1、6 RM K56C20 RESEARCH MEMORANDUM TllXE3-VECTOR DETERMINED LATERAL DERIVATIVES OF A SWEPT-WING FIGmR-TYPE AIRPLANE WITR THREE DPFERENT VERTICAL TA.ILS AT MACH Nuh?BERs BETWEEN 0.70 AND 1.48 By Chester H. Wolmicz L-2 A - “ “ “ “ NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WASHINGTON June 5, 1956 Provid
2、ed by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-iP .* w NACA FM H56C20 - NATIONAL ADVISORY COMMlTIYEE FOR AEFONAIJTICS DEE“ VERTICAL TAIIS AT MACE NUMB33.S BZZWEEN 0.70 AND 1.48 By Chester H. Wolowicz As part of the flight research program coducted on a sw
3、ept-wing fighter-type airplane, rudder-pulse maneuvers were performed at altitudes from 30,OOO to 43,000 feet over a Mach nmiber range of .O.7l to 1.48 to determine the lateral stability characteristics rehtive to the stability axes, in general, and the lateral derivative cl-mzacteristics, fn partic
4、- ub. The time-vector method of analysis ma used. Four configurations were employed in the investigation. Three configurations involved three different vertical tails with “yhg aspect ratio or area, or both. The fourth configuration emplayed a Large tail, which had been used in the third configurati
5、on, and an extension of the wing tips. The time-vector method of analysis is capable of producing good value6 of the lateral derivatives % fp Gap, CZB, ctp PrMang the damping ratio is lese than qproxFmately 0.3. Reliable values of lateral derivatives (C+ - Cy) ere difficult to determlne because of t
6、he sensitivity of this quanti- to other factors. The expected effects of increasing vertical-tail size, resulting in increasd magnitudes of Czp , and C +, were realized. The ation of however, moderate controlmavements in the transient portion of the maneuver influenced the analytical results. The mo
7、st troublesme data resulted fram maneuvers performed at high angles of attack or at other than lg. Maneuvers were performed at 1 g x. conditions for the four con- figurations at altitudes ranging from 38,000 to 41,000 feet over a Mach number range of 0.73 to 1-35. To extend the Mach nmiber range of
8、the tests to 1.48, maneuvers were performed following a pullout from a dive. These maneuvers were performed th configurations By C, and D at 35,000 f3,OOO feet over a load. range of 1.2g.to L7g. To investigate the effects of angle of attack on the lateral sta- bility characteristics maneuvers were p
9、erformed with configurations C and D during turns and pushovers at Mach numbers of 0.73 to 1.18 at 40,000 22,000 feet and for configuration D at 30,000 f2,OOO feet. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Effects of angle of attack were also
10、investigated over a Mach Tnmber range of 1.03 to 1.31 for onfigur however, because of the time factor and some doubt as to the validity of the results which would be obtained UsFng the avai1a;bI.e flight data, it ua8 decided not to emplay this method. The method of reference 9 is a time-vector appro
11、 however, it is a tabular procedure employing successive approximations and therefore is not a6 desirable as the relatively rqid grqhical time-vector method of analysis explained in references 10 to .E. The graphical time-vector method of references 10 to 12 wa8 ernplqed for the determination of Gy
12、required precision of phase-angle bta precluded the possibility of reliable value8 of (Cyr - Gya or Cy ; therefore it was decided, on a selective basis, to employ estimated values of Cy and to ignore (Cy, - %b) in the solution. The values of C and c”p which were required for the time-vector solution
13、 of the other derivatives were B cw (c., - ens) 9 CZB and Czp. P P 2, - obtained frm theoretfcal estimates. Application of the Time-Vector Method of Analysis No attempt is made in thi8 paper to present the detailed mathematical aspects of the fundmental time-vector properties inesmuch as reference 1
14、0 accaqlishes this quite thoroughly. -Suiice it to say that the time invariance of the phase relationships and amplltudes relative to each other permits the representation of asy one of the Ilnearized equations of motion by vectors. In the four lateral-directional equations”L nanrely, sidesHD,- roll
15、, Ed yaw, each ii.tF%e same fre-cency and damping characteristics. The amplltudes of the various degree8 of freedam in each of the lateral- directional equations have the sane shrinkage rate and the phaee angles remain constant; thus for vector representation, the various amplitudes and phase relati
16、ons are time invsriant. The vector properties described in the preceding paragraph, plus the requirement that the vector polygon representing my one equation must close, makes possible the detemination of two unknowns in any one equa- tion. Inaamuch as it is desired to determine the stability deriva
17、tives fram flight data, it will be convenient to introduce new notations for the stability equations and to establish the equations in the form of ampH- tude ratios. All equations in this paper having absolute value notation8 will be considered to represent vector equations. Hence Provided by IHSNot
18、 for ResaleNo reproduction or networking permitted without license from IHS-,-,-The derivatives with respect to r and 6 have been ccanbined in equations (6), (y), and (8). This was done because. Ir 1 is similar to * I 0 I and is appro-tely 1m0 out of phase with I . The amplitude ratio representation
19、 is“coqenient, inasmuch as it simplifies flight-data reduction and enables a more-dlrect determinatiog . of same of the derivatives. - The period .of. oscillation P is determined directly frm the tran- sient portion of the flight record. To determine the indicated phase angles, the measured time dif
20、ferences of the different peaks of the va?zLous degree6 of freedom were averaged and the simple expression * To determine indicated amplitude ratios relative to the body axes, the envelopes of the transient oscilhtiog regxds are plotted on a semi- loithmFc ELrious wqys such as Rusting (11) ea (E) an
21、d transposing Correctfcm of Lndicated Anrplltude Ratios and Phase Angles AmpHtude ratios are subject to corrections for dynamic magniffca- tion, instrument Location, and reorientation ) is sham in the figure, this deriv- ative was not included in the results of the analysis because ofthe Lack of the
22、 required preci,sion of the value of which would be needed to obtain a fairly rellable first approximation of this derivative. at$ Figure 8(e) shows the vector diagram for the determination of cnP and (Cnr - CY) . NO attempt was made to determine “p in pwe of one of the other two derivatives, since
23、some preUminary work appeared to indicate there would be no advantage in doing this. The section entitled “Discussion“ in this paper considers. sepsitivity of sane of the derivatives to experimental errors as well ura- Figure I1 shows the estimated weight rate of air rewired by the jet engine to mai
24、ntain cruising speed. Figure I2 shows the estimated contri- bution of the intake air of the jet engine to andc Cys ne Following is a summary of the figures presenting the results of this investigation: Limitations of the Time-Vector Method Figure - Influence of c“pandcr“.“ Influence of 21-percent ch
25、ange in C 13 16 Wwence of f0.5 change in . 14 Tlp -“-.-“- Influence of f5-percent change in Opr 15 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-20 y, WA RM H56C20 Static and Dynamic Characteristics results A B c D Comparison of A, B, Comparison of
26、- C and D C, and D with theory and wind tunnel at M = 0.83 and M = 1.12 “ Angle-of-attack effects T Period and asmping Figure Amplitude ratios and )base angles 19 22 25 28 31 “ 34 Static and j;ynamic lateral derivatives 20 23 26 29 32 33 35 . The data for configuration A, shown in figures 18 to X),
27、are meager in the subsonic region and most are subject to inadvertent control move- ments which, although not affecting the periods (fig. 18 a) ) appreciably, - do affect the damping (fig. 18(b) and the phase angles t fig. lg(b) so that no attempt was made to analyze these data for the 40,000-foot c
28、on- dition. The three test points at M = 0.71 constitute the only reliable damping characteristic points in the subsonic region and, as a result, the amplitude ratio curves of figure 19 indicate approximate values only. Despite the lack of sufficient subsonic data, the experimental stability derivat
29、ive characteristics shown in figure 20 are considered to be reli- able within the accuracy indicated previously. Although period and damping curves are shown in figure 18 for a load factor of 1.8 at 40,000 feet, the amplitude ratios and phase angles for this condition were not sufficiently well deff
30、ned to obtain derivatives. The results of- the analysis for configurations B, C, and D (figs. 21. to 29) are based on the availability of a larger amount of pulse data for each configuration: The data for configuration C were sufficient to define characteristic curves for trb Level flight at 31,000
31、feet from M = 0.77 to M = 1.0 as well as for trfm level flight at 40,000 feet (figs. 24 to 26). Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-c . Limitations in the AppLication of the Time-Vector Method of Analysis Although the time-vector method o
32、f analysis requires the sbplest of equipment in its application and is capable of prdding good results, it does have defintte limitations. In considering the Umitations, it is presumed that flight record8 have clear, sharply defined traces, a and th e use of tentplat e aids or analogs-to detenkne th
33、e damping ratio. When the damping ratio I; exceeds 0.2, the accuracy of defining begins to decrease. When 5 exceeds qproximately 0.30, ” ” it is somewhat difficult to determine the period accurately and the T112 values become increasingly doubtful. Also when 5 exceeds 0.4, relia- bility of P and T 1
34、/2 becanes poor. For controls-fixed conditions, the method depends on the analysis of tSe tssient portion of an osciUatom motion. qy inadvertent application of a forcing function during this transient oscillatory motion, wen though it may be small, will tend to influence the results. Ln instances wh
35、ere the forcing flrnction is deliberate and is of a pure sinusoidal nature, the time-vector method is applicableprwiding the Cy6 , Cw, and Cz6 derivatives are available. A third Umirtation of the time-vector method lies in the fact that only two of the three derivatives in each of the lateral eqatio
36、m may be determined by means of the vector diagram. In the case of transverse equation (6), the secondary terms and (Yr - %;) I pl are generally neglected and the result is This simplified expression for C, prwides anmers which are high; B however, the error probably does not exceed 4 percent. The p
37、rincipal Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-22 - NACA RM H56C20 difficulties in obtaining refined values of C, have been Fn the read- ability of the records and the phase lag error of the vane itself. It should be recognfzed that the unk
38、nown phase lag of the vane would enter into the problem and affect the amwere for Cyp, regardless of the method of analysis employed. P 4 m In the case of the ro7Ulng-moment equation (eq. (8) ) it wa deemed advisable to estimate the Vxces of cz, and to obtain Cz and Czp frm the vector diww ST vector
39、 is relative small, especially at high Mach numbers, and a normal error of f5 in Qpr would result in no accuracy in attempting to determine Czr. -. B A limited investigation xnge in Cz,. - P 2p Nomlly, in dealing with the yawing-mment equation (eq. (7) , attempts are made to determine the ( Gr - %)
40、derivatives fram vector diagrams. TuB, either C or Cnp must be obtained by other means to permit cmple-tion of the solution. In the present paper a theoret- ical estimate of (2% w-a made and used to obtain both C however, the addition of extended tips decreased The phase angle Ocpp did not appear to
41、 be influenced in the sub- sonic range by the range of vertical-tail sizes covered, but the addi- tion of the wing extensions had a more significant influence on the phase angle (fig. 31). In the supersonic region configuration A showed less lag in phase angle than did conffgurations B and C, which
42、had practically identical phase-angle characteristics. Ektension of the wlng tips tend supersonically the influence appears to .be negligible. E Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA FM H56C20 ” 27 Canparison With Calculated Charmteria
43、tics and Wind-We1 Data Two sets of calculated characteristics curves .are s.hm in figure 33. The results show that air-intake effects and torsional flexibility of the tail have a pronounced influence on the calculated stability characteristics. Beyond M = 1.25 all the flightdetermined derivatives ex
44、cept (Cn, - Cnp) experience a deteriorating break in magdtude characteristics. The calculated Cy and C chmacteristice indicate this break clearly; calculated C2 chwacteristics show only slight but simila;r trends starting at M = 1.15, calculated C characteristics indicate that damping in roll begin3
45、 to deteriorate fn the vfcinity of M = 1.35. B ”s B lp Inasmuch as is practically dependent on wlng alone, the break in the C curve not accounted for by calculated values of this deriv- ative appears to indicate, as mentFoned in the previous section, the possibility of 5ome shock wave and flow inter
46、ference near the tip of the wings of both configurations which influences the Uft distribution across the span of the wing. Such an influence would rduce the effec- tive dihedral C which tends to became negative at a Mach number of approximately 1.47. czp 2P - - -_ - - ” -. . . . 28 A comparison of.
47、 the calculated derivatives Kith flight results showed fair to god agreement in the subsonic region for all derivatives except (n, - hi) . The calculated values of ( c, - c”B), similar to the low-sped wind-tunnel values, were much lower than flight results. Unpublished w%nd-tunnel static-stebflity d
48、ata for M = 1.41 were corrected for vertical-tail flexibility and air-intake effects of the jet engine and are plotted in figure 33. These modified wind-tunnel data show good agreement with the fllghtdetermined trend of cps and Czp- It is difficult to compare the low-speed wind-tunnel data wlth the
49、subsonic flight results (fig. 33) because of the large Mach number differ- ence. As will be pointed out in the following section, the variation of Cy, C3, and C with angle of attack shown by wind-tunnel data is the opposite of trends shown by flight results; however, it *pears that the magnitudes of C and C from flight and KLnd-tunnel data tend t
