.. 

NASA Contractor Report 177998 

NASA-CR-177998 

19860004750 

AN AIRFOIL FLUTTER MODEL SUSPENSION 

SYSTEM TO ACCOMMODATE 

LARGE STATIC TRANSONIC AIRLOADS 

Wllmer H. Reed, III 

DEI-Tech, Inc. 

11838 Bunker Blvd., Suite 500 

Newport News, VA 23606 

CONTRACT NASl-17686 

OCTOBER 1985 

NI\5J\ 

National Aeronautics and 

Space Administration 

Langley Research Center 

Hampton Virginia 23665 

111111111111111111111111111111111111111111111 

NFOI020 

I I, 
CONTENTS 

Description 

SUMMARY •••••••••••••••••••••••••••••••••••••••••••••••• 2 

I NTRODUCT I ON •••••••••••••••••••••.•••••.••••••••••••••• 2 

SYMBOLS •••••••••••••••••••••••••••••••••••••••••••••••• 3 

WIND TUNNELS ...........•...................•...••..••.. 4 

AIRFOIL MODELS ......................................•.. 4 

Statlc Pressure Dlstribution Models .••....•••••••• 4 

Llghtwelght Flutter Models ..•....•....•.....•..•.. 5 

Statlc Alrloads ................................... 5 

PITCH/PLUNGE AIRFOIL FLUTTER SUPPRESSION SYSTEM ........ 5 

Deslgn Requlrements .........................•••... 5 

Compound Spring Concept ...•....•................•• 6 

Deslgn Implementation .......•...............•.••.. 7 

General Descriptl0n ..•............•.......•.. 7 

Self-Allgnment Control System ....•...•....... 9 

Sprlng Deslgn ............................... 9 

In s trumen ta tlon ............................. 10 

LABORATORY TEST S •.....••••..••••......•••.•••.•••.•••• 10 

Proof Load Test ..............................••.. 10 

Stiffness Measurements .........•...•............• 10 

Modal Characteristlcs ...........•................ 11 

Self-Allgnment Control System .................... 11 

CONCLUDING REMARKS ..................•.......•..•...••. 12 

APPENDICES 

A. Derlvatl0n of Compound Sprlng Equatlons······13 

B. Self Alignment Control System ................ 16 

WirJ.ng Diagram 

Control Panel 

REFERENCES •••••••••••••••••••••••••••••.•••••.•••••••• 18 

1 
Table No. 

I. 

IIa. 

lIb. 

III. 

LIST OF TABLES 

Descrlptlon 

STATIC PRESSURE ORFICE LOCATIONS ON 

MBB-A3 AIRFOIL MODELS 

MBB-A3 UNCAMBERED AIRFOIL COORDINATES 

MBB-A3 CAMBERED AIRFOIL COORDINATES 

SYSTEM WEIGHTS AND INERTIAS 

1 
SUMMARY 

ThlS paper descrlbes the deslgn, fabrlcation and laboratory 

evaluatlon tests of a pltch/plunge flutter model suspension 

system and assoclated two-dlmenslonal MBB-A3 alrfoil models. The 

system lS deslgned for installat10n in the Langley 6-by-19-1nch 

and 6-by-28-1nch transonlC blowdown w1nd tunnels to enable 

systematic study of the transon1C flutter character1st1cs and 

statlc pressure dlstr1but1ons of supercr1t1cal alrfo1ls at 

transon1C Mach numbers. The system features var1able p1tch and 

plunge frequenc1es, changeable alrfoil rotat1on axes and a self 

aligning control system to malntaln a constant mean posltlon of 

the model w1th chang1ng a1rload. A compound spr1ng suspension 

concept 1S 1ntroduced whlch slmultaneously meets requlrements for 

low plunge-mode st1ffness, Ilghtwelght suspended model and large 

steady 11ft due to angle of attack w1thout the need for exceSS1ve 

static deflectlons of the plunge spring. 

INTRODUCTION 

The m1nlmum marg1n of safety from flutter for h1gh performance a1rcraft usually occurs at transon1C speeds where our 

analytical tools for pred1cting flutt2r are least rel1able. 

Recent eV1dence from w1nd tunnel stud1es, fl1ght test and 

theoretlcal analyses suggests that th1S so called "transon1c 

flutter dlp" may be even more severe for supercr1t1cal airfo1ls 

than conventlonal a1rfo1ls (see ref. 1 and 2, for example). 

To ga1n further 1ns1ght 1nto the physlcal phenomena as soc1ated w1th transonlC rlutter of supercrlt1cal a1rfo1ls, the A1r 

Force Systems Comm2~d sponsored an exper1mental research program 

almed at invest1gatlng p1tch/plunge flutter and the assoclated 

static pressure d1str1but1ons on supercr1tical airfoils 1n a 

small transon1C w1nd tunnel. The contract called for the design 

and fabr1cat1on of a p1tch/plunge a1rfo1l flutter test r1g and 

two 6-1nch span by 6-1nch chord supercr1t1cal a1rfoil models 

equipped w1th stat1c pressure orflces. One of the key research 

objectives of this program was to 1nvest1gate and better understand the marked 1nfluence of angle-of-attack on transon1C 

flutter Wh1Ch has been observed 1n pr10r stud1es, such as 

references 3 through 6. ThlS requ1red that the test r1g be 

capable of keep1ng the flexlbly mounted a1rfo1l model centered in 

the w1nd tunnel test sect10n w1th up to 1000 pound steady 11ft 

force developed. Because the system was found to have several 

structural def1c1enc1es and lnadequate center1ng force capabll1ty, the correct1on of Wh1Ch would requ1re maJor mod1f1cat1on, the test phase of the program was cancelled. The two 

a1rfo1l models - MBB-A3 wlth and w1thout camber - met or exceeded 

all requ1rements. 

In a cooperat1ve agreement w1th the A1r Force, 

Research Center subsequently contracted w1th DEI-Tech, 

2 

Langley 

Inc. to 
redesign and fabr1cate a new pitch/plunge a1rfoil test r1g to 

meet the test obJectives originally specif1ed. The new apparatus 

would be designed to enable systemat1c study of transonic flutter 

of 11fting, two-dimensional airfo1ls in the Langley 6-by 28-1nch 

Transonic Blowdown Tunnel. In add1tion to the eX1sting set of 

MBB-A3 airfoil models, a dupl1cate set of lightweight models, 

having the same prof1le but w1thout pressure tubes and orifices, 

was built to enable 1nvestigat1on mass/air dens1ty ratio ~) 

effects on flutter. 

The purpose of th1S report 1S to describe the des1gn, 

implementation, and performance test1ng of a p1tch/plunge airfoil 

flutter suspension system capable of accomodating large static 

transon1C air loads due to angle of attack. 

c 

b 

d 

e 

E 

I 

cg 

K 

o 

l 

L 

m 

P 

SYMBOLS 

A1rfo11 chord, 1n 

Airfoil span, in 

Distance from airfo11 leading edge to airfoil cg, in 

Length ratio of upstream to downstream compress10n 

links 

Modulus of elast1c1ty, PS1 

Uncoupled plunge frequency, hz 

Uncoupled plunge frequency when P = 0, hz 

Uncoupled pitch frequency, hz 

Airfoil mass moment of inertia about c.g., Ib-in2 

Spring constant ofax1al spring, lb/in 

Spr1ng constant of compress1on spring, lb/in 

Effective spr1ng constant of plunge spring, Ib/1n 

Length of down stream compression link, 1n 

L1ft force, lb 

Effective susfended mass of model and suspension 

system, (lb-sec )/in 

Compression spring force, lb 

Compression spring preload, lb 

3 
t 

x 

z 

Critical compression spr1ng preload (stat1c 1nstab1-

lity) , lb 

Leaf spring th1ckness, in 

Airfo11 cordw1se stat10n measured from lead1ng edge, in 

Plunge-mode displacement, 1n 

Airfoil upper surface coord1nate, in 

A1rfoil lower surface coordinate, in 

Free stream density, 2 4 (lb-sec )/1n 

2 Mass dens1ty rat1o, m/~f(c/2) b 

Stat1c deflection of plunge spr1ng, 1n 

WIND TUNNELS 

The airfo11 flutter suspension system descr1bed here1n 1S 

designed for installat10n in either the Langley 6-by 19-1nch or 

the Langley 6-by 28-1nch transon1C blowdown wind tunnels. These 

tunnels have slotted top and bottom walls, turntables 1n both 

s1dewalls, and were developed spec1fically for bas1c aerodynamic 

testing of small two-dimens10nal a1rfoil sect10ns at Mach numbers 

from about 0.3 to 1.2. The 6-by 19-1nch tunnel 1S descr1bed 1n 

reference 7. Compared to the 6-by 28-ingh tunnel, 1t ~s limited 

Reynolds number capaJll1ty (1.5 x 10 to 3.0 x 10 ) and 1tS 

operat10n mode does not permit 1ndependent control of Mach number 

and stagnat10n pressure. In the present program, the 6-by 19-

inch tunnel w111 be used pr1mar1ly for funct10nal checks and 

"tuning up" of the rig pr10r to enter1ng the h1gher performance 

6-by 28-1nch tunnel. The 6-by 28-1nch tunnel, descr1bed 1n 

reference 8, 1S capable of operat1ng at stagnat10n pressures from 

2 to 6 atmospheres. Mach number and stagnat10n pressure are 

1ndependently controllable 1n a manner that tests may be conducted at Mach numbers from 60.S to 1.0 w1th Reynolds number held 

constant up to 10 x 10 based on a 6.0-1nch model chord. The 

operating envelopes of both tunnels are shown 1n F1gure 1. 

AIRFOIL MODELS 

Stat1c Pressure D1str1but1on Models 

Two 6-inch span, 6-1nch chord a1rfo1l models equ1pped w1th 

orif1ces and tub1ng for static pressure d1str1but10n measurements 

were prov1ded by the A1r Force. One model has an MBB-A3 prof1le 

w1th camber; the other, an MBB-3A prof1le w1thout camber. 

The models were mach1ned from stainless steel and pol1shed to a 

mirror-11ke surface f1nish. Or1fice locat1ons are g1ven 1n Table 

I and the theoret1cal and measured a1rfo11 coord1nates are 11sted 

in Table II. 

4 
In addition to static pressure distr1bution tests 1n which 

the airfoil would be rig1dly mounted to turn tables 1n the tunnel 

side walls, the models can also be mounted to the p1tch/plunge 

flutter r1g for flutter test1ng. The a1rfo11 p1tch axes locat1on 

for flutter testing can be either the 15% or 25% chord. Being of 

steel construct1on, these models are relat1vely heavy and, as a 

consequence, the mass/air density scaling parameter would 

probably be higher than that for most a1rcraft. Mass and 

inertia data for these models are given 1n Table III. 

Lightweight Flutter Models 

To 1nvestigate mass/a1r density rat10 effects on flutter, 

two 11ghtweight a1rf011 models were constructed. These models 

have the same geometric profiles of the eX1sting steel airfoil 

models but are without pressure orifices and tubing. Constructed 

of graph1c fiber composite sk1ns with steel end fittings, they 

weigh less than 1/2 lb., about 15% of the steel alrfoil weight. 

The aluminum molds from which the models were formed were 

measured and found to be w1th1n 0.002-inch of the theoretical 

airfoil coordinates. The lightweight models also have optional 

pitch axes locations of 15% and 25% chord. Mass and inertia data 

for these airfoils are also presented in Table III. 

Static Air Loads 

To estlmate the maX1mum static aerodynamic loads expected 

during flutter tests in the 6-by 28-inch tunnel, use was made of 

the statlc pressure dlstribution measurements on the MBB-A3 

airfoil given in reference 9. This estimate is for 0.8 Mach 

number at the maximum available dynamic pressure, 3850 p.s.f., 

and 5 degree angle of attack. The aerodynamic loads associated 

wlth thlS assumed "worst case" design conditions are: 800 

lb. normal force and 1200 in-Ib nose down pitch moment about the 

15% chord. 

PITCH/PLUNGE AIRFOIL FLUTTER SUSPENSION SYSTEM 

Design Requlrements 

The Ob]ectlon of this effort 1S to provlde an experlmental 

capab1lity to perform systemat1c p1tch/plunge-type flutter 

tests of supercritlcal two-dimenslonal alrfoils in Langley 

transonic blowdown wind tunnels. The combinat1ons of pitch, f , 

and plunge, f b , uncoupled frequencies requlred for flutter of the 

MBB-A3 airfoiI at Mach 0.8 as a function of dynamic pressure are 

presented in Figure 2. Also shown are the dynamic pressures 

achievable at 0.8 Mach number in the 6- by 19-inch and the 6- by 

28-inch transonic wind tunnels. These calculations were made by 

J. T. Batina, NASA-Langley, using a transonic unsteady aerodynam1c code for 2-d1mensional airfoils (XTRAN2L). Therefore, as 

5 
a design goal the range of variat10n 1n the uncoupled p1tch 

and plunge mode frequencies to be ach1eved were prescr1bed 

as fo<. = 40hz to 100hz (pitch) and f = 10hz to 40hz (plunge). 

Some other specific des1gn requiremen~s are that the suspension 

system should have: 

o Lightly damped uncoupled modes, character1stic of 

linear single degree-of-freedom dynamic systems. 

o Lightweight suspended mass to enable s1mulation 

of mass/air density ratios representative of modern 

aircraft. 

o Self aligning control system to automat1cally ma1nta1n 

the mean posit10n of the airfoil as air loads change. 

o Quick act1ng a1rfo11 snubber system to suppress 

flutter oscillations. 

o Changeable pivot locations ahead of the airfo11 to 

simulate the steamwise bending mode shape of swept 

back wings which is character1zed by a node line 

ahead the wing leading edge as illustrated in Figure 3. 

o Pitch axis ("elastic axis") locat1on var1able at 

15% and 25% chord. 

The mass and stiffness properties of the suspension system 

are d1ctated by flutter scaling cons1derations, that is, the 

suspended masses must be lightweight 1n order to simulate 

realistic mass/air density react10ns and the suspension stiffness 

such that flutter can occur w1th1n the w1nd tunnel operat1ng 

envelope. With the additional requirement that the system also 

accomodate large steady air loads, the static deflections of the 

suspension springs may exceed practical limits. This is espec1ally cr1tical for the plunge mode at low frequency settlings. 

By way of illustration, assume that the moving mass of the 

suspension system w1th the airfo11 model installed 1S 2.5 pounds 

and the plunge mode frequency, f = 10 hz. The correspond1ng 

plunge spr1ng stiffness, K , 1S 2 s: 6 lb/ in. Thus, to counteract 

the 800 lb. design lift force the plunge spr1ng must deflect 31 

1nches. 

Compound Spring Concept 

The search for a solution to meet these confl1ct1ng requ1rements-- that the spr1ng system have low stiffness, h1gh load 

carrying capability and a minimum weight-- led to a concept 

originally investigated by Molyneux in 1961 (ref. 10 ) as a means 

of v1bration isolation and subsequently was further developed 1n 

unpublished work by Robert Herr of NASA Langley Research Center. 

6 
This concept involves two spr~ngs and p~n-ended r~g~d links 

conf~gured as ~ndicated schemat1cally 1n the sketch A below: 

Sketch A: Compound sprlng concept 

The hor1zontal spring, K , ~s pre loaded to produce a controllable compressive force,!P, in the rigid llnks. When the 

joined end of the llnks is displaced vert~cally through a 

distance z, as shown, these compressive forces act in the same 

direction as the displacement and thereby function as a negat1ve 

stiffness tending to counteract the pos1t1ve stiffness, K , in 

the aX1al spring. The net stiffness ~n the z direction ~s ~iven 

by the equation (see Appendix A for deviation.) 

where 

dL = K = K ( 1 - PIP ) dZ z 0 c 

P 

c = K 1 (e ) o 1 + e 

P is the critical compress1ve force at which the system 

become~ stat1cally unstable. (analogous to the critical load 

in column buckling.) Therefore, by varying the compressive 

force in the links the effective stiffness, K can be varied 

from a maximum value of K to a m~n1mum app~oach~ng zero. 

An important feature of th~ compound-spring system 1S that 

the static deflection, ST' needed to counteract a glven load 

depends only on K , irrespect~ve of the lower-valued effect~ve 

stiffness. By cont~ast, the stat1c deflection of a s~ngle linear 

spring system varies inversely with st~ffness. Shown in f1gure 4 

are stat1c deflect10ns versus plunge-mode frequency for a 

slngle-spring and compound-spring system. These results are for 

the same 2.5 pound suspended mass and 800 pound lift force 

considered in the previous example. In this case K was sized to 

produce a fh = 40hz (plunge-mode frequency whe~ there is no 

force in the ~ompression links). Note that static deflection 

7 
associated with the 800 pound 11ft force is approximately 2 

inches, for all frequencies below 40hz. 

DESIGN IMPLEMENTATION 

General Descript10n 

The 1mplementation of suspension system design concepts 1nto 

functional hardware may be described by referring to f1gures 

5 through 7. Figure 5 shows drawings for the suspens10n system 

installation in the 6- by 28-inch wind tunnel. The pitch/plunge 

linkage mechan1sm which suspends the airfoil model, 1S mounted to 

and rotates with turntables installed in the test section slde 

walls of either the 6- by 19-inch or 6- by 28-inch tunnel. 

Photographs of this linkage mechanism (figure 6) and an exploded 

view of the model attachment components (figure 7) reveal some 

construction details. 

The airfoil model is supported at each end by drag links 

Wh1Ch extend forward to pivot axes on the C-frame mount1ng 

fixture wh1ch attaches to the turntable. When the drag llnks are 

configured as a four-bar parallelogram, the plunge mode exh1bits 

pure translation. Also, to enable simulat10n of the bend1ng mode 

of a swept back wing, two forward knife-edge pivot locat10ns are 

ava1lable, as shown at the top of f1gure 5. To minimize friction, rotational bear1ngs throughout the system are e1ther 

cross-beam flexures or knife edges. 

Plunge mode stiffness and 11ft balanc1ng forces are provided by cant1levered leaf springs located above and below the model 

on either side of the test section. These springs are connected 

to the model by means of slngle-strand wires. (It was found that 

braided wire cable produced excessive damping.) The lower spr1ng 

set with two springs on each side, is designed to counteract 

a1rfo1l 11ft and the upper spr1ngs serve to mainta1n tens10n in 

the system. These springs, as well as those used for the pitch 

mode, are made of lam1nated f1berglass sheet stock w1th constant 

th1ckness and tapered planform. Some s1gn1ficant benef1ts 

offered by the use of fiberglass over other candidate spring 

materials are discussed later in the paper. 

To implement the compound-spring concept 1llustrated earlier, the compression spring (K1 in sketch A) takes the form of 

an elastically deformed beam supported at the center by a 

compression link and loaded at each end by threaded tension rods 

with nuts as shown in figures 5 and 6. The compression force, 

and consequently the plunge-mode frequency, is proportional to 

the number of turns of the nuts used to deform the compression spring. 

To suppress flutter, quick-acting snubbers are provided 

which apply a braking force to the plunge mode via the pretension 

8 
wires. 

The pltch sprlng stlffness and statlc balanclng moments are 

lmparted to the model through a pltch arm connected by tensl0ned 

Wlres to the maln pltch sprlngs and pre-tensl0n sprlng as 

lndlcated In figure 6. The alrfOl1 pltch shaft and cross-beam 

flexure are clamped In the pltch arm houslng, provldlng frlctl0no less rotatl0n of the alrfol1 through +5 relatlve to the mean 

angle-of-attack setting WhlCh lS controlled by the turntable 

angle. 

Self Allgnrnent Control System 

The suspensl0n system lS equlpped wlth a dual mode control 

system. The control system may be operated In elther a manual 

mode, allowlng full manual control over alrfol1 pltch and plunge 

posltlon, or In automatlc mode WhlCh automatlcally malntalns the 

alrfol1 In a prevl0usly establlshed neutral posltl0n. The 

alr£011 is posltloned and balanced In the neutral zone by means 

of two 1500 lb. 11near electrlc-motor-drlven actuators. Each 

actuator has a four-lnch stroke WhlCh provldes capablilty for 

alrfoil pltch varlatl0ns of +1/20 and plunge variatl0ns of 

+0.5-lnches. Each actuato~ 18 lnde?endently controlled and 

operated Vla a control box. The actuators also malntaln posltl0n 

by counteractlng the statlc 11ft and pltchlng alrloads. Detal1s 

of the control box, control panel layout, and complete Clrcult 

dlagram for the control system electronlcs are contalned in 

Appendlx B. To avold the addltl0n of damplng, non-contactlng 

optlcal sensors are used to sense the alrfol1 posltlons. The 

OptlC sensors are operatlonal In auLomatlc mode and provlde 

slgnals to engage the approprlate actuator and drlve the alrfol1 

back to the neutral posltl0n. The contro] panel lndlcators, also 

operatl0nal In automatlc mode, lndlcate general alrfoll posltlon 

and operatl0nal status of actuators. Foul 11ghts are provided to 

slgnal the alrfol1 contactlng the stops. Foul lndlcators are 

operational In elther manual or automatlc modes. 

The control box contalns the snubber actuatl0n sWltch and 

snubber lndlcator 11ght. The snubber lS provided as a manual 

flutter suppressl0n system. 

Sprlng Deslgn 

A considerable number of englneerlng trade-off studles were 

made to determlne the sprlng deslgn and materlal propertles best 

sUlted to satisfy confllctlng requlrement regardlng stlffness, 

st~ength, welght and statlc deflection. These studles led to the 

selectlon of a unlformly stressec cantllevered leaf sprlng havlng 

constant thlckness, 11nearly tapered planform, and loaded at the 

tip. For a given length and base dlmensl0n of the sprlng, the 

thlckness requlred to provlde a speclfled sprlng constant was 

determined by 11near theory In terms of the bendlng modulus of 

9 
elast1c1ty of the spr1ng mater1al. Spec1f1cat10n of a static 

app11ed load at the end of the spr1ng then def1nes the stress. 

Figure 8 shows results of calculations of the var1at10n of stress 

w1th bending modulus of elast1city for g1ven spr1ng st1ffnesses. 

These results are also for the 2.5 pound suspended mass and 800 

pound 11ft cond1t1on cons1dered 1n ear11er examples. The 

suspended mass and lift load 1S assumed to be equally shared by'a 

set of four plunge spr1ngs, the length and base w1dth of wh1ch 

are 11 1nches and 2.5 1nches. The fam11y of curves 1n f1gure 8 

are presented 1n terms of plunge-mode frequenc1es and spr1ng 

thicknesses for PIP = O. Trends shown 1n f1gure 8 obv10usly 

pOlnt toward the se1..ectl0n of a low elastlc modulus, hlgh 

strength spr1ng mater1al. For the present des1gn the cho1ce was 

laminated flberglas6 sheet stock having a modulus of elastlclty 

of about 3.5 x 10 psi and an ult1mate stress of 80,000 pS1. 

Also shown in figure 8, for comparison, 1S stainless st~e1 spr1ng 

mater1al w1th a modulus of elastlclty of 30 x 10 PS1 and 

ultlmate stress of 155,000 pS1. 

Instrumentatl0n 

Pretension sprlngs are 1nstrumented wlth stra1n gauges to 

enable the measurement of pltch and plunge mode deflect1ons. In 

add1t1on, a more sens1t1ve measure of a1rfo11 p1tch angle 1S 

obta1nable Vla a metal11c film potent1ometer connected 1n a 

br1dge C1rcu1t to sense mot1on of the pitch arm. The mean normal 

force and pitchlng moment loads on the airfol1 are mon1tored by 

means of stra1n-gauged r1ng-type load cells installed 1n the 

pltch and plunge spring cables. 

LABORATORY TESTS 

Proof Load Test 

To demonstrate the structural 1ntegr1ty of the suspens10n 

system, proof load tests were performed at 120% of des1gn load 

condlt1ons. The load1ng f1xture cons1sted of a metal-beam frame 

wh1ch duplicated the w1nd tunnel structure 1n the v1c1n1ty of the 

turn tables and other system tle down pOlnts. A metal loadlng 

pad, bonded to the undersurface of the a1rfo1l model, was blocked 

from beneath by a spanwlse roller PlvOt at mld chord. US1ng the 

plunge-mode actuator, a vert1cal force was produced at the 

airfoil pitch aX1S (15% chord) and reacted by an 0ppos1ng "11ft" 

force acting at the m1dchord. Several structural weaknesses 

were d1scovered and corrected dur1ng load bU11d up, after 

wh1ch the suspenS10n system successfully w1thstood the 1000 

pound maximum s1mulated 11ft load. 

St1ffness Measurements 

10 
P1tch and plunge stiffness measurements were obta1ned by 

applying an upward force at the a1rfoil mid chord and measur1ng 

the resultant p1tch angle and vertical d1splacements relative to 

the neutral pos1t1on. Some typ1cal results from such measurements shown in f1gures 9 and 10. For the plunge mode, (figure 9) 

the vertical deflect10n due to vertical force is glven for three 

compression force ratios: pip = 0, 0.37, and 0.75. Also shown 

for compar1son w1th the measu~ed data are predictions based on 

theory (see equat10n 5 1n Append1X A.) Note that both theory and 

exper1ment ind1cated a tendency toward increas1ng stiffness 

for spr1ng deflections greater than about 0.25 inches. The 

maX1mum plunge deflection 1S Ilm1ted by mechanical stops set 

at + 1/2 1nch. 

Pitch-mode st1ffness character1st1cs are presented in Figure 

10. Over the 00 to 20 p1tch angle range of the test, the variat10n of pitch angle w1th applied moment is essentially linear and 

1nsens1t1ve compressive force ratios. 

Modal Character1st1cs 

To determ1ne modal frequency and damp1ng character1st1cs of 

the suspens10n system, frequency response functions were measured 

uS1ng a dig1tal modal analyzer and impact testing techn1ques. 

The a1rfo11 model was tapped w1th an 1nstrumented hammer and the 

accelerat10n response measured. 

Some typ1cal frequency response measurements obtained on the 

suspens10n system are shown 1n f1gure 11. Note that as the 

spring compress1on force is increased from zero to 87% of its 

cr1t1cal value, the plunge mode frequency decreases from 28.5hz 

to 11.6hz. Also, damp1ng of the plunge becomes more pronounced 

w1th increas1ng compress1on force. Exper1ence w1th the system 

has shown that there is an upper practical limit for the compress1ve force above which the plunge mode ceases to behave as a 

llghtly damped slngle degree-of-freedom s stem. This usuall~ 

occurs 1n t e V1C1n1t of P P 0.8 to 0 9. The pitch-mode 

frequency and damp1ng, on the o~ er hand, is unaffected by such 

changes. 

The change 1n plunge-mode frequenc1es ind1cated by the frequency response funct10ns (f1gure 11) is plotted in f1gure 12 as 

a function of the compress1on force rat10 Pip. Also plotted are 

s1m1lar results obta1ned using a stiffer se~ of plunge springs 

which provide a maximum frequency of fh = 37.4hz. The predicted 

curve shown 1n f1gure 12 is seen to D~ in reasonable agreement 

with the measured results. 

Self Alignment Control System 

The self al1gning control system funct10ns to mainta1n the 

11 
alrfoll's ve~tlcal posltl0n and pltch. angle wlthln prescrlbed 

bounds for changlng mean aerodynamic load condltlons. The 

accuracy of positlon control depends upon the width of the 

deadband setting within WhlCh the Optlc positlon sensors are 

inactive. The choice of a sUltable deadband setting lnvolves 

trade-offs between positloning accuracy and stable operation. 

The smaller the deadband the better the accuracy. Howev&r, 

should the deadband become too small the control system will 

encounter limit cycle oscillations. 

To evaluate the performance characterlstics of the selfalignment control system, the transient response of the system 

following the abrupt release fa a lOa-lb. normal force actlng at 

the alrfoil midchord (pitch aX1S at 1/4 chord) was measured. 

flgure 13 shows sample tlme histories of pitch and plunge motlon 

as the actuators drive the airfoil back to ltS lnitlal trlmmed 

state. TYPlcally, the control system malntalns steady state 

alignment of the airfoil with accuracies better than +0.1" 

plunge deflection and + 0.1 degrees pitch angle. 

CONCLUDING REMARKS 

This paper has described a flutter model suspenslon system 

deslgned to enable systematlc lnvestigatlons of pitch/plunge 

flutter characterlstlcs of two-dlmenslonal alrfolls ln the 

Langley 6-by 28-1nch transonlC wind tunnel. Also descrlbed were 

the MBB-A3 alrfoil models to be used to obtain flutter stablllty 

boundaries and statlc pressure distrlbutlons. 

The suspenslon system deslgn approach lntroduced a compound 

sprlng concept WhlCh slmultaneously meets requlrements for 

relatively low plunge mode stiffnesses, 11ghtweight suspended 

models, and large steady lift force due to angle of attack whlle 

keeping the static deflections of the plunge spring within 

reasonable 11mlts. The system features pitch and plunge frequencies that can be varled over a wide range, 11ghtweight moving 

masses needed to slmulate the mass-alr denslty scallng parameter, 

changeable alrfol1 rotatlon axes, and a self allgning control 

system which malntains posltion of the airfol1 ln test sectlon 

under changlng airloads. In addltl0n, PlvOt axes ahead of the 

alrfol1 are provided so that the bending motions of sweptback 

wlngs can be simulated by the airfol1 plunge mode. 

It is antlclpated that thlS alrfol1 flutter testlng apparatus will provide a research tool to enable better understandlng of the transonlC flutter behavl0r of the MBB-A3 and 

other supercritical airfoils to follow. 

12 
APPENDIX A: Derivat10n of Compound Spring Equations 

L 

i 

Compound Spr1ng System 

The compound spring system shown 1n the sketch cons1sts of 

rigid members AB and BC that are h1nged at p01nt B and subJected 

to compressive force P due to compreSS1on of the horizontal 

spring K. Let L be the vert1cal force (llft) acting at B 

required to displace B at d1stance z. Th1s movement is resisted 

by the stretching of spring Ko but 1S ass1sted by forces in the 

compression links as they become incl1ned upward. In other 

words, the compreSS1on links act as negative springs in opposition to the restoring force of spr1ng Ko. 

Assume z to be small relat1ve to the length of members AB 

and BC. P Band PBC are the aX1al forces in links AB and BC 

necessary to balance the vert1cal component of compression force 

P in spr1ng K . 

The total axial reaction force 1S then 

L = zKo + PAB + PBC 

= ZKo - P(z/rl ) - P(z/r2 ) 

where 

P = P 0 + K 1 l [ (1 + e) - ( r 1 It + r 2 I l ) ] 

Subst1tut1ng equat10ns 3 1nto 2 

13 

(1) 

( 2) 

(3) 
s~nce 

1 I 2 2 ~e - (zl1) 

equat10n 4 can be wr1tten 

L = Kg - z 11 ~ 0 - K 11 (1 + e - ~ e 

2 - ( z 1\ ) 2 - ~ 1- ( z I ~) 2 ~ x 

l

- z + Z] ~e2-(z/t)2 ~1-(Z/112 (5) 

The effect1ve spr1ng constant, K , 1S obta1ned by d1fferent-

~at10n of equat10n 5 Z 

where 

+ B + C ~e2 - (z/1)2 

[1 - (z/U 2 ]3/2 

A = 1 (Ko - 2 K 1 ) 

B ~ K1l(1 + e) - Po 

c = -K 1 1 

2 C (z /1 ) 2 

(6) 

The effect1ve spring constant for the system when the 

external load is counteracted by the static deflect10ns of K is 

o obtained by sett1ng Z = 0 In equatl0n 6 

K zoo = K - P /1 (1 + e ' )' e 

(7 ) 

When K = 0 the system has neutral statlc stablllty, thus 

the rltlcll compresslon force, P f above WhlCh the system 

becom~s statlcally unstable, may be d~termined from equat10n 7 by 

letting K = z= 0 and solv1ng for Po = Pc to obtaln 

z 

(8 ) 

Thus, the effective stlffness for the compound sprlng system 

In ltS neutral posltl0n becomes slmply 

( 9) 

14 
or in terms of the uncoupled plunge mode frequency 

fh = _l-J~ 21t' m 

therefore 

15 

(10) 

(11) 
...... 

0\ 

PLUNGE 

APPENDIX B: Self Alignment Control System 

I kll 

uP 

511/$ORO.4 

, .ftlTTU 

Ik~ 

I 

r*~ ~ r L oJ , 

L '"i: __ 

'Nlnll lUI"'" 

Ik~ 

OJP J ~[NSOI , .. ,"U, 

, " 

WI RI NG DIAGRAM 

10 k.o. 

4 

., .. " .. rj~ 

DOWN' RElA Y 

1200.0. 

, 

'FOLll uP 

= REO 1. 

18 

DO"''''' 

'OUL 

SW'IT(." 

2200.n 

, ~ 

'F"OI.H DOWN ..1- REO -

PITCH +15 V "0 

22.00.0. 

o Sensor plug 

o Relay box plug 

All resistors ~ W unless specified 

All transistors 2N2222 

no Normally open 

nc Normally closed 

I..., 

680.(\ , k.(\ 

.. - G.RE.( N !

-

I ':-

L ~ oJ 22.U. ::fOUL uP 

~ yO 

) ../ 

110(1\ ~IOK.n 

oow. 

SENSOR r 

, 

. .. ,'". 

~ , 2 r ~ ,OIrHrO" 

, l j 

POWER SUPPL Y 

681\ 

--------- "OVA' ~~c o!I ..,.'" 

.8 VAC 

2 AMP 

L J ~ 

00"''' 

22K.(\ 16000P---

S NJBBER 

ON 

-----~/ 

• IS V 

MOM 

ON 

~.D 

-= 

"2200.0. 

, RI.O 

:: ~OUl Dowl\t J 

SNUBBER RELAY 

RED 

SNUBBER 

-= 
CONTROL PANEL 

up foul 

power 

0 red 

up 

PITCH 0 yellow 

up fJ off 0 green snubber down 

light 0 yellow 

snubber off 

switch momentary on 0 red neutral 

on 

manual 

down 

down foul 

Power Button: Activates the control box. 

Automatic/¥~nual Switch: Transfers the system from manual to optic sensor 

automatic control. 

Pitch and Plunge Switches: Are used only in the manual mode. SWitching plunge 

up - drives airfoil up; plunge down - drives the 

airfoil down; pitch up - increases the angle of 

attack; pitch down reduces the angle of attack. 

Indicator Lights: Shows the status of the airfoil. Illum1nation of the red 

lights indicates that the airfoil is against the stops, 

green lights indicate that the airfoil is in the neutral 

position, and yellow lights indicate that the actuator is 

driving the airfoil toward the neutral position. 

Snubber SW1tch: Activates the snubbers which damp vibrations. The snubbers 

may be activated in momentary bursts (the upper switch 

position) or continuously (the down switch position.) 

17 
REFERENCES 

1. Farmer, Moses G.i Hanson, Perry W.; and Wynne, Eleanor C.: 

"Compar1son of Supercr1t1cal and Convent10nal W1ng Flutter 

Character1st1cs." NASA TM-72837, 1976. 

2. Houw1nk, R.i Kraan, A. N.; and Zwaan, R. J.: "A W1nd-Tunnel 

Study of the Flutter Characterist1cs of a Supercr1tical 

Wing." AIAA Paper Number: 81-0651, 1981. 

3. Ashley, H.: "Role of Shocks in the 'Sub-Transonic' Flutter 

Phenomenon." Journal of Aircraft, Volume 17, Number 3, 

March 1980, pages 187-197. 

4. Dobbs, S. K.; Miller, G. D. i and Stevenson, J. R.: "Self 

Induced Oscillations and Wind Tunnel Tests of a Var1able 

Sweep Wing." Presented at the AIAA/ASME/ASCE/AHS 26th 

Annual Structures, Structural Dynamics, and Materials 

Conference, Orlando, Flor1da, April 15-17, 1985. 

5. Yates, E.C., Jr., Wynne, E.C., and Farmer, M.G.: "Measured 

and Calculated Effects of Angle of Attack on the Transon1C 

Flutter of a Supercritical W1ng", Proceedings of the 

AIAA/ASME/ASCE/AHS 23rd Annual Structures, Structural 

Dynamics, and Materials Conference, New Orleans, Louisiana, 

May 1982, pages 122-144. 

6. Edwards, J.W.; Bennett, R.M., Wh1tlow, W., Jr., and Seidel, 

D.A.: "Time-Marching Transonic Flutter Solutions Including 

Angle-of-Attack Effects", Proceedings of the AIAA/ASME/ 

ASCE/AHS 23rd Annual Structures, Structural Dynamics and 

Materials Conference, New Orleans, Lou1siana, May 1982, 

pages 220-233. 

7. Ladson, C.L.: "Description and Calibration of the NASALangley 6- by 19-inch Transonic Wind Tunnel. NASA TN D-7582, 

1973. 

8. Ladson, C.L.: "Descr1ption and Cal1bration of the NASALangley 6- by 28-inch Transonic Wind Tunnel". NASA TN D8070, 1975. 

18 
9. Bucciantini, G.; Oggiano, M.S.; and Onorato, M.: "Supercritical Airfoil MBB-A3 Surface Pressure Distributions, Wake 

and Boundary Condition Measurements." Report of the Fluid 

Dynamics Panel Working Group 04, AGARD Advisory report 

Number 138, May 1979. 

10. Molyneux, W.G.: "Design of Non-Linear Supports for Vibration Isolation of Very Low Frequencies." The Engineer, 

Volume 211, Number 5501, June 1961. 

19 
TABLE I: Static Pressure Orifice Locations pn MBB-A3 Airfo1l Models 

6.0 j 2. 8---'~~ 1 ... ,,"----2 .8 --

Upper Lower 

Surface ~ / Surface 

6 .0 

I 

AIRFOIL PLANFORM 

ORIFICE LOCATIONS 

Upper Surface Lower Surface 

Press. Tap Dist. From Press. Tap Dist. From 

No. L.E. , IN No. L.E. , IN 

1 0 21 5.40 

2 .15 22 4.80 

3 .30 23 4.20 

4 .60 24 3.60 

5 1.20 25 3.00 

6 1.50 26 2.40 

7 1.80 27 1.80 

8 2.10 28 1.20 

9 2.40 29 .60 

10 2.70 30 .30 

11 3.00 31 .15 

12 3.30 

13 3.60 

14 3.90 

15 4.20 

16 4.50 

17 4.80 

18 5.10 

19 5.40 

20 5.70 

20 
TABLE IIa: MBB-A3 Uncambered Airfoil Coordinates 

Theorectical Contour Measured Devlation x 10 3 -

x/c Y Ic YL/c Y Ic YL/c 6Y Ic D. YL/c u u u 

0.0012 0.0048 0.0048 0.0050 0.0045 0.250 0.300 

0.0021 0.0060 0.0060 0.0061 0.0051 0.050 0.967 

0.0125 0.0128 0.0128 0.0130 0.0125 0.280 0.250 

0.0275 0.0174 0.0174 0.0177 0.0172 0.350 0.016 

0.0375 0.0195 0.0195 0.0197 0.0194 0.250 0.083 

0.0541 0.0223 0.0223 0.0225 0.0222 0.180 0.050 

0.0761 0.0254 0.0254 0.0255 0.0253 0.117 0.050 

0.1055 0.0289 0.0289 0.0289 0.0288 0.067 0.067 

0.1602 0.0342 0.0342 0.0343 0.0341 0.067 0.067 

0.2172 0.0384 0.0384 0.0385 0.0384 0.050 0.000 

0.2655 0.0411 0.0411 0.0411 0.0411 0.033 0.016 

0.3919 0.0442 0.0442 0.0442 0.0444 0.017 0.200 

0.4929 0.0423 0.0423 0.0422 0.0424 0.033 0.150 

0.5964 0.0360 0.0360 0.0362 0.0363 0.117 0.267 

0.6478 0.0318 0.0318 0.0319 0.0321 0.113 0.317 

0.7030 0.0267 0.0267 0.0269 0.0271 0.183 0.430 

0.7905 0.0183 0.0183 0.0186 0.0190 0.317 0.730 

0.9078 0.0080 0.0080 0.0086 0.0088 0.583 0.817 

0.9668 0.0034 0.0034 0.0036 0.0041 0.283 0.730 

1.0000 0.0008 0.0008 0.0003 0.0010 0.483 0.250 

21 
TABLE lIb: MBB-A3 cambered Airfoil Coordinates 

Theorectical Contour Measured Deviat10n x 10 3 , 

X/c Y Ic YL/c Y Ic YL/c 6Y Ic 6.YL/c 

u u u 

0.0012 0.0070 0.0072 0.217 

0.0021 0.0088 0.0897 0.167 

0.0075 0.0057 0.0060 0.267 

0.0125 0.0186 0.0189 0.317 

0.0225 0.0088 0.0089 0.050 

0.0275 0.0252 0.0255 0.283 

0.0325 0.0102 0.0102 0.033 

0.0375 0.0282 0.0286 0.330 

0.0480 0.0118 0.0119 0.117 

0.0541 0.0322 0.0325 0.350 

0.0681 0.0136 0.0139 0.230 

0.0761 0.0364 0.0367 0.350 

0.0947 0.0160 0.0163 0.230 

0.1055 0.0408 0.0411 0.350 

0.1602 0.0468 0.0215 0.0471 0.0218 0.280 0.217 

0.2172 0.0513 0.0256 0.0515 0.0258 0.230 0.230 

0.2655 0.0539 0.0283 0.0541 0.0286 0.220 0.267 

0.3919 0.0568 0.0316 0.0570 0.0320 0.230 0.350 

0.4927 0.0553 0.0293 0.0554 0.0296 0.100 0.330 

0.5964 0.0497 0.0224 0.0498 0.0229 0.150 0.483 

0.6428 0.0453 0.0183 0.0455 0.0189 0.180 0.530 

0.7030 0.0394 0.0140 0.0394 0.0147 0.830 0.630 

0.7905 0.0283 0.0082 0.0288 0.0088 0.450 0.567 

0.9078 0.0134 0.0026 0.0142 0.0033 0.820 0.650 

0.9668 0.0059 0.0008 0.0067 0.0013 0.850 0.467 

1.0000 0.0016 0.0000 0.0021 0.0015 0.517 0.150 

22 
Table III: System Weights and Inertias 

AIRFOIL MODELS 

MBB-A3 MATERIAL dlc Wt. , 

AIRFOIL lb. 

Cambered Steel .449 2.837 

Symmetrl.c Steel .445 2.782 

Cambered Graphite .292 .451 

Symmetric Graphite .292 .442 

SUSPENSION SYSTEM 

Effectl.ve moving weight = 2.13 lb 

Inertia about pitch axis = 2.20 lb-in2 

23 

Icg 2 lb-l.n 

6.000 

5.930 

.675 

.668 
Dynamic 

pressure, 

psf 

600 

500 

4000 

3000 

2000 

1000 

.2 

Figure 1: 

Stagnation 

pressure, 

psi 90 

6" x 28" tunnel 

6" x 19" tunnel 

1.2 

Dynam1c pressure capabilities of the Langley 6-by 28-inch 

transonic blowdown wind tunnels. 

24 
N 

V1 

Dynamic pressure, 

psf 

4000 fo(, hz 50 60 70 80 90 

3000 

2000 L 

>-

r---- -

1000 

i------------

I 

r 

o L--~-to_--L---_tO--- ~--

f

h , hz 

100 

I 

30 - z!o 

6" x 28" tunnel 

t 

T 

6" x 19" tunnel 

t 

Figure 2: Flutter boundaries predicted for the MBB-AJ ca~bered airfoil model for: 

H = O.R, 0(= 1.00 ,).1.= 100, !t; chord pitch axis 
N 

'" 

PLUNGE ~ODE SHAPES OF 2-D AIRFOIL SECTIONS 

< I::. =. :::-

I 

I 

I 

I 

I 

I 

I 

I 

elastic axis 

straight wing 

forward 

pivot 

I 

I / 

:1 

--1::::::~ 

I 

I 

first bending r- ---/ ( , I 

typical section 

node line ~ 

~ elastic axis 

f 

\ 

\ 

sweptback wing 

Figure 3: 2-D airfoil representation of bending modes of straight and sweptback wings. 
N 

--.. 

Static deflection, 

inches 

Lift 

40 -

30 

j 1 s" 

20 

Lift 

10 

o ___ L ~ IE" -- b 101 

I 2 

I 

o 30 I 40 

Plunge frequency, hz 

Figure 4: Static spring deflection required to counteract 800-lb steady lift on 2.5-

lb. suspended mass for single-spring and compound-spring suspension systems. 
N 

00 

FLOW ;>-

PITCH 

PITCH SPRING 

CLAMP 

SIDE VIEW 

ALTERNATE FORWARD 

PIVOT ASSEMBLIES 

PRETENSION 

PLUNGE SPRING 

PITCH AXIS FLEXURE 

COMPRESSION LINK 

2 DIMENSIONAL AIRFOIL 

COMPRESSION SPRING 

- THREADED ROD 

L 

PRETENSION 

PITCH SPRING 

=::::::::::::::::::::Ct::: 

PLUNGE SPRING 

CLAMP 

I 

~ 

F1gure 5. P1tch/plunge a1rfoil flutter suspensions system 1nstallation in the Langley 

6-by-28 1nch transonic tunnel 

" " " I' 

" 

FRONT VIEW l 

SLOTTED 

CEILING 

AIRFOIL 

PITCH ARM 

SLOTTED 

FLOOR 
pitch 

spring 

Pretension spring 

~ 

\ 

Plunge 

Figure 6: Plunge mode 1 

29 

arrangcment 

COIiipression force 

adjustment nut 

ssion spring 

Turntable 
w 

o 

pre tens~on 

t r 

pltch,. ~ 

spnng :;;;5 -" ... d 

plunge 

pitch flexure 

~ plunge spring 

F~gure 7: A~rfo~l model attachment deta~ls 

l~nk 

" " 

6" x 6" a~rfo~l 

pre tension 
200 

150 

stress, ks~ 

VJ 

...... 

100 

50 

"Ultimate stress 

I 

T 

sta~nless 

1 

I 

I 

I 

I 

I 

steel--........... .1 

0.175 

0.20 

0.25 

0.30 

0.40 

0.50 

~~~~~~;:==~~----io----~'----3300 ~II 6 x 10 I 

20 , ~ .~ I 

Modulus of elast~c~ty, E, ps~ 

t, in 

1 111n -4 ~::=JJ~1n 

stat~c load 

t 

in 

F~gure 8: Plunge spr~ng des~gn curves. 
W 

N 

force, lb 

200 

160 

120 

80 

40 

P/Pc 

theory (eq. 5) 

o 0 A measured 

0.37 

0.75 

0.1 0.2 0.3 0.4 o 

Deflection, In. 

Figure 9: Plunge mode stlffness characteristlcs. 
Pitch Moment, 

in-lb 

240 

PiPe 

0 0 

00.37 

200 !-- 00.75 

160 

120 

80 

40 

o 

o 

J!,.r----+6.-r"4 -----*""6 .""""9 ---+-1."""2 ----I-i.~6 ----.It 0 

Pitch angle, deg 

Figure 10: Pitch-mode stiffness characteristics. 

33 
Magnitude 

o 

mode freq. hz 

plunge 28.5 

pitch 17 .0 

PiPe = 0 

50 

Frequency, hz 

damping I 

t 

0.737-

0.37% 

I 1 t 

100 o 

Figure 11: Suspension system frequency response measurements. 

I 

mode freq. hz 

plunge 24.5 

pitch 77 .0 

PIPe'" 0.28 

50 

Frequency, hz 

damping 

0.607-

• 0.377-

100 
1.0 

.8 

.6 

.4 

.2 

o 

.2 .4 .6 

PIPc 

fo = 37.4 hz 

fo = 28.5 hz 

theory (equation 1) 

.8 

Figure 12: Plunge frequency variation with spring compression 

force ratio. 

35 

" 1.0 " " 
W 

0\ 

Plunge 

deflection 

Pitch 

deflection 

--.--1 

0,5" 

~~- -- --

T-' 

I 

7.00 V ~ 

I-t -~ 

o 0.8 

I 

---

----

- --

I T 

~ "-.. 

1.6 2.4 3.2 

Timet sec 

Figure 13: Response of self-alignment system after release of 100-lb lift load acting 

at midchord. (Pitch axis at 1/4 chord) 

4.0 
Standard BlblJographlc Page 

1 Report No t 2 Govemmeut A~OD No 3 Reclpumt'. Cataloc No 

NASA CR-177998 

4 TItle aud SubtItle 5 Report Date 

An Airfoil Flutter Model Suspension System October 1985 

to Accommodate Large Static Transonic Airloads 6 Performmg OrgaDlJlatlon Code 

7 Author(s) 8 Performmg Orgamsatlon Report No 

Wilmer H. Reed. III D-8402-3 

9 Performmg Orgamzatlon Name and Addrme 10 Work Umt No 

DEI-Tech, Inc. 11 Contract or Grant No 

11838 Bunker Boulevard. Suite 500 NASl-17686 Newport News, VA 23606 

12 Sponaonng Agency Name and Addrme 

13 Type of Report and Penod Covered 

National Aeronautics and Space Administration Contractor Reoort 

14 Sponaonng Agency Code 

Wash1ngton, DC 20546 505-63-21-02 

15 Supplementary Notes 

Langley Technical Monitor: Maynard C. Sandford - Final Report 

16 Abetract 

This paper describes a pitch/plunge flutter model suspension system and 

associated two-dimensional MBB-A3 airfoil models. The system is designed for 

installation in the Langley 6-by-19-inch and 6-by-18-inch transonic blowdown 

wind tunnels to enable systematic study of the transon1C flutter characteristics 

and static pressure distributions of supercritical airfoils at transonic Mach 

numbers. A compound spring suspension concept is introduced which s1multaneously meets requirements for low plunge-mode stiffness, lightweight 

suspended model and large steady lift due to angle of attack without the need 

for excessive static deflections of the plunge spring. The system features 

variable pitch and plunge frequencies, changeable airfoil rotation axes and 

a self aligning control system to maintain a constant mean position of the 

model with changing airload. 

17 Key Words (Suggested by Authors(.» 18 Dl8tnbutlon Statement 

Flutter Unclassified - Unlimited 

2-D Airfoil 

Transonic Wind Tunnel Subject Category 02 

Suspension Systems 

19 Secunty Classlf (of thIs report) 

1

20 Secunty Classd (of thIs page) 21 No ofPages122 Pnce 

Unclassified Unclassified 38 A03 

For sale by the NatIonal Techmcallnformatlon ServIce, Spnngfield, Vllpma 22161 

NASA L .... I).,. Form 6S (JUD. 11115) 
End of Document