C.P. No. 534 :

MINISTRY OF AVIATION

AERONAUTICAL RESEARCH COUNCIL

CURRENT PAPERS

Measurements of Pitching Oscillation Derivatives

at Subsonic and Transonic Speeds for a Cropped

Delta Wing of Aspect Ratio 1.8

(Interim Report)

C. J. W. Miles, J. B. Bratt, B.A, BSc.,

and

K. B. Bridgembn of the Aedynamics Division, N.P.L.

LONDON: HER MAJESTY’S STATIONERY OFFICE

1961

Price 3s. 6d. net

c.Pe No.534

Measurements of Pitching Oscillation Derivatives at Subsonic and Transonic Speeds for a Cropped

Delta Wing of Aspect Ratio 1.8 (Interim Report)

- By - C. J. W. Miles, J. B. Bratt, B.A., E.Sc., and

K. B, Bridgman of the Aerodynamics Division, N.P.L.

5th February, 1960

Measurements of the direct and indirect derivatives for pitching oscillations on a cropped delta wing of aspect ratio 1.3 have been made at subsonic and trsnsonic speeds.

The effects of frequency parameter,- amplitude of oscillation and mean incidence have been investigated. Tests were also made to determine the effects on the measurements of a root fence.

Comparisons with subsonic theory are reasonably satisfactory but agreement with supersonic theory is poor.

1. Introduction

The measurements described in this report form part of a general prog.:amme of derivative tests made in the N.P.L. 9* in. high-speed tunnel on a half-v;ing model of a cropped delta wing of aspect ratio 3.8 with a trailing-edge flap. Measurements of the direct hinge moment derivatives hzve already been completed and .ire given in an earlier report', For the present tests the flap ~,as rigidly clampod to the wing and measurements of oscillatory pitching moment and lift were obtained for pitching oscillations about two axis positions, in order to give sufficient information for deducing plunging motion derivatives.

A Mach number range from 0.4 to l.A2 was covered in the tests, in general at amplitudes of oscillation of both I* abd 2*, The direct derivatives m, and m;, were measured at two frequencies of approximately 25 c/s and 100 c/s and at mean incidences ranging from O* to IO*, The indirect derivatives C, and C;, were obtained only for the lowest frequency (25 c/s) and zero mean incidence at an amplitude of 2'.

A preliminary series of tests was made in which m and m* were measured with a fence in the form of a thin metal plate fixe 2 at the goat of the model to reduce effects of flew through th e narrow gap between the root and the tunnel wall. The fence also covered holes in the tunnel wall for connections between model and apparatus. Fences of different size and shape wore tested in order to give some guid:nce on the design of a fence for the main body of the tests.

2./

. . .--.“--- -_____--------------______^____I________--- ---------------c----I_____

previously issued as h.Ii.C.21,662.

-2-

2. Technique of Measurement

The apparatus used in these tests employed an electrically sclf- excited system, and is described in detail in Ref.2.

2.1 Direct derivatives me

For measurements of rnd and mW the apparatus inner frame was clamped to the earthed structure. The stiffness derivative coefficient met was measured by observing the change of frequency of the oscillating system on running the tunnel whilst the damping derivative coefficient rn. was obtained as the change in useful electrical power required to maintaina constant amplitude. k more detailed description of the measurements involved is given in Ref.2.

Some cases were encountered where ma and consequently the change in frequency cf the system was veq small and tended to be masked by the effects due to changes in temperature, In these cases the sequence of measurements was dcsigned to minimise temperature effects.

2.2 Indirect derivatives 4.d

For the measurement of do, by the force units and observations

and "5 the inner frame was supported of the oscillator-- lift forces appearing

at these units were made. Reduction of the observations to the coefficients % and -9 involved a dynamic calibration cf the system in which a known oscillatory lift force was simulated by a mass attached to the oscillating made1 by means of a light Tufnol clamp. Two spanwise positions for the mass were used and in each case tep+ 0>vs were m::de with the mass both forward of the L.E., and behind the T.E. 'moasurcd forcc'/'cnlculated force

The average value of ' for all loading positions and both axes

of oscillation was l.05. the total phase

The dynamic calibration also gave a value for

and involved shift through the me,asuring system, which amounted to 0.2O

a correction to Q of the order of IO,3 in the worst case.

Drifts of the force unit outputs at first to be troublesome.

due to temperature changes proved R fair degree of temperature stabilisation

was achieved by circulating water at constant temperature through small tanks of simple construction attached to the bases of the force units. The residual drifts, whilst allowing the oscillatory lift forces to be mcnsured, proved to be too large for the measurement of static forces.

Considerable difficulty was and .G

at first experienced in measuring e, due to the presence of relatively high-frequency noise signals

superigposed on the lift signal when the tunnel was running. In marJ cases the noise swamped the lift signal and lead to cut-off in amplifier circuits and transformer effects in the dynamometer iwattmeter used for measuring the vector components. The difficulty wzs finally overcome by the use of a suitable filter and auxiliary phase-shifter, a simple technique being developed for adjusting the latter to compensate for the phase shift introduced by the filter.

3. Notxtion

The complex pitching moment and lift relating to a pitching oscillation are expressed in the following form:-

where the symbols arc defined below

s 4

’ I

L

CO

F

f

I\1

S

v

X

a

aO

P

w

2-L a

Iii l a

1

“a ’

4,;

!

-3-

pitching moment (positive nose up)

lift (positive up)

root chord

mean chord

frequency of oscillation

Mach number

area of wing

wind speed

distance forward of trailing edge

pitching disR1ncemen.t (positive nose up)

amplitude of oscillation

air density (free stream)

frequency parameter (= 2zf+J)

non-dimensional derivative coefficients as defined in Ref.3

4. Experimental Results

No tunnel corrections have been applied to any of the expcrimentul results given in this paper.

The variation of the frequency parameter w with &ch number for the two frequencies of the tests is shown in Fig.14.

4.1 Tests with various root fences

The five fences used in the tests are illustrated in Fig.2. a11 show the sane characteristics of increasing kdth rearwards, the reason for this being the presence of a lug extending from the flap through a hole in the tunnel wall. The modifications in No.3 and No.4 were introduced to increase the overlap on the hole in the tunnel mall accommodating the tongue of the model for the res;sective axis positions.

The effects of the various fences on -ma and -mh are shown in Figs.lO(a), 10(b), II(s) and U(b), the tests being made at the highest frequency of the range. It seems that all the fences are more or less equally effective up to l'yr = 1 , 0 , with'onc exception shown in Fig.lS (b). This, however, is likely to be a sensitive c,Ace since -m Above 1/l = 1.0 fluctuations in

a is very small. the curves tend to appear, and some attempt

was made to correlate these v;iti; shock have RAtterns, but without SUCCOSS. Finally the smallest fence (X0.1) was selected as bt;ing the Icast likely to product undesirable effecLs at transonic speeds.

4.2/

-4-

&2 hfoasurenients of rnde at zero mean incidence

Curves of -ma and -rnh against Mach number for zero mean incidence are shown in Figs.&(a), 4(b), 5(z) and 5(b). For both axes of oscillation -mm rises at at"about ifi

a steadily increztsing rate with Mach number up to a peak value = 1 .o. Por still higher values of I';';, -me falls rapidly in the

case of the rearmost axis position, but for the forvvar$' axis the curve shows

only a small dip. The stiffness derivative -m, shows very little change with Mach number up to M = 0.9, At higher value s of Iv1 the changes become more rapid.

A large frequency effect can be seen on -mu for the forward axis (Fig.T(a)). The similar effect in Fig.5(b) is actually a very small shift of the curve if plotted on the same scale as Fig,5(a), and corresponds to a change in a very small quantity. A similar trend with frequency is observable in the case of -mk for the forward axis position (Fig.b(a)).

Comparisons cf results with and without fence are given in Figs.6 to 9. In general the effect of the fence is to produce a numerical increase below H = 1.0.

Tests were made on a dummy fence with the model removed. The forces measured on this fence were negligible.

4.3 Effect of mean incidence on m d* a

Values of -m, and -m; plotted against mean incidence for three Mach numbers generally are shown in Figs.l2(a), 12(b), 13(a) and 13(b). For the rearward axis of oscillation -me shows a large and sharp peak value at the higher Mach nuTnhers for a mean igcidence of 7.5 to 8.0 degrees. An attempt was made to correlate this result with the surface flow on the wing for static conditions using the oil flow technique. The starting position of the L.E. vortex is plotted against incidence in Pig.15, and for the two higher Mach numbers shows a delayed movement with increasing incidence at 7.00 to 8.00.

4.4 Xffects of transition

The major part of the experiment was carried out with free transition and laminar boundary layer, but a few measurements of ma, and m; were made with a turbulent boundary layer, transition being fixed by means of a strip of carborundum powder at the wing L.E. The effect of making the boundary layer turbulent was small and is shown in Figs.1 6(a), 16(b),

4.5 gsurements of &&

Curves of 4 for zero mean incidence plotted against Mach number are shown ?n iFis.$(a), 17(b), 18(a) and 18(b) Over the whole Mach number range E, shows a slight increase whilst 4* ihows a small decrease at the lower 14ach numbers with a sudden, small &crease at about w = c.9.

5. Comparisons with Theory

Subsonic theoretical values or" the derivative coefficients relating to a pitching oscillation have been obtained by Garner&. The subsonic curves for -m;, shown in Figs.&(a) and 4(b) are in good agreement with experiment for the lowest frequency in the region of M = 0.9, but show a steeper rise with Uach number. in the cases of -mu and 6 lG(b)) the trlcoretical values

(Figs.5(a), 5(b), 18(a) and are somczhat great& numerically than the

experimental values, but 4; shows (Figs.1 7(a) and 17(b)).

an opposite trend below M = 0.85

The/

-5-

The supersonic theoqy due to :/atson5 shows in general unsatisfactory agreenent with experiment either in magnitude or trend.

6. ~C0nclUSiOiX3

(1) The use of a root fence appears to be &some importance, and in general incre ases the numerical value of the derivative at bIach numbers below Iti = 1 .O.

=n th(e2)c spEfef:ect of frequency on ma and. m; is quite marked except g, > & for the rearmost axis position.

(3) Incidence effects are most marked in the case of -m* for the rearmost axis v?here a pronounced peak appears at a mean incidek of approximately 8.0°. This is correlated with a discontinuity in the movement of the L.E. vortex with change in incidence, for the static condition.

(I+) comparisons with subsonic theory are reasonably satisfactory but agreement with supersonic theory is poor.

References

p& Autkior(s)

1 J. E. Bratt, c, J. W. idilcs and R, E'. Johnson

2 J. B, Bratt

Title, etc.

lkieasurement s of the direct hinge moment derivatives at subsonic and transonic speeds for a crouped delta wing with oscillating flap. I?.. & 8.3l63. May, 1957.

A note on derivative apparatus for the N.P.L. y& in, High Speed Tunnel. A.R.C. C.P.263. January, 'I 956.

3 I. T. Minhinnick Tables of functions for evaluation of wing and control surface flutter derivatives for incompressible flow. A.R.C.l3,730. July, 1950.

.!+ ii. C. Gnrncr

5 J. Watson

Application of Multhopp's lifting-surface theory to the lift, pitching moment and hinge moment on a slowly pitching cropped delta wing with oscillating flap. (To b e written).

Calculation of cierivativcs for a cropped delta wing with subsonic loading edges oscillating

a supersonic air stream. . & r:i.jCr;'J, 1958.

1. KG.

----

I-

--

0

0

0

0

,Tunnd wal I

Diagram of model --m

FIG. 2

Fence No. I

Fence No.2

Fence No.3

Fence No.4

Fence No. 5

Scale V3 (appr0x1

Fence profiles

Fence

Fence No. 1 with root profile

Full scale

Axis 0*3&c, - Fence No I l-8 fi6.4 (a if 6) EG.4 (CL)

. L I ncory ‘(Garner)

O-8 athi-

0.6 Theory (W&on) -

---- w--96 c/s,ao-tO1 I a ----e-27&, a, -1' 1 I I I I I

Axis 006275 co Fence No. I. o-7

I I I

---n---99c/s, a0 - to I

Theory 1

0.6 ----+---99 C/s, 111. - 2”

-27 C/S, a, - I“

Y 27 c/s, a, - 2” 0*5

0.4

fiG.4b)

D-4 0.5 0.6 O-9 I I I 1

Comparison of -711.2 with theory.

Axis O-315c0 Fence No.1. I-4 FIG.~ (a8 b) (a] ho.5

I I I --- x --- 96 c/s, a, -lo

I*2 __a__ 27 c/s , a0 =I'

- - 24 c/s, a, -2O

0.4 O*S 0*6 O-7 M O-8 0

Axis 04 6275 c, Fence No. I.

o*io FIG. 5 (b) t 1 I I I

----x--- 99 c/s ( a* = to

o*os ---+--- 99 c/s, a0 = 2O

- 27 c/s, aa = lo

-a-----o--- 27 c/s, a, = 2’

3 0.4 0.5 0.6 C t-7 O-8 M o-9 I-0 l-l

Comparison of -ma with theorq.

- \ I

Th&j (Garner)

l-2 3

FIG. 6 (ae. b) FlG.6(4 1.8 I

0.4 --- --- %

t- '

96 c/s, QC, = I0 with fence

JL 96 @,a, s I” without fence

(6) FIG.~

I-0

-m&

0.8 m-j+-- 27c/s , a, = lo

046 - ---+--- 24 c/s, a0 = 2' with fence

- 27c/s, a0 - I0 0.4. A v >

without fence , 24 c/s, a, - 2”

0.2

Effect of fence No. I on -mu for the O-315 c, axis

--- -x --- 95 +I, a, = lo with fence

- 96 cls, a, - lowithout fence I-0 ’

2 / _,/f

/

* ___---. -----I.------*--- -----

-%

0.6

o-5 O-6 0.7 M O-8 009

7(b) FIG. l- 27 c/s,

24 c/s,

27 c/s,

24 c/s,

I

a, - I0

a0 -2’

’ i

d, - I0

a, =2’

I

with f&Ice

Without fence

I

0 I I I I 0.3

I 0*4 0.5 O-6 O-7 M 0.8 0.9 1.0 1.1 I.2

Effect of fence No.1 on -ma for the 0s 315 c, axis.

__- X--- yy ys, aQ- I-

----+- e-e 99 c/s, a0 = 2* pith fen-ii;

I 0.6

l- I .

- 99 c/s, a. = 1’ -- Without fence

i $-’ I ,‘+ A A I I

I q+- 99 c/s, a, - 2-J I

o-3 @4 0.5 Oe6 0*7 M O-8 0.9 I*2

O-6

o-5

-I)c' a 0*4

0*9

0.2

o* I

9

Fm. 8 (6)

- .- 27 c/s, a0 - lo

3 0.4 0,5 O-6 0.7 M 0.8 0.9 l-0 1-I I-2

Effect of fence No.1 on -rn; for the 0 a6275 co axis.

FIG. 9 (a&b) FIG. 3 hl

---g---

--- 99 c/s, ao= 2 - 99c/s,a,=I

-0 * 15

-0.20 0.3 0#4 O-5 0.6 0;7 04 M 0.9 Ia0

0. I5

0. IC

O-O!

-ma

C

I I 1

27 c/s, I0

5 I

--- % -- - a0 -

27 2' witfi fence

---- + --- c/s, a0 = -1 27 c/s. a, = I' V

- 27c/s, a, -2’ Without fence

I

Effect of fence No. I on -m, for the 0.6275 c, axis.

I Axis o-315 G, '

I - - - Without fence I I’0 F

-- - rlnal fence (Ng- I) * b-tee NO- 2

1.7 --+ Fence N4c4 ---t)--- Fence NO-5

, I /’ . I

,.I .

I ’ Without fence -+-- /- I

s I I !

Note false origin

FIG. lo(b) --

O-6 Axis 0.6275 c, --- ---

Effect of various fences on -m;,

I I I FIG. ~(aab) FIG. Ii(a)

I I I I ’ Axis 0.315 co- ' - - m Without fence

_ ---- Final fence ( NO- I) ” Fence ND-2 ’ - A ” Fence NO-4 n Y Fence NE 5 I I I I I

Without fence

0.3 O-4 CP5 0*6 0.7 M O-8 0.9 I.0 1.1 I-2

Ta

0

--- Without fence ----

0.3 0*4 0.5 O-6 O-7 M O-8 0.9 I-0 I.1 l-2

Effect of various fences on -m,.

I I I

- Axis 0.315 c, Fence ND- 1 - V

- M = 0-596

- ---X-w a-o- a M = O-896 -+-- M = 1.117

96 c/s, q,= 1’

- -t- M = O-596 Y M = U-896

Y M=1.117 29c/s, uo= I0

I I Mean incidence

-+- + +-- \

b \ \ \o d

I I I I

Axis OS'6275 c, Fence NO I -- x-- M = O-596 -- o-- M = O-896 m/s, a,= I0 -- Q-- M = 1.117 -7tr -+- M = O-596 101__ M = 1.117

29 c/s, do- P

Points with-tails”, q, = 2“

E f feet of mean incidence on - m,

I

Mean incidence

I0 ZOO 4*0° 6-O' 8.0° 10-o* O0 2:o" ' 0 & 0 6-O' 8-O"

I I I iO*O"

I I 10

. v .

FIG. /3(a a b) --

“0 6 -

0 0 do

3 c

-t .- 0

co0 .- cb

C

2 t

“0 - 4’

0 0

-(;I

0 0

0 0

A

0 0 do al

2 2 ,- .E”o

- ;o C

ii! z

0 0

-. t

0 0

-64

0 a

0

Frcs. 14 B 15 FIG. J4.

O-8

o-7

”

. -It-

. V

xc* / o-4

o-3

O-2

0.1

0

O-6 o-7 O-8 M

o-9

Variation of w with Mach number. FIG. IS.

I Inc,idence I 1

Variation of vortex starting position with incidence.

.

FIG. 16(a & b)

-m. a

o-3

o-2 Axis O-6275 co , 99 C/S, ao=2'

. Q I I CI-;AIC a I Turbulent D.I,. ~a~ll~lal U-L.

0-I +i f

-- t-- With fen ce ND-2

a-)(-- Without rcIv= Cnwberr

I

0 I I I I I I I O-3 o-4 O-5 0.6 0.7 M O-8 O-9 I.0 I-1 I-2

0. IO

1 1 1 T&dent K. Laminar f3.L

-0.15 , -v -- t -- With fenceN0-2

-v --)q-- Without fence

-0.20 I I I- O-3 O-4 O-5 0.6 0.7

M 0.8 0.9 I-O I.1 I.2

Effect of turbulent 6.1. on -m6 and-m, .

FJG. IT(a II b) f-IG. 17(a)

Axis - 0-3~5 co - Fence Ng I

a, = 2O f = 25 c/s I

I-T Theory

(Watson )

( > a -L O-3 O-4 O-5 O-6 O-7 M O-8 O-9 J-0 J-i l-2 l-3

I I I 1 1

Axis = 0*6275c,- Fence NW ”

a, = 2*

f = 25 c/s

I Theory

(Garner)

Theory (Game?)" atIvf=O

w

FIG. u(b) FIG. u(b)

Theory

h/a bon)

I

o-3 O-4 O-5 0*6 O-7 M

O-8 0.9 I.0 I-J I-2 I*3

Comparison of e;L with theory.

. IsC .

cd

I*C

V!

c

i-

Theory (Garner) at M=O Y

FIG. 18(a % b)

Theo&

Axis = 0.315 co - fence NO- I

ao = 20

f = 25 c/s

I

b- E- The&-y

(Watson)

FIG. 18(b)

Axis = 0~617~ c, - fence N2 I

a, =2O

Theory

- (Watson)

0.3 O-4 O-5 O-6 O-7 M O-8 O-9 i-0 1-l

Comparison of & with theory.

__.___I I - - - - - - - -~- - - -

C.P. No. 534 C.P. No. 534

Miles, C. J. W., Bratt, J. B. and Brldgman, K. B. Nat. Phys. Lab. Miles, C. J. W., Bratt, J. B. and Bridgman, K. B. Nat. Pbys. Lab.

MEASUREMENTS OF PITCHING OSCILLATION DERIVATIVES AT SUBSONIC AND TRANSONIC MEASUREMENTS OF PITCHING OSCILLATION DERIVATIVES AT SUBSONIC AND TRANSONIC SPEEDS FOR A CROPPED DELTA WING OF ASPECT RATIO 1.8. (INTERIM REPORT) SPEEDS FOR A CROPPED DELTA WING OF ASPECT RATIO 1.8. (INTERIM REPORT)

Measurements of the direct and indirect derivatives for pitching Measurements of the direct and indirect derivatives for pitching oscillations on a cropped delta wing of aspect ratio 1.8 have been made at oscillations on a cropped delta Wang of aspect ratio 1.8 have been made at subsonic and transonic speeds. subsonic and transonic speeds.

The effects of frequency parameter, amplitude of oscillation and mean The effects of frequency parameter, amplitude of oscillation and mean incidence have been investigated. Tests were also made to determine the incidence have been investigated. Tests were also made to determine the effects on the measurements of a root fence. effects on the measurements of a root fence.

Comparisons with subsonic theory are reasonably satisfactory but Comparisons with subsonic theory are reasonably satisfactory but agreement agreement with supersonic theory is poor. with supersonic theory is poor.

- - “----*--------_-~~-

C.P. No. 534 C.P. No. 534

Miles, C. J. W., Bratt, J. B. and Bridgman, K. B. Nat. Phys. Lab. Miles, C. J. W., Bratt, J. B. and Bridgman, K. B. Nat. Phys. Lab.

MEASUREMENTS OF PITCHING OSCILLATION DERIVATIVES AT SUBSONIC AND TRANSONIC MEASUREMENTS OF PITCHING OSCILLATION DERIVATIVES AT SUBSONIC AND TRANSONIC SPEEDS FOR A CROPPED DELTA WING OF ASPECT RATIO 1.8. (INTERIM REPORT) SPEEDS FUR A CROPPED DELTA WING OF ASPECT RATIO 1.8, (INTERIM REPORT)

Measurements of the direct and indirect derivatives for pitching Measurements of the direct and indirect derivatives for pitching oscillations on a cropped delta wing of aspect ratio 1.8 have been made at oscillate ons on a cropped delta wing of aspect ratio 1.8 have been made at subsonic and transonic speeds. subsonic and transonic speeds.

The effects of frequency parameter, amplitude of oscillationand mean The effects of frequency parameter,amplitude of oscillation and mean incidence have been investigated. Tests were also made to determine the incidence have been investigated. Tests were also made to determine the effects on the measurements of a root fence. effects on the measurements of a root fence,

Comparisons with subsonic theory are reasonably satisfactory but Comparisons with subsonic theory are reasonably satisfactory but agreement with supersonic theory is poor. agreement with supersonic theory is poor.

!--

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@ Crown copyright 1961

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C.P. No. 534