wfvcftu-'\si y CB No. IAH14 NATIONAL ADVISORy COMMITTEE FOR AERONAUTICS WARTIME REPORT ORIGINALLY ISSUED August 191^'! as Confidential Biaietln Ll^Hll* AHALYSIS OF VERTICAL-TAIL LOADS IK ROLLING PULL-OUT MANEUVERS By Robert R. Gilruth Langley Memorial Aeronautical Laboratory Langley Field, Va. UNIVERSIl'Y OF FLORIDA DOCUMENTS DEPARTMENT 1 20 MARSTON SCIENCE UBRARY P.O. BOX 117011 GAINESVILLE. PL 32611-7011 USA MAC A \ '; WASHINGTON NACA Wartime reports are reprints of papers originaUy issued to provide rapid distribution of ' advance research results to an authorized group requiring them for the war effort. They were pre- viously held under a security status but are now unclassified. Some of these reports were not tech- nically edited. All have been reproduced without change in order to expedite general distribution. L - 181 /;l*/ oIT 9o& ^^^^ NACA CB No. LL^Ell+ MTIOIJAL ADVISORY COIJMITTES FOR AERONAUTICS C OKF IDEF T I AL BTOLET IN ANALYSIS OF VT^RTICAL-TAIL LOADS IN ROLLING PIJLL-OTJT MANEUVERS B;' Robert R. Gilruth 3TBIMARY An analys'-S is presented of the vertical-ts.ll loads to be expected as a result of abrtipt aileron action in accelerated flight, as In rolls from turns or pull-outs, for exarriple . The formulas derived shoiv that the vertical-tail loads obtained in rolling pull-out maneuvers are directly proportional to the lead factor, wing loading, and aileron effectiveness and are inversely proportional to directional stability. Sample calc-alations for an assumed fighter airplane are presented and discussed. It appears that critical tall loads may occur in rolling pull-out maneuvers, particularly on airplanes with good ailerons and low directional stability. INTRODUCTION In fighter and dive-bomber elrnlanes, abrupt aileron action is frequently used in accelerated flight, as in rolls from turns or pull-outs, for exam.ple . ^ Because of the large yavi'lng moments produced by ailerons In accelerated flight and because of the increase In aileron pov/er achieved since the 'war, the vertical-tail loads obtainable in rolling pull-r^ut maneuvers have been examined analytically and the factors on which the loads depend have been determined. SYJ..IBOLS N yawing moment, foot-pounds Cj-^ yawing-moment coefficient 2 CONPIDaNTlAL NAG A CB Wo. ll^Elk C-^ fting lift coefficient p rolling v3locit,7, radians per second b wing .span, feet V true airspeed, feet per second pt)/2V helix angle generated by wing tip, radian p sideslip angle, degrees dCj/dp airplane directional stability per degree q d-7na'riio rre.osrre, poands per square foot S vertlcal-t--ii.l area, square feet dC^T/dp slope of tail norr.ial-force-cocf ficient curve per degree n load factor, g S wing area, square feet W ar'rplane gross weight, pounds l^ tail length, foet Lv load on vertical tail, pounds DEVELOPMEFT OF PCRI'.IULAS FOR DETEHI'-IININa VERTICAL-TAIL LOADS IN ROLLINCr PULL-OITTS For ellintical soan loading, the yawing monont due to aileron deflection' and rolling velocity r.ay be expressed with sufficient accuracy in terns of the wing lift coefficient and the helix angle in the roll as ^2il (1) ^^ 8 2V The sidesllTD sngle p developed in the roll with rudder fixed is obtained, to a first approximation, by dividing the yawing-moment coefficient of equation (1) by th:-- directional-stability coefficient of the airplane; thus , CONFIDENTIAL NAG A CB Fo. ihmk CONFIDEFTIAL QG^/dp ^L pb ]. 8 27 cCn/cip (2) T'^iS vertical-tail loads resulting frcrn sideslip angles are the jrroduct of the side slip angle, the vertical-tail area, the dynamic pressure, and the slope of the tail noriral-f orce-cO'^fficient curve; that is." cC' Lv = PS^^ -~f (5) Since qCr^ is equivalent to the product of wing loading and the load factor, equation (3) -Tiay be rev.'ritton as ^ 8 3 2V ^ dp dC^/dp ^"^ From equation (1^) the vertical-tail lead in a roll may be seen to increase in direct proportion to the load factor, "che wing loading, and the aileroii effectiveness. The loads are also proportional to the vertical-tail 'area and normal-force -coefficient slope c:;n.d are inversely proportional to directional stability. Increasing the tail size and aspect ratio should, in general, reduce the loads becauae the directional sbability increases faster than tne product of area and normal-forco- coefficient slope; that is, an increase in tail effec- tiveness should reduce the loads by restricting the sideslip angles and thereby reducing the unstable moments contributed by the fusela.ge and propeller. The loads represented by equation (Lj.) vj-ould be chiefly loads on the fin due to angle of attack of the vertical tail. If the rudder were sufficiently light per degree of "deflectio;a and rolls could be nerfectly coordinated, the tail load v/ould be ^ _ N A- O _ n W job Gb ,j.. " 8 C 27 It '■'' CONPTDENTIAL 1^ CONFTD^^KTIAL ITACA CE No. I^Hllj. This lor.d wov.ld be pri'Tiarily a rudder load and, in £sneral, would be considerably smaller than that of eqvi.ation (1^.) although the value of pb/2V might be sorriev/hiat increased by the rolling moment due to ycwlng. It should be noted in addition, hcwevor, that with a light rudder the riTdder could be applied after substantial sideslip had developed so that rudder loads would be added to the loads of equa- tion ()|). CALCULATION OF TAIL L0AD5J ?GR A TYPICAL PIG^TFR AIRFLAFE In order tc ill-'.-jstrate the order of magnitude of loads to be expected in rcllinr pull-out maneuvers, sample calculations are presented for a typical case. The assuiiicd dir.ensions and characteristics of the air- pldne are as follov/e; S, . square feet 2j0 W/S, pounds T)er square foot ..„...,. > b , fee t 3 Sv, square feet , . . , 2o dG|^/dp, per degree 0. 0.'x^ dCri/di? f per degree . -0. OCO^ l^, feet , 17 The variation v/ith Indicated airsptied of pb/2V obta'n- able with a 5*^-po"'.ind stick fo:"ce for the assu-'.ied airplane is shown in fi,t;ure 1(a). The calcvilated angles cf side- slip p produced as a result of rolling with a 50-pcund stick force combined witli ncrinal accelerations cf 5j and 6g are shov/n as a function of indicated airspeed in figure 1(b). The calculated loads on the vertical tail that result from the sideslip developed are sho^i^n in figiiT'e 1(c). The load on. the tail vvith bg normal acceleration and a pO-pound stick force, "...ut with rudder used to maintain zero sideslip, is also shovm in figure 1(c). DISC US 3 IGF As may be seen from figure 1 or from formulas (1) tc (5) from which figure 1 was constructed, large COIIPIDSFriAL NACA CB No. Ll^Hllj. Cr^NPIDEKTlAL 5 verticel-tail loads rsia^^ lie prodr.ced by the aileron control. Although the loads are nr'jch lower '^/hcn the rudder is usod to riaDntain zero sideslipj rudder forces are, in general, far too h,eavy to rerinit use of the rudder except at relatively Iojj speeds. Also to he corsidered is the case in which the rudder is aoplied after sideslip has deve- loped so that the rudder action would tend to increase rather than to decrease the loads. In the exanple shown in figr.re 1, the directional stability was assu'-ned to be constaxit over the range of sideslip angle. In most actual cases, however, the yawing-morrient-Goefriclent slope is small through a moderate range of sideslip angle and generally becomes great at larger angles. A STiall slope through neutral will cause the ria-xiinvrri tail loads to be produced at speeds higher than those shovvn In figure 1. In an, actual case calculations v/ould have to be nade frcri the yawing-moinent curve obtained frora v;ind-tunnel tests luade on a model on which a propeller having the proper side- force factor was installed. Present luethods of calculating the sideslip angles and therefore the loads resulting fror:i aileron action are open to question. The approxiTiate method presented herein is believed to give scnev.'hat smaller sideslip angles than those actually obtained in flight and the sample loads presented are therefore probably too small, CONCLUDING REMARKS Tbe analysis presented iniicates tbat i.arge and perhaps critical loads on the vertical tail will cccui' in rolling pull-outs. These loads are dir^^ctly pi'o- ncrtional to the load factor, wing loading, and aileron effectiveness and are inversely proportional to the directional stability of the airplane, More exact methods of calculating these loads are being developed. Langley Memorial Aeronautical Laboratory National Advisory Com::iittee for Aeronautics Langle;/ Fie 1:1, Va. C0i;JPID3I?JTIA.L NACA CB No. L4H14 Fig. 1 .12 a « a > dS ■H ^ o oj CM OP t. a (D .04 1 1 n; tional COMMi TEE FOf wyisoRi AERONAJTICS ^ \, \ ^ 1 (a) Assumed values of pb/2V obtainable with 50-pound stick force. ^ to OS « ■d o, ■H « f-i ax o