1、NATIONALADVISORYCOMMITTEEFOR AERONAUTICSTECHNICAL NOTE 3677INVESTIGAON OF LATERAL CONTROL NEfU3 THE STALLANALYSM FOR REQUIRED LONGITUDINAL TRIMCHARACTERlSl13CS AND DISCUSSCONOF DESIGN VARIABLESBy Fred E. Weick and H. Norman AbramsonAgricultural end Mechanical College of TexasWashingtonJune 1956,4 i.
2、 .+9.-, ,.- “.- t.:J-;., -Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-TECHLIBRARYKAFB,”NMP 1111111111111NATIONAL ADVISORY COMMITTEEFOR AERONAUTICS CIIILL352INVESTIGATIONTECHNICAL NOTE 3677OF IATERAL CONTROL NE/U?THE SI%ILANALYSIS FOR REQUIRED LON
3、GITUDINALCHARACTERISTICSAND DISCUSSIONOF DESIGN VARIABIJ3STRIMBy Fred E. Weick and H. Nomnan AbramsonEXJMMARYIt has been recognized for some the and shown quantitativelyby* the results of flight testsj that low-speed lateral control of airplanes,.,may be insured by a simple limitation of the maximum
4、 elevator deflection4so that the maximum angle of attack maintainable is.that which will stillallow satisfactory lateral control characteristics. However this pro-cedure places severe requirements on the longitudinaltrim characteristicsof the airplane, inasmuch as this maximum elevator deflection mu
5、st be ade-quate for the range of power settings and center-of-gravitylocationsencountered in flight. The purpose of this report is to provide theanalyticalmeans by which designersmay estimate the elevator deflectionrequired to trim in steady longitudinal flight and to demonstrate in aquantitativeman
6、ner the effects on longitudinaltrim of changes in someof the more important design parameters.Simplifiedmethods and semiempirical data have been summarized fromexisting literature and employed to provide analytical procedures thatare simple to apply but yet are accurate enough for use in preliminary
7、design. Two light aircraft are analyzed quantitativelyby the proceduresgiven, for both power-on and power-off conditions, in order to demonstratethe use of the analyticalmethods and to provide a comparison with flight-iest results. Computed and flight-test values of elevator deflection arein good ag
8、reement. Calculated values of elevator deflection are also pre-sented for both aircraft to demonstratethe quantitativeeffects of changesin some of the more important variables as well as the effects of power.Applications to design are discussed.It is concludedthat these procedures can result in a de
9、sign in which*the maximum up-elevator deflectionmaybe maintained within the highestvalue that will result in satisfactory dsznpingin roll and reliable lateral? control under all flight conditions,while, at the same time adeqwtelongitudinal control is available. Provided by IHSNot for ResaleNo reprod
10、uction or networking permitted without license from IHS-,-,-2INTRODUCTIONNAC!ATN 3677This report is the third and final one in a seriesproblem of lateral control of airplanes near the stall.has been reported in references 1 and 2.dealing with thePrevious workThe maor objective of this program has be
11、en to provide the designerwith quantitativedesign informationfrom which the proper combination ofvariables may be selectedto insure satisfactorycontrol near the stall.In general, there are two methods by which reliable low-speed lat-eral control characteristicsmay be obtained. One of these is to inc
12、reasethe angle of attack for the stall of the wing, or at least the outboardportions of the wing, to a point beyond the highest angle that is requiredin steady flight or in landing, thus maintaining effective dsnping-in-rollcharacteristics. This method utilizes aerodynamic devices such asleading-edg
13、e slots and wing washout. In reference 1 results were pre-sented of flight tests employingthis method; the results showed thateffective and reliable low-speed lateral control could be attained withthe airplane cotiigurationtested but only for power-off flight and anarrow range of center-of-gravitypo
14、sitions.The second method consists of simply limiting the elevator deflec-tion so that the maximum angle of attack maintainable is that which willstill allow satisfactorylateral control characteristics. It was shownin reference 2 that satisfactorylateral control was obtained, for allairplanes tested
15、, up to a “critical” angle of attack that was within 2of the angle of attack at which the airplane stalled;the reduction inminimum speed was almost negligible. However, this approach is a diffic-ult one because the elevator deflections required for longitudinaltrimusually vary greatly with center-of
16、-gravitylocation and power setting;the elevator deflection required to land causes further scatter of therange of required elevator deflections. Nevertheless,the designer doeshave a certain degree of control over longitudinaltrim characteristicsby means of a number of design variables. Flight tests
17、on several air-planes, conductedto obtain quantitativeinformationregardingthe rangeof elevator deflections encountered,are reported in reference 2. Thereare also includedthe results of flight tests on one airplane utilizingdifferent horizontal tail configurationswlhichwere proportioned so asto minim
18、ize the change in horizontal trim caused by application of power.The results of the flight investigationsshowed that it is feasibleto have airplane configurationsfor which apication of power makes avery slight change in the angle of attack at which the airplane trimswith a given elevator setting. Th
19、e results also showed that for moderate “ranges of center-of-gravitytravel a singlemaximum elevator deflectiongave acceptable low-speedperformance (themaximum up-elevator deflection ?-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACATN 3677 3that
20、would produce the critical angleof-gravity conditionwould produce anforward center-of-gravitycondition).of attack with the rearward center-acceptableminimum speed in theWith airplanes having tail-wheel-type landing gears, however, it appears to be extremely difficult tocover the three-point-landings
21、it correction factors which experience has shown areusually small (as, for example, the effect of the wake on downwash angleand the actual value of the thrust coefficient in the windmilling pro-peller condition),at least for light aircraft, have sometimesbeenomitted. Nevertheless, it is believed tha
22、t the procedures describedherein are sufficientlyaccurate for preliminary design purposes.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-4 NACATN 3677When comparisonswith flight-test results are attempted later inthis report it should be kept in min
23、d that (1) the simplifiedproceduresutilized will result in computedvalues which might be improved samewhatby the use of more ect methods; (2) the flight-test results should beconsidered in the light of the limited accuracy of experimentalmeasure-ment; and (3) measurementsmade by flight test more oft
24、en than not reflectpilot technique in sane measure. In view of these ccmmentss it tillbeconsidered satisfactory,ifcomputedvalues of control-surfacedeflectionare within about *h” of the correspondingexperimentalvalues. In aprevious unrelated study (ref. 3), a correlation of about 3 was con-sidered ac
25、ceptable; however in that investigationthe computed resultswere obtained by employing data obtained directly from flight testswherever feasible. The philosophy of the present report is to presentmethods which may be used in the preliminary design stage where accurateor even adequate data are often n
26、ot available; therefore it is notunrealistic to accept differences of scmewhatmore than 3. It is empha-sized once again that the guiding principle of this report is the pre-sentation of methods which may be used to predict the effects of changesin design variables.It might be mentioned that the meth
27、ods of analysis presented herein a71will also yield information concerningthe longitudinal static stability.Calculationsmay be made for the pitching moment about the center of kgravity (zero elevator deflection) for several values of lift coefficient.The customary plot of pitching moment versus lift
28、 coefficientll showthe static stability characteristicby the slope of the resulting curve.The authors wish to thank Mr. James D. Barnard for his assistancein performing computationsand in preparing the figures. This work wasconducted at the Aircraft Research Center of the Texas EngineeringExperiment
29、 Stationj Texas Agricultural and Mechanical College System,under the sponsorship and with the financial assistance of the NationalAdvisory Committee for Aeronautics.ANALYSISPower OffBasic anQysis.- The equilibrium equation for steady longitudinalflight may be written from a considerationof the force
30、s and momentsacting in the plane of symmetry. Assuming that(1) There are no power effects (direct or indirect)(2)The aircraft is not in close proximity to the ground(3)Moments contributed_W the drag forcesj except wing drag, arenegligibleProvided by IHSNot for ResaleNo reproduction or networking per
31、mitted without license from IHS-,-,-NACATN 3677 5b(4)The only lifting elements are the wing and horizontal tailthe equilibrium equation isThe meaning of each symbolin(-iw+cos(-iw)-% h-sJt(%? - +it+T5e)Vt=0(1)this equation may be found in the list ofsymbols given in the appendix. (See fig. 1 also.)Th
32、e moment contributedby the fuselage may be estimated by the sim-ple formula (ref. 3)2Kfuwfu %?UCmfu = sww% c%? (2)The factor uj which depends on the wing location on the body, may bedetermined from figure 2.Ttiehorizontal tail lift-curve slope maybe obtained from figure 3as a function of tail aspect
33、 ratio (ref. 4). In the absence of morereliable data, the upper curves in figure 3 may be utilized for estimatingthe wing lift-curve slope, depending on the section lift-curve slope ao.The downwash angle e is a very important quantity;howeverj itsaccurate determinationrequires exceedingly complex pr
34、ocedures. For mostanalyses, it will be adequate to determine e by means of convenientdesign charts (ref. 5). These charts, which are reproduced here in fig-ures 4 to 13, give downwash angles for plain and flapped untwisted wings.The wings considered include both elliptical and tapered plan forms (ta
35、perratios of 1 22 3, and 5) with aspect ratios of 6 and 9 and flaps covering40 and 70 percent of the wing span.The following procedures govern the use of these charts:Plain wings: The procedure for plain wings is as follows: (1) Findthe longitudinal distance x of the elevator hinge axis from the qua
36、rter-chord point of the root section and the vertical distance m (with respectwto the airplane reference line) Of the hinge axis from the wing trailingedge (negativedown). (2) Find the contribution of the plain wing3 to the downward displacement of the wake center line at the distance xProvided by I
37、HSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-6 NACATN 3677from the quatier-chordpoint by multiplying the value at the distance xa71on the correspondingdisplacementchart by the lift coefficient. (3) Locatethe point (x, m+ hwl)on the downwash contour chart and m
38、ultiply the cor- tiresponding downwash angle by the lift coefficientand by the correctionfactor obtained from figure 14 which accounts for the variation of down-wash angle across the span of the horizontal tail (ref.).Flapped wings: For flapped wings the procedure is as follows:(1) Find the longitud
39、inaldistance x of the elevator hinge axis fromthe quarter-chordpoint of the root section and the vertical distance mof the hinge axis from a point (the wake origin) lying at a distance hobelow the trailing edge of the wing, where() sin bf + kwho =b/2and k is given in figure 15. (2)Find the contribut
40、ion hw of the(3)plain wing to the downward displacement of the wake center line at dis-tance x from the quarter-chordpoint by multiplying the value on thecorrespondingdisplacement chart (plainwing), at the distanceC%. (3)Find the contribution hfX, byof the flap to the downward dis-placement by multi
41、plying the value on the correspondingchart (flap),atthe distance X, by C%. (4) Locate the point (x, m + hw + hfI) onthe contour charts for the plain wing and for the flap; multiply the cor-responding downwash angles, respectively,by C and C% and by thecorrectionfactor from figure 14 and add in order
42、 to obtain the downwashangle.A slight correction is often added to the downwash angles obtainedby the procedures just describedwhich accounts for the effect of thewake on the downwash angle. The effect is to Increase the downwash abovethe wake center line (locatedby m + or, in the case of a flappedw
43、ing, by m + + hf) and to decreasethe downwashbelow it. The cor-rection is usually negligible for plain wings; for flapped wings withsmall flap deflectionsa correction of 1.5 within the wake to 1 at thewake edge should be adequate, while for large flap deflectionsthosevalues shouldbe doubled. The loc
44、ation of the horizontal tail with respectto the wake maybe determinedfrom figures 16 and 17. For a more accuratedetermination of the magnitude of the wake correction,reference 5 shouldbe consulted.For wings or flap spans other than those included in these charts,linear interpolationor extrapolation
45、is usually quite sufficient. Forwings which possess considerabletwist, the downwash due to twist must be *calculatedfrom the spanwise load distributionat the zero-lift condition$wProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACATN 3677*and this is
46、 used as an increment ofa found by the procedures outlined ondownwash to be addedthe preceding page.1-7to the downwashThe contribution of flaps to the wing lift, drag, and moment mayalso be accounted for convenientlyby means of certain design charts(refs. 5 and 6). The increase in section lift coeff
47、icient, correspondingto a given flap deflection, IMY be obtained from figure Ma); the increasein total wing lift coefficientmay thenbe obtained from figwre 18(b). Theincrements in wing section moment coefficient and total wing drag may befound from figure 19. These design charts should only be used
48、in theabsence of more reliable aerodynamic data pertaining to the particulardesign.Deflection of the elevator serves to change the effective angle ofattack of the horizontal tail. The change of with elevator deflec-tion thus constitutes an tiportantparsmeter T, known as the elevatoreffectiveness fac
49、tor. An empirically derived curve for T (ref. 6), asa function of Se/St, is shown in figure 20.k The dynamic pressure in the vicinity of the horizontal tail is oftenquite different from the free-stream dynsmic pressure; the ratio qt/q= ?t4 is called the tail efficiency factor. For power-offflight, T IS lessthan unity because of the unavoidable l
