit, that is - - Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-6 N.A.C.A. Technical Noto Ko. 667 vt c. S = - 42 In this form, the operational equivalent is readily found from the relation - oh* = JJ - t l(s) (See reforonce 2) (14) D-h

15、 whence D +D) = Co -I- C1 - D +c,- D - X1 D -Y A, (15) _.-.- The calculation of lift under a prescribed variation -r / of anglo of attack can be illustrated-by assuming that the airfoil is given a sinusoidal motion . . a(s) (or O(s) = R.P. or I.P. of eins (16) * - This variation is reduced to operat

16、ional form (see equation (14): D E(D) = - D - in (17) czn(s) = p D D - .-+ 0 - in (See equations (12) and (15),) The resulting operator may be-evaluated by the Heavl-.- _ ti side expansion theorem: f(D) f(O) c f(h) As !qEj- l =k(o)+ GFq-ye where the AS are the roots of F(D) = 0. (19) . .- l ., Provi

17、ded by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-. .* N,A,.C.I. Technical Note No, 667 7 CL. (s) = - v inelns + co+cl-=- + c, in l.,inst . A: . .-* n in- h, in-h, _I _ .i + Cl Al ha _L- *hls + c, - h 1 - in A, -in QhC (20) The terms involving ehs disappear

18、 in time and hence may be disregarded ina continuous oscillation. Tha terms I- G 1 - z. -:;-zL-z yield approximate expressions of the l:ift functions fOT .L- tno oscillating airfoil fntroduced by Thoodorsen (refer- ence 3): n2 2 2rrF(n) n = co -I- c, -+ca -s Ala + n2 2 h, fn a (2% 2rrG(n) = - C, h1n

19、 - ca h2n + Al2 + n2 haa +n VI - -.- As pointed out by Garrick (reference 4), Thoodrosenls function for sinusoidal motion -_ - - : . . C(in) = F(n) + iG(n) (equation (21) -_ may bo regarded as the operational equivalent of Wagnors curve, i.e., 2rrC(D)l = c, (D)l = c1 (5) (23) 1 . t , This fact may b

20、e verified by referring to equation (15). This relation is especially intoresting because i-t shows a - connection between the Fourier and the operational analyses. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-8 N.A.C.A. Technical Note No 667 Thus

21、, if the response of a linear sy-stem to a cant-inuous sinusoidal excitation is known, I Rn(s) = f(in) oins (24) _ = Then the function f furnishes immediately the operational equivalent of the unit-response so that for any variable excitation Z(s), R(s) = f(D) ,2(E) = f(D) z(D) 1 (25) In general, th

22、e motion of the airfoil or airplane will not be prescribed beforehand but must be determined from dynamical equations, This type of problem can be il- lustrated simply by considering the disturbed vertical mo- tion of the airplane without pitching. The dynamical equation in this ca,se is . . dw m- r

23、esisting force = impressed force, Z (26) at . . . where w is the vertical velocity of the airplane and m is the mass including the virtual additional-mass of the wing. Since mdw 2m V2 da = - dt x s /i/2 c/2 x - - s P/2 c c/2 ds Xaking ths,substltution 2 9 - =-Q s P/2 c (27) - (28). (29) and writing

24、the equation in coefficient form, aDa +-c, (I) a = c1 (s) 1 0 (30) Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-N.A.C.A. Technfcal.Noto No. 657 9 where cLO is the lift coefficient of the given disturb- ing force. The operational solution is - .- .

25、- a(s) = 1. Cl (d (31) aD -I- cl,(D) o Again, as in the case.of the lift, the solution for.the elementary jump is the key to solutions for variable con- ditions. 1 a, (4 = 1 oD + F,;D) (32) Replacing “I (D) by (15) and simplffyrng: 3. (D - a,(s) = - A,) (D - ha) 1, = - f(D) 1 (33) aD3 + bD2 -I- CD -

26、I- d F(D) . which is in standard form for evaluation by the expansion theroem (19). Finally, a(s) = Cl (0 0 s S 1 a,(s) + a,(s - so 0 ) 3 I(so) ds, (34) 0 The extension of this treatment to problems involv- -.- _ .- ing a number of degrees of freedom will be evident, - -.v Langley Memorial Aeronauti

27、cal Laboratory,. Xational Advisory Committ.ee for -haronautics, Langley-Field, Va., September 12, 1938. . i Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-10 N.A.C.A. Technical Note.No. 667 REFERENCES 1 .: 1. Wagner, Herbert: Uber die Entstehung des

28、 dynamischen Auftriebes-von fragfltigeln. Z.f.a.M.IL., Bd. 5, 1 Heft 1, Feb. 1925, S. 17-35. 2, Carson, J. R.: Electric Circuit Theory and Operational ._ _ Calculus. McGraw-Hill Book Co., Inc., 1926, .- 3. Theodorscn, Theodore: General Theory of Aerodynamic s Instability and the Mechanism of Flutter

29、. T.R. No, - - 496, N.A.C.A., 1934, 4. Garrick, I. E.: On Some Reciprocal Relations in the Theory of Nonstationary Flows. T.R. No. 629, W.A.C.A., -_ 1938. . - Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-N.A.C.A. Technical Note No. 667 Fig. 1 8 - 150 -4 25 - d V - 0 L - -. ._ Pigure l.- Moving azcs. a = w/V ; 8 = vt c/2 I . Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-

copyright@ 2008-2019 麦多课文库(www.mydoc123.com)网站版权所有
备案/许可证编号:苏ICP备17064731号-1