. A Reproduced Copy - NASA · related to the spln-damping properties of the tail. Previous...

A/¢5_L'£../62 ,._TT

NASA-CR-168578

fq_9_ooi1350

"_.. A Reproduced Copy• OF

///AdA EZ-/_ _-TF ,

Reproduced for. NASA

by the

NASA Scientific and Technical Information Facility

:7

FFNo 672 Aug 65

https://ntrs.nasa.gov/search.jsp?R=19820011350 2020-02-27T13:37:21+00:00Z

Unci"':.>0919S

.,"......

.. ~ ", ~~i~;:'·.~~~:-;l.~ . .,~t~';;:'.. ~':'.~~,:"j'~'~" ~'<~_,,:,,!I, ::=t~ ~'t:-·,;~:.~, .. ~3:;, ,<~rr~~)'T~:~,'-"'< ,"~t: ":~', '• ~'~." ",': .", '.V' ,

. J

-\\

.. -

(U.SA-CR-loti57U) A&I EIPl;;Ill:U.IiTAL S1UIiY 0'-'-TUE EfP£CT Of TAIL CONfIGUbA1IC~ OM ThESPIHIIU~ CHARAC1ERISTICS Of ~&dEaAL A~IAIIOHllHCBlfT ft.~. 1hcsis (f~nuhylvaDi4 ~tat~IJniv.) 181 p ilC AIl~/"F AO 1 CS'..:L 01C G)/Od

-"

.. : .

'. i: . ,~"

," :" 'J..,. "-'

\,' ...' :

. '.~

:,:,.- .". .~

. 'j

:~,

- ,

- "'_e Pennsylvania State University

The Graduate School

Depar_ent of Aerospace Engineering

An Experimental Study of the Effect ofTail Configuration on the Spinning Characteristics

of General Aviation Aircraft

A Thesis in

Aerospace Engineering

by

• Hark G. B_lltn i

Submitted In Partial _Ifillment

of the Requirementsfor the Degree of

.R_sterof Science

Mnrch1982

I grant The Pennsylvania State University the nonexcluslve rightto use this work for the University's own purposes and to make sln£1e

copies of the work available tO the public on a not-for-proflt basisif copies are not otherwise available.

m

Hark G. 5allin

J

We approve the thesis of Mark G. Ballln.

Date o£ Signature: Signatories:

c

Barnes W. McCormick, Professor andHead of Aerospace EngineeringThesis Adviser

Joseph J. Eisenhuth, AssociateProfessor of Aerospace Englneeriug

Hubert C. Smith,AssistantProfessorof AerospaceEngineering

• • .• .

iii !

ABSTRACT

Spinning characteristics of general aviation aircraft are closely i

related to the spln-damping properties of the tail. Previous

experimental studies have concentrated on obt_Inlng aerodynamic

characteristics of a complete airplane, making dynamic testing necessary

to duplicate the effects of a rotational flow field. In studies of an

isolated tail, static testing may be possible. The purpose of this

investigation is to determine the feasibility of using static wind

tunnel tests to obtain information about spin damping characteristics of ..... •

an isolated general aviation aircraft tail. A representative tall

section was oriented to the tunnel free streamline at angles simulating.

an equilibrium spin. A full range of normally encountered spin

conditions was employed. In addition, parametric studies were performed

to determine the effect of spin damping on several tail design

parameters. _e results show satisfactory agreement with NASA rotary

balance tests. Wing and body interference effects are present in the

NASA studles at stedpspin attitudes, but agreement improves with

increasing pitch angle a_d spin rate, suggesting that rotational flow•

effects are minimal. Vertical position of the horizontal stabilizer is

found to be a primary parameter affecting yaw damping, and horizontal

tail chordwise position induces a substantial effect on pitching moment.

A full-_pan rudder produces greater yawing moments than a partlal-span

rudder under steep spin conditions, while differences are small under

flat spin conditions. Correlation of yawing moments to exposed vertical

tall area is fair for steep spin =onditlons. For a flat spin, a three-

dimensional model of the separated r_<_:.onabove the horizontal tall is

necessary for an improved correlat[_,:_.

iv

T_BLE OF CONTENTS

Pa e.

A_STRACT ............................ ill

LIST OF TABLES ......................... vi

LIST OF FIGURES ........................ vii

LIST OF SYMBOLS ........................ xiii

ACKNOWLEDG-------------------_I.'TS ." ....................... xv

CHAPTER I - INTRODUCTION I

Overview of Spin Dynamics ................. iScope of the Present Testing ................ 5"

CHAPTERIf. PREVIOUS RESEARCH .................. 7

Early Studies ....................... 7The Tail Damping power Factor ............... 8Recent Free-Flight Spin Tunnel Tests ........... 12

15Rotary Balance Tests ................... '

• CHAPTERIII. EXPERI_TAL PROCEDURE .............. 18

Spin Orientations ..................... 18Model Configurations .......... ..... • •.. • 23General Experimental Design ................ 31Model Construction Considerations ............. 33

Testing Considerations ................. 39Sources of Experimental Error ............... 40Data Redu¢tlon ....................... 41

CHAPTER IV. RESULTS AND DISCUSSION .............. 43

Effects of Spin Rate on Aerodynamic Moment Coefficients . . 43Comparison with Rotary Balance Data ...... 44Effects of Horizontal Tail Vertical Position ....... 51

Effects of Vertical Tail Aspect Ratio ........... 66Effects of Horizontal Tail Aspect Ratio .......... 80Effects of the Horizontal Tail =hordwise Position ..... 90Effects of Control Deflectionr .............. I00

CIIAPTERV. DEVELOPMENT OF A PREDICTIVE PARAMETER ....... 10b ii

Adequacy of the Tail Damping Power Factor ......... II0 !

Moment Correlation with a Modified Anti-Spin Parameter . 112 Ir

• i

i!

|

vB--

I!J

i" Pa.__eCHAPTERVI. CONCLUSIONSAND RECON/MENDATIONS.......... 118

i- REFERENCES........................... 120

APPENDIXA. MODELAND APPARATUSDIMENSIONSAND CONFIGURATIONS. 122

i APPENDIXB. AERODYNAMICMOMENTCOEFFICIENTSAS FUNCTIONSOFSPIN RATE......................... 127

, APPENDIXC TESTDATA " 152I

. .

i .

lvi

q

LIST OF TA._LES

Table Page

: 3-1 Angleof Attackas a Fu,:c_ionof PitchAngleand Spin' RateforTestOrientations 22% • • • • • • • • • • • • • • • •

A-I ConfigurationDimensions .... 123

C-I ConfigurationA TestData ................ 153

C-2 ConfigurationB T.-,rData ................ 154

C 3 C fig ti D "'' 155- on ura on C Test ata ................

C-4 Configuration D Test Data ................. 156

C-5 ConfigurationE TestData ................. 157'.

C-6 ConfigurationF TestData ................ 158

C-7 ConfigurationG TestData ................ 159

C-8 Configuration H Test Data ................ i60

C-9 Configuration J Test Data ................ 161

C-10 ConfigurationK TestData ................ 162

fi t o .... 163C-II Con gura i n L Test Data ................

C-12 Configuration M Test Data . 164 •

C-13 Control Deflection Test I Data, 8 = 40°, u = 20.71° • • . 165v

C-14 Control Deflectiov Test 2 Data, 8 = 80°, a = 30.08Q . . . 166v

vii

LIST OF FIGURES

I-i Aircraft Flight Path in an Equilibrium Spin ....... 3

1-2 Balance of Forces Necessary for Equilibrium Spin .... 4

2-I Computation of the Tall Damping Power Factor ...... I0 .

2-2 Tail Damping Power Factor as a Function of IYMP,-< 15 ......................... II

2-3 General Aviation Spin Criterion Based on the TDPF (1947). 13

2-4 NASA Typical Single-Engine Genera_ Aviation Design • • • 14

2-5 NASA-LaRCRotary Balance Apparatus ..... ...... 16

3-1 Velocities Affecting Tail in an Idealized Spin ..... 19

3-2 Tall Orientation with Respect to Total Velocity Vector . 20

3-3 Configuration A ..................... 26 ,

3-4 Variation of h/bv .................... 27

3-5 Variation of Tailplane Chordwise Position ........ 28

3-6 Variation of ARv ............. • • • •-__ •.• • 29.°

3-7 Variation of ARh .................... 30

3-8 Schematic of Model and Measurement System ........ 32

3-9 Model and Support in Test Section, Configuration A;6 = 15o, _ i 25o ................... 34e r

3-10 Configuration B in Test Section ............. 35

3-11 Configuration M; Alignment Position ........... 36

3-12 Fuselage and Vertical Tail Models ............ 37

3-13 Horizontal Tail Models ................ 38

4-1 Tails Used in Comparison with NASA Rotary Balance Data . 45

4-2 Pitching Moment as a Function of O and _,Configuration C ..................... 47

viii

4-3 Yawing Moment as a Function of 8 and _,Configuration C ..................... 48

4-4 Pitching Moment as a Function of e and _,Configuration B .................. . . . 49

4-5 Yawing Moment as a Function of O and _,Configuration B ..................... 50

4-6 PitchingMomentas a Functionof VerticalPoSitionof< HorizontalTail,u - 0 ................. 52

4-7 PitchingMomentas a Functionof VerticalPositionofHorizontalTail,_ - .3 ................ 53

4-8 PitchingMomentas a Functionof VerticalPositionofHorizontalTail,_ = .5 ................. 54

4-9 Pitching Moment as a Function of Vertical Position ofHorizontal Tail, _ = .7 ................. 55

4-10 Pitching Moment as a Function of Vertical Position ofHorizontal Tail, _ - .9 ................. 56

4-11 Flow About Configurations C and D at High Spin Rate . . 57

4-12 Yawing Moment as a Function of Vertical Position ofHorizontal Tail, _ - .3 ................. 59

_- 4-13 Yawing Moment as a Function of Vertical Position ofHorizontal Tail, _ = .5 ................. 600

. 4-14 Yawing Moment as a Function of Vertical Position of

Horizontal Tail, _ = .7 ................. 61

4-15 _awing Moment as a Function of Vertical Position of

HorizontalTail,_ = .9 ................. 624-16 Yawing Moment as a Function of Horigontal Tall

Vertical Position .................... 634-17 Yawing Moment as a Function of Horizontal Tail

Vertical Position for a Flat Spin ............ 64

4-18 K as a Function of Vertical Position of Horizontal

Tail, _• .5 ...................... 67

i 4-19 Pitching Moment as a Function of Vertical Tail AspectRatio, _ = .3 ...................... 69

ix

.°

mgure• °

4-20 Pitching Moment as a Function of Vertleal Tall Aspect- 70Ratio, _ = .5 ......................

4-21 Pitching Moment as a Function of Vertlcal Tall Aspect- 71Ratio, _ = .7 ......................

4-22 PitchingMomentas a Functionof VerticalTallAspectRatio _ = 9 72, • eeeeoooeeeleeeeoeoeeeo

" 4-23 Yawing Moment as a Function of Vertical Tall AspectRatio, _ = .3 ....... ............... 73

." 4-24 Yawing Moment as a Function of Vertical Tail AspectRatio, _ = .5 ...................... 74

4-25 Yawing Moment as a Function of Vertical Tall AspectRatio _ = 7 75, • eeeeeoeoeoQoQoe_eeeeeo

4-26 Yawing Moment as a Function of Vertlcal Tall Aspect 6Ratio, _ = .9 ...................... 7

4-27 Effect of 8 and _v on Unblanketed Vertical Tall Area atLow Spin Rates ..................... 77

t

4-28 Definitionof SideslipAngle .............. 78 •

4-29 VerticalTailNormalForceas a Functionof SideslipAngle, Configuration A ................. 79

4-30 ?itchlng'Moment as a Function of Horizontal TallAspect Ratio, _ = 0 ................... 81

4-31 Pitching Moment as a Function of Horizontal TallAspect Ratio, _ = .3 .................. 82

4-32 Pitching Moment as a Function of Horizontal TallAspect Ratio, _ = .5 .................. 83

4-33 Pitching Moment as a Function of Hor--lzontalTailAspect Ratio, _ = .7 .................. 84

4-34 PitchingMomentas a Functionof HorizontalTallAspect Ratio, _ = .9 .................. 35

4-35 Yawing Moment as a Function of Horizontal Tall AspectRatio,_ = .3 ...................... 86

x

b

!P._mm

! 4-36 Yawing Moment as a Functiozt of Horizontal Tail Aspect5 87 --Ratio, - ......................

! 4-37 Yawing Moment as a Function of Horizontal Tail Aspect

' Ratio, _ = .7 ........ . ............. 88

1 4-38 Yawing Moment as a Function of Horizontal Tail Aspect' Ratio _ = .9 ...................... 89%

_- 4-39 PitchingMomentas a Functionof HorizontalPositionof Horizontal Tail, _ - 0 ................ 91

.- 4-40 Pitching Moment as a Function of Horizontal PositionI

i of Horizontal Tail, _ - .3 ............... 92

4-41 Pitching Moment as a Function of Horizontal Position°_

' of Horizortal Tail, _ - .5 ....... " 93• eeoeeo

4-42 • Pitching Moment as a Function of Horizontal Position iof Horizontal Tail, _ = .7 .............. 94

4-43 Pitching Moment as a Function of Horizontal Position iof Horizontal Tail, _ - .9 .............. 95

4-44 Yawing Moment as a Function of Horizontal Position ofHorizontal Tail, _ = .3 ................. 96

4-45 Yawing Moment as a Function of Horizontal Position ofHorizontal Tail, _ = .5 . . 9_

4-46 Yawing Moment as a Function of Horizontal Position ofHorizontal Tail, _ = .7 ................. 98

4-47 Yawing Moment as a Fu _n of Horizontal Position ofHorizontal Tail, _ = .9 ................. 99

4-48 PitL.ning !_oment as a Function of Elevator Deflection i01

4-49 Yawing Moment as a Function of Elevator Deflection 102

4-50 Pitching Moment as a Function of Rudder Deflection,- .5 ......................... 103

4-51 Yawing Moment as a Function of Rudder Deflection,- .5 • . ........................ 104

4-52 Pitching Moment as a Function of Co_ined ControlDeflections, _ - .5 ................... 105

xi

F_ure Pa_e

4-53 Yawing Moment as a Function of CemSined ControlDeflections, _ = 5 ................... 106

: 5-i Yawing Moment as a Function of Tail Damping Power _"Factor ......................... iii

5-2 Actual Flow Around a Stalled Airfoil Compared with theMcCormick Image Model .................. 114

5-3 Approximation of Unblanketed Vertical Tall Area ..... 115

5-4 Yawing Moment as a Function of Tail Anti-Spln Parameter . 117

A-I Orienting Support and Strut ............... 124

A-2 NASA IR-21 Balance ................... 125

A-3 Forward Body ...................... 126

B-I Pitching Moment as a Function of 8 and _,Configuration A ..................... 128

- B-2 Pitching Moment as a Function of O and _,

Configuration B ..................... 129" ,

B-3 Pitching Moment as a Function of 8 and _,Configuration C ..................... 130

B-4 Pitching Moment as a Function of 8 and _,°

Configuration D ..................... 131

B-5 Pitching Moment as a •Functionof @ and _,

ConfigurationE ..................... 132

B-6 Pitching Moment as a Function of 0 and _,Configuration F ..................... 133

B-7 P_tching Moment as a Function of @ and _,Configuration G ..................... 134

B-8 Pitching Moment as a Function of 9 and _,Configuration H ..................... 135

B-9 Pitching Moment as a Function of 8 and _,Configuration J ..................... 136 •.

B-IO Pitching Moment as a Function of 0 and _,Configuration K ..................... 137

;

xfi

B-!I PitchingMomentas a Functionof @ and_,Configuration L ...................... !38

B-12 Pitching Moment as a Function of @ and _,Configuration M ..................... 139

B-13 Yawing Moment as a Function of 8 and _, Configuration A. 140

B-14 Yawing Moment as a Function of e and _, Configuration B . 141

B.-15 Yawing Moment as a Function of 8 and _, Configuration C . 142

B-16 Yawing Moment as a Function of e and _, Configuration D . i_3

B-17 Yawing Moment as a Function of 0 and _, Configuration E 144

B-18 Yawing Moment as a Function of 0 and _, Conflguraclon F . 145 "

B-19 Yawlh_Momentas a Functionof 8 _-d_, ConfigurationG . 146

B-20 YawingMomentas a Functionof O and_, ConfigurationH . 147

B-J1 Ya%!ng Mome.mtas a Function of @ and _, Configuration J . 148

i_-22 Yawing Moment as a Function of @ and _, Configuration K . 149

B-23 Yawing Moment as a Function of @ and _, Configuration L . 150

B'24 Yawln_ Moment as a Function of 8 and _ Configuration H . 151

.0 q

1

: 1xiii

! I|

LIST OF SYMBOLSt _

A axial force

: AR aspect ratio

b span of win_ or tall surface , :

CL llft coefficient for a finite wing or airplane, L/-12O V2 Si

t#

CL llft curve slope for a finite wing or airplane, "".'"a

1 _L

112 '_V2 S _

CI section llft curve slope, I/ O V2 € _ ..._

I V2CF side force coefglclent, Fs/_ 0 S

s

• V2_m pitching moment coefficient m/½0 Sc

C. normal force coefficient• N/10 V2 Si_ ..

C yawing mo._entcoefflci_nt, n/_ C V2 Sb

I

Cp pressure coefficient, p/_ O V"

c chord length

mean aerodynamic chord

F side forcet_

g acceleration of gravity

h vertical distance from the horizontal stabilizer to the

fuselage reference line$

h/b ratio of horizontal stabilizer height to vertical tail spanV

I monent of inertia about the x-axisx

I moment of inertia about the y-axisY

K pressure d._.stributlon under the horizontal tail

K1 constant used in spin predictive parameter

xiv

K2 constant used in _pln predictive parameter

L llft

1 distance from horizontal tail I/4-chord point to e.g.t

m pitching moment; aircraft m=sn ....

S normal force

n yawing moment

R sptn radium ..n

S area of wing or ta_l surface

Vd descent velocity .'. ""

VT total velocity

x, y. = body-fixed coordinate axes; x positive forward, z positive

down• . . • .

a angle at which flow approaches the tail in the plane parallelv

to the spin axis and the body-fixed y-axis

;v 'tail, body-fixed sideslip angle - . "

a pitch angle

:: density coefficient, m/." Sb

," density

roll angle

_ spin rate. radians per second

nondi_ensional spin rate. _,;

h hori--onesI tail

- i!

v vertical tatl ;.I:1

w main wtnq !!

I! ,

xv

" ACKNOt_'LEDGE._IEh_S

I would like to express my apprectatlo|_ to Dr. Barnes W. McCormick

for his ._utdance tn the conception and reallzation of this work. I am

albo indebted to Hr. Rex Jacobs c_nd Hr. Leon Fetterolf for thelr help trr

designing and buildlnR t.heexperiment_tl apparatus.

)

!

, I

ClIAPTER l

Ih_RODUCTION

In a steady spin, the velocity at the tall of an airplane results

from the vector sum of the vertical descent velocity and transverse

velocity caused by rotation of the airplane. The resulting flow

therefore approaches the tall from below and to one side, at an angle

?

which Is dependent on pitch and roll attitude, spin rate. and descent

velocity. From the aircraft reference frame, the flow is rotational,

making conventional wind tunnel studies inappropriate for determining i

aerodynamic forces on a complete airplane. The purpose of this

lnvest[gation is to determine whether or not forces at the tail can be

accurately obtained with static wind tunnel te_ts by orienting a model ..

tail to the flow at ang!es duplicating an actual spin. In addition, the i

effectiveness of several tall configurations to damp a spln is

investigated through parametric studies of horizontal and Vertical

stabilizer placement, planform shape, and size, using a representative ' 'J

general aviation aircraft ,.all. The effectiveness of spin recovery I

controls in providing pitching and yawing moment changes is also

examined,

Overview of Spin Dynamics

The spin iS defined as the motion of an airplane, usually at an

angle of attack above stall but under gO°, descendln_:towards the earth

'ahile rotating about a vertical axis (Nethouse et al. 19bO). The motion

involves rollln_,,pltchlnR, and ya_'Inqas the airplane operates in the

• • . . . • ,

• . • . • • . . .

2

nonllnearaerodynamtcreglon.wellbeyondstall. As shownIn flgure.IT[,

the center of gravity of the spinning aircraft describes a helix. TF_..

distance from the center of gravity to the vertical axis is defined as

the spin radius, Rs, and 0 is defined as the pitch angle with respect to

- the vertical flight path.

Splnnlng is caused by a combination of aerodynamic and inertial

forces operating simultaneously, Yawing moments are created by the

autorotattve effect of a stalled wing and rotation of the tall and

fuselage about the flight path. Rolling and yawing moments are created

by the negative lift slope of a stalled wing; in a roll, the down'going-

wing experiences reduced lift, thereby perpetuating the roll. A Nose-

down pitching moment is created by flat plate drag of the horizontal(

tail operating at a high angle of attack. Gyroscopic moments created bY ......

centrifugal forces on the nose, tall, and wings tend to oppose tile

principal aerodynamic _oments. An equilibrium spin is attained when the

nose_down aerodvnamic moment equals the nose-up inertial moment, and• . . • . . . , .

aerodynamic moments tending to rotate the aircraft about the spin axis

are balanced by spin-damping aerodynamic and inertial moments. Figure

1-2 shows typical curves of eqL_ilibrium about earth-flxed y and z-axes

when plotted as functions of pitch angle and dpin rate. The

intersection of the two curves results in an equilibrium spin.

The complexity of the spin phenomenon has made analytical studies

difficult, so spin research has traditionally involved a large amount of

empirical analysis. Similarly, this report is concerned primarily with

experimental studies of spin dynamics. For more information on the

analysis of spinning, the reader is referred to Blhrle and Barnhart or

McCormick (1981). Testing technhtues involve the use of spin-tunnel

Spin Axis

I

.o

Horizon

. _ 0

Figure i-l. Aircraft FllRht Path in an Equilibrium Spin

!r

4

I

J

ROTATIONRATE

• Equilibrium About / i

• , . °

" Pitch Equilibrium

PITCH INCIDENCE

Figure i-2. Balance of Forces Necessary for Equilibrium Spin

• . • . . .

5

models In both free-fllght and rotary balance studies; dynamically

scaled model flight tests, and full scale filght tests. Such tests

allow controlled study of the Influences of configuration and mass '

distribution on equilibrium spin modes and recovery characteristics, and

analysis of spin recovery techniques. In much of the testing, special .'

consideration must be given to time scaling of the dynamic tests and

scaled model mass distribution, as well as re-creatlon of the rotational

flow field experlenced by the spinning aircraft. These factors .....

complicate the testing process t but are important in simulating the

actual spin dynamics. ''.

Scope of the Present Testing

Almost all past tall studies have involved an entire spinning

aircraft or model in order to duplicate actual spin conditions. Many of

these tests have beenqualltatlve in nature and were concerned only with

determining equilibrium spin modes and departure/recovery

characteristics. The tests have not attempted to isolate airplane

components to examine their separate influences.

The present study investigates the feasibility of using static

testing techniques in a conventional wind tunnel to study the isolated

effects of an aircraft tall in spin. The testing consisted of static

wind tunnel force measurements of several tall configurations. The

tails were positioned in the tunnel at extreme angles of attack as

determined by the spin rate, pitch angle, and vertical descent velocity.

m

Spin orientations covered a full range of equilibrium spin conditions

typical for general aviation aircraft. A representative general

aviation alrcraft tail, designed to Incorporate average characteristics

• 6

• of Severai aircraft currently produced, was used for the testing. The

aft fuselage shape was not a test parameter and its cross-section was

therefore chosen to Influence experimental results as little as

possible. Configuration parameters consisted of vertical and horizontal

placement cf the horizontal stabillzer, vertical and horizontal tall

aspect ratios, and deflection of elevator and rudder controls. Airfoil

cross-sectlon, horizontal tall dihedral angle, angles-of-sweep, and

taper ratios were considered of secondary importance and were held

constant for all tests.

• •

i -

CHAPTERI I

i PREVIOUS RESEARCH

l

°

Early Studies

I The first theoretical description of spinning and recovery

i techniques was presented in Great Britain during World War I. At this!

time the spin was actually used as a tactical maneuver to evade combat.

[-I •During the 1920"s, the first rotary balance measurements were performedD

in conventional wind tunnels, while in the next decade, the first spin

tunnels were developed and the importance of inertia and tall design

became apparent (Chambers 1980).

The Inertia Yawing Moment Parameter (IYMP), defined by

I - IIYMP = x y

mb2

was foundtobe an importantfactorin spinningcharacteristicsa1:dspin

recovery. If the aircraft weight is distributed mainly along the wing

(the case of a multl-englned airplane with wlng-mounted nacelles), the

moment of inertia about the roll axis is greater than the moment in

pitch' and IYMP will be positive. If the pitching moment of inertia is

greater than "therolling inertia, as is the case for most modern fighter

aircraft, the loading is defined as negative. For most general

aviation aircraft, I_IP is found to be close to zero. Spinning

characteris_i<s and recovery procedures are quite different for the• . • . . . • .

.... . . . . +

8

three major mass distributions. For the zero loading condition, the "

most effective recovery controls are found to be positive (down) " "

elevator and a rudder deflection opposing the yaw rotation.

Early research concentrated on the importance of the tail in

damping the spin. This led to the Tail Damping Power Factor (TDPF), a/

/ design criterion which later research proved to be of questionable

value. The TDPF was an attempt to define satisfactory recovery

_=haraeteristics of an aircraft through a methodical description of the ....

geometry of the tail. Unfortunately, the early research failed to

isolate tall effects from the rest of the airplane. This was the rest,lt'

of underestimating the importance of other factors which can override

the anti-spin properties of the tail. :_

As recently as 1971, the three most Influential factors were _sted_

as relative distribution of mass between wing and fuselage; density of

the aircraft relative to that of air; and tail design (Bowman). More

recent research 'has shown definite contributions from•such parameters as"

wing leading edge shape, aft fuselage shape, strakes and ventral fins,

outboard wing leading edge droop, and wing placement.

The Tall DamplngPower Factor

The Tall damping Power Factor was derived from early spin research

conducted by the British Royal Aircraft Establishment in the late 1920"s

and early 1930's. It is actually the product of two terms, the

Unshi_ided Rudder Volume Coefficient (URVC) and the Tall Damping Ratio

ITDR). The two terms, although developed independently, were thought to

be of equal importance in determination of spinning qualities, and were

therefore multiplled to form the TDPF.

The URVC, developed by the Royal Aircraft Establishment, is used to

provide an indication e_ rudder recovery effectiveness. Referring to

Figure 2-I, it is determined by the equation

LI + L2SR1 SR2

URVC - S(b/2)

The TDR, defined by

Sr L2TDR =S(b/2) 2

is determined for body and/or vertical tail area beneath the horizontal

tail. It was developed by NACA in 1939 from the previously used Body

Damping Ratio in an effort to improve correlation with spin tunnel

findings. '

Because the density coefficient, _, and the Inertia Yawing Moment

Parameter were known to be significant factors affecting recovery

characteristics, they were used as parameters in determining boundaries

for satisfactory spin recoveries. Figure 2-2 is typical of those

developed in the late 1940"s by NACA, based on spin tunnel recovery

studies of over I00 military and civil airplane designs.

In the studies, a spin tunnel model was considered to have

satisfactory recovery characteristics if it stopped spinning within two

turns of application of recovery controls. In addition, recovery tests

were performed with a modified control configuration, based on the

assumption that it is unrealistic to expect a pilot to apply perfect

recovery controls. This relaxed recovery criterion was referred to as

L1 "]

.... SRI

Ful"-Span 30°

' Rudder _

SR 2

I- L I.= L 2

/// ll6o° >

_&_/_oo i/ll_°,_,,___Part ial-Span .5°

Rudder - _ l

/ _F SF

v_ ITDR < 0.019 TDR > 0.019

Angle of Relative Wind Angle of Relative WindAssumed to be 45 ° Assumed to be 30_

TDPF = URVC x TDR

L1 + L2 L2SRI SR 2 SF

TDPF = x

S(B/2) S(b/2)2Q

• . Figure 2-1. Computation of the Tail Damping Power Factor _

i

....

2000 _o o O

xlO-6 o RECOVERY

O Reversal of Rudder Aloneo 0 Satisfactory

• Reversal of Rudder AloneD Unsatlsfaetory

1600 D Slmultaneous Reversal of Rudderm and Elevator Satisfactory

- . Slmultaneous Reversal of Rudder, " o and Elevator Unsatisfactory

o o. (I] o

oo

1200 o o Oo GDO

Oo

o o O

+0 -ooi++O0 _ D M 0

0 _ 0

Region for Satis- OS

factory Recovery by° ,_°a o Oo° _AT_I_ o OD .400Rob.orRe o alA1o e__0 _ 0 _/.,._"_n ^ 0 €_ • Region for Satisfac,ory Recovery= Ou m "0_-O°_o__ _%_ • by Simultaneous Reve.sa! of Both

o _ _f_¢_!d",..,o,/,,,,__ • _ oo• "

-'_20 -240 -160 -80 0 80 160 240 x I0-_I - Ix_/____Z

mb2 :e• _ i

Figure 2-2. Tall Damping Power Factor as-a Fv,,ctlono[ IYMP-,p. < 15 _ i

|

...." 12D

the "criterion spln." It was defined as that recovery effected by the

application of one-thlrd of full aileron deflection in the direction

oppostn_ spin recovery (usually stlck-left in ar{ght spin), two-thlrds

of full negative elevator deflection, and one-thlrd of full pro-recovery

rudder deflection. A model was Judged satisfactory l_ it recovered

within 2.25 turns.

The results show a significant scatter among sotisfactory and

unsatisfactory designs, making the determined boundaries questionable.

It was concluded at the time that "...other factors (such as wing

design) undoubtedlyinfluencerecovery characteristics _nd _ay account

in part for some mixture of the satisfactory and unsatisfactory points

shown" (Nelhouse et aI. 1946).

The TDPFwas applied to light general aviation aircraft tn a 1947

NACAstudy (Nethouse). The criterion devlsed (Figure 2-3) was developed

from the prevtou_ testing, using only those configurations resembling. •

general aviation types. Aileron control effects were not considered.• 1

The criterion is conservative In that boundarles are determined such tg

that no unsatisfactory recoveries lie in the satisfactory region,

although several satlsf,lctory recoveries !ie in the unsatisfactory

regio n . Recovery require_ents were relaxed, however, for general

aviation aircraft. Recovery was considered satisfactory if the models

recovered within 2.2g turns after initiation of full recovery controls.

Recent Free-Fllght Spin Tunnel Tests

Si=ilar studies have been conducted =ore r2cently usln_ the

"typical _tnglc_enqine "_• gcn_ral aviation de_i_n" _hown in Figure 2-4.

T_e cfferts Of control deflections _cre a_aln studied as functions of• . . . • . . .• , . . . • . •

Satisf._c :oryRecov_.ry b'! Rudder Alone

' Satisfactory orRecov,-ry by Rudder and Elevator I;nsatlsfa,:tory

• . 600 . • . • ...

_- 400

209%

]o

I 1 I I I j

- 20 -_0 -4fJ 0 40 f_O 120 X I0-4

Ix - I¥

Inertia Yawln_, Ho._nt Parameter, =_2

•• . +

Fl_.ure 2-3. C*_.neralAviation Spin 'f.ri'terlonBase'd'on "theTDPF (1947)

-"_'J_ _ 10.4:) J

.3 i

. 24.4_) _ 1=.95 ' _ iL_

Figur e 2-6. [IASA Typical" Single-Engine General .Aviation DesiRn

!

15 i\ .II

tail confLguratlon, e.g. position, and fuselage/wlng modifications. The

results showed that, although tail configuration is an important

parameter, other features such as rounded fuselage bottom, the addition

of ventral fins, wing fillets and strakes had an appreciable effect on

the equilibrium spin modes and recovery characteristics. Conclusions

made about tail configuration were minimal, although several possible

trends were noted. The tests also proved that the TDPF did not

correctly predict spin recoveries, and it was concluded that "...thel

existing tall design criterion obviously cannot be used to predlct

recovery characteristics" (Burk et al. I_/7).

Rotary Balance Tests

Spin tunnel rotary balance tests conducted by NASA have proven to

be useful in analytical studies of fully developed spins. Rotary

balances have.been in use for several years, but the ability of a "

balance to obtain accurate and repeatable data has been a recent

development. The rotary balance apparatus enables net forces and

moments due to aeredynamlc and inertia effects to be measured as

functions of spin rare, orientation, and spin radius. It consists of a

strain gage balance attached to a rotating rig as shown in Figure 2-5.

The present balance has a pitch angle range of 0 to 90 ° , a roll angle

range of + 15.° , and a rotation rate of 0 to 90 rpm.

Isolated aerodynamic forces may be measured by enclosing the model.

In a box structure, making aerodynamic forces negligibly small. The

test is performed for a given condition, and isolated inertial lurers

are recorded. The test is then repeated without the model •enclosure, ""

and Inertial;forces are subtracted from the net force measurements.

. • . . .. . . . .

|

!

Ii ........

4i

I

I

Figure 2-5. ,']A.qA-LaRC Rotnr3' Bnlnnce App;Ir;itu.q

17

Data presented by Bihrle et al. (1978) are the results of tests

• run for Rs equal to O, 0 ranging from 30 to 90°, and a roll angle, €, J

approxlmarely equal to O. The present testing duplicates these

conditions ,anda comparison of the two tests is presented In Chapter IV.

|i

ClL_TER III iJ

EXPERIMENTALPROCEDURE i

I

Spln Orientations

The major spin orientation parameters were simulated in the wind ! ""

tunnel by orienting a model tall at pre-determlned angles to the tunnel !

free streamline. Relevant angles are presented in Figures 3-I and 3-2.

As seen In the first figure, the aircraft Is assumed to be spinning

about a vertical axls passing =hrough its e.g., with _ equal to 0. The

tall experiences a net velocity containing components from the descent

velocity, Vd, and the product of the spin rate and horizontal distance

to the spin axis, _ltsiue. The angle In the vertical plane at which the

resultant velocity impinges the vertical tail, ev, Is a primary "

controller of spin damping. Note that for these static wind tunnel

tests, Vd is related to the test section velocity by

Vd=VTC°Sv"

Pitch angle•also has a large Influence by determining the shape of

the separated region above the horizontal stabilizer. Pitch angle is

related to ev by the equation

= tan _ sln0av [Vd J

= tan S

Figure 3-1. Velocities Affecting Tat1 in an Idealized £pin

" 20

t

z%

VT

VT cos a v

"- VT cos av cos O

sin %

Figure 3-2. Tail Orientation with Respect to Total Velocity Vector

i

i

!

I

21 I ,!i ;

w_ere !

_=____2Vd "

The dimensionless spin rate, _, is an important parameter in scale3 spin

studies. Equilibrium values of _ for actual spins vary depending on the

degree of spin. Steep spins are normally characterized by low values of

6 and low spin rates, with a pitch angle of 40° and a spin rate of O.3

being typical. Flat spins normally possess high theta values, usually

above 60 °, with _ typically having a value of 0.7. Equilibrium spin

states are strongly dependent on mass-inertia properties and aerodynamic

characteristics of an aircraft, and therefore will vary from one

configuration to another.

The present testing is concerned with a wide range of spin rates

and pitch angles to obtain information about equilibrium conditions of a

..

variety of aircraft configurations. Over the range tested, values of av

were determined •usingreference values of It and b, and are presented in

table 3-I.

The assumption that Rs is equal to 0 should not affect results

greatly. Spin radius can be approximated as a function of pitch

attitude by equating gyroscopic and aerodynamic forces acting on the

aircraft. For an aircraft in an equilibrium spin having a negligible

roll angle, .

R = g (derived in McCormick 1981)s _2 tan0

For a t'latspin, Rs is therefore small compared to the wingspan. The

• . . . . . , . • . .

Table 3-1

Angle of Attack as a Function of

, Pitch Angle and Spin Ratefor Test Orientations

av (Degrees)8 " 40= 60° 80°

I 0 0 0 -.3 12.78 17.00 -

..

t .5 20.71 27.00 3O.O8

.7 27.89 35.50 39.04

i "• .9 - 42.52 46.20

assumptlon is less valid for low theta values. Because the aircraft is

nosed inward toward the spin axis, the principal effect of neglecting Rs• . . •

is an Underestlmationof yawdamping. The assumptionis therefore

conservative for steep spin conditions, it should be noted, however,

that any analysis of spin departure should include the effects of spin

radius.

The roll angle is also assumed to be zero. Full scale flight tests

show this assumption to be valid for flat spins, while steep spins

possess a slight roll angle, having the effect of increasing pitching

moment and decreasing yawing moment tall contributions. Such effects

are probably negilglble because of the small magnitudes of #. However,

flight test results show that roll angle is o_cillatory in an actual

spin (Stough and Patton 1979). Roll angle should therefore be an

additional parameter for _ complete dynamic analysis.

1 !23

!

"1 " Model Configurations

The tail section models were designed to be typical of general

aviation aircraft tails, based on available information. The baseline

model configuration (Configuration A) was designed based on average tall

volume coefficients and tail planforms of several light single-englne

aircraft. Because of the wide differences in planform and

configuration, however, some assumptions were necessary. The vertical

tail angle-of-sweep, sometimes used to increase the moment arm and

stalling angle of attack of the vertical tail, was found to vary

., considerably between manufacturers. Angle-of-sweep was set equal to

zero a_ mld-chord to result in a vertical tail planform resembling that

of the .NASAtests. Many aircraft use varlable-lncldence horizontal

stabilizers (also known as all-movlng tails) which allow greater e.g.

range and better control. The fixed tail configuration is equally

popular, and was used in the present testing. Most aircraft have cross-

sections varying from root to tip, averaging approximately 8% thickness..

Construction complexity and strength considerations necessitated a

horizontal stabilizer of constant thickness with respect to span, and

slightly increased thickness for extra strength. A symmetrical NACA

0012 airfoil section was used for all surfaces.

Because of Its variable influence, _Ft fuselage cross-sectlonal

shape should be the subject of a separate test program, and its

influence was not determined in the present studies. A circular cross-

section was used, preventLng a propelling yawing moment under all test

orientations. Although points of flow separation are not well-defined

on a fuselage shape of this type, they do not change position with cLv

orientation. The primary influence of the aft fuselage is therefore a

24

I fairly constant force in the dlrectIGn of V.

I A scale drawing of the baseline configuration is presented inFigure 3-3. Note that the horizontal tail is placed at a mid-span

position on r._evertical tail. Horizontal and vertical tall tips are

formed by revolving the airfoil ,.ectionaround the tail surface tips.

Test parameters consist of Lhe vertical position of the horizontal

' tail, chordwise position of the horizontal tail, vertical tail aspecti

ratio, and horizontal tail aspect ratio. The effects of control

i deflections are also studied, for buth full-span and partlal-span rudder

• configurations.i

The verti__alposition of the horizontal tail can have an

• appreciable effect on yaw damping characteristics. It is expressed in

terms of the height, h, of the horizontal tall above the fuselage

/ reference line, divided by the vertical tall span, bv. Configurations

B, A, C, and D were used in variation of h/bv from 0 to 1.0, as

indicated in Figure 3-4. Five distinct locations were used in the

earlier NASA spin tunnel studies. In the present study, four locations

are used because of difficulty in mating the horizontal tail to the

curved upper fuselage. Also, note that construction of Configuratloa D,

with h/bv equal to 0, necessitated cutting approximately 3.4 square

inches from the root of the horizontal tail.

The chord_risepo3ition of the horizontal tall may have an effect on

pitch and yaw damping through mow_nt variation and vertical tail

- , blanketing. Three chordwise positions were employed: 20% of the chord

forward of the neutr._lposition; neutral; and 20% of the chord aft of

neutral, represented by Configurations E, A, and F (see Figure 3-5).

The vertical tail aspect ratio, ARv, is defined as the vertical

fl 25 Itail span squared dividedby the vertlcal tail area, hv2/Sv. " It is • i

L

I found to vary conslderably among standard tall configurations, with a ... ,.

value of 1.3 being an approximate average. Aspect raclo was varied from

i a minimum value of I.! to a maximum of 1.7 in the testing, measured from

the reference centerline of the fuselage. Ta!,erratio was held

constant, resulting in varying leading and trailing edge sweep angles.

i As indicated in Figure 3-6, Conflguratlons G, H, A, and J represent the

variation of ARv and its effect on vertical tall planfcrm.

Finally, the horizontal tall aspect ratio, ARh, was varied while

maintaining constant horizontal tall llft effectiveness at low angi_s of"

attack. The three-dimenslona] lift curve slope can be obtained from

approximate lifting surface theory by: i

CL _ CI_ ARa AR + [2(AR + 4)/AR + 2] "

Thus_ In order to malntain the same llft effectlveness,

ARh ShANh + [2(ARh + 4)/ARh + 2] = C

This, of course, assvmr" a constant C1 for all horizontal taJl

surfaces.

Four horizontal _tabilizers were constructed, varying _Rh from a

minimum of 3.48 to a maximum of 5.40, represented by Configuca,ions K,

A, L, and M (see Figure 3-7).

26

I

i

"I

Scale 1:4

b h i 20 in.

bv - 7.5 in.

"_1 TM 100 in."

Sv " 37.5 in.-

ARh " 4.0

,U_," 1.5

h/b v " O. 5

• . • • . . .

Fft;ure 3-3. Confi_,uration A

I

27

i ..I:

ConfiRuration B

hv

!

Con flg_sration C

Fi._ur,, _-._. V,irl:ltion of h/bV

I.I

• .

28

Flqurt_ 3-5. Variation of T.ailplane Chordwfse Position

1

i

29

'!

Configuration G /

Figure 3-tb. "ariatlon of ARV

I.3O

Figure 3-7. Variation of ARh

f

I

! 31 'i

Rudder travel is equal to _ 25° for both full-span and partial-span

controls. The partial-span rudder extends from h/bv equal to 0.2 to

l.O. Elevator travel is equal to _ 15°. Relevant dimensions and test

parameters for each conflguration are presented in Appendix A.

" Because of the limited range of parameters feasible in an

experiment of this scope, some parameters were elimlnated. Horizontal

tall taper ratio, angle-of-sweep, and dihedral angle were held constant

for all test configurations. Vertical tall taper ratlo and angle-of-

sweep were also held fixed. Such parameters may influence tall damping

characteristics appreciably and should be included in future studies..

Gener_l Experimental Design

The experimental set-up is shown in Figure 3-8. The tests were ."

performed in a four-foot by flve-foot atmospheric closed-return wlnd

tunnel. All tails were mounted on a supporting structure which allowed

rotation about the body-flxed y-axls and the tunnel-fixed x-axls.

Orlentatlonswere roaintainedthrouRh a pln-locklng system as show_ in

Figure A-L. An internally-mounted strain-gage balance, borrowed from

NASA-Langley Research Center, was used for all force and moment

measurements.

A forward body which abuts, but does not touch, the aft fuselage

was used In order to provide a continuous fuselage surface. In

addition, under steep spin cot._itton_,t:_terfereneeor flow Interuptton

from a forward fuselage may be slgnifIcaut, making an abutting fuselage

necessary for accurate modelling of the actual flow field. Moreover,

the forward fuselage eliminates flow ImpIn_InR directly on the exposed

part of the balance and It mtnLmLzes strut Interference. The fuselage".-

1i

1i4

PitchAxis

InternalBalance

Roll

Axis_ -.",,

i;

" _i_j

%

Abutting !Fuselage

To

Microvoltraeter ;.

50rlenting

SupportStrut ..

Figure: 3-_8. Schematic of ,Model and ._leasurt'ment S\',,itera.." . .

. • . . .

• , . . • . . . .

7• 33 _,

I

was attached to the forward part of the orienting support, andtherefore" :

did not directly contribute to the forces and moments which were

measured on the tail, A scale drawing of the forward fuselage is

presented in Figure A-2. Note that a door was cut in order to provlde

access to the pitch adjustment without disassembly.

The model was centered laterally in the wind tunnel for all tests,

and angles were adjusted during assembly from an alignment position

designed into the orienting support, This zero position corresponded to ..... _ "

a pJtch :ingleof 90° and an av equal to O, as shown in Figure 3-11.

A 5 volt balance excitation was provided by a d.c. power supply ..

which maintained constant voltage to _ O.02Z. Output voltage was

obtained from an integrating microvoltmeter. The strain gage balance

f-

was provided with an extensive set of calibration equations containing ..

linear and nonlinear Interactlot_terms. A full calibration of the

balance was last performed by NASA-LaRC in 1977. A rough check of the

calibratlon showed'agreement to within approximately "1%.

Model Construction Considerations

All test models were built by the author fro_ Philippine mahogany,

lami:.cted to prevent warpage. Vertical tail surfaces were reinforced

with O.125-1nch T-3 aluminum bars, and horizontal tall surfaces were

reinforced with steel rods extending the entire span of each horizontal

tall. Vertical tails were bolted to the aft fuselage, while horizontal

tails were held in place by tenslon, which could be adjusted by bolts in

each wlngtlp. Bending of the models due to wind forces was too small to

be measurable. Wood outer surfaces were finished in gloss polyurethane

coating, hand •rubbed with rottenstone and glass polish. Outer wingtip

ItC,a,_t_,,:,,- i'A'-_.

- BI.ACK AND WHITE PHOTOGRAPh

L

: G

Figure 3-9. Model- and Support in Test Section,Configuration A; _e = 15°' _r = 25°

ORIGINAl:PAGE 35BLACKAND WHITE PHOTO_

"I.:.

.°!

_2

• °

• • . . • .

s

_°.

-. Figure 3-10. Configuration B in Test Section

! •

. ..- -., - ----.-.•..._-'-"'--~."-'~~-~~-----\\."------------------"~Il..

: ~, :,~'..,'. .' .

I '.

'1i ".

,1I

. I

\(

i.

tI

f

[I,,

IIL.t

,."

Figure 3-11. Configuration H; Alignment Position

..... _'f

/

37

"" ' t - ' ORIGit_AL"PAGE.BLACKAND WHITE PHOTOGRAPH

!

Forward Body Aft Fuselage ,

Fi_,ure 3-12. Fuselage and Vertical Tail Models

38

Figure 3-13. Horizontal 'rail Models ...

• • • . . ,

• • . . •

II

39

i

fairlngs were cast fromwood molds using a mixture of White spot putty

and fiberglass resin. All final surfaces were waxed before testlns.

o

Testing Cons_deratlons

At the angles of attack simulating the empennage in a spin,

separation is weil-deflned at the leading and traillng edges of the tall

surfaces. Reynolds number effects should therefore be small, as shown

by spin tunnel tests run at Reynolds numbers as low as 6% of full-scale.

The tests demonstrated that longitudinal aerodynamic characteristics are.j

not significantly affected by RE for pitch attitudes greater th_n 30°

(Bihrle et al. 1978). Preliminary tests were run to determine the

effect of RE In the present testing, and a small variation was noted in

the force measurements. This variation may ha,'ebeen caused by a change ""

in tunnel turbulence level with tunnel velocity. The increasedi

turbulence may have affected the separation noint on the aft fuselage

enough to cause a variation in the data in so_ cases. Orientation

changes made the use of a boundary layer trip wire Impractical, and it

was therefore derided to #erf0rm all tests at the relatively high tunnel

speed of I00 f[s. The Reynolds number, based on reference main wing

MAC, was thus equal to 4.59 x 105, which was approxl_ately 21% ot full

scale.

Wall "terference effects were minimized by use of model wingspans

- which werL less than 50% of the test section height. Corrections were

not feasible because of the lack of appl_cabliity of current corrective

methods. Heyson (1962; 1971) has developed a linearlzed boundary

correction to account for the large wake deflections characterizing

V/STOL testlng. Unfortunately, large transverse velocities encountered

in most test orientations prevented its appllcatton. Solid blockage and

wake blockage corrections wPre estimated, based on model projected area, / .

using the approximation presented by Pope (1954). Their effects were

- found to be negli81ble.

, The testing procedure was straightfot_ard, with no unexpected

difficulties occurring. Each configuration was aligned after assembly.

and balance alignment was checked periodically. The balance was zeroed

before each test to compensate for model weight, excitation voltage

fluctuations, and temperature changes. Tunnel velocity was allowed to

stabilize before readings were taken. Velocity was determined by means

of a pltot-static tube connected to a water manometer, and temperature

was measured with a thermometer mounted in the settling sectiot,.

Sources of Experiment_l Error

There are several p_sslble sources of error," but their effects on

the final resultsare minimal. Errors caused by voltage oscillations in

the readings _ere reduced by the use of an inregratlng mlcrovoltmeter. - "-.

These Fluctuations were caused by wind tunnel turbulence previously

mentioned, and by vortices sbedded from the forward and aft fuselages.

_" Moreover, a large air compressor located in clos_ proximity to the wind

tunnei created a noticable lo_frequeney vibration. Lateral

osclltatlons were reduced with the addltlon of a supporting brace, seen

In Figure 3-9..

The compressor also contributed to llne fluctuations, which varied

periodically by approximately + 5 _V. Excltatlon voltage also drifted,

but the balance cal[bration check suggested it had a minimal effect onI

.,, , .. . , . , • .

readlngs..... • • . . .

41

' All support angle rne,tsurementa and posltlt_n raeasurements were

It=lied by tolerencew associated uith r=etat work. l_ecau_e of the

support design, assail pitch angl,_ errors can result [n angular errors at

the bal,_nc# center. The support was aligned and poatttoned In the teat

section manually, also resulting h_ possible errors.

Small 4ources of error are also Inherent In the r_odel design. The

effect of ftov on the front surface of the aft fuselage ts unkns_wn_but

- It probably has an Insignificant effect on tail norra4l and aide forces. ' •

&lthough the flow teas taint_l=ed uith the use of the abutting body. aerie

test orientations _ay create a higher dynarIlcpressure Inside the ..

forvard fuselage, causing bleed floe between the two fuselages. Control

horns. _lsed to natntatn control surface angular position, raay also have

' a snail effect on.force measurements. They were placed on the leeward

side o[ all rail surfaces (wlthln the stalled air cavity) to _Intmi=e

their influences.

_odel dirnensionn were accurate to uithin + 0,025 inches and all

surt_cea were _r_ooth. |loles and gaps bet_en tail surfaces _.'ere filled

with clay, making errors originating fro_ model construction and

configuration changes negli,qihIy s_alI.

Dat.t Redttet ion

Three forces and throt: moment ¢omponent.a sure recorded for each

teat run. Moraents _ere re=t_lved about the balance center, which was

located 4.05 inches foruard of the l/4-chord point of the baseline

hor',zont al tail. ,_

Experl,,entaiprecl._[onwas satisfactory, Two base,line rests,

corrected for dtflertng t_m=h,l vel_cttiea and per[orbed ot_ different

" -" "" ; _ " "L._• _..-,...., .,,.."_ 2 _ ...

W 42

I days, resulted in an averag_ normal force error of -0.7%, an axial force

error of 14.0_, and a side force error of 1.91%. The higher axial force.error Is somewhat =tsleadlng because extremely sm_,ll forces were

[ experienced In the axial direction.

In order to present the data in a usable for=, typical reference

values of It, Su, cw, and bu were employed tn converting to

r dt=enstonless moment coef[tctents resolved about an aircraft center ofi

gravity. Based on a ty_tcal horizontal tail volume coefficient of 0.596

..-and an average value of Sh/Sw of 0.169, the following reference !t

quantities were used. I!

Sw=591.2 In. 2

. . Cw-9.92 In. . ;_

bw=59.5 in. !_

lt=35.0 In.

All data were reduced using the above referencevalues nnd the descent

velocity, Yd.

e

. .., .

CIIAPTER IV

RESULTS AND DISCUSSION

The following discussion will consider the pitching and yawing

reorientsgenerated by the tall about the aiy'craftcenter of gravity. .

Tall forct,coefficients and rolling moments ._renot discussed because of

their comparatively small effect on aircraft spin characteristics. For

completeness, ho_a_ver. they are presented in. Aypondtx C.[ "

Effects of Spin Rate on Aerodynamic. Homent Coefficients al

I Measured raoments _tt' functions of spin rate are presented tnAppendix B for,sll tail configurations. As indicated in Figures B-I " .. i

1 through B-12, higher pitch angles result in larger pitching moraents, ii

caused bv the greater profll_ drag associated with larger angleA of _ii

attack. The curves also display "1 concave downward characteristic, with

Cm increasing In magnitude with increasing splt_ rate. Yawing moment

B-,,*. ltlght, r spin rateseffects are presented in Figures 8-13 through _'

, result in greater y-direction velocity components, creating greater

I

magnitudes of Cn. Interference fro_a the horizontal tail Is evident tn

the plots, caused primarily by blanketing effects op.d horizontal tail

posit losing.

It in interesting to not¢, that in several )'awing moment ph_ts,

curves of con,q toni d intersect e,l¢h other in the region of ,-_ equal ""

0.3. Pitching raoment €'urves suggest that errors caused by inc,_rrect

orientation are negligible. Pos_',ble causes for the phenomenon will be

dt:;cussed. .. ..

• . • .. • . . .

J• . -, • • •

44

Comparison with Rotary Balance Data

To determine the usefulness of a conventional wind tunnel in

isolated tall studies, repre_entatlv6 conflRurattons can be compared"I

with similar NASA test configurations used in the rotary balance studies

of Bihrle etal. (1978). ¢onfiguration B was found to resemble tall 5

of the NASA testa, with the major difference hefng the lover horizontal

tail aspect ratto and higher taper ratio of the NASA tatI.

Configuration C la similar to NASA tail 3 except for the above planform

dlfference_ and a lower horizontal tail vertical placement, as _hown in. . •

Figure _-1, " -.!

For propnr comparison, test data was adjusted to conform to NASA

test conditions as closely as possible by calculating moments using

reference lengths'and areaJ based on the NASA test airplane. Scaling o_ ".

these values was based on the area_ of the vertical tails, which are t€

similar .in planfgrm.. _te effect of changing to the NASA reference

quantities is slgni_icant, as can be seen by comparison of test data In

Figure B-3 with that of Figure 4-2. Because of this, moment'

coefficients presented in Appendix C are resolved about the balance

center,

Figure _-2 is a pitching moment co_parlson o_ Configuration C with

NASA body and tall data BII3V. Results from the two tests show a high

correlation, especially at low theta atlgles, At higher angles of pitch,

Configuratlon C di_pl^ys a pitching moment of higher magnitude, but the

change of C with spin rate [s similar for both tests. The discrepancy .

at high theta anglos may possibly be attributed to horizontal tail area

differencea. Because scaling of referet_ce values ts based ot_ vertical\

' 1

tail area, thescal.d hortzoutal tail area of the NASA rests is

45

Figure 4-I. Tails Used in Comparison with

NASA Ro_ary Balance Data

!46

J

approxlmately 70Z of that of Configuration C. This results in net Cm

values of lower magnitude, notably at lower spin rates and higher pitch

rates where normal force at the tall is caused almost entirely from

. flat-plate drag effects.

IYawing results are affected by contributions from the fuselage of

the aircraft, l_nilefuselage effects are not accounted for In the

present tall studies, all rotary balance data contain body tare and

interference effects. In order to obtain the correlation sho_n in i

Figure 4-3, body data were subtracted from the NASA body-tall data. i

Although this assumption of superposition does not account for the

interference effects, it does partially account for the fuselage

contribution to the net moment. The figure suggests that at higher spln

rates, fuselage Interfetsnce is significant. The large divergence at O

equal to 80° is probably caused by differences in h/bv values for the

two tails. As will be discussed, there is a discrepancy between NASA

results and the present results concerning the effect of h/bv at high" i

pitch angles.

Retary balance data for the T-tall configuration is available only II

for a complete wlng-body-tall combination. As in the previous case,

wing and body Contributions were subtracted from the complete airplane

data using measurements from an isolated wing-body test in order to

obtain isolated tall moments. Figures 4-4 and 4-5 show that

interference effects, probably from the stalled main wing, are

conslderable, partlcularly under steep spin conditions. The yawing

moment comparison shows a strong correlation at the high pitch angle,

lending support to the premise that wing wake interference is

significant at.lower pitch angles.

I 47

1 ••" T.HEI"_

NASABH3V --- o A0 ..qE_E.S.

I TEST DATA -- a 63 DEGRE_.b 80,DEGREES

-_. 252

!.o

!_._._ _---.--e-----_.. . ..

-_]./5' _"_.._..._.._._,_._ "_-,.,,.._, "_ .

' _",, ""_

Cm t _%-.,,

-I./5.-

" 0._ 0., 3.i 0._ O._ ,9.9 O.O :J.l 9.9 _].a

Nomdlmoa_'Ior_ai 901o ROt,cJ

..

Figure4-2. Pltchln_ Moment as a Function _Z e and _,Conf iF,urat ion C

_t

!}

48

• . °

..

NASA BH3V- B --- T.'_"IRTESTDATA _ o 4BDEGREESu 60 DEGREES

a 8Q gEOREES

ram.:.!!J /I /41J

,i

-D.

JJ

-_. ",2sq

i

i

3.[} :].L 21.2 _9.3 D.4 _.5 _.6 3.1 _.S 3. o

._o."_lmenel,3nrJI Spin .Rule

Figure 4-3. Yawing Homent as a Function of 8 and _, '"

Configuration C

I 49

!NASA_N1H5V- BW1- o- "l"_E!'.q

I TEST DATA _ • 4_]DE_Sr, 8:3DEGREESA 9_ DEGREES

I

-I]. 51]-1 .J-_-

_1],.;5-_ _ "-..

Cr A _ '""'--._,,.,

-i,..:3D_. x• . . . • .

-_. 2S-

i

-i. _.0.

I

- 15

• :].3 .'l.t _.2 .3._ 13." _3._ D.{3 .g.l 0._ :3.Q

Ho.".zllmon_'l.cno;_pin RoLo

Figure.4-4. Pitching Moment as a Function of _ and _, ..' Configuration B "

• . • • . , .

X

- -o. 125...... ; r ........ _ ........ I 11 ITI _i , , _ ; { ;; llt llill Itl .... i , = ; , , i I I = I I ITI I I , I ; ; I l' i"

_.3 0._ 0.2 _.3 _._. O.S O.O 3./ O.S .'1._

Nonol;,n.oncl_nol _pln RoLe

Figure 4-5. Yawing Moment as a Function of O and _,

Configuration B

51

In additlonto those already noted, there are several differences

in the two studies whlch make quantitative comparison difficult. The

NASA tests used a descent velocity of 25 feet per second, considerably

Slower than that used in the present testing. However, studies.

performed with the rotary balance tests showed Reynold3 number effects

to be small (see Blhrle et al.). The NASA aft fuselage directly under

the horizontal tall has a flat bottom, which may cause interference

effects which could not be accounted for by subtracting body data from

body-tall data. Finally, the NASA tests were performed at non-zero roll

angles. The roll angles _ere measured in fractions o_ a degree,

however, and their effects are probably Inslgnlflcant.

o_ ......_._

Effects of Horizontal Tall Vertical Posltlon ""

Figures 4-6 through 4-10 show the effects of h/bv oz,pltchlng

moment. At low sPln rates, they are minimal, with a larger effects

developing with increasing _. At moderate spin rates and higher pitch

rates, a low horizontal tall appears most favorable, while at high spin

rates, a mld-span horizontal tall placement results in stronger pitching

moments The first effect is a direct result of fuselage and vertical

tall blanketing of the leewlrd horizontal tall surface at high values of

h/bv. A second effect may arise from a h6_Izontal tall-fuselage

interaction as shown in Figure 4-11. Configuration C, with h/bv equal

to 0.25, may produce a larger net downwash than Configuration D, even

though the leeward surface is largely blanketed. A larger increase in

h/bv destroys such a llft effect because flow is more prone to deflect

around the leading and trailing edges of the vertical tail.

At 0 equal to 40°, a combination of interference effects causes an

'.

52

THETAo "" DEGR~£Sc 63 DEGREES

-0.50

-0.'75p----5---~~-----_~

-1.50

-2.~nI.

:J.:J 0.2 0.4 O.G 0.9 1.3

h/bv

Fi8ur~ 4':"6. Pitching r:oment as a Function of VerticalPosition of Horizontal Tail, w -= 0

:\....../" .

".,

, .'" ." \,

.. .... -.

.....-' ..' .

~'i ::.~-

.."' ..;i:!"'". -1,:::., ;0;;_r ':c"

t i'.,..:

.:" ~ :". :-.

l'" "

.' r "'~

I 53

THETA. .o l~ DEGREESr:l62 DEGREES

-3.'33

-13.75

I'

!i -1.2~

.,

J iI,

I I1

\-1.25-..,f, em

"

I.'.

-1. c;c- .

f-I

-1.15-j

) 'f.( ,-"

I . ~ •

a.s"r-l"'T"T"T-r-l"'T"T"T-r-......T"T.............................. r-.-r ro,..., 'T'",-,""'" '"'T,."..,......, .."...,..."r-~ r T---.-.-.-.--2.:ma.~

FiRure 4-7. Pitching Mo~ent as a Function of VerticalPosition of Horizontal Tail, W~ .3

J.,

~ '" .'(~;:II '

~~;\;:~,~~;:<~<;y~/.Jl,',I':,. '.;.' - r -. 'ft •, j'

-.~ ........

54 .'.'-

:.:"..--

i-

\II1\iI

lI

f'- .1 -

/':-

·r:;~~ ...-,

J.9D.GO.J

THETR0.£:] DEGREESc 6a rn::~EES

A 62 DEGREES

-1. /5·

-1.:l3

i..~

.'oJJl·'ri...,...,...,..,.,...,-.·-.'....,...,'~i .-,.-,...., ..-,~,..., ..., ...,....-rj...,...,-.,-.,-.,r-.r-,......., .-,T"I..-,..-,......., ..., ..., ..., ..., ..,.,~,-.,-.,-.,-.,r-,......, ........,.,...,...J

-aosaL ...·----..---.aoI5~

Fi~;ure:4·-8. Pitc"i:1~ ~O~f\t <\s i1 Function of Vcrt1c.11rusition of Horizont:ll Tail, w•. 5

-1.25-em

\\I

'\..

"

.- ..

-". _...... , • _ ... -1 ... - ....

", ...:

.. .... ~ ......::.. ..

."

-a. 1331I

II'

-3.'75

-------,,-

55

THETAo 4" DEGREESa 63 DEGREESA 63 DEGREES

-.;, ......

....

." '.,..''.

,".

..":..::..........,. ....

(

1~:'O •

.. .... _-.- ":0--1 .- ~.

1 -.-.- ..

-,'

-..:.

Fi~ure 4-9. Pitchinr, ~!or:'Cnt ::19 a Function of VerticalPosition of Horirontal Tail. ~ - .7

..." ..... ~. ..... . ~

......'_~~:":' . .;.,. _ --;'!'"__.. "'-tr~·~-,. ~ ...

I.J

~.- .._. :~-

0.3n.G0.-

'.or .." - ~ ..... ---...... \.

3.3

l-,.",,]

",.......,-"-,,...,..,......-...., .....II...., ...., ..., ..., ........"Y""T..,.,...............,......-................,.......................................,......-......-.............T""'\"I •• i' •• , ; i 'i ., ., i • ii' i' i'

~ . .!

-.

•\-.

...

-O.15.

r"

-1.75-

"4

t

: 23 i

_Jb,,1

""" Figure "-10. Pitchtn_ ._ment as a Ft,nct!on_of Vertical. IPo._ftlon of Hori=ontal Tall, _ ,, .9 t

/x I

a

,"

--_...--,- .

57

\'T

-------~-~--------~ratlon D

Conf1~ur3tion C

j

1J

IfI1Ii

F1,~ure 4-11. :'~low About ConfiRurations C nnd D at High Spin Rate

I

• o

S-shaped curve at low spln rates. Horizontal tall blanketing effects ..

described earlier result in a positive slope, and forward fuselage wake "Interact{on lowers the overall pitching moment at an h/bv value of 0.25.

f jAt higher values of h/bv, the horizontal tall is clear of the fuselage

wake.

Variation of h/b v has a substantial effect on yawing moment, as

I indicated in Figures 4-12 through 4-15. The T-tall provides by far thegreatest side forces in _llcaces, while at moderate spin rates, the

I au_orotatlve effect of the horizontal tall actually provides a

propelling yawing moment, Because of differences in horizontal tall.ot

! planform and area, this effect is not seen in the NASA test data for the

steep spin case (Figure 4-16). In fact, variation of horizontal tall

height showed llttle effect on yawing moment In NASA steep spin data.

It Is suspected that lower aft fuselage shape has a substantial effect

on the autorotative force crea_ed by the horizontal tall at low values

of h/bv. Further testing in this area would be helpful.

A flat spin yawing moment comparison is shown in Figure 4-17.

Despite differing horizontal tail planforms, spin velocities, and

fuselage effects, similar trends are indicated in both tests at lower

pitch angles. Again, the autorotative component of side force is

present, notably at a pitch angle of 60°• At low h/bv and high

values, however, the correlation breaks down. This may be caused by

differing horizontal tall planforms; at high pitch angles, vertical tall

blanketing is large for the low aspect ratio NASA horizontal tail. It

i

must also be noted that fuselage effects were not subtracted out of the

NASA data.

Analytica_ prediction of the effect of horizontal tail vertical

59

'i

TI'IL_I.qo 40 DE_,',6{3DEGREES

0._5-

B.308-

-O._25

I

-_._50.Cn

-O.375 }

=O.L3O

-_.125

8.: 0.2 O._ 0.13 0.8 1.3

hlov

Figure 4-12. Yawing Moment as a Function of VerticalPosition of IIorlzontal Tail, _ - .3

.................... y-_,.q

60

•-_. i_] -

-13.i2.€ -• ,.,,, ,,,, I,, ,,,,,,Vl,, ,,,11,,i,1 ,,, ,, , , i , , , , , , T , , l

0.3 0.2 _." _.G _.9 1.3

hlb v

Figure 4-13. Yawing Horent as a Function of Vertical

" Position of Horizontal Tail, _ = .5

• , • • , .

61

• 48 DE_k'_3

_" o 6_ DECR_-ESA 8'3DEnS

8._25-

!l 8._B ...................................................................................

T -8._25, "'" "}

-_. i25

_.3 0.2 0.,_ 0.6 0.9 I..3

h/bv

Figure 4-16. Yawing Moment as a Function of VerticalPosition of Horizontal Tail, _ TM .7

......... 62 _1o.

TI-_Ri

n 6_ 9EI_EE8" 80 9E_EE8

8._]25-

Figure 4-15. Yawing Mordent as a Function of VerticalPosition of Horizontal Tail, _ = .9

]63

THETA• 30 DEGREES• 40 DE&REES• 45 DEGREES

o= 60 DEGREES

TestData: Open Symbols;_ - 0.3{_.325- NASANetMomentData: SolidSymbols;_ = 0.25

D

1] -_._2s. i

D

Cn

..

-B.375. "

8.3 B.2 Q._ _.6 _.S i.3

_. h/b v _

'' i

Figure 4-16. Yawing _1oment as a Function of ,HorizontalTail VerticalPosition ' i. - • ,• , , . ,

1. . ' , . :

%4

• • . , •

64

THOR......• _ 4{_ DEGREES

I o 60 DEGREES• _ 8_ OEGREES

Test Data: Open Symbols; G - 0.7

U NASANetMomentData: SolidSymbols;G - 0.6

i .....

0.ZZS- ......................................

]- -6. _25,

T-0. _50_

Cn

-0. _75.

°.

-0. _25, i w , , , i , w i i i ,,i , J i i |

_}._ {].2 0.4 6.8 {}.8 1.3

h/b v

Figure 4-17. Yawing Moment as a Function of Horizontal"" Tall Verti._al Position for a Flat Spin

g

Ii •• I' "" " posltion has not previously met with success because of the need for

I

isolated tall slde force data for comparison, McCormick (1979)

Investigated the simple relation presented below, which is further i

examined using side force data from the present testing.

If the local difference in pressure coefficient along the vertical

tall Is assumed to be a function of the distance doom from the

horizontal tall relative to h, then side force can be expressed as

i

I 1 V2 S h

_ s v o Pwhere z is defined as the vertical distance from the given vertical tail

i

location to the fuselage reference line. The above equation may be

• simplified tO

1

i V2 (_3 f C (x)dx ." Fs = _ 0 Sv P• V O .' .

Ignoring interference and vertical tall planform effects, let

if c (x) dx = Ko P

Since

Fs

CF -s 1/2 0 V2 Sh

Sv h

CFs = Sh bv K

66 :s'_'__"

! ,/£P_ .

• ,,.:,.-..or 9<

•4 " • )"

K - cF s h " ,.s v _-_.,

.._._

A plot of K versus horizontal tall vertical position is shown in _

Figure 4-18 for _ equal to 0.5. Curves for other spin rates displayed .'._.2_'€'_ o'

" similar characteristics. The results show that K cannot be considered a =-'f,,;

constant for any position of the horizontal tail. In addition to _.._-_.. _#

interferenceeffectsfromthe fuselage,thehorizontaltallmay createa -_.-_"_

high dynamic pressure on the vertical tall area Immediately below it. ._,_._,.. :_

Thlshighpressureregionmaybe independentof horizontaltallvertical -._._.

position, making K strongly dependent on both h/bv and vertical tall .I

r°_f -.

It is evident from model and full-scale flight testing that the _

highestvalueof h/bv possibleis favorablefor spinsafety. In fact, e'i":"

testtall5 (h/bv equalto 1.0)did not havea flatsplnmode. This "_:

suggests that increasing yaw damping to prevent equilibrium is more ,,,'_'_ ,'2

•_,,--,_._,,_effective than increasing the'nose-down pitching moment, and that the

,_._.pitching penalty paid for Increasing h/by Is minor compared to the ._,'_,

: m,advantages of increased yaw damping. :iv+_'

../,.; :-.t:Z' -' '

Effects of Vertical Tall AspectRatio ,_-___-r-

• .o

The change•in Cm with a change in vertical tail aspect ratio is

small, as shown in Figures 4-19 through 4-22. The differences seen In

some curves are believed to be the result of experimental scatter or _

minor Interference effects. 4-

Yawing moment effects are more noticeable. At _ equal to 0.3

....4

• . . .. .

., '_.. :- ., .-" ...-_ /: -"

, : "{ THETA': * *40 DEGREES

_;.:.: o613 DEGREES_.,_:' A80 DEGREES• .j.

, ..\

•,': 2. S-A

• ....._. •

..... 1.5- _ A

e ,_,-. 0

K A1.1_- <> 13

0.5-

' 0.0-'''' ..... I''' ...... I ......... i'''''''''l' ..... '''I'''''''''I'''''''''I ''''' .... I'''''''''I .... '''''I

., 0.13 :a. I 0.2 0.3 0.4 0.S 13.6 0.7 0.8 0.9 I .0

h/b v

Figure 4-18. K as a Function of Vertical Position of Horizontal Tail, _ = .5

O_

• • • . •

........ o

o.

68

(F:_ure 4-23), lines of constant 9 are seen to cross at a value of ARv

equal to 1.45. Vertical tail area above the horizontal tail apparently

causes larger yawing moments at the lower theta value. On_ possible %

explanation is that unblanketed area in this region decreases _ith i

increasing theta, rather than increasing, as it would at high s/in rates _!

• when transverse flow becomes large (see Figure 4-27). Test results fro_

the T-tall configuration, which does not show _he effect, substant'.ate _!

this conclusion. The yaw damping effectiveness of the vertical tall at

low pitch angles ls another possible factor. At low values of O, the

• angle of attack as seen by the vertical tall is sm_ll. Because the two- _

dimensional normal force curve reac_es a local maximum Immedlately

I before stall, such low'angles of attack may produce a larger normal

force on the exposed part of the vertical tail.

I To investigate th_ phenomenon more closely, the body-fixed sideslip

, angle seen by the vertical rail, _v, _;asdetermined for each orientation(see Figure 4-2_). The vertical tall formal force _s then plotted as a

function of _v for the baseline configuration as shown in Figure 4-29.

Because of the lack of expe=Imental data be _e_ _v values _f 0 and 17°,

it is difficult to determine the influet,ceof the unstalled part of the

! curve. The f_gure does indicate, howev_c, that ther_ is a strong pitch

angle influence on y....damping force, with lower pitch angles providing •_

higher forces. This result suggests that ta!l geometry, and not

stalling an_le of attd_k, is the more influential factor. Note tha,

lines of const_fit_ are nearly llne_r, increasing in slope With _ i

increasing _.agnttudeof spin rqte. It can b_ seen that the curve

corre_pondlng to _n _ of 0.3 has a slightly negativ_ slope, giving rise _'-

to the Intersecting curves of Figure 4-23.

• . • • . . ,

|

69t+

•. T,HET_ _:

€363 0g1_:£5

ii!

,\ I._

-

-a 15f

I- " 0 (:] .. _j ....

Cm

-2:,L2_ . . + ....... ; . . ,_.i l.a "_.g I./

Figure :,-19. Pltchln_ .tlo.._'nta,J a Functter, of Vertical .."a(.1 Aspect Ratio. _, " .3

1-)l

j ...

¶ .+

Figure 4-20. Pltchin_ ,Honent as a Function of VerticalTall Aspect R_itlo,_ ,,.5

\71

-t.15-

i

? i

_, t.a ts _./ ilqRv '

?

• IFigur:c4-21. Pitching Homent as a Function of Vertical " ,

. .""...... Tail Aspect Ratio, _a- .1 '"" " (t1

• J• • . - . - . .

72

I . • .- . •

TttETFI.•

u 8_ DEGREES"a 8_ DEGREES

l It -B./5-t

{-1._-

: -1.2S- " " o __...._._ ..

I

@

Crn

! .. _ • .

-1. iS.

i1

-2.:_}-_, i

i.i' 1.3 I._ I.I _

!qRv _'t'

Figure _-_22. Pitching ._Ioment as a Function of Vertical

Tail Aspect Ratio, _ - .9 i

!

73

• ° . °.

THETR• 48 DE_EE':3

i

Cn

-_. _l_

-0. _25

l.i" 1.3 i.5 l.i

.q._v

Figure 4-23. Yawing Moment as a Functlon of Vertical

Tail Aspect Ratio, _- .3

74

°.

THETRo 4B DEGREES'_6_1DEC.R_EEBA 88 13ECR_EES

B.g_ -

-B._5 -

4 i I

I.'_ 1.3 I._ I.l

i .qRv

Figure " _'

t _-_4. Yawing Homent as a Function of Vertical.•' Tall Aspect Ratio, _ - .5

. • . . . . . . . . .

,i

• . .. . • .

-0._25-

I." 1.._ I._ l./

_Rv

Figure. 4-25. Yawing ,tiomentas a Function of VerticalTail Aspect Ratio, _ - .7

T_=T.qI

! Q 6_ DEGREESz_8B DEGREES

I, •

Figure 4-26. Yawing Mome_nt as a Function of Vertical

• Tall Aspect Ratio, _ = .9

77

t

• _-0.3

VT Direction

8 = 40°

Figure 4-27. Effect of 0 and c_v on Unblanketed VerticalTail Area at Low Spin Rates

• • . • .

r78

• ° _ ..

Figure 4-28. Definition of Sideslip Angle

THETAo48 DEGREES

a68 DEGREESA80 DEGREES

-. / _=0.9

!/J

0.8- / ////

0.6- / / _. _ _= 0.7

CN 0.4- _ _ = 0.5

0.2 °

o. 0--1"' ..... "'' I'" ....... I ''" l'' .... I ...... '' 'I'" ....... I ....... '' I" ..... "''' I ......... I .... '''' 'I

O 10 20 30 40 50 60 70 80 90

•_ CDQgreQ=)V

•Figure 4-29.. Vertical Tail Normal Force as a F_ctioqof Sideslip _'gle, Configuration A

tn

!

| "JL

80 ,,_.,-_

T "4"1

At larger values of _, the low vertical tail aspect ratfo :.

surprisingly results in greater yawing moments than intermediate values _

of ARv, as shown in Figures 4-24 through 4-26. For each vertical tail, _

T the horizontal tall height above the fuselage centerline, h, was .

constant. This was done to prevent h/bv effects from dominating the g¢%" ,

results. The configurations were nearly identical below the horizontal /'_\

. _ .tail level, The unexpected result must therefore again be related to

interference effects of the vertical tall area above the horizontal

T /'; tail, _._

.. At high spin rates_ the beneficial effect of a low aspect ratio q_

I"disappears because the high aspect ratio vertical tails are not totally -.¢

" blanketed by the stalled air cavity above the horizontal tai!. This _'._)

phenomenon leaves the tail designer with the dilemma of choosing between

satisfactory steep spin or flat spin characteristics. Fortunately,

increasing exposed area under the horizontal stabilizer can provide

satisfact0ry characteristlcs for both spin modes. _.

Effects of Horizontal Tail Aspect Ratio

The horizontal tall aspect ratio plays a small part in the overall

pitchlng moment contribution of the tail. As seen in Flguces 4-30

through 4-34, Cm is greatest in magnitude at the lowest aspect ratio,

ARh equal to 3.48, and it decreases with increasing ARh. Although all

horlzontaltails tested were designed to possess identical llft

effectiveness at small angles of attack, they obviously do not possess

/ similar llft characteristics in stall. The results show that it

benefits the designer to employ a lower aspect ratio, lower efficiency

horlzontal tall for spin safety. At h_Bh spin rates, however, fuselage

• . . • . .

o "r r

_-_ - 81

€". . '],i!.: ... .

,_:_'.,. "rHETRr o 4_]DEG_EE_.

_'_ [ o 15;]DEC4_EE8•

_,'=.'- ;.,o ,

l :o !. -"a ..... 8.'15. I_""43--"_- t

V

) ,t z_L •. :'

J

,_ - ,%

(

-|. 25.," Cm , i•_ /

L;'.

-i.=.;_-

'_" !°

I'

-i. 15_

, -2.3-_-

1.4 3.9 4.2 4.0 5._ E.$

£._h ,.

Figure •4-30. Pitching Moment as a Function of HorizontalTail Aspect Ratio, _ = 0

• !1

•i_ . ..- J

1!

, ° _ ,.

-; _.. • .. _... -. ,. * .-- .. .. ..

82

, J

i-_./5 -_ _-

1

!

4

-i;25_cm ]

4

4

4

4

i

I4

4-;./54

4

4

i1

*

3.4 _.€ 4.2 4.C 5._ _._

Figure 4-3[. Pz2chin_ Moment as a Function qf tiorfzontal

T,,11 A';pect Ratio, '_,_ .3

83

i!£Tq(I .&3 :JiGl\EESc G:l DEGREES0\ ~ DEGREES

C:.J

~~_-~---iJ

4,~

g

arn

~-3. :::J-j

~

U1· +··J·

U-J. i5~

•I1•

t~

JJ;~

t -L~-I;i~•·~'I

em-1. ....5-l

1

~1'.~ 1. C:J ~·i·~,l

, '5 i-" I ~•

1111J

, 1

J.. .:, ~;J-l

\ ,3,'& 3.:3

Fl-:Ilr., ... - , ... l'lt\'hln~ ~,'~'nt .\'; ,I Flln=t1<'1l ." .!i.'rl::"llt,ll7.111 ASpl.. ,'t f\.\t 1,\, ....1 •• ~

_._.- --11.!

-a. J5-

Figure "-33. Pttchlng _k'r_,nt as ,_ Function of Itorizont+l!

T.111 Aspect R_itio, ,o- .7

t -3./5k

FIRure 4-34. Pitching Hov_,,Atas a Functlon of Horizontal

Tall Aspec,_ ,_itlo. _ - .9 ..

l° m

THET.q

i o A_}BEt_SEES= 63 DEG_ES

;- _. ;_2S-ti

_, -*----o*-°o** .... . .... °.....°....° oooo.° ..... ...o....o......... ..... ...

!.-8. :}25J

' !'1

• .j

-i}. :}S_'_ . •Cn

1

1

1

3.4 3._ 4.2 4.6 5.,} 5.4_Rh

Ftgnre ,_-35. Yawing ._loment a.q a FLmction of !tori:ontalTail Aspe_'t Ratio, _,_- .3

• • , . . ,

, , . . .

1 i• 87

• . •

T!'_R " i .• 4_ DECREES

_'8_ DECW_F.Eg."

8._325-

-8._B - .•

Cn"4

i

4

-_. _75 _

-ft. _SB-]

-O. x25-

3.4, 3.3 4.2 4.0 5._ 5.4

.q._h

Figure 4-36. Yawing Homent as a Function of llorlzontalTall Aspect Ratio, to- .5

88

m

THEIR. (, 4_ DEGREE,R

,_ 63 DEGREESB:_ DEGREE5

_] 3.325

_3-- g -B._25

i I • x., • [ T T l _ ( , , ..... lift ' , , _ 1 [ 1 " " _1_ T FI, • _j • , _ • " _ " T I

3. 3. S 4.2 4.G 5.3 5.4

? q.R_

"' FLgure 4_-37. Yawfng Homent as a _Function of Horizontal ..Tail Aspect Ratfo, ,o " .7

• 89

i_HE_R

i" = 60 [:]EI:;REESA _3_DEGREES

i o._2s\a

i

i" 8._08-_-........................................................................

i" :l

" !4

+ !cn _i.-=

-o._Ts_1,I

Figure 4-38. Yawing Moment as ;I Function of l!orfzontalTail _qpcct Ratio, _ - .9

, • • .• • , . ,

.. • . , .• , , , , + .

!90

]blanketing ofthe leeward tall can cause the higher aspect rat[o_ longer

span ho_Iz0ntal tall to have a slight advantage ¢as seen in Figure

4-34). In most test cases, this interference effect is outweighed by

the greater flat-plate drag of the lower aspect ratio tail surface.

T Horizontal tall aspect ratio also has a relatively small effect on

" yawing moment (Figures 4-35 through 4-38). Complex effects from the

- altered chord and span of the horizontal tail surface make expl_nation

of the results difficul_. Nevertheless, defini=e trends can be noticed:

under flat spin conditions, the higher aspect ratio tails provide

.. stronger yawing moments; under steep spln conditions, a _alue of ARh •I

equal to 4.62 appears to be the optimum value for the configuration

T- tested.

As staged previously, under zero-loadlng condi=lons, preventing ?r

breaking equilibrium in yaw appears to be the dominant factor In spin

safety. Therefore, a moderately high aspec[ "atlo horizontal tail

, p#obably has _a _light spin-damplng advantage. Relative magnitudes of

the effects are small, however, and ARh should not be considered a

primary design parameter to prevent spin.

Effects of the Horizontal Tail Cl_ordwisePosition

The horizontal position of the horizontal tall has a significant

effect on the pitching moment of the aircraft, particularly at hlgh spIn

rates. Figures 4-39 through 4-43 show that the aft posltion of the

horizontal tail is most favorable for breaking pitch equilibrium. Note

* that the resultant curves are nearly linear in the intermediate spin

range, probably caused by the increased moment arm associated with the

aft position. The eonfigurat[on tested, with h/bv equal to 0'5, also

_

91

r_q,48 DEC._EESa 68 DE_EES

•-1.25. -Cm

-I.15

°.

1

"" -2. __!,,,

M-To_i Poe_L:on _n _ Cho:'d [ * Fo-_ar.d)

Figure 4-39. Pitching Moment as a Function of Horizontal

Position of Horizontal Tail, w - 0

UI] cm-"_i

.°

y -1.58 -

i-1. JS-

T -2.Z__

"" -2_ -1_ _ 1_] 2_

"- H-Ta',I Po_l_on "_ _ Cho,_cl ( . Fo.'.o:". d}

Figure.4-40. Pitching Homent as a Function of Horizontal. ." ... Positionof HoL'izontalTail, _ " .3

1

-i._ !i.

t-2._'_, , ....... , ......... _ ......... , .........

H-Toii Po_,!{,Ion In _ Cho."-d ( + Po.,"wa.'-di

Figure 4-41. Pitching _loment as a Function of llorizontalPosition of Horizontal Tail, _ = .5

'.

...

94

-rHETRo .to DEGREESc 6~ Dr'"JkEE5b. S~ DEGREES

-e."'1~

~__---y--..-----~-f1-e.15j

i

-l.J __---------~~--------- ~-

-,.JCrr. ~

-1.50

-Lls·1

-2J~Ii --r-r-r~""""lI.......-r-r-r""""""'-'-r-"lji~'-'--'-'-r-r-'I ~,...-.---.-..,...-,-,--,-,I

-20 1~

H-To' I Po,,:l :.:-', '., t Chor-d ( + Fcrwo,...dl

1Figur~ 4-42. Pitching }!omen:: as a Function of Horizont;.;.l

Position of ~orizontal Tail, ~ - .7

Flgure 4-43. Pitchin_ .Hor_nt as a Function of l|orlzontal

Position of i!_rizontal Tail, _- .9

6

96• . •

[_Tq• _8 _G£EES

4

g _4I

o .... •-o .... ,, ....... ,,,,,.ooe.,o .... , ,.., o.. +o oo oo,,., _..e ...... o .......

_J L _ -_-- -_,_ .',

" 0 _i

..i+. -

n.

+.

q

• "j +4

i

1

iJ :++

"] +,_.25 4!

• .

i |',.,st.t<.,,',tt ,,,t H,,rt:,,t_t,ll T.zll. ,,,- . I

97 i

l._-l.q

: ] :

" _._-i- ........................................................................

- 11

I O ----

4-_. _-_ ._

I Cn _,,i

4T i! 1' -B._7_--,

!]IIq

'I

i-a._!

J

,i

'4

-& ,.-"5 ,i -

... . .

Figure, ,,'-'5,,. Y.,wt.ng ._!,,ment ,le_ a Functt_,n of !{orl. zm_tal-" . t',,siti,,n ,,f i:,,ri.=.ont._l Tall. ,:, " <'• . • , . . . • . - . . . .

• . ". . • . .

Fl<ur_'._.-_.b. YJwinc, ._'or._,nt ._ ,_ l-'m_ction ,,l lh, ri:onr;tl, I',,_iti,,_ ol l{ori:_nt.ll T,lil, ., - .7

Figure 4-_7. Y,lwinv, Hor_'nt as ,l Function of Horizontal

; Po._Iti_n of l{ortzontal Tail, _._- .9

[ 100

showed an increase in normal force with aft positioning, suggesting a

fuselage blockage effect in the forward positLon.

Yawing results are affected greatly by 3. At low spin rates

(Figure 4-44), constant Ocurves intersect between the 0 and 20%-chord

data points. The phenomenoncausing greater yawing moments at steep

spin values is evidently also related to cherdu'ise horizontal tallI

i location. Possibly the greater exposed vertical tall area in the

horizontal tail-aft con[.tguration tends to amplify the trends noted

previously. At intermediate and high spin rates (Figures _-45 through :

- 4-47), a concave downward trend is seen, resulting in higher yawing

• moments for both forward and aft horizontal tail poaitio_m. In the

forward position, more rudder area Is exposed, and in Lhe aft position,

more forward Vertical tall area is exposed. - ,. #

NASA testing was limited to the low hort=ontal tail conftguration,

r where [or_ardpositioning of the horizontal tail (NASA tail I) resultedi

in a slightly flatter steep spin which requtred elevator defXectton as

l well as rudder reversal for Criterion spin recovery. Possibly rudderblanketing was a factor in the tests, and the small differences indicate

that, despite large relative effects on pitching moment, chordwise

i horizontal tail location is not a primary parameter.

1

Effects of Control Deflections

" All control effectiveness tests were performedat an Intermediate!

spin rate of _ equal go 0.5. Time considerations limited the tests to

two theta angles, simulating a steep and a flat spin. All tests were

performed wi:th the baseline configuration. Elevator deflection alone

Induced small changes to pitch and yaw_ as shown In Figures 4-48 and

I .i01

_ = .5 T_n .= 0 o 4B OEOREES

r " 8_ OEGREE_

I

TJ .....

L

-_._5

Cm -1.25

" _ -I._.8

1l

-1./5!

-2._

_. 5 l_ 15 .

Elovo_,_ Dotloc_'on {Oo_r'_oe)

Figure 4-48. PitchlnR Moment as a Functionof Elevator Deflection

102

= .5 THETR

_r = 0 _ 48 DEGREES" 8_ I_.GREES

-B._5.

-8.i_.

m. ..

" " " 51-t3. L2

• " EiovaLor 5ol'locL_on(Oogroeel

Figure 4-49. Yawing !foment as a Functionof El*_vator Deflection

103

• THETA: 4@ DEGREESA 7HETA: 8_ UEOREESo THETA: 4_ OEGREES PQRTIQL_N RUOOERR THETFI= 8_ DEGREES PQ,RTIRLSPQN RlFOOER

-8.58-/

[ -8./5.

-l.Z_.

l

I Cm_l.2fi.

1-I._B

-I.IS

t_

'i ,_uddorOafl_l.lon (Oe_9,'-goel

:_ ' Figure 4-50. Pitching Homent as ,iFunction of_! Rudder Deflection, w - .5

• • • . , .

I06

o ffk:'TR: 48 BE_EESTHET.q: _:_DEC4_EES

o T."Lr'TR: 48 OF--C,!REESI:_qRT!ALb'F_flNRUDOERuTHETR : _ DECRR_E5 P.qRTIRLb-'F_qNRUOn.,ER

,,, _._25-

U

-0._75

-D.i_

-g. x_

.£udd_r Do{"i ocL 1on _Oogrooe i

•Figure4-51. Yawin&Momentas a [unctionofRudderDeflection,_ " .5

@

105

*THETA : 4@DEGREES

_ THETA= _ DEGREESoTHETR: 4@DEGREES P.qRT.tRLSPRNRU[73ER_THETA: 8_ DEGREES PARTIPLSPANRUDDER

-I._-

o°

,

°.

' -1.25Cm

-1.58-

-l.75-

-2. _;'1.

ControiDeflecLtone_ of Fuil)

•Figure 4-52. Pitching l•_omentas a Function of ..Combined Control Deflections, _ = .5 "

Im

106

o "i'HET.B: 41_DEOREEBAI'HETA: 88 OF'OREES

o THETA: 4_ OE_RFFS ._.RTIAL_P.qNRUDI3ER#THETA : 8_ DEGREES t]RTIALSPAN RUDDER

_.Z25-°

" -B._SBCn

-B. _75

-D.i25

ConLroi Oof'locL'.one(% o.r Fuil)

Figure •4-53. Yawin_ Moment as a Function of• .' .. Combined Control Deflections, _ = .5 "

. .. • . • •

107

U . . •4-49. At a pitch _ngle of 40°, elevator deflection resulted in a 14%

increment to Cm at the maximum positive deflection of 15°. Yawing

moment was also affected at a low pitch angle, probably by increased

vertical tall blanketing. Flat spln elevator deflections resulted in

minimal pitch and yaw effects. The results Illustrate the danger In

I relying on the elevator for spin recovery. In some aircraft, however,

high wing loadlngs make rudder reversal ineffective, leaving theelevator as the primary recovery control. Tall designs which maximize

i the nose-down pitching moment are necessary for such aircraft. -

• • , . •

_ The effects of rudder defleetfo_ "_npitch and yaw are shown In

, Figures 4-50 and 4-51. Effects on pitching moment are small, but yawing

"• moment is strongly Influenced by rudder reversal. Steep spin results

Indicate a 53% increment in yawing moment at the maximum rudder "

deflection of 25°. Note that rudder effectiveness decreases wlth

increasing pitch. The high spin rates common at hlgher pitch angles

would probably tend to minimize this loss of influence.

The partlal-span rudder is much less effective than the full-span•

rudder under steep spin conditions. At a pitch angle of 80°, the

differences are small, with the suggestion of reversal of the above

trend: yawlng moments produced by the partlal-span rudder are slightly

greater than those produced by the full-span rudder. This result is in

agreement with Y LSA tests, where Lt was found that NASA tall 2,

identical to tall 3 except for its partlal-span rudder, did not have a

flat spln mode, while tall 3 exhibited an unrecoverable flat spin mode

as well as a moderately flat steep spin mode. Such a control

configuration apparently prevents a spin in two ways: by reduced rudder

effectiveness While deflected in a pro-spln direction, and by increased

108

•, yaw d_mplng after rudder reversal. It is questionable whether this

i slight increase In flat spin Cn i_ worth the trade-off in lowered steepr

spin damping. NASA testing indicates that it i_, 8t least by preventing

• _ high pro-spln yawing moments _h_n the rudder Ls deflected in a pro-_pln

direction.

n Simultaneous deflection of the elevator and rudder provides _ery

little additional positive effect, a_ide from the fact that it sums theeffects of each control surface. Overall control effectiveness is very

poor under flat spin conditions. Under steep spin condi=ions, rudderl

effectiveness is actually lessened with the combined deflections because

of increased rudder blanketing caused by the deflected elevator. For

this reason, standard recovery procedure consists of rudder reversalfollowed by elevator deflection, applied before the spin becomes fully

developed.

iIi

• .

............................ T"I

I "CFAPTER V

i DEVELOFHEh'rOF A PREDICTIVE PARA.V_TER ..

.IAs previous research has shown, the Tail Da:_Ing Power Factor and

i its associated general aviation aircraft design criterion Imve proven to

be insufficient for prediction of satisfactory spin characteristics and

recovery. This is due in part to the contributions of other _Irplane

components. Nevertheless, a trulF effective design criterion forgener_l avlatlon tails would be useful to the designer. It must

• • .

l incorporate a measure uf control effectiveness while accounting for

effects of possible adverse aileron deflection (Burk et al. 1977). It

=ust also be dependent on the nlrcraft density coefficient and pitch

angle. !n addition, because spfn has been shown to be dependent on

method of control reversal, the parameter must also account for

incorrect or insufficient (criterion) control deflections.

A design crlterlon such as described above would be less than

practical because of its co_plexlty. Certainly it would involve

extensive spln tunnel and radio controlled model tests. A =ore feasible

_.iternatlvewould be extensive wind tunnel studles of tail

configurations, with tabulation of nondlmensiona[ force and moment

coefficients for varying pitch, roll, and sideslip angles. Control

derivatives could also be tabulated for spin conditions. Nith the use

of one of the rannynonllnear numerical simulation routines becoming

available, the designer _ould then be able to study the spin

charactertstlcs of several configuratlons and choose the opt[-.alone for

his needs. Of course, full scale flight testing would still be

necessary, but by increasing confidence in predictive _ethods, :uch

II0

!

t effort ¢ouhl bL, x_ved in other prt+li_Inarv Jt_|diem,

i _deqoacy of ti_e T,+ll flapping Po_r Factt_rTile dexi_ner would al._o find useful ,s_ri_erion whlch _rovtdex a

" [ r,mgh IPali_'a_l,+nof the \pin characteristic\ o! the tall, Soch a

crlteriL_n would be helpful durlng preliminary lavL_it and sizing, The

l +pre_ent tail ,le_Ign criterion for light general aviation aircraft Ix not

a¢¢eptable,.._.t,h'ast in its prexent for_, P_-cauxe of It_ conservative.

i+ature0 ,_ever.il,tesl_ns showing acceptable mpin recovery are deemedF

tm,_ccept.sb|e b\' the criterlon _see Ch.:pter 2), ..

t.lll .h,_Ign criteri,_n _hlch would r._:t be mialeading mu_t only

t',,_cert; thi.+d,mptn_ clusrncteristicM ,at the tall, Thttx. tt i+ necessary

to develop a fact,+r which approximately predict\ pitching and yawing

._=ent_ and indt_'ate,_ contrt_l effectlvene_ in tercel.of increased .,

-_or'_,nts. Flgt_re 5-1 is a plot of \'awin._mo_s:t as a \traction ,_t ti_,

T.I|I l+._._pin_ i',++¢,r F.+¢tor f,+r t,_Cll ¢onl+l_uratlon tested. _rt, t° tvpicai!

spln condltl+_ns art, +h,+wn. Correl.ltion of the _+I'F +ith v+_wln,_ m_+raent

i._ p,+,+r, p+|rtlcul,srly under t l,st spin co_xlltion_.

Th,-*re art, +cver.;l re.+mon._ toe ti|e ina,iequ,scv of the Tt+PF. _,¢atsse

it is ._._dt" up _t tl+ produ_'t of t_o other crlt_,rla, the t'_VC and the

T:+R, it ¢,-ttttx_+t .'_€,.'It_urt. st, par,_t.e cotl;rtbut ionm t_+ \'awin_ ,.'_+ment ot+ e+l_'h

t,l_'t,+r; tht, ru,hi,,r act\\+stir h+ss tlm, ,ha.st pure+me of contributl:_R to t:

tx :t,_ _tn,i_,tlt,¢te,i p,_lth',n, and co, tritest t_t a i_slttve vawin}_

in_'reme|It while _|ellected. l_ add_.tlo:_, the Tall D+_'_pin_ Rati_ wa,

_rbltr,|ritv set tip t_ i:_<lud_, _¢rc-a only _i,+r the, tx,_rteotxt._ _, _t,_bilLrer..• ,

tht' h_+rl+'_+;xt,_t ".at| sit+hit;' ,-.+t_ t_._.,, .1 ,¢r,_.-_,i! _" ,+t:t,,'t ,m t+t,, T:+R.

I

oTHETA = 40 DEGREEScTHETA ft 60 DEGREESaTHETA c 80 DEGREES

Q co .3Q .... 5(Ja .9

. ~ 6 ..o . 0001-:- ------ - - -------- -----~-.~.---~----------:--~-----------------.-------------------

~ (> g 6' v¢ .~-3.025~ c

~ Demo J5..,-J

-0 OSO~...1:l

en -0. 075~ 6-...I.,

1 t:..,-O.IC0"j

,i..,

A

A

D

III

I12 ".

Spln angles used in the TDPFare set up arbitrarily, The alrcraft is

D spln at a pitch angle uses a full-span rudder.afisume_ to of 45° if tt

If a partial-span rudder is used, it may spin at an attitude of 30° or

45° , depending on the value of the TDR. Finally, there is no estimation

of the shape of the blanketed region on the vertical tall.u

Moment Correlaclonwith a Hodlfled Antt-SplnParameter

Perhaps the greatest utilityof any criteriondeveloped is in

.. providing some measure of correlation with the many factors influencing

tail forces. The TDPF has proven to be unsatisfactory; a true damping

. parameter must correlate with generated moments. Tb.ls discussion is

concerned_ith simple improvementsbased on tail geometryand shape of'.

the air cavity in two dimensions, and it will therefore be approximate.

Testing has shown that For a zero-loaded aircraft, yawing velocity

is the =aJor contributor to inertial moments which perpetuate a spin.

The vertical tail and rudder thus provide the largest tail contribut!on

to spin damping. For this reason, a tail anti-spin parameter (referred

to as TASP below) should be based primarily on unblanketed vertical tail

area. Rudder contribution to yawing moment should be added as a

separate factor, and only during separate co=parlsot_ of rudder

effectiveness:

Unblanketed Area" TASP - S(b/2) + K2 x Rudder Volume Coefficient

the constant K1 is needed to prevent the first terra from dominating the

para=eter, and. must be deter rained through a study of the relative

importance ofeach term.

;, ,. . ...... . ......... 4~. _..-,_ .....

" _ 113

n The cavity which blankets part of the vertical tall is of the shape

shown in Figure 5-2. McCormick, in an unpublished study, derived anumerical method for determining two-dimenslonal cavity shapes of flat

plates at high angles of attack. ExsmfnatIon of theresults 8how_ that

cavity width in the plane of the plate is relatively constant withI| respect to e.

I It is this research which forms the basis for the tail volumecalculation as shown in Figure 5-3. The cavity has been simplified to

form a blanketing area determined in size by lines 11 and 12, arewhich

separated a distance of 2.282 in the plane of the horizontal tail. The€

J lines are parallel and at an angle of 0 to the horizontal. Areas are

" defined below:

- AI Area of the vertical tall not in the blanketed region or

defined by other areas..

A2 Triangular area forward of the leading edge of the horizontal

tail; determined by a llne extending forward from the leading

edge at an angle of 45°.

A3 Upper forward tip of the vertical tail; bounded by the line

11•

A4 Triangular area aft of the trailing edge of the horizontal

- tail; determined by a line extending aft from the leading ed&e

at an angle of 45°.

A 5 High pressure region immediately below the horizontal tail and

above the unblanketed lower area, A I.

114

I

U

It'4

Figure 5-2. Actual Flow Around a Stalled Airfoil

Compared with the McCormick Image Model

t

t

A.t • ."

i]

• !

A 2 _" .... ..... A 5

At

Figure 5-3. Approximation of Unblanketed Vertical Tail Area

, . _. , . L ........ I ........... "1

116

The actual dimensions of the high pressure region should be

determined experimentally, For the appoxd-_tlon presented, the height

of A5 was arbitrarily set at O.l_, and the width was set equal to _.

. The resulting coefficient becomes

AIL 1 + A2L2 + A3L3 + A4L4 + K2A5L5TASP =

S(D/2)

4

T where LI through L5 represent the distances from the aircraft e.g. to

the centrold of each area. The variable K2 represents the value qAS/qA1

' and must be determined experimentally. A value of 1.2 was used in the

following analysis.o-

Results are presented in Figure 5-4. They show a fair correlation .

i under steep spin conditions, but the relationship breaks down at highspin rates and pitch angles. The major cause for poor correlation is

the highly three-dimenslonal flow which occurs at high spln rates, '

affecting the shape of the cavity. Results also indicate, even at low

pitch angles, that blar&eted area is being overestimated. Perhaps the

-- roundeJ leading edge of the horizontal tall affects the forward shape of

the cavity, creating a larger unblanketed vertical tail area. In

addition, autorotatlve effects witnessed in the testing were not

accounted for, and aft fuselage shape was not considered..

: Better correlation may be obtained by applying some theory

estimating the three-dimenslonal cavity shape formed by the horizontal

tail. This would allow parameters AR h and Sh_tail as well as a v to beA

taken into account.

i J

CTHETA = 40 DEGREES _ = .SaTHETA = 60 DEGREES _ = .SATHETA = 8B DEGREES _ = .9

. 0 O00-4, "

l-0 025-_

-0 O50 i 13Cn -0 07E_ A

I

A A_-0 10_-

A

A ,, !_-0 125- ',

-0 150-"-_--r_r_-_-T-r-r_-i-_-,- t-_-_-_-F-t _ .=_:_ ,,_'_-T-r_r_ l_-r- r , , , , .

0.00 0.02 0.04 0.08 0.08

Toll AnSI-Spln PoromoL_r

' Figure 5-4. Yawing Moment as a Function of Tail Antl-SplnParameter

]i ,

/

CPAPTER VI

CONCLUSIONS _D RECOMMENDATIONS '

The present tests have shown the possibility of using conventiuaal

wind tunnel testing to obtain information about aerodynamic moments

produced by the tail of a spinning airplane. The tests enable tail

parametric studies to he performed without influence from a main wing

and body, and they allow for intensive studies of the causes of

aerodynamic interference from the aft fuselage and horizontal tail. The

major conclusions of the present study are summarized below.

I I. The tests show satisfactory agreement with NASA rotary balance data,with discrepancies at low pitch angles and spin rates attributable to -"

wing and body interference effects not modelled in the present studies. _

The influence of a rotational flow field on tall forces is considered to

be minimal.

2. The primary parameter influencing spin damping is horizontal tail

vertical position. Vertical tail aspect ratio can also have a largeyawing effect for high values of ARv.

r[ 3. Horizontal tail aspect ratio has a small effect on spin damping,

' with a moderately high ARh inducing larger yawing monents because of

reduced vertical tail blanketing."j

4. Horizontal tail chordwlse position has an appreciable effect on

pitching moment, but a small effect on yaw damping. This parameter may

be important to aircraft which must break pitch equilibrium for

recover_.

iI

119

I 5. The rudder Is a more effective spin recovery control t!:anthe

[- elevator under equilibrium conditions, incrementing yawing moment as

much as 50% in some cases. The partial-span rudder configuration

_ displays some advantage under flat spin conditions.

T 6. Some low horizontal tail configurations can actually produce pro--

spln moments under steep spin conditions.

I7. To be useful, any parameter developed to predict tail damping

charac_erlstics must _ccount for all major interference effects of thai

horizontal tall, and It will be strongly dependent on the spin rate. A

simple tail volume related factor will probably not be usable.

Addit:i0na_ testing of tall parameters to provide data for .'

analytical studies and numerical simulations is hfghl/ recommended.Specifically, further study is needed to determine the effect of

fuselage shape directly below the horizontal tall on the pro-spln forces

encountered at low values of h/bv. Control effectiveness should be

determined for all configurations, with special study of the influence

| of h/bv and chordwlse position of the horizontal tall on rudderI

effectiveness. The effect of a partlal-span rudder to increase yawing

I forces at hlgh spin rates should also be thoroughly investigated.

For a satisfactory analytical model of tall forces to be developed,

further testing would also be necessary. Tests should be performed

which determine the pressure distribution over the vertical tall,!

particularly in the region below the horlzontal tail. Flow measurement

and visuallzat[on would also be helpful in the development of a tl_ree-

dimensional cavity model, which is necessary to accurately predict the "

effect of tall configuration on yawing moment under flat spla conditions.

|" REFERENCES

]- I. Ballln,MarkG. and Zilliac,GregoryG., "Reporton the Conditionof the Low-SpeedWind Tunnel." (Interdepartmentalreport,Departmentof AerospaceEngineering,The PennsylvaniaState

: University,1980.)

!2. Beauraln,L., "GeneralStudy of Light Plane Spin, Aft Fuselage

Geometry,Part I," NASA TechnicalTranslationTTF-17,446.- Washington,D.C.: GovernmentPrintingOffice, 1977.

3. Bihrle, William,Jr., Hultberg,Randy S., and Mulcay, William,"RotaryBalance Da=a for a Typical Single-Englne,Low Wing GeneralAviation Design for an Angle-of-AttackRange of 30° to 90o,''NASAUontractor Report 2972. Washington, D.C.: Government Printing

Office, 1978.

.r

4. R!hrle, William, Jr., and Barnhart, William, "Spin Predlctlon

_echnlques," AIAA Paper 80-1564. New York: American Institute of

Aeronautics and Astronautics, 1980.

5. Bo%=an, James S., Jr., "Summary of Spin Technology as related to

Light General-Avlatlon Airplanes," NASA Technical Note D-6575.

Washington, D.C.: Government Printing Office, 1971.b

6. Burk, Sanger M., Jr., Bowman, James S., Jr., and White, William L.,

"Spln-Tunnel Investigation of the Spinning Characteristics of

Typical Single-Engine General Aviation Airplane Designs, I - Low-

WingModel A: Effects of Tall Configurations," NASA Technical Paper •

1009. Washington, D.C.: Government Printing Office, 1977.

7. Burns, B.R.A., "Golng for a Spin - Fighter Style."

_/L_9_.t.l_11£_, April 8, 1978, pp. 985-989.

8. Chambers, Joseph R., "Overview of Stall/Spln Technology," AIAAPaper 80-1580. New York: Americsn Institute of Aeronautics and

Astronautics, 1980.

9. Grunwald_ Kalman J., "Wall Effects and Scale Effects in V/STOL

I Model Testing." AIA!%.Aerodynami_ Testln_ Conference, Mar_h 9-I0_1964. New York: American Institl,te of Aeronautics and

Astronautics, 1964.

I0. Heyson, Harry H., "Linearized Theory of Wind Tunnel Jet Boundary. Corrections and Ground _ffect for VTOL-STOL Aircraft," NASA •

Technical Report R-124. Washington, D.C.: Government Printing

Office, 1962.

II. Heyson, Harry H., "Rapid Estlmatlon of Wind Tunnel Corrections with

Application to Wind Tunnel Model Design," NASA Technical Note

D-6416. Washln_ton, D.C.: Government Printing Office, 1971.

12. McCormick, Barnes W., Aerodvnamles of V/STOL Fli_ht. New YorkiAcademlc Press, 1967.

•. ]

121 :

1-13. McCormick, Barnes I_.,Aerodynamics. Aeronautics. and FllRht ..

Mechanics. New York: John Wiley and Sons, 1979.

• 14. McCormick, Barnes W., "Equilibrium Splnnlng of a Typical Single-Engine Low-Wing Aircraft," AIAA Paper 81-4076. New York: American

- _ Institute of Aeronautics and Astronautics, 1981.

15. Neihouse, Anshal I., "Tail Design Requirements for Satisfactory

_ Spin Recovery for Personal Owner Type Light Airplanes," NACATechnical Note 1329. Washington, D.C.: Government Printing Office,1947.

16. Neihouse, Anshal I., Licht=nsteln, Jacob H., and Pepoon, Philip W., ...."Tail Design Requirements for Satisfactory Spin Recovery," NACATechnical Note 1045. Washington, D.C.: Government Printing Office,1946.

17. Nelhouse, Anshal I., Klinar, Walter J., and Scher, Stanley H.,

"Status of Spin Research for Recent Airplane Designs," NASATechnical Report R-57. Washington, D.C.: Government PrintingOffice, 1960.

• i 18. Polhamus, Edward C., "Effect of Flow Incidence and Reynolds Numberon Low-Speed Aerodynamic Characteristics of Several Non-Circular

/ Cylinders with Application to Directional Stability and Spinning,"......... NASA Technical t_ote4176. Washington, D.C.: Government Printing

1 Office, 1958.

19. Pope, Alin, W_d Tunnel Testing, 2nd ed. New Yor_: John Wiley and

I Sons, 1954.

20. Scher, Stanley H., "An Analytical Investigation of Airplane Spin-

Recovery Motion by Use of Rotary Balance Aerodynamic Data," NACATechnical Note 3188. Washington, D.C.: Government Printing Office,1954.

21. Stough, H.P., III, and Patton, J.M., Jr., "The Effects ofConfiguration Changes on Spin and Recovery Characteristics of aLow-Wing General Aviation Research Airplane," AIAA Paper 79-1786.

New York: American Institute of Aeronautics and Astronautics, 1979.

22. Torenbeek, Egbert, Synthesis of Subsonic A%rp%_ne Design.

Rotterdam: Delft University Press, 1976.

il ,i

APPENDIX AMODEL AND APPARATUS DLMENSIONS AND CONFIGURATIOI_S

• IL I i

s

Table A-1 _

ConfigurationDimensions i

v bh v Sh llln_e Position r X_ Tallplane I

uration (in) (in) (in 2) (In 2) ARv APes (.) Rudder Elevator Position

A 7.5 20 37.b 100 1.5 4.0 15.O 60 60 0.5 Neutral

B 7.5 20 37.5 IO0 1.5 4.0 15.O 60 60 l.O Neutral

C 7.5 20 37.5 1OO 1.5 4.0 15.O 60 60 0.25 Neutral

D 7.5 20 37.5 100 1.5 4.0 15.O 60 60 O Neutral :

E 7.5 20 37.5 I00 1.5 4.0 15.0 60 60 0.5: 20X Forward

F 7.5 20 37.5 100 1.5 4.0 15.O 60 60 0.5 20Z Af_

G 5.5 20 27.5 i00 i.I 4.0 20.0 60 60 0.5 Neutral

II 6.5 2_, 32.5 100 1.3 4.0 17.O 60 60 0.5 Neutral

J 8.5 20 42.5 100 1.7 4.0 12.5 60 60 0.5 Neutral

K 7.5 19.3 37.5 107.1 1.5 3.48 15.0 60 60 0.5 Neutral

L 7.5 20.8 37.5 93.75 1.5 4.62 15.0 60 60 0.5 Neutral

H 7.5 21.1t 37.5 88.23 1.5 5.40 15.0 60 60 0.5 Neutral

All Configurations - _v = 0.5, _h =1"0, tic - .12 .f°r all surfaces,, fiv(C/2)'. ,= O, /[h = 0 "_'_ ]g_

J!( i

\. -.

· I! :~ :• i· ., '

1

!. i.:,

I, ,!

II

1

j1

I

I._ ..J

26.7')"

.R7,)-20 nm

I/

'" "......... __ ... "

..---1----'

• 3R Rt~JCI

-'..-1,,-· - - - - _,.... _._---'\..-----~·t.-L·~oc__.---=-----.J

""--Bal;,~cc Support

(J AdjuHr:lCnt·v

SO!:le dc::tails omittedfor clarity.'

F1 v,lJrc A- L odc.. t ln~ S.t~pport and Stn,lt

fl[.

iI

I

Scale2:3 .i

•' " -i.5 " _',

4t" _

; O.75_'- 2.0®

+1---] t_0.875- 20 TXD i+ n Ho te

Attached to Aft Fuselage Attached to Support

Figure A-2. NASA IR-21 Balance

Scale 2:3

j ,,_ -

ii

----.I, _

Figure A-]. Forward Body

t_O_

i . .

APPENDIX B

AERODYNAMIC MOMENT COEFFICIENTS AS FUNCTIONS OF SPIN RATE -.

°

f

Y128

"" THETR. _ 4_ _EE_

,_ o 6_ O£G,_EE._A 8_ DEGREES

-0,15 _

N,J41

-1. lS-J

1..?

-2.30 -

_.O 0._ _._ 13.j 0.4 O._ _.0 ;J./ O. :.'.9 o.q

Nondi'_en^_omui So;". _Jte

FIRurtl B-1. Pltchfn_ Homent as a Function of O and _','.,. Configuration A '

. • , , .• . , , . ,

• • .. ,

!129

;

o 4_DEGREES_ 6S D£GR£ES

, A 8_ DEGR_S

7"

1

1

;- ]

i -8.15 a-

__._J "-

•" " " ' ' t "

-I.'25r-m

1. "t . .

t-i._

, -_. ;5-

• .-2.23-

3._ 8 L 132 0.3 O _ _.5 _.O 3 1 _ 9 :_o

-- Nondl_onetonai $01_ RoLe

Figure B-2. Pitching Homent as a Function of 0 and _,. Configuration B

130

• {.• o • j

I _HETR• 4_ DE_gESm 6_ DEGRgE_

I A 80 DEGREE._ ,{

-_.5B-

-O.15

/

-i. ,_._

Cm

-I.qB.

-i.;5

II

. -2._

O._ 8._ 3.2 _.3 O.z 8._ 8. C _.t 8._ _.o

_iRure B-3. Pitchin_ Moment as a Function of 0 and _,Configuration C "

{131

i

THETR• 4Z DEGREESD 6Z DEGREES

8S DEGREEs

-Z.5_

.1

-8.15 -

o

; Cm -1.25

-I._._,

-_.15-

-2. _

_.,.3 ,3.i. ,3.2 .'1.3 0._ £].=j £].6 _./ 3.9 ,3.9Nondi_en_,ianoi Soln ,quLe

Figure Br4. Pitchin_ Moment as a Function of 0 and _, '".. Configuration D

• . , . ,

• . -. . . . .

°.

.

•132.

I THETR"

i

4B DECREES

= 6_ DEGREES8_ DEGREES

i -_. 5B-

;

; -3.75 -....

[ " .

I o . • •

[

Cm -1.2S ,

-_. 15,

-2. _.

_.3 0. I _.2 _.3 0.4 _.5 _.8 _./ _._ _.9

Nondl_en_lonai Spin RoLO

Figure B-5. Pitching Moment as a Function of 0 and G,

Configuration E

.,..

133

•. THET.q• 48 DEGREES

i m 6B DEGREES! A 8_ DEGREES

• !

4' II1

, iCm

--l.=.O . . - "-I.75

- -2.JO

_..O B.i 0.2 0._ _._ 13._ _.O 0./ O.B O.Q "

Nondlmeneionui Spln ._OLO

Figur e B-6. Pitching Moment as a Dunction of e and w, ..• Confi_urat ion F

134

tTHETR

I o 41_DF'OREESa 6_ DEC,REE_)A 8_ DECREES

I -8"_B-

U -B.7E "

-l._-

U ..

U -1.2_. -Cm . ..

-1.5_

.1I

• -2.294 ..... , .... ....... ,...... , ....... ,....... , ........ . ....... , .........21.:] D.i g.2 .';"1.3 O.t- -q._ _.6 :;"1.I g.8 .'1.9

Noncli_eneianni St.,in R_i.,e ...

• .'," . . . • .

Figure B-? Pitchinp_ Moment as a Function of 0 and _,• . . . . • . .

Configuration G

i 135

THETFI .

i o 48DEC,RgESM BB DEC,REE._A Sa DEC,REKB

T-

i -_'_L

io

I

'. -3.75 ......

.. ]

1" "..i": 4

-I.2,_.Cm

-l.qZI

-I. 15

II

1m

°' ,-23Z

13.3 D.i :3.2 D.3 _.d 13.5 G._ _.! 3.9 :3.q

.Nondi'_en-tonoi_pln .Rote

Figure B-8. Pitching Moment as a Function of 0 and g,Confi£uration H

t-0. ?5.

-I. IS-

-2..Il ....... I ..... | ........ + ........ +' ' + ........ i ...... + ....... +..... '':+

,0.21 0._. g.2 g._ g._ ._.5 ,_.6 O.l I:]._ 13.9

Nondlmenelonoi _pfn £obe

Figure B-9. Pitching Moment as a Function of 0 and _, '

Configuration J

4

137• • . •

Fizure B-IO. Pitchln_ Yo,-,:ntas a Function of '_and _,

Configuration K

"

'-.

"--,--,-~--'-,,.~~_._-.-~.._---

-J.::J.

, , q, ,

138

ft1£~q

• 4,1 ~h~£E~o fO Gf.l",l\£L'6\ SJ ~t:.e.-:£E~~

"'.2"(4 (

1

I,f1j! \

~-

..._-~----..- -.J , _ t'

"

r1~lIrl' !I-It. l'lt"h:l'~~ ~1"~'l1t ;1'; ,I FWd·tl,'t1 "f :\ .'1!l,t .•'(''!If (':\I';,\i ("11 l.

-_.:' ....~ ......

/°

4

139!

Pli.;tirt. I!-|. _. !'lt_-htl_ _!,..-,1.11t ,l:i .i P_l_i_-tion oi ;i ilild .,,1"011! 1_t4tll.i[ I[011 ,_1

• . . . , • , .

t--

140

j!1E'T~ .\) 4;) Dt"~EE"~

c eJ GE,--",EES0\ ~J aEGREES

I

1. i

1-J.•,~~ J

1

;'J . .~-i'

I, .. J. ,~~-4

~-................~.......

--- - -.- .

~, ....~ ., ,., .

Figllr~' 11-:13. Y.I\.:in~: ~1<'r.l1.·lIt .IS .1 FIII\<'[1"n ,'I II ;111<\ u'.t\'1lIi~lIr.lt1ll~1 "

l

Figure B-I:+. Yawing .Hotr_.,nt_ls a Function of 0 and t_, ,.

• Con figurnt lon B

142

I "f.q..PTq• aft DFGRK£S

• a _:3DF._EE.q

.. $. 925 t"i1

•i t3.3_ , -...........................

-ft. 32s -

i --

C.n 1?

1,;3.ff7.'5_

I4

g ,

143

!

THE'I,q " "o 48 DE_EE._.

"o _.3DEO_EE._ •a _0 DEGREES.."

1.....

I _"_=__ ............• ] . • . . .

_i.+ " .

,. tP i

i 1-_._.__.. .._ c_

i it

!t -_""_"!

4

I!

" -_ ,kFi+ .+ o- ,; + ..,. _+=.... ,&,- ....... i.+....... _++,..... .;-.,,,,,,+;+- ...... _ .... .

_._ _.L ,].2 _.3 O.* 3._ _.C 0.," O._ 3._

Figure B-It_. YawlnR Horn,hi a,q a Function of O and _o.

Configuration D

-3. l;=F

3.3 9.'_ 9.-' O.,z 3.4 3.5 O.C 3./ 3.9 3.q

, ._o_JimonPI3noi _oin _,J_,O

Figure B-IT. Yawing Motr_nt as a Functlonof 0 and _, '."

Configuration E

Figu_e'B-18. Yawing Moment as a Function of 0 and _,

..... Configuration F "

. , • , .

I

Figure B-19. Yawing _oment as a Function of 0 and _,Configuration G

147

J

Figure:B-20. Yawing Moment as a Function of 0 and _, ' "Configuration H

[

[

... -~.. -...

148

'':''!.i .

\IIII

l,!

f.T!iET~

o 4:l DEGREERc 6~ DEGREES~ S~ DEGREES

~.:l~~ ••..•••... --- .. - -- .. --.- - -- ".' .• n _ .. _n ••

4oj

4

-••J251

~.I1

-0. ~!3~ ~en ~

il

-~. :]75 ~1

1j

-0. ·.~a-J

. ~~. \

'. ~ . \

~ \-D. 12;:; ~...., .......,..".cr'.cr,~'l"'".......,.."'''''''''''''.1"''''.,..,....,..,...,.....,..'"",'''''.T''..,.,..""',.~,,..,.... ,..,.... ~~"""""'.""'.""".,..,..,....., ~~.,...,..,..,..,...,..,.... "",:,.,......,......,..,--:-

JIJ1,

D.I ~.2 D.3 D.'3 ~. /

~o~dlmon~i~nal ~pin ~aLo

FigureB-21. Yawing Moment ~s a Function of e and W,Configuration J

....... .:-.~,....- ...-.. ~.~..-,,,,.~~.....:...... -•.•- _"~_'_~-.--...,..;.... ~ ....,~.~~.........( '7",.........."'.""&........,..............: ...1.•~:>E.• ·.·=..., ...~. "\ .. ·....·~O;:'· ..-_·_t ..... ",_...~., . ... ·- ...~_~Ly-....,.-_ -.,. .•• _-...- ._~ -----....;O--::--~;--.............-....'f~_.

149

THETR~ 4::l DEGREESo 6n DEGREESA an DEGREES

'"

'--... ~...

);]).....r'

.;.': '-I

.. '\'..-..~~ .;..

f,-

, ... J 0_.

"

\ '

. "'1.

.ft,.fl.. f .1' .. f"" .. I,f ..~f .. tf .iI . . t. . .. if

::J.2 O. .:J n.4 ::J.S (l.G n,l ::J.9

U251

1·:3. ~m~ -; n un - n _. • n n .. n -_. - - ---

..~. 050en ,

~.

-0.075i~1~,

-::1. i~G ~1

-O.iJ "i. .f it.f

:J.:J lJ. L

J1

I

Figure B-22. Yawing Moment as a Function of e and w,Configuration K

.~- ...-' .. : (

.... _/' "'" y •. i._/"'-

,; ,. ~ t.

., ~:,

':-'_~.:.,

-.. r"

;' ..,:/,.l:.., :f:j~ :.?~~_); l;~-:::! ~}:'~~~ ~ .;~; :,:;~

I150

• . I i, i

THE'I'gT

:3813DEGREES-__ gEG_EES

' "I

- t

, .1, .,3._I_ --I................................................ i ............................

_, __-'._

•

:i "'_• • \\

"_. _°-_-_._°i"_J . ,

L..

-o._ \'? •

_", -0."L313,' J ,J"

,_ ]\ ,

t • _ •' , [ ]_,%

'/" -o. ,2_--11"i _':_ " .,21._ 8.:_ 3.2 13.3 0.,_ ,"l.= _.i3 D.i 13.:,9, 3.0,I p,t

:_j__:_ ._o.",dl"_n,:lcnoi $oIn _c,Le

,_.• ._,_ .."'_'_ Figure B-23. Yawing Moment as a Function of @ and _,

_;'" Configuration L

., _,'_ ; __< _.,%, ... ,, .:. ,. ,. . . . . .,." ........ _. - '. - .,.i -f..,,,_!._.!..:,_._.,.._. • %'-,....._."...:_,,:'-,,,._' ,.>". -,. .;_'.- 'X ,, "_ " , '

151

• . • ..

\TH_A

o 4_ _E_EE5n 63 DEGREES,, _ DF..CRE£S

Fi_urt, B- _'_. Y4win_ ,'4o..,_,nt :is a Function of 4. ,and _J,(;,_n,_iqurati_m :I

:. :. ...-- .._ - ,. :,:. . . . - - . - - ...% . . "__ ._--. , . ..-" i - - _ • o

-..,

TEST DATA

o"

I% %

!"" _2t-

%" .

t

x_

Table C-I

•_ Co,'.figuration A Test Data*

I),:n._ i t / .qor=a 1 Axial Pitching Rolling Yawing Side.... (_lug._/ VT Vd For_:e Force Ho_-.en t Moment MG=ent Force

• 6. 'tv f.t3) • (ft/st.c) (ft/sec) (lb) (lb). (in-lb) (ln-lb) (ln-lb) (Ib)i , .'

'. 80 /,6.20 0.00225 99.14 68.62 8.967 1.082 52.35 -18.02 -14.79 -3.351

,- SO _9.,)a 0.00223 100.8 78.31 9.853 0.9789 55.78 -15.07 -13.00 -2.939

" BO 30.0_ 0.00223 100.7 87.14 10.34 0.9767 59.30 -11.71 -9.937 -2.246

60 42.52 0.00223 101.3 74.68 8.180 0.7844 46.42 -14.60 -9.827 -2.387

,, 60 35.50 0.00222 101.2 82.43 8.758 0.7419 48.65 -12.28 -10.39 -2.421

_:) 27.00 0.00222 102.0 90.91 9.288 1.007 53.31 -9.444 -8.381 -1.951

60 17.f_O 0.00222 101.8 97.40 9.774 0.7440 53.13 -6.309 -4.615 -1.014

60 0 0.00221 101.8 101.8 9.677 0.4420 52.77 1.807 -1.040 -0.2517

40 27.89 0.00221 99.08 87.56 6.728 0.2325 36.99 -7.327 -8.936 -2.006

40 20.71 0.00221 101.2 94.62 7.222 O.3221 39.17 -3.631 -7.070 -1.513

40 12.7,_ 0.00220 102.5 99.95 7._6B 0.1501 39.73 -0.8351 -5.842 -1.147

40 0 0.00220 102.9 102.9 7.550 0.00_5 40.09 4.155 0.4996 0.1269

t.m, %1,,c_,.ntsresolvedaboutbalancecenter, t_

,'°[ •

Table C-2

Configuration B Test Data j

Density Normal Axlal Pitching Polllng Yawing Side(slugs/ VT Vd Force Force Homent Homent Homent Force

0 'Uv ft 3) (ft/sec) (ft/sec) (lb) (lb) (in-lb). (in-lb) (in-lo) (lb)

80 46.20 0.00221 99.04 68.55 7.'335 0.9574 43.43 -23.42 -21.13 -4.307

80 39.04 0.00220 97.93 76.00 8.009 0.997 48.59 -19.35 -19.54 -3.875

80 30.08 0.00220 99.55 86.13 9.659 1.074 57.37 -16.25 -16.79 -3.137

60 42.52 0.00219 98.54 72.65 5.946 0.7250 34.74 -25.54 -20.12 -4.020

60 35.50 0.00218 100.3 81.66 6.666 0.7515 38.70 -23.25 -19.03 -3.682

60 27.00 0.00218 99.05 88.25 7.295 0.7428 41.40 -15.10 -14.46 -2.768

60 17.00 0.00220 I01.I 96.69 8.637 0.8780 48.68 -9.402 -I0.647 -1.928

60 0 0.00219 100.4 100.4 9.471 0.5492 52.58 -0.8055 -0.3213 -0.0067

40 27.89 0.00219 99.50 87.93 5.471 0.1837 30.43 -20.27 -16.02 -3.358

.U 20.71 0.00218 98.63 92.26 5.542 0.1776 30.79 -14.90 -12.07 -2.460

40 12.78 0.00218 102.6 I00.I 6.769 0.1550 36.32 -9.851 -8.075 -1.493

40 0 0.00220 100.4 100.4 7.064 0.2103 37.85 2.13 -1.738 -0.1400

. °

Table C-3

ConflgurP "on C Test Data

Density _;or_ml Axial Pitching Roiling Yawing Side(slugs/ VT Vd Force Force Moment Moment Moment Force

0 av ft 3) (ft/sec) (ft/sec) (Ib) (lb) (ln-lb) (]n-lb) (in-lb) (lb)

80 46.20 0.00223 100.8 69.76 9.586 1.311 55.40 -23.53 -14.71 -3.401

80 39.04 0.00223 101.8 79.19 10.38 1.116 60.14 -17.68 -9.276 -2.468

80 30.08 0.00222 100.9 87.32 10.63 1.083 61.02 -10.55 -4.937 -1.761

60 42.52 0.00221 102.4 75.50 9.534 0.8713 54.21 -15.85 -2.730 -1.218

60 35.50 0.00221 102.8 83.71 10.20 0.7863 55.43 -12.38 -2.166 -1.114

60 27.00 0.00220 101.6 90.55 9.645 0.7070 52.77 -8.818 -2.470 -1.104

60 17.00 0.00221 101.6 97.14 9.888 0.7641 53.16 -6.022 0.1714 -0.4951

60 0 0.00221 102.6 102.6 9.901 0.7000 53.08 1.841 -3.526 -0.5929

40 27.89 0.00219 101.8 89.95 6.988 0.1612 38.27 -9.634 -5.061 -1.495

40 20.71 0.00218 101.2 94.68 6.'839 0.1230 36.60 -6.870 -3.780 -1.028

40 12.78 0.00218 101.7 99.2 6.911 0.1418 36.50 -2.683 -3.878 -0.8700

40 0 0.00218 100.0 100.0 6.707 -0.0571 34.Q7 2.334 -0.6667 0.0014

Table C-4

Configuration D Test Data

Density Normal Axial Pitching Rolling Yawing Side(slugs/ VT Vd Force Force Moment Moment Moment Force

i O .... _v ft 3) (ft/sec) (ft/sec) (lb) (lb) (tn-lb) (In-lb) (_n-lb) (lb)

80 46.20 0.00222 101.5 70.27 8.288 0.8700 46.60 -20.67 -I3.15 -2.846

80 39.04 0.00221 101.9 79.22 9.891 0.933 55.25 -20.55 -8.436 -1.954

80 30.08 0.00220 101.8 88.12 11.10 0.8743 60.85 -15.61 -0.9707 -0.5459

60 42.52 0.00220 102.5 75.61 9.203 0.5290 50.02 -17.67 -4.803 -1.178

60 35.50 0.00219 101.0 82.23 10.35 0.5080 55.51 -16.02 1.163 -0 2536

60 27.00 0.00219 103.1 91.86 10.68 0.4840 56.55 -11.28 3.766 0.1490

60 17.00 0.00219 101.2 96.82 9.924 0.5080 51.81 -7.260 3.564 0.2731

60 O 0.00218 102.5 102.5 9.845 0.4346 50.73 1.059 -2.330 O.1570

40 27.89 0.00218 101.8 90.01 7.215 0.0825 37.59 -12.24 -2.838 -0.9210

40 20.71 0.00217 102.8 96.24 7.501 -0.0099 38.35 -9.708 -0.0154 -0.2726

40 12.7_ 0.00222 i01.i 98.64 7.444 0.0128 37.75 -5.862 1.811 0.1715

40 0 0.00220 102.6 102.6 7.546 -0.1465 37.74 2.711 0.2775 0.0025

Table C-5

Configuration E Test Data

Density Normal Axial Pltchlng Roiling Yawing Side

(slugs/ VT Vd Force Force Moment Moment Moment Force

0 av ft 3) (ft/sec) (ft/sec) (lb) (lb} (in-lb) (in-lb) (in-lb) (lb)

80 46.20 0.00222 99.82 69.09 8.250 0.6216 38.42 •'21.10 -16.56 -3.624

80 39.04 0.00222 102.0 79.27 9.380 0.6394 43.66 -15.56 -13.74 -2.942

80 30.08 0.00221 i00.I 86.60 9.933 0.7065 46.05 -11.56 -11.61 -2.373

60 42.52 0.00220 i01.0 74.49 7.870 0.4904 36.03 -15.85 -10.80 -2.519

60 35.50 0.00220 100.4 81.72 8.285 0.5003 37.49 -13.18 -11.28 -2.453

60 27.00 0.00220 102.2 91.10 9.113 0.5000 40.80 -10.80 -9.784 -2.013

60 17.00 0.00219 100.4 95.99 9.053 0.4307 39.87 -7.271 -5.953 -I.010

60 0 0.00218 99.32 99.32 9.193 0.3500 41.38 0.6631 -0.4553 -0.3815

40 27.89 0.00219 102.0 90.12 6.774 0.0144 30.03 -10.54 -10.06 -2.140

40 20.71 0.00219 100.4 93.94 6.84"7 -0.0115 29.55 -6.423 -7.002 -1.424

40 17.78 0.00218 101.2 9_.70 7.225 -0.0197 31.09 -2.676 -5.118 -1.015

40 0 0.00218 101.5 101.5 7.714 -0.2290 32.33 2.23i -0.847 -0.1833

••

Q .

Table C-6

Configuration F Test DataT

Density _ Vd Normal Axial Pitching Rolling Yawing Side(slugs/ T Force Force Moment Homent Moment Force0 av ft3) (ftisee) (ft/sec) (Ib) (ib) (In-lb) (in-lb) (in-lb) (Ib)

80 46.20 0.00222 102.0 70.64 10.79 0.7426 69.43 -22.23 -17.23 -3.574

80 39.04 0.00221 10].3 78.85 10.75 0.6369 69.77 -16.80 -16.36 -3.201

80 30.08 0.00221 100.6 87.06 i1.08 0.7081 71.41 -ll.16 -12.84 -2.498

60 42.52 0.00221 101.9 75.1 8.591 0.4486 55.41 , -14.72 -12.65 -2.695

60 35.50 0.00220 99.4_ 80.96 8.493 0.4080 55.07 -I1.79 -i1.06 -2.341

60 27.00 0.00220 100.2 89.28 9.421 0.3947 59.65 -9.105 -8.081 -1.593

60 17.00 0.00220 I01.7 97.30 10.06 0.3769 63.30 -7.024 -5.626 -0.9724

60 0 0.00219 100.5 100.5 9.696 0.1924 60.32 2.153 -2.222 -0.2758

40 27.89 0.00220 100.9 89.22 6.943 -0.0547 44.43 -9.076 -11.20 -2.613

40 20.71 0.00219 101.2 94.74 7.195 -0.1580 45.03 -7.045 -7.359 -1.614

40 12.78 0.00219 101.8 99.36 7.285 -0.1727 45.03 -2.637 -5.768 -I.172

40 0 0.00219 101.2 101.2 7.633 -0.3056 45.96 2.4_3 -0.6820 -0.0151

tJ1

• . •

:I

Table ¢-7

Configuration G Test Data

Density Normal Axial Pitching Rolling Yawing Side• .- "'" (slugs/ V Vd

• O. a T Force Force Moment Moment Moment Forcev 'ft3) (ft/sec) (ft/sec) (ib_ (ib) (In'Ib) (In-lb) (In-lb) (Ib)

80 46.20 0.00219 97.88 67.75 8.377 0.8273 43.11 -15.83 -14.35 -3.145

80 39.04 0.00219 196.10 74.68 8.826 0.8112 49.58 -13.77 -11.64 -3.529

80 30.08 0.00217 100.9 87.36 10.29 0.8861 57.95 -11.82 -12.03 -2.367

60 42.52 0.00217 98.47 72.60 7.362 0.5836 41.30 -13.12 -12.14 -2.667:

60 35.50 0.00216 101.0 82.20 8.442 0.5930 46.73 -12.41 -12.63 -2.668

60 27.00 0.00216 100.1 89.23 8.?98 0.6815 48.80 -9.136 -10.73 -2.174

60 17.00 0.00216 98.69 94.38 8.786 0.5966 48.07 -6.863 -7.019 " -1.282

60 0 0.00215 97.39 97.39 8.705 0.3?02 47.18 0.6196 -1.905 -0.3098

40 27.89 0.00215 101.0 89.26 6.592 0.2802 36.89 -7.591 -9.975 -2.196

40 20.71 0.00215 98.38 92.03 6.546 6.1999 34.75 -3.938 -7.322 -1.632

40 12.78 0.00215 101.6 99.05 7.3088 0.2153 38.19 -1.564 -6.002 -1.179

40 0 0.00215 101.6 101.6 7.146 0.0428 37.47 2.903 -1.386 -0.1860

° ,

Table C-8

Configuration H Test l)ata

Normal Axial Pitching Rolling Yawing Side

Density VT Vd Moment Moment Force(slugs/ Force Force Moment

0 av ft3) (ft/sec) (ft/sec) (ib) (Ib) (in-lb) (in-lb) (in-lb) (Ib)

80 46.20 0.00221 102.5 70.93 5.277 6.8919 54.32 -18214 -15.15 -3.426

80 39.04 0.00220 100.8 78.35 9.645 0.9158 55.85 -15.11 -13.83 -3.052

80 30.08 0.00220 99.26 85.87 lO.Ol 0.9780 57.07 -9.124 -10.50 -2.252

60 42.52 0.00220 98.82 72.86 7.706 0.5983 42.74 -13109 -12.05 -2.720

60 35.50 0.00218 102.4 83.34 9.401 0.8688 49.55 -12.06 -12.54 -2.540

60 27.00 0.00219 99.29 88.47 8.775 0.5747 48.03 -9.338 -I0.39 -2.058

60 17.00 0.00218 102.4 98.0 9.470 0.5422 52.13 -6.697 -6.578 -1.223

60 0 0.00217 102.0 102.0 9.518 0.4223 51.77 2.116 -1.530 -0.2918

40 27.89 0.00223 I01.3 89.55 7.153 0.3169 39.62 -5.269 -9.325 -1.939

40 20.71 0.00222 102.4 95.83 7.609 0.3386 41.13 -3.517 -7.116 -1.370

40 12.78 0.00222 102.1 99.58 7.365 0.1661 40.01 -0.9997 -5.036 -0.9825

40 0 0.00221 102.8 102.8 7.409 -0.1185 38.89 41.122 0.1996 0.1122

O',• O

• • • . ., .

.dl

Table C-9

Configuration J Test Data

Density Normal Axial Pitching Rolling Yawing Side(slugs/ VT Vd Force Force Moment Moment Moment Force

0 _v ft 3) (ft/sec) (ft/sec) (Ib) (lb) (In-lb) (in-lb) (In-lb) (lb)

80 46.20 0.00219 100.9 69.86 9;049 0.8401 52.65 -18.91 -16.46 -4.524

80 39.04 0.00219 99.98 77.70 9.656 0.8376 55.54 -13.48 -14.63 -13.14

80 30.08 0.00218 98.68 85.37 9.987 0.8899 56.76 -9.153 -11.08 -2.274

60 42.52 0.00217 102.2 75.35 8.502 0.5544 47.40 -]4.06 -12.13 -2.785

60 35.50 0.00217 i01.i 82.28 8.747 0.5906 47.73 -11.04 -11.82 -2.780

60 27.00 0.00222 102.4 91.24 9.450 0.6101 52.54 -8.{52 -10.07 -1.926

60 17.00 0.00222 101.7 97.23 9.777 0.5460 52.88 -5.517 -5.553 -1.083

60 0 0.00220 101.9 101.9 9.669 0.3995 53.42 2.512 -36991 -0.7147

40 27.89 0.00219 I00.0 88.41 6.548 0.0481 36.32 -7.486 -10.67 -2.181

40 20.71 0.00219 101.2 94.68 6,816 0.1508 37.78 -3.700 -9.290 -1.930

40 12.78 0.00218 102.6 i00.I 7.518 0.0715 39.29 -1.507 -8.108 -1.585

40 0 0.00218 101.3 101.3 7.124 -0.1159 37.58 3.274 -0.9248 -0.1179

Table C-10 i

Conf_gur_tlon K Test Data

...... Density VT Vd Nor_l Axial Pitching Rolling Yawing Side• @ _ •(slugs/ Force Force Moment Moment Moment Force• v ' ft3) (ft/sec) (ft/sec) (Ib) (Ib) (In-lb) (in-lb) (in-lb) (Ib)

80 46.20 0.00224 101.6 20.36 9.362 0.8510 51.89 -19.24 -15.74 -3.445

80 39.04 0.00222 101.8 79.15 10.26 0.8238 56.43 -16.42 -13.98 -3.048

80 30.08 0.00222 102.5 88.71 I. O 0.9397 61.57 -12.76 -0.879 -2.210

60 42.52 0.00221 101.4 74.75 8.746 0.6441 46.91 -17.29 -ii.ii -2.585

60 35.50 0.00221 i01.0 82.20 8.998 0.6776 48.23 -13.43 -11.20 -2.504

60 27.00 0.00220 102.5 91.37 9.822 0.6691 51.•92 -11.86 -9.370 -1.906

_0 17.00 0.00221 102.4 97.92 10.39 0.6763 53.99 -8.957 -5.253 -1.049

60 0 0.00220 i01.0 i01.0 I_.06 0.4040 52.67 1.6308 -2.069 -0.3340

40 27.89 0.00219 103.5 91.52 7.112 0.1223 37.24 -9.418 -9.564 -1.824

40 20.71 0.00219 102.1 95.54 7.169 0.1361 36.89 -5.920 -6.346 -1.202

40 12.78 0.00219 102.3 99.78 7,968 0.1556 39.34 -0.2904 -10.43 -2.092

40 0 0.00219 102.8 102.8 8.320 -0.0724 41.62 3.434 -0.9978 -0.0350

Table C-11

Configuration L Test Data

Densl ty Normal Axial Pitching Rolling Yawing Side

• (slugs/ VT Vd Force Force Moment Moment Moment Force0 av ft3) (ft/sec) (ft/sec) (Ib) _ib) (in-lb) _In-ib) (in-lb) _Ib)

80 46.20 0.00223 100.3 69.46 8.658 0.9847 49.97 -22.66 -19.74 -3.736

80 39.04 0.00222 102.2 79.47 9..299 0.8981 53.24 -16.08 -16.00 -3.095

80 30.08 0.00222 101.4 87.75 10.02 0.9209 54.79 -12.51 -12.50 -2.290

60 42.52 0.00221 100.1 73.82 7.529 -1.717 42.01 -14.40 -i1.83 -2.402

60 35.50 0.00221 102.1 83.14 8.236 0.6844 45.64 -13.70 -14.27 -3.071

60 27.00 0.00220 102.5 91.33 8.683 0.6752 47.64 -10.90 -11.13 -1.979

60 17.00 0.00220 101.7 97.22 8.861 0.6516 48.22 -8.175 -7.071 -1.125x_

60 0 0.00219 i00.i i00.i 8.684 0.4754 47.61 0.7864 -3.372 -0.1832

40 27.89 0.00220 102.9 90.91 7.052 0.3476 39.57 -9.709 -11.83 -2.330

. 40 20.71 0.00220 I01.0 94.44 7.015 0.3752 37.81 -2.130 -10.32 -1.911

'%40 12.78 0.00218 102.4 99.87 7.127 0.2025 38.69 -1.1306 -8.054 -I..456

40 0 0.00218 100.9 100.9 6.858 0.0078 36.91 2.664 -1.877 -0.1218

)_ , '. .- ,

. ......

_., _ 4_ • i" sJ • • : " " _ _ ° . _ l

\. Table C-12

;_ Configuration M Test Data

i; Density Normal Axial Pitching Rolling Yawing Side

(slugs/ V Vd

..., O a T " Force Force Moment • Moment Moment Forcev .ft3) (ft/sec) (ft/see) (ib) (ib) (in-lb) (_n-lb) (In-lb) _Ib)

x

"' 80 46.20 0.00216 98.66 68.28 7'482 0.8048 42.85 -26.92 -18.52 -3.790

80 39 04 0,00216 I00.I 77.77 8.691 0.6662 47.70 -18.81 -15.79 -3.089

-" 80 30 08 0.00217 98.52• 85.23 8.902 0.6197 47.76 -13.00 -11.37 -2.166

_ 60 42 52 0.00217 98.77 72.82 7.162 0.4261 38.67 -14.01 -9.718 -2.064

60 35 50 0.00217 99.60 81.08 7.960 0.1446 42.62 -12.59 -10.69 -2.181

60 27O0 0.00218 100.6 89.68 8.129 0.4749 43.57 -10.43 -9.897 -1.907

60 17 O0 0.00217 100.7 96.30 8.233 0.3553 43.89 -7.234 -5.994 -1.068

60 0 0.00217 99.31 99.31 8.077 0.1944 43.41 1.081 -1.002 -0.1263

40 27.89 0.00218 99.94 88.32 5.895 -0.0161 33.00 •-8.631 -9.874 -2.128

40 20.71 0.00218 102.0 95.39 6.406 -0.0478 34.68 -5.777 -7.896 .-1.665

40 12.78 0.00219 102.7 100.2 6.642 -0.0830 35.46 -1.853 -6.521 -1.268

40 0 0.00220 102.6 _02.6 6.917 -0.2370 35.54 2.458 0.1934 0.1185 i

TMJle C-13

C_nt_ol l)eflL.ctJon Test 1 Data, 0 - 40.0", _ - 20.71 °v

- "2't _" _-_ .'.L.Z --" -- Z-.LT.-.-q--_-_Z.-_ -_"_-----

, L,,.::;it>, t_ormal Axial Pitching Rolling Yawing Sidec r (slugs/ V_, Vd " Force Force Moment :lonL.nt Ho=_ent Force

.!_ ......... (o) ....... _it_3)..... j_ft./suc) (ft/sec) (lb) (lb) (in-lh) (tn-lb) (tn-lb) (lb)• . . .

:) 0 0.00223 I00.I 93.67 7 158 0.2473 38.48 -4.048 -6.833 -1.435

Io 0 ..00222 101.1 94.58 7.874 0.0300 43.46 -4.856 -6.489 -1.531

13 0 [).00221 100.4 93.97 8.205 -0.1807 44.43 -5.645 -6.174 -1.318

t] _5.7 0.00220 10i.0 94.54 7.390 -0.0059 39.93 -6.796 -10.86 -2.197

0 25 6.(}t)220 101.8 95.19 7.418 -0.0733 40.81 -7.?22 -12.13 -2.257

15 25 0.00220 I00.9 9_.36 8.652 -0.4007 "5.59 -7.050 -I1.46 -2.095

I0 16.7 0.00220 100.6 94.14 8.000 -0.2470 43.06 -7.76J -I0.58 -2.061

0 16.7P* 0.00220 100.6 94.14 7.163 0.1940 38.98 -?.07g -9.200 -1.836

0 251' 0.00219 101.8 95.28 7.216 0.1208 40.38 -7.595 -10.26 -2.009

15 25P 0.00219 ,-3u.2 93.74 8.215 -0.2170 44.83 -7.239 -8.988 -1.818

I0 16.71' 0.00219 99.Z,9 93.07 7.750 -0.0527 42.15 -7.406 -8.514 -1.741

* Partial-span rudder.

• . • . .Q . * . •

"

:. ,,..... r'" ""," 1.2c " • " .,. • I .',_ . • ,..,_ .", •" '..... _" " ,u ._ , . ,;_" .; ,: : _ ".'"

• _, - o.,._.,. . -,, .:- .. .-" . -;." './ .- .

Table C-14

Control Deflection Test 2 Data, 0 = 80 =, cA = 30.O8"• .V

Dt.n:, i ty Norr_aI Axial Pitching Rolling Yawing Sidet _ Vc r (._lug:s/ VT d Force Force Ho=ent Moment Moment Force

(o) to) ft 3) (ft/sc.c) (f'./st-c) (lb) (lb) __ (ln;lb) (ln-lb) (ln-lb,

0 0 0.00224 I¢)2.2 83.43 Ih.86 1.0_,0 61.55 -10.93 -10.67 -2.339

IO 0 0.00222 lhO 3 86.77 10.68 0.4996 58.40 -10.97 -1,3.64 -2.162

I _. 0 0.tj0222 10¢) 1 86.65 10.59 0.2023 _7.45 -11.14 -i0.98 -2.173

€) 16.7 0.f)0221 lOtj 8 87.21 10.32 O.8001 5d.OO -11.28 -12.17 -2.543

O 25 O.O0220 IO1 3 87.61 10.46 0.7079 58.59 -11.28 -12.56 -2.631

" 15 25 0.00220 101 6 87.94 10.59 -0.0394 58.04 -11.59 -13.25 -2.611

I0 I:).7 0.0q220 I00 7 87.13 10.51 0.3405 57.96 -11.43 -12,63 -2.546

:) I;,.7P* 0.09219 IGI 1 87.49 10.61 ;1.9559 59.04 -11.70 -12.67 -2.641 ,

tj 25P 0.h0218 9g 64 85.34 9,_g2 0.9032 56.16 -11.04 -12.25 -2.5t, l

15 25P 0.002 ]hi I01 0 87.37 10.71 0.3027 58.19 -11.94 -13.23 -2.667

]O I,;.7P O.0:)2"20 I01 O 87.37 10.77 0.6336 59.q,7 -11.48 -:2.76 -2.628

: ..............................

* i'.Lrttal--_;_a;, rudJ,:r.J

• _

• )

.................'...........................,: _-:.'..:,."..: ,-," ..'.,./-:"."".. .._, "(,,[.. ", _"_,'' ...,.,:'.;...€,.;'.,;.->-.0..y.f'_',_'_._';'-;_.• , , . ;t [i ! • .. " , '_',"- ",_j _". ;# ':.4. _ _ " ;_

. A Reproduced Copy - NASA · related to the spln-damping properties of the tail. Previous...

Documents

Transcript of . A Reproduced Copy - NASA · related to the spln-damping properties of the tail. Previous...