A note on the total drag of jet flapped wings

~ :c

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TECHNISCHE HOGESCHOOL DELFT

VLiêGTUI':;30UWiCU."OE Michiel de r.uyterweg 10 • DELFT

Z9

dec. 1960

A NOTE ON THE TOTAL DRAG OF JET FLAPPED WINGS by

G. K. Korbacher and K. Sridhar

by

G. K. Korbacher and K. Sridhar

Title:

Authors:

UNIVERSITY OF TORONTO

UTIA TECHNICAL NOTE NO. 30 (1959)

On the One -Dimensional Overtaking of a Shock Wave by a Rarefaction Wave

1. 1. Glass, L. E. Heuckroth and S. Molder

ERRATA

Please make the following changes in Sec. 6. Dis-cussions and Conclusions: paragraph No. 1. line 2. change to read, were discussed. and in line No. 3. read Fig. 12; paragraph No. 2. line No. 1. read Fig. 11. line No. 6. read Fig. 12. line No. 8. read Fig. 10. line No. 11. read Fig. 9. line No. 15. read Fig. 12.

The authors are indebted to Dr. G. N. Patterson, Director

of the Institute, for providing the opportunity to work on this subject.

This work was supported by a grant from the Defence Research Board of Canada.

The limitations of

2the drag hypothesis for jet flapped wings

(i. e. J dCOT

I

dCLT 2 = dC

'DI

dCL ) are discussed from the theoretical and experimental point of view.

An empirical relation (COT

=

C '0

+

0. 63·

ctA-'

sin2Q) for calculating the total drag coefficient of quasi two-dimenslOnal jet flapped

wings at zero incidence is derived and presented. This drag coefficient

relation, combined with the expression for the total lift coefficient provi des

an expression for the slope of the COT vs. CLT2 curve ( dC oT/dcLT2

=

~).

The slopes obtained with this empirical expression are in qualitative K

TABLE OF CONTENTS NOTATION

1. INTRODUCTION

1I. PRESENTATION OF THE PROBLEM lIl. COMPARISON WITH OTHER RESULTS

3.1 Experimental Results

3.2 Semi-Theoretical Predictions

3.2. 1 Drag-Lift Relationships

3.2. 2 Drag-Jet Coefficient Relationships

3.2.3 Lift-Jet Coefficient Relationships

3.3 Lift-Drag Relationships

3. 3.1 Empirical Relationships

3.3.2 Theoretical Relationships

3.4 Values of the Factor K 2

3.5 The predicted Slope dCDT / dCLT 3.6 Limitations of the Drag Hypothesis IV. CONCLUSIONS REFERENCES 1 1 2 2 .3 3 5 6 6 6 7 8 8 9 9 11

NOTATION (see Fig. 1)

J jet momentum ( =. M. V J)

cf-4.- jet momentum coefficient (=J

Iq.

Sw)

M mass flow

V

_o free stream velocity

V

_J jet flow velocity

Sw wing area

C' _D drag coefficient of wing without blowing

CDT total drag coeffîcient of jet flapped wing

C'L lift coefficient of wing without blowing

. ,. CLT total lift coefficient of jet flapped wing

9 jet deflection angle

0( angle of a ttack

CTM total measured thrust as measured with a balance

C TP . ₁ ideal jet induced pressure thrust

C'DP profile drag coefficient for wing without blowing

CTR jet reaction thrust (= c _J-'- . cos t:

a(9) drag parameter, depending on 9

C' D· ₁ induced drag coefficient for wing without blowing

AR aspect ratio

e'

=1/1+6

J

Glauert's induced drag factor

CD· 1

induced drag coefficient of jet flapped wing CLR jet reaction lift coefficient (=c .)Jo- . sin t' )

Subscripts

c

m min

change in total drag coefficient due to blowing

(6C DT

=

C J - CTM - C'D)

a constant

change in total lift coefficient due to blowing

( 6

C LT = C LT - C 'L)

calculated measured minimum

u •

1.

INTRODUCTION

There exists to-day enough theoretical proof and experi-mental evidence to show that the jet flap thrust hypothesis is true. Accord-ingly, the total drag of a jet flapped wing can be obtained experimentally as the difference between the jet reaction force and the balance measured thrust (see Fig. 1.)

A theoretical determination of the total drag would have to be based primarily on Maskell and Spence' sexpression for the induced drag. The additional viscous drag (profile drag) may be obtained from an extention of the techniques used for conventional wings by taking into account the effect of blow ing. A practical approximation to this viscous drag can be provided by negleèting the effect of blowing.

. Empirically, the _{so-called drag hypothesis dCDT /dcLT}2

=

dC

'DI

dC 'L 2 suggested by O. N. E. R. A. (Ref. 9) could pro vide an easy way for the determination of the total drag. It is of course of great significance to know whether this hypothesis is true in general or, if not. its limitations .

To help clarify this point is the object of this note. Il. PRESENTATION OF THE PROBLEM

Under the heading"Jet Flap Thrust Recovery" Foley and Reid (Ref. 2) recently announced the "significant fin ding that substancially complete thrust recovery has been obtained in two-dimensional-flow tests on a jet flap wing". This fin ding is based on experimental results (see

Figs. 3 and 4 of Ref. 2). The constant slope of the lines in Fig. 3 of Ref. 2, the same as the slope (0. 94) in Fig. 4 of Ref. 2, represents a thrust

recovery factor of 0.94. Foley and Reid's finding is substantiated by test results of N. G. T. E. (Refs. 7 and 8) and O. N. E. R. A. (Ref. 9) which, if plotted in the same way as Fig. 3 of Ref. 2 furnish thrust recovery factors of the order of one as shown in Figs. 2 and 3. The points of Fig. 2 suggest slopes which slightly exceed unity. Such slopes are of course not possible. Two reasons may account for this irregularity: the way how these plotted

points had to be determined indirectly or that the jet coefficients used for plotting (as obtained from sta tic tests) are possibly underestimated.

A value of O. 0243 is used in the transformation of the

experimental values of Fig. 3 of Ref. 2 to those of Fig. 4 of Ref. 2. The choice of this value does not affect the slope (0.94) of the "experiment" line in the latter figure. but it changes its intercept with the ordinate axis. As this point of intercept can be obtained from the test results (Fig. 2 of 2 Ref. 2) at c~

=

0, at least as an average value, the value by which CLT has to be multiplied is indirectly fixed.

According to Ref. 2, the value 0.0243 = dC 'DI dC 'L 2 was established by measuring wing forces at various angles of attack with the slot sealed (cf-

=

0) and flap undeflected. One would expect the use of the dCDT/dCLT2 obtained from the jet flapped wing

(cl'!-:.*

0). The use of dC 'DI dC 'L 2 instead implies the "drag hypothesis" (formerly suggested in Ref. 9),

( 1)

If this proposition is true, the following conclusions could be drawn:

1) That the drag of a quasi two-dimension aerofoil - whether conventional or jet flapped - is primarily a function of the total lift.

2) That the means of producing lift - such as the angle of attack (without blowing) or .=;upercirculation (the effect of blowing) at zero incidence - are equivalent in producing drag. 3) That the portion of the to'tal drag of jet flapped wings which

changes with lift can be determined

a) fr om tests of the wing without blowing (if a shroud or a small jet control flap is employed for the purpose of jet deflection) or

b) from the basic aerofoil data sheets (in case of a pure jet flapped wing). for example, see Ref. 6.

No doubt, this relationship would be of great significance if it could be proved to be true. It seems, however, that the results of Ref. 2 leave some doubt ab out the validity of this hypothesis. If one replots the test results of Ref. 2 as CDT vs. CLT2, one obtains Fig. 4. This figure indicates that the slope 0.0243 represents only approximately the experi-mental points and that a line of slope C:! O. 0275 pr.ovides a better fit.

, Additional information about ciC

'DI dC 'L 2 is required from

researchers who worked or work on two- dimensional jet flap wings in order to prove or dis prove Eq. (1) for jet flap wings in general.

lIl. COMPARISON WITH aIHER RESULTS 3. 1 Experimental Results

If CDT vs. CLT2 is plotted for the three different jet flapped aerofoils of Refs. 7, 8 and 9. as shown in Fig. 5 and 6, it seems hardly possible to deduce information in support of Eq. 1 primarily, because the

curves ,of each set do not collapse as they should.

There is another point which for the low c}N -range (0 < c)N

~ 1) raises more doubt on the drag hypothesis. In this range, leading 2 edge separation may occur which obviouslychanges the slope dCDT/dC LT appreciably (see, ,eo g., Fig. 39

oi

Ref. 8). Therefore, it is necessary to specify whether it is the slope bejore or af ter separation which is predicted by

th~

dC'D/dC'L2 of the .conventional wing. If one ass.umes that dC'D/ dC'L gives the ..slope of the total drag vs. total lift squared curve for the jet flapped wing proper before separatiop. occurs, then the usefulness of this relationship (Eq. 1) would be limited to a cfN -range the upper limit of which is defined by separation.

3. 2 Semi-Theoretical Predictions 3.2.1 Drag-Lift Relationships

The total drag of a three.-dimens,ional c.onventional wing is known to be given by

C' 2 C'D

=

C'DP + C'D'

=

C'DP + L

1 .rtAR. e!

(2)

where e.'

=

1/1+5 and C'L (a pre.ssure lift) is the totallift of this wing."

The above equation can also be written as C'D + (C'D)C'L :: 0

+

K'2 . 2 = (C'D)C'L = 0 + K'3' C'L 2 C'L

+

TL AR. e;'

which for the theoretically two.-dimensional wing reduce.s to 2

C'

_L

2

If Eqs. 4 and .3 are differentiated w. r . t. C'L one obtaines for the theoretically two-dimensional case

2

dC'D/dC'L = K'2

and for the thre..e-dimensional wing with e' = 1 dC' /dG' 2

=

K'

~

_1_ D L 3 JrAR (3) (4) (5) (6)

For the so-ca11ed two-dimensional wing of Ref. 2 with the slot sealed and the flap at zero angle of deflection

, 2

dC

'DI

dCL

=

0.0243 ( 7)

was found.

It should be realized that so-caUed two-dimensional jet

flapped model wings are never truly two-dimensional if they are designed to allow for force measurements. In some cases, the effective aspect

ratios of such model wings were found to be below 20 and as low as 6.8.

This fact suggests that even with so-called two-dimensional or better

quasi two-dimensional jet flap model wings, an induced drag component.

however small, contributes to the total drag. In case of the jet flapped

wing without blowing, it means (see Eqs. 3 and 4) that the constant K'3

deviates from K '2 the more, the higher C 'L and the smaller the effective aspect ratio. To get an idea of the induced drag contributions of quasi two-dimensional configurations, let us assume an effective aspect ratio

of AR

=

20 and a value of e'

=

1. The induced drag would then be

C'D-

=

1 1

re

AR C 'L 2

₌

O. 0159 . C 'L2 ( 8)

If, in E q. (3) we select a typical value for K '3 ~ O. 03, we see that the

induced drag contribution at AR = 20 is not negligible.

In case of quasi two-dimensional jet flapped wings, the~total

drag becomes more difficult to analyse. In analogy to that of the convenl

tional wing the total drag of a jet flapped aerofoil can be written as:

(9)

where C LT , - the total lift - is the integrated force acting on the wing-jet

flap combination and where CDi - according to Maskell and Spence (Refs.

10 and 11) is gi ven by

2

CLT (10)

nAR

+

2 c~ Tt AR (1

+

2cjJ,. ITCAR)

If _{C DT vs. C LT}2 is plotted with the test results of Ref. 2,

Fig. 4 is obtained. No doubt. agreement of the plotted points with the suggested

( 11)

!

relati.onship c.ould be better. N.ote that a pl.ot (Fig. 7) .of d( A CDT)/d( 1::. CLT)2

is m.ore satisfact.ory in this respect. 3.2. 2 Drag-Jet C.oefficient Relati.onships

(12)

If all available quasi tW.o-dimens~.onal test results (Refs.

2, 7, 8 and 9) f.or q(" = 0 are pl.ottedas CDT vs. cfl-' ' .one .obtains Figs.

8, 9 and 10. N.ote that all curves .in these figures are straight lines and can be de.scribed by an equati.on of the f.orm

C_DT ;: CID

+

a(9).

<JL

at least .ove.r the range .ofcjlv ~ 1. A similar relati.onship

CDP = C 'DP

+ À

ct'"

(13)

(14)

was f.ound by Dirnm.ock (see Fig. 32 .of Ref. 7) t.o apply f.or the pr.ofile drag .of a tW.o-dimensi.onal jet flapped wing at small

clL

-value.s and f.or 9 and

oc

equal t.o zer.o. .F.or the N. G. T. E. wing, Eq. (13) was J.ound t.o h.old g.o.on (see Fig. 10) up t.o)u- -value.s even as large as 5.

Fr.om Figs. 8, 9 and 10, the sl.opes

dCDT/dc~ = a(9-) (15)

(where a is a functi.on .of the jet deflecti.on angle 9 .only) .of all CDT vs.

<Je-curves are readily .obtained. If these a(9)-values are pl.otted vs. sin2g, Fig. 11 results which indicates that

(16) where a .o is the value .of a(.9) at 9

=

O. There are tw.o reas.ons f.or sele. ct-ing the Se.c . .ond p.ower f.or sin 9 in this pl.ot. The Jirst .one is that a(g) vs. sin2 9 can be appr.oximated by a straight line. The s.ec.ond and m.ore 2 imp.ortant .one is that this selecti.on gave an expressi.on f.or dCDT/dC LT (see -Sec. 3.2.4) ipdependent .of 9 and in qualitative agreement with the.ory.

Subsiituting Eq. (16) in Eq. (13) we get

C DT = CID

+

al (9-) cJA-

+

_{a .o . c?'} (17) Equati.on (17) has t.o reduce t.o Eq. (14) f.or a truly tW.o-dimensi.onal wing

when 9 and c:L _{are zer.o. Theref.ore a .o is equal t.o} ~ _{The :value .of a .o}

value is ~ .0. 06 which is in close agreement w~th Dimmock1_{s value for À} In Fig. J1, the plot of a(9) vs. sin29 is approximated by a straight line passing through the origin. A slope d a(9-)/.d sin29 equal to

0.63 and thefollowing equations

a(9) = 0.63 sin2.9 (18)

CDT

=

CID

+

~

.

0.63 sin29 (19)

are obtained.

3. 2. 3 Lift-Jet Coefficient Relationships

Spence (Ref. 12) has derived the follow~ng expre.ssion for the total lift ofa twordimensional jet flapped wing

CL T

=

K .

i

cf,v' sin 9 (20) where K is a factor given by

K

= 2·Jt 1/2

+

O.

325.~

1/2

+

O. 156 .

'JA-

(21)

which, for small ~ -values

k).A.

~ 1) can be considered as a constant of magnitude K = 2· Jr.,1/2 = 3.54. For larger

~

-values, K increaseB with

jtt,

.

Empirical approximations

oi

Eq. (20) are given in Refs. 9 and 13 for c:J.,

=

0

. sin 9 (22) and

C LT

=

5.

1

~I

• sin 9 (23)

respectively. These relationships are cla~med to hold for je~ deflection angles .up to 700 . Equations (22) and (23) mayalso be written in a more

general form as

2 2

CLT

=

K . . sln . 2n .0 (24)

and test re.sults indicate that K changes as a function of the characteristics of the jet flapped wing under consideration.

3.3 Lift-Drag Relationships

3.3. 1 Empirical Relationship"

Next, ,we shall proceed to derive a relationship between the lift and drag c.oefficient of a quasi two-dimensional jet-flapped wing:

"

Equation (24) may be rewritten as 2

C J).' s1'n2g

=

CLT

I K2

(24a)

Substituting the above equation into E q. (19) one gets

C Cl 0.63 C 2 DT

=

D

+

K2

LT (25) and

=

0.63

?

(26) 3.3. 2 Theoretica1 Re1ationship

Maskell and Spence (Ref. 10) have derived the following expression for the induced drag of a three- dimensiona1 jet flapped wing with elliptic loading

CD· ₁

=

TCAR

+

2

c,...

2 .

Since C DT

=

C DP

+

CD.' dCDTI dC_{LT follows from}.

1 2 C LT C DT = _{C DP}

+

1t.AR

+

2

cfA'

2 . after differentiation (neg1ecting the small dCDPI _{dC LT ) as}

1 KAR (1

+

2 cJN )' JtAR (27) (28) (29) 2

Equation (29) indicates that dCDT/dC LT can on1y be con-sidered a constant if Jl: AR

»

2 cf" . In the case of quasi two- dimensiona1 jet flapped wings, the above condition seems to be satisfied up to cf"

-va1ues of about 2 (see Fig. 12).

A comparison of Eq. (29) with Eq. (26) therefore suggests that K shou1d be a constant over the same

cfN.

-range. However, since Eq. (26) was derived fr om quasi two-dimensiona1 test results, this com-parison can lead only to qualitative conc1usions.

3.4 Va lues of the Factor K

If for all available quasi two- dimensional jet flapped aero-foils (Refs. 2, 7, 8 and 9), c}N . sin2g _{is plotted against C LT 2}, Figs. 12,

13 and 14 are obtained. From F igs. 13 and 14 it is seen that for c fA-~ 1 the slope K 2 can be considered a constant whereas Fig. 12 shows that this approximation does not hold good for cp-. -values larger than 2. From these figures, the following values of K can be obtained.

ReL 2 (Fig. 14) 7 and 8 (Fig. 12) 9 (Fig. 13) K from CLT 2 5.0 5.0(seeEq. 23) 3.9 (see Eq. 22)

K from AC LT 2 4.56 5. 0 5. 21

2

Note, that as in Figs. 4 and 7, plotting A _{C DT vs.} A _{C LT}

seems to be better suited than plotting it against C LT2

2

3. 5 The Predicted Slope dCDT/dCLT

If K is known for any particular jet flapped aerofoil (see tabie, Sec. 3.4) Eq. 36 furnishes dCDT/dCLT2. Figure 15 is added here to facilitate finding the numericai slope value. For the K-va1ues of Sec. 3.4, the followi_{ng dCDT/dC LT}2 values were calculated with the aid of Eq. 26.

Reference 2(Figs.4 & 7) 7 & 8 (Fig. 6) 9 (Fig. 5)

O. 63 C 2 . O. 0251 0.0252 0. 0414

KT

with K fromAÇLT 2 _{.. ; LT} -0.0302 0.0252 0. 0232 If one adds these slopes in the respective figures 4, 5, 6 and 1, one finds

reasonably good agreement between slope and test results of ReL 2

(Fig. 4). In Fig. 5, the calculated slope is larger than that suggested by the test points. This discrepancy is believed to result from the fact that the test data of Ref. 9 are presented in parameters different from those best suitable for this note. Unfortunately, there is not enough information in ReL 9 to permit a proper transformation of numericai values. Figure 6 demonstrates two things, the pronounced effects of L. E. separation (change of slope) and that thi"s...derivalion does not hold for ~et coefficient much larger than unity. Note also, that dCDT/d( ÄCLT) = O. 63/K2 (where K is obtained by using ACLT 2) agrees very weU with the slope of the experimental results of Ref. 2 as shown in Fig. 7.

3.6 Limitations of the nrag Hypothesis

The drag hypothesis (Ref. 9) suggests that

= dC'n

dC'

_L 2

(30)

This proposition is exactly true only if either

cJA-

.= 0 or the aspect ratio

is infinity. Bothconditions are trivial.

Since CnT can be written as

+

( J(.. AR

+

2 cjN ) .

e

then 1 dc"n =

AR(1+2c~

e

+

dC' 2

.xAR

L

= 1 x·AR.e'

But if .;c·AR ~ 2 ~ • . we gei

(31)

(32)

2 2

dCnT/dCLT ,...., 1/( Je·AR. en

=

dG'n/dC"L (33)

2

Fro~ Eq. (33) we see that dCDT/dCLT can be conside~ed equal to dC'n/

dG'L only at small c -values for both quasi two·-dimensional and

three-dirnens~onal

wings. tte

~-

range of approximation increases with AR.

IV CONCL USIONS

The follow.ing conclusions may be drawn from the material pre.sented in this note for quasi two-dimensional jet flapped aerofoils at zero incidence!

1) a)

b)

A theoretical investigation shows that

2 2

the drag hypothesis (dCnT/dCLT

=

dC'n/dC'L ) is

exactly true only for eithercj-l'

=

0 or AR

=

co and

it is approximately true (for, quasi two- and three,..

2)

a) b)

3)

4)

Experimental evidence indicates that

dCDT/dCLT2

~

const. only for 0 < c

JN ' 2 and

2 2

dCDT

I

dCLT is approximately equal to dC

'DI

dC 'L for c.,..., -va lues less than two.

Not enough experimental data are available for a direct verification of the drag hypothesis.

It was found that the total drag can be calculated from the simple empirical re lationship.

C DT = C'D

+

0. 63 . c,., . sin2g

where the constant 0. 63 was obtained from all available quasi two-dimensional jet flap results.

5) It was found that the total drag is related to the square of the tota 1 lift by

dC

I

dC 2 - O. 63

DT LT -

KT"

where K is a characteristic constant of the jet flapped aerofoil under consideration. This constant can be obtained from

dCLT2/d(c,. . sin 2 g)

=

K 2 (provided

Cft~2)

6) Attention should be drawn to the fact that. if the increase in tota 1 drag (

A

C DT) and the change in tota 1 lift (A C LT) due to blowing of the jet flap is used, the above reported relationships predict the total drag in better agreement with experimental results.

1. Korbacher. G. K. Sridhar, K. 2 . F 0 ley. W. M. Reid. E. G. 3. Stratford. B. S. 4. Woods. L. C. 5. Woods, L. C. 6. Jacobs. E.N. A bbott. 1. H. 7. Dimmock. N. A . 8. Dimmock. N. A. 9. Malavard. L. Poisson-Quinton. Ph. Jousserandot. P. 10. Maskell. E. C. Spence. D. A. REFERENCES

A Review of the Jet Flap.

UTIA Review No. 14. Oct.. 1959

Jet Flap Thrust Recovery.

Jour. Aero/Space Sciences. Vol. 26.

No. 6. Readers' Forum. June. 1959 Early Thoughts on the Jet Flap.

Aero Quat., Vol. VII. Part I. Feb .• 1956 On the Theory of Jet Controls.

Fluid Motion Sub-Committee. F . M. 2007.

Perf. 1192. Jan .• 1953

On the Thrust Due to an Air Jet Flowing From a Wing Placed in a Wind Tunnel.

Jour. Fluid Mech .• Vol. I. Part I.

May, 1956

Airfoil Section Data Obtained in the N. A. C. A. Variable-Density Tunnel as Affected by

Support Interference and other Corrections.

N.A.C.A. Rep. No. 669

An Experimental Introduction to the Jet Flap.

N.G.T.E. Rep. No. R175. July. 1955

Some Further Jet Flap Experirrtents.

N.G.T.E. Memo No. M255. 1956

A.R.C. Tech. Rep. C. P. No. 345 (18.657),

1957

Theoretical and Experimental Investigations of C irc ula ti on C ontro l.

O. N. E. R.A. Tech. Note. No. 37. June.

1956 .• Aero Digest. Sept to Nov . • 1956

Princeton University (Dept. Aero. Eng.)

Rep. No. 358, July. 1956.

A Theory of the Jet Flap in Three

Dimensions.

R. A. E. Rep. Aero 2612. Sept .• 1958 Proc. Roy. Soc .•. V:o,r. ;25.1., ;. .d.J

11. Maskell. E. C. Spenee. D. A.

12. Spenee. D.A.

13. D~mmock. N. A .

On the Induced Drag of a Finite Wing with a Jet Flap.

R. A. E. Rept. No. Aero 2551. June. 1955 A Treatment of the Jet Flap by Thin

Aerofoil Theory (Addendum). R. A. E.

Rep. Aero. 2568. Nov .• 1955

Some Early Jet Flap Experiments. Aero. Quat., Vol. VIII, Part 4, Nov .• 1957

FIG. 1 111:

...

u ~ U

+

) (

+

,

...

u CL

...

(,)

I

111:

...

u I

I

THE FORCES ACTING ON A SYMMETRICAL JET FLAPPED WING AT INCIDENCE

FIG. 2 ~ 0 r r r + r -rr> LL. LaJ ct:

/

/

/

/

- /

/

0 r -_ _ -+ _ _ _ +-_

/

/

I

//I--+--~~

(\J

o

0 0

/

/

Y

*

>-CD 0 0:: / OLaJ

-

>

_o

IC)~

~

U t-Il LaJ (f) a.. ::::>

/U!:i

~~

IC) ₀ IC)

.

₀ 0 N ~ t-U IC) ₀ IC)

.

(\J _{rr> rr>}

THE THRUST VARIATION WITH JET COEFFICIENT AT CONSTANT LIFT (TEST RESULTS OF REF. 7 & 8)

N 0 I FIG. 3

-

~----~---+---4-o

11 CD 0

u:t.

U) 0 0-ct (!) ~ ..J Z LL ~ 0 en

...

0 LIJ ..J LL ~ III LLJ

a:::

I.&J ~

a:

:E ::l

_>

0- (J) 0 <J 0 N V _{- Q} U) <D 0 N 0 ₀

.

_U 0 0

+

~ ~ U

THE THRUST VARIATION WITH JET COEFFICIENT AT CONSTANT LIFT (TEST RESULTS OF REF. 9)

---

---

----

--

--

---

- - -U)

0

FIG. 4 - - - - _ . .

_

_

....

_._

-

--_._-_ ._-- - - - '- -

- _ .

-

---

--.-

..

-00

rr>

V

U) C\J

0

_.

0

11

"!..J

V

U ---+---+---~ C\J

o

LOOOrt>-Ü)rh"':"'m

Cl:> r()

V

lO LO <J

t>

X

+

LO

_.

q-0

₀

t>

rr>

_.

0

r-e

U

N~ U 10 (\J

0

0

C\J

_.

-

.

₀

0

0

THE Taf AL DRAG vs. THE TOTAL LIFT SQUARED

(TEST RESULTS OF REF. 2)

0

00

0

(\J~

FIG. 5 00

o

o

"-o

CD

(5

o

ct U ct Z

-N_ ~ - u <3

VI

1--+---+--+

::t..

U <D

o

o

LO CL ct (J') ..J U. lL. ~ W lA.!

a::: ..,

...

~ o 0 0 0 ft)1O~­ ft) 10 tD .... C\J C\J

o

C\J 00 _ Ol c:: -<D

"~

g.

J5

'+--

Q) o "--. L..-... _ - - - . - - - 4 q- "~ ~

-

Q) 0-::)

E

--1---+--~C\J

E

_N~ U >. (/)

-

IJ ---+--~o~ ~

-

~ ~ C\J

o

u u

<l

<I

-+---100 - ... C\J

o

A TOT AL DRAG vs. TOT AL LIFT SQUARED PLaT OF TEST RESULTS FROM O. N. E. R. A. (REF. 9)

(O.N.E.R.A. TEST RESULTS-DUE TO LACK OF INF

2 0RMA-TION -CANNOT BE CONVERTED TO A CDT vs. CLT PLOf.

A F ACT WHICH MAKES THIS FIGURE USELESS FOR QUANTI-TATIVE COMPARISONS).

0 FIG. 6 Q.. _CD <X -l CD 0 ti-" ,

+

.

I ~ V 0 I.&J ~ VI

,

_.

₀ x I.&J LL _I.&J

<3

~

en

_{a::: a:::}

,...:

::J 11 Q.. ~ N..J 0 U _{<J X} "'0 U) ."

~

0 0

₈

I 0 _U Cl V

-CD 11 )( "'0

;;:;

10

a::

U)

«

₀

.

11 Il) V Cl) 11

Ot\l~

v U

0 If) (\J 10 11 (\J 0 ₀ 0 ₁₀ t\I ti N~ 0 11 (,)

c3'

~-

"-

0 ~ Cl (,) "'0 0

co

U) _V t\I ₀ ~

.

0 _{0 0 0 0}

U

A Taf AL DRAG vs. TaTAL LIFT SQUARED PLOT OF

<D

.

0

FIG. 7 C\J

r0

~ N

ro

0

_.

0

11 ~..J W U

~

_ 0 U _~

'"'0

N

0

r(')

0

_.

C\J

0

11 N

_--..

C\I ~

-

0

..J ~

₀

u

_<l

<l

--

--~

ro

b

u

'"'0

W 0 <J X E> C\I 0 0 0 ₀ LL LO

.

ex:>

ro

-

.

lLJ W

re>

en

a::

re>

~ 10 10 11 _C\J

Cl:>

0 10

.

~

ro

C\J

-

₀

~

.

0

0

0

0

0

0

ü

<I

THE TOf AL DRAG INCREASE DUE TO BLOWING vs.

THE TOf AL LIFT INCREASE SQUARED DUE TO

1.2

RESULTS

FROM REF. 9

1.0

PURE JET FLAP SYM.BLOWING

8=

33°

•

8=

19

°

+

55°

•

36.5°

0

0.8

63°

•

53°

IJ.

C

_OT

71 °

•

67°

0.6

0.4

0.2t----+=

o~

____

~~

__

~

______

~

____

~

______

~

__

~

o

0.2

0.4

0.6

0.8

1.0

1.2

FIG. 8

Cf'

THE TOT AL DRAG INCREASE DUE TO BLOWING VS. THE JET COEFFICIENT. O. N. E. R. A. TEST RESULTS

REF'2 _0.475

6.COT

0.5 36'5 0

x

43·8 V 51'3

+

59·1 II 0.365 0.4 + 0.3~---+---+---O. 2 ~---+--- X

----+---1

I

dC~CfL

=

0.25

O.I~--o

~

______

~

______

~

______

~

______

~---~----~

o

FIG. 9

0.2

0.4 0.6

_C

_0.8

I-'

1.0

THE TOTAL DRAG INCREASE DUE TO BLOWING vs.

THE JET COEFFICIENT. TEST RESULTS OF REF. 2

\04

r--~~-~----,---.----r---r----\.2

1.0

0.8

0.6~--~

COT

0.4J----0.2

0

0

0

0.\

\.0

FIG. 10

REF. 7+8

8

₌

0°

x

31.4°

V

58.1°

II

0.2

0.3

0.4

0.5

0.6-

x

2.0

3.0

4.0

5.0

6.0-

II

GJL

THE TarAL DRAG vs. JET COEFFICIENT

N. G. T. E. TEST RESULTS (REFS. 7 & 8)

0 V

1.2

1.0

0.8

REF.

2

(O.N.E.R.A

- I l -

8

=

36.5~

43.80

JET CONTROL FLAP)

51.3~

59.1 0

REF.

7

a

8

- 0 -

8

=

31.4~

58.1

0

(PURE JET FLAP)

90.0

0

REF.

9

-

+-(PURE JET FLAP)

8

=

33.0~55.0° 63.~71.0~

0(8)

REF.

9

- x -

8

=

19.0~

36.5

0 0

(SYMM. BLOWING)

53.0~67.00 FIG. 11

0.6

J . . . - - - - + - - - - + - - - - + - - - _ _ _ + _

A+

0.4

J - - - - + - - - - + - - - - + x~--+----I

0.2

I - - - - t - - - -'_---c...L.

_{- d o}

o

o

0.2

d

--:-"'28 =

Sin

O. 63

0.8

1.0

THE SLOPE da(Q)jdsin2 Q

=

0.63 AS OBTAINED FROM ALL AVAILABLE QUASI TWO-DIMENSIONAL JET FLAP TESTS

N rt') FIG. 12 ~ <J 11

~:J.

CD C\J

ex>

oa

I'-.

Cl) RL LLI

a::

C\J

x

_<l

o~ 0

-

.

.

_ex>

-rt'>LO 11

Ct>

q

Cl) tD N N ...:

c:

--

Cf)

::t.

U

N

.

L{)

C\J

11 C\J ~ 11

-

Cl) C\J

c:

.-

_U)

:t..

(,)

-~~

11

(,):1..

C\J!:J

1

.g

x

-"'

l!) 11 ~ C\J 11

(,):1..

-

₁₁

o

C\J

o

o

o

o

en

o

CD

o

r--o

tD

N~

oU

LO

o

V

o

rt')

o

C\J

(,):1..

:1..-

-

--u

o

I

CD

o

o

V 0

o

U.t.:T.t.:HMINATION OF K FOR THE N.G. T. E. JET FLAPPED

s

.

w

1.4r'

-'-II-r--r--,---.--.--.----,---r---

i

o

M ~ t%j ~

a=

...

2: :s~ ~~ 2:~

C)~

rn

~~

~~ MI'%j "%jO

.

~ co~ -::t: oM

"0

(")

.

,: 2: '" "rrJ ,... -~ ~

.

~ t'rj ~ "%j t< ~ "ti

~

o

dcET/ d(cp.sin

2

8)

=

K

2

=

15.25

1

K=3.9

I

1.2

REF.9

PURE JET FLAP SYM. BLOWING

• /1

_

e

=

33

°

0

e=

19°

•

1.0

1-1 - - - - +

=

55°

Il

36.5° A

0.8

r-

I --+---&.~

=

63°

x

53°

•

cJLsirfe

0.6.

1

+

-=

71°

V

67°

Y

0.4t-1

- - - +

0.2

o

I C - I I , I I I I I I , I •

o

4

8

12

16

20

24

28

32

36

40

44

48

(~CLT)2

(symmetrical

blowing)

o

FIG. 14 C\J LL W 0::: ex>

o

c> 0 0 LO tO r<) 11 Cl:> <I 0 (X) rr) V

t>

X Xc> <3 )( [> 0 0 X t> 0 0 ft)

--

cri

1O lO IJ) C\J 11 N ~ 11 ...-l{) Ct) -N 11 C _~ "(/)

:t.

U

-'"

N!:i U "'0 X - [ > ~ X C\J

o

<J 0 _ :.

o

o

C\J

co

C\J N~

0

0

ex> C\J

o

DETERMINATION OF K FOR JET FLAPPED WING OF REF. 2

0 lO ₀ lO 0 V rt') _{rt) C\I N C\I} ~

o~

lO

-I .# 0 lO

o

o

v

N

O~

o

r<>

W rt)

0

o

o

C\I

q

o

o

o

o

o

~

q

v

o

lÓ

~

o

U) FIG. 15

o

,...:

GRAPH FOR THE DETERMINATION OF dCDT/dCLT2,