hJhtki'lD?- EB No. L5F27 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WAllTIMIi! REPORT ORIGINALLY ISSUED September 19ij-5 as Eestrlcted Bulletin L5F27 M APPROXIMAIE EETERMIKATIOII OF THE POWER EEQUIRED TO MOVE COHTROL SURFACES AS BELATED TO CONTROL-BOOSTER HESIGN By Harold I. Johnson Langley Memorial Aeronautical Laboratory Langley Field, Va. '^tfeip^ NACA WASHINGTON NACA WARTIME REPORTS are reprints of papers originally 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. 102 DOCUMENTS DE^Ar^rVH-N^ Digitized by tine Internet Arclnive in 2011 witln funding from University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation http://www.archive.org/details/approximatedeterOOIang ^1 l^ll-^i <^ l^ACA RB No. L5P27 Ikl^l^ ^ NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS RESTRICTED BULLETIN AN APPROXIIv^ATE DETSRI.'INATION OF THE PO'JVER REOUIRSD TO MO\rE CONTROL SURFACES AS RELATED TO CONTROL-BOOSTER DESIGN By Harold I. Johnson SUMMARY As a part of a general investiget ion of control boosters ; preliminary calculations were made to indicate the sizes of control boosters necessary to move the con- trols of airplanes of various sizes. The analysis v;as based on the assiomption that the controls v/ere moved with a rapidity and amiDlitude equal to that measured with a fighter airplane in simulated combat, A corollary purpose consisted in determining the effect on reducing booster-power unit size of incorporating an energy accumulator in the booster system. The analysis indicates that up to I5 tlm.es as large a power unit v\fould be required for supplying sudden bursts of power if no accumulated energy were available as com^pared to a power unit capable of supplying the average power used in continuous maneuvering in combi- nation v/ith a relatively small energy accumulator. Results of the calculations show that to operate all the controls of a small fighter-type airplane, a power source of 0.057 horsepower in combination with an accumulator capable of storing 51*^ foot-pounds of energy would be s Lif f iciently large if friction and booster cycle losses ai'e nelgected. In this case, the accumulator would be required to supply bursts of power in amounts up to 0.14.62 horsepov/er for extremely short periods of operation. The power requirements and booster sizes increase rapidly with airplane size. Under the assumptions of the analysis, a power source of 2.05 horsepower in coFi-bination with an accumuls-tor capable of storing 3350 foot-pounds of energy would be required to operate all the controls of a bomber weighing about 70,700 pounds. In this case, the peak- power demand required from, bhe accum.ulator would approxi- mate 20 horsepower. Som.e of the problems Involved in predicting the booster requirements are discussed in relation to the assumptions that Y/ere miade in the NACA RB No. LJPP? prelimlnery evaluation . It is concluded that extensive flight tests are required to deterrdne the effects cf speed, size, and airplane functional type on the booster re qulreiTients . INTRODUCTION A general investigation of control boosters is being conducted at the Langley Laboratory' of the NACA in an effort to provide some of the InforF.ation needed for their design. The investigation is divided into the following four phr-ses: (1) Study of flight tests and hinge -moment data to deter-'fiine the speed with which the controls are usually moved and the po'vver required of a booster system to move them with the desired rapidity, (2) Analysis of booster systems in use or in the design stage. (3) Wind-tunnel and ground tests of the more promising booster systems. (k) Flight tests of airplanes equipped with booster controls . This paper is a contribution to the first ohase of the general investigation. SYMBOLS A3 increment of energy required to drive controls Hp hinge moment on control surface at beginning cf "" increment &l-ccntrol motion during which con- trol is moved at constant rate Hg hinge moment on coritrol surface at end of increm.ental-control motion during which control is moved at constant rate A5 IncremxSnt of control-surface deflection in control motion during v/hich control is m.oved at con- stant rate I NACA R3 Kc. LSF27 5 ^TRr control deflection froiv, trin'. at beginning of " incremental-control movement ^TRf control doflection from trim at end of increment&l- -' control movement 5,',-T average control deflection from trim for increment al-control movement 5p silsron deflection from trim -rno —2 P 5 energy factor, de Trees'^ — 2 p 5-, aileron enere;Y factor, degrees'^ _p , p 5~/t jiower factor, degrees^ per second t t; time, seconas \ d5 T ^dCh> \d5 tctsl rate of change of hinge -moment coefficient T with control-surface deflection, per degree (includes effect of rate of change of hinge- moment coefficient with change in angle of attack) rate of change of hinge-moment coefficient v/ith change in control-surface angle, per degree rate of change of hinge -m.oment coefficient with change in angle of attacK, per degree S control-surface area back of hinge center line, square feet c root-miean-square chord of control surface back of hinge center line, feet q^ impact pressure, pounds per square foot d5« dCh d5 dGvi da dat rate of change of elevator angle v/ith change in angle of attack at the horizontal tail ig., incremental change in total aileron angle (sum of ■" upgoing and dov/ngoing aileron movem.ents) k NACA RB No. L5F27 liJETHOD 0? ANALYSIS AND GENERAL- RESULTS Three essential elements are used in a normal control- booster system: (1) the power unit, which supplies energy to the booster system; (2) the accumulator, which stores up a certain quantity of energy that is instantly avail- able on dem.and; and. (J) the booster unit, which takes energy either from the power unit or accum.ulator and drives the control surface. The function of tlie accumulator is to take care of short-period demands for great amounts of power. The piirpose of the accumulator is to reduce materially the necessary size of the T30V\rer-lnpat unit. The present problem consists in finding the relation between the sizes of the power unit end accumulator that will always satisfy the energy demands involved In moving the controls of an airplane having any given physical dimensions. The results obtained should be applicable to any tyoe of control-booster system, whether hydrauli- cally, electrically, mechanically, or air driven. An analysis was made by selecting an actual vari- ation of airplane control jriotion with time and assuming that this variation is applicable to the general case for T^urposes of computing control energy and power require- inents , Prom a considerable quantity of records available for a highly maneuver able fighter airplane in slm.ulated combat, approximately 25 seconds of typically violent maneuvering 'were selected. Figure 1 is a reproduction of the selected time history of airplane and control motion. If it is assumed that hinge -irioment variations with control deflection are linear and aerodynamic damping of the controls is neglected, a plot may be constructed from the data in figure 1 of the tim.e variation of som^e quantity that is proportional to the energj'" used in deflecting the controls. Under the preceding assumptions, the energy required to deflect the control surface through a given angle mej be determ.ined as the average of che hinge moments acting on the surface rt the beginning and end of the motion m.ultiplied by th3 change in control- surface angle; that is, Hr + He AE = -^— :; A5 NAG A RB No. L5F27 Since the hinge morrient is proportion?! to the control- surface angle, the energy will be proportional to the average of the control-surface angles at the beginning and end of the motion multiplied by the change in control- surface angle, or AE cc A5 = 5rnr) A5 2 ^"av Figure 2 gives the results obtained by summing up the incremental-energy quantities required to drive the aileron control in the maneuver of figure 1. The energy has been expressed in terms of an energy factor 5 , which represents the summation of average control deflec- tion from, trim times incremental control deflection over which the rate of control miotlon was approximately c ons t ant : 5^ = \ 6„„ A5 y -i-t^av The tim.e history v/as broken into incremients during which the rate of control m.otion v»fas approximiately constant in order to determine the variation of the control power input v;lth time. The variation during the misneuver of control poTv'er input with time affects the balance between power unit and accum.ulator sizes. Inasmuch as energy to move the controls is required only when the control is moved away from trim., the numerous flat spots in the curve represent conditions 'where the controls were either fixed or were returning toward trim.. The energy factor plotted in figure 2 m.ay be converted into energy in units of foot- pounds by use of the relation Work = 52 -^ Scq^ (1) Values of K to be used in equation (1) are thj total hinge-moment-coefficient variation for the control surface, which includes the variation of hinge-moment coefficient with angle of attack. Thus, the response characteristics of any particular airplane to which the selected vsriatlon of control h-iotlcn is applied are accounted for in the equation. NACA RB No. L5F27 Figiire 2 and similar plots for the other two controls were used directly to establish general relations between the power input required and the accirriulator capacity necessary to supply every energy demand of the controls. Under the assumption that energy is supplied to the accumulator at a given rate whenever its energy content falls below its rated capacity, a simple trial and error graphical solution was employed to determine the desired relation. This solution consisted in finding, for various assumed energy capacities, the line with the smallest slope (smallest power-input rating) that would provide an energy-available curve which would just meet the energy-required curve at the most critical time. One such trial and. error solution for an accuiaulator capacity factor of 200 degrees^ is shov/n in figure 2. Note that the slope S^/t so determined is a direct measure of 9. minimAim oower-lnput factor which, in combi- nation with the asEur/'ed energy capacity, will satisfy the energy demands of the control throughout the entire 25-second m.aneuver. Just as in the case of energy, the power factor may be converted into 'power in foot-pounds per second by use of equation (1) vi^ith the power factor 'S'^/t in place of the energy factor S^. 5?- K Power = — -yj^ Scqc (2) Results shewing the balance between power input and accumulator capacity required for performing 25-second periods of violent maneuver'ing at widely spaced intervals are given in figure 5 ^o^ ^'H three controls. Attention is directed to the horizontal line labelled "Indefinite maneuvers" in this figure. This line defines the average rate at which, by far, most c-f the energy required to move the controls v/as used and is therefore reoresentative of the minimum power input required for indefinite maneu- vering, A determination of this value for the aileron control is given by the slope of the dashed line in fig- ure 2. Figure 5 shows the isolated maximum power values plotted for accumulator capacities of zero. These points were determined from figure 2 and other simdlar plots by m.easuring the greatest rate of energy output required to drive the controls at any time during the selected m.aneuver . The data of figure 5 indicate that up to IJ times as large a pov^er unit would have to be provided if no accumulator were used as com.pared to the minimum power- NACA RB Ko. L5F27 7 unit rating required fcr indefinite riisneuvering in conbination with e. relatively snail accui-nulator. In tnis connection, it is believed that a cor.bination con- sisting of an extremely giiieII povver unit and a very large accumulator 'would not be considered since this combination wo\ild be satisfactory only for limited-duration maneuvers occurring at v/idely separated times. Probably the best all-around combination v/ould be one j.n which the pov/er unit is the smallest required for indefinite maneuvering together with an accumulntcr of moderate size. APPLICATION TO SPECIFIC AIRPLANES AND DISCUSSION In order to gain some id&s of the sizes of power units and accuiaulators necessary to supply 100 percent of the energy required to move the controls of airplanes of various sizes with a rapidity equal to that attained with the fighter airplane used in the selected maneuver, the data of figure 3 snd equation (1) have been applied with appropriate dimensions to four airplanes covering the range of size of present interest. These calculations were made fcr the m.inim'jm-size booster combinations required for continuous maneuvering. Several assuziTotions apply to the results, which are shovni in table I, as f ollovi^s : (1) All control surfaces are assumed to have no aerodyna:r;^.ic balance. This f.ssu'-'iotion leads to approxi- ■ oCh ' 6Ch mate values of -t-t" of -0.010 per degree and of -r— - of -COOJ per degree for surfaces of usual diiriensions, (.2) All airplanes are assiLmed to have a degree of d5^ stick-fixed lone-itudinal stability such that — - - 1.0. dat This assumption leads to a value of K for the elevator of 0.007 ^'^^ degree. (5) All maneuvex's are aoccmolished v/ith zero sideslip angle. This assumption results in a value of K for the rudder of 0,010 per degr-ee. (Lj.) The effect of change in angle of attack over the ailerons on aileron hinge moments during rolling is neg- lected. This ass'om.ption results in a value of K for the ailerons of 0.010 oer degree. 8 NACA R3 Ko. L5P27 (5) The indicated airspeed is constant, at I75 miles pel"" hour. This condition was very nearly the case in the selected rrianeuver of the fighter air;:) lane. (6) All transfers of energ^i^ in the control-booster sys beru are sccomplished at 100-percent efficiency for purposes of this analysis. Some of the foregoing assumptions are related directly to certain basic control-booster considerations, some of which are discussed in the following paragraphs. In practice some aerodynainic balance would "orobably be used on control surfaces as a means of reducing the size and weight of the booster. In these cases, the booster requirements would be ex;o3cted to vary inversely with the degree of aerodynamic balance employed (as expressed by the factor' K in equation (1)); however, the power required to overcome control-system inertia in order to obtain the desired quickness of response will probably deterrrdne the mariimari size of booster that can be used when the con'"i-cls are closely balanced aero- djmamically, ilo account was ttken of control-system inertia in the illustrative calculations, the results of which are given in table I. Although the illustrative calculations for booster size were made for only one speed, the booster power required is ■'.indoubtedly dependent on the speed of flight. Consider, for instance, the control-power requirements for a fighter airplane in a particiilarly violent type of evasive maneuver. Assume that a pilot rolls an air- plane from 90*^ bank in one direction to 90° bank in the other direction by use of full aileron control and s^af- ficlent rudder deflection to maintain zero sideslip at all times; assume also that the elevator control is used to produce the Dilots' limit load factor '.vhen the air- plane is banked 90*^ -'nd Ig normal acceleration at the instant the airplane passes through laterally level flight, Finally, assiime che maneuver is repeated continuously ■ ("Without pause when the plane reaches 90*^ bank in either direction). Under these conditions, the power necessary to move the ailerons should vary approximately 93 the cube of the indicated airspeed, that ntscessar^jf to move the rudder as the first power of the Indicated airspeed, and that necessary to move the e].evator as the Inverse of the indicated airspeed (at constant altitude). This analysis neglects, of course, the pcsaible adverse effects KACA x^B iJo. L5P27 9 of coForss&ibility on the control forces of airplanes flo'.vn in the critioel-speed re^;ion. Although the use of a booster might considerably alleviate control problems at extreme speeds, no atter.pt to analyze qusntitstively the requirements of a booster system in this regard seeins possible until more complete data on the aerodynamic effects are available. The effect of ^.Irolane size, as related to the rate of response to concrol deflection, must also be con- sidered in any accurate G.nr.l73is of booster requirements. For puj?poses of the illustrative calculations, all the airplanes were ass^iraed to be subjected to the same vari- ation in control motion with time. The ohortco2;dng of this assunrption can be shown by s simple analysis. For exam.ple, supjose a very large airplane, such as air- plane D of table I, were to perform the evasion maneuver suggested above. If the rolling effectiveness of the ailerons were the sam.e (in terms of wing-tip helix angle produced by full aileron deflection) as for the fighter indicated in table I (airplane A), ""^he frequency of control motions for the large airplane v/ould be reduced to about one-tenth the frequency of the control mictions for che fighter because the length of tim.e to roll to 90^ would var;/ approximately as the ratio of the wing spans. The relative control power required vjculd be reduced the s a:ne amount due to the slower response of the larger airplane. Obviously, then, it is not logical to assume that control- pover requirements for airplanes of all sizes and types caxi be determined from any specific variation of con::rol m.otion v/lth time, or for that m.atber, from any specific type of spatial m.aneuver: for, v/hereas fighter airplanes encounter m.ost violent m.aneuvsrlng conditions in com.ba.t, very large airplanes may encounter most violent mianeuvering conditions while flying through gusty air. The preceding considerations serve to outline som.e of the major factors affecting boosber requirements that could not be handled at the present time due to scarcity of appropriate flight data. It appears that extensive flight tests of vaj?ious types of airplanes must be carried out if an accurate predGterm.lnatlon of the control-booster requirements of any projected design is to be made. Such tescs would best be conducted m'ich structurally sound airplanes equipped with overly large control boosters in order that the desired degree of maneuverability could always be aciii^ved. 10 ^ KACA R3 No. T.^FS? From the roregoing discussion the results obtained frcm the Illustrative calculstions for booster sizes (see table I) apr&rently cannot be regarded as accurate quantitative results. For the larger airplanes, particu- larly airplanes C and D, the estimates are liable to be in considerable error. CONCLUDING RE!"' ARKS An analysis of booster requirements presented hss served to provide rough estimates of the sizes of boosters necessar.y for the continuous rapid m^xieuvering of air'- planes of various sizes. Because a specific vai'-iation of control motion with time, taken from data obteinsd with a fighter air'olene in m.ock combat, was applied to airplanes of different sizes and functional types, the results obtained Fre to be regarded as only rough indi- cations of the power i^equirements . A further limitation of the calculations is that the variation in required control-booster power with speed of flight could not be taken into account although a theoretical analysis indi- cates speed of flignt is one of the primary determinants of the required control-booster size. For a miore accurate deteriuinsticn of control-bocstor requirements it appears that extensive flight tests m.ust be made for airplanes of different sizes snd functional types in order to determine the inaneuvering conditions that Bve most critical with reg;ard to the power required to operate controls. Langley Kernxorial Aeronautical Laboratory National Advisory Comir.ittee for Aeronautics Langley Field, Va. 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P © ^ B O .rt t, r-( 3 *J O .r-t 1 O 03 OJ 3 4J o rH a crt^ < « ©w, o u tX) rH CD o o CO rvj 1 to© t.-P t.— © .H .H .r. O. » Q J* 3 J3 O 3 • oO SI. he t. rH O • o rH CC CD • • o ON • E O -H rH o t. o — Z bO» o CO t— o o MS CO o o t- o 8 o bO O — -H t. n «-, OJ o o J- ^ *H rH < a < m o O M e< £ < o z CO o »-H cc |S cc z O Cd M M H Eh < Eh Z l-H E £ O o Fig. 1 NACA RB No. L5F27 7 -^ <; « ^ \ I s-^ \^ -A L a/ A^ '^. V y 1 Trim V / \ \r Vi /O 0) -/O' -^o 1 ^ rn r\ vV 1, rrim j i "^ \, I J \ 1 u u [ — Ch 3 z I o I A r\. ^ \ / \ -—\ u \ \ / V J -^ \ / v "v \ ^ ^ J •v"v / 1 ilo y Si <3 /6(3 Figure i. NATIONAL ADVISORY COMMITTEE FO* AEtOMtUTICS / y ,r w V \ ^ / r- 1 V, V \, / / / V -^ J I i \ \ 2 / b Z I "t T//ve,6ec TUte history of typical airplane and control motion of highly maneuverable fighter airplane In simulated combat. NACA RB No. L5F27 Fig. 2 Record of energu available ■Por example of mmirnum satisfactory booster system ^ jQQQ (Accumulator capacitij -^00 deg V \f=>o\/^er-unit rating = lt>Qdea''/s&o) \^ i. Q -c o c •ti ^ »- Cn cs S. ViO V K VnN -9j /4O0 \ZOQ iOOL Energij required to mo\/e ailerbns BOO 600 ^KX) 10 15 Time , sec Figure 2.- Time record of the growth In energy factor required to move aileron control during maneuver shown In figure 1, aseuralng linear variation of aileron hinge moment with deflection from trim. Fig. 3a NACA RB No. L5F27 ZOO Accumulator capacitij factor^ deg^ (a) Total aileron control, - mo 280 NATIONAL ADVISORY CONMITTEE FOI A£»0»l*UTICS 3Z0 Flgiire 3.- Relation between accumulator capacity factor and power-input factor required to move controls during violent maneuvers as determined from records of a fighter airplane in simulated combat. NACA RB No. L5F27 Fig. 3b -400 350 300 Q) Z50 CTi Q) ■D c ZOO o -f- o eg Q. /so C 1 s. (b i .^ »< !00 50 Accumulator capacity facfor, deg^ (b) Rudder control. ^S'O 300 NATIONAL ADVISORY COMMITTEE FM AERONAUTICS Figure 3,- Continued. Fig. 3c NACA RB No. L5F27 do izo leo ^0 Accumulator capacity ■Pacfory deg^ (c) Elevator control. ^40 ZQO 3Z0 NATIONAL ADVISORY COMMITTEE FM AEROtlAUTICS Figure 3.- Concluded, UNIVERSITY OF FLORIDA 3 1262 07749 260 \ \ UNIVERSITY OF FLORIDA DOCUMENTS DEPARTMENT 1 20 MARSTON SCIENCE UBRARY RO. BOX 11 7011 GAINESVILLE, PL 32611-7011 USA