1、NASA MEMO 4-1-59Laoi!NASAMEMORANDUMEFFECT OF HORIZONTAL-TAIL CHORD ON THE CALCULATEDSUBSONIC SPAN LOADS AND STABILITY DERIVATIVESOF ISOLATED UNSWEPT TAIL ASSEMBLIES INSIDESLIP AND STEADY ROLLBy Katherine W. BoothLangley Research CenterLangley Field, Va.NATIONAL AERONAUTICS ANDSPACE ADMINISTRATIONWAS
2、HI NGTONMarch 1959Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NATIONALAERONAUTICS AND SPACE ADMINISTRATIONMEMORANDUM 4-I-59LEFFECT OF HORIZONTAL-TAI
3、L CHORD ON THE CALCULATEDSUBSONIC SPAN LOADS AND STABILITY DERIVATIVESOF ISOLATED UNSWEPT TAIL ASSEMBLIES INSIDESLIP AND STEADY ROLLBy Katherine W. BoothSUMMARYSubsonic span loads and the resulting stability derivatives havebeen calculated using the discrete-horseshoe-vortex method for a system-atic
4、 series of horizontal tails in combination with a vertical tail ofaspect ratio 1.0 in order to provide information on the effect of varyingthe chord of the horizontal tail for isolated tail assemblies performingsideslip and steady-roll motions. In addition, the effects of horizontal-tail dihedral an
5、gle for the sideslip case were obtained. Each tail sur-face considered had a taper ratio of 0.5 and an unswept quarter-chordline. The investigation covered variations in horizontal-tail chord,horizontal-tail span_ and vertical location of the horizontal tail. Thespan loads and the resulting total st
6、ability derivatives as well as thevertical- and horizontal-tail contributions to these tail-assembly deriv-atives are presented in the figures for the purpose of showing the influ-ence of the geometric variables.The results of this investigation showed trends that were in agree-ment with the results
7、 of previous investigations for variations inhorizontal-tail span and vertical location of the horizontal tail. Var-iations in horizontal-tail chord expressed herein in terms of the root-chord ratio, that is, the ratio of horizontal-tail root chord to vertical-tail root chord, were found to have a p
8、ronounced influence on most ofthe span loads and the resulting stability derivatives. For most of thecases considered, the rate of change of the span load coefficients andthe stability derivatives with the root-chord ratio was found to be amaximum for small values of root-chord ratio and to decrease
9、 as root-chord ratio increased.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-INTRODUCTIONAccurate information on the magnitude and distribution of tail loadsis important in estimating the contribution of tail assemblies to theaerodynamic derivative
10、s of complete airplane configurations and for thestructural design of the tail assembly. For the subsonic-speed range,information on tail loads for a variety of _solated intersecting vertical-and horizontal-tail configurations performillg various motions is avail-able. (For example, see refs. I to 4
11、.) H_lever, theoretical analyseshave considered only configurations for which the vertical- and horizontal-tail root chords are equal. The purpose of the present paper is to pro-vide some information concerning the influe_ce of varying the length ofthe horizontal-tail chord on the span loads and the
12、 resulting stabilityderivatives for isolated unswept tail assemolies in sideslip and steadyroll. In addition, the incremental span loads due to dihedral of thehorizontal-tail surfaces are determined for the sideslip case. Calcu-lations are made using the discrete-horseshge-vortex method (refs. 4to 6
13、) for a single unswept vertical surface of aspect ratio 1.0 and taperratio 0.5 in combination with unswept horizontal surfaces having taperratios of 0.5 and various root chords, semispans, and vertical positionsrelative to the vertical tail.SYM_OLSThe results presented herein are referred to the sta
14、bility systemof axes with the origin at the quarter-chord of the vertical-tail rootchord. (See fig. i.)A aspect ratio, b2/Sb _ span, ftS area, sq ftc local chord, ftaverage geometric chord, ftcr root chord, ftCr,hCr,Vroot-chord ratioProvided by IHSNot for ResaleNo reproduction or networking permitte
15、d without license from IHS-,-,-30VPx,y_zPCyC_c_mass density of air, slugs/cu ftfree-stream velocity, ft/secsideslip angle, radiansdihedral angle of horizontal tail, radianscoordinate distances relative to stability system of axesrate of roll, radians/seclateral-force coefficient, Lateral force0V2Sv2
16、rolling-moment coefficient, Rolling momenti oV2Svbv2section-lift coefficient, Section lifti0V2cr brCy_ bCy_r2 b1-,2r 6PcCyCyp- 8 pbvVProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-CzC1p - PbvVSubscripts :h horizontal tailv vertical tail(CC0hSubscrip
17、ts used in the span load coefficien;s, such as , signify_v_that _ is the average geometric chord of the vertical tail and thatc_ and the chord c are based on horizontal-tail geometry.PRELIMINARY REMARKSThe basic finite-step method used herein is the same as that usedin reference 4 and is an adaptati
18、on of the aethod applied in reference 6to the computation of wing loads. The theoretical considerations involvedin applying this method to intersecting surfaces are not included in thispaper since they are presented in appendix % of reference 4.For all tail configurations considered in this paper, t
19、he verticaltail is represented by 6 equispan horseshoe vortices and the horizontaltail by 12 equispan horseshoe vortices. (S_e fig. 2.) Therefore, eachtail combination is represented by a total _f 18 horseshoe vortices whichresult in a set of 18 simultaneous equations with 18 unknown vortexstrengths
20、. When motions such as rolling an_ sideslip are considered,the horizontal-tail loads are antisymmetric (equal but of opposite signon each panel); therefore, the number of equations may be reduced to 12.All solutions of the simultaneous equations were obtained by use of arelay-type computer.Mach numb
21、er effects were not taken int9 account, and vertical dis-placement of the vortices of the horizontal tail due to dihedral anglewas neglected The angles _, F, and -Pbv are assumed to be suffi- Vcently small so that the sine of the angle can be replaced by the anglein radians and the cosine, by 1.0. A
22、ll calculations were made for atwo-dimensional lift-curve slope of 2_.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-SCOPECalculations were madefor a systematic series of isolated tailassemblies performing sideslip and steady-roll motions. For these
23、 twomotions, three basic span loads, two resulting from the sideslip motionand one from the steady-roll motion, were obtained. The three casesconsidered are:(i) Loads resulting from sideslipping the tail combinations havinghorizontal tails with zero dihedral.(2) Incremental loads resulting from side
24、slipping the horizontaltails having dihedral angle.(3) Loads resulting from rolling the tail combinations about anaxis coincident with the root chord of the vertical tail.The loads calculated for case (2) should be considered as additionalloads due to horizontal-tail dihedral angle. For the small an
25、gles con-sidered herein, it is assumedthat the total load in sideslip on anytail combination having dihedral can be obtained by the proper additionof the loads obtained from case (i) and case (2). In all three cases,the additional restriction that the horizontal surface remains at zerogeometric “ang
26、le of attack was imposed.Span loads and the resulting stability derivatives are presentedfor unswept tail configurations having a single vertical surface ofaspect ratio 1.0 and a taper ratio of 0.5 in combination with a numberof horizontal surfaces, with each horizontal surface having a taper ratioo
27、f 0.5. Horizontal tails having spans bh of _bv, 5_bv,and 4bvwere considered at three vertical locations, at the base, at the midposition, and at the top of the vertical tail. For each span, thehorizontal-tail chord was varied and, since only horizontal tails of0.5 taper ratio were considered, the va
28、riation in horizontal-tail chorde _was expressed herein as a variation in root-chord ratio -r_n. Calcula-Cr,vtions were performed for values of root-chord ratio Cr_h of O, 1/4, 1/2,Cr_v3/4, and 1.0. For all cases, the quarter-chord of the horizontal-tailroot chord intersected the vertical-tall quart
29、er-chord line. Sketchesshowing the plan forms covered in this investigation are presented intable I.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-6PRESENTATION OF RESUltSThe results of the investigation are presented in two main groups,the first gr
30、oup containing span loads (figs. 3 to 5) and the second groupcontaining stability derivatives (figs. 6 to ii). In figures 3 to 5,negative values of the vertical-tail load coefficient indicate a nega-tive lateral force. The horizontal-tail load coefficients are for theright (positive) semispan facing
31、 into the wi:_d, and positive values sig-nify lift loads. Loads on the left semispan of the horizontal tail areequal in magnitude but opposite in sign to tile loads on the right semi-span for the corresponding spanwise station.All derivatives are based o_ the geometcy of the vertical tail inorder to
32、 indicate the relative magnitudes of the vertical- and horizontal-tail contributions to the total derivative for a given tail configura-tion. In order to indicate the influence of the horizontal-tail chord,all derivatives are plotted against root-chord ratios. (The horizontaltails and the vertical t
33、all have a taper ratio of 0.5.)RESULTS AND DISCUSSIONSpan Load Distribut_.onsSidesli_ without dihedral.- The span l,_ads due to sideslip on unswepttail assemblies having horizontal tails of _ero geometric dihedral arepresented in figure 3. The vertical-tail s)an loads presented in fig-ure 3(a) show
34、that changes in root-chord ra_io can provide significantchanges in the magnitude of the end-plate effect when the root-chordratio has a value of 0.5 or less. For horiaontal tails located at themiddle of the vertical tail, the calculations show no noticeable effectof root-chord ratio on the vertical-
35、tail sp_n load.The nondimensional span load coefficicnts for the induced loadingon the horizontal tails are presented in figure 3(b). As expected, thisfigure indicates that for horizontal tails of given span located at eitherextremity of the vertical tail an increase in the root-chord ratio pro-duce
36、d an increase in the magnitude of the induced load on the horizontaltails. An examination of the values of the horizontal-tail span loadcoefficient for the low and high positions indicates that a large per-centage of the induced load shown for a value of Cr_h of 1.O wasCr,vobtained for a root-chord
37、ratio of 0.5. _lis effect of root-chord ratiois, in addition, influenced by horizontal-_ail span as evidenced by theProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-7fact that the rate of change of span load coefficient is almost linearwith root-chord
38、 ratio over the outboard portion of the largest spanhorizontal tails. Figure 3(b) also indicates that the effect ofhorizontal-tail position and horizontal-tail span are consistent withthose shown in reference 4. The negligibly small induced loads shownfor horizontal tails in the mid position are due
39、 directly to the effectof vertical-tail taper.The span loads presented in figure 3(b) are for the right semispanof the horizontal tail. Since the loads on the left semispan are equalin magnitude but opposite in sign, there results for the complete hori-zontal tail a zero lift force and a rolling mom
40、ent about the root chordof the horizontal tail.Sideslip of horizontal tails with dihedral.- The induced span loadsof the vertical tail due to the horizontal-tail dihedral angle are pre-sented in figure 4(a). For horizontal tails located at all three verti-cal locations, figure 4(a) indicates that th
41、e rate of change of spanload coefficient with root-chord ratio is small above root-chord-ratiovalues of about 0.5. Also apparent is the increase in the magnitude ofthe induced load with an increase in horizontal-tail span. The effectof horizontal-tail position is directly associated with the reverse
42、ddirection of the induced load on the vertical tail for portions of thevertical tail above and below the horizontal tail. The effects ofhorizontal-tail span and position are, of course, similar to those shownin reference 4.The span loads on the horizontal tails due to horizontal-taildihedral angle a
43、re presented in figure 4(b). The effect of root-chordratio was about as expected; that is, the span load coefficients showan increase for an increase in root-chord ratio. Calculations were notmade on the isolated horizontal tails for the additional load due todihedral angle; however, span loads are
44、presented in reference 4 forisolated horizontal tails with dihedral, ranging in aspect ratio fromi to 9, having unswept quarter-chord lines, and a taper ratio of 0.50.Steady roll.- Calculated span load distributions on the verticaland horizontal surfaces for tail assemblies in steady roll about an a
45、xiscoincident with the vertical-tail root chord are presented in figure 5.The results indicate that root-chord ratio er_h as well as horizontal-Cr.vtail span and vertical location of the horizontal tall have a largeinfluence on the vertical-tail span load. (See fig. 5(a).) An examina-tion of the ver
46、tical-tail span load coefficients indicates that, in gen-eral, increasing root-chord ratio or horizontal-tail span produces anincrease in the span load for those portions of the vertical tail belowthe horizontal tail and a decrease in the span load for those portionsProvided by IHSNot for ResaleNo r
47、eproduction or networking permitted without license from IHS-,-,-abow“ the horizontal tail as compared to the 3pan load of the verticalt_il alone. In summary, root-chord ratio and horizontal-tail span affectonly the magnitude of the sp_% load coefficie its, whereas horizontal-tail position determine
48、s the overall shape of the load distribution onthe vertical tail.Of particular interest in figure 5(a) is the negligible effect ofroot-chord ratio for configurations having the shortest span horizontaltail in the low position. For these configurations, the increase invertical-tail load duc to end-pl
49、ate effect was almost cancelled by thatlo:_d induced on the vertical tail by the horizontal-tail rolling load.For configurations having the larger span horizontal tails in the lowposition, a reversal in the direction of load occurred over a considerableportion of the vertical-tail span when the root-chord ratio was greaterthan abo
