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1 5 APR. 195^

REPORT No. 66

TECHNISCHE HOGESCHOOL

VUEGTUIGBOUWKUNDE Kanaalitraot 10 - DEUT

THE COLLEGE OF AERONAUTICS

GRANFIELD

TESTING AND ANALYSIS OF A 60° SWEPT BACK WING

WITH RIBS PARALLEL TO THE LINE OF FLIGHT

by

D. HOWE. D.C.Ae.

This Report must not be reproduced without the perrrtission of the Principal oi the College of Aeronautics.

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R e p o r t F o . bo A u g u s t a 1953 T H E G O L I . B G ? ^ O F A E R p y A U T I G S

O R A N F I E L D

Testing and Analysis of a 60° Swept Back Wing v/ith Ribs Parallel to the Line of Plight ^

by

-D» Kowe, DoC.Ae. oOo

SUMMRY

The specimen used in this work represents the load carrying structure of a cambered two spar 60° sweptback wing, having closely pitched ribs of large boom area parallel to the line of flight, and thick skins# The wing has an aspect ratio of 2ok5s a semispan of 101.5" and a taper ratio of 1.50.

Construction was of light alloy, and the root was built into concrete.

LOPding was by bending and torsion couples, and normal shear forces applied at, or near to, the tip. Both strain and deflection measurements were made. The strains in portions of the structure removed from root effects, and the stiffnesses were compared with the oblique coordinate theory of Hemp.^ ' Two versions of this theory were used. A General Theory which considers the camber of the v/ing, and a Simplified Theory, which uses equivalent rectangular sections and allows an approximate root correction for the stiffnesses to be made. Lack of a sui"vable theory prevented strain comparisons at the root.

The more important conclusions reached are as

followsj-/ The use of ...oc

BHF.

This investigation was made daring the tenure by the author of a Clayton Fellov/ship awarded by the Institute of

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The use of oblique coordinate theory is justified for both stiffnesses and strains. For wings in v/hich the camber is not large, the Simplified Theory is sufficiently accurate, although an allowance for root constraint and rivet slip is necessary for stiffness evaluation.

The effect of taper is to reduce the cross sectional variation in strain predicted for. normal shear force loading, a pure couple theory being better for direct strains in this case»

The direct strains build up towards the rear spar at the root, but the shear strain distribution is complex and requires further investigation. A second order discrete rib theory is required to predict this root strain variation.

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3

-LIST OF CONTENTS

1.0 Introduction

Page

2.0 Details of Experimental Apparatus 5

2.1 The Specimen 5

2.2 Root Details 6

2o3 Gauging 6

2.k

Method of Loading 7

3.0 Scope of Work 7

3«1 Preliminary Tests 7

3«2 Loading Cases 7

3«3 Deflection Tests 8

3»k

Strength Tests 8

koO

Calculations 8

l+.l Definitions of Stiffnesses 8

1+.2 Calculations associated with

experimental work 9

14-93

Theoretical Calculations 9

5«0 Presentation of Results 10

6.0 Discussion 11

6.1 Stiffnesses 11

6.2 Deflections 13

6.3 Strains away from root effects 13

6.U Strains at the root 15

7*0 Conclusions 18

References 20

Tables

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- u

-1.00 INTRODUCTION

Despite the considerable use of swept back wings for aircraft during the past few years, very little information is available on the structural characteristics of swept wings

(2) having ribs parallel to the line of flight. Some work^ ' has been carried out on small scale boxes using this rib

configuration, but the published work does not cover the problems associated with an actual wing. The present work is an attempt

to reduce this gap in available information.

The specimen used in these tests was constructed so as to be representative of the load carrying structure of a swept-back wing designed in accordance with current practice.

The vdng has a 6o° sweptback leading edge, a low aspect ratio, and a tapering cambered aerofoil section» The structure is of two spar construction with thick skins and heavy rib booms. As practical aircraft v/ing root conditions vary considerably, a

fully built-in root was chosen as being that which is most commonly considered by theory.

The testing consisted of an investigation of the stiffnessj distortion, and strain characteristics of the structure, both

at the root, and at points removed from the root effects.

The loading was by pure couples, and shear forces normal to the wing. A theoretical analysis of the strains at points avray

from the root, and the stiffnesses, has been made using oblique coordinate theory, and a comparison made with the experimental results»

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5

-2.0 DETAILS OF EXPERIMENTAL APPARATUS

2»1 The Specimen

The wing geometry is shown in Fig.1, the leading edge sweepback being 6o°, the aspect ratio 2.i|5j and the tip chord two thirds the root chord of 120 in. The thickness chord ratio of 13% at the root, falling to 12% at the tip is rather higher than is normal. This is of no importance in the present work as the effect is to alter the magnitude of the skin stresses, leaving the nature of the distribution unchanged. The camber is represented on the specimen by two straight lines, a measure adopted merely to simplify its manufacture.

The structure has a root chord of 6o in, and the length along its centreline, which corresponds to the kOfo chord-line of the wing is 169.3 in. Rib 1 is 22in outboard of the root section, and the rib pitch is 12 in. along the front spar» Fig.2 gives the structural details, which can also be seen in Figs. 5-8.

Light Alloy is used throughout, the skins being 0.08 in. and the spar webs 0.022 in. thick D.T.D. 390. The spar booms are tapered tee section extrusicis, v/hllst the rib booms are built up double angles made from 0.08 in. D.T.D. 390. The diaphragm type rib webs have a thickness of O.036 in. and angle section stiffeners.

Of the five loading points, two are on the front spar, and the remainder on the rear spar. These are arranged to enable the application of pure couples along and normal to the centreline, and shear forces normal to the plane of the wing. Fig-v3 shows the location of these loading points, which are of welded steel construction, and attached to both spar webs and booms.

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6

-2.2 Root Details

In the past it has been fo\md difficult to obtain conditions apertalning to a fixed root, and in an attempt to rectify this, the root of the specimen was built into concrete» The only movement that was measured on the com.pleted root was a rigid body rotation of the whole assembly which was less than 10 radians. Details of the root prior to its being cast into concrete are shown in Fig.6. The edges of the skin were bolted to 32" in. steel angles, which v/ere in turn joined to heavy steel channe]s placed normal to the plan-^ of symmetry of the wing»

Numerous steel reinforcing bars were placed through the skins and in the inside of the root. With the wing in the position shown in Fig.6, the Inside was filled up to the first rib with concrete made by using fine ballast.

Tho k in. thick concrete floor of the laboratory was provided with ^ in» diameter "Loosebolt Rawlbolts", to coincide with four holes in each of the steel channels. When the concrete was set, but still green, the wing was placed In position.

Shuttering was built up round it, and concrete poured in up to the level of the first rib. Pig»3 gives the external dimensions of the concrete block, which v/eighed approximately 35 cwts. When the base was set, the channels were be ;.ted to the floor»

2»3 Gauging

Dial gauges were arranged to record the distortion of the lower surface of the wing, and v/ere positioned as shown in Fig»3 . They were supported on a framework constrvicted of "Dexion" angle.

Electrical resistance strain gauges were placed on the wing in the positions shown in Pig.U. The locations and number of

gauges were chosen to give an overall picture of the stress distribution» It was realised that the number would be

insufficient to investigate detail problems, but It was -desired to avoid the possibility of having more gauges than could be conveniently read and analysed»

In all 110 channels were used, distributed over eight chord-wise sections. Three of these were out from the root, four at the root, and one just Inside the concrete» This last section did not yield satisfactory results»

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TECHNISCHE HOGESCHOOL

VUEGTUIGBOUWKUNDE KanaaUtraat 10 - DELFT

7

-2.U Method of Loading

Two matched hydraulic jacks were used to apply loads to the specimen. In order to facilitate the loading, two 3i in. steel angles were used to join the two loading points at a given rib station, as can be seen in Figs. 7-8. A series of holes in these angles enabled a variety of loading combinations to be used. Nearby test frames were used as earths for the jacks, which were arranged to work on the retraction stroke only.

SCOPE OF WORK

3»1 Preliminary Tests

Control tests were conducted on specimens made from the materials used in the construction of the wing, in order to

determine their elastic properties. The average results obtained were used in the theoretical calculations»

In the past, some difficulty has been found in analysing strain gaiige results for spar booms and webs. An attempt to

overcome this difficulty was made by subjecting the spars to known bending loads, prior to their being used in the wing.

The gauge readings were compared with the equivalent beam theory values, and the resulting calibration curves used in analysing the gauge readings for the completed wing.

3.2 Loading Cases

In the various tests, four different types of loading were

used:-Oac^ 1) Pure "bending" couple, M., applied about an axis in the plane of, and normal to the centreline of the wing. This corresponds to the couple M., of oblique

coordinate theory and was obtained by applying loads at the centres of loading points A-B, and C-D.(See Fig.^ Case 2) Pure "Torsion" couple, T., about the centreline of the

wing, and corresponding to the couple L of oblique coordinate theory. The loads were applied at points A and E«

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8

-Case 3) Loading by a shear force on the centreline of the tip rib, Rib 1U, in a downward direction, this case being denoted by Z. The load ?/as applied at the centre of A-B.

Case U) A shear force on the centreline at Rib 12, in an upward direction, denoted by (-Z^). In this case the

loading point used was the centre of C-D.

The maximum load applied at any one point on the wing was 2100 lb»

3.3 Deflection Tests

The dial gauge readings were taken \inder loading

corresponding to all the above four cases. With the exception of Case k loading, when the front and rear spar gauges only were used, all the gauges were read»

3»U Strength Tests

All strain gauge readings were taken for all the four loading cases.

CALCULATIONS

l^.•^ Definition of Stiffnesses

Throughout this work, two stiffnesses are considered, a "flexural" stiffness and a "torsional" stiffness. The stiff-nesses are those used by Molyneux^ '^, in setting out the

stiffness criteria for the prevention of body fixed flutter and divergence, except that a pure couple is used to define the flexural stiffness rather than a concentrated force»

These are defined as

follows:-1) "Flexural" Stiffness, defined as the couple of the type considered in loading case 1, necessary to cause unit rotation of a given length of the centreline of the wing» 2) "Torsional" Stiffness, defined as the couple, of the tjrpe

considered in loading case 2, required to give unit relative rotation of two section.s normal to the centre-line, and spaced a given distance apart, along it.

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_ 9

-In each case, two different lengths along the centreline have been considered. The first is from stations x = 0" (root)

to x = 111", and includes root effectsj whilst the second length extends from x = 14-6" to x = 111", and is outside the root effects.

Lj..2 Calculations associated with the Experimental Results Two methods were used to derive the actual torsional stiffness of the wing from the experimentally determined

deflections.

The first method consists of using the rotation

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components defined in oblique coordinates^ "^o The torsional rotation at a given section is (p + q cos a), v/here p and q are the rotations about the oblique axes x and y, and a is the angle between the axes. The rotation p is determined from the

relative deflection of the front and rear spars, along the y axis, and q = dW/dx, v/here W is the normal deflection of the x axis.

In the second method, the dial gauge readings were used to plot deflection contours for the wing, and these in turn were used to obtain the distortions of sections normal to the centre-line, as shown in Figs. 12 and 13» The slopes at the points of zero deflection were used to estimate section rotations.

The flexural stiffnesses v/ere derived by using the

method of oblique coordinate rotation components. The rotation in this case is defined as (q sin a ) .

U.3 Theoretical Calculations

The theories applied to the solution of the wing use oblique coordinates, and are those of Hemp^ .

Two solutions are

given:-1) The "General" solution of Ref» 1 Part 3, which makes allowance for the camber of the section, and assimes symmetry about the xOy plane, (plane of the wing), only. No allowance is made for root effects.

2) A "Simplified" solution, of Ref. 1 Part 2» This solution Is based on equivalent rectangular sections having the following

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properties:-- 10

(a) The same torsional stiffness, (Batho), area as the actual section.

(b) The same section moment of inertia. (c) The same total boom area.

(d) The same equivalent skin and web thickness.

It is possible to make an approximate solution for the root problem using these sections, and this has been done in the case of the stiffnesses.

The sections used for the "General" theory are given in Table 1, and those for the "Simplified" theory in Table 2»

5.0 PRESENTATION OF RESULTS

5.1 stiffnesses

The experimental and calculated stiffnesses are given in Table k* The stiffness coefficients, C.., and the rotation

IJ

components of oblique coordinate theory are given in Table 3»

5»2 Deflection Results

All these results are deriveu. from the experimental work» The rib deflections due to the loading cases 1-3? are given in Pigs. 9-11.

Pigs. 12-13 show the deflections of the lower skin across sections normal to the centreline. These were derived from a

plot of the deflection contours.

5»3 Strength Results

The strength test results are presented in the form of strain comparisons. The following strains are

used:-The direct strain, e , in a direction parallel to the x axis. The direct strain, ey^p in a direction normal to the x axis. The direct strain, e , in a direction parallel to the y axis,

being the rib boom strain»

The shear strain, e „, associated with direct strains e and ®YY'

The shear strain e„_, being rib web shear strain.

y2

The shear strain e^_, being spar web shear strain,

Xiu

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11

-For the sections outboard of the root effects, namely Ribs 9-10, 10, and 10-11, comparison is made between experiment and oblique coordinate theory for all four loading cases. The results are given in Figs. 1It.-30. The variation of e along

XX

the centreline is given in Pigs. 31-32.

The results for sections at the root. Ribs 1-2, 2, 2-3 and U-5p are derived from experiment only. These are presented in Figs. 33-54? all four loading cases being used. Figs. 55-57 give the variation of e over the root section for loading cases 1-3s end Pigs» 58-6o the corresponding variation in spar web

shear strain, e^^. xz

6oO DISCUSSION

6.1 Stiffnesses

The stiffnesses are presented in Table U, whilst Table 3 gives the theoretical stiffness coefficients, C. ...

1 J

Stiffness Coefficients.

The C... are used in the calculation of the stiffnesses,

1 J

and in fact define the rotation and deflection of the wingo

The actual relations between the C^^ . and rotations are given in Ref» 1, Part 3» They are entirely dependent upon the structure and with a tapered specimen increase in value towards the tip» The coefficient C.. ^ gives the rotation about the x axis due to normal shear force, and is seen to be very small in this case. It is zero for a wing having symmetry about the xO?. plane, and hence does not appear in the Simplified theory»

The values derived from both the General and Simplified theories are given in Table 3. The most obvious difference is in CM J, 9 v/hlch is higher in the Simplified theory»

Torsional Stiffness away from the root»

The experimental values given in Table U-s have been

derived using the two methods discussed in \k»2.o The result in both cases is a stiffness 108% of the calculated Batho value, which makes no allowance for rib stiffness» The deflection of sections normal to the centreline. Figs» 12 and 13, shov/s that

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12

-the calculation of slopes using relative spar deflections across normal sections is open to considerable error, due to the

distortion of these sections. The method which uses oblique rotation components is better, as the slopes are measured in the plane of the ribs.

The torsional stiffnesses as derived by the General and Simplified theories are in good agreement, although the latter gives a slightly lov/er value. This is a direct result of the higher value of C^^, mentioned above, and is explained by the fact that the Simplified theory uses a rectangular section of equivalent cross sectional area to the cambered section of the General theory, the latter being a nearer approach to the "ideal"

circular section.

These values are higher than the experimental results, a fact which is almost certainly explained by rivet slip. Some

loss of torsional stiffness due to rivet slip is predicted by

Ref.lj.. Considerable care was taken during the manufacture of the specimen in order to reduce rivet slip to a minimum, particular attention being paid to rivet hole clearances.

Torsional Stiffness over the v/hole specimen.

These values are compared v.lth the Batho stiffness which makes no allov/ance for the root constraint effects.

There is some discrepancy in the two experimental values, most probably resulting from inaccuracies in the evaluation of the centreline deflections at the root due to their small values. In all probability the true value lies between the 111% and 115% quoted. In this case the effect of the root constraint Is to Increase the torsional stiffness by som'.' 3%»

The General theory has been applied without any constraint allowance, and gives a high value of 116%, The values for the Simplified theory Include one which has been corrected for root effects. These results are rather low, and the theoretical root constraint allov/ance gives only a 2% increase of stiffness.

It wo\ild appear that the best method of estimating the torsional stiffness would be 00 use the Simplified theory of equivalent rectangular sections, witli a root correction and

reference to the effect of rivet slip»

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13

-Flexural Stiffness away from the root»

Both the General and Simplified theories give the same result, which is somewhat lower than that of experiment.

(2) This has been previously noted^ '•

Flexural Stiffness over the vi^hole specimen.

The effect of the root constraint as applied to the Simplified theory is to increase the stiffness by 5%. Again there is no difference between the General and Simplified theories, when the root effects are not considered, and the theoretical values are low in comparison with the experimental results.

It will be seen that the use of the Simplified theory with a root correction will give the best results, but these nevertheless will underestimate the true value»

6.2 Deflections

The rib deflections under loading by pure couples and a Z wise force are given in Figs. 9-11.

Although there is not a great deformation of the ribs in the case of loading by the couple ;.., Fig» 9? there is a

slight Increase in the slope of the deflection curves towards the front and rear spars. This effect is more pronounced in the case of loading by the Z v/ise force, Flg»11.

The distortion under loading by a torsion couple, T.J is different. As is shown in Fig» 10, there is a large overall bowing of the section, and it demonstrates clearly the necessity of considering the flexibility of the ribs when

ma]rlng calculations associated with this type of loading»

6»3 Strains away from Root Effects (Ribs 9-1I)

The direct and skin shear strains for stations 9-11? the rib boom and web strains at Rib 10, and the spar web strains at station 9-10, due to all four loading cases, are shown in Figs» 1i4--32. Comparison is made between experiment and the General theory, whilst the Simplified theory has also been applied at station 9-10.

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^k

-9 The results show that in the case of direct strain e , due to bending couple M., there is quite good agreement,

XX A

particularly on the compressive skin at the rib boom, but that there is a tendency for the experimental strains to be lovi^. This is most likely due to local variations in the skin thickness and Elastic properties, as the theoretical results are based on

average values. The ef!'ect of camber as given by the General theory is reproduced by the experimental results, but it is not large.

In the case of loading by the torsion couple T., the theoretical and experimental values of e agree on the

centre-XX

line of the wing, but there is a slight experimental variation across the section-, not shown by the theory.

As in the case of loading by the couple M., the

theoretical values for e are higher than those of experiment,

XX

when normal shear forces are applied» In addition, the theories predict a cross section variation which is not found

experimentally. This has previously been noticed on a tapered box, Ref» 2, and it would appear that the effect of taper is to

cancel the e variation due to shear strain» A pure couple

XX

theory gives better agreement In this case.

The comparison of the dirct strains eyy» shov/s that while the theory predicts a mean value, there is some

discrepancy, in particular the experimental values are high on the centreline. This may v/ell be due to the diffusion problem associated with the application of continuous rib theory to a discrete rib specimen. The discrepancies are not large and do not preclude the application of continuous rib theory to more practical structures.

In the case of the skin shear s+rains, ©„y? there is good agreement for the pure couple cases, except that the theory is slightly high for M., and for T. at the rear of station

Ribs 10-11» This latter discrepancy is probably due to the proximity of the loading point» There is much less experimental cross sectional variation due to normal shear forces, than is predicted, and this fact confirms the remarks made above

concerning the e variation in a tapered box»

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TECHNISCHE HOGESCHOOL

VUEGTUIGBOUWKUNDE KanaaUtraat 10 - DELFT 16

An overall picture of the variation in e due to the

XX

couple T., is given in Fig. 56. Although the scale is

exaggerated, it is apparent that there is a rapid variation in the value and nature of the direct strain distribution. At station 1-2, Fig» 23? the strain increases towards the centreline and Is then constant, and at Rib 2, Pig» 39? the centreline values are approximately the s^^me. There is a difference in the two skins at station 2-3? Pig» U3? the top skin value being roughly constant, and the lower increasing towards the rear» This difference is repeated at station U-5? Fig- U9? where the bottom skin strain varies linearly across the section, being zero on the centreline, and the top skin falls to zero at the rear spar»

The direct strain distribution at the root due to normal shear force loading is not unlike that due to M,. It is shown in Fig» 57» There is, however, a fall off at the rear spar»

This is clearly shown in Fig» 3k which Is the

distribution at station 1-2. It is possible that the very high skin shears near the rear spar at the root overcome the direct strain build-up and also, in this case, the effect of the taper of the wing. This is confirmed by the Increased fall off in the case of loading by -Zj., where the direct strain is less»

Fig» UO, shows that the strains at Rib 2 are similar, and give better agreement between the two surfaces» The distribution

at station 2-3? Pigo kk» is like that at station 1-2, and at station i|--5? Pig» 50, there is a constant strain over the centre of the wing with a fall away at the front and rear spars» At this section the strain distribution is beginning to resemble that found at station 9-10.

The variations in the direct strain e^^ due to the couples M, and T. are shown in Figs. 35? ^5 and 51» For the cat-.rj of couple M., there is an increase towards the rear spar at station 1-2, but the tendency is reversed at station 2-3. At station k-d there is an initial increase to the centreline of the section and the lower skin values are higher. The

variation due to T. at station 1-2 takes the form of low values at the spars coupled with a high value on the centreline.

This distribution is repeated at stations 2-3? but at station i|.-5, Byy Increases up to the centreline and is then roughly constant»

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15

-The rib boom strains, e , in Rib 10 shoï/ reasonable agreement between theory and experiment, except that the theory is rather high for couple M., and for the front portion of the tension boom when normal shear force loading is applied.

The theory assTomes zero rib web shear strain, e„_, yz and the experimental value is very low on the centreline, but rather higher adjacent to the spar webs. This is probably connected with the discrete rib diffusion problem.

Although the spar web strains e^^, are of the same xz

order as predicted, there is a discrepancy, in the normal shear force loading cases, explained by the shear relief due to the spar boom loads being affected by the cross sectional e

XX

variation referred to above»

Summarising these results, it will be seen that the oblique coordinate theory is applicable and gives good results» The use of the General theory Is not really necessary for wings having small camber, especially in view of the considerable arithmetic complication» In this case the use of rectangular sections, with a correction as predicted by the beam theory would be the best solution»

6»U Strains at the root

The strains at the root are shown in Figs. 33-60. The values are those obtained experimentally, no suitable theory being available for purposes of comparison.

The variation of e over the root, due to the

X X

application of the couple M^,, is shown in Fig. 55» This

variation is typical of that obtained for a swept wing, with the str-.in build-up towards the rear spar rootr The strain across staclon 1-2 is given in Fig» 33» It increases towards the rear spar, the increase being more rapid as the rear spar is

approached. The value of e at the rear spar is some ten

XX

times that at the front. The strains at Rib 2, Fig. 39? are similar, although there is better agreement between the upper and loTrer surfaces, but at station 2-3? Pig.J^3? there is a fall away at the rear spar» The distribution at station I|.-5? Figol+9? is not unlike that obtained at station 9-10, but there is a

slight increase across the forward part of the skins» / An overall » . . e •

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17

-The Oyy strains due to normal shear force loading are given in Pigs» 36, U6 and 52. There is little agreement between the results for Z and -Z.^, or for the various

stations. However, at station k-5 the values of e™, are approximately constant, apart from a fall off at the spars. This results in some resemblence to the equivalent distribution obtained at stations 9-^ 0.

Pigs» 37, k7 and 53 present the skin shear strains e Y ^^® "1^0 "'^he pure couple loading cases. In both the cases of M. and T. there is a change in the form of the variation from one bay to the next, but again the distributions at stations U-5 have a form not unlike those obtained for the stations away from the root. The normal shear force loading distributions. Pig. 38, US and 5U, indicate a build up in shear strain e „ across the section, which Is not maintained towards the rear spar but drops off locally in some cases.

The direct strains, e in the booms of Rib 2 are shown in Fig. k^ and i+2. In all the loading cases, there is an increase in strain towards the rear spar.

Fig. 58 gives the spar web shear strain, e.^_,

X2

variation at the root for loading by couple M.. Although the value is high at the root, it rapidly decreases. The front web is the higher, due to the lower shear relief from the boom end loads In the front spar. The equivalent variation for the torsion couple loading, T., is Pig. 59» The front and rear spar values are approximately equal, although the front v/eb strain is low at station k-^» This may be due to the

relatively large relief from the boom loads obtained at this point. Figs» kS and 56»

The rapid changes in the web shear caused by normal shear force loading can be seen in Fig» 60. At the root, the front spar strain is very low, and may even be opposite in sign to that at the rear spar» This rapid decrease is shovm in an interesting way by the die away of the buckles in the front spar web near the root, which can be plainly seen in Pig» 8. The rate of increase in the rear spar is not

maintained to the root rib. This may be due to shear relief. The front spar strain reaches a high value by station i|.-5? although it is still less than the rear spar value»

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18

-The results obtained for the strains at the root show that the constraint effects become low at station U.-3 on the rear spar, but are somewhat more prolonged in the front spar.

There is a need for a detailed analysis of the skin shear strain at the root of this type of swept wing. This would be best carried c.-t on a uniform rectangular box, having say, five shear gauges in a chordwise direction, and closely pitched in the spanwise direction, on both surfaces.

A second order discrete rib theory is required in order to obtain a theoretical prediction of these root strains.

CONCLUSIONS

7.1 Stiffnesses

(1) The theoretical values of stiffnesses predicted by the theory allowing for the wing camber, vary little from those predicted by the theory using equivalent rectangular sections»

(2) The experimental torsional stiffness is lower than the theoretical prediction, due to the presence of rivet slip»

(3) The effect of the oblique ribs is to increase the torsional stiffness to 11% greater than the Batho value, whilst the effect of root constraint is to give a further 3% increase.

(k) The experimental flexural stiffness is higher than the theoretical»

(5) Root constraint increases flexural stiffness by 5%» (6) In reducing experimental results to give torsional stiffness, the use of the deflection measurements to calculate the rotations of points on the centreline, and thence the

stiffness is best»

(7) For the theoretical prediction of stiffness, the equivalent rectangular section theory with a correction for

root effects, and an allowance for rivet slip, gives the best results.

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19

-7»2 Deflections

(1) There is an appreciable deformation of the oblique

ribs, particularly in the case of torsional loading, showing the necessity of considering rib flexibility In theoretical

solutions»

(2) The deformatioi. of sections normal to the spars is not linear across the section, and hence it is incorrect to measure the torsional stiffness using the relative spar

displacements of these sections»

7»3 Strain9 away from the root

(1) The oblique coordinate theory, which allows for camber of the section, compares well with experiment for all the more Important strains»

(2) The theory using equivalent rectangular sections also gives good results, which vary little from those of the more accurate theory»

(3) In order to reduce the calculations necessary in cases where the camber is not appreciable, the use of the latter theory, with if necessary a cross sectional correction in accordance

with the beam theory, is advocated»

ik) The effect of taper is to reduce, or even eliminate, the cross sectional variation in the direct strain caused by normal shear force loading. The use of pure couple theory gives a more accurate prediction of the direct strain In this case.

(5) In general, better agreement is obtained between theory and experiment on the compressive surface, particularly at

sections between the ribs»

(6) The discrepancies caused by the application of a continuous rib theory to a wing v\dLth discrete ribs, are not

(21)

20

-7*k strains at the root

(1) The root constraint results in strains which agree with those normally associated with swept back wings. The direct and shear strains in the skins and webs build up towards the rear spar at the root.

(2) The rate of build up of the direct strains across the root section is not maintained up to the rear spar. This is probably due to the effect of verv high local shears.

(3) The shear in the front spar falls to zero at the root» (U) The root constraint effects disappear between Ribs k

and 5 on the rear spar, although they are more prolonged on the front spar.

(5) The shear strain distribution at the root is complicated, and at least a second order discrete rib theory would be necessary to predict the variation.

(6) A careful and detailed experimental investigation of the root strains in a rectangular section uniform swept box is required in order to elucidate the shear strain variation.

REFERENCES No. Author 1 Hemp, W.S. 2 Howe, D. 3 Molyneux, W.G. k Hawker Aircraft Ltd. Title

On the application of oblique coordinates to problems of plane elasticity, and sweptback wing structure.

College of Aeronautics Report No. 31. January 1950 Analysis of experiments on sweptwing

structures.

College of Aeronautics Report No» 65. May 1953

The flutter of svvept and unswept wings with fixed root conditions.

R.A.E. Structures Report No. 58. January 195 0 Rivet slip and the flexure and torsion of

box beams.

Design Department Report No. 1138. September 19U7

(22)

IL4BLE 1

IDEALISED SEOTION GECMEWÏ

P r o n t S p a r Dat-um R e a r S p a r / DatvEi e-^A -SECTION Ribs 1-2 Rib 2 Ribs 2-3 Ribs V-5 Rib 7 Ribs 9--^0 Rib 10 Ribs 10-11 Rib 15 1 (B)

(c)

(D) (E) (P) (Or) (H) b iiit 5.86 5.78 5.71 5.39 V 9 8 4.60 4.52 4.A4 4.05 b ' ' in, 6.34 6.25 6,16 5.78 5.31 4.85 4.76 4.66 4.20 b " in, 7.29 7.19 7.09 6.68 6.13 5 . ^ 5.57 5.47 4.96 c i n . 28.43 28.09 27.73 26.41 24.73 23.04 22.70 22,36 20.68 °1 , ..in.. 5.68 5.62 5.52 5.29 4.95 4.61 4.54 4.47 4.14 t ' in, .08 .08 .08 .08 .08 .08 .08 .08 .08 t w i n . ,022 .022 .022 .022 .022 .02.? .022 .022 .022

K

in. .022 .022 .022 .022 .022 .022 .022 .022 .022 A sq^in. .688 .634 .578 .-524 .452 .3^6 .358 .347 .279 A' .686 .6^ .600 .542 .438 • 35^ .330 .315 .249 X i n . ^' n 5.72 11.45 17.17 40.06 68.68 97.29 103.01 108,74 137.34

(23)

i « (' t i'

EQUIVALENT RECTANGULAR - SBiPLIFIED - SECTIONS

S e c t i o n Rib 1-2 4-5 7 9-10 10 13 GEIJERAL c i n 28.43 26.41 24.76 2 3 . 0 4 22.70 20.68

z

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(24)

« i

STIPPfJESS COEFFICIENTS AI'ID ROTATIONS

Section R i b s 1-2 4-5 7 10 13 General °11 X 1 0 ^ ° 5.74 7.66 10.10 1 3 . 2 8 1 8 . 2 5 ^ 2 = ^21 X10^° - 3.53 - 4.72 - 6,12 - 8.44 -11.96 ^22 X 1 0 ^ ° 4.72 6.31 8.16 11.25 1Ó.04 °13 x 1 0 ^ ° -0,77 -0.07 +0.09 1.02 2.57 ^ « +0.0047 +0.00035 -0.00036 -0.00338 -0.00682 e X 10^° 3?ad/in 5.81 7.72 . 10.36 13.06 17.61 ^ X 1 0 ^ ° r a ^ i n 2.55 3.41 4.41 6.07 8.67 i S i m p l i f i e d 1 «11 X 1 0 ^ ° 6.02 8,07 10.2 13.62 19.10 °12=«21 xlO^O - 3.53 - 4.70 - 6.04 - 8.40 -11.92 «22 x 1 0 ^ « 4.72 6.30 8.10 11.26 15.95 0 X 10^° r a d / l n . 6.38 8.54 10.66 13.79 19.06 ^ x 1 0 ^ « r a d / i n . 2.55 5.40 4.37 6.08 8.62 1 S i m p l i f i e d -Modified A t Root 1 6 X 10^« r a d / i n . 6.07 i ^ d / i n 1.72

(25)

TABLE 4 COIJFAJIISON OF S T I P H C Ï S S E S Torsional Stiffness 1 T h e o r e t i c a l Batho P o m u l a G e n e r a l Oblique Coord. S i r ü p l l f i e d Oblique Coord. S i m p l i f i e d M o d i f i e d a t Root 1 E x p e r i m e n t a l R o t a t i o n Canponents on ^ 1 R e l . S l o p e s a t Zero D e f l e c t i o n • Root t o Sec . X S t i f f n e s s r 1 I ' . b . i n / r a d . x l O " 8.35 9.71 9 . 2 2 9 . 3 2 9.50 9 . 6 2 = 1 1 1 " % Batho 100?^ 116% 109% 111% 111% 115% Sec* X r: 4 6 " t o S t i f f n e s s g I b . i n / r a d . x l O " 1 2 . 4 13.79 1 5 . 5 0 1 3 . 4 1 3 . 4 X = l l l ' l % Batho 10C% 112% 111% 108% 108% Flexural Stiffness T h e o r e t i c a l ; G e n e r a l O b l i q u e Coord. S i m p l i f i e d Oblique Coord. j Sij:iplified M o d i f i e d a t Root E x p e r i m e n t a l R o t a t i o n Components on ^ i Root t o Sec* X = 1 1 1 " S t i f f n e s s r l b . i n / r a d . x 1 0 2 2 . 6 2 2 . 6 24.1 29,1 % EiKpt. 78% 78% 83% 100%

i

Sec* X = 4 6 " t o x = 111" S t i f f n e s s _g l b . i n / r a d . x 1 0 ~ 3 2 . 0 3 2 . 0 5 5 . 0 i % ExpL. 9 2 % 9 2 % 10C%

(26)

COLLEGE OF AERONAUTICS

REPORT No. 66. FIG. I.

in

1

n II ^' -V . !«• . \ \

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1 * 24^" <, \ ^ ^ J>-120' o ~ ~ — - ~ ~ ~ - _ _ ^ . — — — N \ SECTION ON <L SECTION 91 • 5 OUTBOARD. GEOMETRY.

Span 203" Wing Area I6,780 o" Root Chord I20" Aspect Ratio 2-45 Root Chord Vc 13% Taper Ratio I-SO Tip Chord Vc 12% L.E. Sweepback 6 0 °

(27)

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(28)

COLLEGE OF AERONAUTICS

REPORT No. 66. FIG. 3.

RIB 4 7 10 13 Dm.'A' 5775" 5 5-85' Ï I 10" 47 20" 4 2 6 0 " 'B~ 43-1" 4-I-55* 38-3" iSA' 31-a-'c' ZBS" 2 8 + ' 2S4" Z3-3" 21-»' 'D' )4«." I3-5' 1£E" il-fc" I I I ' 8 B J5Ï. ^ ^ - = ^ Mid.. F l o a t A ^ ^C^ UtiT Sp». r 'A' J= ^ - « . 1 - • 1

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- . — S 4 GAUGES SHOWN THUS « OR t LOADING POINTS SHOWN THUS* LoidiM. Points fa Rib 14

SWEPTWING WITH OBLIQUE RIBS. LOCATION OF DIAL GAUGES AND LOADING PTS.

(29)

GAUGES 'a-i WIRED IN SERIES TO GIVE A/ERAGE READING

SECTION OF SPAR BOOM

GAUGES 'a'-'b'-'c' WIRED IN SERIES VIEW ON RIB lO.

RIB 2 SIMILAR - NO WEB GAUGES N O T E : - ODD NUMBERED GAUGES ARE ON OR ABCVE (t_

EVEN NUMBERED GAUGES ARE BELOW 4_

GAUGES MARKED (g) ARE ON BOTH SURFACES - OTHERWISE TOP ONLY SUFFICES -o'-'b'-V DENOTE BOOM GAUGES CONNECTED TO GIVE AVERAGE READING.

VIEW IN DIRECTION 'X' REAR SPAR

WEB GAUGES. 33-FRONT SPAR 35-REAR SPAR. SHEAR GAUGES ON BOTH StlES OF WEB

GAUGE LOCATION

L FRONT SFV^R UPPER BOOM 2. FRONT SMR LOWER BOOM 3. 5. 7 Fwd UPPER SKIN ROSETTE OH DIRECT 9. II. 13. CENTRE. . . . . KX13. 14. • Ü3WER . . K „ IS. 17 I9L Aft. UPPER „ . . „ 21. REAR SPAR UPPER BOOM

22. 1. > LOWER i. 23. Fm. UPPER RIB BOOM 24 „ LOWER .. .. 25. Aft. UPPER .. 26. . LOWER „ 27 Fwd RIB WEB 2ft CENTRE UPPER RIB WEB 30. .. LOWER .. « 3L Aft RIB WEB 33. FRONT SPAR WEB 3& REAR GAUGE SECTIONS A. INBOARD BIB 1. B. RIB 1 - 2 C. RIB 2. D. RIBS 2 - 3 . E. RIBS 4 - 5 . F RIBS 9 - 1 0 . G RIB lO H RIBS l O ' l l . GAUGES DIRECT TINSLEV ROSETTE TINSLEY SHEAR TMSLEY

(30)

COLLEGE OF AERONAUTICS REPORT No. 66.

FIGS. 5 & 6.

(31)

COLLEGE OF AERONAUTICS REPORT No. 66.

FIGS. 7 & 8.

FIG. 7

(32)

COLLEGE OF AERONAUTICS REPORT No. 6 6.

(33)

FIG. lO. COLLEGE OF AERONAUTICS REPORT No. 66.

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COLLEGE OF AERONAUTICS REPORT No. 66. FIG. II. S < > K OD ffi ^ CO Q: (C ce S

(35)

FIG. 12. COLLEGE OF' AERONAUTICS

REPORT No. 66.

DEFLECTION OF SECTION NORMAL TO <|^ AT X = 46'' TORSIONAL LOADING.

(36)

COLLEGE OF AERONAUTICS REPORT No. 6 6 .

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Cytaty

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