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RESEARCH MEMORANDUM

AN EVALUATION OF A ROLLERON-ROLL-RATE STABILIZATION

SYSTEM FOR A CANABJ) MISSILE CONFIGUBATION AT

MACH NUMBERS FROM 0.9 TO 2.8

By Martin L. Mason, Clarence A. Brown, _r.,

sad Rupert S. Rock

Langley Aeronauglcal Laboratory

Langley Field, Va.

NATIONAL ADVISORY COMMITTEEFOR AERONAUTICS

WASH I NGTON

September 15, Ig55

NNACA RM L950

TECH LIBP.ARy KAFS, NM

I BW|minH 1"1143574

NATIC_AL ADVISORY CC_TTEE FCR AERONAD_ICS

RESEARCH __

AN EVALUATION OF A ROLLERON-ROLL-RATE 8TABILIZATION

FCR A CANARD MISSILE CC_FIGURA_ION AT

MAC_ N_ERS FROM 0.9 TO 2.3

BY Martin L. Nason, Clarence A. Brown, Jr.,

and Rupert S. Rock

A linear stability analysis and a flight-test investigation have

been performed on a rolleron-roll-rate stabilization system for a canard

missile configuration through a Mach number range from 0.9 to 2.3. This

type of damper provides roll _mplng by the action of gyro-actuated

uncoupled wing-tip ailerons. A dynamic roll instability pred/cted by

the analysis was confirmed by flight testing and was subsequently elim-

inated by the introduction of control-surface damping about the rolleron

hinge line. The control-surface damping was provided by an orifice-type

damper contained within the control surface. Steady-state rolling veloci-

ties were at all times less than 1 rsxlian per second between Mach numbers

of 0.9 to 2.3 on the configurations tested. After the introduction of

control-surface damping 3 no adverse longitudinal effects were experienced

in flight because of the tendency of the free-floating rollerons to couple

into the pitching motion at the low angles o_ attack and disturbance levels

investigated herein. _*_.

L , , •

I_TRCOUCTION

One of the problems frequently encountered in missile design is that

of providing adequate roll damping. This problem is primarily a conse-

quence of the predominance of low-aspect-ratio surfaces on missile con-

figurations. Very often this problem is solved by a servomechanism which

senses roll rate and actuates a control surface to give the necessary

damping. Unfortunately 3 however, these servomechanisms requlr_ missile

space and their inherent complexity tends to decrease the overall relia-

bility of the missile. Recently, a unique3 slmple_ and purely mechanical

roll damper which requires no internal ccmponents was designed for missile

applications. (See re_. I. ) Roll damping is achieved in this system by

independently actlng wing-tip ailerons with enclosed airstream-impelled

roll-rate-sensitive gyro wheels. The spin axis of the gyro wheel is

perpendicular to the plane of the wing when the aileron is in the uncle-

fleeted position. This type of roll damper is referred to as a rolleron.

A stability analysis has been performe_ on a'eanard missile configurationon which this type of roll damper was installed. In order to determine

• the validity of the analytical appr@ach adopted_ a flight investigationwas initiated and two research models were subsequently flown. Data

obtained from these rocket-model tests confirme_ the analysis an_ thus

provided a reliable design approach for rolleron-type dampers on missileconfigurations.

SYMBOLS

L

H

8

qSc

L5

rolling moment, ft-lb

rolleron hinge moment_ ft-lb.

missile roll angle, deg

rolleron angular deflection, radians

mean value of missile roll velocity 3 deg/sec

missile roll dampS, _, i_t-lb/x_L%an/sec

relleron control effectiveness parameter, _L ft-lb/rad/an

rolleron hinge-moment parameter,

rolleron control-surface damping,

loa_ disturbance in roll, ft-lb

_H ft-lb/_an

ft-lb/r /

t

!

f

m

d

Ix

IG

%

R

M

V

q

mass of rolleron, slugs

distance from missile longitudinal axis to arbitrary masspoint in rollerQn

distance from rolleron hinge line to arbitrary mass pointin rolleron

distance from missile ]'onEit_ axis to rolleron center

of gravity_ ft

distance from rolleron hinge llne to rolleron center of

gravityj ft

mass unbalance parametar, fR _d dm= mY _, slug.ft 2

moment of inertia of missile about longitudinal axis, slug-ft 2

moment of inertia of rolleron about hinge line, slug-ft 2

moment of inertia of rolleron _ wheel about spin axis,slug-ft 2

gyro-wheel angular velocity; radian/sec

angular momentum of gyro wheel, IG_G, slug-ft2---radiau/sec

half amplitude of self-sustained roll-velocity oscillation,

deg/sec

frequency of self-sustained roll oscillation, cps

Reynolds number based on missile length

Mach number

missile velocity, ft/sec

dynamic pressure 3 ib/sq ft

S

C

b

_t

damping ratio of quadratic factor

body cross-sectional area, 0.136 ft 2

body diameter, 0._16 ft

win E span, 1.75 ft

A dot over a symbol denotes a derivative with respect to time.

ROLLERON OPERATION AND MISSILE ROLL SPECIFICATION

Operating Principle

A diagrammatic sketch of the roll-control system is shown in fig-

ure i. The system consists of an aileron hinged near the leading edge,

Enclosed in the aileron is a gyro wheel with the spin axis perpendicular

to the plane of the wing in the undeflected _ileroh position. If the mis-

sile is undergoing a rolling velocity _ indicated by the arrow_ the

aileron will be subjected to a gyroscopic hinge moment K. The gyro-scopic hinge moment causes an aileron deflection which in turn creates

a rolling moment L in a direction opposite to the initially assumed

rolling velocity _. As a result, resistance to rolling is produced and

the roll damping of the missile is greater than the inherent aerodynamic

roll damping by an amount determined by the roll effectiveness of the

aileron. Obviouslyj the utility of this dsmper is determined by the

amount of damping contributed to the missile without simultaneously intro-

ducing undesirable effects on the longitudinal motion and roll stability.

Roll-Performance Specifications

The assumed roll-performance specifications of the missile configu-

ration tested herein which will serve as a criterion in evaluating the

flight-test dat_ are:

(i) Flight condition: It is "required that the missile fly at alti-

tudes from sea level to 40,000 feet and at Mach nmnbers from 1.2 to 2.5.

(2) Static characteristics: The steady-state damped roll rate must

be less than i radian per second.

_ACA _ -L55CZZ _ ,._ 5

(5) Dynamic characteristics: The rolleron system must be dynamically

stable in the sense that any" oscillatory modes present possess positive

demp_.

MODEI_

Detailed sketches of the two test vehicles employed in this investi-gat'ion are illustrated in figure 2 and photographs of the models are pre-

sented in figure 3- Model A (fig. 2(a)) differs from model B (fig. 2(b))in that a control-surface damper about the aileron hinge line has been

added to model B. A detailed discussion of the damper development

construction is included in a later section. Missile lifting and controlsurfaces are shown in figure 4. :The canard surfaces had 66° 37' delta-

wing plan forms with a modified single-wedge airfoil section of constant

thickness. Wings were of trapezoidal plan form with the leading edgeswept back 49 ° •

The experimentally measured mass, inertia, and damping characteris-

tics of each model are given in table I. Slight changes in the param-

eters IR, m, and d from model A to B were due "essentially to the

rolleron structural modifications necessary to increase the control-surface

aamping.

ROLLERON-SYSTEM STABILITY ANALYSIS

Equations of Motion

For analysis purposes it is assumed that the rolling motion isrestricted to two degrees of freedom: (I) missile rotation about the

longitudinal axis _ and .(2)control-surface rotation about the hinge

line 5. If it is further assumed that the aerodynamic forces and moments

depend linearly on the_. respective variables and that the angular momen-tum vector of the gyro wheel is essentially perpendicular to the plane

of the wing, the equations of motion may be expressed as follows._

Rolling moment:

}7-3(1)

_e m_nent:

_8 + _ + _ 57.'-_- _, _" _ _ (2)

The sign convention deflning positive directions of mmments and•angles is shown in figure _. Equatio_ (2) applies to amy one of the four

ailerons, since each is undergoing a similar motion.

Static Relationships

Solving equations (i) and (2) for the ratio o$ applied rolling

moment _ to the steady-state rolling velocity _ss. and control-

surface deflection 8ss , respectively, results in the follow_ equations:

(3)

8S S(4)

The second term on the right-hand si_e of equation (3) is signifi-

cant in that it represents the roll-damping contribution of the rollerons

to the missile and the pertinent physical quantities upon which it _epends.

Exsmination of this term indicates that the rolleron damping contTibutioni_ directly _roportio_al to the gyro.-wheel angular momentum stud the ratio

of aileron roll effectiveness _ to the aileron hlnge-mc_nt param-

eter H5.

Stability-Boundary Charts

Rewriting equations (1)-an_ (2) by uslmg operator notation gives

(6)

NACA _ L55C_

The characteristic equation is

7

where

_o_ +_D2+_ +_ =o (7)

'=2=%2 +_o_.__4_.%-

A stable roll system will exist if, a_ only if, the followingrelationships between the coefficients of the characteristic e_uatlon (7)

are satisfied. See reference 2 for a derivation of these co_itions.

ao>O

a3.>O

ala 2 - aoa 3 > 0 (Oscillatory stability boundary)

a3 > 0 (statics_b___tyb__)

The actual stability boundaries are obtained by setting the above expres-sions equal to zero.

In figures 6 to ii are shown the s_ability-boundary plots, base_upon the above stability con_iti0ns, ob_lue_ by using the measuredrolleron characteristics a_ the roll i_ia at burnout of models A

and B given in table I. Since no experi=ental data exist s_ the present

time for the aeroc_c characterlstics (_, _, a_ HS) , the char_s

were calculated with these parameters as the principal variables. Each

figure has been plotted with _ as _he ordinate and _ as the abscissa

for the estimated mi_ and maximum missile roll damping, L_ = -0.09

and -_.0 f_-ib/ra_lian/sen an_ Erro-wheel spin rates of i0=000, _0,000,

an_ _0,000 revolutions per minute; In order to indicate the effect of

control-surface damping, three arbitrary values of H_ were used in the

calculations, -O.O3_ -0.I0, and -0.25 (Tot model A only) ft-lb/radian/see,

in addition to the experimentally measured control-surface damping of

models A and B. (See table I.) The darkened area in each figure desig-

nates the values of H 5 and 16 anticipated for the operation of the

missile and was estimated from reference 3 and unpublished data. In

table II are shown estimated values of C_ s C_p 3 and Ch6 for three

Mach numbers. A slight increase in the darkened area defined by this

reference and the unpublished data was arbitrarily made to account forunknown factors.

In general, for both models A and B a stable system exists for small

values of control-surface damping if the gyro-wheel speed is sufficiently

low. As the gyro-wheel speed is Increasedj the operatlug region of the

missile lies practically within the dynamically unstable region for rela-

tively low values of control-surface damping. For higher values of

control-surface damping, stability is ach/eved on both models at the

highest gyro-wheel rates shown. _hus, for a given amount of control-

surface damping, there is an ultimate limit of wheel speed correspond/ng

with stability for mo_els A an_ B. Consequently, the steady-state roll-

damping contribution of the rolleron to the missile defined in equation (3)

is restricted by dynamic stability considerations.

The oscillatory stability boundaries drawn for the experimentally

measured control-surface damping of models A and B are shown in figures 6

to Ii by a solid line. Medel A has less than the necessary damping for

stability as evidenced by the respective positions of the oscillatory

boundary and the operating region. Adequate damping is present in model B

since the es_,lma_d operating region lies within the stable region defined

by the conditions of stability. It should be note_ that the position of

the static stability boundary is independent of the control-surface

damping and that the missile inherent roll damping L_ has only a slightr

effect on the dynamic roll stability of the rolleron system.

ROLLERON-DAMPER _ESIG_

Viscous-Type Damper

Preliminary design of the rolleron damper for model B centered on

a viscous type. In order to provide control-surface dam_in_, this device

utilized fluid in a gap between a shaft rigidly connected to the wing

and the cylindrical rolleron housing. A gap of 0.001 inch, together with

the highest viscosity silicone fluid available (106 centistokes ), provided

N

D

a control-surface damping of only -0.06 ft-lb/radisa/sec. Misallnememtproblems associated with the small gap further complicated the use ofthis device.

O_ice-Ty_e De_er

Final design of the orifice-type rolleron damper for model B is

shown in figures 12 and 13. When the rolleron is deflected, fluid damping

is obtained by restricting the flow through the two orifices formed by

an O.001-inch gap between the vane shaft rigidly fastened to the wing

and the knife edges of the veezinserts mounted inside the rolleron cylin-

drical housing. Each orifice had a design area of 0.00162 square inch}

however, no rigid control of the tolerances on the machine work for the

components was made audit% is estimated that actual orifice area plusleakage around the vane and vee-block ends varied the design value by

approximately 23 percent. The vane shaft was taper pinned to the wing

at both ands and positioning of the rolleron on the shaft was accomplished

by means of shims at each end. Leakage was controlled by conventionalO-rlng s@als. A special tool was required for installation of the vee-

inserts to maintain the proper alinement.

Selection of the viscosity of the damper fluid for this unit was

made on the basis of eliminating any spring effects due to the flexibility

of the vane shaft, since the rolleron hlnge_noment parameter N5 is the

sum of the aerodynamic and damper Imtermal spring force. In order to

simplify the rolleron installation procedure, the viscosity of the damperfluid was standardized for the four units. Other tests indicated that

the machine tolerauces employ_l were adequate for the rauge of viscosities

presently available in the silicone fluids.

Experimental Technique and Measurements

The effectiveness of the dampers was ascertained by. experimental

measurement. The laboratory test rig used is shown in figure i_. The

experimental technique was based on the following ass_tions:

(i) The rollaron motion was confined to one-degree-of-freedom

rotation about the hinge line.

(2) The rolleron, when sprlag restrained and damped, cam be repre-sented by a linear second-oxxler system.

The values of _ were calculated frem the relationship _ = _\Iv _--V_

where equaled 0.29 for all the test rums. The damping ratio

was obtaine_ by comparison of.the system translent response with typicalresponse curves of second-order systems to s_-function disturbances.

Admittedly, the final dsmper deslgned for model B is not a linear device;however, bench tests appear to validate the use of linear f/leory for

_esign _90ses ..

On the basis of laboratory tests, silicone fluid with a viscosity

of 20,000 centistokes was selecte_ as approaching the dam_ing specified.

Transient responses of the rollerons insTalle_ on model B, subsequentto an initial deflection of i0O, are shown in figure 19. The average

value of _ = -0.21 ft-lb/radian/sec, for the four rollercms meets the

damping requirements. Rolleron number 4 exhibited the least damping,probably because of larger tolerances in cons%ructicm} however, the shapeof the transient response is an excellem_ illus_ration to substantiate

the linear-second-order-system assumption. _he response of rollerc_nnumber i implies a higher order response an_ is attribute_ to closerconstruction tolerances. FurZher tests with higher viscosity flulas

aggravated this type of response, which was apparently caused by a secon_

spring constant in%reducea by a la_k of riEidity of the vane shaft.Rollerons 2 an_ 3 exhibite_ a damping ratio greater than uni_y.

Experience with the orifice damper showe_ no loss of effectiveness

due to leakage over a period of more than two months, when the _olleronsremained locke_ in the streamline position. Tests ludicated that %he

rigidity of the vane shaft shouSA be increase_ for future use of this

device if greater dampin_ is desired.

Measurements on the rollerons of mo_el A, which &id not have rolleron

dampers, obtained by using the technique _eseribed above indicated thata control-surface damping of -0.0036 ft-lb/radian/sec could be used

to represent the hinge-pln friction for purposes of roll-system stabilitycalculations.

MODEL FLIgHT-TEST TECHNIQUE

Instrumenf_tion

Model A was equipl_ with a four-ehau_el telemeter which %vansmlt%e_

a continuous record of normal and transverse acceleration, rate of yaw,

and rate of roll. Model B was e_uil_ed with a five-elmmnel telemeterwhich transmitted a continuous record of normal an_ transverse acceler-

ation, rate of yaw, rate of roll, and Erro-wheel s_ee_.

NACA RM L95C22 _ 11

5[_hemeasured response of %he instrument rate _yro "used to measure

rate of roll and rate of yaw is given below.

Rate of yaw

Rate of roll

_ndan_ed _ttu_al ,frequency,

cps

Model A

5O

,ModelB

T5

T_

Critical damping,

percent

Model A

?0

7O

Model B

In general, the accuracy of the telemetered data is approximately 2

to 9 percent of full scale if the frequemeles encountered do mot exceed

the instrument undamped natural frequency.

The model trajectory was determtued by a modified SCR _ radar

tracking unit. Model velocity _ obtained from a CW Doppler velocim-

eter. A radiosonde released at the time of flight measured atmospheric

temperature an_ pressure through the altitude range traversed by themodels.

Free-Flight a=l launch/rag Conditions

The models were boosted "to supersonic velocities by a solid-

propellant rocket motor which delivered approximately 6,000 pounds of

thrust for 3.0 seconds. A sustainer, made as an integral part of %he

models, delivered approximately 3,000 pounds of thrust for 2.6 seconds

and propelled model A and model B to peak Mach numbers of 2._ and 2.37,

respectively. Presented in figures 16 amd 17 are the flight time his-

tories of velocity, Mach number 3 and dynamic pressure for both models A

and B. Reynolds number based on body lenghh is shown plotted against

Mach number in figure 18.

Prior to the flight test of the models, the gyro wheel of the rol-

lerons on both models was given an initial rotational speed. This initial

speed given the gyro wheels tended to overcome the starting inertia and

friction of the gyro wheel and thus simu/ated more accurately an a_ual

operational missile air launch. The initial rotational speed of the

rollerons was accomplished by applying a source of air to each of the

rollerons while the model was on the launcher and allowing this air

supply to turn the rollerons until the model had move_ clear of the

launcher. Presented in figure 19 is a photoEraph of model A and boosteron the launcher showing the arraugemant used to apply the air to the

rollerons prior to firing. The launching angle was 60° with respect to

the horizontal. Gyro-wheel speed of model B is shown in figure 17.Firings of the models were conducted at the Langley Pilotless AircraftResearch Station at Wallops Island, Va.

BES_LTS AND DISCUSSION

Roll Dynamic Stability

The roll stability of the free-flight tes_ models A a_d B is clearlydemonstrated by the time history of the mo_el roll velocity shown in

selected portions of the continuous-type telemeter record reproduced in

figures 20 and 21. In the uncalibrated telemeter-record reproductions 3 therunning variable, in all cases, is time and the uncalibrate_ deflection

from an arbitrary base line represents the relative magnitude of themeasured quantities indicated. NO programmed model disturbances weregenerated during coasting; therefore, rolling maments applie_ to themissile were caused by the aerodynamic out-of-trim condltian due to model

construction asymmetries 2 gusts 3 an_ inertia coupling from other missile

modes of motion. These disturbances were apparently sufficient, since_as predicted, model A di_ reveal an inherent dynamic instability in theform of a _Ivergent oscillatory roll oscillatlon at M = 2.07. Redivergence progressed for approxlmate_y 0.4 secon_ and was immediately

followe_ by a self-sustained oscillation, characterized by two predomlnantfrequencies, which were _resen_ for the remainder of the model flight.Envelope half-amplitude and frequency plots of the self-sustained oscil-

lation (lower frequency mnde only) are shown in figure 22 for mo_el A.

In general, both the frequency and oscillation amplitude decreased with

decreasing Mach number. By integration of the roll-velocity time history_the roll-oscillation amplitude was shown to be T2.5 ° a_ M = 1.6 a_l

±5.0 ° at M = 0.6. No corrections to the roll-velocity record to account

for the ban_-pass characteristics of the ins_tation were made because

the frequencies encountered ware well below the undsmped natural frequencyof the roll-velocity instrumant.

Model B was dyn-m_e, lly stable in roll throughout the flight as

illustrated in figure 21. Since the I_ difference between models A

and B was the amount of control-surface damping, the complete elimination

of any undesirable unstable oscillatory modes can only be attribute_ to

this cause. Reexamination of the stability boundary plots for models Aand B (figs. 6 to ii) reveals the possibility of ot_er system modifications

which would have achieved stability. For exsm_le_ if the operatlng region

could have been rotated in a countarclocEwise &Erection by either an

increase in _ or a decrease in _, then stable operation would have

resulted. However t by equation (3)3 it is seen that a decrease in the

missile roll-damplng contribution would have been produced by either of

these system modifidatiomm. Obviously, the optimum design is that which

gives the greatest missile roll damping without enticing a dynamic roll

instability by operation too close to an oscillatory stability boundary.

For the missile au_ control-surface configuration investigated, the

greater the control-surface damping, the greater the gyro-wheel angular

momentum permissible consistent with stability. Since the rolleron-to-

missile roll-damping contribution was previously shown to be directly

proportional to the gyro-wheel angular mamentum, the addition of control-

surface damping was the most desirable and practical rolleron-systemmodification.

Rolleron Roll-Damplng Effectiveness

The mean roll velocities of models A and B are plotted against Machnumber in figure 23. During the self-sustained roll oscillation of

model A, the mean roll velocity is illustrated since this is the effective

rate which eventually produces rotation of the missile fram some arbitraryroll reference position. The roll damping of the missile-rolleron system

cannot be measured with the instrumentation employed because the applied

rolling moment is unknown. Nevertheless, these two models could very well

be considered to represent typical production missiles and since the

steady-state roll rate is within the assumed roll specifications, the rol-lerons apparently did provide satisfactory roll damping. Theoretical

estimates of the missile-rolleron combination roll damping indicate a

fivefold to tenfold improvement over the inherent missile aerodynamicroll.damping without rollerons.

Model A exhibited a significant increase in subsonic roll rate which

w_s not present in model B. The reason for this effect is unknown; how-ever, roll velocities on the order of 190 degrees per second to 200 degrees

per second are not unusually high for missiles of this type on which no

quality control of the minimization of out-of-trim rolling moment duringmodel construction was undertaken. Because of this situation and since

the gyro-wheel speed of model A was not measured, a comparison of theroll dampin_ of models A and B on the basis of the measured roll rate isnot valid.

Rolleron Gyro-Wheel Speed

The gyro-wheel angular velocity is plotted against Mach number for

model B in figure" 23. The magnitude obtained on the flight test was of

the order anticipated and did not exceed the maximum design estimates.

A peak angular rate of approximately 4_O00 revolutions per minute which

corresponds to a peripheral gyru-wheei velocity of 590 feet per second

resulted. No meaningful correlation of the gyro-wheel speed with mis-

sile forward velocity is _ossible which woul_ allow a designer to predict

transient (as in this flight) or steady-state wheel ra_es under a dlf-

•ferent set of flight and launching conditions. This is primarily a

consequence of the unavoidable and somewhat complex interdependence of

gyro-wheel aerodynamic and bearing friction torques as well as initial

conditions on the missile forwar_ velocity an_ E_ro-wheel angular speed.

Rolleron Longitmd/nal _stics

_alitative information was obtained on the longitu_inal effects of

the rollerons from the normal- and transverse-acceleration time histories.

Mo_el A exhibited a s_newhat spa_ic variation of normal an_ transverse

acceleration with time during the self-s_sT_Ined roll oscillation, which

was at all times less than 2g. (See fig. 20.) A pitch frequency that

was approximately equal to the higher of the two predc_inant roll fre-

quencies discernible was detectable on the record. Apparently, coupling

between the roll and pitch modes was in evidence. Model B was subJecte&

to a slight d/sturbance near sustainer-roc_et-mo_or burnout. (See

fig. 24. ) The source of this disturbance is not _nown but it may have

been produced by uneven rocket-propellant burning. Two well-_efine_

pitch frequencies are present on the recor@ 2 the m-Y_ normal accel-

eration being less than 6g. _ oscillaT_ry modes are stable and

possess adequate damping. A theoretical lon_Lt_zdinal-stability study

of free-floating pitch-control surfaces s reporte_ in reference 4, pre-

dicts the presence of these two oscill_tory modes. Although the arrange-

ment of the control surfaces utillze_ an_ the alrfrsme investigated in

reference 4 are not identical to models A an_ B, the results obtained

therein should be indicative since the rolleron i_rro wheels remain

inactive to pitching motion for relatively small control-surfacedeflections.

CONCLUDING P_MARKS

Rollerons furnished effective roll-rate stabilization on the two

research configurations tested° The measured mean roll rate on both models

was less than i radlan per second and within the assumed roll specifica-

tions throughout the assume_ operatln_ flight co_uXitions of the missile.

An undesirably high-frequency (_0 cps) self-sustained roll oscillation,

due primarily to a dynamic roll i_stabili_y which was predictable on

the basis of linear theory, was present on the first flight-test mo_el.

_his oscillation was e]_Imlua4_l on'_he secon_ model flown by only the

introduction of damping about the h_e line of each rolleron control sur-

face. The addition of control-surface dsmpin_ not only improved the roll

characteristics but also apparently prevented the occurrence of continuous

__._ff_ '

high-frequency pitching oscillations, which were present during the

self-sustained roll oscillation experienced on the model tested withoutd_ers.

System modifications, other than the control-surface damping inves-

tigated herein, might have ellmlnate_ the objectionable high-frequency

self-sustalned roll oscillati6n but may have resulte_ in smaller steady-state roll damping of the overall missile-rolleron roll-rate stabiliza-

tion system. Fm_cher research would be necessary to establish the

advantages and suitability of other modifications. The applicabilityof rollerons to other similar missile configurations as a means of

improving the .inherent roll damping could be ascea_cained, with a fair

degree of reliability, by the stability-analysis methods employed herein

for the detection and suppression of an un_eslrable d_namic rollinstability.

Langley Aeronautical Laboratory,

National Advisory Cammittee for Aeronautics,

Langley Fiela, Vs. t March 18p i_3_.

REFERENCES

I. LaBerge, Walter B., au_ I_ter, W. Dale: Preliminary Emaluaticm

of a Simpllfie_ Roll-Rate S%ahillzation System. NAVOED Rep. 1269

(NOTS 339), U. S. Naval Ord. Test Station (Inyokern, Calif.),Jan. 8, l_l.

2. Routh, Edward John: Dynamics of a System of Rigi_ Bo_es. Part If.

Sixth ed., rev. and eml., MA_cm111-n am_ Co., LTxl., 1905, l_p. 223-250.

e Tucker, Warren A., aud Nelson, Robert I_ : Thearetical Characteristics

in Supersonic Flow of Comstaut-Ch_ Partlal-Spam Control Surfaces

on Rectangular WinEs E_vimg Finite Thickness. NACA _ 1708, 1948.

_e Curfman, Howard J., Jr., Strass, H. Kurt, au_ Crane t Harol_ L.:Investigations Toward Siu_lificaticm of Missile Control Systems.

NACA RM-L_3121a, 195_.

16 _ACA _ L_5C22

TABLE I

MASS AND Imm_F/A CHAIUk_C8

(a) socket models

Model A Model B

Take-off weight, ib ..........

Burnout weight, ib ...........Take-off mass, slugs ..........

Btuulout mass, slugs ..........

Take-ofT center-of-gravity location

(measure_ from nose), in.......Burnout center-of-gravlty locatiun

(measured from nose), in .......

Iy (burnout), slug-ft 2 .........

IX (burnout), slug-f% 2 .........

_8.91o5.o4.615.26

95.63

_9.75

31.08

0.30

149.2,,o8.94.643.)7

56-72

91.3030.17

0.30

(b) Rollermm

IR, slug-ft 2 .............

TG, slug-ft 2 .............

mj slug ........:..:.::::::::

_ ft ........

........

Model A

o.o_7o_o.0oo198

o.o_loo.77_

o.129_._36

Model B

o.ooo849

o._oe_

o. oe970.775o.148-O.21

NACAI_ L_5¢22

I

17

TABLE II

ES_ AERODYNAMIC COEFFICIENTS OF ROCKET MODELS

M

1.2

1.6

2.0

C_6

0..7_

-53

.41

-6.75

-6.61

-9.66

-0.14

-.51

-.e7

F-ro

_Ji,I>

.Jg0n-

i,i_Jm

(n00

ILl

(n00

/

._I

ztlJ

0

:E

o

\

,,-I

14

1.1.1

0

UJ_9Z

"1-

0

Q.0(_)(n0n.->-(.9

\

lJ

I=o

I"o

I

0

"O

®

_-,-I._,I_ 1_,_._j _b_

_J

CQ_

0r_

_-I a_

!

c_

q_

2O NACJLI_ L5_C22

!c_

v

f-

2qJ

"5

NA_ I_ L55022 :"-'_im1_r_2.1

i-

C)i-I0_

CDI

i-I

_ o_J f ,

j!

r_

° _

_°

m !o

l

i

l

l

!:i

rih

J

O_C_

D.--GO

fi-I

_ v_ •

¢)

d

uo

"o

oco

o

IN

-qn

N

v

4

v

I

, _D ---_ II,z

ooi

()

IB

IO

O

oc-

of.)o

c

o r-III

v

aJ

o

0

!

.-4

I1

IN

o

i!1

m

24 I_CA 1_ L_9C22

ROLL AXIS

HINGE

Figure _.- Sign convention ind/catlng positive directions

of moments an_ au61es.

NACA _ L_SC_?

Measured control-surface damping

------Assumed control-surface damping

25

_.:.:.:.:,:-:.:.:.

-300

Operating region s,o_• Unstable

c0

-200o

.a

I

_- -100

_0z

-30(

,

-I0 0 0 -500 0 500 I000

L B , ft-lb/radlan

(,_)g---0.05_-_/_u.,.,d,,ec.

1500 2000

0

-I000 -500 0 500 IO00 1500 2000

L 8 , ft-lb/radian

Figure 6.- Stabllity-bound_ry plots showing the effect of control-

surface and missile-roll damping for model A at a 8yro-wheel speed.of I0,000 revolutions _er _4uute.

. • ,4b _,

26 • llw ,

--Measured controi-s'urfoce

------Assumed aontrol-surface

_g.:-:.::_ 0 pe ro f i n g

NACA 1_ LS_C_

damping

damping

Sta_region ", " Unstable

g:0

,m

"o

z_

%.4=

Iql-

q..

A"I"

-I000 -500 0 500 IOQO 1500 2000

L 8 , ft-lb/rodlon

Ca3 _ = -o.o5 rt-zb/_=_,/,e_.

"o

L_

I

q--

A"I-

boundor

H_=-0.0036

0

-lO O0 -500 0 500 I000 1500 2000

L_ ft-lb/radiono I

Figure 7.- Stability-bou_ plots show_ the effect of control-

surface and missile-roll da=pin8 f_r =od_l A at a gyro-wheel speedof 30,000 revolutions per _Luute.

t_

NACA _H L_C22 27

Measured control-surface

------Assumed control-surface

Operating region

damping

dam.ping

St a b I_..1_'1""q " Unstable

ieta blllt

0

-I000 -500 0 500 I000 1500 2000

L 8 , ft-lb/rodion

-300

¢:o

'¢1o

.43

|4-

A

-200

-!00

0

-iO O0 -500 0 500 t000 1500 2000

L 8 , ft-ib/rodian

(b3 _ = -p.o _,-_,/_-_._,_/.e_.

-. Figure 8.- STabiliCy-_oundary :plots showing the effect of control-

surface an_ missile-roll .clamping fo_ model A at a gyro-wheel spee&

of 50_000 revolutions _er mtnu%e.

28 ___ NACA RM L55C22

Measured control-surface damping------Assumed control-surface damping

Operating regibn

o

0t.

%.

Iq-

_03:

-200

-I00

0

-I000 -500 0 500 tO00 1500 2000

L_; , ft-lb./radlan

= -o.o5

-300

c-o

oi._

m

!4--

q--

-r

-200

--I00

Hi0

-I0 O0 -500 0 500 I000 15 O0 2000

L 8 , ft-lb/radion

Figure 9-- Stability-boundary plots showing the effect of control-surface and mlssile-roll damping for model B &t a gyro-wheel s_esd

of I0,000 revolutions per minute.

NACARM L55C_ 29

-300

_Measured

_ Assumed

Operofing region

control-surface dampingconfrot-surface damping

, StabS, f"_" Unsta.l)le

t-o

"oo6

I,e-

@o:Z:

-200

--I00

-300

0

-iO00 -500 .0 500 I000 1500 2000

L 8 , ft-lb/radfan

Ca) = -o.o

Ct3

"oo

.Q

I4.-

e,

-2O 0

--I00 ;tabillty_b0undar

i=-0.210

-I0 O0 -500 0 500 lO00 1500 2000

L 8 , ft-lb/radlan

Figure I0.- Stabillty-_ou_ plots showing the effect of control-

surface and mlssile-roll dampi_ for model B at a gyro-wheel speedof 30,000 revolutions per minute.

3o NACA _ L_SC_

--Measured c0ntrol*surfo©e damping.... Assumed control- surface damping

O

"¢3

0t,.

J=

!

q-

3:

Operating region St o b_."r j U.stable

-i0 O0 -500 0 500 [0 O0

L 8 , ft-lb/rodlon

1500 2000

= -o.o

-300

0

_o -2000L

.o

!

-- -IOC

co-I-

C

-I0 O0

]_stabtlity

-500 0 500 I000 1500 20 O0

L 8 ,ft-lb/rod=an

(b) L_ = -3.0 ft-lb/rad_u/eec.

Figure ll.- Stabillty-boundary plots shu_ing the effect of control-surface and missile-roll dam_ing for model B at _ gyro-_heel sloeeclof 30,000 revolutions per minute.

h-

0

d

" __ -. o/!t----=t. o L_H[ _ l_p_--_ -._ ___

o q _ od 0 __=

o >• • t-

• . J _,

° OI

_ _ "1 , , ,

'7

oI--

EoO

cO

O

tD.Eor_

e-

ot.,o

0m

0

>

o

2

r-!

o ,,r.t

o

!

.... , , | . -- _ .........

32

e

\

!

k

0

o

I

N

•_ _-_.

iN

33

i' L

/

,el

0 _

o !-I-_ r.t

_o

I

34

• _ P'--1/60 sec . _ .

_e . _.

_j_-" I0 ° H_ =--0.,?.4T

Rolleron no. I

.. _ _ 1/60 sec

-j

<__._.--"-" I0° H_=-0.25

Rolleron no. 2 ......... '

...... "_" ........ ___. _ .'.. _ }-'-./6u.._ ,, _,.,:.:,.'b.i --

.. I 0 sec

<_/ 10° H_=--0.25-" T

.......... RoHeron no. 3= .... _"-"

.... _, _ n/6b sec-......J

/ io° _=-o.Jo

............. Rolleron no. 4-

Figure l_.- Rolleron control-surface translent resp_ses i_cati_g

damping characteristics of orifice d_er for model R.

s

................ _...... _ .................. _ .... .°

00

04 8 12 16 20

Flight time, sec

2.8

(a) _le_" A.

O

E

2.4

2.0

1.6

J= 1.2¢)

:S0.8

0.4

:_ 12004-"

o 800

>400

04 8 i2 16 20

Flight time, sec

B.

Figure 16.- Variatioh of veloci_ sm_ Mach number with flight time farmodels A an_ B.

36 NACA RM L55C22

5600

4--

N-

O"

\

0c,

d

4800

4000

3200

i

1600

800

56000 5600

4 8 12

Flight tlme, sec

(a) Model A.

16 20

48000 4800

40000 4- 4000

= 32000 = 3200

24000 _ 2400

2° °16000 _ 1600

8000el s

04 8 12 16 20

Flight • tlme, sec

(b).o_z B.

Figure 17.- Variation of dynamic pressure an_ gyro-_heel speed with flight

time for models A an_ B. @yro-wheel spee_ _e measured only on model B.

NACA RM L_C22 __ 37

ne

E

m

m

OC

o.)re

Iv"

e_

E

C

"IO

Or-

_e

120 _ 106 ....

8O

0.6 1.0

120

1.4 1.8

Mach number

(a) Model A.

2.2 2.6

8O

40

, . _

.6 1,0 1.4 .8 2.2 2.6

Mach number

(b) Hod_l B.

Figure 18.- Variation of Reynolds number, based on missile length, withMach number for models A an_ B.

_Ac__M I_SC_

L

L-82276 .I

Figure 19.- Photograph of m_lel a=l booster priur to launehlng.

.- . • .....

NACA I_ L5_C9_ "__I_ 39

I

Q

O

o

o

D

o

1;

uu

O

I

a.

o

P

o

v 4_

!

8

.,.4

_o NACA I_ L_C22

\

m

q

,t:l

r_

4_Lr_

o_

rc_

!

Oq_

_L

o

0

_L-F

a_

m

m

0

G0

0

j-

oJ

o

Er_

/\

f

f_

i

0

0 r_4_

!0

v

42

-I

s

qb-.

1-

4_h

v_

oIb_r

"v

° _u " i°E_

I-0

r,.J

q_

h.

I-

!

_ _ °.

3c

n-

i

f-

._,',

tJ

,i

,.'1

,!i;!

i!

o

°iloI

q

i,

0

Lr_

aJv

_3

W4._

,,-J

!

O,I

I

IiIH':

,!_

G0

kg

D

uO

o E

a- Z

I

LI

°t

#

-°

%

I"

°°

• _ _

o _

J_'.

.,,i

ii0:,

'I.11'| F

:.1tl

:!tl0

.l

'1'taI

'1

',J'1,,f I

t"l

i

1

.I I

'il.,

.q

II

il

';I

','i

0;!,Z

I |

. !f,"ll00

m

04_

o

I

r4

o6.

Q4--

G:

O

°im

o

oI

0

u

40

3O

6

500

1.0 1.4 !.8 2.2 2.6

Moth number

400

300

<¢

I00

0 1,0 1.4 1.8 2.2 2.6

Moch number

Figure 22.- Variation of h_If-an_litude az_ frequency of self-sustaine_roll oscillation with M_ch number for model A.

........... N ...............

t_CA _ _5C_-2

I80

160

140

120

I00

080

\

o

•" 40

20

0

-206 1.0 1.4 1.8 2.2 2.6

Mo¢h number

(s) y_xtezA.

56000

48000 120

--= 40000E

32000et

oo

24000

¢.') 16000 .

8000..e.E

80

60

4C

20

% 1.0 1.4 1.8 2.2 2.6

Moch number

(_) _z ]3.

Figure 23.- Mean roll velocity an_ gyro-wheel angular-speed variation

with Mach number for mo_els A and B. The _DTo-wheel speed was

measure_ only on model B.

NACA -maa_,y _,_. Va.

._&.._-°

• 2h. °

_.'_. .

._ -° ,e_ •

'_ ,t"

D

° •

i

4

P pC0

g

- I _U

"_ -_o E

rl: z

i

0

Qme

}';r" ,,f

o

o

_J

_o

i St

._°o