Design, construction and testing of an AGARD standard model D for oscillatory derivatives measurements

...

r

van KARM:AN INSTITUTE

FOR FLUID DYNAMICS

TECHNICAL NOTE 21

DE$IGN. CONSTRUCTION AND TESTING

OF AN ~GARD STANDARD MODEL D

FOR OSCILLATORY DERIVATIVES MEASUREMENTS

by

Ho STARKEN

RHODE-SAINT-GENESE, BELGIUM

von KARMAN INSTITUTE FOR FLUID DYNAMICS

TECHNICAL NOTE 21

DESIGN, CONSTRUCTION AND TESTING

OF AN AGARD STANDARD MOD~t D

FOR OSCILLATORY DERIVATIVES MEASUREMENTS

by

Ho STARKEN

i

SUMMARY

Some (measurements of pitching moment derivatives of AGARD calibration model D have been p~rformedo A rigidly forced technique with a mass balance system has been used o Tests have been made for a reduced frequency parameter in the range from 0 0003 to 0018 (005 to 12 cps) o The results for the damping and 'stiffness term show reasonable agreement with tests made in other low speed wind tunnelso

ii

TABLE OF CON~ENTS

Li st of SymbCtls

List of Figures

Introduction

20 Theoretical Analysis of the Stability Derivatives

Apparatus

Test Procedure

Results and Discussion

Conclusions Reference s Figures Tables Page i i i iv 1 2 5 7 8 10 12

LIST OF SYMBOLS c centerline chord

=

001 m f frequency of oseillation (c/s) K L M q R s v e

redueed frequency parameter

=

(w· cY2v length of the supporting sting

=

00 45 m pitching moment (m KE)

angular veloeity in pitch (rad/s) Reynolds number

=

Voc'p/~

wing area

=

0 00324 m2

free stream velocity (m/s) angle of incidence

.

.

(

2/

4)

mass dens~ty of a~r Kgos m viscosity of air (Kgos/m2)

w circular frequency of oscillation

=

2~f(rad/S)

Coefficients C

=

M m 2 (!Y2): 0 s 0 c rie ac C

=

m C

=

m m _m&. • 2 q _{a ~ a ~} 2v _4v 2 oC ac C

₌

m C

=

6 m m oa mo a (LoC a a

-2v F oL F 0 0 L e

₌

fl C

=

C

P

),,2 me (/:v

Pi

2 °SoCoa m·· e (~ .socoaoK iii

ivo

LIST OF FIGURES

10 AGARD Calibration Model D

20 General Configuration

30 Mass Balance System

40

Balance and Support

50

Electronic System

60

Pitching Moment Derivatives

70

Measured Stiffness Derivative

80

Measured Damping Derivative

90 Measured Stiffness Derivative at Constant Frequencies 100 Measured Damping Derivative at Constant Frequencies

10 Introduction

The deve~opment or high speed airplanes required new investigations or the stability derivatives. because the quasi steady theory is no longer valid.

To be able to compare the results obtaine4 in

dirrerent countries with dirrerent oscillating systems. the AGARD calibration ving D was d~signed ror measurements in

1.

low speed wind tunnels o ~he model is a wing vith a rectangular center section and tapered tips and it is supported by a

sting. Figo 1 (ReL 6)0

Tests have been made so rar in rour dirrerent lov speed vind tunnels (Rer o 1. 2. 3. 4.

7)

ror a range or the frequency parameter rrom 00015 to 00045 (r

=

0092to2.4).

The presented measurements. made vith the symmetrical _,

m~unted ving oscillating in pitc-hing motion. cover a much

Theoretical analysis of the stability derivatives

The following method has been used to get the stability derivatives in pitching motion:

The wing is vertically mounted and oscillates around the axis

o-z

(Figure 2) 0 It is rigidly forced through a

d~iving rod and \an excenter-system at one side of 'the model. The aerodynamic forces are directly measured as reactions at the driving rod, whilst the inertia forces are balanced out by a special system o dM

₌

M

=

dc

=

m dc _m

=

The aerodynamic moment of the whole system is:

aM aM - 0 dq + ~ 0

aq

aq

dqo + ~ 0 da + ~ • dä

aa

aa

c m

a

c

a

ê: ~ 0 dq + ~

aq

aq

c o - 0 2v

ac

m

-

aa

o da +

ac

m

ä&

K ( c •

1.

0 dq + c 0

1.

0

d~)

+ C m w mo w m q a a

• do

1 da + - 0 2 w c _ma • d q

The linearized form of this equation for small deflections:

c

m = c m

a

a +

In the case of' sinusodial motion of the wing r,te gein

a = a 0 sin wt 0 • _wt a = a 0 w 0 cos = q 0 ä _{= -a} 0 _w 2 0 _{sin wt} = q 0 0

and therefore the moment coefficient become~g

c = m a o (c m a 2 _ K 0 c ) mo q sin wt + K 0 a (c + o m q

Stiffness Or ~n phase componen~g

c

=

IIla

2 c - K 0 m a

Damping or quadrature componentg

c mo

a

= c m _q + C mo a c ) mo a o cos wt

The derivatives e and e ean be ea1eu1ated in first

approxi-me mo

mation (small va1ues of K)eby neg1eeting the terms e and c :

mq

m&

oe

wing oeL wing L m ₊ e :r _e

=

0

-me m _a oa oa e

=

oeL wing 2L 2 c e

₌

-

0

---"2

mo m aa

e

q

e

For the AGARD ea1ibration model used in this ~ext:

=

4

oe

m wing _=-0 0 03 oa This gives: e := -162 mo

e

The data reduetion of the te.t resh1ts has been made with the

fo11owing equations:

Fe 0 L

=

(%) v2 0 s 0 c o a

50 with S 0 00324 2 = m a = :1:10 035° 0 c = 0 01 m L = 0045 m we get _F c = 7680

~

ma _{(.Q. )v} 2 and F 0 oL c =

a

mo _{(~)v 2 oK} a osocoa ₀ Fo c = 7680

a

mo Ko(..e.)v 2 a 2 30 Apparatus

The tests have been made in the closed test section (2 m di ameter) of the low speed wing tunnel L 10

In order to get a high natural frequency of the system a small model with a chord-length of 001 m has been chosen o

Fot the same reason and in addition to small ben ding deflections _e the sting of the AGARD model has been modifiedo The aerodynamic influence of thi s is assumed to be negligibleo

At the axis of' oscil;lation OZ the sting is mounted with ft system of' f'oup crossed springs to the wind tunnel support

(Figure

4}0

The sting is f'orced f'rom one side of' the wind tunnel through an excenter rod of' one meter length, which is driven from a DoCo motor o

In order to get no vertical movement and f'orces at the force transducer_a the balance system is guided by a tube, which leads outside the wind tunnel o

Accörding to a suggestion of' Pro Smolderen a mass-balanced system has been used from which a principle sketch

is given in Figure 30 The inertia f'orces are compensated by the reactions of' an adjustable counter-weight~ so that the transducer does not f'eel any mass-f'orces o Theref'ore the transducer can be made very sensitive and it is possible to measure very small f'orces at the wingo The only limit is due to the natural f'requency of' the system0 which has to be well

above the maximum test f'requencyo

The experiments showed that the condition of' mass-balance is maintained f'or all frequencies of' oscillation o

A powerful resonance of' the second harmonie was f'ound at 17 cps and a slight increase of' amplitude at 805 cps

f'or the fourth harmonico The resonance of' the f'undamental natural frequency will theref'ore occur at --]4 cps 0 Therefore

good results can be expected up to about 11 cpso

. A test without wing-mass gave the theoretical calculated values up to 13 cpso

The higher harmonies do not affect the readings,

because the instruments do not measure themo

The measurements have been taken by feeding the

strain gauges of the force transducer with a voltage obtained

from a sine-eosine resolver driven by the DoCo motor (Figure 5)0

This gives strain gauge output signals proportional to the forces

in phase or in quadrature with the mödelo To be abl~ to use

a resolver in the form of a rotating transformer~ a carrier

frequency system (1000 cps) has been appliedo The reading

of the low response galvanometer

• 2 • 2

Fa 0 s~n wt or Fe 0 s~n wt

the interesting components ~~ and

a

is an ave rage value of

and therefore one half of

Errors by gain fluctuations and non linearity effects

of the amplifier and galvanometer are avoided by using a zero

reading methodo

Te st Proce dure

Calibration of the force transducer: Forces up to

7 02 Ki have been· applied at the quarter chord position of

the wing in order to get the calibration curve of the

strain gauge transducer o The displacement of the wing has

been measured in the same wayo

b)o Adjustment of the counter-weight~ In a test without

wind, the counter-weight has been adjusted at a position

where the in phase component gave nearly no reading in

cL

50

Ca~ibration of the wind influence over the system:

A test series has been made without a wing but an

equiva~ent mas! in order to find the influence of the air

flow over the driving and measuring systemo The test

has been made at different speeds and frequencies 0

Measurement of the in-phase and quadrature component

of the aerodynamic forcezn Two main test series have

(

been performedo Dne with a const~nt windvelocity and

varying frequency from 005 to ~2 cps and the other with

constant f'requency and varying velocity from 22 to 5B m/so

An additional test has been made with removed mass-balance

to check the influence of the counter-weight o

Results aod discussion _;..

A~~ the measurements of the in-phase and of the

quadrature component are given in tab~es 1 to Band in

Figures 7 and Bo

The results show good agreement with measurements

made in other wind tunne~s (Figure

6

)

even though ~here is

quite a large scatter between the pointso The unsteadiness

of the wind tunnel in velocity and direction of' the air flow

may be one mai n reason .for this o Especially because these

tests have been made wi th an oscil~ation of

!

lO~ whilst

most of the others tested with much larger amplitudeo

Sma~~ deflection combined with small size of the wing

gave very sma~~ damping forces at low values of the frequency

parameter Kt and therefore low accuracy with large scatter

90

The in phase component was nearly constant with

varying air speed. as theory predicts. but there was a

considerable increase of the rea ding with increasing frequency

(Figure 9) 0

No explanation for this could be found so far in

the mechanicalor electronic systemo One test was made

without counter-weight and therefore much higher natural

frequency of the systemo The results showed the same

increasing tendency as tests made with massbalance (Table

5)0

The scatter in these measurements can easily be

explained by th~ method o Two measured quantities have to be

subtracted and the error can become very large for small

readings (low accuracy of the measurements) and for large

readings 0

The increase with frequency can only be explained by an aerodynamic effect of the wing or of the support and

balance system o The latter has to be investigated in more

detailo

Withou~ wing~ complete ba~ance of the forces could be

achieved for the wind-off condi~~ono At wind-on a slight increase

with frequency was found~ but this cannot explain the large

increase of the measurements o It can only shçw. that the effect

is probably due to an ~erodynamic influence on the systemo

The results have been corrected for the additional

deflection of the wing due to load on the systemo The deflection

of 000008 rad/K~ is mainly given fr om the dispiacement of the

force transducer and therefore a pure additional value to the

The.overall accuracy of the measurements is believed

+

%

•

to be about - 5 • Errors are poss1ble:

1).

in the measurement of the air sp~ed. It was not possible to keep constant speed during a test. _,

2)0 due to fluctuations in the direction of the air flow in the wind tunnel o

3}.

due to fluctuations of the frequency of oscillationo

4}0

due to incorrect adjustment of the resolver.

5).

due to zero shift in the electronic system o

6}.

due to aerodynamic influence on the balance o

7}0

1n taking the reading fr om the instrument. The averaged value of the forces was not constant with time. See error 1 to 3. Normally a middle value was taken. but this is not necessarily the right one.

6. Conclusions

The measurements of the AGARD calibration wing D. oscillating in pitching motion have been made in the range of 0.005 to 0018 for the frequency paramete~o

The results agree with tests made 1n other countries. The damping term seems to be constant and independent from the frequency parameter as theory predicts. The stiffness term

110

increases wit~ increasing frequencyo This should be checked by further tests to investigate w~ether a systematic error of the instrumentation or an aerodynamic effect of the wing is responsible o

The applied rigidly driven oscillation technique with a special mass-balance system gave' good repeatable results even at ~igh frequencieso

12.

REEERENCES

1. OoNoEoRoAo Mesure des Dérivées Aérodynamiquee en

Incompressible à la Soufflerie dV_{Algero OoNoEoRoAo}

Fiche Documentaire Prc~isoire. No o 200. avril 19580

20 Yff9 Jo : Measurements of Some Low Speed Oscillatory

Stab-ility Derivatives of the AGARD Wing Model Do NoLoRo

(Amsterdam)~ TMF 195, December 1956 0

30 Letko, Wo g Wind Tunnel Investigation of Low-Speed

Oscillatory Derivatives in Pitch and in Rollof AGARD

Model Di NACA 19~6~

40 Valensi i Jo: Détermination en Soufflerie des Dérivées

Aérodynamiques de la Maquette Etalon AGARD D et Comparaison

des Résultats avec ceux Obtenus à l 60 0NoEoRoAo

Institut de Méchanique des Fluides de Marseille. Rapport Eo 73. juin 19570

50 Valensi. Jo A Review of the Techniques of Measuring

Oscillatory Aerodynamic Forces and Moments on Models

Oscillating in Wind Tunnels o Fifth Meeting of AGARD

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( Not e: 0;' th e (ig ure, th e win gis rep r es ent e d in symmetrieal mounfing. For dissymmetrie al mount"ing XX' moves lp ot)

Yawing and pitehing, OZ NACA 64 AT 012.

1/2 body of revolution gerterated by 'he wing tip profile.

Serves toeover the balanee, shown only as an example.

ACjARDCalibration Model 0

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CONSTANT FREQUENCY TABLE 1 1

₌

_{0 014 t 0038} 0106 1 _R

₌

₀₀₁₄ t 00380106 :f

=

1099 - R :f

=

5-s e s e V 1 1 1 1 v 1

lc

1 1

'2

Fe -c - Fo -c K

2'

Fe - Fo -c (~) K 2 me 2 e 2 mo (!! ) 2 ma 2 e 2 mo

(kp)

(kp)

a

(kp)

(kp)

a s s 2205 0.0278 0 0036 90 2 -00009 -83 22.5 00070 0 0038 907 -(}Q024 -88 2902 0.0214 0 0061 902 -0 0011 -79 29.0 000542 0.064 908 -0 0027 -77 35.3 000177 0 0088 9.1 eO oOll -65 35.8 000439 0.094 904 -00031 -72 4101 0 00152 0 0120 901 -0.011 -56 4101 0 00383 0 0129 9 08 -0.034 -69 46 04 0 00135 0 0152 9 00 -0.011 -49 46 08 0 00336 0 0167 907 -0 0036 -64 5201 0 0012 00196 90 2 -00011 -44 52 00 000302 0 0208 9.8 -0 0040 -64 58 03 0 00107 0 0250 903 -0.011 -40 58.0 000271 0 0263 909 -0 0046 -65

- CONSTANT FREQUENCY TABLE 2 1

₌

0014 t 0.38 0106 1

=

0014 t 00380106 f

=

6 097 - R f

=

9.93 - R 25 e _{s e} 1 _lc 1 1 1 1 1 1 v

_2'

_Fe - Fo _{- c} v

_'2

_Fe -c - Fa -c K 2 me 2 e 2 me K 2 me 2 e 2 mo (~) (~p)

(kp)

e (~)

(kp)

(kp)

e !It !': 2203 000983 0 0039 1000 -00034 -89 2203 0 014 00040 1004 -00048 -~9 29 00 000755 00064 908 -00040 -81 2902 0 0107 00069 1004 -00060 -86 3505 000611 00094 906 -00046 -77 3509 00087 00102 1002 -00064 -74 4101 000533 00130 909 -00051 -15 41 02 00076 b 0

14.0

100 6 -00080 -81 46 08 00 0468 0 0172 10.0 -0.059 -75 46 08 0 0067 00185 10.7: -0 0093 -82 5200 000421 00216 10.2 -0 0066 -75 5800 0.0371 0.263 909 -00074 -15

CONSTANT FREQUENCY TABLE 3 f

₌

1109-1 R

=

0013 t 0030106 S e v 1 1 1 1 K

'2

Fe

'2

c - Fo

'2

c (~) me 2 e mo s (kp) (kp) e 20~O 00185 0.040 12.0 -0.053 -88 -2202 0.1685 ~ 00049 12.1 -0.057 -86 -- - - -- -- - - --~---- -- - -25.2 001483 1 0.062 11.9 -00062 -82 I - --- - - - --- -28.6 00131 00074 110 0 -0.69 -80 +----35.0 I I 0.107 0.108 10.7 -00084 -80 I -.l 40.4 , 0.0925 00145 10.7 -0.095 -79 I ----_. '--- I - -

---i I 450 0

I

0.083 001841 110 0 - 00106 -79

CONSTANT VELOCITY. WITHOUT MASS BALANCE TABLE 4 'y :;: 20Q2~ _R

=

₀01360106 v

=

2808~ R

=

0.1930106 s e s e f

I

1 1 1 1 f 1 1

(1:.

)

K

_'2

_{Fe -2 c me 2 - F· e -2 c m·}

_{(1:. )}

K

_'2

_Fe -₂ c _me -1 F· -1 c 2(k~) 2 m· s (kp) (kp) e s (kp'

e

I I 1092 00 0299 0.029 8 09 -0.009 -92 2.0 0.0218 0 0056 8.4 2097 000462 0&032 908 -0.013 -86 2.96 00 0323 0.059 8 09 -0 0010

-47

4 00 000622 0 0034 10.3 -0 0016 -79 3 087 000422 0 0061 901 -0 0016 -57 4093 000768 0.034 10 03 -0.020 -80 5.07 000553 0.065 907 -00028 -76 5095 0 00925 0 0035 1005 -0.025 -83 6 00 0.0655 0 0067 909 -0.027 -65 6 09 0 01074 0.035 10.5 -0 0032 -91 6.85 0.0748 00070 10 03 -00034 -69 . _

-B

o03 00125 0.037 1100 -0 0040 -98 8.0 0.0873 0.073 10 06 -0 0044 -76 9 00 0.140 0.040 1109 -0 0043 -94 10.0 0.1090 0 0071 10.3 -0.055 -76

--9095 0.155 0.032 905 -0.048 -95 10.9 00119 0.067 9.7 -0.069 -87 _. - _. -_.- _{- - - -- - - - -}

_

. . _ - - - ---11.0 0.171 00035 10.3 -0 0040 -72 1203 0.134 00085 12 01 -00062 -70 --_._--r - - - _._ --l2015 00189 0.060 1705 -0.062 -101

TABLE 5

CONSTANT VELOCITY, WITHOUT MASS BALANCE

v = 40

_·

3m

_s

R = 002710106 e :f

_{~ F}

1 1 1

2'

c - F·

-

c (1) K 2(k~) me 2(k~) 2 m_e o s 1 .09 000085 00121 902 2005 0 00160 00118 900 3008 0002'40 00121 9.2 -00015 -48 40 02 0.0314 00120 901 -0.022 -54 5 000 000390 00125 904 -0.027 -53 6e 05 000472 0.130 9.8 -0 0039 -64 6. 88 000537 0.139 10 04 -0.043 -62 7093 000618 00135 10.1 -0.055 -68 9 085 000768 00150 1100 -0.088 -88 11 00 000857 00156 11.4 -0.088 -79 1202 000950 00149 10.8 -00102 -82

.

I

CONSTANT VELOCITY TABLE 6

! v

=

2809~ _s R _e

= 0 018 010

6 v

=

4104~ _s R _e

=

0026 0106 f 1 1 1 1 f 1 1 1 1 (1)

'2

Fe - c _ Fo _{- c} K

'2 _

_

F e - c - Fo - c K

_(kp)

2 me 2

₍

_kp)

e 2 m-e (1)

_(kp)

2 mE 2

_(kp)

e

2 me o s s 0057 000062 00059 901 0 0 00122 901 I 1096 000213 0.061 904 -00010 -73 0 055 000041 0 0113 8 05 I ! I .- _ .. I 2097 000323 00061 904 -0 0015 ~72 2aOO 000152 00120 900 -0 0012 -62 4 001 000436 00063 907 -0 0021 -75 3 000 0 00227 00122 901 -0 0019 ~66 5004 000548 00063 907 -0 0028 -79 3098 000302 0.125 903 -0 0025 -65 5093 000646 00063 907 -0 0034 -81 5 003 0.0382 0~125 903 -0 0036 -72 6093 000755 00063 907 -00 040 -82 5098 000453 00127 905 -0 0045 -75 . 8003 0 00873 00064 908 - 0.045 -79 6 086 000520 00127 905 -0 0050 -73 900 0.0978 00069 10 06 -00049 -78 7 088 0-.0597 00131 9 08 -0 0061 -78 9093 0.108 00070 10 08 -0.059 -85 8.88 00 0673 0 0138 10 03 -0 0070 -79 ~0.10 00 0765 0 0143 1007 ~00082 -82

Co.NSTANT VELo.CITY _{TABL'E 7} m R

=

O038el06 v

=

65~ R

=

0.42010G v

=

58 Q 5-s e s e f 1 1 1 1 f 1 1 1 1 (1) _K

'2

Fe -2 c

m

-2 Fe a

'2

c

m

e

( 1-)

_K

2'

Fe -2 c

me

-2 F

e

a -2 c

m

e

(

kp)

e

(

kp)

e

(kp)

(kp)

e

s s 0.056 0.00.03 0.0257 9.5 -0. 00.0.45 -57 0.057 0.00.0.28 0.0330. 9 08 -0..0.0.7 -77 " ---200. 000108 0.0251 9.3 -0.009 -32 1098 0 00.0.96 0 0313 904 ~00016 _-51 2095 1000. 1 5 8 0.0257 905 -0 0024 -58 3.0.8 000.149 00320 906 0 0024 -50. 3099 !000.214 0. 0257 9.5 -0..0.35 -62 3.99 0.00.;1..93 0. 0319

I

905 -0.00.37 I· -59 I ! I 0.00.268 0.0261 _{907 1-0.00.48} -68 000242

_I

₉₀₇ I 500. 500.1 0.0323 _{1-0. 00 55} -70 I 5.96 1000.320. 0.0270 1000 -0.0.56 -67

!

5098 0..0289 0. 0323 9.9 -0.055 -59 6093 ,0.0 0.373 0. 0271 10. 01 -0 00.72 -73 700. 0.00339 00336 100 0 -00080 -73 i 800.2 10.00.432 0.0281 10. 04 -0.0.90. -79 7.97 0..0385 0..357 10 07 -0 0102 -81 i 900. _10.0 0.483 0.0291 10.8 -0.0i0.2 -80. 900.3 0..0.431 0.0 357 10. 07 -0..0.98 -69 909 !000.532 0..298 11.0 -0.117 -84 1.0.05 0 00487 0.0 384 1105 -0. 0142 -90. i - - - --

-CONSTANT VELOCITY TABLE 8 I I m R

=

001360106 v

=

28 09.! R

=

001490106 v

=

200 2-s e s e 1 1 1 1 _f 1 1 1 1 f

_'2

_{Fa - c} - Fo _{- c}

_2'

_Fa - c _ Fa - c 2 ma 2 8 2 me _{2 ma} 2

e

2 m -(l._s ) K _{(kp )} (kp)

e

('i1 ) K (kp) (kp) a 5 000778 0 0034 1003 - 00020 -78 4097 00054 00065 905 -00024 -67 I 7 00109 00034 1003 -00029 -~1 609 00075 00065 905 ~00036 -72 . 9093 00155 00036 1008 -00044 - 87 1001 00110 00072 1005 -00053 -72 , 11 0 0171 00038 11 04 - 00048 -86 11 00120 00079 1105 -00059 - 74 1- -12 0 0187 00039 1107 -0 0056 -91 1201 0013a 0 0078 1102 -00072 - 82 i . V

=

40 04.! s R e

=

002710106 4.094 000384 00122 903 -00027 -54 1000 00078 0 0136 1004 -00074 -82 100 9 000847 00147 1101 -00082 -83 1200 0 00932 00143 1008 -00098 -90 1209 0 01003 0 0148 1101 -00100 -86

V.K.I. TN 21

von Karman Institute tor Flu1ds Dynamios, 1964.

DESIGN, CONSTRUCT ION AND TESTING OF AN AGARD STANDARD MODEL D FOR OSCILLATORY DERIVATIVES MEASUREMENTS, by H. Starken.

Some measurements of pitoh1ng moment

deriva-tives

ot

AGARD oa11brat1on model D. have been

pertormed. A r1g1dly foroed techn1que w1th a

mass balance system has been used. Tests have

been made trom 0.003 to 0.18 (0.5 to 12 ops).

The results for the damping and stitfness term show reasonable agreement w1th tests made 1n

other low speed w1nd tunnels.

V.K.I. TN 21

von Karman Inst1tute tor F1uid .Dynamics, 1964

DESIGN, CONSTRUCTION AND TESTING OF AN AGARD STANDARD MODEL D FOROSCILLATORY DERIVATIVES MEASUREMENTS, by H. Starken.

Some measurements

ot

p1toh1ng. moment

der1va-t1ves

ot

AGARD oa11brat1on model D have been

pertormed. A r1g1dly toroed teohn1que w1th a

maas balanoe system haa been uaed. Tests have

been made trom 0.003 to 0.18

{0.5

to 12. opa).

The results for the damp~ng and st1ttneas term

show reasonable agreement w1th testa made 1n

other low apeed wind tunnels.

V.K.I. TN 21

von Karman Institute tor Flu1ds Dynam1cs, 1964.

DESIGN, CONSTRUCTION AND TESTING OF AN AGARD STANDARD MODEL D FOR OSCILLATORY DERIVATIVES MEASUREMENTS, by H. Starken.

Some measurements

ot

p1tching moment

der1va-t1ves

ot

AGARD oa11brat1on model D have been

performed. A rigidly foroed teohnique with a

mass balanoe system has beenused. Tests have

been made from 0.003 to 0.18 (0.5 to 12 cps).

The results tor the damp1ng and stiffness term show reasonable agreement with tests made in

other low speed wind tunnels.

V.K.I. TN 21

von Karman Inst1tute for Fluid Dynamios,1964.

DESIGN, CONSTRUCTION AND TESTING OF AN AGARD STANDARD MODEL D FOR OSCILLATORY DERIVATIVES MEASUREMENTS, by H. Starken.

Some measur.~.nts of p1toh1ng moment

deriva-t1ves of AGARD oalibration model D have been performed. A rigidly foroed teohn1que with a

mass balanoe system has been used. Tests have

been made trom 0.003 to 0.18 (0.5 to 12 ops).

The results tor the damp1ng .and st1tnnes term

show reasonable agreement with tests made in