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Report CopyRight/DMCA Form For : Airplane Aerodynamics Charles O Neill
CHAPTER 12,Theory and Design of Control,12 1 Control Surface Terminology Symbols. In general a control surface may be considered as a movable or. hinged flap which forms a portion usually the aft portion of a fixed. aerodynamic surface wing horizontal tail vertical tail and which is. employed to vary the lift coefficient of that surface Several sketches. are shown in Fig 12 1 to supplement the following list of definitions with. physical pictures,angle of attack of fixed surface deg. b surface span ft,c chord of any surface fixed or movable ft. effective flap chord root mean square value ft a,Ch hinge moment coefficient. as or C h rate of change of flap hinge moment coefficient with change. in fixed surface angle of attack flap deflection held constant. ach or C ho rate of change of flap hinge moment coefficient with change. as in angle of surface deflection angle of attack of fixed. surface constant, AC A part of Ch due to angle of attack equal numerically to. Theory and Design of Control Surfaces 389, ACh 6 part of C4 due to angle of deflection equal numerically to. angle of deflection of any movable surface with respect to. surface to which it is attached,Airplane reference. axis Geometric chord of fixed surface,Relative wind. Fixed surface Tab,Hinge axis Tab hinge,Movable surface or flap. Fm 12 1 Control surface geometry, rate of change of fixed surface lift coefficient with variation. in angle of attack flap deflection constant or slope of. curve of surface CL versus cc, rate of change of fixed surface lift coefficient with variation. ds in flap deflection angle of attack constant or flap effective. ness parameter,H flap hinge moment lb ft,k control system mechanical advantage ft. S surface area ft 2,T alternative flap effectiveness parameter. 390 Airplane Aerodynamics, Subscripts used with the foregoing symbols are edge. a aileron f any flap remai,b leading edge balance r rudder that. e elevator t tab tail airfoil, 12 2 General Considerations Types of Controls or ye. A control may be considered as a device or means by which the air. plane is caused to roll pitch or yaw to the flight attitude desired by the. pilot human or mechanical In practice the pilot moves the control. and the airplane responding to the effect of the control movement. reflects the will of the pilot A control must be adequate that is it. must be effective in causing the airplane to perform all required flight. maneuvers in a safe fashion and the forces involved in moving the controls. should be logical in direction and within the physical capabilities of the. In general a control functions by causing a change in the pressure. distribution on the surface of which it is a part which results in a change. in the lift coefficient of the surface This change in lift coefficient causes. a change in the moment balance of the airplane and results in angular. movement about one or more of the airplane s axes The longitudinal. control which controls the airplane s attitude in pitch is called the. elevator The lateral control which controls the airplane s attitude in. roll is called an aileron The directional control which controls the. airplane in yaw is called the rudder, In this chapter we shall consider only the basic characteristics of the. several types of surfaces namely, a Control effectiveness which is the effectiveness of control deflection. in changing the lift or force characteristics of the surface of which it is a. b Control hinge moments which govern the forces required to move. the controls, c Type of control surface balances used to vary hinge moments Fm. d Special types of controls, In considering the ability of the controls to maneuver an airplane and aft of. the control forces required it is necessary to consider the stability charac flap. teristics of the airplane together with the control surface characteristics just e. This tie in will be made in the following chapters on longitudinal and open. lateral stability airfoil,12 3 Control Effectiveness the se. The concept of control surface or flap effectiveness can be illustrated deflect. by a practical approach In Chapter 5 the effect of a flap at the trailing It. Theory and Design of Control Surfaces 391, edge of an airfoil in increasing the section lift coefficient while the airfoil. remained at the same angle of attack was demonstrated It was shown. that the general effect of a flap was to change the camber of the basic. We shall take as the starting point a section often used for horizontal. or vertical tail surfaces the NACA 0009 with a plain flap whose chord. c 1 0 1 5c,15 10 5 0 5 10,Angle of attack a deg, Flo 12 2 NACA 0009 airfoil with 0 15c plain flap and 0 005c gap National. Advisory Committee for Aeronautics, aft of the hinge line is 0 15 of the airfoil chord or cf c 0 15 By plain. flap we mean no effective area of the flap is forward of the hinge line. just enough radius is allowed to permit rotation of the flap A nominal. open gap of 0 005c is left to allow free movement of the surface This. airfoil flap combination with pertinent dimensions expressed in terms of. the chord c is shown in Fig 12 2 A series of curves consisting of. the section lift coefficient c t versus angle of attack a for varying flap. deflections Of aro also given in Fig 12 2, It can be seen that the slope of the family of curves of CL versus a. 392 Airplane Aerodynamics, is merely the slope of the normal CL versus a curve for the particular c c of. airfoil Deflection of the flap does not sensibly change this slope but the oth. merely changes the angle of attack for zero lift and the angle of attack for and cdc. any numerical value of C L az We conclude that for a given surface the linearit. lift slope dCL da is not affected by flap deflection but depends upon the flap deft. effective aspect ratio of the entire surface as discussed in Chapter 5 or differ. Going back to Fig 12 2 and selecting any constant angle of attack a convent. we find that a change in 6 produces a change in CL A flap deflection The sig. 1 0 GyQ bO,rAPPI CI IC 5,t5 0 2 40 All,0 I I t 1 I. 0 10 15 20 25 30,Flap deflection 6f deg Flo 1,0009 airfoi. Fin 12 3 Change in lift coefficient with constant angle of attack versus flap de LIcla for. deflection for several values of flap airfoil chord ratios NACA t1009 airfoil with plain. unsealed flap and 0 005c gap, that produces a positive change in C L of a surface is given a positive sign of a mo. In the case of a horizontal surface down flap would be positive If we. take a 0 we find that changing 6 from 0 to 10 gives a change In so. in lift coefficient AC of 0 23 Increasing 6 to 20 gives a total presenti. AC of 0 45 It is to be noted that for the linear portions of the. curves of CL versus a the values of AC E for given values of Of remain. constant for any value of a We can therefore cross plot and derive. curves of AC L versus 6 This is done in Fig 12 3 The lower curve. marked cf c 0 15 is for the airfoil flap combination used as the example. in the foregoing discussion If the same type of data as given in Fig Fig l. 12 2 is prepared for the same airfoil but using flap chord ratios of can be ea. Theory and Design of Control Surfaces 393, cf c of 0 20 0 30 and 0 40 we can cross plot AC L versus 6 and obtain. the other three curves given in Fig 12 3 marked cdc 0 20 cdc 0 30. and cdc 0 40 Inspection shows that these curves retain approximate. linearity for values of 6 up to about 15 We then express the effect of. flap deflection for this linear range as the slope of the AC L versus 6 curve. or differentially as dCL d6f It is noted that owing to the choice of sign. convention a Of produces a LC L and a 6 produces a AC L. The sign of dC Lid6 is therefore always positive The derivative dCL do. 47 t asPec,0 Extrapolated values,0 02 04 0 6 08 1 0. Flap airfoil chord ratio cdc, FIG 12 4 Flap effectiveness parameter versus flap airfoil chord ratio for NACA. 0009 airfoil with plain unsealed flap and 0 005c gap For cifc 1 dC L dc5f is equal to. dC L Ida for the aspect ratio of the surface under consideration. is called the flap or control effectiveness parameter and expresses the ability. of a movable flap to change the lift coefficient of the surface of which it. In some of the literature a term T is used as an alternative method of. presenting flap effectiveness giving, Fig 12 3 gives data for four values of cf c This family of curves. can be extended to other values of cdc from test data of flaps on airfoils. 394 Airplane Aerodynamics, Assuming reasonable linearity up to 6 15 we can then plot the that n. flap effectiveness parameter dCL c 6 as a function of the cdc ratio This numbe. is done in Fig 12 4 The solid portion of the curve covers the range of Th. c1 c from 0 15 to 0 30 The dotted portions are extrapolated values It purpos. may be seen that when cdc 1 0 we have the case of the all movable engine. control surface and the control or flap effectiveness parameter dCL d6. is equal to the value of the surface lift slope dCL doc NACA data Ref 1 12 4. indicate that flap effectiveness as presented in the foregoing discussion If. is practically independent of surface planform It is also indicated that pressur. the section data of dCL d8 may be used with reasonable accuracy for. finite span surfaces Only the shape of the basic lift curve dCLIda must. be corrected for aspect ratio An example is given as follows. ILLUSTRATIVE EXAMPLE The horizontal tail on an airplane employs Relati. an NACA 0009 airfoil and has a full span elevator whose chord is 27. of the total chord Find,a The elevator effectiveness parameter dCL d6. SOLUTION This value may be found directly from Fig 12 4 which. for cjc 0 27 gives, b The tail lift coefficient when at 3 and 6 6 for infinite. SOLUTION Relati,C 4t CLof 0 68 d,When a t 3 and 6 0 Fig 12 2 gives. C Ls 0 27 6 0 0405 0 027 duce tte, Several factors may tend to alter the value of dCL c 6 Sealing the 1. gap between the flap and fixed surface tends to raise the value because. this prevents leakage flow between upper and lower surfaces Extending the flat. the portion forward of the hinge line for aerodynamic balance tends to its hin. increase the control effectiveness provided the balance portion is exposed applied. to the wind stream The use of tabs as discussed in a later section can Thi. either increase or decrease the control effectiveness A leading tab one design. that moves in the same direction as the flap increases the effectiveness has be. and a lagging tab one that moves in opposite direction from the flap added. decreases the flap effectiveness It can be seen that a tab is a flap on a pressur. flap and its effect is either additive to or subtractive from the flap to airfoil. which it is attached about, The best source of data on control surface effectiveness is test data been c. Theory and Design of Control Surfaces 395, that may be found in the various NACA reports on the subject A. number of these reports aro listed in the bibliography for this chapter. The data for the NACA 0009 airfoil with a plain flap are given for the. purpose of illustrating the principles involved and not for use as exact. engineering design data,12 4 Hinge Moments, If we examine an airfoil with a hinged flap it is evident that the. pressure distribution on the flap can cause a moment to be set up about. Flo 12 5 Pressure distributions abolit a typical symmetrical airfoil which pro. duce aerodynamic hinge moments a a 0 6 f 0 basic pressure distribution. b a 15 6 f 0 change in pressure distribution duo to change in a c a 0. 6f 15 change in pressure distribution due to change in 6 f. the flap hinge Such a moment will either cause the flap to rotate about. its hinge or will require an equal and opposite restraining moment to be. applied to the flap in order to hold it at a given deflection. This moment is called the hinge moment of the flap Fig 12 5 is. designed to illustrate this point A symmetrical airfoil at a OW L 0. has been chosen as a starting point A plain flap of any chord has been. added In part a of the figure it can be seen that a symmetrical. pressure distribution exists over both upper and lower surfaces of the. airfoil including the flap Consequently there is no resultant moment. about the hinge axis In part b the angle of attack of the airfoil has. been changed to 15 and the flap deflection has been held at 0 It. 396 Airplane Aerodynamics, can be seen from the resultant pressure distribution particularly aft of essen. the hinge axis that positive pressures exist on the lower surface and from. negative pressures exist on the upper surface The resultant is a force to a. upward aft of the hinge axis that tends to rotate the flap up This hinge cury. moment that results from change in angle of attack of the basic airfoil is. termed the hinge moment due to angle of attack In part c the angle of. attack is again 0 as in part a but the flap has been deflected down to wher. 15 It can be seen that a rather distinct change has taken place in. the pressure distribution particularly the formation of a positive pres. sure area on the lower surface of the flap It can be seen again that. the resultant force on the flap is up and aft of the hinge axis producing S. a moment tending to rotate the flap up This hinge moment that results abov. from flap deflection is termed the hinge moment due to deflection of 6. Hinge moments are designated by the symbol H f and have the units cury. of pounds feet Mathematically the hinge moment is expressed in an of e. equation analogous to the wing pitching moment equation as follows coeffi. H qbfaf2 Ch 12 2, where Ch is the nondimensional hinge moment coefficient The group of. terms bA 2 can be broken down into, where Of is equivalent to the flap area S r If the hinge moment of. a given surface is known the hinge moment coefficient can be determined. Ch gbtcf and s, Experimentally hinge moments are measured on a surface for varying. angle of attack and for varying flap deflections Hinge moment coeffi. cients are determined from Eq 12 3 and the data are plotted as curves. of Cif versus cc one curve being drawn for each value of flap deflection 6f when. A series of these curves are given in Fig 12 2 for the NACA 0009 airfoil of Ec. with a 0 15c plain flap as discussed in Sec 12 3 Using these data it is E. possible to enter the curves directly with giVen values of a and 6 and read varia. the value of the flap hinge moment coefficient Chf This value may then tion. be applied directly with known values of dynamic pressure q and flap have. size b and e to Eq 12 2 and the hinge moment may be computed math. This direct procedure using test curves to select points does not genei. lend itself readily to analytical procedures such as will be presented in T. the following chapters on stability and control Therefore an additional tench. method of treating hinge moment data will be presented Examination giver. of the hinge moment coefficient curves in Fig 12 2 indicates two facts creas. First the curves of Ch versus a for flap deflections of up to 30 are men t. Theory and Design of Control Surfaces 397, essentially straight lines over a range of angles of attack of about 12. from a for zero lift The part of the total hinge moment coefficient due. to angle of attack can then be expressed as the slope of the C h versus a. curves multiplied by the angle of attack that is,AC h a jif 12 4. where z1Ch the part of C due to angle of attack,the slope of the C12 versus a curves. Second at any given angle of attack in the linear range discussed. above it may be noticed that the curves of Ch versus a for various values. of 0 up to 30 have a uniform spacing Cross plotting these data as. curves of Ch versus 0 for constant values of a will again give a family. of essentially straight lines The part of the total hinge moment. coefficient due to flap deflection may be expressed as the slope of Ch. versus ol curves multiplied by the flap deflection or. AChf o 5 6 ft 12 5,where WO the part of Ch due to flap deflection. the slope of the C I versus 3 curves,The total hinge moment coefficient is. Ch 17 AC hf ct 1Chf 6 12 6,and substituting from Eqs 12 4 and 12 5 we get. Ch a hi 12 7, In some cases Ch is not zero when a and 0 are zero as in the case. where a trim tab is deflected and a term Cho is then added to the left side. of Eq 12 7 to account for this, Equation 12 7 may be used for any type of surface that has linear. variation of hinge moment coefficient with angle of attack or flap deflec. tion It will be demonstrated later that some surface configurations may. have nonlinear characteristics These are not only difficult to handle. mathematically but also produce undesirable flying characteristics In. general surfaces with linear characteristics should be selected. The sign convention for hinge moments is logical A moment that. tends to rotate the flap so as to increase 0 in a positive sense downward is. given a nositive sicrn And a mrimart,398 Airplane Aerodynamics. increment in a causes a negative increment in C hi the sign of dCh Da is. positive The converse would make the sign of thhf Da negative charac. Referring to Fig 12 5 b it is seen that the hinge moment that results system. from a positive change in angle of attack is negative and tends to rotate is equa. the flap so as to reduce the angle that it makes with the relative wind thus k is th e. representing a negative achpoc The parameter aChpa is often referred k is de. to as the floating tendency The plain flap of Fig 12 5 has then a. negative floating tendency In a similar manner if a positive increment. in O causes a positive increment in Chl or a negative increment in O. causes a negative increment in Chi the sign of DC i1D6f is positive The. converse makes the sign of DC D6 negative Referring again to the. plain flap of Fig 12 5 it is seen that DChlaof is negative Inspection of. 14t F pull,Relative Sununu,Fla 12 6 Elevator control system. the hinge moment coefficient curves of Fig 12 2 shows again that the. plain flap possesses a negative DC hpot and a negative DChr O6f. The consequences of control surface hinge moments are important. The surfaces are connected to the airplane controls In general every. time the attitude of the airplane changes or the deflection of a surface is. changed to maneuver the airplane the pilot must exert a force on the. control Fig 12 6 shows a schematic elevator control system connected. in the conventional manner so that rearward movement of the stick. causes an upward or negative O f, Assuming a plain flap with a DCh a6f and using Eq 12 7 we get or. Therefore if Ch is positive when it is used in Eq 12 2 H is also. positive that is tends to move the elevator to a more positive value of. S Conversely if the elevator is moved down 6 is positive and. applying it as before in Eq 12 7 we get,be hs Ch pull ro. As before if Ch is negative when it is used in Eq 12 2 we find that tries n. Theory and Design of Control Surfaces 399, the hinge moment H is also negative If we establish the mechanical. characteristics of the linkage system which connects to the control. system it can be shown that the force required on the control stick F. is equal to some constant k times the hinge moment H This constant. k is the mechanical advantage of the system For the case in Fig 12 6. k is derived below where,A the elevator hinge axis. B the control stick pivot axis,d length of the elevator horn ft. 1 length of control stick below pivot axis ft,2 length of control stick between center of. hand grip and pivot axis ft,k mechanical advantage of control system. Summing moments about A we get,Summing moments about B we get. Fe 1 2 F1 11, Equating the two expressions for the common force F1 and solving. for F8 we obtain,or alternatively,F kqb e 2Ch 12 8A. The details of the derivation presented above are for the simple push. pull rod type of elevator control system shown in Fig 12 6 Employ. ment of cables and pulleys intermediate bell cranks worm gears eccen. trics and the like will change the details of calculating k which in the. 400 Airplane Aerodynamics, final analysis is a relatively simple mechanics problem Once the details. of any control system have been selected and the value of k has been. determined Eq 12 8 applies in the computation of the control forces. from the known hinge moment H The control force is given the sign. of the hinge moment For the elevator system shown a pull force to. the rear is positive Care must be taken in all control force computations. to establish correct sign notations and to see that they are preserved throughout. all computations, The principles of hinge moments discussed so far apply not only to. the determination of control surface characteristics but also to the. solution of such problems as the loads involved in the lowering of landing. flaps extension of dive brakes and the like Airfoil data for airfoils with. various kinds of flaps generally include hinge moment data. Examination of the basic hinge moment Eq 12 2 shows several. interesting facts The equation is repeated below, Eq 12 7 which is repeated below gives Chf in terms of the basic. hinge moment parameters,Substituting for Cht in Eq 12 2 we get. Hf qb ler2, The effect of air speed is given by the term q It shows that if all. other factors are held constant the hinge moment hence the control. force varies directly as the square of the equivalent air speed or directly. as the density p times the true air speed squared V T 2 If the speed is. doubled the control force will be four times as great The effect of size. is given by the product b fet2 If all other factors are held constant the. hinge moment varies as the cube of the scale Doubling the size of an. airplane will increase the control forces eightfold The hinge moment. parameters enter the picture linearly The combination of large size and. high indicated speeds can produce enormous control forces that con. ceivably may be beyond the capabilities of a pilot to handle unless the. hinge moment coefficients are reduced to low values For a given fixed. area of control surface it can be seen that if the chord is kept small the. forces will be lowered These effects should be kept in mind in the. discussion to follow It will be shown later in the chapters on stability. and control that this basic hinge moment equation can be tied to the. Theory and Design of Control Surfaces 401, stability characteristics of the airplane giving a rather complete picture. of the control forces involved in flying an airplane. The hinge moment parameters of a plain flap on an NACA 0009. airfoil may be conveniently summarized by the type of curves given in. Fig 12 7 The values of Dc hlacc and aChIN are plotted as functions of. the ratio of flap chord to the airfoil chord Use of these parameters for. the plain flap in the hinge moment equation to determine control forces. will show that for low equivalent air speeds and very small airplanes that. is small surfaces a plain flap is satisfactory As indicated air speeds. Flap chord ratio c,0 0 2 0 4 06 0 8 1 0, Fm 12 7 Hinge moment parameter ac dace or ack w versus flap chord ratio c1 c. increase and as the size of the airplane increases the forces resulting. from plain flaps are too great for apilot to handle An illustrative example. is given below, ILLUSTRATIVE EX AMPLE Two geometrically similar airplanes use. a tail incorporating an NACA 0009 airfoil with plain flap elevators. having cdc 0 30 When airplane 1 is at V 150 knots and airplane. 2 is at V 1 300 knots both have a stabilizer angle of attack of 1. and an elevator deflection of 3 For both airplanes the elevator. control system mechanical advantage is k 0 35 Airplane 1 has an. elevator span of 8 0 ft and an elevator chord of 1 0 ft Airplane 2 has. an elevator span of 16 0 ft and an elevator chord of 2 0 ft Find the. elevator control force for each airplane, SOLUTION Airplane 1 From the curves of Fig 12 7 when.
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VI // Euskaltegiak UROLA KOSTAKO HITZA Osteguna, 2017ko irailaren 14a Ikasturte hasieran norbere buruari jarri ohi zaion helburuetako bat izaten da titu -
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