MEASUREMENTS, AT MACH NUMBERS UP TO 2.8, OF THE LONGITUDINAL CHARACTERISTICS OF ONE PLANE AND THREE CAMBERED SLENDER OGEE WINGS
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Measurements, at Mach Numbers up to 2.8, of
the Longitudinal Characteristics of One Plane
and Three Cambered Slender ' Ogee ' Wings
By C. R. TAYLOR
COMMUNICATED BY TIIE DEPUTY CONTROLLER AIRCRAFT (RESEARCH AND DEVELOPMEN r),
MINISTRY OF AVIATION
Reports and Memoranda No. 3328*
December, 1961
Summary.
Measurements have been made of the longitudinal characteristics of one plane and three cambered slen ler
ogee wings (p = 0.45, = 0208). at two subsonic and eight supersonic Mach numbers up to 2.8. he
tests also included measurements of the zerolift pressure drag and support interference of the plane wing.
The results have been analysed to give data for estimating the performance of supersonic transport aircra r.
LIST OF CONTENTS
Section
1. Introduction
2. Description of the Models
3. Details of the Tests
4. Presentation and Discussion of the Results
4.1 Introductory remarks
4.2 Results for subsonic speeds
4.3 Zerolift drag of the plane wing
4.4 Dragduetolift at supersonic speeds
4.5 Lift and pitching moment at supersonic speeds
5. Conclusions
6. Acknowledgements
List of Symbols
List of References
Appendix ICorrections to measured lift and pitching moment for asymmetry ot
the sting shroud
Appendix II?Kell's freeflight measurements of the zerolift drag of the plane wing
Table?Details of the models
Illustrations Figs. 1 to 40
Detachable Abstract Cards
* Replaces R.A.E. Report No. Aero. 2658ARC. 23,776.
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LIST OF ILLUSTRATIONS
Figure
1. The planform
2. Variation of leadingedge sweepback across the span
3. Variation of thickness/chord ratio across the span
4. The thickness distributionchordwise sections
5. The thickness distribution spanwise sections
6. Crosssectional area distribution
7. Centreline camber, wings 16, 17 and 18
8. Chordwise variation of camber loading for wings 16, 17 and 18
9. Details of wings 16, 17 and 18
10. Details of model supports
11. Lift vs. incidence, 114 = 0.3
12. Pitching moment vs. lift, M 0? 3
13. Drag vs. lift, M 0?3
14. Lift vs. incidence, M 0.8
15. Pitching moment vs. lift, M O? 8
16. Drag vs. lift, M 08
17. Lift vs. incidence, M == 1.4 and 1.8
18. Lift vs. incidence, M = 2.2 and 2.6
19. Pitching moment vs. lift, M = 1.4 and 2.6
20. Pitching moment vs. lift, M 1.8 and 2.2
21. Drag vs. lift, M = 1.4 and 18
22. Drag vs. lift, M = 2.2 and 2.6
23. Variation of aerodynamiccentre position with lift coefficient, M 0.3
24. Variation of aerodynamiccentre of nonlinear lift, wing 15, M 0? 3
25. Analysis of zerolift drag of wing 15
26. Variation of K, with Mach number
27. Comparison of measured pressure distribution for wing 15, at CI, = 0, with t k4'0
theoretical distributions, M = 2.2
28. Variation with Mach number of zerolift pressure distribution for wing 15
29. Variation of dragduetolift factors with Mach number
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LIST OF 11,I,USTRAT ONS?continued
Figure
30. Liftdependent drag of the plane wing, C1 = 0.10
31. Variation of 7rAa/C, with p for plane wings
32. Variation of 0C1/acx with Mach number, wing 15
33. Variation of ? ac?,iac, with Mach number, wing 15
34. Variation with Mach number of ACm at constant CL, wings 16 to 18
35. Effective C for C = 0.075, wings 16 to 18
36. Variation of CL and Cm at design attitude with Mach number, wings 16,17 and 18
37. Notation for Appendix I
38. Freeflight measurements of zerolift drag of wing 15
39. Freeflight model
40. Comparison of freeflight measurements with tunnel results
1. Introduction.
The purpose of this report is to describe tests, in the 8 ft x 8 ft Tunnel at Bedford, on tot r
slender ogee wings. All four wings had the same planform (p 0.45, ST/Co = 0208) one ?51
plane and three were cambered to give varying amounts of centreofpressure shift at superson:e
speeds. Measurements of lift, drag and pitching moment were made at two subsonic and eight
supersonic speeds up to M = 2.8 and the tests also included pressure measurements to determine
the zerolift pressure drag and support interference for the plane wing at supersonic speeds.
The present tests contribute to an extensive investigation of the aerodynamics of slender shap( s
and their suitability for longrange supersonic transport aircraft. As a result of earlier work in aus
investigation it has been suggested that it should be possible to design an aircraft having a
acceptable performance and flight characteristics, utilizing wing flows which are both computabL
and physically realizable, provided that: (a) its planform is slender with streamwise tips (at all flighi
speeds the leading edges are 'subsonic') and the trailing edge is either straight or only slightl,
swept; (b) it is integrated, in the sense that the wing and body are smoothly blended together t
form a single smooth winglike shape, capable of lifting over its entire length; and (c) the leadin
edges are sharp and if the wing is cambered (in order to bring the centre of lift at cruising condition.
near the position of the aerodynamic centre at low speeds), the camber loading is zero at the leadin
edges, so that the leading edges are attachment lines at the design incidence and at other incidencei
the flow separations are either wholly above or wholly below the wine, 2.3 A fundamental featur
of the flow past these wings is that at all flight conditions there is primary separation from all edge;
and, under cruising conditions, the wing surface is free from shock waves. It should be noted that th
3
(87542) A 2
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aerodynamic design point is not normally a flight condition. This is because, for wings with sharp
and highly swept leading edges, the existing methods of design are only valid when du eading
edges are attachment lines and it has been found that lower cruising drags are obtained by iisir 9 design
lift coefficients lower than the cruise value.
Earlier work in the slenderwing programme concentrated on wings of simple shape (e wings
with rhombic transverse crosssections, having planforms and centreline sections Jefined b.! simple
polynomials), and the principal object of the tests described here, was to deterrrime to vkt.t; r extent
changes towards what was considered to be a more realistic shape would affea the highspeed
drag and the ability of a simply designed camber to trim the wing: Thus, although the present
wings conform to the restrictions of the preceding paragraph, considerations of an rircrait.t.towage,
balance and structural requirements have influenced the choice of planform and thickness c istribu
tion. Consequently, they have much of their volume concentrated near the centreline and, eonipared
with most of the earlier wings, the position of maximum crosssectional area is farther aft, tht mean
trailingedge angle and the minimum leadingedge angle are greater, and the planform oatarneter,
p elco, has been reduced by 'waisting' the planform. For these wings the cruise concition is
assumed to be C.,, = 0075, M = 2.2.
2. Description of the Models.
Four shapes were tested, one plane, the others cambered; all four had the sar le plain and
thickness distribution.
The planform, which is defined by the equation
.s3 XA
4:7.? = 1 ? 2 ? 24 2.2 1 3 ?3 ?
CO C0 Co
ST
L= 0208,.
co
is shown in Fig. 1, where it is compared with two gothic wings and two other o7lee wings of the
same slenderness parameter (s/c0). It will be seen that the lower pvalue for the present ?;): pe has
been obtained by waisting the planform while maintaining an apex angle comparable with that of
the gothic wing with p = 7/12. This has resulted in a shape having two points of Inflexion ud an
uneven variation of leadingedge sweepback across the span (see Fig. 2).
The thickness distribution (Figs. 3, 4 and 5) is a 'lofted' shape without a defining eq,iation.
It is an example of how a smooth integrated fairing could enclose a realistic pressure cabin and
outboard fuel tanks. For these wings it was proposed that the engines should be enclosed in
underwing boxes whose shapes followed those of the cleanaircraft streamlines. Me stramwise
variation of crosssectional area is less smooth than those of earlier wings, the position of maximum
area is farther back, and both the slope and curvature at the trailing edge are larger (see 1og 6).
The camber surfaces for these wings were designed by the slenderwingth( ory method of
Ref. 4*. Inboard of the 'shoulder lines' the streamwise slope of the mean surface i:. consttit Along
the span but outboard of the shoulders it varies parabolically with the spanwise c )ordim,te. The
* A computing programme for calculating the camber shape by linearized thinwing theor\ vtai not
available at the time. Slenderwing theory was chosen in preference to notsoslender thew117. 21 te7ause
of its simplicity.
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ratio between the values of the slope at the leading edge and at the centre is chosen such that the
load vanishes at the leading edge. The ordinates of the mean surfaces have been obtain( d by
integrating the surface slopes from a straight hingeline at 95% root chord. The equation of the
shoulder position is
th)(x) = 05
0.5 + fax _1\2 co
2/
The shoulder position was chosen to be well inboard near the apex in order to avoid large ac verse
pressure gradients; it was chosen to be farther outboard near the trailing edge to obtain a low l ortex
drag'. The wings were cambered to give the following lift and pitchingmoment coefficients:
Wing
CL(/
Cmd
ad
0
15 (plane wing)
0
0
0
0
0
16
0
000853
0
30?
0.00853
17
0.025
000800
10
500
000853
18
0.025
0.00435
10
40?
000487
The design incidence ad is the inclination of the central part of the mean surface at the trailing
edge (a = 0 corresponds to the nolift attitude according to slenderwing theory). The values of
0 quoted are the maximum angles of leadingedge droop. At a lift coefficient of 0.075 the cambered
wings are intended to have their centres of lift either 40/0 co (wing 18) or 7% co (wings 16 ar d 18%
forward of that of the plane wing.
In order to be able to use slenderwing (i.e. M = 1) theory to design a camber surface to live a
prescribed shift of centre of pressure at a cruise Mach number of 2.2, it has been assumed that
even though the centreofpressure positions of the wings may change with Mach number, th(
difference in Cm between the plane and cambered wings, at the cruise CL, will not change an 1 wil'
be equal to the difference. at the design lift coefficient. To decide the centreofpressure movement
needed, it was also assumed that the aerodynamic centre at low speeds would not be affect:td 13N,
wing camber. With these assumptions it was expected that the ACm required for this planform at
CL = 0.075 would fall between the two values chosen (i.e. between 000487 and 0.00853)
Details of the camber loadings and the shapes of the cambered wings are shown in Figs. 7, 8 and 9
Except for the nose sections, wings 15 and 16 were machined from steel, whereas wings 17 and
18 were fabricated from glasscloth bonded with Araldite. For the force tests the models were
supported by a sting of 2. 1 in. diameter and included a sixcomponent straingauge balance (Fit. 10)
On all the models the cylindrical sting shroud was symmetrically disposed at the trailing edge
An additional model of wing 15 was used for the pressure measurements; this was connecte i to a
cranked sting by a thin yoke near the trailing edge (Fig. 10), which was designed to leave the ippei
surface of the wing free from support influence for M 1.4. The pressure holes (100 in nu nber)
were distributed along five chordwise stations, located so that they represented equal amounts of
frontal area, i.e. at yls,,,  0.032, 0096, 0176, 0336 and 0656. A dummy sting shroud was
available for the tests to investigate the shroud effect on zerolift drag.
Table 1 lists all the model dimensions.
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3. Details of the Tests.
In the force tests, measurements of normal force, pitching moment and axial forct were m2cle at
Mach numbers 0 3 (approximately), 0.8 (approximately) and 1.4 (0.2) 2.8, at a con ;tant Rey.iolds
number of 107, based on root chord. 'File incidence range used was:
A = ? 6(10)0(,0)60(10)120
except at M 0.3 where
= ? 60(10)200
.
The models were tested both rightwayup and inverted in order to isolate the offects f flow
deflections in the airstream (all the graphs in this Report refer to the mean of rightway up and
modelinverted results). All force coefficients are based on the plan area of the wings; the reference
length for C?, is e (the second mean chord) and the moment reference point is at 0.5, i.e. at the
centre of the plan area.
The pressure measurements on wing 15 were made at M = 1.4, 1 8, 2.2 and 2.6 mv the
Reynolds number again being 107, with an additional test at M = 2.2, R = x . The
incidences tested were a =  2'(1?)2' and A = 0 model inverted. The tests with the curium/ ,litoud
fitted were done only at zero incidence.
At M = 2.0 additional force measurements were made at Reynolds numbers of 5 aid 15 nTilions,
and the results were used to estimate the effects of model distortion under load. The iesults fo the
metal models showed no change with dynamic pressure (apart from the expected sh ft in th,T level
of the drag polars), whereas for models 17 and 18 there were measurable changes in pit,:hing m mn,Trit
and lift. The distortion corrections, at M = 2.0, for R = 107 were found to be: AAP = 
SC,?,/CL = ? 0.010; these corrections have been applied to the results for all supersonic Mach
numbers.
The drag results in Figs. 13, 16, 21 and 22 are not corrected for the presence of the sting sl,rolid,
except that the axial force has been corrected to freestream static pressure at the shroud bam. The
correction to the zerolift drag of the plane wing has been derived from the pressure measure merits,
it is closely approximated by A C,? = 0.00088 ? 0.00053 log and is taken into account n The
analysis of the zerolift drag measurements on wing 15 in Section 4.3. On the carAlered wings,
?
except at the trailing edges, the sting shroud protruded from the upper and lower surfacs by different
amounts, in effect distorting the camber surface. The estimated corrections for this are (see Apneldi 1
for details):
Wing 16 AC?, = 00003/p
17 000843
18 0.0005/p
these are included in all the plotted results for supersonic speeds.
The following tunnelconstraint corrections were applied to the results for subsom speecs:
M 0.3
M 08
Aa/ C1,
072?
082?
0056
0093
A C?/CL2
0010
0010
where a is measured from the nolift attitude. These figures were derived by applyin.?, the rthTtn,Td
of Ref. 5 to this planform. The small blockage effect of these wings was allowed for !)y corn eing
the values of p, and .121)172 given to the computer.
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Estimates of the accuracy of the tests suggest that the errors in the plotted results are within the
following limits:
C1: + 0.001 + 0?01CL
Cm: + 0.0002 + 0 ? 01 Cm
: + 0.0003 + 0?008CL2
except for M 0.3, where, due to the low dynamic pressure, the errors may be three times these
values. For the pressure coefficients the random scatter, due to errors in pressure measurement.
is thought to be less than 0.004; an additional error, due to uncertainty in the measurement of the
true static pressure in the tunnel, is probably about + 0.005 (this would affect all the readings at
one Mach number by the same amount and would not affect the measured pressure drag).
An additional error in pitching moment may arise from the unaccountedfor variation with Mach
number of the distortion correction.
To promote boundarylayer transition near the leading edges, bands of 60 grade carborundum in
Araldite were applied to the wings; these were in. wide and were located Tiu in. from the leading
edges. This size of roughness (approximately 0.010 in.) was that required to cause transition at
M = 2.8; it is estimated that at M = 14 it is 1.7 times, and at M = 0.3 twice, the size needed.
It did not cause transition at M = 20, R = 5 x 106.
Further measurements of the zerolift drag of wing 15 were made while this report was being
prepared, using a more sensitive balance which has recently become available. The conditions for
these tests were:
(a) R = 107, M = 1.4,1.8,2.2,2.4,2.6, and
(b) R = 1.5 x 107, M = 14 (0.2) 2.2.
The errors in C, for these tests are thought to be less than 0.0002.
4. Presentation and Discussion of the Results.
.4.1. Introductory Remarks.
The results of the force measurements at subsonic speeds are plotted in Figs. 11 to 16; Figs. 17
to 22 contain a selection of the force results for supersonic speeds and Figs. 27 and 28 show the
measured pressure distributions for the plane wing.
In the analysis of windtunnel results for performance estimation it is current practice to divide
the drag of the aircraft into three separate, and additive, components, via.
=
4 C
CD DWI" + CM;
(1)
of which only one, the skinfriction drag Cm., is sensitive to changes in Reynolds number*. Of the
remaining terms, CDory is the wave drag due to thickness and CDL is the drag increment due to lift.
For the present series of tests, C Dow is the zerolift wave drag as measured on the plane wing and
if this is expressed as
128 V2
CDOTT
4K0, (2)
IT Sen
then K, is the ratio of the zerolift wave drag of a wing to that of the minimumdrag body of revolution
having the same length and volume. No distinction is made between zerolift wave drag and zerolift
pressure drag.
* The Reynolds number, based on length, for the fullscale aircraft at cruise is approximately 3.5 ; 108.
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The liftdependent drag, C?,,, may be expressed in the forms*:
CDL  C 2
7T A
CI 2 (Kr 2
" +2/32  h?.),
ITAc?2
where, in theory, K,. = 1 for an elliptic spanwise distribution of lift and K?. 1 in the approximation
of notsoslenderwing theory for slender wings having an elliptic streamwise distribi.r ion (1
The values of C?, for Kr = 1 ? K?, are sometimes known as R. T. Jones's lower hot nd foi the
drag due to lift l,2,6. In general, K? and K,r will vary with Mach number and lift coeffi,ient.
In the following sections we consider first the subsonic characteristics of the wing., then the
breakdown of the drag, according to equation (1), and finally the lift and pitchit gmomr.a t
characteristics.
4.2. Results for Subsonic Speeds.
In this section we consider those aspects of the results for subsonic speeds which are ,elevaia t )
the performance of the aircraft, particularly those which affect the interpretation of the results tor
supersonic speeds. It should he noted that, for these wings: (a) the incidence corresponding to ih
landingapproach condition is about 14? and (b) the lift coefficient for 'hold' or `diversh.n' at bign
subsonic speeds is approximately 0.10.
The lift vs. incidence plots for M 0? 3 arid M 0.8 (Figs. 11 and 14) show an increas in
liftcurve slope with incidence as is usual for slender wings, the curves for all four w ngs being
virtually parallel in the region of interest. The 'approach' incidence can be seen to correq)ond to
lift coefficient of approximately 045. At M 03 the lift curve of the plane wing is clowk,
approximated by C?fa = 121 {1 + 145a2/31, where a is in radians, a similar, but larger vari.iti )1,
of lift with incidence is given by the slenderwing theories of Adams and Edwards (cf. Ref. 7).
The measured lift is approximately 7% more than that given by Peckham's generalised curve tor
flatplate delta and gothic wings", if a small allowance for Mach number is made by repha i
CL by ,8'2CL, a by p'cx and sTico by g'sTlco; 13' = v/(1? M2).
An important feature of the results for M 0?3 is the severe pitchup (Figs. 12 and 22). For tlt
plane wing the aerodynamiccentre position moves forward about 4% e with an increase i,i CL iron
zero to the approach value; the movements are greater for the cambered wings and inci ease kith
increasing amounts of leadingedge droop. The aerodynamic centre of the nonlinear lift on ta(
plane wing has been estimated by assuming that the aerodynamic centre of the linear lin reniailF
fixed at 05, its position at C1 = 0, and the linear and nonlinear lift components are given in
1.21a (rad) and 1.7606513(rad) respectively. This shows, Fig. 24, that the aerodynamic centre or the
nonlinear lift is always ahead of that of the linear lift and moves forward rapidly with nereasnig
lift coefficient. At M 0.8, camber again has a destabilizing effect, but the pitchup is less Than
at M 0.3 and only occurs at lift coefficients greater than the flight value.
At both subsonic Mach numbers camber has little effect on drag due to lift; at M 03 lie
cambered wings have slightly more drag than the plane wing, at M 0.8 slightly less. At M 1,
the drag polar for the plane wing is a parabola with K? = 1.54. The cambered wings have vor7cx
drag factors, at C1, = 0.1, based on the C,o of the plane wing, of 1?44 (wings 16 at d 18) or
? 36 (wing 17).
* Throughout the analysis C111, is the difference between CD of the cambered wing and C,,, of the fiane win z.
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4.3.. ZeroLift Drag of the Plane Wing.
In this section we consider the first two terms in the drag breakdown {equation (1)}, i.e. we
consider the division of the zerolift drag of the plane wing into the skinfriction and pressuredrag
components. The pressure tests on the plane wing were specifically designed to facilitate this analysis
by providing measurements of the effects of the sting shroud and a direct measurement of the
zerolift pressure drag. A comparison of the measured pressure distributions with those given by
slenderwing theory and linearised thinwing theory was also intended.
Earlier tests in the slenderwing programme, mainly those on delta wings with rhombic cross
sections and Newby or Lord V area distributions (cf. Fig. 6), have shown that the friction drag of
these wings can be accurately estimated by calculating the drag of a flat plate of the same planform,
assuming the boundary layer is locally twodimensional, and multiplying this value by the ratio of
the wetted area of the model to that of the flat plate. This method of estimating the skin friction has
also been used here. The pressure drags of these earlier models are in close agreement with both
lineartheory and slenderbodytheory estimates of wave drag at low values of ,8s/c0, where the
results from the two theories agree; but at higher values of the slenderness parameter, where the
theoretical values diverge, the experimental drags followed the lower (i.e. slenderbody) estimate.
The breakdown of the zerolift drag of wing 15 is shown in Fig. 25. The measured totaldrag
coefficients are increased by the correction for the masking effect and pressure field of the sting
shroud. The difference between this corrected C,? and the estimated frictiondrag coefficient should
be equal to the measured pressure drag but it is, in fact, 00003 to 0.0006 higher. The errors in the
various measurements are thought to be within the following ranges:
C,? + 0.0003 (? 0.0002 for later tests)
Shroud correction + 0.0001
Pressure drag + 0.0001
so that the most adverse combination of these errors cannot entirely account for the discrepancies.
It must be concluded therefore, that the friction drag is at least 5% higher than estimated.*
A comparison of the measured pressure drag with slenderbody theory9f and linearized thinwing
theorymt estimates of the wave drag, Fig. 26, shows good agreement with linearized theory at all
Mach numbers, and poor agreement with slenderbody theory, thus reversing the trend of earlier
results. However, the general level of K, is higher than that for wings with Newby or Lord V area
distributions. It should be noted that, for wing 15, the difference between linearized and slender
body theories at the higher values of/3s1/c0 is much larger than for Newby and Lord V area distribu
tions and that Weber" has shown that differences of this order are typical of wings with comparably
large values of ? c02S/(x)/I7 and ? c03S"(x)/17 at the trailing edge. For these locally 'nonslender'
wings one must expect the zerolift wave drag to be much closer to the linearizedtheory value than
to the slenderbodytheory value. Recent calculations of the zerolift wave drag of a family of delta
wings with rhombic crosssections'', using linearized theory, have shown that, even for the
* In the light of more recent tests this conclusion should be modified. It now appears that the friction drag
is no greater than was estimated. The discrepancies noted arc due to the drag of the bands of carborundum grit
used to fix transition (cf. Appendix II).
t See Acknowledgements,
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'optimum'* wings, the values of K, increase when the position of maximum crosssectional ar _.a is
moved aft beyond 0?65c0. Thus, it can be expected that the relatively high drag of wing 15 is manly
due to the relatively rearward position of the maximum crosssectional area (see Fig. 6), which is
partly a result of the low pvalue of the planform.
Further confirmation of the accuracy of linearized theory' is given by the excellent agreement of
the theoretical pressure distribution with the measured values for M = 22, shown in Fig_ 27.
The agreement here appears to be much better than, for example, that normally found between
pressure distributions in twodimensional flow over aerofoil sections at low speeds and the
corresponding linearized approximations. By comparison, the slenderthinwingtheory" estir late,
while giving reasonable accuracy over the front of the wing, is seriously in error over the rear
25% c0, where the shape becomes nonslender. It should be noticed that the measured pre sure
coefficients are quite small (Figs. 27 and 28) and therefore an important assumption in linearized
theory, viz, that the perturbations are small, is genuinely satisfied.
4.4. DragduetoLift at Supersonic Speeds.
We turn now to the last term in the drag breakdown and consider the liftdependent drag f all
four wings.
In the absence of any theoretical method of estimating the liftdependent drag for wings with
leadingedge separation we rely entirely on windtunnel measurements and their analysis in terms of
simple geometric parameters. Such an analysis of early measurements of the liftdependent drag of
plane slender wings has been made by Courtney". He found that if he plotted K=77A(C )? Cm)/ CL2,
for CL = 0.1, against gA, all the points for sharpedged plane wings with streamwise tips lay close
to the line
K 075 + 0 64/3A , 1.2 SA 3.2.
These values of K, and also those for sharpedged delta wings, are, in general, lower than the ;e for
roundnosed delta wings collected and analysed by Cane and Collingbourne some years earlier ,
implying that the loss of leadingedge thrust due to sharpening the leading edge is more than
compensated by the resulting leadingedge flow separation, (a) increasing the lift for a given incilence
and (b) producing higher overwing suctions than underwing pressures on the forwardlacing
surfaces near the leading edges. For camber distributions with attached flow at a CI, lower thi,n tht
cruise C, the high loadings near the leading edges act on the drooped parts of the wing, wi h th(
result that, although the minimum drag coefficient may be increased slightly, the curvature if tilt
drag polar is reduced sufficiently to give a lower CD, and hence K, at the cruising C1, (as in Figs. 21
and 22). Thus the values of K given by Courtney's curve form an upper limit to the range of alue,
we would expect for cambered wings; a lower limit is given by R. T. Jones's lower boun:11,2,6
although this is no real physical limit and lower values may, in principle, be obtainable.
The values of K derived from a comparison of the drags of the cambered wings with the zerolift
drag of the plane wing are shown in Fig. 29. It should be noted that although the potential errors iti
these plots are quite large (e.g. AK = + 0045 + 0? 0018/C,2 for the worst combination of the errors
listed in Section 3) the actual uncertainty in the points plotted is thought to be no more th in the
* The 'optimum' wings are those members of the family having the smallest drag for a fixed post non of
the maximum crosssectional area, at a given gs,,fro.
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scatter about the mean lines shown on the figures. For all the wings the variation of K with M ich
number is of the form K = K, 2K,d32?,7, 02
2/cwith the following values for Kr and
Wing
?
K,
0.075
K.
C =
K
0.100
K?,
C,=
K?
0.125
K?.
15
1.28
210
1.44
1.94
148
194
16
1.33
1.70
139
1.57
141
164
17
118
2.04
l? 22
1.76
1.22
178
18
1.23
1.74
1.22
1.76
130
156
All the cambered wings have lower values of K, and Ku., and hence lower values of K, than he
plane wing. For the range of leadingedge droop angle covered by the cambered wings (i.e. 30? to .5 r)
an increase in droop decreases increases K? and, in general, decreases K. For = O? 10 it
is only the more highly cambered wings which have values of K lower than those of Courtne: 's
curve. The drag factors for the plane wing are at least 0 ? 15 higher than his values but, neverthekss,
they are still 0.25 lower than the value for zero axial force (i.e. 7rAoc/cr, in Fig. 30), which is better
than average for wings of this V/Se*, implying that the main reason for the high liftdependent
drag of this family of wings is the low liftcurve slope of the planform. This is a direct consequence
of the low value of p; as is shown in Fig. 31, where values of 77Acil Cr, for CI, = 01, obtained from
recent tests on plane gothic and ogee wings15, 16, 17, 18, are compared with the value for wing 15 at the
same f3sT/co and the same A.
4.5. Lift and Pitching Moment at Supersonic Speeds.
In this section we discuss the supersonic lift and pitchingmoment characteristics and assess the
effectiveness of the camber designs as means of trimming the wings at the cruise condition. In the
previous section it was shown that for lift coefficients greater than about 0.07 the cambered wir gs
have lower drags than the plane wing. It is also known that conventional trailingedge controls may
be very inefficient trimming devices (e.g. windtunnel tests of a model of the F.D.2 deltawing
research aircraftn have shown that, at supersonic speeds, the liftdependent drag factor of the
trimmed configuration is twice that for the fixedelevator cases). Thus there is a considerable
incentive to trim a supersonic aircraft, at cruising conditions, using camber alone.
A comparison of the lift vs. incidence curves of the four wings shows that the cambers tested hAel
no significant effect on the development of lift with departures from the design incidence (to make
this comparison in Figs. 17 and 18 the curves for wings 17 and 18 should be displaced 1? to the
left). Similarly, if allowance is made for the possible errors in the distortion correctiOns for wings 17
and 18, it is found that the camber has very little effect on the aerodynamiccentre position at
supersonic speeds. The variations of aCjace and  ac?,lac,, for the plane wing, shown in Figs. 3 2
and 33, therefore may be regarded as representative of all four wings. At all Mach numbers the lift
vs. incidence curves become straight for [3(a. ? ocd) greater than about 3? and two values of ac,,),
are plotted in Fig. 32. It is noticeable that, at the lower supersonic Mach numbers, where there is
* e.g. (7rAolICL? K) varies varies from 0?10 to 0.30 for the wings of Refs. 16 to 19.
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more lift due to leadingedge separation, the Cm vs. CL curves are quite straight, implyin that tt e
centres of linear and nonlinear lift are virtually coincident. At the higher Mach number i there ,s
less nonlinear lift but the aerodynamiccentre position moves forward with increasing C.
.
Figs. 32 and 33 also show values of these two derivatives given by two approximate theones,
both of which assume that the flow remains attached at the leading edge. Notsoslenderwing
theory", which has given good agreement with linear theory for conical wings and r,asonaitle
agreement with experimental results for sharpedged gothic wings21, is clearly of limited use for
the present planform, with its highly curved leading edge. On the other hand Evvard's approxirnaa:
theor y22, 237 which was not expected to be of much use for this slender highly curved planform,
appears to give a fair estimate of the liftcurve slope at zero incidence and a quite reasonable estimate
of the aerodynamiccentre position at zero lift.
Turning to the trimming effectiveness of the wings, we recall that the cruising conuition was
assumed to be CL = 0.075 at M = 2.2* and at this condition the wings should give centreof
pressure shifts of either 4% c? (wing 18) or 7% co (wings 16 and 17). Further, the lowspeed results
have shown that, at approach conditions, there is a progressive forward movement of the aer.)
dynamiccentre position with increasing leadingedge droop. Thus in considering the trimming
effectiveness of the camber we must take into account the fact that each wing will have ;. differeit
most rearward e.g. position, dictated by the lowspeed longitudinal stability requirementi.
Reference to the Cn, vs. CL curves for M = 2.2 in Fig. 20 shows immediately that none 01 the
cambered wings achieves a satisfactory trimmed CL. The values of AC (i.e. C?, ? (Cm)wing at
the same CL) and the shift of the centre of pressure for CL = 0.075 actually obtained ;,re showr
in Fig. 34. It appears that, without allowing for the lowspeed characteristics, wings 17 and 18 givt
about half the C.P. shift assumed and wing 16 about one third. However, when the pitchingmoinens
reference points are moved forward to coincide with the lowspeed aerodynamiccentre position:
for CL = 0.45, as in Fig. 35, then, at M = 2.2, the effective centreofpressure movements art
only 1Mc0 for wing 16, 2% co for wing 17 and 1% co for wing 18, when a shift of *X, c?
needed to trim.
Some indication of the manner in which the camber designs have failed to give their desiox
performance is given by the variation of lift and pitching moment with Mach number at desigri
attitude (Fig. 36). These plots show that, if the design CL and Cm are attained at fls;r/co = 0, then
there must be a very rapid increase in CL at ad with Mach number for 1 M 1 4, due, no doubt,
to loss of the designed negative lift near the trailing edge (see Fig. 8)?wing 16, which c.11s for the
largest amount of negative lift, being the most sensitive to changes in Mach number. Meawreniciit:;
of the load distribution on wing 1724 confirm that for this wing the designed negative lit near ttit
trailing edge is not achieved, even at M = 1 ? 4, and also show that, at low Mach numbers, ttp:
region near the apex develops considerably more than the design lift. The rearward movement or
the centre of pressure with further increases in Mach number is due to increasing liit near tit
trailing edge and decreasing lift near the apex.
On any nonconical cambered wing one must expect a rearward movement of the centre ot
pressure of the camber loading with increasing Mach number above M = 1; one must iiso expect
a rearward movement of the aerodynamiccentre position. Whether the changes in these two
quantities follow one another in such a way that the value of Cm, remains constant must depend (id
* Higher lift coefficients, of the order 0.10, are now being considered.
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both the planform and the camber loading. Clearly, the planforms with higher values of p,
their larger chords near the tips, will have larger movements of aerodynamiccentre posit on
(e.g. for a gothic wing, the change in x?(. in going from M 1 to M = 2 is 12% c015, compa ed
with 3% c, for wing 15) and correspondingly larger changes in the centreofpressure position of
the camber loading can be tolerated. The present wings failed to maintain their designed A
because the changes in the centres of pressure of the camber loadings outstripped the shift in aei ?
dynamic centre (which was not as large as expected), mainly due, as we have seen, to the rapillv
varying camber loadings near the trailing edge being too sensitive to changes in Mach numLer.
A morefavourable result could be expected from wings with lesscurved planforms and hiver
values of p, using smoother camber loadings. However, it may not be possible to utilize planforms
and camber loadings which are smooth enough to justify the use of slenderwing theory and, in
general, it would seem necessary to calculate the shape of the mean surface by linearized theory
for the cruise Mach number.
5. Conclusions.
Analysis of the results to provide data for performance estimation, and comparisons with ear ler
results, has shown that:
(i) the zerolift wave drag and zerolift pressure distribution for the plane wing are both in cl se
agreement with predictions of linearized thinwing theory;
(ii) the zerolift wave drag of the plane wing is higher than the values for wings of the same
volume and length obtained in the earlier tests; this is attributed to the relatively rearward posit on
of the maximum crosssectional area, which partly results from the relatively low value of :he
planform shape parameter, p
(iii) the liftdependent drag factors of the wings are higher than those of other slender wings,
when compared at the same value of /3A; this is mainly due to the low liftcurve slope of the wings,
which, in turn, is due to the low value of p;
(iv) the camber shapes designed by slenderwing theory do not give the desired changes in centre
of pressure at M = 2.2, the 'nonslender' camber loadings being more sensitive to changes in A/Leh
number than the incidence loading;
(v) the trimming effectiveness of the cambered wings is significantly reduced by 'pitchup' at
the lowspeed approach condition, the morecambered wings being more affected.
An obvious implication of these conclusions is that a better aerodynamic performance would be
obtained from a wing with a lesscurved planform, having a higher value of p. Such a wing would be
expected to have: (a) a more forward position of maximum crosssectional area and therefore a lover
zerolift wave drag, (h) a higher liftcurve slope and therefore a lower liftdependent drag, and
(c) less pitchup at low speeds. A better trimming effectiveness of the camber for such a wing would
also be expected if a smoother camber loading were used and the mean surface were calculated by
linearized theory.
6. Acknowledgements.
The author is indebted to Dr. J. Weber (R.A.E. Farnborough) for her calculation of he
slenderbodytheory and lineartheory wave drags for wing 15 (Fig. 26), to Mr. J. H. B. Smith
(R.A.E. Farnborough) for the linear thinwingtheory pressure distribution and to Dr. C. S. Sinnott
(HawkerSiddeley Aviation Limited) for the slenderthinwing pressure distribution for wing 15
(Fig. 27).
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LIST OF SYMBOLS
A Aspect ratio, 4s7,2/S
c(y) Local wing chord
c, Root chord
First mean chord
Second (aerodynamic) mean chord
CD Drag coefficient
CD0 Zerolift drag coefficient of plane wing
CDT, CD  C?,, where C?, is zerolift drag of plane wing
CL Lift coefficient
C10, Design lift coefficient
Pitchingmoment coefficient (based on e)
Design pitchingmoment coefficient
Pressure coefficient
Liftdependent drag factor (see Fig. 29)
L(x) Spanwise integral of loading/4U'
Mach number of free stream
Planform parameter, elco
Reynolds number based on c,
s(x) Local semispan
s,, Semispan
Plan area
S(x) Crosssectional area (Fig. 6)
I(Y) Local maximum wing thickness
V Wing volume
x, y, z Cartesian coordinates with origin at wing apex
Incidence (in degrees unless stated otherwise)
LY,t Incidence at design attitude
g / _ 1)
V(1 ?1112)
A Angle of sweepback of leading edge
Volume parameter, V/S""2
= C?, ? ?, at constant CL
(AC,,,) = AC,,,, referred to lowspeed A.C. for CL = 0.45
e = tx + c(y) c0}/c(y), nondimensional chordwisc coordinate
7/(x) = S(X)
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REFERENCES
Author(s) Title, etc.
1
D. Kuchemann .
Aircraft shapes and their aerodynamics for flight at supersoni
speeds.
Advances in Aeronautical Sciences, Vol. 3, p. 221. Pergarno
Press. 1961.
Proc. 2nd int. congr. Aero. Sci., Zurich. 12 to 16 September, 1960.
2
E. C. Maskell and J. Weber
On the aerodynamic design of slender wings.
J. R. Ae. Soc., Vol. 63, No. 588, p. 709. December, 1959.
3
J. H. 13. Smith .
The problem of trim for a supersonic slenderwing aircraft.
Unpublished M.o.A. Report.
4
J. Weber
Design of warped slender wings with the attachment line alohg
the leading edge.
A.R.C. 20,051. September, 1957.
5
S. B. Berndt
Windtunnel interference due to lift for delta wings of small
aspect ratio.
K.T.H. Aero. Tech. Note 19. Sweden. 1950.
6
R. T. Jones
The minimum drag of thin wings in frictionless flow.
J. Ae. Sci., Vol. 18, No. 2, p. 75. February, 1951.
7
J. Weber .
Some effects of flow separation on slender delta wings.
A.R.C. 18,073. November, 1955.
8
D. H. Peckham
Lowspeed windtunnel tests on a series of uncambered dent er
pointed wings with sharp edges.
A.R.C. R. & M. 3186. December, 1958.
9
M. J. Lighthill .
The wave drag at zero lift of slender delta wings and similar
configurations.
J. Fluid Mech., Vol. 1, Part 3, p. 337. September, 1956.
10
H. Lomax ..
The wave drag of arbitrary configurations in linearized flow, as
determined by areas and forces in oblique planes.
N.A.C.A. Research Memo. A55A18. March, 1955.
11
J. Weber ..
Some notes on the zerolift wave drag of slender wings with
unswept trailing edge.
A.R.C. R. & M. 3222. December, 1959.
12
J. H. B. Smith and W. Thomson
The calculated effect of the station of maximum crosssecticiial
area on the wave drag of delta wings.
A.R.C. C.P. 606. September, 1961.
13
J. Weber .
Slender delta wings with sharp edges at zero lift.
A.R.C. 19,549. May, 1957.
14
A. L. Courtney .
A collection of data on the liftdependent drag of uncambi red
slender wings at supersonic speeds.
Unpublished M.o.A. Report.
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R EFERENCEScontinued
Author(s) Title, etc.
15
L. C. Squire . ?
An experimental investigation at supersonic speeds of the
characteristics of two gothic wings, one plane and one cambered.
A.R.C. R. & M. 3211. May, 1959.
16
L. C. Squire
'I'he characteristics of some slender cambered wings a Mac
numbers from 0 4 to 20.
Unpublished M.o.A. Report.
17
D. G. Mabey and G. P. Ilott .
The characteristics of three slender 'mild ogee' wings a Mach
numbers from 0 4 to 20.
Unpublished M.o.A. Report.
18
A. L. Courtney and A. 0. Ormerod
Pressure plotting and force tests at Mach numbers up to 28 of
an uncambered slender wing of p srlc?  (1 landley
Page Ogee).
A.R.C. 23,109. May, 1961.
19
C. R. Taylor and T. A. Cook ..
Six component force measurements on a 1/9th scale modei of the
Fairy Delta 2 research aircraft at Mach numbers up to 2 ? 0.
Unpublished M.o.A. Report.
20
MacC. Adams and W. R. Sears ..
Slenderbodytheory review and extension.
J. Ae. Sci., Vol. 20, No. 2. August, 1959.
21
L. C. Squire
Some applications of 'notsoslender' wing theory to winf.,s vvitn
curved leading edges.
A.R.C. R. & M. 3278. July, 1960.
22
J. C. Evvard
The effects of yawing thin pointed wings at supersonic seeds.
N.A.C.A. Tech. Note 1429. September, 1947.
. 23
J. Gilbert ..
Approximate method for computing the pressure distribu7ion on
wings with subsonic leading edges in a steady stream.
English Electric Aero. Tech. Memo. AM18. 1956.
24
J. Britton .
Pressure measurements on a cambered ogee wing (p = 0 45) at
Mach numbers up to 2.6.
Unpublished M.o.A. Report.
25
W. R. Sears (editor) .
General theory of high speed aerodynamics. (Vol. VI of Speed
Aerodynamics and Jet Propulsion.)
Princeton University Press. 1955.
26
J. C. Evvard
Use of source distributions for evaluating theoretical aerody ainic
of thin finite wings at supersonic speeds.
N.A.C.A. Report 951. A.R.C. 13,821. 1950.
27
C. Kell
Freeflight measurements of the zerolift drag of a slende, winf
at Mach numbers between 1.4 and 2.7.
A.R.C. 23,511. August, 1961.
28
R. J. Monaghan ..
Formulae and approximations for aerodynamic heating rites iii
high speed flight.
A.R.C. C.P. 360. October, 1955.
29
J. B. W. Edwards
Freeflight measurements of the zerolift drag of a slendef oget
wing at transonic and supersonic speeds.
A.R.C. 24,448. October, 1962.
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Corrections to Measured Lift and Pitching Moment for Asymmetry of the Sting Shroud
The asymmetry of the sting shroud distorts the mean surface. In the notation of Fig. 37 the
distortion is
Az(x, y) = {Azu(x, y) ? Azdx, y)}
and the corresponding additional incidence is
0
Aa(x, y)  ? y).
(6)
To calculate the additional lift AL(x) induced by the distortion on the segment of the w ng
between x' = 0 and x' = x we utilize a flowreversal theorem (cf. p. 235 of Ref. 25) which, or
the present application, states that:
AL(x) = 0 fr Aa(x', y') x) dy' dx'
r a
7)
where Lip(x', y': x) is the loading, at a point (x', y'), on a flatplate wing, of the same planform as
the wing segment 0 x' < x, at incidence a in reverse flow.
It follows from relations (5) and (6) that
d r
, y')dy' 1
2 dx; (Az,? Az2)dy'
r
 2 dx'
where a(x') is the difference between the additional crosssectional areas on the upper and low er
surfaces. We may approximate Ap(x", y': x) in the region 0 ty' I r(x) by its value in the cent re
and thus obtain for AL(x) the approximate value
AL(x) = ? f dx'
J o a
The wing segments in reversed flow are wings with supersonic leading edges and subsonic trailing
edges. If x ? x' < ,es(x), then the loading is the same as in twodimensional flow:
2 Ap 4
pU2 a p ?
If ,Bs(x) x ? x' ,Bs(x) + 2gs(x0), then the loading on the centreline can be determined I y
Evvard's26 method. The solution which satisfies the KuttaJoukowski condition at the suhson
trailing edges reads:
(87542)
2 Ap
pU2
8 Ft
sgn y,  {(x _ x,)2 isoy2}1/2dy
77 ? 0
8 , Py,
s n
X 
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When the upper and lowersurface distortion fields do not interact, i.e. when x < Ps(x),
2 _ 2
AL(x) o(x)
pU2
and, since the loading Ap/a is constant over the entire area of the distortion, this exp ession s
exact. In other cases yi must be found by geometrical construction and AL(x) by integration.
The corrections to measured lift and pitching moment are:
A CL = 2 AL(x)
p S
and, for moment coefficients about 1/2, based on e,
A Cfl, = ? A CL ? pU2 2 ? fxT AL(x)dx.
S1
For wings 16 to 18, xr/sT = 1.5 so that for M ?? 1.8:
AC1 = 2o(x)
I3S
and
AC? = 2 xT
a(x)dx
IRS'e
 00003//3 for wing 16
 00008/f3 for wing 17
 00005//3 for wing 18.
At M = 1.4 and 1.6 the calculated differences from the above values were less than the probable
experimental errors.
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APPENDIX II
Kell's freeflight measurements of the zerolift drag of the plane wing
In Ref. 27 Kell describes his freeflight measurements of the zerolift drag of the plane w rig
(i.e. wing 15) between M = 14 and 2.7. His results are reproduced in Fig. 38; also shown in this
figure are his estimates of the drag of the small sting and stabilising fin (see Fig. 39) and the w ng
friction drag. The model was flown with transition fixing bands of 0007 in. carborundum crit
0.5 in. wide, located in. from the leading edges. The turbulentskinfriction drag was estima' ed
using the intermediateenthalpy methods of Ref. 28. Estimates of the probable heating rates of he
model were based on the flight history and the known thermal properties of the model. In order to
illustrate the significance of the heattransfer rate, Kell estimated values of skinfriction d ag
assuming full and zero heat transfer; these are also plotted in Fig. 38. These last two estimates ire
only intended to illustrate the significance of the heattransfer conditions, they are not intended to
indicate the limits of accuracy of the skinfriction estimates.
The Reynolds number during the test varied from 42 x 106 at M = 14 to 105 x 106 at M = 2 7.
The comparison of the 'apparent wave drag' deduced from the freeflight results with that fn)rri
the tunnel force measurements for R = 107 and with the tunnel measurements of pressure dr4 is
shown in Fig. 40. The 'apparent wave drag' is the total measured drag less the sum of the estimated
friction drag and the sting drag, and fin drag (if any). In the region of principal interest, i.e. near
M = 2.2, the freeflight results are about 0.0005 higher than the tunnel force results and 00( 08
higher than the measured pressure drag. It is now recognised that, in both the tunnel and f1.4 ht
tests, there were significant drag increments due to the roughness bands which were not taken into
account in the analyses of zerolift drag.* The roughness drag increment in the freeflight tests is
expected to be larger than that for the tunnel tests since the grit used in flight was excessively
coarse for the high Reynolds number of the tests. In view of the surprisingly large drag increments
in the tunnel0.0003 at R = 107 and 0.0005 at R = 15 x 107 for a grit which did not prow ke
transition completely at R = 0.5 x 107 it could be anticipated that the drag of the transition trip
accounts for, at least, a major part of the discrepancy between the apparent wave drag derived frc,rn
the flight measurements and the tunnel measurement of pressure drag.
* See footnote in Section 4.3 and Section 4.5 of Ref. 29.
(87542)
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TABLE
Details of the Models
Length (c0) 60 in.
Span (2sT) 24.96 in.
Plan area (S) 674 in.2
Volume (V) 726 in.3 (excluding sting shroud)
Surface area 1420 in.2 (including sting shroud)
Stingshroud diameter
Sting diameter
2.60 in.
210 in.
Planform parameter (p)
045
Aspect ratio
0.924
c/co
0.616
T V/S3 2
00415
vise
0.040
4
'77' Co
KCILD? = S
406.5
128 V2
Moment reference point at 0.5e (i.e. at centre of plan area)
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I \ \
I\
\ \
I \ \
V\
I
\ \
\ p= 57/3 UoTH1C
p .;12. Gomic
p /15 OGEE (COURTNEY)
p a OGEE (COLLINGSOURNE)
WINGS 581 ('; 0.45)
5T/.. = 0.208
ii
FIG. 1. The planform.
0
IS
SA.tori A0
1 0
0'5
0
008
0.06
0.04
002
1
WiNG5 1518 .0 .45)
? ? QUARTIC OGEE 1...0.5)
?COLLINGBOURNE. OGEE 0 '5)
? ? ? 'COURTNEY' MILO 0G52 .0. 533)
0 02 0.4 06 05 o
FIG. 2. Variation of leadingedge sweep
back across the span.
0.040
0 05 04 0.6 043 1.0
WsT
FIG. 3. Variation of thickness, chord ratio
across the span.
8Z00080001?000tIZZ80081./dCltlVI3 : 91./01./ZOOZ eseeletl JOd PeA0AdV
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FIG. 4. The thickness distribution?chordwise sections.
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?
04
NOTE
THE VERTICAL AND SPANN/10E?
OIMEN5ION5 ARE MAGNIFIED 42.4.)
FIG. 5. The thickness distribution
spanwise sections.
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2.0
1518
g 14.2
0: g
75
WINGS
LORD
7
14
12
48
NEWBY
 
o.s
0.1
02
03
0.4
0.5 0.6 0.7
3C/c.
FIG. 6. Crosssectional area distribution.
24
0.8
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1 0 "
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0 04
0.02
WING 16
WING 17
WING 18
0.10
E 0.05
LOE.)
ST
0.2
04
08 G
/C0
0.8 ID
FIG. 7. Centreline camber, wings
16, 17 and 18.
/ __,
...\\\:\
\
\
?
\
?
/1
iii
I,
FIG. 8. Chordwise variation of camber
loading for wings 16, 17 and 18, as assumed
in slenderwing theory.
NOTE:
VERTICAL GPANWISE
DIMENSIONS MAGNIFIED (2.4)
 WING 16
WING 17
WING 18
10
FIG. 9. Details of wings 16, 17 and 18.
Approved For Release 2002/10/16 : CIARDP71600822R0001000800028
Approved For Release 2002/10/16 : CIARDP71600822R0001000800028
STING SUPPORT
(FORCE TESTS
ONLY)
24%
STING SHROUD (2.6 DIA)

H.7\ MOMENT REFERENCE PT
60.
/ SUPPORT FOR PREStURE PLOTTING MODEL
FIG. 10. Details of model supports.
26
Approved For Release 2002/10/16 : CIARDP71600822R0001000800028
Approved For Release 2002/10/16 : CIARDP711300822R0001000800028
/
/
,
Y
/
/
,
/
/
,
/
/
r
/
////
i
wiNG i5
WING 17
WING le
?
?
/
I .
i
4' e
1 .
I
1
i
a.
le
d.
a,
FIG. 11. Lift vs. incidence, A/ 0.3.
0 OS
0 04
003
0 02
001
0 I
1
WING IS
WING 16
WING 17
WING IS


. /
/
? /
. /
,...,
?.?,
/?..,
/ 77/
.> 7

,
....
,...
r
..

., ,?
.
001
+ 0.1
2 0.3 0.4
CI.
0.5
.6
07
FIG. 12. Pitching moment vs. lift, _11= 0.3.
Approved For Release 2002/10/16 : CIARDP71600822R0001000800028
0 24
0 20
0 15
co
0 12
0.0e
04
I.__
0.1 0
Approved For Release 2002/10/16 : CIARDP71600822R0001000800028
WiNG 15
WING 16
WING r7
WING le
I
?
?  
.
7
.
/
. .

04
FIG. 13. Drag vs. lift, M 0.3.
04
0.7
0
0
0
0
0
0
0
.40
.35
/
..
2
WING
WING
WING
IS
17
le
/
/
20
/
/
,.
r
/
II
/? ///
/
/
)5

400
FIG. 14. Lift vs. incidence, Al 0.8.
Approved For Release 2002/10/16 : CIARDP71600822R0001000800028
0 012
Approved For Release 2002/10/16 : CIARDP71600822R0001000800028
WING IS
WINO Pe
WING
WING 18
FIG. 15. Pitching moment vs. lift, M 0.8.

?0035
win* 15
WING IG
WING n
WING IS
/
?
 ?
/
r
0 025
co
?0.020
,,
,
0.015
.
?0010
???%,.........
?0 005
ci
0.05
+005
0.10 015
oeo
FIG. 16. Drag vs. lift, M 0.8.
Approved For Release 2002/10/16 : CIARDP71600822R0001000800028
25
Approved For Release 2002/10/16 : CIARDP71600822R0001000800028
w NG 15
WING 16
WING 17
WING A
/
.
......,,,
,
0I5
012
0 08
.7/
77X"
......X.77/
,4
./....4"./..
/
M?t6
0
3' 4 5'
7'
'GU
/ 16
t
12
Z"
08
,
101
_...007/t1.1?4
5
6
FIG. 17. Lift vs. incidence, 31 = 1.4 and 1.8.
a
02
0
c?
0
To
r
_
WING 15
WING 16
WING I?
WING
...."
...,"
...
...""
....."
.../
...."
....".
...."
...,
../
/
el t 6
+16
2"
4' 5'
.c
6'
ucv
016
CI.
0 12
/
../
./'
.
../..".."
. ..../.
.
/'''
0 .05
...,"
....."
....1".'4
0.04
....../.2".
:1622.
+I.
e
3'
4." S.
6
FIG. 18. Litt vs. incidence, M = 2,2 and 2.6.
Approved For Release 2002/10/16 : CIARDP711300822R0001000800028
Approved For Release 2002/10/16 : CIARDP71600822R0001000800028
.0.0080
004
0.
c,?
00040
?.6008
MZ 6
1 0 12 0 6
.............
CL,.."z
MUM
YANG 15
WING 16
WING 17
WING 18
,c1Lneg
NN.
i M ? 1.4
N.\\N,s.
N. N..,
'N.........\\
?
.\\
? N
0
04
+604
016 0
C,
00040
Cm.
'N
600120
=00160
FIG. 19. Pitching moment vs. lift, M =
14 and 2.6.
0
0
1?1+2?2
0
004
N
0040
00080
00120
N. .?......... + 0 12
.......N.N
\
\ .".".... ......,_ ? ........_
.... \ ::"... ......_
 ..... \ .....7.. ....i
0IS 010
CL
?,60080 
004
WING 15
WING 16
WING 17
WING 18
0
?60040
600060
600120
.00160
N.
+ 004' 001ir ? 612
N.
010 020
CL
FIG. 20. Pitching moment vs. lift, M =
18 and 2.2.
A roved For Release 2002/10/16 : CIARDP71600822R0001000800028
Approved For Release 2002/10/16 : CIARDP71600822R0001000800028
0 024
0 020
?0012
14?14
?0006
?0004
II
?0024
?0020
0016
?000$
?0004
?18
WING 15
WING 16
WING 17
WING IA
0
0.04 0 #004 006 012 016 004 0 +0.04 006
CL
c,
FIG. 21. Drag vs. lift, M = 14 and 1.8.
0 024
0020
0 016
Co
0004
0.04
2 2
WING 15
W1N4 16
WINO 17
WING 1B
0.04
0.013 0'12
GL
012
?0004
016 004
+ 004 002 012
CL
FIG. 22. Drag vs: lift, M = 2.2 and 26.
32
Approved For Release 2002/10/16 : CIARDP71600822R0001000800028
0.16
(87542)
Approved For Release 2002/10/16 : CIARDP71600822R0001000800028
0 10
004
002
?64
%
?65
77.,
 ? A.C.(%
c)
'
?72.
?66
X;
,..?..,"...
?67
..'2
.../ ,,
,/
"?666,
?69
0 1
0.2
03 04
CL
FIG. 23. Variation of aerodynamiccentre positions
with lift coefficient, M 03.
05
0.6
I i
'\,,,,N.N...1...................................
Ci..1.21 it 4 MIK %
eCaYaC,)0 .0 42
664
6
60
0402
0,
FIG. 24. Variation of aerodynamic
centre of nonlinear lift; wing 15,
M 03.
33
Approved For Release 2002/10/16 : CIARDP71600822R0001000800028
Approved For Release 2002/10/16 : CIARDP71600822R0001000800028
0.010
0.006
CD
0004
0.002
O MEASURED Co.
o MEASURED Co. + SHROUD CORRECTION  ESTIMATED Cr
O MEASURED PRESSURE DRAG
DASHED SYMBOLS DENOTE LATER TESTS
SHROUD CORRECTION
1.2 I 4 1:6 I 8 2.0 2.2
0.010
0008
0006
Co
0004
0002
(a) R = 107.
24 26 28
? MEASURED CD.
111 MEASURED Co. + SHROUD CORRECTION  ESTIMATED CF
? MEASURED PRESSURE DRAB
0
I 2
CORRECTION
t 4 I? 6 1'8 2.0 2.2 24
(b) R = 1.5 X 10 7 (later tests).
FIG. 25. Analysis of zerolift drag of wing 15.
34
Approved For Release 2002/10/16 : CIARDP71600822R0001000800028
Approved For Release 2002/10/16 : CIARDP71600822R0001000800028
K0
e MEASURED PRESSURE DRAG
 SLENDER WIN qTHEORY
WAVE DRAG
 LINEAR  THEORY }
1.2
0.8
04
K0 ? Trziza C04/0 0wz9,
_
`..
N.N..
g I
I. C
''''`.............
1111
l? 8 E.0
.....,
2.2
"..........,
24 26
.......T........".
2.8
M = 1.4
0.1
FIG. 26.
02
03 04
ST/c.
0.5
0.6
Variation of K, with Mach number,
wing 15.
35
Approved For Release 2002/10/16 : CIARDP71600822R0001000800028
Approved For Release 2002/10/16 : CIARDP71600822R0001000800028
LINEAR THIN  WING THEORY
SLENDERTHIN WING THEORY
MEASURED VALUES (R .1.5 .107)
 0 05 0 ?176
cp
0.05
Op
0.05 ,/sT . 0.656
cp
vsT"'336
0.9
?
.0.05
0.3 0.4 0.5
0.6 0.7
0.8
FIG. 27. Comparison of measured pressure distribution for wing 15, at CL = 0, with two
theoretical distributions. M = 2.2.
36
Approved For Release 2002/10/16 : CIARDP71600822R0001000800028
 010
 0.05
c,
Approved For Release 2002/10/16 : CIARDP71600822R0001000800028
?
o
/er'r
10.05
04
+0.10 ,
x100?5 0.6
010
005
C,
4005
+ 010
+ 015
06 08
0.7 08
9./s.r. 0.336
d9 JO
 0 I 0
cp
0 05
+0051 ,
Dc/0.. 0.75 080 085
? M.14
? M? 1.6
? M? 2.6
......?..ir
,s
/V 
04 06 08
0 656
ST
090 095
to m?14
? 11?2.6
^
..."..
.....C
? 4
ar'
&?
a
o(O
03
.
4.... .
_ 
06
07
0.8
09
ill
E/
sr '0.03
2
X/c.. 01
02
0.3
04
0.5
0.6
07
0.8
0.9
10
Fro. 28. Variation with Mach number of zerolift pressure distribution for wing 15.
37
Approved For Release 2002/10/16 : CIARDP71600822R0001000800028
Approved For Release 2002/10/16 : CIARDP71600822R0001000800028
K ? it A (Co 
WHERE Co. is ZEROLIFT DRAG
COEFF. OF WING 15
WiNG 15
WING 16
o ? WING 17
? WINO 18
25
20
O.. 010
I 00
25
20
IS
I0
0 01 02 03 04 05
201840.a
I I
II I 4 16 I 20 22 24 26
25
20
5
to
..??"'" '
t.
..
......o?
*
?.Jo'
_......tr
....?...
,...
,c,.....0
 
..1... , a>
3.......
...:..C
K?127510640A
01
2/6 ST/
04 0 5
M 14 16 1 B 20 22 24 26
CL. 0075
.  2
?????".....d.891..5.:......4
?
...
,?*4
... ....?....ArP
.;;;. III
1
I
I 1
14 s 14
16 I8
00
2 2
04 2,
01 02 05
ZA ST/Coa
FIG. 29. Variation of dragduetolift factors with Mach number.
Approved For Release 2002/10/16 : CIARDP71600822R0001000800028
04
6
05
30
25
20
Is
10
s
2.0
'5
I0
Approved For Release 2002/10/16 : CIARDP71600822R0001000800028
..../
le"
.....'"
,3

"'ji
,  .... . 
n A.5.c.../...
K..
.
..""
.....
,.
? ../..
.
FIG. 30.
01 02
Liftdependent drag of the plane
wing, CL = 0.10.
O WING 1 IMF. 15
A WING 8 REF St.
? WING 9 REF I 7 37/0.?0'25
+ WING 15 PM 18
X %ONG 15
5
0.433
0.40 045
fiA?1.30
060 065 0/0
P ? a 5%. A ? a/Co
r 'c, "
20
16
I 2
KL
PER RAO
08
0
e MEASURED VALUES o.0
 MEASURED VALUES /3 > 3'
'NOT50 SLENDER' THEORY
EVVARD'S APPROX. THEORY
\
\
?
?
\
a.
M'
1
1.4
1
1.6
1
1.11
1
20
I i
2.2 .2.4
21.6
2.. ii
0.05 0.10 0.15 0.20
/3157a
FIG. 32. Variation of CCL/aa with Mach number,
winv 15.
?
30
Approved For Release 2002/10/16 : CIARDP71600822R0001000800028
0.16
0.12
 bet,
0 05
Approved For Release 2002/1.0/16 : CIARDP71600822R0001000800028
MEA5LRE0 VALUES CL
MEASURED 'VALUES
'NOT 50 SLENDER THEORY
EVVARD'S APPROX. THEORY
004;
M 1.6 1.8
0.05 010
2.0 22 2.4
0' '5 0 20
s
FIG. 33. Variation of ? Jicmiac,, with Mach
number, wing 15.
211
025
030
0012
0008
0004
0
0
CL ? 0075
4
2
0
1 6 1. 6 I6 2.0 2 2 24 2.6
IA
FIG. 34. Variation with Mach number of
AC?,, at constant CL, wings 16 to 18.
v
WING 16
WING 17
WING 16
MINIMUM (A C.X170 TI AT CL .0075
wig
ooe
:,,$)*t
......... 's?
?
A
1 4 6 13 20 22 24 5
FIG. 35. Effective AC for CI, = 0.075.
ripnc 16 tn 1Q
!Approved For Release 2002/10/16 : CIARDP71600822R0001000800028
8
6
4
2
0
CP SHIFT (% C.)
CL
004
002
0 010
0006
0.004
0002
0
'Approved For Release 2002/10/16 : CIARDP711300822R0001000800028
0 005 010 a 015
pa Sric:
020 0.25
M2 14 16 I5 20 22 2.4 2.6
?
I 1
WING 16
WING 17
WING le
DESIGN P75
?
?. ?
?.
0
\\NN
...
\
22
NN's
\
?
?
'....?........,?.?,..........
'.:::??....??
1
N
?
?
?
?
?
? ?
..Z....,.... ....
? ..... ..... _
005
010 015
(31
C 20
0 25
FIG. 36. Variation of Cr, and Cm at design
attitude with Mach number, wings 16, 17
and 18,
UNDISTORTED
MEAN SURFACE
?
......_ "i2I3.(x24)?/'
DISTORTED MEAN
SURFACE
STING SHROUD
(RAOILIS ?r)
17Tr. 1'7
Approved For Release 2002/10/16 : CIARDP71600822R0001000800028
tont 1 0
Approved For Release 2002/10/16 : CIARDP71600822R0001000800028
0010
0008
0006
CD?
0004
0.002
.
MEASURED
TOTAL
DRAG
MAX
4_
MOST
7.
ZERO HI.
H.T.
_
PROBABLE
........
I
HEAT TRANSFER

ESTIMATED
FIN
I STING
DRAG
1
14
16
II
20
22
2.4
2.6
STIMATED WING
FRICTION DRAG
211
k
FIG. 38. Freeflight measurements of zerolift drag of wing 15.
FIG. 39. Freeflight model.
42
Approved For Release 2002/10/16 : CIARDP71600822R0001000800028
Approved For Release 2002/10/16 : CIARDP71600822R0001000800028
0006
0.006
CD
0.004
0002
APPARENT WAVE DRAG, FREE FLIGHT
APPARENT WAVE DRAG. TUNNEL, R 2z104
MEASURED PRESSURE DRAG
1.4
(87542) Wt. 64,11857 1s.5 8/63
1.6 16
29 p,A 2.2 24
26 26
FIG. 40. Comparison of freeflight measurements with
tunnel results.
43
Approved For Release 2002/10/16 : CIARDP71600822R0001000800028
Approved For Release 2002/10/16 : CIARDP71600822R0001000800028
A.R.C. R. & M. No. 3328
December, 1961
C. R. Taylor
533.693.3:
533.6.011.34/.5:
533.6.013.12/.13:
533.6.013.15
MEASUREMENTS, AT MACH NUMBERS UP TO 2.8, OF THE
LONGITUDINAL CHARACTERISTICS OF ONE PLANE AND
THREE CAMBERED SLENDER 'OGEE' WINGS
Measurements have been made of the longitudinal characteristics of one
plane and three cambered slender ogee wings (p = 0.45, sr/co = 0208)
at two subsonic and eight supersonic Mach numbers up to 28. The tests
also included measurements of the zerolift pressure drag and support
interference of the plane wing. The results have been analysed to give data
for estimating the performance of supersonic transport aircraft.
A.R.C. R. & M. No. 3328
December, 1961
C. R. Taylor
533.693.3:
533.6.011.34/.5:
533.6.013.12/.13:
533.6.013.15
MEASUREMENTS, AT MACH NUMBERS UP TO 28, OF THE
LONGITUDINAL CHARACTERISTICS OF ONE PLANE AND
THREE CAMBERED SLENDER 'OGEE' WINGS
Measurements have been made of the longitudinal characteristics of one
plane and three cambered slender ogee wings (p = 045, sr/co = 0208)
at two subsonic and eight supersonic Mach numbers up to 2.8. The tests
also included measurements of the zerolift pressure drag and support
interference of the plane wing. The results have been analysed to give data
for estimating the performance of supersonic transport aircraft.
A.R.C. R. & M. No. 3328
December, 1961
C. R. Taylor
533.693.3:
533.6.011.34/.5:
533.6.013.12/.13:
533.6.013.15
MEASUREMENTS, AT MACH NUMBERS UP TO 2.8, OF THE
LONGITUDINAL CHARACTERISTICS OF ONE PLANE AND
THREE CAMBERED SLENDER 'OGEE' WINGS
Measurements have been made of the longitudinal characteristics of one
plane and three cambered slender ogee wings (p = 045, sr/co = 0.208)
at two subsonic and eight supersonic Mach numbers up to 2.8. The tests
also included measurements of the serolift pressure drag and support
interference of the plane wing. The results have been analysed to give data
for estimating the performance of supersonic transport aircraft.
A.R.C. R. & M. No. 3328
December, 1961
C. R. Taylor
533.693.3:
533.6.011.34/.5:
533.6.013.12/.13:
533.6.013.15
MEASUREMENTS, AT MACH NUMBERS UP TO 28, OF THE
LONGITUDINAL CHARACTERISTICS OF ONE PLANE AND
THREE CAMBERED SLENDER 'OGEE' WINGS
Measurements have been made of the longitudinal characteristics of one
plane and three cambered slender ogee wings (p = 0.45, sr/co = 0.208)
at two subsonic and eight supersonic Mach numbers up to 28. The tests
also included measurements of the zerolift pressure drag and support
interference of the plane wing. The results have been analysed to give data
for estimating the performance of supersonic transport aircraft.
Approved For Release 2002/10/16 : CIARDP71600822R0001000800028