The investigation of a variable camber blade lift control for helicopter rotor systems

CHAPTER 1 INTRODUCTION AND BACKGROUND Over the years, the design of helicopters has undergone cycles of refinement taking advantage of developments in advanced technology Increased demand in payload, hover performance and (reference ,?1).

speed have forced the researcher to examine over and over the limits of rotor design and operation. One of the elements establishing these limits is the sectional performance of the airfoil employed.

Because of the progress in theoretical airfoil analysis, it has become possible to estimate two-dimensional characteristics which, until recently, could be quantified only experimentally. The new methods have permitted the definition of advanced airfoils which, compared to airfoils in use today, display improved drag divergence and maximum lift charac- teristics while retaining low pitching moment levels and acceptable pro- file drag.

The key sectional characteristics of the airfoils employed on a rotor can be separated into three flow regions: l Supercritical flow at low lift, typical of the advancing blade tip in forward flight.

l Lift levels of CL = 0.6 at Mach number near M = 0.6, representative of hover requirements.

l High lift at Mach number in the range of 0.3 < M ( 0.5 over the retreating blade. Most helicopters airfoil design objectives fall

illustrated in Figure 1.1 (see

within one of these three regions, Reference 2).

1.f REGION III FORWARD FLIGHT RETREATING BLADE STALL REGION II HOVER REGION I FdiWARD FLIGHT / 0 1 0.82 1.0 9.2 0.4 0.6 MACH NUMBER, M COMP.3ZSSIBILITY I -0.4 EFFECTS ON ADVANCING BLADE (SZJXCE: REFEIXNCE 2) Figure 1.1. LIFT COEFFICIENT AND KACH NUMBER COMBINATIONS (ROTOR ENVIRONMENT) It is difficult to quantify the local flow along a rotor blade so that airfoil design objectives can be set. This difficulty arises from any or all of the following effects: l Tip relief l Blade elastic characteristics l Unsteady aerodynamics l Tip sweep l Tip planform variation l Reynolds number Consequently, the design of a rotor with fixed geometry inevitably involves compromises in the choice of the blade airfoil section. A rotor utilizing variable geometry has the potential of eliminating or alleviating some of these compromises.

This project then explores an innovative idea of improvement of heli- This concept uses variable camber for blade lift control to copters.

reduce control loads and improve performance, while keeping the rotor control system as simple as possible. The variable camber rotor has the advantage of providing more mean-line curvature where high lift is re- quired and reduced curvature at low lift and transonic conditions as required near the advancing blade tip, thus changing the design restric- tions of fixed-contour rotor blades.

The advanced rotor development carried out during the late 1960's and early 1970's showed that helicopter rotors in high speed flight can become limited by advancing blade loads as well as retreating blade stall.

New guidelines were then set to control the margin between the,drag rise and the growth in pitching moments at high subsonic Mach numbers. Figure 1.2 shows the regions in the rotor disc where phenomena take place which limit the rotor operation because of the rapid growth in drag (power re- quired), the growth in sectional pitching moments (advancing blade loads or "Mach tuck"), and possibly local loss of lift, also associated with power and load penalties.

IplrTElWEDIATE $ = 180' SECTIONS OPTIMIZED FOR RETREATING BLADESTALL JI = 270' CM'RESSIBILITY REVERSE FIAW REGION ' %Do

db I'

O ?44cHTUCK JI = o" ' DRAG Figure 1.2.

ROTOR ENVIRONYENT - FORWARDFLIGHT After a preliminary investigation, the variable camber concept was selected, because it would yield airfoils which exceed the present bound- ary. In addition, an investigation of variable camber by use of the Boeing Vertol VR-7 airfoil modified with a 50 percent chord trailing-edge flap deflected 0 to 20 degrees illustrates the potential benefits of improved airfoil designs in terms of a potential improvement over the undeflected (Figure 3, Vertol VR-7 airfoil or the best current advanced airfoils.

Ref. 3 ) illustrates the present state of helicopter airfoil optimization based on advanced/retreating blade characteristics.

CHAPTER 2 DESCRIPTION OF THE VARIABLE CAMBER ROTOR SYSTEM 2.1 General - The variable camber rotor model is a four-bladed fully articulated system, with the same physical characteristics as an H-34 Variable camber is provided in the form helicopter blade (see ref. 4).

of deflectable trailing edge flaps on the blade. The rotor blades flap about a hinge that is offset from the shaft axis.

2.2 Blades - The airfoil section are VR-7 from root cutout to 0.9R and VR-8 from 0.9R to tip. An internally sealed flap in the inboard trailing edge area has an envelope of 0.5~ and 0.9R. The overall changes imply that the trailing portion of the blade will be deflected about a hinge from some neutral position.

The sketches in figures 2.1 and 2.2 shows the variable camber rotor with the flap neutral and with the flap deflected 20 degrees respec- tively, and also delineates other features of the concept that are vital The primary features and their to achieving the design objectives.

functions are as follows: l The primary load carrying structure is the forward section of the blade and is not connected to the control system.

l The aft section or flap is attached to the forward section by a pin joint arrangement. It is also connected to the rotor contro.1 system for the control of rotor thrust level and vec- toring. This section is configured by aerodynamic and mechanical BLADE FORWARD FLAP TO CONTROL ROTOR LIFT T TO FLAP DEFLECTION (STANDARD CONTROL MOTIONS WITH SWASHPLATE MECHANISMS) Figure 2.1. - Variable Camber rotor blade with flap neutral.

BLADE FOR\\‘ARD SECTION ROTOR LIFT (hr = 20”) PILOT INPUT TO FLAP DEFLECTION (STANDARD CONTROL MOTIONS WITH S\VASHPLATE hlECHANlSMS) Figure 2.2 - Variable Camber rotor blade wi tB a 0.5~ Trailing edge flap deflected 20 .

techniques to achieve low flap hinge moments.

l The forward section has structural properties that are stiffer than the aft section in all directions.

l The rotor considered has conventional flap and lag hinges.

l The rotor hub is a conventional articulated hub.

o Control by cyclic pitch change will be accomplished by a linkage from the blade flaps to a "swash plate", which is a rotating plane that defines the pitch of the blades.

2.3 Articulated Rotor System - The blades are attached to the hub by hinges, free to flap up and down and swing back and forth. The main characteristics of this system are: 1) Blade root moments are small; 2) The articulated hinges can be offset from the center of rotation to pro- duce high control moments, thus permitting large allowable travel of c.g.; 3) Lead-lag dampers are usually required (see ref. 5 ).

2.4 Design Criteria - The geometry of the hypothetical conventional rotor is given in table 2.1.

Table 2.1. Rotor Blade Geometry GEOMETRICAL DEFINITION DIMENSION - -- ---.

~1 ~- Rotor radius, R 28 FT I Blade chord, c 1.367 FT Cutout radius 4.48 FT I Rotor Solidity, bc/rR 0.0622 Blade moment of inertia about flapping hinge 1264 FT-IB-SEC2 Flapping hinge offset 1.0 FT Number of blades Blade taper ratio 1.0" I Normal tip speed 700 FPS a

CHAPTER 3 AERODYNAMIC SECTION ANALYSIS This chapter detail the process by which one particular flapped rotor configuration was chosen and evaluated as to its potential for pro- viding a relatively high final maximum lift coefficient (in the 1.67-1.9 range) with a small flap deflection (no more than 15-20 degrees); small deflections are desirable, since they minimize the drag increment in- volved. Although not presently a key design criterion, some consider- ation was given to the increase in pitching moment due to flap deflection.

The lift and drag characteristics of the chosen section were obtain- ed by inserting the airfoil's geometrical coordinates into an airfoil analysis computer program.

As is implied above, this analysis covers only a single configura- tion which was chosen with only very rough optimization criteria. The two-dimensional airfoil analysis methods used herein permitted the pre- diction of the effects of flap configurations on airfoil characteristics.

Though large amounts of empirical data are available on lift characteris- tics of many specific flap arrangements, and some reasonably reliable, somewhat generalized semi-empirical methods are available for analyzing limited classes of flap types and deflections (see Refs. 6 and 7), more reliable methods are avaiable in (Refs. 8 and 9) of a sufficient flex- ible and general nature to permit a broad and comprehensive optimization with regard to the two-dimensional characteristics of flapped airfoils.

3.1 Section Selection - The Vertol VR-7 airfoil was selected because it afforded a higher CL max and low speed capability than another section commonly used in rotors, the NACA 0012 (see Ref. 3, figure 3).

The maximum lift coefficient for the unflapped VR-7 airfoil (for the viscous/potential flow interaction, Reynolds number of 1.592 x 106) is 1.22. This figure had to be increased by 0.68 to put in it the desired maximum lift coefficient range. Simultaneously, parasite drag increments had to be minimized; there was no Clear Ceiling ValUe for ACdo, but it was clear that the increments caused by such typical configurations as 25% chord plain flaps deflected 30-60 degrees would be unacceptably large (ACd approximately .08-.20, representing easily an order of magni- tude drag increase) (see Ref. 6, Fig. 6.1.7-22). It appeared that only by using large-chord flaps with small deflections would one escape large drag penalties.

Based on preliminary investigation through literature search etc., a configuration was adopted which included a plain flap with .50 chord ratio. The 0.50 chord ratio was selected because it appeared to repre- sent a reasonable compromise between flap effectiveness and the tendency to increase drag (that is dCl/da and dCd/da) (see Refs. 10, 11 and Appen- dix G, Ref. 7). Also, within the analysis performed here, it is assumed that the flap is of the sealed-gap type and, furthermore, that the blade surface remains continous and unbroken even with the flap deflected (see Figure 3.1), and (also ref. 8).

The two-dimensional lift, drag and pitchinq moment characteristics of the section were found by using the Ames Multielement airfoil analysis (a) FLAP NEUTRAL (b) FLAP DEFLECTED 20” -Radius = .l( 16OC flap Chord line flap (c) COMBINATION OF FIGURES (a) AND (b) Figure 3.1. - Boeing Vertol VR-7 with Flap neutral and with .5OC flap deflected 20 .

computer code (Ref. 12) and (Ref 13), which required as inputs, the airfoil geometrical coordinates (percent of chord deviation vertically from the airfoil chord line as a function of percent of chord length, Mach number, Rqynolds number, free stream velocity and angle-of-attack.

The coordinates of the flapped airfoil were determined by graphical superimposition of the aft-chord of the Boeing Vertol VR-7 airfoil de- flected 2 to 20 deqrees on the undeflected forward half-chord (see Fig. 3.1). The effective point of rotation in this graphical process was taken to be at the 50-percent chord point on the airfoil's lower surface. Some interpolation and smoothing were applied to both the upper and lower surface coordinates to preserve a continous surface.

The overall changes imply that the trailing portion of the blade will be deflected about a hjnge from some neutral position.

Mach number and Reynolds number ranges were established based on the rotor environment in forward flight (see Ref. 3, figures 2 and 3), free stream velocity and assuming the rotor to be a four-bladed, fully artic- ulated rotor system (see Ref. 4), with some gross physical dimensions as an H-34 standard blade (radius of 28.0 ft, constant blade chord of 1.367 ft, tip speed of 700 fps). With these specification and assuming sea-level day ambient conditions, tip Mach number was approximately 0.6, while tip Reynolds number was about 2.4 x 106; these quantities were decreased proportional to radius for stations farther inboard.

Lift coefficient versus angle-of-attack values were generated up to stall for flap deflections from 0 to 20 degrees. Simultaneously, the drag and pitching moment coefficients corresponding to these values were generated herein. Plots of the results are shown in figure 3.2, along with the curve for the unflapped VR-7 section generated by the same computer program.

Based on these results, it was shown that the changes obtained were associated with large increase in maximum lift, substantial shifts in the angle of zero lift (more negative without changing the lift-curve slope) and large pitching moment changes (more negative).

This is due in part to the fact that for a cambered airfoil, the flow comes smoothly onto the nose at some angle which in general is different from zero.

This angle is called ideal angle of attack, ai (see Refs. 14 and 15). At angle different from ai, the strength of the singularity increases with -a i)2, that is, the pressure distribution at the nose may be cor- b related with a - ai. This, of course, is correlated with the stagnation point location; at a - aj the staqnation point is at the nose.

It has been known that for a straight airfoil, the lift coefficient Cl = 0 at a = 0; but for cambered airfoils there is a basic lift, Cl = Clb at a = aj. It is called the basic lift because it is independent of the nose singularity, depend only on the camber. At angles different from ai there is an additional lift, which is equal to 2n(a - ai), and is These concepts are outlined by Allen thus related to the singularity.

in Ref 15, where the expressions are given as follows: cl = clb + i?m(a - ai) (3-l)

P

clb = 2 (3-2)

I

lT ai = _ (3-3) ‘II where x = l/2 (1 - cos e) The angle o is related to the chordwise coordinate x by the last equa- tion, and is illustrated in the sketch below. dyc/dx is the slope of the camberline. If ye(x) is given analytically, it can be transform to ~~(0) and the above expressions integrated for Clb and ai.

-Source: Ref. 16 : r Trailing edge where f, is referred to as the flap chord, and could be expressed as: f = 1/2 (1 + COS eh) Though the lift, drag and pitching moments coefficients values gen- erated herein by the airfoil analysis computer codes are considered reasonable, the magnitude of the increment of the profile drag coeffi- cients was compared by plotting the lift coefficient versus drag coeffi- cient (see Figure 3.4). Figure 3.4 shows that there is only a minimal difference between the profile drag coefficient for the flapped airfoil deflected 2 degrees and the unflapped airfoil. Also by comparing with data from a 65-210 airfoil for a 0.50~ flap deflected 0 to 10 degrees the difference in drag coefficient between given in Ref. 11, there, the unflapped airfoil and the airfoil with the flap deflected 10 degrees is .002. However, in the present analysis, it was assumed that there was no unanticipated roughness and that there was perfect continuity in the airfoil surface near the flap hinge, which would ensure that perfor- mance estimates were conservative, at least with regard to what is pre- sently known about the drag of flapped airfoils.

3.2 Pressure Distribution - The results of the pressure distribution for the VR-7 airfoil with a 50 percent chord trailing edge flap are shown in the form of resultant-pressure increment diagrams (see Fig. 3.2); which represent changes in resultant pressure distribution caused by a change in angle of anyone part or a combination of the component parts of the air- foil with regard to the flap.

AIRFOIL f?NALYSJS

R l.59*10C LEGEND o- b’ -6.00 n- -40 0 - 0’ -4.00 n- .40 A - 0’ -2.00 n- .40 * - 0’ 0.00 n- .40 FLAP NEUTRAL x/c LEGEND o- 0’ n- .40 m o- 0’ -6.00 n- .40 d- A - o- -6.00 H- -40 + - (D 0’ -4.00 n- -40 h’ Figure 3.2. Numerical analysis of the resultant pressure distribution over the VR-7 airfoil at various angles of attack.

Flap neutral and flap deflected 10 degrees.

1.6 The analysis were computed at angles of attack range (-16 to + 12 degrees) at interval of 2 degrees. The flapped configurations were set at angles of 0 to 20 degrees. Values were generated throughout the en- tire angle-of-attack range for each flap deflection. All diagrams of the resultant pressure or resultant pressure increment of the airfoil due to flap were computed and plotted as pressure coefficient (C,) which can be represented by the following equation: = PR = P-P, (3-4) CP -7 where P, is the static pressure at a point on the airfoil; PO is the static pressure in the free air stream; and q, is the dynamic pressure of the free air stream.

The pressure distributions for the various flap deflections showed peaks on the upper and lower surface near the 50 percent chordwise posi- tion where the direction of the surface changes rapidly. This imply that the deflection of the flap causes an increment of pressure over the entire airfoil, this increment reaching peak values at both the nose and at the hinge axis (see Refs. 11 and 16).

3.3 Trailing-edge Flap Characteristics - The downward deflection of the modified VR-7 airfoil with the 50 percent chord trailing edge flap effectively makes the ordinates of the mean camber line more positive in this region. As a consequence, the angle-of-zero lift (aLo) become more negative and the lift at a given geometrical angle is increased.

Thus the term (case-l), expressed in (Ref. 17, chapter 5, equation 34) in equation: 'II dz (Coso-1)do vanishes at the leading edge where 0 = 0: ceo = L I H Odx and its absolute values reaches maximum at the trailing edge where o = II (see Ref. 17).

The lift curve is disolaced to the left as a result of an increase in alo negatively (see Figure 3.3). The gain in lift at the given geo- metric angle of attack is shown as ACJ. By reference to Fig. 3.3, ~~~ is given by the formula (see Ref. 17): Aqo = (AC-~/&T) = [(H - eh) + 2 Sin eh] 6f/H (3-5) where eh is related to the hinge location by the expression xh = f =1/2 Equation (3-5) show that the incremental values of lift (1 + c0sq.J.

coefficient (Cl) about the aerodynamic center and aLo vary linearly with the flap deflection. Thus the portion of the mean camber line in the vicinity of the trailing edge powerfully influences the value of aLo.

Though the stalling angle (%) is reduced b.y the deflection of the reduction is not great enough to remove the qain arising a flap, from the increase in CL and the shift of the curve as a whole (see Figure max 3.3).

This analysis further indicate, that with the flap neutral, the curve is linear to within 1 or 2 degrees of the airfoil stall, whereas with the flap deflected 10 to 20 degrees, the curve is linear for a range of angle of attack, and then assumes a break as the flap stalls. Beyond ia 2.0 -. 4.

I I I 1 1 I I A L -2.0 -16 -12 -8 -4 0 4 8 12 ANGLE0FATTACK.a Mz0.4 RN = 1 .6x106.

Figure 3.3 - Numerical,analysis of the effect of flap deflection on lift curve.

a.

,4.

.O.

n=.40 6- neutral 2O I I 1 I 1 4 0 .005 .Ol .015 .02 .025 .03 SECTION DRAG COEFFICIENT, CD Figure 3.4 - Numerical analysis of th.e drag curves for the VR-7 airfoil section at flap neutral and 2 degrees flap deflection.

RN = 1.6~10~.

the flap stall, the curve become more gradual, indicating that separation is continuing to build up over the airfoil proper as the lift increases until the airfoil stalls.

Also, it is known that for a thin airfoil, stalling occurs at the nose, and is determined principally by the history of the development of the boundary layer from the stagnation point on the lower surface, around the nose, into the adverse gradient downstream of the suction peak, on the upper surface (see Ref. 16).

The important developments occur within the first few percent of the airfoil chord. This suggests the idea that a family of airfoils having the same nose but different after-bodies (camber, thickness distribution, etc.) should exhibit a correlation at stalling, namely, that at stall the conditions at the This implies that the stagna- nose are identical for all the airfoils.

tion point location is at the same location in a:1 cases and that the pressure distribution around the nose is a function only of stagnation The latter point has, infact, been demonstrated by point location.

Rettie (Ref. 18). While in the case of the trailing edge, the stall starts at the trailing edge and depends on the whole boundary layer devel- opment history up to there. Also, the airfoil continues to develop lift after separation has occured; and the progress of development after separation is different for different airfoils (see Ref. 16).

3.4 Flap Deflection Range - The projected flap deflection range were based on the maximum allowable flap deflections for the linear limit of the airfoil characteristics up to stall conditions at several angle-of- attack ranges.

The allowable range of flap deflection (6f) required for this con- figuration is 0 to +20 degrees.

3.5 Trailing-edge Plain Flaps - The term "plain flaps" as used here- in includes any conventional flap type airfoil, regardless of contours, that has not been modified with any form of internal balance, overhang balance or tab balance, etc to reduce the hinge moment (see chapter 4).

Plain trailing edge flaps are formed by hinging the rearmost part of the wing section about a point within the contour (see ref. 19).

Figure 3.1.A shows the general planform of the VR-7 with flap neutral 6f = O"), while Figure 3.1.8 shows the modified VR-7 airfoil with a ( i.e.

50 percent chord trailing edge plain flap deflected 20 degrees.

Thus, the plain trailing edge flap can then be considered as a start- ing point for all forms of controls. The effectiveness of the flap de- rives from the fact that on rotation it changes the camber of the section and so permits of a change of circulation and therefore, of lift at a given incidence.

Then, when applied to rotor analysis, the change in chordwise load- ing produced by a positive setting of the flap in this investigation will have a maximum near the rotor leading edge and a secondary peak at the flap hinge, falling to zero at the flap trailing edge (see Figure 3.2).

CHAPTER 4 HINGE MOMENTPREDICTION TECHNIQUES __--------- This chapter discusses the characteristics of existing flap control devices, analyzes the effects of the existing devices to the variable camber flap configuration, propose new devices that show promise of lower- ing the hinge moment characteristics of those now in use.

Descriptions of the criteria for hinge-moment characteristics along with various types of aerodynamic balances are presented together with assumptions made in the derivations and the limitations of the method as applicable to the present configuration. Also, assessment is made as to the feasibility for getting low hinge-moments of control surfaces.

Due to lack of test data for the present analysis, only quantitative or rough qualitative evaluations of any of the effects were made. The methods presented herein, therefore, are considered to be reasonable; but not sufficiently reliable to enable a designer to arrive at a satisfactory final flap configuration without some development work on a full/large- scale wind-tunnel model or in flight. The me+ .s are useful, however, for making preliminary design or for deciding the manner in which exist- ing flaps should be modified in order to obtain desired changes in charac- teristics.

4.1 Hinge Moment Characteristics - The hinge moment characteristics of flaps have been found to be critically dependent on the flap contour near the trailing edge. In general, any increase in trailing-edge angle whether obtained by changing the basic airfoil section or by modifying the contour of a given airfoil section, may be expected to reduce the degree of unbalance of the plain flap. The greatest balancing effect of a large trailing-edge angles occurs at small angles of attack and at smal'l flap deflections; therefore the hinge-moment curves of flaps having large trailing angles usually are characterized by a high degree of linearity.

The explanation for the balancing effect resulting from the change of a large trailing-edge angle can be made on the basis of an effective change in airfoil camber. As an approximation, the effective contour of an airfoil in a viscous fluid of the contour is obtained by adding the boundary-layer displacement thickness on each airfoil surface to the geo- metrical coordinates of that surface. With positive angle of attack or flap deflection, the boundary-layer displacement thickness increases on the upper surface of the airfoil (where the pressure gradient become more adverse) and the boundary-layer-displacement thickness decreases on the lower surface of the airfoil (where the pressure gradient becomes less adverse). This change in boundary-layer-displacement thickness causes an unswept effective camber change which in turn, cause reductions in the effective flap deflection and therefore, a lower hinge moment.

The changes in effective camber near the trailing edge are much more influential on hinge-moments than on lift, because the small AL at the trailing edge act on a long momentum. The magnitudes of the camber changes seems to depend to a large extent on the magnitude of the trail- ing-edge angle, the greater changes occuring for the larger trailing-edge angles. An open gap at the nose of the flap allows the boundary-layer air to flow from the high-pressure airfoil surface to the low-pressure airfoil surface.

The effective change in camber and consequently the effect of the boundary layer on the hinge-moments, particularly for flaps having larger trailing-edge angles, therefore are greater when the gap is open than when the gap is closed.

4.2 Plain Flap Hinge Moment Coefficient - The expression for calcul- ating the hinge-moment coefficient (Ch) in subsonic two-dimensional com- pressible flow has already been deduced in Appendix A (also see Ref. 20) as : bla2 - a2bP 6f ch = b0 - bl.50 +$: CL - > a1 a1 where the quanties a,, al, a2, bl, b2, and b are defined as follows: a0 = (CL)~' = 6f = 0, al = = 6f = 0, b = b, 2 a7 - apbp= - and - a1 while CL is the lift coefficient, 6f, is the flap deflection, measured positively for a downward movement of the flap and a', is the incidence of the front part of the airfoil measured from the 6f = 0 chord line.

4.3 Beveled Trailing Edge Balance - It was shown in Ref. 21 that when a beveled trailing edge is added to a flap profile, the lift, pitch- ing moment and hinge moment characteristics of the airfoil are markedly changed from those of the unbeveled a flap of airfoil contour.

The slope of the lift curve Cla and the lift effectiveness a6 are decreased.

The aerodynamic centers of the lift due to angle of attack and of the .lift due to flap deflection are both moved forward. The rate of change of hinge-moment coefficient both with angle of attack Cha and the flap deflection Chs are increased positively. At small flap deflections, the bevel tends to have the same effect on hinge-moment as a balancing tab (see section 4.4); but at large deflections its effect is more nearly like that of a trim tab (see section 4.4).

The effect of gap at the flap nose is critical, the parameter Ch6 being much more positive at small deflections with an open gap than with a sealed gap. This effect generally causes the hinge-moment characteristics of a flap with beveled trailing edge to be undesirably nonlinear unless the gap at the flap nose is sealed.

A preliminary correlation of hinge-moment data for sealed flaps with beveled trailing edges is given in reference 22. It was shown that the trailing edge angle is of fundamental importance in determining the hinge-moment slopes of beveled flaps. The result of correlating the hinge-moment characteristics of. 16 different flap arrangements indicated that the effects of a beveled trailing-edge may be expressed by the fol- lowing relations: Acha = .00113 A$ CL a (c,/c)-l*o (4-2) ACh& = .ollA&~~ (c,/c)o*4 (4-3) The parameters ACha and ACha are the if’ICreiIIentS in hinge-moment coeffi- cient slopes caused by changing the trailing-edge angle of a flap by the The slopes CL~ and CL& are those for the rotor (wing) amount A$ degrees.

with an airfoil contour flap. Equations (4-2) and (4-3) were obtained from the equations for the curves of (figure 150, Ref. 21), faired through the experimentally determined points.

The hinge-moment characteristics of a beveled-trailing-edge flap can be predicted, by adding the incremen- tal hinge moment due to bevel (see equation 4-2 and 4-3) to the hinge- moment characteristics of a flap without a bevel.

The results of the calculations for determining the flap chord and the trailing-edge angle required to obtain desired values of Cha and Chs are shown in (figure 4, Ref. 22). From the curve of (figure 4, Ref. 22), it is evident that, if a flap is fitted with a bevel to reduce Ch6 to zero or to a small negative value, Cha will have a large positive value. For beveled flaps the adverse effect is not so great as would be indicated by the value of Cha at 6f = 0", because the effect of the bevel on Chatends to disappear at large values of 6f. As shown in (fig- ure 2, Ref. 22), the effect of the bevel on Chd becomes greater and the effect on Cha becomes smaller as the flap is increased. Reference 22 indicated that, to reduce both Cha and Ch6 to zero, it would be necessary to use flap chords and trailing-edge angles outside the range covered by the available data.

The data in Refs. 23 to 26 indicated that thickening and beveling the control-surface trailing-edge reduce the slope of the airfoil lift- (Cla) and also the lift effectiveness ( as) of the con- curve trol surface. The maximum flap deflection generally can be sufficiently increased to counteract the loss in control associated with the use of bevels.

4.4 Tabs - An analysis was made in Ref.

27 for the hinge-moment altering effectiveness of the tab based on the available two-and three-dimensionals tab data of references 21 and 28, with additional data from references 26 and 29 to 40. The results of the analysis indicated that the effects of tabs on control-surface hinge-moments can be estimated from geometric characteristics of the tab-flap-airfoil combination with a reasonable degree of accuracy.

In general, the tab effect on the control-surface hinge-moments is reduced by increasing the airfoil trailing-edge angle and by any alter- ation of the airfoil surface condition or of the airstream, such as mov- ing the transition forward, roughening the surface, or increasing the turbulence, that tends to increase the boundary-layer thickness near the trailing edge.

No data were presented on the tab lift effectiveness, which deter- mines the loss in control-surface lift effectiveness resulting from balancing-tab action. The control surface lift effect can be evtiluated as indicated by the analysis in Ref. 41. The data used in the correla- tion came from the following ranges of tab variables: tab-flap chord ratio from 0.10 to 0.50, flap-airfoil chord ratio from 0.12 to 0.60 and trail- ing edge angle from 7 to 31 degrees.

Sufficient data were available from which to draw quantitative con- clusions concerning the effects of changing the size of the tab relative to the flap-airfoil combination, the effect of the trailing-edge angle, and the effect of control-surface overhang balance on the tab hinge- moment effectiveness. Insufficient data were available to determine quantitatively the effect of the parameters that varied the tab hinge- moment effectiveness by changing the boundary-layer thickness over the tab. Sufficient data were available, however upon which to base quali- tative conclusions concerning such effects.

Reference 42, also presented an analysis of a tab that is linked in such a manner that the tab deflection is proportional to the flap deflec- tion and this is commonly referred to as a linked tab. Such a tab is a very convenient device in that it can be combined with any of the flap internal balance, overhang balance etc.) and also because balances (e.g.

the balancing or unbalancing effect can be altered rapidly by changing the ratio of tab deflection with flap deflection.

A unique characteristic of a linked tab is that a large change in Chd can be produced without causing any appreciable change in Cha; a small effect on Cha introduced by the linkage usually may be neglected. Almost any desired Val Ues Of Cha and Ch6 can therefore be obtained by combining the linked tab with one of the other balancing devices.

Since a balancing linked tab deflects in a direction opposite to that of the flap to which it is attached (see Figure 4.1), a reduction

occurs in the net lift resulting from flap deflection. An analysis of a

large amount of pressure-distribution data from Ref. 21 indicated that the most efficient trailing-edge balancing tab is one having a chord between 20 and 25 percent of the flap chord, because such a tab produces the least change in lift for a given change in flap hinge moment. On the other hand, a linked tab used to augment the lift of a flap (leading or unbalancing tab) should produce the greatest change in lift for a FLAP HINGE LINE AIRFOIL CONTOUR (SOURCE: REF. 43) iling-edge tab.

of Flap and tra Figure 4.1. - Cross Sect ion given change in flap hinge-moment. A tab of this type is most efficient when the tab chord is equal to about 50 percent of the flap chord (see Ref. 42).

It was shown in Refs. 44 and42, that the effect of linked tabs on the hinge-moment of flaps can be expressed as a function of the deflec- tion ratio aSt/a6f and of four factors that are defined as follows: (4-4) F3=kt c

(9 bf Cf

F4 = (Ct/Cf)o*7 + 0.51 C,/C (4-5) F5 = 1.3 - 0.026$ (4-6) Fs=l- (4-7) o-84g -Pzff I The factor F3 accounts for the effects of the span and the spanwise location of the tab. The factor F4 accounts for the effects of the The factor F5 accounts for the effect tab chord and the flap chord.

of the trailing-edge angle, and the factor F6 accounts for the effect of the tab on the pressure difference across a flap overhang balance (either exposed or internal). The inclusion of the factor F6 in the tab correlation makes unnecessary an adjustment in the increment AChs resulting from a flap overhang balance for the effect of the tab on the pressure across the overhang balance.

The term in the factors F3, F4, and F5 can be evaluated, from charts given in (figure 40, Ref. 42), while the factor F6 can be eval- uated, from the chart in (figure 25, Ref.42).

The correlation of the effect of linked tabs on the flap hinge- moment parameter Ch6 is given in (figure 41, Ref. 42) and is based on data from reference 27. The equation of the correlation curve is Ach& = 0.0222 F3F4F5F6 ast (4-B) -- a6f ( 1 This equation may be used to estimate the incremental changes in Ch6 of a flap resulting from a given linked tab or to determine the configur- ations of tabs that are capable of producing a given change in Ch6 of . a flap.

4.5 Allowable Tab Deflection - Experimental investigations conducted in references 32, 45, 46 and 47 indicated that the tab effectiveness de- creases with an increase in the flap deflection. They also indicated that there was reason to believe that a satisfactory maximum tab deflec- tion exists between the angles of +20 degrees for moderate flap deflec- tions. The results indicated that, for a constant tab chord, it was better to use a large-span tab deflected to a small angle than a short- span tab deflected to a large angle.

4.6 Overhang Balance - Reference 48 presented an analysis of data The analysis was for control surfaces having plain-overhang balance.

limited to the effects of overhang, nose shapes, gap and Mach number.

Some empirical relations were derived that can be used for the predic- tion of the characteristics of balanced control surfaces from geometric constants (see also Ref. 44). Reference 48 considered the empirical relations only applicable to the preliminary design of control surface balances and to modifications of balances already in use.

The aerodynamic balancing effect of an overhang balance is consi- dered to be a maximum when the contour of the balance conforms to the contour of the airfoil for the entire length of the overhang. Rounding or tapering the nose causes a reduction in the effect of the balance.

The effects of variations in the nose shape were found to depend on the overhang length. Ref. 47, therefore, introduced a product of two factors as a measure of the net balancing effect of plain-overhang balances. The two factors are F1,which is related to the length of the overhang, and F2, which is related to the sectional shape of the balance nose. Thus, Ref.

47 finds as a balance factor (see also Ref. 44): = FlF'2 Kl (4-g) F1= [ gg2 - p&f)’ 1% (4-10) and the expression for F'2 is given in figure 4.2 for three general types and T indicate the root-mean square balance chord, of nose shapes. ?b, cf, control surface chord, and airfoil section thickness at the hinge line re- spectively. bb altd bf indicate the span of the plain overhang balance and the span of the control surface. As may be seen from figure 4.2, the ex- the product of an area-moment ratio and pression for F'2 is, in general, a basic nose-shape factor that specifies the relative location of the point A

1-f-w

REF.42) (SOURCE: (Where Cb and Cbl are the root-mean square balance chord and root-mean square contour balance chord over the span of the control surface re- spectively.)

Figure 4.2.

- Various nose shapes considered in correlation of plain-overhang and corresponding expressions for nose-shape factor of tangency of a circular-arc- nose and the airfoil contour. The basic nose-shape factor F2 is defined (see also Ref. 42) as: F2 =l- (4.11) q-?J With the con- where Fb is the root-mean-square contour balance chord.

tour balance chord is meant the distance from the hinge line to the lead- ing edge of the plain-overhang balance. It should be noted that for any overhang having a nose formed by circular arcs (nose types 0, A and B of figure 4.2) F'p = F2 (4-12) Graphical solutions of the expressions for the overhang factor F1 (for overhangs having spans equal to the control-surface span) and the basic nose shape factor F2 are presented in figure 4.3. The value of F1 for balances which do not extend over the entire span of the control surface is obtained by multiplying the value of F1 obtained from figure 4.3 by the ratio of balance span to control-surface span. The use of figure 4.3 should allow a rapid determination of F1 and F2, provided the geometric constants cb, cb , x and cf are known.

An analysis in Reference 22 of data on control surfaces with beveled trailing edges indicated that the effect of plan form of the wing could be accounted for reasonably well by assuming that both the lift-curve slope and the increment of hinge-moment slopes due to aerodynamic balance are affected by plan form changes in the same manner. The same assumption was made in Ref. 48 for the variation of hinge-moments with control deflection.

-20 LO .8 .7 .6 ft .4 .2 .I ” 0 .I 2 .3 .4 .5 .6 .7 wi Charts for Determining Numerical Values of Figure4.3.

Overhang Factor F1 and of hone-Shape Factor Fp from Geometric Constants of Balanced Flap Ref. 48 uses (figure 2, Ref 48) to determine the effects of over- hang balances on the variation of hinge-moment coefficient with control deflection. Figure 2 (Ref. 48) present curves Of ACh6/Clla or AChB/Cllor plotted against the balance factor Kl. The parameter Clla is the average value of the lift-curve slope over the span of the control surface and will be generally somewhat different for the lift-curve slope of the A method for estimating the value of CTla entire rotor (see Ref. 48).

for flaps of wings -of various plan forms is given in Ref. 22. Figure 2, reference 48 indicated that the variation of the parameter AC&Clla with K1 for finite span flaps was the same as the variation of AChS/Clla with K1 for two-dimensional flaps. The following equations were given in Ref. 44 for the hinge-moment parameter increments: Acha = 0.017 AR F1 (4-13) AR + 2 (4-14) AChG = 0.10 AR FlF'2 AR + 2 The data used in the correlation of AChs were obtained from two-dimen- sional flap models.

Charts for estimating the required length of balances having several representative nose shapes (see figure 4.2) are presented in (figure 27 Ref. 44). For a given design problem, the value of the product FlF'2 cor- responding to the required value of AChs must first be obtained from the correlation presented in (figure 26, Ref. 44). The value of cbflf required for this value of FlF'2 may be estimated from (figure 27, Ref 44) for,any of the nose shapes considered. The charts given in (figure 27, Ref. 44) were derived for flaps on airfoils having the thickness distribution de- The charts may be used, however, to obtain first fined in reference 49.

for flaps on airfoils having approximations to the required overhangs For such airfoils, more other thickness distributions (see Ref. 44).

accurate values for the required overhangs can be obtained by calculating the value of the product FlF'2 corresponding to the first approximation value of Cb/Cf from the expressions given in Figure 5.2 for F'2 and the charts of Figure 4.3 for F1 and Fp. However, if the calculated value is Ref. 48), a new value of cb/cf must be assumed obtained from (figure 2, and the process repeated until satisfactory agreement is reached between the required and the calculated values of FlF'2.

The lift-effectiveness parameter Au/AS is changed somewhat by an overhang balance and the magnitude of the change is dependent on the gap at the balance nose. A correlation of these effects is given in Reference 21, 44, and 48; and the faired curves of that correlation are reproduced The value of Au/A6 increases as the balance (de- in (fig. 29, ref. 44).

fined by the product FlF2) is increased and the rate of increase is greater for the larger gaps. For the sealed-gap condition, the increase in A~/AS with increased flap balance results from an increase in C16; whereas, for highly balanced flaps, the increase in Aa/ A6 with increased gap size is caused primarily by a decrease in Cla (see refs. 21 and 44). The As/AS values given in (figure 29, ref. 44) are applicable only to small deflections, and because of the reduction with increased balance of critical deflection (6cr), the maximum lift increment of a highly balanced flap usually is considerably less than the maximum lift increment of the corresponding plain flap. The critical flap deflection (6cr) is defined as that deflection at which plain-overhang balance is onger effective in reducing the slope of the hinge-moment curve.

no varies approximately as F'2fi, whereas AChd The fact that 6cr es as F$Fl, indicates that for the same degree of a balance a var larger increment of lift probably can be obtained from a flap having a long overhang and a moderate nose shape type 6 (fig. 4.2) than from a flap having a short overhang and a blunt nose shape similar to type A (see fig.

4.2).

A factor that is probably quite closely related to 6c, is the magni- tude of the peak pressures over the balance nose.

If bChg is assumed to remain the same, a short blunt-nose balance produces higher peak pres- sures than a long balance with a moderate nose shape.

The high peak pressure associated with the very blunt nose shape increases the possi- bility that the control surface may become overbalanced at high Mach numbers and probably increase the rate at which Mach number reduces the value of 6,,. The peak pressures increase the possibility that super- critical local velocities will be reached over the nose of the balance.

With regard to the rotor the long overhangs will permit static balance to be obtained by the addition of a minimum of otherwise nonuseful weight.

Control surfaces with bluntnose overhangs (types A and B), figure 4.2 have already shown some tendency toward increased balance at high deflec- tions (see refs. 50 and 51).

As pointed out earlier in the section, the parameter AChcr iS relatively independent of nose shape for sealed balances and appears to depend prin- cipally on the balance chord. The choice of the best combination of nose shape and overhang for a given AChs may therefore be influenced by the Value of ACha obtained; and the degree of influence may depend on the specific application.

The choice of an open or sealed gap for use with the overhang will be influenced by the fact that the nose shape has more effect on Cha with the gap open than with the gap sealed.

For balances having values of K1 (balance factor) greater than about 0.05, the use of an open gap generally increase the lift-effectiveness parameter of the control sur- face (see refs. 50 and 51). Part of the gain in the lift-effectiveness parameter of the control surface, however, is obtained at the expense of a loss in Cla.

For the variable camber flap arrangements, the selection of over- hang and nose shape may be made principally from a consideration of the value of Ch6 required; but the adjustment of the nose shape or overhang of flaps to obtain a desired value of Cha is not recommended. A nose shape similar to type B (see figure 4.2) seems the most promising of those tested: therefore, for the present analysis, it should only be necessary to determine the overhang for a nose shape of type B (fig. 4.2) required to give a value of Chs already decided upon. The value of Ch6 actually obtained may be adjusted later within a limited range, by making minor modifications to the nose shape, without, changing the length of the The effect of nose shape on the peak pressures, overhang (see ref. 44).

the critical deflection, however, must be given consideration.

The hinge-moment parameters ChB and Cha are of almost equal impor- tance for control surfaces, and the selection of the overhang and nose shape therefore depends on obtaining desirable values for each of these As it has already been pointed out, the nose shape has parameters.

little effect on Cha provided the gap is sealed. The overhang may consequently be selected to obta ired value of Cha; and the nose in the des shape may then be selected to obtain the desired value of Chd, due con- sideration being taken of the effect of nose shape on the peak pressure, on the critical deflection; and on the variation of Ch6 with deflection.

If the desired value of Chd cannot be obtained by selection of only some adjustment of the overhang may be necessary, and the nose shape, compromise values of Chs and Cha will thereby be obtained.

4.7 Sealed Internal Balance - An internal balance is a feasible and an aerodynamically desirable means of controlling the magnitude and the direction of the rate of change of flap hinge moment with angle of attack and with the flap deflection. Because the internal balance is entirely concealed within the airfoil contour, the lift, the drag, and the pitch- ing-moment characteristics of the control surface are in no way affected by the presence of the balancing surface. the internal balance Thus, can then be referred to as a mechanism by which the pressure difference between two points on the airfoil is used to act upon a flat plate or similar devices entirely enclosed with the airfoil profile and thus to work in deflecting the control surface.

Several types of internal balances were discussed in ref. 52. It although not necessarily the most was shown that the most commonly used, aerodynamically desirable type of internal balance is that with a balanc- ing plate rigidly attached to the flap and with the vents located near the hinge axis.

It was shown in ref. 21, that the increments of hinge-moment coef- ficient slope caused by a sealed internal balance vented near the hinge may be expressed by the equation for the faired correlation data (also see ref. 53) as: (4-15) .0237[ [+f 1’ -\sf,' I,,,2 "ha + (4-16) Achtj = o*35gk )' -(%I] [+f)1'4 where Cb is the chord of the balancing surface, cf is the chord of the flap measured at any airfoil section from hinge axis to trailing edge of the airfoil, c is the chord of the airfoil section; and t is the thickness These correlations are believed to be of the control surface at hinge.

most reliable when the following conditions (also see ref. 21) apply: (1) The balance plates are attached rigidly to the noses of the flaps and the vents are as close to the hinge line as prac- ticable.

(2) There is no leakage across the seal.

(3) The cover plates are of airfoil contour.

Small variations in any of these conditions may cause large changes in the effect of an internal balance.

Refs. 44 and 54, also discussed sealed internal balances. They in- dicated that the chordwise pressure distributions of a rotor (wing) with a plain sealed flap are unaffected by the addition of a sealed internal balance.

Sealed internal balances for use with flaps (see ref. 44) usually consist of a plate (attached rigidly to the flap nose) in a chamber that is vented to the airstream in such a manner that a pressure difference across the plate is created principally by flap deflection and to a lesser degree by changes in the angle of attack because this is where it ex- perience the greatest pressure differential in the vicinity of the flap.

A flexible seal connects the nose of the balance plate to the forward wall of the balance chamber.

For a sealed internal balance, the balancing force can normally be obtained from the pressure differences between two chambers in which the The balancing moment can then be derived from air is essentially static.

the geometry of the system provided the pressure difference is known.

For the variable camber rotor flap arrangements, the configuration consist mainly of overhang balance (balancing surface), sealed to the forward structure by a flexible material, capable of sustaining only tensile stresses (see figure 4.4).

“l-l- r- SOURCE: Ktt.33 Figure 4.4 Schematic diagram of a typical internal-balance arrangement for the Variable Camber flap on a rotor.

The moment resulting from the type of balance shown in figure 4.4 can be determined by the following methods: (1) The method of resolution of forces consists of finding the forces exerted by each part of balance system as a result of a pressure difference across these parts.

The moments of these forces about the control-surface hinge are then added to get the total moment of the balance system..

(2) The method of volume displacement consists of finding the rate of change of volume swept by the balance with deflection. The moment of the balance is: (4-17) MB = ($, AP where Ap is the pressure difference across the balance.

An internal balance with seal and vertical-line backplate is shown in figure 4.5. The moments of such balance can be written as the sum of SOURCE: REF.54 f3..ckp& f c Y d I I (Seal lying against the overhang) Figure 4.5 - Internal balance with Seal and vertical-line backplate the moment resulting from the overhang and that resulting from the seal; therefore: MB = A& Cb2 - (t/2)2 + MS (4-18) [ where Cb is the overhang chord; t is the thickness of overhang at hinge axis; and Ms is the seal-moment or incremental hinge-moment resulting from seal of unit span (two-dimensional). The moment exerted by a seal can be expressed in terms of the seal-moment ratio (ms) as: -(t/2j2 + Al’ C$Tis

1 -2-

(4-19) or, the increment of hinge-moment coefficient caused by the balance can be related to the pressure coefficient across the balance or resultant pressure coefficient (PR) and to the geometry of the system by the follow- ing equation for a unit span (two-dimensional) (also see ref. 55) as : 2 (1 + ms ) - T/2 2 (4-20)

(-I 1

cf where ??b is the root-mean square chord of the balance plate and ms is the ratio of the moment contributed by the balance plate,3 is the root- mean square section thickness at the flap hinge line.

To obtain numerical values for ACh, an investigation was made as to the variation of the seal-moment ratio (ms) with two important balance dimensions-the width of the gap to be sealed and the developed width of the seal. Values of ms were determined analytically in ref. 54; and checked experimentally in ref. 55 for several typical balance arrangements.

The characteristics of a flap having almost any arrangements of the balance plate and of the flexible seal can be calculated from the charac- teristics measured for one particular balance configuration provided the pressure difference between the two chambers are known.

For the arrangement represented in this analysis, the balanced sur- face is attached rigidly to the flap in such a manner that its angular or linear travel is directly proportional to the flap deflection; the vents are so located that the balanced-actuating pressure varies with flap deflection and with angle of attack in approximately the same manner as does the hinge-moment of the unbalanced flap. If the pressure coeffi- cient across balance (PR) which was obtained from the pressure distribu- tion of the VR-7 airfoil modified with a 0.50~ trailing edge flap and the balance plate deflection (Bb) are of the same algebraic sign, values should be taken from (figs. 14 to 21, ref. 55), but on the other of ms hand, if PR and 6b are of opposite siqns, values of mS should be taken at IIegatiVe ValLIeS Of 6b (figs. 14 t0 21, ref. 55). Also see figure 5.6 for sign conventions for overhang deflection.

Hinge moments of internally balanced control surface normal1.y become large at large deflections as a .result of a decrease in aPR/as with de- flection. In order to offset somewhat the effect of a decrease in aPR/as with deflection and to give the most nearly linear control-surface hinge moments, ams/a&b should have a positive value. (A positive value of ans/aQ, that increased with deflection would even be more desireable but generally cannot be obtained). The positive value of am,/a6, may be considered favorable inasmuch as linear or nearly linear control-surface SOURCE: REF.54

I

A irfo,‘/ -4 ---- -- <-- 1” 1” (9/ “2, /005/%ve - (9/ “2, /005/%ve~ ,a--- ,a--- -A -- -- -- -- -- -- -- -/-- ---- -- -- --I -1 \ + H/+2 or/s -\.

-I -- -&~~*,~~o&F.

-- --2 Figure 4.6. Sign Conventions for Overhang deflection hinge moments, although not altogether necessary, are generally desireable (see ref. 54).

4.8 Flexible Seals - The flexible seals analyzed in refs.54 and55 were assumed to be nonporous, inextensible, perfectly flexible, and These assumptions imply that the unrestrained part of the weightless.

seal forms an arc of a circle and has a tensile force per unit span, of T = 4pr acting everywhere tanqent to the arc (see fig. 4.5). The moments resulting from these seal arise either from the tensile stress in the seal or from the seal lying along and equalizing the pressure over part of the overhang (see ref. 54).

If the resolution-of-forces method (see section 4.7) is applied to the seal shown in figure 4.5, the lever arm of the tensile force in the seal is zero. The reduction in effective overhang chord caused by such seals is equal to the amount of overhang covered by the seal; this amount can be determined as follows (also see ref. 54).

s= d t (d t x2 tan 6b) tan 90" - &b (4-21) t (d t cb t X2 SeC 6b) where the first term in equation (4-21) represents the width of the seal in a free arc; the second term the width of seal lying along the backplate; In order and the third term, the width of seal lying along the overhang.

to find the amount of overhang covered by the seal, the distance (d) must be known. This quantity can most conveniently be found if d is plotted against the seal width s for various overhang deflections (see ref. 54).

Appropriate values can then be read from the curves.

The seal-moment characteristics over the deflection range for various sizes of fabric seal and sealed nose gap, with and without overhead limit were investigated in ref. 55. The effect of changes in gap width can be seen best by reference to (figure 10, ref. 54 and figure 15, ref. 55) respectively, where it is evident that an increase in gap width for a seal of constant width increases the seal moment at small positive deflec- tion and decreases the seal moment at large positive deflections; the effect is therefore, a change in ams/asb in the negative unfavorable condition. If the most nearly linear control-surface hinge-moment charac- teristics over the entire deflection range are desired, small gaps of the order of g G 0.1 should be used (preferably g = 0.005). In terms of con- trol-surface hinge-moments, increasing the gap width tends to result in high control-surface hinge moments at large control-surface deflections and low or overbalanced moments at small control-surface deflection.

The effect on the seal moment characteristics of varying the seal width, with other variables kept constant, is evident in (figures 14 to 19, ref. 55). The curves indicated that ms which depends on seal width, for a given sealed-gap width decreases at small positive deflections and increases at large positive deflections as the seal width increases. The curves also indicated that, for a given sealed-gap width, as the seal width increases, the maximum value of m, generally increases; and occurs at an overhang deflection that increases the seal width. It appeared, therefore, that an optimum balance configuration would employ a seal width such that the seal would barely touch the chamber ceiling when maximum deflection is' attained (see figs. 5 and 8, ref. 55).

4.9 Off-Center Seal Attachment - A comparison of seal-moment charac- teristics obtained with various types of seal attachments was made in ref. 55. The result showed that the seal-moment characteristics obtained with the off-center attachment were generally unfavorable over the deflec- tion range because a decreasing balancing tendency or an increasing un- balancing tendency is indicated, regardless of the point of attachment.

It was shown that when attached above center, the seal invariably lay against the'backplate and there was an overhead restriction at positive deflections (see figures 7 and 12, ref. 55); while, when attached below the center, the seal had a moment vector that tend to decrease positively, and then increase negatively with overhang deflection (see figs. 6 and 13, ref. 55). The effects account for the unbalancing characteristics of this types of seal attachment.

The effect of attaching the seal off-center to a backplate, when the seal did not contact the balance-chamber ceiling was to shift the seal- moment curve by an angle the sine of which was equal to the off-center displacement (expressed as a fraction of the overhang). The curve of (fig. 25, ref. 55) approximately verify this conclusion.

Since an off-center seal attachment produces an unbalancing effect on the overhang caused by flap deflection or the increase in the angle of attack, this type of seal attachment is believed by the author to be un- desirable and should be avoided.

- An indication of 4.10 Effect of Vent location on PPn and PM the probable effects of changes in the chordwise location of the balance- chamber vents (determined from data in refs. 21 and 53) is given in (fig.

36, ref. 42). It was noticed, that moving the vents forward of the hinge line causes PPa = (ER) to increase and PRY = (apR to decrease.

6a a6)a For the type of internal balance, considered in the correlations, the variation of the resultant pressure across the balance plate with deflec- tion was about two-thirds the variation of the peak resultant pressure at the hinge with deflection. Also it has already been indicated in sec- tion 4.7, that the vents are to be close to the hinge line as practicable; but contour changes caused by aerodynamic forces may be of sufficient magnitude to produce objectionable stick-force characteristics for flaps that otherwise would be satisfactory. The type and extent of covering distortion depends on the external pressure distribution over the surface of the flap, on the pressure inside the flap, on the initial tension of the covering material, on the modulus of elasticity of the covering ma- terial, and on the method of attachment of the covering material. Also different vent locations may cause positive, negative or static internal pressures.

Positive internal pressures causes both surfaces of the flap to (1) bulge. Bulging of the forward part of the flap seems to have little effect on the hinge-moment parameters, but the increase in trailing edge angle causes these parameters to become less The stick forces, therefore, are decreased and may negative.

become overbalanced if the undistorted flap is designed to give stick forces within the required limits. Also large positive internal pressures can result in complete failure of fabric- covered flaps and in the failure of rivets used to attach the metal skin to the flap ribs. Loads of this type can be con- trolled to some extent by careful selection of the vent loca- tions, but the possibility of high skin stresses resulting from inadvertent variation in the vent locations should not be overlooked (see ref. 42).

(2) Negative internal pressures causes both flap surfaces to be drawn in with the result that the trailing edge-angle is de- creased. The parameters Cha and Ch6 therefore become more negative and the stick forces may increase to such an extent that the pilot's ability to control the helicopter may be seriously restricted at high speeds.

(3) For internal pressures near static pressure, the external- pressure differential can cause both surfaces to bow in the same direction.

4.11 Effect of Cover-plate Misalignment on Cha and Chs - The char- ~--_~ acteristics of an internally balanced flaps have been found to be ver.y sensitive to the alignment of the cover plates .just forward of the The effects of misalignment as determined in a few tests, are vents.

ref. 42) and the data are presented in ref. 18.

shown in (figure 37, When small flap deflections and small changes in angle of attack are considered, bending the cover plates slightly out had been shown to decrease the effect of the balance on Cha and increases the effect of While bending the cover plates out had been shown the balance on Ch6.

to decrease the deflection range for which the balance has an effect on the hinge-moment slopes, probably because of earlier separation of the flow.

- Though it is known that the 4.12 Influence of Gap at Flap Nose existence of a gap at the flap nose has an effect on the hinge-moment.

parameters; and though many publications studied the influence of such a gap, no analytical method was found to take the influence of a gap into account. Reason for this is probably the fact that the influence of the gap is dependent upon size and location of the gap as well as on the nose shape of the control surface (blunt, medium or sharp). Reference56 pre- sents the following empirical method to estimate the influence of some of the variables on the lift-curve slope CL,.

was given in Ref.56 by the following The wing lift-curve slope CL, relation: CLa = AR Cla ARE, + 57.3 Cla (4-22) where Ee is the effective edge velocity correction factor (see ref. 57); and the value of Cla for a given section is expressed empirically as follows: (Cla)gap open (Cla) sealed (4-23) cLa = cLa o (‘la) gap sealed (cla) faired where Cla can be read from (fig. 42, ref. 56) which shows the effect of airfoil thickness and trailing-edge angle on section lift-curve slope.

Figure 43 (see ref. 56 ) shows the Plots Of((C1 a) gap open ) /( (Cla) gap sealed] against break location for various gap sizes. The break location indi- The curves in (fig. 43, cates the position of the gap along the chord.

ref. 56) show that ((Cl.) gap open ) /((Cla) gap sealed)decreases as the gap is moved toward the leading edge of the airfoil until it reaches a The gap sizes ranges from 0.001~ to 0.010~ and position of about 0.50~.

the data indicate a decrease in ((Cla) gap open j/((Cl,) gap seal&) as the gap size increase.

II.

Figure 44 (see Reference.56) presents the plots of((Cla) sealed )/ against break location giving the effect of the break ((Cla))faired in the airfoil contour on ((Cla) sealed )/((Cl,) faired ). Comparison of measured values of the lift-curve slope with calculated values using the above method is shown in Ref.56.

Generally, the plain flap gives a greater lift effectiveness with smaller hinge-moments with the flap gap sealed than with it unsealed. The negative slope of Cha and Ch6 decreases with sealing the gap at the nose of the flap.

For flaps having overhang balance and aerodynamic balance, the fol- lowing effects of the gap can be noticed. Unsealing the gap generally causes an increase in lift-effectiveness WS for flaps with blunt and medium nose overhangs and a decrease in a6 for plain flaps and flaps with elliptical nosed overhang. Unsealing the gap at the flap nose makes Cha and Chs less negative. Changing the nose shape from blunt to ellip- tical makes Cha more negative for the sealed gap and less negative for the unsealed gap.

It has already been mentioned in section 4.7, that the presence of a gap i.e. the existence of a leakage, causes large unpredictable effect in case of an internal balance. Also the effect of a gap at the nose of a tab may be very large, although the available data on this effect are too inconsistent to permit any reliable correlation. For some flaps, such a gap has resulted in a reduction of the tab balancing effect by as much as 50 percent. In any design the tab should be sealed or at least made as small as possible (see section 4.4).

From the above discussion, the difficulty in predicting the influ- ence of a gap at the flap nose on the hinge-moment parameters become clear.

4.13 Application of Equations and Design Charts - The procedure to be followed in the preliminary design of flaps for the Variable Camber Rotor depends to a large extent on other aspects of the rotor design. In the present analysis an investigation is made of the chordwise parts of the rotor that must be allocated to the flaps plus balance in order that spec- The flap configuration chosen in this ified stick forces may be obtained.

design consists of a sealed internally balanced flap. Some of the equa- tions and charts, which already have been presented in earlier sections, are used in arriving at the flap arrangements that would be expected to meet certain required conditions.

In order to show how the characteristics of a sealed internally balanced flap can be obtained from those of the sealed unbalanced flap (plain flap) and to indicate the magnitude of some of the effects about which analysis have been drawn, the effect of the balanced configuration on the hinge-moment characteristics for the section shown in fig. 4.4 has been determined. The characteristics of the unbalanced flap section are shown in figure 4.7. From equation (4-20) the incremental hinge-moment coefficient were computed for four balances having vertical-line back- plate. The values of the pressure coefficient across the balance PR for use in equation (4-20) were obtained from the calculated value for the VR-7 airfoil (see chapter 3). The vertical line clearance (LI) (see figure 4.5) required for seal to develop moments for the variable camber 6 PLAIN SEAL FLAP (UNBALANCED) 0 --cb = 0.005 0 -c,, = 0.20 I SEALED INTERNALLY - CL = 0.30 BALANCED FLAP a- 0 -cb=o.40 I 4’ e 72 16 20 24 FMP DEFLECTION. hfs deg - i(inoe-mment characteristics of a flap on the ST-7 airfoil havina fcur balance confiouration with the sa;le vertical-line bzCkDlzt2.- 0 = 0’ flap arrangement was obtained from (fig. 14, ref. 54) as LI = 0.34 for a deflection range of 0 to ?20 degrees, ample space is provided for the The width seal to develop the moments indicated in (fig. 10, ref. 54).

of the seal(s) used in this analysis was obtained from (fig. 14, ref. 54), and was believed to be approximately 0.4 ft. In ref. 54, it was shown that if the most nearly linear control-surface hinge-moment characteristics over the entire deflection range is desired, small gaps of the order of In light of the numerous literature surveyed, it g < 0.1 should be used.

is recommended that the gap size to be considered for this present ana- lysis should be 0.005 ft (0.6 in). Values of mS for computing the exact balancing moment over the deflection range for a seal width(s) of 0.4 and a sealed gap width of 0.005 were interpolated from the data in (figure 10, ref. 54 and figs. 14 and 15, ref. 55) respectively.

The hinge-moment parameters of the balance flap were obtained by considering the plain flap and the effect of the balance separately as follows (see also refs. 44 and 55): (4-24) (Ch)b;;;;ced = (ch)g;;;n + (ACh)balance Table 4-l shows a sample of the computations required for obtaining hinge- moments of the balanced flap from this equation.

4.14 Assessment of Feasibility for Getting Low Hinge-Moment - The estimation of control-surface hinge-moments is one of the most important and one of the most difficult problems confronting the aerodynamicist.

This is due to the fact that these moments create the forces which the pilot must overcome at his cockpit controls and which give him a sense of "feel" of the helicopter/airplane (see ref. 58).

Prediction of the control forces required of the pilot for maneuver- ing the helicopter within its aerodynamic and structural limitations for the variable camber configuration will be based on an estimate of these parameters, and the success of the concept depends largely on how accu- rately this estimate is made.

The many variables encountered in the aerodynamic design of a flapped lifting surface make it difficult to obtain a generalized solution. Thus the theoretical results presented in this analysis may be limited to (1) the range wherein the variation of hinge-moment coefficient with anqle-of- attack and with flap deflection is linear; (2) flaps having internally sealed radius noses; (3) low subsonic speed.

In sections 4.1 to 4.13, several methods of predictinq the hinqe- moment parameters of various types of control surfaces were discussed.

The correlations that have been presented may be used to illustrate the relative effects of the various balancing devices on the hinge moment parameters of Cha and Ch6. The variation in these parameters that miqht be expected to accompany the addition of each of the balances for a 0.50~ plain flap on an H-34 standard four-bladed, fully articulated helicopter rotor are shown in table 4-l. By means of methods which have already been described, the values of Cha and Ch6 of the true-con- tour plain flap were estimated. The incremental bCh6 required for a given reduction in stick force is largest for balances that produce the Table 4-l COMPUTATIONOF HINGE MOMENTCOEFFICIENTS OF BALANCED FLAP FROM THOSE OF UNBALANCEOR PLAIN FLAP: a =O" and Cb = 0.30 Flap Resultant Balance iM;;;;tll/2 &Cd')" ~~i;;:;:~;;;;;ti (Ch)plain / (Ch)balance Deflection Pressure Plate I I [coefficient 1 flap coefficientjDeflection\Ratio 1 x I.9777 (deg6f) pR / ab 1 "' / (2) 1 (i) lc~~~~~c~ i unbayince (7) (8) t (5) x (6) : 0 I 0 15080 I ) 1.4857 -.104 -.0187 1 -.0278 1 -.0218 -. 0496 2 .0431 2 1.4990 1 .0078 1.4677 .0114 -.01194 -. 00054

I I

I 5 .204 1 5 l*4625 I I 1 1*44o2 .0367 I .0529 -.0888 ( -.0359

I

) 10 I l 44g I lo l*38oo I .081 / 1.3577 1 .1099 1 -.1457 1 -.0358

I I I l5 1 .638 I l5 I.1850 .115 1.1627 .1337 -.1949 -.0612 20 .752 20 -.315 .135 0.6627 .0895 -.2527 -. 1632 greatest changes in Cha for a given change in Ch6. In the order of increasing effects on Cha for a given effect on Chs, the various balances may in general be listed as follows: balancing tab, sealed in- ternal balance, plain-overhang balance, and balance obtained by increas- ing the trailing-edge angle.

It was found that all the devices discussed will give lower level hinge-moment than that experienced by the plain flaps. Adequate compar- isons between the different devices themselves to establish the superi- ority of one system over another was not made in any of the reviewed reports. It was not possible to make this comparisons here due to the many differences in test conditions within the literature surveyed.

The wide variation in the forms of aerodynamic balances employed is indicative of the lack of any completely satisfactory method of balance.

The reduction in control force provided by the balance is usually accom- panied by one or more disadvantages, such as insufficient balance or over- balance for some flight conditions, reduction in control effectiveness, loss of "feel" in the control, etc. Other considerations which may impose limitations is the most desirable length of overhang to be used for aero- dynamic balance; since a long overhang will require a large part of the fixed structure (forward section) of the rotor to be cut away to allow for free movement of the balance.

It is frequently found that full balance cannot be obtained in a satisfactory manner by the use of a single device; for example, a large degree of balance with the inset-hinge type of control surface requires such a long overhang that the permissible deflection of the flap is limited. It is helpful, therefore, to.have available several indepen- dent means of reducing hinge-moments.

To be able to state that one system is the best in reducing hinge- the following should be done: moment, (1) The qualities wanted must be stated. These qualities will be specifications of hinge-moment level wanted or desired.

(2) Enough tests must be run using different systems and devices to determine the performance level of each. A comparison between each devices or system can then be made.

The combinations of two or possibly three types of balance may be desir- able to obtain specified values of the flap hinqe-moment parameters or to avoid the difficulties that are encountered almost invariably when a larqe amount of one type of balance is used. A system, using a spring- tab with an aerodynamic balance has been known to reduce hinge moment to any desired level UP to deflections at which the tab has lost effective- An alternative arranqement may be to use a narrow chord flap with ness.

a sealed trailing edge in combination with sealed internal balance vented The bevel will cause a larqe reduction in Cha at the hinge line.

and small reduction in Chs, whereas the sealed internal balance vented at the hinge line will cause a large reduction in Ch6 and a small re- duction in Cha. With such a combination, the hinge-moment parameters probably could be ad.justed to any desired value. Also the beveled trail- ing edqe should be useful in combination with other types of balances, because it involves no additional linkages (see ref. 59).

In view of the various aerodynamics techniques to minimize hinge- moments level discussed, it is the author's feeling that a system incor- porating a sealed, internally balanced flap with a tab offers the greatest possibility in reducing hinge-moment. But the final selection of an aerodynamic.balance for the variable camber rotor flap arrangements must be a compromise depending on the relative importance of the various factors to be considered.

From the foregoing discussions, it may be concluded by saying, that recommended.

for the present analysis, a sealed internal balance is

CHAPTER 5 HOVERING ROTOR PERFORMANCE The hover performance characteristics of a rotor blade equipped with a trailing-edge flap was obtained by utilizing a prescribed wake hover computer program, call PWAKE (see ref. 60). The PWAKE is based on the application of lifting line theory to the calculation of rotor hover performance, with a prescribed wake representation derived from experimental flow visualization studies of model rotor wakes. The PWAKE program was run first with the flapped rotor blade at values of CT/a of .06, .078 and .09, a range which covers most of the hover regime of helicopters, and then again with a rotor with the unflapped airfoil; in this way, a direct evaluation of the effect of flaps are made.

The section aerodynamic characteristics required are the static lift and drag coefficients as a function of angle of attack and Mach number: CL (a, M) and Cd (a,M).

The program input was arranged such that the model rotor blade was configured as follows: the inboard portion (at .Ol of radius) is the VR-7 with 2 degrees flap deflection extending to 90% of radius.

From this point to the tip, the unflapped VR-8 section was used. Both the flapped and the unflapped rotor blades had a linear geometeric twist.

Figure 5.1, illustrates the rotor blade section aerodynamic angles The angle 4 is the relative to each other and to the rotor disk plane.

The blade inflow angle of attack and contains the induced vleocity V.

ROTOR DISK PLANE - Rotor Blade Section Aerodynamic Figure 5.1.

pitch angle 8 is measured from the chordline of the airfoil section to the plane of the rotor disk. The two-dimensional blade angle of attack, a is therefore seen to be the difference between the blade pitch and while 6f is the flap deflection.

inflow angles, The principal overall result is shown in Figure 5.2, a plot of This plot shows power coefficient for various thrust conditions.

clearly a saving in power consumption for the flapped rotor as compared with the unflapped case. This result is clearly reflected in Figure 5.3, in which the area under each of the curves represents the induced it is apparent that induced torque is lower with torque for that case; the flap deflected rather than with it retracted. The profile power distribution is displayed in Figure 5.4.

The total power breakdown is as follows for the case of CT/a = .078: Profile Induced Total Power(HP) Power(HP) Power(HP) Unflapped Rotor 219 893 1112 Flapped Rotor 211 872 1083 AHP Due to Flaps -8 -21 -29 Thus, there is an improvement of 21 hp in induced power and a reduction of 8 hp in profile power, giving a total improvement of 29 hp or 2.6% over the unflapped case.

Figures 5.5 and 5.6 show further details of this effect. In Figure 5.5, it is seen that the flap deflection changes the magnitude of the inflow velocity and redistribute it over the radius. This can be inferred from figure 5.5 by the integral: ~~~~ vrdr/R + 111 vrdr/RSl::, vrdr/R till vrdr/R which relate to the power distribution and also by (Cl sin Q dr/r which relates to the induced power.

Also in Figure 5.6 lies the reason why the profile drag near the tip is actually less in the flapped case than in the unflapped case. In the flapped case, the lift coefficient distribution near the tip is lower than in the unflapped configuration.

Since the profile drag increment due to compressibility effects near the tip is a strong function of lift coefficient, the lower tip loading of the flapped rotor leads to a reduction in profile drag in this re- gion relative to the unflapped rotor.

.oo: . OOL . OOI = .002378 = 43 Twisi Collective pitch = 6.56" Coning angle = 4.447" Blade flapping hinge offset = .O36 6f = 2" QR = 700 fps b=4 0 UNFLAPPED 0 FLAPPED .OOl * I I I .06 .07 .08 .09 .lO ROTOR THRUST COEFFICIENT, CT/u Figure 5.2. - Numerical analysis of rotor power coefficient versus rotor thrust coefficient.

I 0 UNFLAPPED 0 FLAPPED p = .002378 Twist = -8 Collective pitch = 6.56" Coning angle = 4.447" Bl.?ide.flapping 'hinge offSet = 0.036 bf = 2" QR = 700 fps b=4 .4 1.0 0 .1 .2 .3 .4 .5 .6 .7 .8 BLADE RADIAL STATION, r/R Figure 5.3. - Numerical analysis of induced torque loading versus blade radial station.

L 0 UNFLAPPED 0 FLAPPED Twist = -8 Collective pitch = 6.56" Coning angle = 4.447" Blade flapping hinge offset = 0.036 csf = 20 nR = 700 fps 120 b=4 p = .002378 4 1 L L L 4 .6 .7 '.8 .9 1.0 0 .l .2 .3 .4 .5 BLADE RADIAL STATION, r/R Figure 5.4. - Numerical analysis of profile drag loading vs. blade radial station.

- -10

\

\

I

I

= .002378

I

= 43 Ywist Collective pitch = 6.56'

b

Coning angle = 4.447" Blade flappins hinse offset = 0.036 . . - - cjf = 2" nR = 700 fps b=4 0 UNFLAPPED -60 0 FLAPPED 0 .l .2 .3 .4 .5 .6 .7 .8 .9 1.0 BLADE RADIAL STATION Figure 5.5. - Numerical analysis of the induced velocity versus blade radial station.

Twist = -8 Collective pitch = 6.56" Coning angle = 4.447" Blade flapping hinge offset = 0.036 csf = 2O nR = 700 fps b=4 p = .002378 0 UNFLAPPED 0 FLAPPED .

I I I I I I I I I I .l .2 .3 .4 .5 .6 .7 .8 .9 1.0 BLADE RADIAL STATION, r/R Numerical analysis of the lift coefficient Figure 6.6. - versus blade radial station.

CHAPTER 6 PHYSICAL CONCEPTSOF BLADE MOTION AND ROTOR CONTROL 1_ A knowledge of the Physical Concepts of blade motion and rotor control is useful in gaining a physical understanding of the behavior of the variable camber rotor concept in forward flight, as well as in estimating the maximum flap deflections that would be required, as the rotor blade moves into forward flight, from the hover region with the flap deflected 2 degrees. The equations for computing the lift, pro- pulsive forces and the control setting are available from various theories, however, to reduce computations to a minimum, due to the many variables involved, this analysis presents charts, whereby experi- mental values can be obtained directly.

Positive directions of forces and moments are shown 4-n the following sketch: CL, (S~UROES REF. 61 ) ROTOR DESCRIPTION The experimentally derived charts in the 40- by 80-Foot Wind Tunnel (see ref. 4) for a wide range of lift and propulsive force coefficients, are presented in figures 6.2 to 6.4 for an H-34 helicopter rotor blade (see chapter 2), having a linear twist of -8 degrees, and operating in forward flight at tip-speed ratios ranging from 0.30 to 0.46.

The rotor blade section aerodynamic for the hovering performance was illustrated in chapter 5, by utilizing a sketch with the same Rotor disk plane b Rotor Blade Section Aerodynamics.

Figure 6.1. - physical characteristics as figure 6.1, and the values taken from PWAKE at 0.75 radius are presented in table 6.1.

Table 6.1-Rotor Blade Section Geometry Pitch angle, e = 8 hover 4.9 degs.

4.36 degs.

Inflow angle, 0 I ( Effective angle of attack, a 0.538 deg.

2 degs.

Flap deflection, 6f = 6f hover I I Also, it was shown in ref. 62, that the "effective" change in angle of attack for a unit change in flap deflection could be repre- sented by the following parameter: as = (6.1) aa I a6f (CL = constant From PWAKE (chapter 5), the value of a& taken at 0.75R was 0.886.

6.1 Computation of Control Setting for Required Lift and Propulsive .__-~~ Force - The steps required for calculating the control axis and propulsive force coefficients were as follows (for a given U) for the known para- meters, L, D or f, p, s, and QR: Compute C,R/o from the relationship (1) CxR/a = Drag/ps(nR) or use f = 0.09 EZ-R Compute CLR/a from the relationship (2) CLR/U = Lift/Ps(nR)2.

Find as from figures 6.2 to 6.4.

(3) Find 9.75 from figures 6.2 to 6.4 (4) Find % from figures 6.2 to 6.4 or (5) from aC = a~ - Bls.

Compute Bls from the relationship (6) Bls = QS - aC.

Compute Geometric 8 for CT/u = 0.078 at (7) forward flight from the relationship 8 = e-75 + Bls for $I = 270' Geometric The computed values are presented in Table 6.2.

6.2 Calculation of Required Flap Deflections - To estimate the flap deflection that would be required by the helicopter rotor blade flying at a given tip-speed ratio, the procedure was as follows for the known parameters 8 and V.

' Q6 hover (1) COmpUte A9 from the relationship flap (6.2) AI3 =0 - 8 flap Geometric hover.

(2) Compute 6f from the relationship 6f = A8 /as.

(6.3) flap The computed values are presented in Table 6.3, and also shown in figure 6.5 is a plot of the maximum flap deflection versus the free stream velocity. The results indicated that the flap deflections vary linearly with the free stream velocity, and that the required flap deflection at forward flight for an internally sealed flap in the inboard trailing edge area having an envelope of 0.5~ and 0.90R is approximately 9 to 22 degrees for tip speed ratios ranging from 0.30 to 0.46.

TABLE 6.2 - CONTROLAXIS AND PROPULSIVE FORCE COEFFICIENTS GEOMETRIC ATTACK DINAL CYCLIC e AT C 6T,u OF 0.078 AT FORWARD FLIGHT e GEOMETRIC 0.30 0.74 0.42 .0041 -3.6 7 -10 6.4 13.4 ' 0.40 0.82 0.36 .0072 -6.5 11 -16 9.5 20;5 0.46 0.82 0.324 .0095 -7.5 13.5 -18.5 11 24.5 - REQUIRED FLAP DEFLECTION TABLE 6.3 I v I P Ael \ : f Ift/sec 1 flap I 210 0.30 8.5 9.6 280 0.40 15.6 17.6 322 0.46 19.6 22.12 i ‘\ \ \$hO’\ 2 I \ .04 Ii?

\I1 I’ /’ aC, deg -.020 -.Ol6 -.012 -.OOB -.004 0 ,004 .008 .012 ,016 %/Q (SOURCE: REF. 4) Control axis and propulsive force coefficients.

Figure 6.2.

- Articulated rotor with el = -8', V/nR = 0.30.

, ‘\

\

\

.04 ‘7

\

\ \

(.\

\

\

i( / \

\ \ h’ .02 ’ \ 9.7j=-4 Flop to rl9ht denotes b,,= 5” ‘\ d \ b .Flo9 to left denotes b,,=-5” d , ‘-10 5\\ “.?/I

T

-020 -16 -12 -6 L4 0 4

6 I2

a~, de9 -.Ol6 -.012 -.006 -.004 0 ,004 ,006 .Ol2 ,016 %f (SOURCE: REF. 4) Control axis and propulsive force coefficients.

Figure 6.3. - Articulated rotor with el = -8', V/,R = 0.40.

.06 I2 I6 ‘,” \ L \ .04 \ + \ .02 ’ +b as-10 Flog to left denotes bt,=-5O I I I- I k!! t-l J v-20 -16 -12 -0 -4 0 4 0 I2 “cl deg -.Ol6 -.Ol2 -008 -.004 0 ,004 .000 ,012 .Ol6 .020 (SOURCE: REF. 41 %4/ Control axis and propulsive force coefficients.

Articulated rotor with el = -8', V/,R = 0.46.

Figure 6.4. - 4 = .002378 s = 153.1 ft2 R = 700 fps CT/a = .078 Y = 270" a. = 0.886 8hove; = 4.9” (Trim Condition) 200 300 400 0 100 FREE-STREAM VELOCITY, ft/sec.

Figure 6.5 - Numerical analysis of flap deflection versus free stream velocity.

CHAPTER 7 ASSESSMENTOF PAYOFF FOR TOTAL CONFIGURATION The assessment of payoff for the total configuration is important in the evaluation of the variable camber rotor concept. The variable camber rotor has the advantage of providing more meanline curvature where high lift is required and reduced curvature at low liftandtransonic condi- tion as required near the advancing blade tip, thus changing the design restrictions of fixed-contour rotor blades.

In evaluating the aerodynamic section, the analysis shows that the variable camber obtained by a large chord flap deflection permitted the attainment of low drags at lift coefficients above the design range of the plain VR-7 airfoil.

In assessing the various aerodynamics techniques to reduce the levels it was found that all the devices discussed will give of hinge moments, lower level hinge moment than that experienced by the plain flaps. Ade- quate comparisons between the different devices themselves to establish the superiority of one system over another was not made in this analysis, due to the many differences in test conditions within the literature sur- veyed. The wide variation in the forms of aerodynamic balances employed is indicative of the lack of any completely satisfactory method of balance.

The results of the various analyses indicated that for a given lift coef- ficient, the reduction in flap section hinge-moment coefficient obtainable by the addition of a small aerodynamic overhang balance will change with the variation of the flap nose shape and the size of the gap at the flap nose. In general, the lift effectiveness of the flap was the same as for a plain flap and was unaffected by the small amount of aerodynamic over- hanging balance.

The variable camber rotor has also been shown to be effective in im- proving hover shaft power by approximately 3%. This improvement was the result of change in the rotor spanwise lift distribution decreasing both profile and induced power of the entire rotor. It was also the result of reduced profile drag near the tip for the flapped rotor as compared to the unflapped configuration. Since the profile drag increment due to compres- sibility effects near the tip is a stronq function of the lift coefficient, the lower tip loading of the flapped rotor leads to a reduction in profile drag in this region relative to the unflapped rotor.

As indicated above, the configuration analyzed herein does achieve the goal of a reduction in both induced and profile power, however, other factors need to be kept in mind which could affect this result. First, the effect of the airfoil pitching moment on blade aerodynamics has not been considered in this model. However, the section pitchinq moment as- sociated with large chord flap deflection is small as compared with that for an ordinary small-chord deflected to produce the same lift-curve displacement. The pitching moment seem to vary greatly along the radius, as shown in Table 8.1: TABLE 8.1. - PITCHING MOMENTCOEFFICIENT ‘li; (All these values are somewhat approximate, but should be accurate f .005).

Thus, pitching moment causing blade torsion should be large but not unmanageably so; as long as these loads are steady (as they would be, in hover) they should present no great problem in control system design.

However, this relatively large blade pitching moment could have an adverse effect on rotor performance because of changes in effective twist due to torsion on the blade. The negative (nose down) moments could well reduce the blade angle-of-attack on blade section such that some or all of the performance gains due to flap deflections are wiped out.

More sophisticated models of flapped rotors must be design which take such effects into account.

Also, the structural analysis for the concept was not considered in this analysis, and at first sight, the structural problems associated with the 0.5~ flap appear formidable. But with the forward section having structural properties that are stiffer than the aft section in all directions, this should permit the application of the large chord flap without major changes in the structure (also see ref. 63).

In addition, attention must be given to experimenting with various flapped rotor configurations. In all probability large-chord, small deflection configurations will be found to be best, and Air Force sources on maneuvers flaps in fighters should be consulted to verify the perfor- Special empha- mance of such devices in a variety of flight conditions.

sis should be placed on obtaining reliable method for drag prediction for flapped airfoils, since, this is a key area in the profile power-induced power tradeoff and the drag model used herein is sketchy and approximate.

Finally some thought should be given to purely mechanical issues: to achieve a flap deflection along the radius, as is proposed in the pre- sent configuration. A number of questions about drag and aeroelasticity effects must be answered before a reliable evaluation of the flapped rotor concept can be made.

CHAPTER 8 CONCLUDING REMARKSAND RECOMMENDATIONS 8.1 Concluding Remarks 8.1.1. Airfoil Section Analysis: - The airfoil section analysis at different Mach numbers and Reynolds numbers on the VR-7 with a 50-percent chord flap deflected 0 to 20 degrees indicated the following conclusions: Considerable reduction of the drag coefficients above the low 1.

drag range of the plain airfoil may be effected by use of small deflections of a large-chord flap.

2. The variation of maximum lift, minimum drag, and pitching moment at minimum drag with flap deflection were nearly linear within the range of flap deflections analyzed.

3. Reasonably accurate values of the angle of zero lift and the pitching moment coefficient for airfoils with large-chord flaps may be obtained from the analysis.

8.1.2 Hinge Moment Prediction Techniques: - The hinge- moment charac- teristics for various arrangements of sealed internal balances were inves- tigated theoretically for the variable camber rotor. The results of the investigation indicated the following conclusions: 1. The flap with a sealed gap gave a smaller minimum profile- drag coefficient than the flap with the unsealed gap.

Unsealing the gap at the flap nose appreciably decreased the 2.

flap lift effectiveness, and the lift curve for the airfoil was also decreased.

3. Increasing the gap width for a seal of constant width or de- creasing the developed seal width tends to result in reduced balance effectiveness.

4. Varying the cross-section of the overhang from that of a thin plate presents no important aerodynamic disadvantage, and if such a change is desired for structural reasons, a considerable range of design is available in which the seal moments are unaltered.

Variation of the width of the seal, the sealed gap, or the loca- 5.

tion of the seal attachment to the forward portion of the rotor blade (wing) structure was shown to affect the seal moments through most of the overhang deflection range.

6. The presence of a small gap at the nose of a plain-overhang balanced flap and of the corresponding unbalanced flap does not appreciably alter the rate of change of hinge moment plotted against control deflection.

7. The tab was effective in producing increments of flap hinge moment at all deflections at which analysis were made and was slightly more effective when the angle of attack and the tab deflection were of the same sign.

8. The characteristics 'of the tab appear to be independent of .

flap nose shape and the small amount of flap overhang for the unstalled conditions of the airfoil-flap-tab combinations.

The amount of data concerning beveled trailing edges available 9.

during the investigation is considered too small to justify any definite conclusions. It is believed, however, that use of the method presented herein will lead to reasonably accurate estimates of the effects of beveled trailing edges on the hinge-moment characteristics of sealed control surfaces. The available data were insufficient, however, to extend the correlation to include unsealed control surfaces.

10. No correlation factor was obtained that would adequately account for all the variables which affect rate of change of hinge moment coefficient with angle of attack or which affect the deflection range over which the balance is effective.

11. For positive and zero angles of attack the gap at the flap nose reduced the balance effectiveness at positive deflections of the flap.

The data were too meager to justify any definite generaliza- 12.

tions concerning the effects of Mach number on plain-overhang balances except that increases in Mach number consistently decreased the deflection range over which the balance was effective in reducing the slope of the hinge moment curve.

13. The results of the various analyses indicated that for a given lift coefficient, the reduction in flap section hinge- moment coefficient obtainable by the addition of a small aerodynamic overhanging balance will change with the variation of the flap nose shape and the s.ize of the gap at the flap nose. In general, the lift effectiveness of the flap was the same as for a plain flap and was unaffected by the small amount of aerodynamic overhanging balance.

8.1.3 Hovering Rotor Performance: - The analysis for the hovering rotor performance showed the following conclusions: 1. The variable camber rotor has been shown to be effective in reducing power consumption. This improvement was the result of change in rotor spanwise lift distribution which is lower near the tip for the flapped case than the unflapped configu- ration. Since the profile drag increment due to compressibi- lity is a strong function of lift coefficient, the lower tip loading of the flapped rotor leads to a reduction in profile drag in this region relative to the unflapped rotor.

The flap deflection changes the magnitude of the inflow velocity 2.

and redistribute it over the radius, which reduce induce power.

8.1.4 Physical Concepts of Blade Motion and Rotor Control: - Charts ---__-___ based on several full-scale wind-tunnel tests were used from which lift, propulsive forces and control setting were computed. The results of the lection vary linearly with ana lysis indicated that the maximum flap def _.-. ..-.. .._._. ., ., , the free stream velocity and also, that the required flap deflection at forward flight for a rat io of thrust coefficient to solidity of 0.078 is approximatly 9 to 22 degrees at tip speed ratios ranging from 0.30 to 0.46.

8.2 Recommendations Special emphasis should be placed on obtaining reliable methods 1.

of draq prediction for flapped airfoils, since this is a key issue in the profile power induced power tradeoff.

A design study should be qiven to purely mechanical techniques 2.

to achieve a flap deflection along the radius.

3. Further analytical studies should be conducted to examine the dynamic and structural characteristics of the variable camber rotor concept, with particular emphasis on the coupling between the flap deflection and the blade bending and flap/lag motion.

Make recommendations for experimental research to develop the 4.

concept.

REFERENCES 1. Dadone, L.: Rotor Airfoil Optimization - An Understanding of the Physical Limits. In: Proceedings of the 34th Annual Forum of the American Helicopter Society, May 15-17, 1978.

2. Dadone, L. U. : Design and Analytical Study of a.Rotor Airfoil.

NASA CR 2988, 1978.

3. Awani, A. 0.: Doctor of Engineering Project Proposal for the Analysis of a Variable Camber Rotor. University of Kansas, Lawrence, Kansas, KU-CRINC-480-1, Sept. 1980.

4.

McCloud III, 3. L.; Biggers, J. C.; and Stroub, R. H.: An Investi- gation of Full-Scale Helicopter Rotors at High Advance Ratios and Advancing Tip Mach Numbers. NASA TN D-4632, July 1968.

5. Awani, A. 0.: Analysis of a Variable Camber Device for Helicopter Rotor Systems, Doctoral Dissertation, University of Kansas, Lawrence, Kansas, Aug. 1981.

6. USAF Stability and Control Handbook (DATCOM). Air Force Flight Dynamics Laboratory, Wright-Patterson AFB, Ohio, July 1979.

7. Torenbeek, E.: Synthesis of Subsonic Airplane Design. Delft University Press, 1976.

8. Abbott, Ira H.; and Von Doenhoff, Albert E.: Theory of Wing Sections, Including a Surrmary of Airfoil Data. McGraw Hill Book Co., 1949.

9. Hoerner, S. F.; and Borst, H. V.: Fluid Dynamic Lift: Practical Information on Aerodynamic and Hydrodynamic Lift, 1975.

10. Cahill, Jones F.: Summary of Section Data on Trailing-Edge High- Lift Devices. NACA RM L8D09, Aug. 1948.

11. Klein, Milton M.: Pressure Distributions and Force Tests of an NACA 65-210 Airfoil Section with a 50-Percent Chord Flap. NACA TN 1167, Jan. 1947.

12. Olson, L. E.; James, W. D.; and McGown, P. R.:- Theoretical and Experimental Study of the Drag of Single and Multielement Airfoils.

J. Aircraft, Vol. 16, No. 7, July 1979.

13. Bauer, Frances; Garabedian, Paul; Korn, David; and Jameson, Antony: Supercritical Wing Sections II. Lecture Notes in Economics and Mathematical Systems, Vol. 108, Springer-Verlag, 1975.

14. Roshko, Anatol: Pressure Distribution at the Nose of a Thin Lifting Airfoil. Douglas Aircraft Co. Rept. SM-23368, 1958.

General Theory of Airfoil Sections Having Arbi- 15. Allen, H. Julian: trary Shape or Pressure Distribution. NACA Rept. 833, 1945.

16. Roshko, Anatol: Computation of the Increment of Maximum Lift Due to Flaps. Douglas Aircraft Co. Rept. SM-23626, July 1959.

17. Kuethe, Arnold M.; and Chuen-Yen, Chow: Foundations of Aerodynamics.

John Wiley & Sons, 1976.

An Investigati-on of the Velocity Distribution 18. Rettie, I. H.: Around the Nose of the Aerfoil with a Flap. A.R.C. R & M 3027, 1957.

19. Lan, C. E.; and Roskam, Jan: Airplane Aerodynamics and Performance.

Roskam Aviation and Engineering Corp., Ottawa, Kansas, 1981.

20. Woods, L. C.: The Theory of Airfoils with Hinged Flaps in Two- Dimensional Compressible Flow. C. P. No. 138, Aug. 1952.

21. Sears, Richard I.: Wind-Tunnel Data on the Aerodynamic Characteris- tics of Airplane Control Surfaces. NACA A.C.R. 3LO8 (WR L-663), Dec. 1943.

and Gillis, Clarence L.: Preliminary Correlation 22. Purser, Paul E.; of the Effects of Beveled Trailing Edges on the Hinge-Moment Charac- teristics of Control Surfaces. NACA CB 3E14, 1943.

23. Jones, Robert T.; and Ames, Milton, B., Jr.: Wind-Tunnel Investiga- tion of Control-Surface Characteristics. V - The Use of a Beveled Trailing-Edge to Reduce the Hinge Moment of a Control Surface.

NACA WR L-464, March 1942.

24. Hoggard, H. Page, Jr.: Wind Tunnel Investigation of Control-Surface Characteristics. X - A 30-Percent-Chord Plain Flap with Straight Contour on the NACA 0015 Airfoil. NACA WR L-366, Sept. 1942.

25. Rogallo, Francis M.; and Purser, Paul E.: Wind Tunnel Investigation of a Plain Aileron with Various Training-Edge Modifications on a Tapered Wing. II - Ailerons with Thickened and Beveled Trailing- Edges. NACA WR L-228, Oct. 1942.

26. Purser, P. E.; and McKee, John W.: Wind Tunnel Investigation of a Plain Aileron with Thickened and Beveled Trailing Edges on a Tapered Low-Drag Wing. NACA WR L-526, Jan. 1943.

27. Crandall, Stewart M.; and Murray, H. E.: Analysis of Available Data NACA TN 1049, on the Effects of Tabs on Control-Surface Hinge Moments.

May 1946.

Collection of Balanced-Aileron Test Data. NACA 28. Rogallo, F. M.: WR L-419, 1944.

29. Sears, Richard I.: Wind-Tunnel Investigation of Control-Surface Characteristics. I - Effect of Gap on the Aerodynamic Characteristics of an NACA 0009 Airfoil with a 30-Percent-Chord Plain Flap. NACA WR L-377, June 1941.

30. Sears, R. I.; and Liddell; Robert B.: Wind-Tunnel Investigation of Control-Surface Characteristics. VI - A 30-Percent-Chord Plain Flap on the NACA 0015 Airfoil. NACA WR L-454, June 1942.

31. Gillis, Clarence L.; and Lockwood, Vernard E.: Wind-Tunnel Investi- gation of Control-Surface Characteristics. XIII - Various Flap Overhangs Used with a 30-Percent-Chord Flap on an NACA 66-009 Airfoil.

NACA WR L-314, 1943.

32. Harris, Thomas A.: Reduction of Hinge Moments of Airplane Control Surfaces by Tabs. NACA Rept. 528, 1935.

33. Rogallo, F. M.; and Lowry, John G.: Wind Tunnel Development of Ailerons for the Curtiss XP-60 Airplane. NACA A.C.R., Sept. 1942.

34. Rogallo, F. M.; and Crandall, Stewart M.: Wind-Tunnel Investigation of Trimming Tabs on a Thickened and Beveled Aileron on a Tapered Low- Drag Wing. NACA A.C.R., March 1943.

35. Sears, R. I.; and Hoggard, H. Page, Jr.: Characteristics of Plain and Balanced Elevators on a Typical Pursuit Fuselage at Attitudes Simulating Normal-Flight and Spin Conditions. NACA WR L-379, March 1942.

36. Garner, I. Elizabeth: Wind-Tunnel Investigation of Control-Surface Characteristics. XX - Plain and Balanced Flaps on an NACA 0009 Rectangular Semispan Tail Surface. NACA ARR L4Illf, 1944.

37. Lowry, John G.; Maloney, James A.; and Garner, I. Elizabeth: Wind-Tunnel Investigation of Shielded Horn Balances and Tabs on a 0.7-Scale Model of XF6F Vertical Tail Surface. NACA WR L-516, 1944.

38. Rogallo, F. M.; and Purser, Paul E.: Wind-Tunnel Investigation of a Plain Aileron with Various Trailing-Edge Modifications on a Tapered Wing. III - Ailerons with Simple and Spring-Linked Baalancing Tabs.

NACA WR L-470, Jan. 1943.

39. Bryant, L. W.; Burge, C. H.; Sweeting, N. E.; and Greening, J. R.: Experiments on the Balancing of Ailerons by Geared Tabs and Trailing S. & C. 1195a, British A.R.C., April 5, 1941.

Edge Strips.

40. Phillips, William H.; and Nissen, James M.: Flight Tests of Various Tail Modifications on the Brewster XSBA-1 Airplane. I - Measurements NACA WR L-412, of Flying Qualities with Original Tail Surfaces.

1943.

41. Swanson, Robert S.; and Crandall, Stewart M.: Analysis of Available Data on the Effectiveness of Ailerons Without Exposed Overhang Balance.

NACA A.C.R. L4E01, 1944.

42. Toll, T. A.: Summary of Lateral-Control Research. NACA TN 1245, March 1947.

43. Imlay, Frederick H.; and Bird, J. D.: Wind-Tunnel Tests of Hinge- Moment Characteristics of Spring-Tab Ailerons. NACA ARR 4A26 (WR L-318), Jan. 1944.

44. Toll, Thomas A.: Sumnary of Lateral-Control Research. NACA Rept.

868.

45. Street, William G.; and Ames, Milton, B., Jr.: Pressure-Distribution Investigation of an NACA 0009 Airfoil with a 50-Percent-Chord Plain Flap and Three Tabs. NACA TN 734, Nov. 1939.

46. Ames, Milton B., Jr.; and Sears, Richard I.: Pressure-Distribution Investigation of an NACA 0009 Airfoil with a 30-Percent-Chord Plain Flap and Three Tabs. NACA TN 759, May 1940.

47. Ames, M. B., Jr.; and Sears, R. I.: Pressure-Distribution Investiga- tion of an NACA 0009 Airfoil with an 80-Percent-Chord Plain Flap and Three Tabs. NACA TN 761, May 1940.

48. Purser, P. E.; and Toll, Thomas A.: Analysis of Available Data on Control Surfaces Having Plain-Overhand and Frise Balances. NACA ACR L4E13 (WR L-665), 1944.

49. Jacobs, Eastman, N.; Ward, Kenneth E.; and Pinkerton, Robert M.: The Characteristics of 78 Related Airfoil Sections from Tests in the Variable-Density Wind Tunnel. NACA Rept. 460, 1933.

and Toll, Thomas A.: Wind-Tunnel Investigation of 50. Purser, P. E.; the Characteristics of Blunt-Nose Ailerons on a Tapered Wing. NACA WR L-262, Feb. 1943.

51. Letko, W.; Hollingworth, T. A.; and Anderson, R. A.: Wind-Tunnel Tests of Ailerons at Various Speeds. IV - Ailerons of 0.20 Airfoil Chord and True Contour with 0.35 Aileron-Chord Extreme Blunt-Nose Balance on the NACA 23012 Airfoil. NACA ACR 3H28 (WR L-433), Aug.

1943 and March 1947.

Wind-Tunnel Investiga- 52. Sears, Richard I.; and Gillis, Clarence L.: tion of Control Surface Characteristics. VIII - A Large Aerody- namic Balance of Two Nose Shapes Used with a 30-Percent-Chord Flap NACA WR L-378, July 1942.

on a NACA 0015 Airfoil.

Resume of Data for Internally 53. Rogallo, F. M.; and Lowry, J. G.: Balanced Ailerons. NACA RB 41, March 1943.

54. Murray, Harry E.; and Erwin, Mary A.: Hinge Moments of Sealed- Internal-Balance Arrangements for Control Surfaces. I - Theoretical NACA ARR L5F30 (WR L-174), Aug. 1945.

Investigation.

Hinge Moments of Sealed-Internal-Balance Arrangements 55. Fischel, Jack: for Control Surfaces. II - Experimental Investigation of Fabric Seals in the Presence of a Thin-Plate Overhang. NACA ARR L5F30a (WR L-52), Aug. 1945.

56. Bates, William R.: Collection and Analysis of Wind-Tunnel Data on the Characteristics of Isolated Tail Surfaces with and without End Plates. NACA TN 1291, May 1947.

57. Swanson, Robert S.; and Priddy, E. Verne: Lifting-Surface-Theory Values of the Damping in Roll and of the Parameters Used in Estimat- ing Aileron Stick Forces. NACA ARR L5FZ3 (WR L-53), Aug. 1945.

58. Perkins, C. D.; and Hage, R. E.: Airplane Performance Stability and Control. John Wiley & Sons,.l949.

59. Jones, Robert T.; and Ames, Milton B., Jr.: Wind Tunnel Investigation of Control-Surface Characteristics. V - The Use of a Beveled Trailing Edge to Reduce the Hinge Moment of a Control Surface. NACA ARR (WR L-464), March 1942.

60. Landgrebe, Anton J.: An Analytical and Experimental Investigation of Helicopter Rotor Hover Performance and Wake Geometry Characteristics.

USAAMRDLTR 71-24, June 1971.

61. Stroub, R. H.: An Investigation of a Full-Scale Rotor with Four Blade Tip Planform Shapes. NASA TM 78580, May 1979.

62. Roskam, Jan: Flight Dynamics of Rigid and Elastic Airplanes, Part I.

Roskam Aviation and Engineering Corp., Lawrence, Kansas, 1972.

63. Powlishen, F.: K-16B Rotor Stress Analysis. Kaman Aircraft Corp., Rept. G-113-24, Nov. 18, 1960.

64. Woods, L. C.: The Application of the Polygon Method to the Calculation of the Compressible Subsonic Flow Round Two-Dimensional Profiles.

ARC CP 115, 1953.

65. Von Karman, T.: Compressibility Effects in Aerodynamics. Journal of the Aeronautical Sciences, Vol. 8, No. 9, July 1941, pp. 337-356.

66. Woods, L. C.: The Two-Dimensional Subsonic Flow of an Inviscid Fluid About an Aerofoil of Arbitrary Shape. ARC R & M 2811, Nov. 1950.

APPENDIX A METHOD FOR DETERMINING HINGE MOMENTCHARACTERISTICS This analysis gives methods for calculating the quantities a0, aI, bI, b2, and b defined in the List of Symbols, in sub- a~, mg, h, bg, sonic two-dimensional compressible flow. The theory is applicable to airfoil of moderate thickness (say up to 20% thick) and for small values of flap deflection (6f) say ( 20 degrees.

An exact method for the calculation of a0, aI and h for airfoils of any thickness in incompressible flow is given in (Appendix I, Ref. 20).

The exact theory of hinged flat plate in incompressible flow but without restrictions on the value of 6f is given in (Appendix IV, Ref. 20).

The independent variables of the theory given in Ref. 20 are n and y defined in the List of Symbols, while the dependent variables are y and 8.

The quantity y can be readily evaluated as a function of q/U. It has been shown (see Ref. 64) that when the approximation M = M, (A.11 is admissible, y and e are conjugate harmonic functions in the W plane.

Equation (B.l) and an equation similar to y = 1/2(m + a) p.

,;.. p d [log u )= y q\were first used by Von Ka*rma'n (see Ref. 65) to show yj (Ti,.

that 8 and $ are approximate harmonic functions in the ( y, e) plane.

Although the theory given below is not really valid when M, is greater than the critical value corresponding to the first appearance of sonic speed locally (m = l-M')I/' it can still be applied = B PO/P , Eo P with some confidence to calculate the subsonic field when small super- sonic patches exist. This point is important in the theory of controls as a high but localized velocity peak does occur at the flap hinge on the upper surface when 6f is positive.

The complex number defined by f=r+ie (A.21 is approximately an analytical function of W(r and e being conjugate harmonic functions), but if the flow is incompressible, r = log (U/q), w = $ + i$, and so: f = log (;eie) = log ( g) (A-3) Thus whence, it follows that f is exactly an analytical function of w.

the theory of section A.1 (but not of section A.2) will be exact in in- compressible flow.

A.1 Basic Mathematical Theory - The theory of this section is quite general and applies to airfoils with and without deflected flaps.

If 0 and 8, are measured from the direction of flow at infinity, ie, if em= earn= 0, it follows from r q and equation (A.2) that ( ) ii f, = f, = 0 (A-4) Now f is an analytical function of W = -2a cosFj = -2a cash (n +iy) and there it is an analytical function of 3. In fact, as shown in Ref. 66 ,

‘II

f(C) = -1 log sinh 1/2(iy* - S)de(y*), * = -51 ii Y (A-5) where e(y*) is the value of e on the airfoil surface. Equation (A.5) is the no-lift solution. If the airfoil is placed at small absolute angle of incidence a , then on the Joukowski Hypothesis, as in Ref. 64, ia -log Sinh l/2(5 + 2ia)

f, (5) = f(S) -

sinh l/2 5 (A-6) in which it is assumed that the trailing edge is at y = n, and the stream direction is from x = -m (see fig. A.l).

The form of equation (A.6) shows that the effect of incidence on the front stagnation point is to displace it from y = 0 to y = -2a.

Important auxiliary equations can be deduced by considering the form of f, takes near infinity. From equations (A.5) and (A.6) it fol- lows 'II n f=tl y*Wy*) (y2c+log Web*) - 1 - IT 2r I- tia n -iy* +5 te 2ie sina t 1 e WY*) I n I -I *z-n Y t2ia 51 -2iy* +25 te ie sin 2a t 1 e de(y*) + I I ZT I y*=-n comparing the equation with equation (A.4), it was concl uded that 'II de(y*) = 0 (A.7) y*=-n I and 'II (A.81 y*de(y*) = - e(y*)dy* = 0 y*=-* Equation (A.7) is the obvious requirement that e(y*) = e(2n t y*), while equation (A.8) fixes the orientation of the airfoil for the no-lift position. If e is measured from the airfoil chord then e = 8 t ao and (A.8) yields 'II a, = -1 t (y*)dy*, %l ( -‘II (A-9) which fixes the value of no-lift angle.

From the definition, when W -MOimplies.that c+-m, and +5 -at0 a e = 3, ii w ( 1 and so the expansion for f, can be written tia 'TI -iy* f=-a 2 sina t 1 e WY*) f (AJO) t a w rr I y*=-* t2ia 'II sin2a t 1 e-2iade(y*) }t O(+ )3 T?Tl y*=q From this equation it was concluded that

lT

‘IT

cosy* de(y*) = siny*de(y*) = 0 (A.ll) y*=-* y*=-a otherwise when a = 0, f will have a term o d , and since from definition W of y.

-Y/BCO 4 +e U (A.12) q/u will have the form 1 t A/lWl for large IWl, and a lift producing circulation will exist. (An alternative proof for the case of incom- pressible flows appears in (Appendix I, Ref. 20).

Finally it follows from dg = qds, d$ = a/a qdn and cp = -2a cos y that on the airfoil surface (A.13) where the origin of S is taken at the front stagnation point.

The Airfoil with a Hinged Flap - The theory to be presented A.2 below is only valid for small values of flap deflection angle (6f < 20").

In general if 6f > 20 degrees or large, the only recourse is to find the il and flap ab initio for each value of 6f. The poly- flow about the airfo gon method (see ref.

64) would be very suitable for such a calculation.

However, as shown be low, a theory applicable even to comparatively thick airfoils can be developed when terms o(sf2) can be neglected.

A.2.1 The Velocity Distribution - Subscripts a and 6f will be used to denote values when the airfoil is at incidence absolute a with a flap deflection( while the absence of subscript denote the case a= 6f = 0.

Consider the airfoil, for which a =6f = 0, shown in Figure A.2(a). Since solution has been obtained for this case, we can therefore deduce q/u and s/c as functions of y(defined by 8 = -2a cos y) and(Figure A.l).

If the polygon method had been used to find the solution, q/u and s/c will be immediately available as functions of y(see example (b), section 5, ref. 20); otherwise suppose q/u is given as a function of S, then the equation s/c

dud (s/c) -1

which follows from d$ = qds, d$ = G/cOqdn and 4 = -2a cosy, enables = s/c(y), and hence q/u =q/u(y) to be calculated. The constant s/c (cU/Ea) must satisfy p/c q/U d(s/c) where p is the perimeter distance from the leading to the trailing edge.

In figure A.2 the flap surface is shown starting at c, where y = x0, and F, where y = -XI. When 6f = 0, each of c and F correspond to a value of x/c of 1-E. The hinge will be taken to be at x/c = l-E’, and of course for thin airfoil E + E'.

The most important increments (ep, say) to e due to the deflec- tion of the flap are shown in figure A.3. They are due to (i) the front stagnation point shifts to some point A, where y = x say, and conse- quently the flow direction between A and B is reversed, i.e. 8 is decreased byninO<y GX, (ii) the deflection of the flap reduces 8 by 6f in -n<yGXl, Xo<y<n, and (iii) 8 is incresed by a' - a in - n < y < n 0 0 due to a change in the no-lift angle from Q to a'o. Unfortunately these are not the only increment to 0, for the modification to the velocity distribution which they produce (see equation A.26 below) slightly distorts the relation between s and x (equation (A.13))and consequently causes a slight change (Ae) in e(y). Thus 0 can be written for 6f t; 0 as: e =0 +8+AO 6 0 P f where e. is the value of e when Bf=O. For a thin airfoil the distortion in the (s,y) relation will result in quite small values of Ae away from the nose of the airfoil as A0 = AS/R, where AS is the change in s. The largest values of A8 will be near the nose, but these will have a com- paratively small effect on the velocity distribution over the flap, and Thus only a small error will be introduced (except therefore on Ch.

ting in the velocity distribution, near the nose) by wr e = e. + ep (A.15) 6f and since esfmust Now e. satisfies equations (A.7), (A.8) and (A.ll) also satisfy these equations, this must also be true of op. The incre- ment ep is a step function with jumps in value as set out in the fol- lowing table:- and consequently the Stieltjes integrals in equations (A.8) and (A.ll) degenerate to 2n ( 6 -a’ +a’ ) - 6 (I + X ) + *A = 0 (A.16) fo 0 f 1 0 6 (cos x - cos X ) + n(l - COS 1) = 0 (A.17) f 0 1 6 (sin X + sin X ) - n sin h = 0 (A.18) f 0 1 Equation (A.7) is obviously satisfied by ep. Equations (A.17) and (A.18) yield x -A =x (A.19) 0 1 and sin l/2 X = bf sin X Ir m (A.20) where x = 1/2(x + x ) (A.21) m 0 1 These equations imply that we cannot fix the postions of c and F (see Fig. A.2) independently.

It is convenient to regard 6f and Xm as the dependent variables. Equation (A.16) fixes the value of (ah- ao), the change in no-lift angle due to the flap deflection. Using equation (A.20) and ignoring the terms o(6f2) give - h + sin;Gn) (A.22) n n whence = 1 - h+ sin XQ n n (A.23) In (Appendix III, ref. 15), it is shown that these equations are exact for incompressible flow about a flat hinged plate.

Substitution of equation (A.15) into equation (A.5) yields f ,6 (5) = f(c) - i(6 - a’ ) + if log 0 f f 0 n + log sinh l/2 5 .

sinh 1/2(s-ix) If the airfoil is now placed at an absolute incidence of a the front stagnation point will be displaced from y = x to y = x -2a, and hence (c.f. equation (A.6)) will give fa.bfS) = f(c) - o(S - a’ + a + a ) + if log sinh l/2 s-ix,) --+-.

f 0 0 n slnh 1 2 ~-1~1) + log sinh l/25 (A.24) sinh 1/2(5+2ia-iX) on the airfoi surface, n=O, and equation (A.24) becomes with the aid of (A.19) and (A.21) + tSf log sin 1/2(y - 12 a - h) n sin 1/2(y -l/2 X = h) (A.25) + log sin l/2 y sin l/2 (y + 2a- A) where X and X, are related by equation (A.20). The velocity distribu- tion now follows from the expression for r defined earlier. At low Mach numbers the approximation (A.12) is valid, when equation (A. 25) yields (A.26) In the calculations of the various derivatives for CL, Cm and Ch it would be convenient at first to regard a and 6f as independent variables. Subsequently a will be replaced by (a = a0 + w when 6f i 0 and equation (A.22)) a = a’ + a t 6 (1 - am t sin Am) (A.27) 0 f rr n so that a’ and &f become the independent variables.

A.2.2 Calculation of C - The lift coefficient, CL, is defined by the contour integral taken round the airfoil surface.

CL = - 1 Cp cos E-Ids , c 4 where the pressure coefficient Cp is a function of y, 6f and a. Thus since 1 cos e ds = cos 0 d$ = 2a U cos e sin y dy, ( H 1 c UC cq 4 n (A.28) Cp siny Ucos e dy CL = -($ ( ) -n If v is the ratio of the specific heats, Cp is given by cp= 2 l- x I[ from which it folows that (A.29) It is easily deduced from y(q/U), equations (A.20) and (A.25) that cot l/2 y

a(p =

& (+)( %iJ f?

( 1

a=&=0 f and + sin Xm cot l/2 y , n and hence from equation (A.29) aC, =- (A.30)

& Xpfcot l/2 Y

aa ( > a=&0 f and ac = 2 log si; :$ 1; I Zuni t sinnXm cot l/2 y - x ($I2 + -q Boa

( >

a= $0 (A.31) where is a function of q/U. This function is given in (Table 2, ref. 64 for M, = 0.5 to 0.79). Differentiating equation (A.28) with respect to a and 6f and making use of equations (A.30) and (A.31), give n X(q/U cos 0) cos2 l/2 ydy (A.32) and n X(q/U cos e) sin y - n If the polgon method of calculating q/u has been used,(4a/uc), q(y) U and e(y) will be known, X(y) can be readily deduced from tables such as those given in ref. 64, and so the integral in (A.32) can be evaluated numerically without difficulty. A calculation of this type appears in ref. 64.

A simple approximation can be found by writing x = q/u cos e = 1 (A.34) in the integrals of equations (A.32) and (A.33). It was found that = 2n 4a 8CL aa UC zi

( )

a=6 =0 (A.35) f and = a=4 = 0 (A.36) Equation (A.36) is in any case obvious since CL depends only on a. From CL = a t 6 , 3CL 3CL f aa adf ( >

(, )

a=6 = 0 a=6 = 0 f f and equations (A.27), (A.35) and (A.36), it follows that + sin Am CL=>% a +a’+ 6f l- JITJ .

( )I 0 ( n n f3m UC )1 A comparison of this equation with the expression for CL = aotaIa'ta26f yields (A.37) a = 2n 4a ' (A.38) El IF ( 1 and ap/aI = 1 - Xm t sin Xm (A.39) T n CL = a taa'taS 0 1 2 f It is well known that for thick airfoil in incompressible flow, equa- tions (A.38) and (A.39) are exact (see Appendix I, ref. 20), while in (Appendix IV, ref. 20) it is shown that equation (A.39) is exact for the flat plate in incompressible flow. An approximation for the parameter (4a/UC), which occurs throughout the analysis, is given in (Appendix II, ref. 20).

A.2.3 Calculation of Cm, h and MO - The equation corresponding to (A.28) for the moment coefficient about the leading edge is Cm= ($, jn Cp( ; t $ tan 8 )( +j cos e)sin y dy -71 where x/c is measured from the leading edge. Differentiating this equation with respect to a and 6f and making use of equations (A.30) and (A.31) give aC, =- [I X( ;+$tan e )@cos e)cos' l/5 dy, f ($1 aa a= 6f=O and 'II x 1 log si; W& ; &n{ + sinnxm cot l/5 f siny dy f Y which can be evaluated directly when q/u has been calculated by the polygon method (see reference 64).

Approximations to these equations can be found by writing Ux = 2a + 4, which lead to x = l/2 4a (1 - cos y), c UC ( 1 ignoring the very small "xtan 0” term, and using equation (A.34).

C The results are 4a 2,

aC, =-

2k E aa

1 1

(A.40) a=6f=O

( >

= - 1 4a 2 sinXm (1 - cos xm), and aC, UC 2f3ca adf -( 1 0 a=6f=O but Cl = ala, and so it follows from equations(A.35) (A.40) and the definition of h and m. that h = l/4 (4a/Uc) (A.41) m. = 1 (4a/Uc)2 sin xm(1 - cos xm).

28m Thus Cm = - hCL - mo6f A.2.4 Calculation of Ch, b,&l, and b2 - By comparing with the equation for Cm given in section A.2.3, it is clear that the coefficient of the hing-moment, Ch is given by ch = (2) k2( I- “1+ [)cp f 3 - 1 + E’ + $ tan fo ~0s 0 )sinydy, -n (A.42) the hinge being at x/c = l-E', where y = X'm. From equations (A.19) and (A.21), 6f + 0 implies Xl + X0 -t Xm. Thus u cos 0 sin y Q

( )

which has to be calculated numerically just as in the exact treatment of equation (A.32) Differentiating equation (A.41) give, with the aid of equations (A.30) and (A.31), ach = - 2 B2 aa co a=q=o cos2 l/2 y dy and -Xm n -n Xm x sin Xm cot l/2 y + 1. log sin 1/2(y - Xm (i ‘OS e)sin ’ {T n d] dy* The expression 3Cl-l neglected a very small term due to the dependence of hf) a=tif=O the limits of the integrals in equation (A.42) on 6f. Equation (A.44) can be evaluated numerically, but for thin airfoils travelling at speeds such that M, is well below the critical Mach number the following approx- 1 be sufficiently accurate. It can be shown that mation wil xx- 1 - El tstam e} (gcos e)= l/2 cosh'm - cos y).

t c which results in = - 4a2 x sinXm(1 t l/2 cosXm - cosA'm) aCcl $-E2 aa UC 1 ( 1 ( If a=+=0 a0 t (n - Xm)(cosX'm - l/2) , and = - 2 sinAm x ((n - xm)(l - coslm) - sinAm 25-l +E2 (%> ( ) aa a=q=o (1 t cosXm - 2 cosX'm)).

Now , Ch = (Ch) a=6f=O a=&if=O a=6f=O and using equation (8.27) gives Ch = (Ch) + '=o (gh) + a' (gh) I a= 6f=O I a=6f=O a=&f=O t 6f 1 - Am t sinAm .

-- n n I( a=6 f=O comparing the expression Ch = b, t bla' t b26f, and using the values of the derivatives found above, it can be concluded that =- a sinxm(1 + l/2 cosXm - cosl'm)

b = (c,)

( ) i?E2 $? 0 a=6f=O m , +(n - X,)(cosX'm - l/2) sinXm(1 t l/2 cosXm - cosl'm) + (n - Xm)(cosX'm -l/2)) b=- 1 4a 2 -( P 8,Ep 55 b=- 1 n8, t2 (4a)2{(n-Am)sinAm t l/2 sin2xm - (l/2 - cosA'm)(n-Am)2t while from CL = ala and the definition of b can be shown as follows: 2 sinAm{ (n - Xm)(l - cosXm) - sinlm(1 t cosXm "=z&-s (i2, - 2 cosl'm)) (A.46) FIG. A.1 FIG. A.2 (a) 2, plana (a) i planu, 6f - 0 -- -- -pJiq--& -- a. = (8) w plane (zero circulation) w planfz

(4

(SOURCE: REF. 20) FIG. A.3 FIG. A.4 (at) Z plana (4 t plana, 6f + 0, 0P t + -7f -& $ 0 A+d&+ lo W 7 F OH if A 8: t --- - W

6) @a Y>

6) @,, 7) Figures 1-4

APPENDIX B AIRFOIL COORDINATES VI+7 WITn 0' T.E. TAB 'arKmIt:

B-r

tXMETERISTfC5 AIRlWILcooRDINATES m Thickness, t/c = 0.12 -

l .kad.inQ Edge Circle

J8 Y/C, r/c = -0113 a.

0. 0.

Center at x/.c = -01055 ,oos -0165 -.OOf75 -01 ala11 -.OOBl tit/c = -004 -02 -0298 -.0109 -03 -03615 -.Ol29 l Trailing Edge Tab -04 ,041s -:01445 -05 .046OS -~01595 from x/c = -96 -0502S --.01710 -06 G/C - 1.01 -07 .OS41 -.0100s TX. Tab Thickness, .QBS -0593 -~01¶85 t/c - 0,005 ,202 .ous -.02145 -0691 -22 -.02ZBS -14 .I737 -.0241 TYPE OF DATA AND METXODOF TEST --0251 -16 -0775 -18 AIDI -.ozco -20 .0838 -.026C hrc+dinmmsionaltz5tin thesub- -22s ,OB67 -.0273 8bnic insert of the Boeing -25s .a992 -.ozmo Supersonic Wind Tunnel in Seattle, -29 .v909 -,02l5 -33 b09U -A289 Yash.

-17 .oses -.029D -41 BOB@7 --0285 Lfft 8nd pit&in9 aomenw Were .OIS6 -.D275 3 .I#16 -,0260 amuurmdvith abrlance.

.O')L7 23 -.a240 -57 -0710 -.0220 Al A646 9.0199 Drag vu datamined by a tra- -65 mO580 9.0179 ver8iag wake probe 8mvey.

A9 -0514 -m0158 -73 -0147 m.0l.M 37 -0174 l .01075 Ho&l Chard - 6.38 in -81 .OSBl l ,OOUS Spaa - 12 in ,845 ,023) 'row4 ru .0267 ~A0425 -81 .0105 ,rlO22S ,SJS rDol2 brnDDC .u r8eSD t-0 -01 ,.050 LO , IVR-8 with 0. T.E.' TAB AI&IL: .- /--+---- 0 Thicknera, t/x = 0.08 ,005 .00850 -,oos35.

0 Leading Edge Circle: -01 .01175 0.0737 r/c = 0.00585 ,015 -0142s -.00880 ,025 -0183 -.01090 Center at x/c - 0.0058 ,035 -0217 -.0125s Y/C = 0.00088 -05 -0261 -.01465 0 Trailing,Edge %.b: -07 -0309 -,01685 ,095 .0357 -.0190 fmm x/c = 0.96 ,125 -0402 -.0212 to rt/c = -3.03 -16 -0444 w-0232 T-E: Tab !Fhickaess, t/c - 0.005 -20 -0480 -,0250 w-0266.

w-25 - OS10 ‘TYPE OF DATA AUD mn’HOb OF TEST .30 -0530 -. 0277 a5 .0535 .-I 0280 %o-diaensionalmtest in the sub- .40 .os25 -. 0276 sonic insert of the Boeing super- -45 -0502 9.0265 sonic vind tunnel in Seattle, *SO -0467 -. 0247 Wishington.

-55 .0426 -- 0225 -60 -0380 -. 0200 Lift and Pitching moments were -65 * 0333 -,0175 neasured with a-balance.

-70 a 0285 -.0150 .7s -0237 -,4125 Drag wus determined by a traversing -80 -0190 -. 0100 wake probe survey.

.a5 -01428 -.0075 -09 -01048 -,0055 model Chord - 6.38 in -92 -00761 -. 0040 span -12. in ,945 m00524 -. 00275 ;96 SODICE -01 Dadone, t- , 6 HcHullen, 3., QTJi/ ATC Rotor Systemiwa-dimensional Airfoil zest-, gbeing Ihxzlment, 0301-10071-1, Decoder, 1971 3. Recipient’s Catalog NO.

1 2. Government Accsrrion No.

1. Report No.

NASA CR-3503 I I 1 5. Report Date 4. Title and Subtitle THE INVESTIGATION OF A VARIABLE CAMBERBLADE LIFT _

January.1982

6. Performing brganiration code CONTROL FOR HELICOPTER ROTOR SYSTEMS 8. Performing Orgnizrtion Report NO.

7. Au;brbl Alfred 0. Awani . 10. Work Unit No.

9. %for.ming Org+ation Name and Addrm 532-03-U University of Kansas Center for Research Inc.

11. Contract or Grant No.

2291 Irving Hill Dr. - Campus West

NCC-292 Lawrence, KS 66045 13. lype of Report and Period Covered 12. Sponsoring Agency NUTMZ md Address Contractor Report National Aeronautics and Space Administration 14. Sponsoring Agency code Washington, D.C. 20546 15. Suppfernentary Notes Point of Contact: Robert II.

Stroub, Ames Research Center, Mail Stop 247-1,

Yoffett Field, CA. 94335 415-965-6653, FTS 448-6653

16. Abstract A new rotor configuration called the variable camber rotor was inves- tigated numerically for its potential to reduce helicopter control loads and improve hover performance. This rotor differs from a conventional rotor in that it incorporates a deflectable 50% chord trailing edge flap to control rotor lift, and a non-feathering (fixed) forward portion. Lift control is achieved by linking the blade flap to a conventional swashplate mechanism; therefore, it is pilot action to the flap deflection that con- trols rotor lift and tip path plane tilt.

This report presents the aerodynamic characteristics of the flapped and unflapped airfoils, evaluations of aerodynamics techniques to minimize flap hinge moment, comparative hover rotor performance and the physical concepts of the blade motion and rotor control. All the results presented herein are based on numerical analyses.

The assessment of payoff for the total configuration in comparison with a conventional blade, having the same physical characteristics as an H-34 helicopter. rotor blade, was examined for hover only.

The variable camber rotor configuration is shown to reduce hover power required by at least 2.6% for a flap deflection of 2 degrees. This power improvement was attri- buted to a change in the spanwise lift distribution decreasing both profile and induced power of the rotor.

16. Distribution Stalement 7. Key Words (Supgqted.by Authorlrl) Larqe trailing edge flaps FEDD Distribution Variable camber rotor Aerodynamic sections (VR-7, VR-8) Subject Category 02 Hinge moment balance technique Hovering rotor performance 22 Price 21. No. of Pages 20. Security Classif. lof this pnge) 9. Saxriw Cbnif. (ol this reportI Unclassified Unclassified -- Available: NASA's Industrial Applications Centers NASA-Langley, 1982