1、., I. ., ,. FOR AERONAUTICS ” “ I ., ” NOTE.-In the present analysis, the choice of a reference chord is not critical. If preferred, the mean aerodynamic chord as defined by ,2 s b/2 s 0 c,2 dy, where c, is the local chord and y is the distance along the span (ft), may be used. What,ever chord is se
2、lected as the reference chord should, of course, be used consistently for the pur- pose of data comparison. e base of the natural system of logarithms a acceleration due to gravity, ft/sec2 gust-gradient distance (horizontal distance from zero t.o masimum gust velocity), chords alleviation factor de
3、fined in reference 2 gust factor (revised alleviation factor) average flight miles to equal or exceed a given value of gust velocity wing lift-curve slope, per radian airplane mass, slugs total number of observations in a sample of clata probability that the maximum value in a sample of data will eq
4、ual or exceed a given value wing area, sq ft clistance of penetration into gust, chords dummy variable in superposition integral, chords time, set dummy variable in superposition integra.1, set gust velocity (maximum value), fps “derived” gust velocity, fps effective gust velocity defined in referen
5、ce 2, fps gust velocity at any penetration distance, fps airspeed, fps design cruising speed, mph (ref. 1, p. 3) equivalent airspeed, Tu, fps (see ref. 8) airplane weight, lb airplane vertical displacement (positive upward),ft location parameter of distribution of extreme values (symbol u in ref. 9,
6、 p. 2) scale parameter of clistribution of extreme values (symbol a! in ref. 9, p. 2) airplane mass ratio (sometimes referred to as 2w “mass parameter” in the past), mpccb9 .I air density, slugs/cu ft air density at sea level, slugs/cu ft air-density ratio, p/p0 average flight time per IT-G recorcl,
7、 hr Subscript: maa maximum value A bar over a symbol denotes the mean value of the variable. REVISED GUST-LOAD FORMULA DERIVATION OF REVISED FORMULA The revised gust-load formula to be derived herein, like the original formula, was obtained from solutions of an equation of airplane vertical motion i
8、n an isolated gust. The use of the formula to transfer accelerations from one airplane to another for continuous rough air implies, therefore, the assumption that the relative loads for single isolated gusts are a measure of the relative loads in a sequence of gusts. In regard to t.his assumption, i
9、t is recognized that some of the more recent methods for analysis of airplane loads in con- tinuous rough air with proper allowance for various degrees of freedom of airplane motion may in due course be adopted; however, for the present, it remains desirable to retain the simplicity of the original
10、method. As in the case of the original formula, the present method will not be suitable for all airplane configurations. Unusual airplanes will require special analysis. After the presentation of the revised gust- load formula, a brief comparison of features of the original and revised formulas is g
11、iven. III II I 111 1111 I III11 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Basic assumptions and equation of motion-The equation of motion is based on the following assumptions commonly used in gust-load problems: REVISED GUST-LOAD FORMULA AND R
12、E-EVALUATION OF V-G DATA TAKEN ON CIVIL TRANSPORT AIRPLANES 3 and an, is a convenient reference acceleration which may be interpreted as the acceleration that would result solely from a lift force equal to the steady-state lift associated with the maximum velocity of the gust. The second term is ass
13、o- ciated with the damping due to the airplane vertical velocity and the remaining terms are associated directly with the gust. It can be remarked that the mass ratio lg is a basic parameter in equation (2). (1) The airplane is a rigid body. (2) The airplane forward speed is constant. (3) The airpla
14、ne is in steady level flight prior to entry into the gust. _ -. -.- (4) The airplane can rise butcannot pitch. (5) The lift increments of the fuselage and horizontal tail are negligible in comparison with the wing lift increment. (6) The gust velocity is uniform across the wing span and is parallel
15、to the vertical axis of the airplane at any instant. If the forces associated with steady level flight are disre- garded, a summation of vertical or normal forces on the airplane in a gust yields the following equation of motion: Solution of the equation of motion._Equation (2) was solved for histor
16、ies of the acceleration ratio a,(s)/a,# on the basis of the following transient lift functions and gust shape. The transient lift functions used are $ Ls)=1.OOO-O.236e-o116s-O.5l3e-o7z*-O.l7le-44 (6) d22 p 21/f clt”+Z V2Sm S os the first term is the force due to a gust having zero velocity at the be
17、ginning of penetration by the airplane and the second term is the force due to a. gust having an initial velocity other than zero at the beginning of penetration. By using the relationships $=aZg and t=$, equation (1) can be written in nondimensional form as S d UC%) zz2 L-1 os $; CL,bSl -g- 40) 1 d
18、SlfT G GE(S) (2) where 2w - cc,- m pcgS and the functions CL and CL* are the transient lift responses of a wing to a penetrltion of a sharp-edge gust and t.o a unit- jump change in angle of attack, respectively. In equation (2), a, is the vertical acceleration that results from the gust 33218i-55-2
19、These are the transient lift functions for infinite aspect ratio given in reference 10, normalized to asymptotic values of unity. These expressions, rather than finite-aspect-ratio functions (such as those given in ref. lo), were used for sim- plicity in order to provide solutions of the equation of
20、 motion independent of aspect ratio except, of course, as aspect ratio affects the slope of the lift curve. Thus, in effect, only the shapes of the infinite-aspect-ratio functions are used, the appropriate finite-aspect-rat,io lift-c.urve slope being used in evaluating the mass ratio pg. The results
21、 obtained through the use of equations (5) and (6), however, are probably less thau 5 perc,ent different from the results that would be ob- tained through the use of the finite-aspect-ratio functions, as indicated by some limited information in reference 11. This reference also indicates that the di
22、fferences might be slightly larger wheu the transient lift functions for a Mach number of 0.7 are used. The gust, shape used was that designated by the ANC-1 Panel, that is, l$Lf (I-cos g)=sinz $ (Os2H) where H was designated equal to 12.5 chords. (Inasmuch as the initial portion of the revised gust
23、 profile is relatively in- effective, the gradient distance of 12.5 chords corresponds roughly to the lo-chord gradient distance for the original ramp profile.) With these lift functions and gust shape, equation (2) is noted to depend on only one parameter, the mass ratio A. Solutions of the equatio
24、n were obtained for a range of pZ, by the numerical recurrence method presented in reference 12 for the case of a rigid airplane. Although solutions of the equation also can be obtained in closed form when equations Provided by IHSNot for ResaleNo reproduction or networking permitted without license
25、 from IHS-,-,-4 REPORT 1206-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS (5) and (6) are used, the numerical method was chosen be- cause it is much more rapid, is easy to apply, and gives good accuracy (error in an/an, less than f0.005). Sample histories of the calculated acceleration ratio for three
26、 different values of clg are presented in figure 1. Revised gust factor and gust-load formula.-Since the maximum value of a,/a, with respect to gust penetration distance (see fig. 1) defines the maximum acceleration exper- ienced by the airplane, it is of primary concern in design. This maximum valu
27、e is herein designated as the “gust fac- tor” and is labeled Kg; that is, (8) The variation of this gust factor with mass ratio is shown in In terms of equivalent speeds this equation becomes .;” - .6 e c .r” p .4 u iti a. .2 I- I 0 2 4 6 El IO 12 14 16 Gust penetration distance, S, chords FIGURE I.
28、-Representative histories of acceleration ratio. figure 2. No closed-form analytical expression for the curve of K, can be written, since it was obtained by a numerica. procedure. A convenient expression which closely approxi- mates the curve was found, however, and is presented below: 0.88Pg Kg=5.3
29、+pg (9) This simple expression gives Kg with an error less than f 0.01. The revised gust-load formula follows directly from equa- tion (8) ; that is, a%,z- ns -a K, mpSVU K = 2w g (101 m pOsveude 2w K it is the same as that in item (c). The original formula, as inclicated in reference 2, has been su
30、bject to scrutiny in the form of continuing experiments in regard to usefulness for conventional airplanes and in regard to the effects of various other factors not explicitly taken into account in its derivation. This background of experience can be carried over in the use of the revised formula as
31、 well. In the same vein, the allowance for effects of pitching motion macle in the derivation of the alleviation factor but not, explicitly taken into account in the derivation of the gust factor nevertheless can be included in the use of the gust factor. The pitch correction was not directly applie
32、d to the gust factor because it would cancel out of calculations relating the acceleration of one. airplane to that of another airplane. As mentioned earlier, in the use of the formulas to evaluate measured accelerations, the derived gust velocity lr, ancl the effec,tive gust velocity U, are both de
33、rived rather than measured quantities. They differ, however, as indicated by item (f), in that U, corresponds to the maximum equivalent velocity of the gust shape, whereas U, corresponds to only a fraction of the maximum equivalent velocity of the original gust shape. This fraction stems from the va
34、lue used to normalize the alleviation-factor curve at W/S=16 lb/sq ft. There is no single constant proportional relationship between U, and Ue for all airplanes because of their respective mass-ratio and wing-loading bases. Subsequent sections of this report will be devoted to an application of the
35、revised formula to some previously obtained and reportecl NACA gust data. SUMMARY OF RE-EVALUATED GUST-VELOCITY DATA FROM V-G RECORDS A principal application of the original gust-load formula by the NACA has been to obtain effective gust velocities from normal acceleration and airspeed data of V-G r
36、ecords. Since, however, the revised formula will be usecl in evaluating future relevant NACA gust-research data, some previously reported V-G data evaluated by use of the original formula have been re-evaluated by use of the revised formula in order to place them on a comparable basis with future da
37、ta. The re-evaluated data are summarized herein. Provided by IHS Not for ResaleNo reproduction or networking permitted without license from IHS-,-,-6 REPORT 1206-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS Scope of data.-Table.1 shows the scope of the V-G data collected from 1933 to 1950 as presente
38、d in references 3 to 7. In accordance with the procedures of these references, the data are grouped into three time intervals-1933 to 1941, 1941 to 1945, and 1945 to 1950-to denote the operations prior to, during, and after a wartime period. The type of airplane and the route are identified by combi
39、nations of a capital letter and a Roman numeral, such as A-I, B-II, and C-III. The airplanes and routes which correspond to those given in reference 3 are identified herein by the same com- binations to facilitate comparisons of present and older results. Table II gives the airplane characteristics
40、used for evaluat- ing the data. The values given either were obtained from the Civil Aeronautics Administration, the design manual of the airplane manufacturer, or were computed as indicated in the table. TABLE I.-SCOPE OF V-G DATA ANALYZED IN AIRLINE Application of gu3Qt; III Miami-Buenos Aires-.-
41、Agcci913g; IV Sa;o:F-Hawsii-Hong June i93fi to Dec. 1941 I Ne,ark-Seattle-Oakland. _ July 1937 to Dec. 1941 V Boston-Newark-Los bngeles. Feb. 1937 to Oct. 1939 VI Newark-Kansas City-Los Sept. 1938 to Angeles. act. 1940 III Caribbean region and north- Apr. 1940 to em part of South America. Dec. 1941
42、(13) where again a, and V, are the accelerations and associated airspeeds giving the maximum positive and negative gust velocities. Method of re-evaluation and results.-The method of converting the measurements of Ue,= into terms of U, follows directly from the definitions of t,he two quantitiig Fro
43、m equations (12) and (13) Period from 1941 to 1945 D 30 I 36. 1 1,084 E I Seark-Seattle-Oakland. F Period fron 1945 to 1950 VII New Orleans-Kn nsas City- Oct. 1948 to 79 303 23,940 Minot, N. I). Feb. 1950 II New York-M iam i ._._._. Nov. 1947 to 194 248 48,187 This relation permits simple conversion
44、 of the values of Feb. 1950 III Miami-Caribbe an region- Nov. 1947 to 1 I 2i 1 24i 6.6i7 u South America. May 1949 emBZ obtained from measurements from a given airplane to IV San Francisco-.4ustralia- Aug. 1947 to 69 231 values of Ude,. It might be noted that in calculating Orient. Apr. 1949 VIII Ne
45、w York-Seattle _. . Dee. 1948 to 388 ! ; 99.4 , / I T de,L,z the effects of air density on the airplane response are Apr. 1950 included, since the value of K, depends upon the mass ratio TABLE II.-AIRPLAKE CHARACTERISTICS Esti- Gust factor Slope of Des Mass mated lift curve, ccg opqroting ratio, com
46、putccl v, ;de, ;p, K, from 6A a m=A+2 4. 60 4. 76 5.04 4.78 4.92 : iif 4. 96 5. Ml 6.6 i. 7 10.4 7.9 9. 1 7. 8 9.2 9. 5 10.1 0.960 1.83 1.008 1. 77 I. 098 1.73 1.045 2.02 1.064 1. il 1.097 1.80 1.190 1.64 1.166 1. 64 1.160 1.60 180 5,000 i. 94 215 i+E 9. i5 181 13.85 168 5: oal 7.62 211 2E 12.85 230
47、 10: OOQ 11.75 2il 23.60 % 10, 5, oo+J fn!O 21.57 23.58 13,400 18.560 41, ooo % 45: ooo 94,000 iO.700 39,900 (a) For 0.85 gross weight at estimated operating altitude. (b) For 0.85 gross weight. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-REVISED
48、 GUST-LOAD FORMULA AND RE-EVALUATION OF V-G DATA TAKEN ON CIVIL TRANSPORT AIRPLANES 7 which in turn is a function of air density. For the present calculations (as was done in ref. 3 and refs. 5 to 7), an operat- ing weight was assumed equal to 85 percent of the airplane weight and a lift-curve slope
49、 was computed by using the 6A relation m=- as indicated in table II. A+2 (Gust velocities are not given in reference 4 ; therefore, the normal-acceleration and airspeed data upon which that paper is based were re- evaluated to obtain values of Ue, and U,m, for this report.) Inasmuch as V-G records do not indicate the altitudes flown, it was necessary to estimate average operating alti- tudes from information rec
