Section
CONTENTS Page Section Volume 1 v Summary vii Introduction 1 -i 1 Trajectory Analysis 2 -i 2 Vehicle Loads 3 -i 3 Aerodynamic Heating Analysis 4-i 4 Materials Evaluation 5-i 5 Material and Process Development Testing 6-1 6 Structural Analysis Model 7 -i A Plane Strain Analysis for Determining Thermal Stresses 8-1 8 Structural Internal Loads (Air and Thermal) 9 -i 9 Internal Temperature Analysis 10-1 10 Optimization Procedure for Panels of Monocoque Structure Volume 2 11 Optimization Procedure for Panels of Circular-Arc 11-1 Corrugation Shear Webs 12 Optimization Procedure for Panels of Semimonocoque 12-1 Structure 13 -i 13 Primary Structure Sizing and Weights 14-1 14 Panel Flutter 1 5 4 15 Vehicle Flutter 1 6 4 16 Sonic Fatigue 17-1 17 Fatigue 18-1 18 Creep 19 -i 19 Optimization Procedure for Heat Shields 20-1 20 Heat Shield Sizing and Weights 21-1 21 Leading Edge Analysis 22-1 22 Tota'r Wing Weight Analysis Volume 3 23 -i 23 Cost Analysis 24-1 24 Performance Analysis 25-1 Reliability Analysis 26-1 26 Interaction Analysis 27-1 27 Structural Element Testing iii SUMMARY An analytical and experimental evaluation was performed for several promising structural concepts to provide the basis of minimum total-system-cost for selection of the best concepts for the design of a hypersonic vehicle wing.
Results, procedures, and principal justification of results are presented in reference 1. Detailed substantiation data are given herein. Each major analysis is presented in a separate section. Vehicle loads and temperatures are given w i t h each structural analysis that influences weight. In addition to the weight analysis, fabrication cost, performance penalties (surface roughness drag), reliabili,ty, and total-system-cost analyses are presented.
Reference 1 . Plank, P. P.; Sakata, I. F.; Davis, G. W.; and Richie, C. C . : Hypersonic Cruise Vehicle Wing Structur,e. Evaluation, NASA CR-1568, 1970.
The utility of a hypersonic cruise vehicle depends upon a low structural mass fraction in a high-temperature envirormcnt. Unfortunately, this requirement exceeds the limits of state-of-the-art structures. The only hypersonic structures flown to date have been the X-15 research airplane and the ASSET unmanned lifting reentry test vehicle, both of which are unsuitable for cruising flight.
For the past several years, the NASA Lasgley Research Center and other agencies have been investigacing promising structural concepts, such as those discussed in references 2, 3, and 4, and the 1967 Conference on Hypersonic Aircraft Technology (ref. 5 ) was devoted to the subject.
An evaluation was performed of promising wing structure concepts to the same in-depth analyses, including all known envirwrnental. structural considerations that could affect the four evaluation factors: weight, cost, performance, and reliability.
These factors were then interacted in a total-system-cost study for a system range- payload capability of 205 billion ton-miles to provide the basis for selecting the best structural concept for the wing structure of minimum total-system-cost.
Results of this structural evaluation are reported in referelice 1. This reference also includes the procedures and principal justification of results, whereas this report gives detailed substantiation of the results in reference 1.
Principal analytical and test efforts are presented in separate sections. This report is bound as three separate volumes.
REFERENCES Heldenfels, R . R. : Structural Prospects for Hypersonic A i r Vehicle ICAS 2.
paper, 1966.
3. Plank, P. P.; and MacMiller, C. I,: Analytical Investigation of Candidate Thermal-Structural Concepts Applicable to Wing, Fuselage, and Inlet Structure o f a Manned Hypersonic Vehicle. AFFDL-TR-66-15, 2966 (cod).
4. Plank, P. P. : Hypersonic Thermal-Structural Concept Trends. SAE paper 660678, 1966, 5. NASA-SP-148 (Cod). Conference on Hypersonic Technology, Ames Research Center, 1967.
vii ACKNOWLEDGEMENT This investigation was conducted under NASA Contract No. NAS1-7573, Research and Development Program for Developptsnt and Validation of Structural Concepts for a Hypersonic Cruise Vehicle W i n g Structure. The study was originated at the Lockheed-California Company, Burbank, California and completed at Lockheed Missiles & Space Company, Sunnyvale, California.
I ? . P. Plank w a s the Program Technical Manager, I. F. Sakata and G. W. Davis the Project Engineers, and C. C. Richie was head of structural concept optimiza- tion. The other contributors to the program are acknowledge at each section.
Four Lockheed-California Company personnel acted in an advisory capacity.
They are L. W. Nelson, Structure Division Engineer, Structures Division; E. J. Himmel, Department Manager, Stress Analysis; W . J. Crichlow, Depart- ment Manager, Advanced Materials and Structural Mechanics; and M. G. Childers, Manager, Physical Sciences Laboratory Development Engineer.
Dr. M. S . Anderson, L . R . Jackson, and J. C. Robinson of the Structures Research Division, NASA Langley Research Center, Hampton, Virginia, were the Program Manager, Technical Representative of the Contracting Officer (TRCO), and Assistant TRCO, respectively, for the project.
Section ll
Section ll OPTIMIZATION PROCEDURE FOR PANELS OF CIRCULAR-ARC CORRIEATION SHEAR WEBS bY G . W.- Davis I 11-i SYMBOLS b Width of panel Stiffness coefficients of governing differentis?.. equation D1j D2 of p l a t e Modulus of elasticity mastic modulus of a l a s t i c i t y Buckling coefficients i n analyses of shear buckling Shear buckling force i n xy coordinate systen p e r unit length of section R Radius t Thickness Minimum thickness tmin T Equivalent panel thickness Effective aspect ratio Efficiency f a c t o r € tl Plasticity reduction f a c t o r secant p l a s t i c i t y reduction f a c t o r Qsec Esec/E , tangent p l a s t i c i t y reduction f a c t o r
%an ’
Stiffness parameter 11-iii
Section 11
Section 11 OPTIMIZATX9N PROCEDURE FOR PANEIS OF CIRCULAR-ARC CORRUGKCION SHEAR WEBS To minimize thermal stresses, webs of circular-arc: corrugation (fig. 11-1) are used for the ribs and spars. The intensity of tho buckling force of a corrugated panel is expressed with equation (10-36) of Section 10 as where (11- 2b )
D 2 = n 1 E e l ts2( 2 1 - 5
s i n 4 Substituting equation6 (11-2) into equation (11-I), neglecting the s u l l effect of Poisson's r a t i o , and then dividing by t h e thickness t gives t h e stress : following expression of t h e buckling 2 3/2
(u-'
f ( $ 1
f s ,cr = 5.29 k n I E e l (E) ( F )
11-1 The l o c a l buckling s t r e s s i s (ref. 11-1) ( 1 1 . 6 ) Multiplying equations (11-4) and (11-6) by t and then using the second resulting expression t o eliminate R i n the first expression yields or -’.n which e i s an efficiency coefficient and (11-8a) (11-8b) From equations (11-6), (11-p) ana (11-8b), The optimum corrugation angle is obtained by maximizing the efficiency The radius and thickness are then determined with Equation (U-D) factor.
(11-8b) ana (21-9).
For problems i n which the thickness i s constrained, equation (ll-7a) becomes 11-2 (11- 10) from whick.
[f(P)11'2 = 0.58 (11-11) In reference 11-1, the optimum angle for a design with an unrestrained thickness is shown to be 80". Because of manufacturing limitations, an angle Noting of 60" was used for all cormgation panels of the present investigation.
that BS = 0 andK-0, a v&lue of 3 . 3 from fig. 10-8 of Section 10 was used for the buckliq; coefficient k k& I . -.
Figure i. Corrugated shear web -' r REFERENCE O p t M z a t i m of Multirib and Multiweb 1-1. Emero, Donald H.; S p a t , Leonard: Wing Box Structures &der Shear and Moment Loads. AIAA 6 t h Structures and Materials Conference, American I n s t i t u t e of Aeronautics and Astronautics (New York, N e w York), l$5, P. 346.
11-4
Section 12
Section 12 0PTI.KIZATION PROCEDW F O R PANELS O F SEMIMONOCOQUE STRUCTURE R. E . Hubka
coNTms
Page 12-1 PANEI; LOADING 12-4 STRESS ANALYSIS 12-4 ANALYSIS O F LOCAL BUCKLING 12-1 PANEL NO. 1 , BEADED 12-8 PANFZ NO. 2 , TRAPEZOIDAL CONFIGURATION 12-10 PANELS NO. 3, TUBULAR, AM) NO. 4 , CONVEX-BEADEl 12-11 OPTIMIZATION PROCEDURE 12-12 SECTION PROPERTfES AND STIFFNESS 12-12 ' PANEL NO. 1 , B W E D 12-16 PANEL NO. 2, TRJPEZXCDAL CORRUGATION 12-17 PANEL NO. 3, TUBULAR 12-18 PANEL NO. 4 , CONVEX-BEADED 12-20 REFERENCE 12-21 FIGURES IUUSTRAT IONS Page Figure 12-1 Geometry and loading CrF panels of semimonocoque 12-21 structure 12-21 Panel N o . 1, beaded 12-21 Panel N o . 2, trapezoidal corrugation
1 2 - 22
'lane1 No, 3, tubular 12- 22
Panel No. 4, convex-beaded
12-iii SYMBOLS Mean area enclosed by outer and inner boundaries x and y distances between simply supported edges of p l a t e r? ,D D Stiffness coefficients of governing d i f f e r e n t i a l equation
... 2' 3
of plate d Width of diagonal element of trapezoidal corrugation Elastic modulus of elasticity Eel Eccentricity (deflection) of center of panel due t o et'ey thermal bowing (subscript t ) and difference between end shear axis and centroidal distance (subscript y) Bending, compressive, and shear stress f f f Bending, compressive, and shear buckling stress b,cr' c,cr' s,cr Elastic shear modulus Gel Depth of cross section h
i Moment of i n e r t i a p e r u n i t length of section
Moments of i n e r t i a per unit length of sections associated
T ,T
X Y with x and y bending of orthotropic p l a t e Torsional s t i f f n e s s p e r unit length of section Buckling coefficients i n analysis of compressive and kc.'ks shear buckling Length L Bending moments and twisting moments i n xy coordinate system per unit length of section 12-77 m Number of half waves i n p l a t e buckling equations M e n s i o n a l forces and shear forces i n xy coordinates Nx9Ny.Nxy per unit length of section Pressure R Radius Stress r a t i o s f o r compression and shear %JRs t Thickness Equivalent extensional thickness
-
Equivalent shear thickness tS U Utilization f a c t o r Location of neutral surface of panel
s
Mean coefficient of thermal expansion
a
Effective aspect r a t i o Shear and compressive s t r a i n s corresponding t o t h e m a l loads Stowell‘s p l a s t i c i t y reduction f a c t o r Secant p l a s t i c i t y reduction f a c t o r Tsec Tangenk p l a s t i c i t y reduction f a c t o r “ton Poisson1 s r a t i o V Shear buckling stress as defined i n reference 12-3 rcr 12-vi
Section 1 2
Section 1 2 OFTIMIZATION PROCEDURE FOR PANELS OF SEMIMONOCOQUE STRUCTURE Equations o f the Fortran computer programs which were used t o determine i n the d e t a i l analysis of the four panel concepts the minimum weight designs : ! h e analyses, o f t h e semimonocoque structure are presented in t h i s section.
formulated f o r the d i r e c t search method, are discussed in t h e following para- (3) analysis of local buckling, graphs: (1) panel loading, (2) s t r e s s analysis, ( 4 ) optimization procedure, and ( 5 ) section properties and stiftnesses.
PANEL LOADING The t o t a l inplane s t r e s s resultants acting on the stiffened panels (fig. 12-1) a r e (12-1) I
-
N = N x Y + ? I G <
Xy xy,T e l s where NJ, and a r e loading components i n which thermal e f f e c t s a r e
excluded, FT and 3 a r e the compressive and shear s t r a i n s corresponding
t o thermal loads o f the structural model, and E e l 5 and GelTs are the e l a s t i c The stiffness coefficients which are defined a t the end of this section.
the thermal portion of the inplane loading is con- procedure f o r calculating s i s t e n t with the redundant-force used f o r calculating the internal loads of the aircraft.
A conservative approximation of the bending moment a t the center of the panel. i n the zy plane is )c (12-2)
M = My/(l - ' G I )
Y
*
Vor P a n P l s No. 1, where My i s the moment based on small deflection theory.
2 , and 3
sL2 + e + 0.003, L) Ny
$ = - + (ey
8 I T I
12-1 wlit'rc. (1 tleriott.s u n i I'orm pressure which is always n p c ~ i I'ied w i t 1 1 a positi-vc a i c n , 0.001 L i s thr i n i t i a l del'lcction, 1.5 t f o r Panel No. 1 for Panel No. 2 e = [o 2 t f o r Pane1 NO. 3 and e~ i s the dezlection due t o thermalbowing. Assuming a inear temperature gradient through the thickness, which i s considered t o be adequate for t h e present investigation, the deflection a t the center of a simply supported panel due t o the thermal bowing can be approximated as L CYAT e = - (12-4) T 8h where CY i s the mean coefficient o f thermal expansion and AT i s the change i n temperature through the cross section of depth h. The temperature increment i s positive when the temperature of the outer surface of the panel i s larger than that of the inner surface.
For Panel No. 4 and i n which the subscripts 0 and I denote moments for designing the outer and inner portions of the panel. Note t h a t the pressure i s always specified w i t h a positive sign. The dimension 8, which i s expressed i n the last paragraph of t h i s section, i s measured fromthe interface of the two portions of the panel. Hence, it i s a negative quantity.
Using t h e interaction equation R c f R = 1 S 12-2 i n wliich Rc = N ' N Y ' Y , C r ( 12-6 ) t h e u t i l i z a t i o n factor of equation (12-2) f o r combined compressive and shear loading is Considering simply supported, wide column theory for compressive buckling, "2D2
N -- - (12-8a)
Y Y C r L2 It is t o be noted t h a t the above equation significantly underestimates t h e buckling loads of Panels No. 3 and 4, because of thei.r relatively I.arge twisting stiffnesses "he shear buckling load intensity is expressed with sitnply sup- ported, orthotropic p l a t e theory as (ref. 12-1) = 46.8 (D D ) 1/2 /L 2 N 2 3 XY ¶ cr The expression, for ',he corrugation concepts from for the tubular concepts.
Section 10, is 12-3 STRESS ANALYSIS The s t r e s s a t t h e centroid of t h e cmss section
f c = N p (12-10)
The bending stress for Panels No. 1, 2 and 3 is
= M Z/Y
(12-1h) fb Y x and f o r %ne1 No. 4,
-
f = M z /Ix ( e = 0,I) (12-llb)
bye Y 9 e e
Neglecting twisting due t o edge eccentricities, t h e shear stresses of t h e panels are as follows : For N n e l s No. 1 and 2, (12-12a) fs = N /t XY Fcr Panel No. 3, fs = N / 2 t ( 12 -12b ) XY For Panel No. 4, ( 12 -1.2c ) ANALYSIS O F IDCAL BUCKLING Panel No. 1, Beaded Five modes of buckling of t h e beaded configuration (Fig. 12-1) are considered as follows: (1) buckling of most or a l l of t h e porYL-lon of t h e pmc.3 between centerlines of continuous a r c s due t o a uniform compressive stress, (3) buckling of t h e circular (2) buckling of t h e circular a r c due t o bending, arc due t o shear, (4) buckling of the flat segment due t o compression, and ( 5 ) buckling of Slat segment due t o shear. Appropriate interaction equations a r e used f o r combined loading.
Simply supported, orthotropic plate theory i s uE?d t o analyze the panel Using t h e notation of figure 12-1 and f o r the first mode of i n i t i a l buckling.
t h e compressive buckling theory of Section 1 0 , the buckling s t r e s s can be expressed as
= DI
= k -
f c,cr where 2 2 (12-13b) C m X X I I1 i n which
xI i s t h e - bead (circular-arc) length. The stiffnesses and t h e average thick-
ness, tV of e:yations (12-13) are defined i n t h e last paragraphs of t h i s section. The buckling s t r e s s is t h e minimum value of fC,Cr with respect t o positive integers of m and t h e angle 82 ( f i g . 12-1).
I n the anslysis of a t e s t specimen, 82 = 0 and m = 2 gave the minimum stress. However, 8 = 13" and m = 3 gave essentially the same results. The theoretical buckling s t r e s s was i n reasonably good agreement with the i n i t i a l buckling stre?.: of the t e s t pane;. It i s t o be noted t h a t 02 = 0 was used for t h e desi&,. of the beaded panels.
The i n i t i a l buckling stress due t o bending is approximated with an expression t h a t was suggested by NASA for compressive buckling of long cylinders with an R / t range which i s consistent with those of t h e c i r c u l a r a r c s of Panels No. 1, 3 and 4 . The buckling stress expression i s (12-14) where the p l a s t i c i t y coefficients, qsec and tan, are based on the stresses f,, fb, and fs,which are given by equations ~ I Z - ~ O ) , (12-11) and (12-12). The equivalent stress for evaluating the p l a s t i c i t y coefficients i s determined with the octahedral shear s t r e s s theory of reference 12-2.
The circular arc of the cross section was considered c r i t i c a l with respect t c shear buckling, an ass-r;aption which needs t o b e > v e r i f i e dby t e s t .
Using buckling theory for curved plates of large aspect r a t i o s , t h e i n i t i a l shear buckling s t r e s s is (ref. 12-3) where (12-16) and from Section 10 '1 secEe 1 (12-17) T c r = 4.40
2 0 "
1 - 'el
i n which S i s the developed length of the arc. The plastl-city coef1Xcien-b i s evaluated the same as those of equation (12-14).
Using t.he interaction equation r + r n = l c,b s i n which r c,b = fclfc,cr fb/fb,cr
* S = fs/fs,cr
12-6 the u t i l i z a t i o n factor for combined stresses due t o compression, bendineand shear can be expressed as ( 12-18) S i x ? no test data were available t o evaluate t h 2 exponent n 01’ equation (32-l8), a value of 1.75, which i s considered t o be conservative, was used I‘or t h e design 01’ the panels.
T’,e flat segment of the beaded configuration is analyzed for buckling with long, simply supported, isotropic plate theory. The expression of the u t i l i z a t i o n factor is Using equations of Section 10, t h e stress ratios can be expressed as
’STEel (k) “1
(12-20a)
rc = fc [ 3.29
1 - “el
(12-2Ob) where ST is evaluated with equation (10-12a) of Section 10. Vtan and qseC of t h e equation are based on t h e stresses f , and fs, which are given by is determined with the equations (D-10) and (12-12a) The equivalent stress It is t o be mted t h a t octahedral shear stress theory of reference 12-2.
beaded t h i s mode of buckling was not encountered i n tb.e design of the skin panels, since b was fixed a t 0.5 inch.
Panel No. 2 , Trapezoidal Corrugation The trapezoidal corrugation ( f i g . 12-1) is analyzed for: (1) simultaneous buckling of t h e horizontal and diagonal elements due t o compression, (2) simul- taricous huck.Ling of t h e elements due t o shear, (3) compressive buckling of t h e horizontal element due t o bending of the panel, and (4) buckling of the diagonal elcnient due t o bending of t h e panel.
Appropriate interaction equations are used f o r combined loading of t h e corrugation elements.
The compressive and shearing buckling s t r e s s e s which produce the first two niodes of buckling are (ref. 12-4)
= k * 'STEel
( 12-21b)
( : ) fs,d,cr
s y d 12 (1 - &)
where t h e buckling coefficients, which pertain t o t h e diagonal element of the corrugatlon, are given i n t a b l e 12-1.
TABLE 12-1 COMPRESSIVE AND SIIEAR BUCKLING COKVFICIENTS b/d 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.0 1.0 k 5.65 4.86 4.67 4.40 4.00 5.45 5.30 5.17 5.04 c,d 6.86 6.65 7.17 6.56 6.45 6.32 6.11 5.82 5.35 ks,d Treating t h e diagonal element as a long, simply supported isotropic plate and using the e l a s t i c theory of reference 12-1, t h e buckling stress due tobending i s approximated as (12-21c ) 12-8 The p l a s t i c i t y coefficient of equations (12-21) is evaluated w i t h equation (10-12) of Section 10, 'Itan andqse of which are then conservatively determined with the same procedure as t h e p l a s t i c i t y coefficients of equation (12-14) for t h e beaded skin panel.
1.75 + r c . ') = 1 'c,d 'b,tf e ,d w!iere r = 1 ' / I ' c,d c c,d,cr = I ' /r r b,d b b,ti,cr r - s,d - I's/'s,d,cr t h e u t i l i z a t i o n factor €or combined loading ol' the diagonal element can be written as ( 12 -24 ) When rb = 0, t h e above equation is equivalent t o equation ( ~ - 1 9 ) .
Also, when rs = 0, t h e equation correlates w e l l w i t h t h e buckling theory of reference 12-1 f o r long, simply supported isotropic plates subejected t o com- bined compression and bending. Compared t o the theory of reference 12-1 f o r buckling of plates due t o combined bending and shear, t h e equation is con- servative when rc = 0.
It is considered t o be adequate f o r t h e present investigation.
Treating t h e horizontal element of t h e trapezoidal corrugation as 8 long, simply supported plate, the ratio of the c'inpressive stress due t o bending divided by t h e i n i t i a l buckling stress is 12 -9 and t . 1 ~ u t i l i z a t i o n factor for combined loading of t h e hor,i.,ontal element i s (12-26) trtierc r 2 . r -I- 1 ’ c,b,h c,h b y h
Panels No. 3 , Tubular, and No. 4 , Convex-Beaded
The system of equations is formulated f o r t h e l o c a l buckling analyses of Panels No. 3 and 4 (fig. 12-1). Using compressfve buckling theory for bending, ( 1 .- 0,l.) (12-27a) where TC and fb,a are given b y equations (12-10) and (12-11b).
Curved plate theory, as used f o r the beaded configuration, is used t o determine t h e shear i n i t i a l buckling stress of t h e c i r c u l a r a r c s of Panels No. 3 and 4 . Hence, t h e shear s t r e s s r a t i o can be expressed as 12-10 where ( 12 -28) and f, is given by equation (12-12c). The p l a s t i c i t y coefficients of equations (12-27) are based on the combined stress state.
The expression of t h e u t i l i z a t i o n factor is Equations (12-27) through (12-29) are formulated for Panel No. 4. With t h e subscript 1 removed, t h e equations apply t o Panel No. 3, t h e application f o r which t h e stresses m e given by equations (12-lo), (12-1h) and (12-12b).
OPTIMIZATION PROCEDURE Equations f o r the stress and l o c a l buckling analyses of the Fortran optimization programs which were used t o determine t h e f i n a l minimum weight panels of t h e semimonocoque structure have been presented. Variab-es of t h e programs are os follows: (Panel No. 1)
b Y R, t, el
(Panel No. 2) b/d, h Y t , e (Panel No. 3) b, R, t, 0 Note t h a t the height/chord r a t i o of the outer arc of Panel No. 1 1 is fixed a t a specified value.
12-11 In the input data of t h e programs, upper ap.d lower l i m i t s o r the variables and the incremerit f o r varying each variable between l i m i t s are specil'iecl, to@lier. w i t h tlic panel loadin[:, t1ie:rnial : ; Lrain:;, material propcrtl.c:: , a mini- mum q atirl otJitir prnblcm conr.l;ant::. 1'hc: prol:ram:: ana1y.r.e a17 po:::;il) I [?
rlc>::i;:n:: l'roin 1 . 1 1 ~ ma1,r.i x ol' t l i r r i c x i : : . i on:: I.lic:y jy:rii!rtj.Lc awl ::clcc:l, L l i o : : ~ I,II:J.L liavc u1.i I i : c i L i o n ~ ' u ~ ~ I . o i * : : 111, ricar utle, w l i i t r l i l!(JZ'I'II::PO!llk bo a zero ni:j.rv:iti oL' :::~.I'cty.
N01.c L1i:j.L 1.11(~ :x:u.~irn in;: proccns iriv'ol vc:: l.wo u t i 1 izution .I':.ictor:: i n Lhc cleo i rcn 0 1 ' P:~.ticlr. No. .I , : ' j anit )I and only om? ['actor i n Llic desir:n of Panel. No. 3.
'l'tic pro,:rtLmr, havt! provi:;fonc for rcjc!cl.i 1 4 : uriaccepl,able cic::i ;<ns bel'ore the an:il.ysi:: i.:: c~o~r~pl~~I.(~cI; I'or examplc, w l i m Uc; > ~Ic,,,,,..~ unci q~~~~ < 0 . 1 .
For t h e present irivcstigatiori of Panels No. 1, 3 and 11, b was i ' i s t d at.
iricli ~)acuusc o r practical considemtiorlo. ~ I C heiglit/cliord m t ~ o oi* tlic 0. I, outer are of &ne1 N o . )+ was fixed at an upper linnit of 0.2 because 01' aero-
dynamic requirements. I n addition,€$ of Panel N o . 1, 8 of Panel N o . 3 , .and eI
of Panel No. 4 were fixed a t an upper l i m i t of T7.5° because of manufacturing l i m i t a t 'oris .
SECTION PROPERIIES AND STIFFNESSES A l l section properties and stiffnesses which are used i n t h e loads, stress, and local buckling analysis of t h e panels of t h e semimonocoque structure are presented i n thiz section.
Panel No. 1, Beaded The bending stiffhess coefficients of t h e beaded skin panel where 12-12 and where o r Equation (1203%) is used for computing the stress ratio Rc and equation (l2-33b), f o r computing 1 1 , . Tlic plasl;i.cit;y coefficicnts qt. utid tisec arc based on Ltie
stresses f , , i i anti fS, the equivalent strcss of which is detcritti.tieci w i t . l t
octahedral shear stress theory.
Additional properties which are required for the analyses of panel loading and stresses are
F = s t / a
-
tS = a t / s (3-2-34) Stiffness coefficients which are required f o r the f i ~ a t . mL\di\ \'I' l k \ , * : 1 l buckling are in v!iich 12-14
- R COS COS
c and
s 2 = 0 . B f R ( e l - e2)
Jkpressionsof the dimensions x and z are 2 2
x = a - R s i n e 2
2 = cos e 2 - cos e,)
12-15 P1rlsti.city coefficients of equation (12-35) are based on t h e stresses f uruJ f , , , thc cxpiivalcnt stress of which is determined w i t h octahedral. shear s t rcsE theory.
-
The effective thickness tL of equation ( E - l 3 a ) is expressed as Panel N o . 2, Trapezoidal Corrugation The bending s t i f f n e s s coefficients of t h e trapezoidal .orrugation are given by equation (12-30) where (12-40)
.tdh2 I
= +(O.‘jh) I
+ - 12
xx P i n which d = h/sin 0 p = 2(b + d cos e ) (12-41) s = b + d The p1a:;ticity cocfl.’icients are evaluaLed the same as thonc 0 1 ’ Fairel N \ l . 1.
Additional properties which arc required for t h e analyses of p n e 3 J a d i n g and stresses are
-
t = 2st/p I (12-42) ts = pt/2s z = 0.511 22-16 ( 12 0'1.3 ) E 'lsec el D = 0.25 3 1 + v e l where in which p = b f 2R sin 8
A = R2(28 - s i n 26)
The procedure for evaluating the p l a s t i c i t y coefficients of equation ( 12-43) is the same as t h a t for equation (32-30).
Additional prqwrties which are required for t h e analysis o l ' t.he panel are
-
I ; = 2 s q p 't: = 2pt/s S (12-44)
z = R ( l - COS 6)
where s = b -f- 2R9 12-17 Panel No. 4 , Convex Beaded S t i f f n e s s coefficients of the tubuhr panel of insymmetric cross section are given by equation (12-43) i n which (ref. 12-5) where p = b + 2RI s i n 0 I (12-h6)
-
z I ,arc 2 s i n
( B 2 0,J.) + sin cos 9~ -
I e,arc
9e
12-18 I and The expression of the chord dimension of equation (12-47) is
c = 2R s i n e 1 ( 12-48)
I The plasticity coefficients are evaluated the same as those 01' Panel No. 3 .
Additional properties which are required for the analysis of the panel are h = A / p Y
-
z 0 = h 0 - Z
= -R$ - cos $) - 7 z
ZX where 12- 1 9 12-1 Timoshenko, Stephen P.; and Gere, James M.: Theory of Elastic S t a b i l i t y .
Second ed., McGraw-Hill Book Co., Inc., 1361.
12-2 Nadai, A.: Theory of Flow and Fracture of Solids. Vol. I, Second ed., McGraW-Hill Book Company, Inc., 195.0.
12-3 Gerard, George; and Becker, Herbert: Handbook of Structural S t a b i l i t y .
Part 111 - Buckling of Curved Plates and Shells. NASA TN 3783, 1957.
12-4 Ellison, A . M.: Optimum Open Corrugation Wing Covers ( I n i t i a l Buckling).
I&lSC/HREC A782409 (Also, HFW/7796-1), Lockheed Missiles and Space company, 1 9 6 6 .
12-5 Roark, Raymond J.: Formulas for Stress and Strain, Third ed., McGraw-Hill Book Company, Inc., 1954.
12-20 M Y
Notation of panel length and stress resultants I
Cross section of panel No. 1, beaded
. --
- - .
1’i.~Urt~lZ-%. Wometry and loading of panels of smimonocoque structure 12=21 z
r b 7
$ 7 \ 7
L X
- 2 3 -
Cross section o f panel No. 2, trapezoidal corrugation - x 0.5b -x convex beaded section of panel No. 4, Cross Figure 12-1 ( ConclurieB) 12-22 S ~ T I O N 13 PRIMARY- STRUCTURE WEIGHT ANALYSIS C. C . Richie, G . W . Davis, W . A. Claus, D . G . Watson, F . I C . Bevan 13-i Page INITIAL WEIGH" SCREENING 13-1 MONOCOQUE 13-1 STATICALLY DFTERMINATE 13-4 INTERNEDIATE WEIGHT SCREENING 13-4 MONOCOQUE WAFFLE 3-3-5 MONOCOQUE HONEYCOMB-CORE SANDWICH 13-8 SEMIMONOCOQUE SPANWISE 13-9 SEMIMONOCOQUE CHORDWISE 13-11 FINAL STRUCTURAL WEIGHTS 13-14 MONOCOQUE WAFFLE CONCEPT 13-14 MONOCOQUE HONEYCOMELCORE SANDWICH CONCEET 13-16 SEMIMONOCOQUE SPANWISE CONCEPTS 13- 17 SEMIMONOCOQUE CHORDWISE CONCEFT 13-20 STATICALLY DETEIiMINATE CONCEPT 13-21 PHIMARY-STRUCTURE WEIGHT SUMMARY 13- 24 1 3 - i i i TABLES Table Page 13-1 I n i t i a l panel weight screening of mcriocoque primary structure 13-27 13-2 I n i t i a l screening of semiinonocoque spanwise- stiffened concepts
13 - 28
I n i t i a l screening of semimonocque chordwfse- 13-3 stiffened concepts 13-29 13-4 Manufacturing processes f o r candidate inonocoque panel confiwrations 13-30 Intermediate weigh%-screening r e s u l t s . for. RenerU panels 13-5 13-31 13-6 Evaluation of monocoque waffle grid plate 13-32 Weight comparison of monocoque waffle panel designs 13-7 ( lb/ft2) 13-33 13-8 Weight cortiparison of upper and lower surfaces of monocoque waffle designs 13-34 Monocoque waffle panel-width optimization matrix 13-9 13-35 13-10 Vonocoque waffle desfgn data for wing inboard area 13-36 Monocoque waffle design data for wing outboard area 13-11 13-37 13-12 Monocoque waffle single shear j o i n t dimensions 13-38 Monocoque waffle double shear j o i n t dimensions 13-13 3-3-39 13-14 Monocoque waffle component wing weights, inboard area, a/b = 2.0 13-40 Monocoque waffle component wing weights, outboard 13-15 area, a/b = 2.0 13-41 13-42 13-16 Monocoque waffle panel aspect r a t i o optimization matrix Monocoque waffle component wing weights, inboard area, 13-17 b = 2 0 inches 13-43 13-12 Honeycomb-core sandwich panel closeout compar'son 13-44 Design data for monocoque honeycomb-core sandwich 13-19 panels 13-45 Page Tab le 13-20 Wing unit weights f o r monocoque honeycomb-core sandwich panels, including smooth closeout 13-46 13-21. Optimum wing section weights and spar/rib spacings senrimonocoque spanwise-stiffened trapezoidal- corrugation panels, further intermediate scieening 13-47 13-22 Detail geoaetry of senimonocoque spanwise-stiffened 13-48 trapezoidal-corrugation panels, no insulation Detail geometry of sernimonocoque spanwise-stiffened 13-23 trapezoidal-corrugation panels, insulation lower surface batboard 13-49 Conponents weichts for semimonocoque spanwise- 13-24 stiffened trapezoidal-corrugation panels 13- 50 13-25 Detail 6;;eometry of semimonocoque chrodwise-stiffened tubular panels, no insulation 13-51 13-26 Detail geometry of semirnonocoque chordwise-stiffened tubul.ar panels, w i t h insulation 13-5F 13-27 Detail Geometry of sernimonocoque chordwise-stiffened convex-beaded up?er/tubular lower panels, no insulation 13-53 Detail Keometry of semimonocoque chordwise-stiffened, 13-28 convex-bezded upper/tubular lcwer panels, with S.nsul/-t?.rn 13-5'F D - . ' . . ~ >..5 : p w ; t r ; r t 3 : : ~ ~ ~ i . - . i o ? ~ ~ c ~ [ 4 ~ ~ ~ chordwisc-sti Pfiinc!d 13-55 c - ; - ~ ~ ~ x - k e : d e 4 Seth surfaces, no 5 nsu7iitlc-m ikt::-* 1 p.::;.c!tq of sC:idiqnnocoque chordwSsc!-stiffened convex-beaded/tubular lower outboard 13-56 Detail geometry of semimonocoque chordwise-stiffened convex-beaded/tubular lower outboanl, with insulation 13-57 Intermediate screening f o r chordwise-stiffened candidate concepts 13-55 Weights of rnonocoque waffle panel and. various thermal- protection arrangements 13-53 Design temperatures and geometry f o r monocoque waffle panels, p a r t i a l heat shield at outboard area,lower 13-60 surface Design teniueratures and geometry for monocoque waffle 13-35 panels, p a r t i a l heat shield at outboard area lower 13-60 surface, with insulat ion 134.
Tab le page Design temperatures and geometry f o r monocoque 13-36 waffle panels, heat shield c n e n t i r e lower surface 13-61 Design teniperatures and geometry f o r monocoqm wal fle 13-37 panels, heat shield on entire lower surface, with insulation at outboard area 13-61 Design temperatures and geometry f o r monocoque waffle 13-38 panels, no heat shield and no insulation 13-62 Corriponent weights f o r monocoque waffle concept, 13-33 p a r t i a l heat shield a t outboard area lower surface 13-63 13-40 Breakdown of wing weights f o r monocoque waffle panels w i t h lower surface outboard heat shield and insulation 13-64 13-41 Component weights for nionocoque waffle concept, heat s h l e l d on e n t i r e lower surface 13 -6 5 13-42 Coxponent weights f o r nionocoque waffle concepts, heat shield on e n t i r e lower surface, with insulation a t outboard area 13-66 Component weights f o r monocoque waffle concept, no 13-43 heat shields and no insulation 13-67 13-44 Average wing unit weights for various panel widths and aspect ratios, monocoque honeycomb-core sandwich panels 13-68 13-45 Final tempera'tures and geometry for monocoque honeycomb- core sandwich panels with outboard lower surface heat shield and insulation 13-69 13-46 Breakdown of wing weights f o r monocoque honeycomb- core sandwich panels with lower surface outboard heat shield and insulation 13-70 Optimum wing section f i n a l weights and spar/rib 13-47 spacings f o r semimonocoque spanwi se-sti f fened tubular concepts 13-71 Fi r ~ l ,poi:ietr>r for sernimonocoque spanwi se-sti f fened tubular pa.nels 13-72 Breakdown o f iring weights f o r sernimonocoque spanwise stiffened Lubular panels w i t h f u l l heat shields and lower surface outboard insulation 13-73 Optimum wing section f i n a l weights and spar/rib 13-40 spacings for semimonocoque spanwise-stiffened beaded 13-7!+ panels Final geometry f o r semimonocoque spanwise-stiffened 13-51 beaded panels 13-75 13-vii Page Table Detail breakdown of wing weights f o r sernimonocoque 13-52 spanwise- sti f fened beaded panels with f’ull heat s h i e l d s and lower surface outboard insulation 13-76 Final geometry for semiinonocoque chordwise-stiffened 13-43 tubular and convex beaded panels 13-77 Detail breakdown of wing weights f o r semimonocoque 13-54 chordwi se- st i f fened tubular/convex-beaded panels w i t h f u l l lower surface heat shield and outboard lower surface insulation 13-78 Weights of s t a t i c a l l y determinate panel and various 13-55 the mal-protec t i on arrangements 13-79 Final p,eometry for lowest weight s t a t i c a l l y 13-56 determinate panels 13-80 Breakdown of w i n g weights f o r s t a t i c a l l y determinate 13-57 panels t r i t h f u l l heat shields and no insulation 13-81.
Ytmicturd. margins of safety 1 3 4 2 13- 54 13-viii IUUSTRATIONS Figure Page 13-1 Typical edge closeouts f o r candidate monocoque panel configurations 13-83 13-2 Semimonocoque stiffened panels, wide column curves 13-8h Notation f o r monocoque w a f f l e panel design data 13-3 13-85 Monocoque waffle cap and closeout detail 13-4 13-85 Monocoque waffle panel-width optimization f o r 13-5 inboard wing area, a/b = 2.0 13-86 Monocoque waffle panel-width Optimization fox# out- 13-6 board wing area, a/b = 2.0 13-86 Panel aspect r a t i o optimization f o r inboard wing area 13-7 of monococ-te waffle concept, b = 20 in.
13-87 Monocoque honeycomb sandwich panel sizes 13-8 13-88 Effective thickness versus length of semimoncoque 13-9 spanwise-stiffened beaded panels, lower surface,
BL 120 - BL 220
13-89 13-10 Effective thickness versus length of semimonocoque spanwise-stiffened beaded panels, upper surface, centerliqe t o BL 220 13-90 13-11 Effective thickness versus length of semimonocoque spanwise-stiffened tubular panels, upper surface, centerline t o BL 220 i3-91 13-12 Effective thickness versus length of semimonocoque spanwise-stiffened tubu3ar panels, lower surface, BL 120 t o RL 212 13-92 Effective thickness versus length of semimonocoque 13-13 spanwise-corrugation stiffened panels, upper surface, BL 120 t o BL 212 13-93 Wfective thickness versus length of semhonocoque 13-4 spanwise-trapezoidal corrugated panels, lower surface, BL 120 t? BL 220 13-94 E f e c t i v e thickness versus length of semimonocoque 13-15 spanwiso-trapezoidal corrugated panels, upper surface, centerline t o BL 220 13-95 Figure Page 13-16 Optimum semimonocoque spanwise-stif fened beaded concept 13-96
13-17 Optimum s emimonocoque spanwi s e - s t if f ened tubular
concept 13-97 13 -18 Weight optimization of semixonocoque spanwise- stiffened t u l u l a r panels, BL 120 t o BL 212 13-98 Weight optimization of semimonocoque spanwise- 13-19 stiffened tubular panels, BL 212 t o BL 350 13-99 13-20 Weight optimization of semimonocoque spanwise- stiffened beaded panels, BL 120 t o BL 212 13-100 13-21 Weight optimization of semimonocoque spanwise- stiffened beaded panels, BL 212 t o BL 350 13-101 13-22 Weight optimization of semimonocoque spanwise- trapezoidal-corrugated panels, BL 120 t o BL 212 13-102 Weight optimization of semimonocoque spanwise- 13-23 trapezoidal-corrugated panels, BL 212 t o BL 350 13-10;
Wejght optimization of wing area A (fr t o BL 120) of
13-24 semimonocoque spanwi s e t r a p e5 oidal-c orrug&ed panels, insulation outboard lower surface 13-104 Weight optimization of wing area B (BL 120 t o BL 212) 13-25 of semimonocoque spanwise trapezoidal-oorrugated panels, insulation outboard lower surface 13-105 13-26 Weight optimization of wing area C (BL 212 t o BL 350) of semimonocoque spanwise trapezoidal-corrugated panels, insulation outboard lower surface 13-106
13-27 Weight optimization of iring area A (E, t o BL 120) of
semimonocoque spanwise trapezoidal-cormgat ed panels, no insulation 13-107 13-28 Weight optimization of wing area B (BL 120 t o BL 212) of semimonocoque spanwise trapezoidal-corrugated panels, no insulation 13-108 Weight optimization of wing C (BL 212 to BL 350) of 13-29 semimonocoque spanwtse txvapeaoidal-corruga%edpanels, no insulation 13-109 Weight optimization af wing area A ( t o BL 120) of 13-30 smimonocoque chordwise-stiffened no insulation 13-110 13-x Pigure Page Weight optimization of wing area B (BL 120 t o BL 212) 13-31 of semimonocoque chordwise-stiffened tubular panels, no indulation 13-1u Weight optimization of wing area C (BL 212 t o BL 350) 13-32 of semimonocoque chordwise-stiff ened tubular panels, no insulation 13-112 Weight optimization of wing area A (g t o BL 120) of semi- 13-33 monocoque chordwise-stiffened tubular panelsI w i t h insulation 13-=3 Weight aptimization of wing area E (EL 120 t o BL 212) 13-34 of semimonocoque chordwise-stiffened tubular panels, with insulation 13-lJ-4 deight o 3 t W z a t i o n of wing area C (FL 212 t o BL 350) 13-35 of semimonocoque chordwise-stiffened tubular panels, w:th insulation 13-lJ-5
Weight optimization of wire area A (E to BL 120) of
13-36 seminocoque chordwise-stiffened convex-beaded upper/ tubular l o ~ w panels, no insulation 13-116 Weigh+, --.ffmiaation of wing area B (BL 120 t o RL 212) 13-37 of sem ..' - . soque chodiri se-st;iff ened convex-beadd uppedtubular lower panels, no insulation 1+117 13-38 Weight optimtaatim of wing area C (BL 212 to BL 350) of semimonocoque chordwiss-stiffened convex-beaded lower panels, no insulation upyr/tubular 13-118
Weight optimization of wing area A (fi t o BL 1 2 0 ) cf
13-39 semimonocoque chordwise-stiff ened convex-beaded up,-r/ tubular lower panels, with insulation 13-113 13-40 Weight optiglization of Wing area B (BL 120 t o BL 212) of serimonocoque chordwise-stiffened convex-beaded upper/tubular lower, with insula; i m 13-120 Weight optimization g f wing area C (9L 212 t o BL 350) of semimonocoque chordwise-stiffened convex-beaded upper/tubular lower panels, dith insulation 13-121
Weight optimization of wing area A (g t o BL 120) of
13-42 semimonocoque chordwise-stiff ened convex-beaded panels, no insulation 13-122 Weight odAaization of wing area B (BL 123 t o BL 212) 13-4 7 of sminionocoque chordwis e-sti f f enee convex-bsaded panels, no Insulation 13-123 Figure Page Weight optimization of wing area C (BL 212 t o BL $0) 13-44 of semimonocoque chordwise-stiffened convex-bezded panels, no insulation 13 -1.24 Weight optimjzation of wing area A (f: t o BL 120) of i3-45 s emirnonocoque cho r d w i s e-s tif f ened convex-beaded/tubula r lower outboard, no insfiation 13-125 Weight optimization of wing area B (BL 120 t o BL 212) 13-46 of semimonocoque chordwise-stiffened convex--beaded/ tubular lower outboard, no insulation 13-126 Weight optimization of wing area C (BL 212 to BL 350) 13-47 of semimonocoque chordwise-stiff ened convex-beaded/ tubular lower outboard, no insulation 13-127 Weight optimization of wing area A (g t o BE 120) of 13-46 semirnonocoque chordwise-stif f ened convex-beaded/ tubular lower outboard, with insulation 13-128 Optimization of wing area B (BL 120 t o BL 212) of 13-49 semimonocoque chordwise-stif f ened convex-beaded/ tubular lower outboard, with insulation 13-129 Weight optimization cf wing area C (BL 212 t o BL 350) 13-50 of semimonocoque chordwise-stif f ened convex4 ? a d d tubular lower outboard, with insulation 13-130 Aspect r a t i o weight sumrnary, w a f f l e construction 13-131 13-51 lbtation f o r monocoque .*affle panel design data 13-132 13-52 Monocoque w a f f l e primary structure concept 13-53 13-133 Honeycomb-core sandwich panel s i z e requirements 13-% 13-135 Final design of rnonocoque honeycomb sandwich p r i m r y 13-55 structure concept 13-136 Shear allowable vcrsus R / t of v e r t i c a l c i r c u l a r a r c 13-56 webs at l3OOOF 13-138 Shear allowable vmsus R/t of v e r t i c a l circular-arc 13-57 webs at 1400°F 13-139 Shear allowable versus R / t of v e r t i c a l circular-arc 13-58 webs at 1500?F 1 3 - f i O 13-59 Allowable compression stress versus thickness of rih and spar caps 13-60 Cap ares vs thickness of r i b and spar caps 13-61 Optimum rib spacing f o r center area of semimonocoque spanwise-stiffened tubular panels with heat shields and partj.al insulation outboard 13-43 13-xii Page Figure 13-62 Optimum rib spacing f m spanwise-stiffened t u b d a r panels with p a r t i a l insulation outboard Optimum r i b spacing f o r outboard area of semimonocoque 13-63 spanwise-stiffened tubular panels with heat shields and p a r t i a l insulation outboard 13-45 Opthum r i b spacing f o r center area of semimonocoque 13-64 spanwise-stiffened tubular panels with no insulation 13-46 Optimum r i b spacing f o r inboard area of semimonocoque 13-65 spanwise-stiffened tubular panels with no insulation 13-47 Optimum r i b spacing f o r outboard area of semimonocoque 13-66 spanwise-stiffened tubular panels with no insulation 13-l-48 Final design of semimonocoque spanwise tubular concept 13-67 13-lk9 Opthum r i b spacing f o r center area of semimonocoque 13-68 spanwise-stiffened beaded panels with heat shields and p a r t i a l insulation outboard 13-151 Optimum r i b spacing f - b r semimonocoque beaded skin concept 13-152 13-69 Optimum rib spacbk . . C L outboard area of semimonocoque 13-70 spanwise-stiffened beaded panels with heat shields and p a r t i a l insulation outboard 13-153 Optimum r i b spacing f o r center area of semimor?ocoque 13-71 spanwise-stiffened beaded panels with no insulation 13-154 Optimum r i b spacing f o r inboard area of semimonocoque 13-72 spanwise-stiffened beaded panels with no i n s f i a t i o n
13-155
Optimm ig-b spacing f o r outboard area of semimonocoque 13-73 spanwise-stiffened beaded panels with no insulation 13-156 Final design of semimonocoque spanwise beaded concept 13-74 13-15?
Optimum spar spacing f o r center area of semimonocoque 13-75 chordwise-stiffened tubular lower surface and convex beaded upper surface with lower heat shields and p a r t i a l insulation outboard 13-159 13-76 Optimum spar spacing f o r semimonocoque chordwise 13-160 stiffened concept Optimum spar spacing f o r outboard area of semimonocoque 13-77 chordwise-stiffened tubular panels with lower surface heat shield and p a r t i a l insulation outboard 13-161 Final design of semimonocoque chordwise concept, 13-162 13-78 Figure Page Optimum rib spacing f o r center area of s t a t i c a l l y 13-79 determinate badedpanels with heat shields and no insulation 13-164 Optimum rib spacing f o r s t a t i c a l l y detemLnate beaded 13-80 concept 13-165 13-81 Statically determinate concept optimum r i b spacing 13-166 13-82 Statically determinate beaded primary-structure concept 13-167 13-xiv x and y distance between simply supported edges of pane?.; b i s also trapezoidal corrugation crest width and width D f flats of panels.
A Area of nth element of a cross section Area All Area A Area between % and BL 120 of wing investigation area Area B Area between BL 120 and BL 212 of wing investigation area Area between BL 212 and BL 350 of wing investigatiion area Area C BL Butt l i n e Width of flange of flanged waffle b f Pitch bS Distance from crest-to-crest of circular-arc, corrugated b W shear webs Width of nth element used i n determining coapression allowable Panel aspect r a t i o Geometric chord Hole diameter Width of diagonal element of trapezoidal corrugation decibels Modulus of a3asticity e Panel edge eccentricity; elongation &tensional eccentricity of waffle @ll Shear eccentricity of waffle e33 13-xv Allowable crippling s t r e s s Allowable shear stress Gravitational acceleretion Hertz Height hv Stiffener height of waffle K Buckling coefficient L Length N Force per unit length Esrtensional forces and shear. force i n xy coordinate system
Nx, Ny, Nxy
per unit length of section n Expnent of weight index used i n wide-column curve P Pitch Pressure Dynamic pressure Radius Radius of internal arc of convex-beaded configuration Radius of external arc of convex-beaded configuration Cell s t z e of honeycomb-core Maximum c e l l s i z e %ax Minimum c e l l s i z e %in T Temperature t Thickness
1/2 (ts + tc) f o r waffle single shear j o i n t
1/2 (ts + tb + t , ) f o r waffle double shear joint; tb Cap thickness
ts + e l l ; corrugation thickness; cap thickness; core f o i l
1/2 t C thickness f o r honeycomb- and truss-core panels Skin thickness tS Stiffener thickness f o r waffle configuration I, W Thickness of internal arc of convex-beaded configuration tl Thickness of external arc of convex-beaded configuration t u Skin thickness of internal face sheet of honeycomb- and truss-core sandwich Skin thickness of external face sheet of honeycomb- and t 2 truss- core sandwich
z Equivalent th2 ?kness
-
Equivalent thickness of panel without nonoptimum factor tEiasic
-
Equivalent thickness of heat shield tHeat Shield Equivalent thickness of panel w i t h nonoptimum factor included - Total equivalent thickness tTotal W Unit weight Maximum panel deflection wO
-
Z Location of neutral surface from extreme f i b e r Semi-apex angle of beaded concepts a AT Temperature difference Equivalent thickness difference A T S ' k f l e c t i o n E Efficiency factor used i n wide-culm equation P l a s t i c i t y factor Ratio of pitch t o radius A Density of honeycomb-core P C S w a t ion
c
Q Semi-apex angle of circular-ar . ;orrugation
Section 13
Section 13 PRIMARY-STRUCTITFE WEIGHT ANALYSIS Data obtained from the analysis of trajectory, vehicle loads, aerodynamic heating, and candidate materials were applied t o a detailed weight analysis of the primary structure ( i n i t i a l screening, intermediate screening, and f i n a l structural sizing).
INITIAL WEIGH!T SCREENING Loads are shown in Table 8-i and t h e design temperatures f o r t h e monocoque, semimonocoque spanwise, and semimonocoque chordwise concepts used for the i n i t i a l panel-weight screening are shown i n tables 13-1, 13-2, and 13-3. Selected-size panels were designed and optimized.
I n i t i a l panel-screening r e s u l t s a r e shown for monocoque and semimonocoque primary structures, (spanwise and chordwise-stiffmed) using Rene' 41 and Haynes 25 materials. Following t h i s , certain panel configurations and t h e use of Haynes 25 materials were eliminated because of t h e i r weight.
Monocoque I n i t i a l screening of leading candidate panel configurations for the monocoque primary structure concept was accomplished using the structural synthesis optimization procedure presented i n section 10. Optimum structural configurations, within prescribed constraints and for multiple design condi- tions, were determined for s i x different types of simply supported rectangular 13-1.
panels a s presented i n table Constraints on minimum gages f o r t h e leading candidate panel configura- tions were as follows: 1. Waffle grid (-45" x 45" and 0" x 9") skin thickness, t, = 0.020 in.
s t i f f e n e r thickness, tw = 0.020 in.
2. Honeycomb sandwich internal skin thickness, tl = 0.010 in.
external skin thickness (exposed), t 2 = 0.015 in.
core f o i l thickness, tc = 0.002 in.
3. Truss-core sandwich internal skin thickness, ti = 0.010 in.
external skin thickness (exposed), t 2 = 0.015 in.
core web thickness, tc = C,010 in.
13-1 Additional constraints f o r the honeyccmb-core sandwich were: 1. Maximum (square) c e l l size, %ax = 0.375 in.
2. Minimum (square) c e l l size, %in = 0.125 in.
Additional constraints f o r the waffle grid (-45" x 45" and 0" x 90") were:
1 . M a x : J I s t i f f e n e r height/thickness r a t i o , ($)
= 2 5 m a x 2. Maximum flange width/stiffener pitch r a t i o (flanged waffle grid onljr), bf
(T)max = 0*5
3. Maximum s t i f f e n e r spacing aspect r a t i o (0' x 90" waffle only)
(&) = 3.0
max Typical spar caps and edge closeouts, shown i n figure 13-1, were used t o determine nonoptimum weight factors f o r the candidate patlel concepts. Manu- facturing processes used f o r the weight analysis of panel concepts are shown in table 13-4.
Weight data presented i n table 13-1 indicate t h a t the least-weight panel concept on the upper wing surface is the -45" x 45" unflanged waffle grid. O n the lower wing surface, t h e least-weight panel concept I s the 0" x 90" flanged g r i d , with the 0" x 90" unflanged and 45" x 45" flanged and unflanged waffle waffle grids being s l i g h t l y heavier. Based on t h e combined weight of the upper and lower surfaces the two lower weight configurations, -45" x 45" (4.37 l b / f t 2 ) and 0" x 90" unflanged (4.56 lb/ft2) waffle grids were selected for further Also, since panel weights f o r Rene'41 are less than those for screening.
Haynes 25 on both the upper and lower surface, Rene'41 was selected a s the primary structural panel material.
I n i t i a l l y , only the waffle panel was retained for f'urther analysis.
However, a t the end of the f i n a l analysis, t h e waffle weight was found t o have increased significantly, primarily as a r e s u l t of pressure loads and the f a c t t h a t the waffle panel i s l e s s e f f i c i e n t when applied t o t h e complete wing structure than other concept Thus, the f i n a l r e s u l t s did not present the best choice for E. raonocoque . .icept, and t h e i n i t i a l screening r e s u l t s were reconsidered. Consequently, ,oneycomb sandwich was chosen as the panel exhibit- ing the greatest potential f c * support of pressure and inplane loadings for monocoque studies. The hone, -omb sandvich was then selected f o r f i n a l detailed analysis.
13-2 Semimonocoque Panel weight, closeout weight, minimu.. gages, and typical heat-shield wei.r:ht, were considered i n the i n i t i a l screening of a l l candidate semimonocoque spanwise- and chordwise-stiffened panels. Nonoptimum factors were based on t h e weiiTht, of panel-edge closeout designs i n which the fasterier shear force and panel centroidal axis a r e aligned. The typical heat-shield weight was based on a refur'Jishable corrugated skin w i t h two transverse hat-section s t i f f e n e r s and four post suppxts. Table 4-5 of section 4 contains the manufacturable minimum gage constraints imposed on the concepts.
T'e panels were analyzed using the general and l o c a l structural s t a b i l i t y Written i n the general form, the wide- procedures 8 s derived i n section 12.
column equation i s n N LE A plot of weight index ( t / L ) versus load index (N/LE Q) i s shown i n figure 13-2; t h i s figure also contains t h e efficiency factors ( E ) and weight 1, 2, 4, index exponents in) f o r the candidate concepts considered. Curves 6, and 9 were used f o r the i n i t i a l panel-weight screening. Later, it was found t h a t the corrugation-stiffened configuration was limited by fabrication, as represented by curve 3 o f figure 13-2. The corrugation-stiffened configuration had a 60-deg i n t e r i o r angle and a f l a t / s l a n t height r a t i o of 0.80, which is nonoptimum, as a result, of the fabrication stretch-forming limitations. ZF=e trapezoidal corrugation was analyzed f o r t h e optimum 60-deg i n t e r i o r angle and a fl-at/slant height r a t i o of 0.85. Also, l a t e r i n t h e study, the beaded and a constant semie.pex a g l e of 77.5 deg, tubular p;nd concepts were based on reduced from the e a r l i e r W-deg a r c because of t h e elongation l i n i t a t i o n s of fabricating these configurations by stretch-forming. Dning the intermediats screening, the room- temperature beaded-panel c~lwn t e s t (presented i n section 27) resulted i n a f a i l u r e a t a lower stress t i n @ . a.nt.ici2ated. The l o c a l insta- b i l i t y allowable f o r the beaded panel was i n i t i a l l y asswned t o depend on the radius-to-thickness yatio ( R / t ) of the arc; thSs was substantiated by local buckling t e s t s . However, on the basis of orthotropic plate theory, the column panel t e s t f a i l u r e corresponded t o an upper bound stress. Therefore, a new optimization procedure (see section 1 2 ) was developed f o r the f i n a l structural sizing of the beaded concept, as represented by curve 8 of figure 13-2, Spanwise concepts. "he results of t h e i n i t i a l spnwise-stiffened panel scraening given i n table 13-4 indicate t h a t a11 of the spanwise panel configura- tions are of approximately t h e same efficiency. The heaviest is indicated t o ' be t h e tubular panel however, t h i s panel ehswed t h e potential for much greate..
efficiency at longer lengths than used. Therefore, a l l four configurations were sub jccted t o an additional detailed panel evaluation during t h e intermedi- a t e screening in which t o t a l wing cross-section weights were considered.
Results showed t h a t t h e Haynes 25 all-oy p n d s were not competitive with the Rene' 41 panels .
13- 3
Chordwise concepts. - The results of the initial chordwise panel screen-
ing presented in table 13-5 show that the convex beaded version (unshielded design) has the lowest weight, 3 . 2 0 lb/ft2 for combined upper and lower surfaces.
However, selection was not made until results of the intermediate analyses of the spanwise concepts were known. This delay was to allow a better evaluation of the weight of these primary-structure concepts as a function of m e 1 size and ‘.o allow selection of a concept identical to one of the spanwise concepts in order to make a direct comparison of panel orientotion.
Statically Determinate The minimum- The statically determinate structure is spanwise ssiffened.
weight pmel concept for the spanwise semimonocoque structure wo-dld also be very efficient for the statically determinatt panels, since the loading con- ditions are similar. Thus, no screening was done for the statically determin?+.e structure, a n , ‘ , h e panel selection f o r final weight analyeis of this type of structure was the least-weight spanwise semimonoc(,que panel.
INTERMEDIATE WEIGHT SCREENINC The intermediate screening considered normal pressure as well as inplane loadings for total wing cross-section opthuization; rib and spar spacing were varied. Preliminary considerations for thermal protection (heat shield) were included to keep the primary structure below 16000~. Calculated weights were primary structure, base4 T Vene’41 material and include3 AB following items: typical : l * d * ~ t shields, spars and ribs, and panel closeouts. Heat-shield weight waE based on a refurbishable corrugated skin with two transverse hat-section s-tfffenersand four post supports, l h addition to the elimination of certain panel constructions, the results of the intermediate screening provided the ncvssary structural data for input into the final redundant-model loads analysis. For this intermediate screening analysis, the prelimiriary redundant- model internal loads shown in table 8-2 of section 8 were used.
A survey of the preliminary trwsient-temperature data for the three fiight conditions (-0.5-g, +2.0-g, and cruise) and the loads of table 8-2 led to the choice o f the 4-2.0-gmaneuver condition as the controlling design for the intermediate screening. The thermal strains, rather than the thermal loads of table 8-2, were combined with t;he air loads and the tempera xres of the preliminary transient analysis f o r each concept-. The semitaonol- Jque arrangements were optimized for bending and compression, ‘The waffle and honey- comb optimizations included shear, bending, and compression.
The results of the intermediate weight screening ahown in table 13-5 include temperatures, rib and spar spacings, and weightti (lb/ft2) for the primary structural concepts investigated.
Mono co que U a f f l e A psrametric aspect r a t i o study involving 45" x 45" and 0" x 90" waffle panels indicated that a geometrical configuration i n which a/b = 2.0, with r i b spacing b of 20 in., provides optiinum weights. This 20-by-40 in. s i z e w a s then used for the panel evaluations shwm in table 13-6.
Since t h e 45" x 45" grid w a s more efficien+,, waffle weights and shapes (including substructure) were determined f o r t h e 45" grid t o provide 3nput data f o r obtaining f u a l redundant analysis loads. The d e t a i l s of the nionocoque waffle intermediate screening are presented below.
I n i t i a l panel aspect r a t i o and panel dimension investigation - The
i n i t i a l panel aspect r a t i o and panel dimension investigation encompassed t h e follcwing main areas : 0 F'urther assessment of the -45" x 45" and 0" x 9" waffle grid was made t o provide additional substantiating data f o r the waffle grid selection (see i n i t i a l panel screening).
0 Aerodynamic pressure effects were consldered f o r designing unflanged -45" x 45" and 0" x 90" waffle plates subjected to zombined inplane and out-of-plane loading.
the unflanged -45" x 45" and 0" x 9" waffle The evaluation matrix f o r grid using inplane loads is shown in table 13-6. A s a conservative design approach, only compression loads were considered in the panel sizing. By neglecting the beneficial effects of t e m i o n on panel general instability, Panels are located between BL 120 and a small weight penalty was incurred.
220 without heat shields. Assumed temperatures f o r the comparison were 1400°F and 1 6 0 0 " ~ f o r the upper and lower surface panels, respectively. Rene 41' material properties were used. Aspect r a t i o s of 1 and 2 were assumed f o r panel widths of 20, 40, and 60 in., considering both chordwise and spanwise orientation. A summary of unit veights f o r t h i s aspect r a t i o study is shown in table 13-7. The conclusions of the waffle assessment are: 0 The 45" x 45" waffle r e s u l t s i n lower weight f o r plate applications (lower surface spanwise orientation).
0 The 0" x 9" waffle i s lower weight f o r wide column applications (lower surface spanwise orientation).
0 The effective r i b cap area (spanwise joint plus r i b cap) f o r both the 45" x 45" and 0" x 9" panels i s essentially the same because the distance from the outer pannel surface t o the neutral axis i s approximately the same.
13- 5 0 The effective spar cap area (chordwise joint plus spar cap) for the 45" x 45" waffle is less than the 0" x 90" waffle since the distance from the outer panel surface t o the neutral axis is l e s s for t h e 45" x 45" waffle.
Chordwise panel orientation is the most appropriate approach with r i b s being placed closer than spars.
The evaluation of normal pressure effects (internal, venting) on the -45" x 45" and 0" x 90" waffle panels is shown i n table 13-8. The comparison was based on design loads shown i n table 8-2 f o r the 2g maneuver condition.
Panels are between BL 120 - 220 without heat shields. Chordwise pane$ orienta-
Rend41 tion, aspect r a t i o of 2.0, and width of 20 in. were considered.
material proper%i,es and panel temperature of 1400°F w a s used. L i m 2 t wing pressure data a r e taken from section 2 .
The r e s u l t s of the upper surface panel evaluation are presented in table 13-8. The comparison i n d h a t e s t h a t upper surface panel weights (for the particular panel size considered) increase approxhately 32 percent f o r both the -45" x 45" and 0" x 90" waffle grids when normal pressures are con- sidered. O n the upper surface, unit panel weights of the 0" x 90" waffle grid Since the upper are s l i g h t l y less than those f o r the -45" x 45" waffle grid.
surface loads a r e higher i n the short panel direction, the weight difference between the waffle grids indicates that the 0" x ?Oo waffle i s also more e f f i c i e n t a s a wide column when the effects of pressure are included.
The r e s u l t s of the lower surface panel evaluation shown in table 13-8 indicate that pressure has a significant effect on panelweights. For the -45" x 45" waffle grid, unit panel weights increase 33.5 percent and 49 percent for panel widths of 20 in. and 40 in., respectively. For the 0" x 90" waffle grid, unit panel weights increase 34 percent and 43 percent f o r panel widths of 20 in. and 40 in., respectively. Thus, the increase i n unit panel weight due t o pressure is approximately the same f o r both the -45" x 45" and 0" x 90" waffle grids.
O n the lower surface, unit panel weights of the -45" x 45" waffle grid are considerably l e s s than those of the 0" x 90" waffle grid. Since the lower surface Loads are higher i n the long panel direction, the weight difference between the waffle grids indicates t h a t the -45" x 45" waffle i s also more efficient as a plate when the effects o f pressure a r e included.
Since t o t a l panel weights f o r the -45" x 45" waffle grid a r e l e s s than those for the 0" x 90" waffle grid (see table 13-8), the -45" x 45" waffle grid was selected f o r the monocoque waffle primary-structure panel concept.
I n i t i a l wing geometry (rib and spar spacing). - I n i t i a l wing geometry
was determined t o provide more refined redundant -model input data for the monocoque waffle primary- structure concept. The i n i t i a l Gib and spar spacing was determined by the following optimization procedure: 13-6 The panel width w a s optimized f o r a chordwise panel orientation of 2.0.
and panel aspect r a t i o These i n i t i a l assumptions were sapported by the comparison of various panel conTigurations shown i n table 13-7.
e The panel aspect r a t i o w a s optimized using the panel width deter- mined i n the f i r s t step.
Panel design f o r the i n i t i a l r i b and spar spacing was based on constant airloads and thermal strains.
Thus, p e l thermal loads were proportional t o t h e panel stiffness. This design procedure ensures consistency between re- dendant model and panel loads. Redundant model airloads depend mainly on equilibrium and, therefore, were assumed t o be constant w i t h changes i n panel stiffness. Similarly, redundant model thermal s t r a i n s depend mainly on com- p a t i 5 i l i t y conditions and were also assumed t o be constant w i t h changes i n panel stifmess.
The procedure of section 10 was used f o r optimization of the -45" x 45" unflanged waffle grid panels subjected t o combined inplane and out-of-plane loading. In a d a t i o n t o the i n i t i a l inplane and pressure loads, an edge eccentricity of 20.02 inch and an initial deflection due t o bowing of 0 . 0 0 1 ~ b Although a l l three loading conditions were considered, the 2g was assumed.
maneuver condition w a s the only active design condition.
The panel width 0ptimizati.J matrix is shown in table 13-9. Optimum
panel widths were determined f o r the inboard area between BL 120 - 220 and
h w e r surface thermal protection f o r the outboard area between BL 220 - 350.
the panel width study consists of k a t shields i n t h e outboard area. To select an optimum thermal protection arrangement f o r t h e monocoque waffle primary- structure concept, further assessment of t h e effects of heat shields (with and without insulation) w i l l be considered i n the f i n a l evaluation. Temperatures are based on preljminary thermal analysis data. A t o t a l of 16 panels were !Lbe results of t h i s optimiza- optimized f o r widths of 10, 20, 30 and 40 in.
tion, including panel weights, dimensions, eccentricities, and tmximum deflec- t i o m , are shown i n tables 13-L2 and 13-13 f o r the inboard and outboard areas of the wing, respectively. Notation f o r t h e panel dimensions i s presented in figure 13-3.
Based on extensional eccentricities from tables 13-10 and 13-11, incre- mental weights f o r typical single and double shear j o i n t s (figure 13-4) are shown i n tables 13-12 and 13-13. Small weight differences between the two For the determination of the r i b and spar requirements, joint concepts result.
the single shear joint i s selected because of design simplicity.
A summary of component wing weights including panels, closeouts, sib/spar webs and caps, and heat shields, i s shown i n tables 13-14 and 13-15 f o r the Circular-arc corrugated webs of 0,015 in.
inboard and outboard areas of the wing.
(minimum gage) analyzed for local i n s t a b i l i t y , general i n s t a b i l i t y , stiffness, 13-7 and resistance t o flexure-induced crushing are used for both r i b s and spars.
A minimum gage (0.010-in. ) circtllar-arc corrugated post-supprted heat shield is also considered.
Optimization of the r i b and spar requirements i s shown i n figures 13-5 and 13-6. Based on an aspect r a t i o of 2, the optimum panel width is 20 in. for both the inboard and outboard areas as indicated. Based on the foregoing panel Azes, the corresponding u n i t wing weights a r e 8.9 l b / f t 2 for the inboard area and 8.5 l b / f t 2 for the outboard area.
The panel aspect r a t i o optimization matrix is shown i n table 13-16.
Optimum panel aspect r a t i o was determined only f o r the inbbard area. lower Temperatures a r e based on preliminary surface heat shields a r e assumed.
a panel width of Eight panels were optimized for thermal analysis data.
20 in. and panel aspect r a t i o s of 1.0, 1.5, 2.0, and 2.5. A summary of com- ponent wing weights including panels, closeouts, rib/spar webs and caps and heat shields, i s shown i n table 13-17. Figure. 13-7 indicates t h a t t h e optimum aspect r a t i o i s approximately 2.5. However, the difference i n wing weight for panel aspect r a t i o s between 2.0 and 3.0 i s small, i.e., l e s s than one percent.
Monocoque Honeycomb- Core Sandwich A s indicated i n the i n i t i a l panel-weight screening, honeycomb-core sand- wich was selected f o r the f i n a l structural analysis. Weights for t h i s panel are not presented i n the intermediate screening data of table 13-5. However, an intermediate screening was conducted t o determine input for the redundant loads analysis, required f o r the f i n a l structural analysis.
The intermediate screening of the honeycomb-core sandwich concept was accomplished a f t e r the f i n a l structural sizing of the lightest-weight waffle arrangement and could, therefore, use the f i n a l waffle redundant model loads.
13-18) includes both smooth and recessed The honeycomb inboard wing data (table closeouts and indicates t h a t the recessed closeout design r e s u l t s i n lower weight. The recessed closecut requires that both face sheets be curved t o orient the p a e l centroidal axis with the substructure fastener, resulting i n increased drag and increased local thermal stresses from uneven heating, as well as increased manufacturing complexity.
The most important decision factor, i n addition t o panel weight, was Therefore, t o t a l wing aerodynamic performance analysis (drag) increased drag.
was conducted for the two closeout approaches, i n terms of f u e l increment (as compared t o an all-smooth wing). The resulting f u e l increments were 9 790 lb for the recessed and 126 l b for the smooth closeout design.
The entire wing weights and the drag penalties are summarized i n table 13-18, which shows a vehicle weight advantage of 7416 lb for the smooth closeout design, which was therefore chosen for d e t a i l sizing. However, a more gradual recess geometry than t h a t sei-ected would lessen the drag, and since the recessed design has l e s s we9ght than the smooth design, the recessed design may offer lower wing weight and lower t o t a l system cost.
An initial panel aspect ratio (figure 13-7) and panel dimension investi- gation was conducted (figure 13-8), resulting in minimum-weight geometry of a/b = 2, with a rib spacing b of 4-0 in. The honeycomb thermal protection was lower surface outboard heat shields and insulation. The geometry for the honey- comb sandwich panels are shown in table 13-19. These panel stiffhesses along w . L t , h the substructure stiffness were used for input data for obtaSning final redundant. ana1ysi.s loads. Table 13-20 indicates weight results for the center
( 5 to BL 120), inboard (BL 120 to 2 1 2 ) , and outboard (BL 212 to 350) areas of
the wine invesl;ir:ation section. A honeycomb sandwich average weight of 6.44 l b / r t 2 was obtained for the total wing investigation section.
Semimonocoque Spanwise All semimonocoque spanwise-stiffened structures, except the smooth corrugation-stiffened panels, employed heat shields on all exposed surfaces to reduce temperatures and provide aerodynamic smoothness.
The surface panels for each of the spanwise cand5.dates were sized for the inplane and normal loads. The typical results of this analysis are pre- sented in figures 13-9 through 13-15 for panels between BL 120 and 2l2.
The beaded and tubular panel concepts were based on a constant semiapex
angle of 7 7 . 5 . This angle was required for fabrication reasons. The elonga-
tion, efficiency, and geometry versus semiapex ang1.e are presented in figures 13-16 and 13-17.
These calculations were based on a 30.0 i n . long panel car- rying an inplane load of 2 0 0 0 lb/in.
The corrugation-stiffened skin panel weight is for the upper surface between BL 120 and 212. The constant geometry parameters used for this section were a 60" interior angle and a flat/slant height ratio of 0 . 8 0 as required for fabrication. The trapezoidal corrugation was analyzed for a 60" interior angle and a flatlslant height ratio of 0 . 8 5 .
During this intermediate structural screening, the corrugatian-stiffened skin was eliminated, since it was found to be considerably heavier than the other three candidates. For example, for a 30-in. rib spacing, the upper surface corrugation-stiffened skin panel is 2-1/2 times as heavy as the upper surface trapezoidal corrugation, as shown in table 13-5.
- \ Weight optimization of the tubular concept is presented in figures 13-18 and 13-19 for the representative areas of the wing. The optimum rib spacing is approximately 40 in.; however, definition of the minimum of the curve indicates that the rib spacing can be varied from 3 8 to 48 in. without appre- ciably increasing total cross-sectional weights.
Results of weight optimization of the beaded concept are presented in figures 13-20 and 13-21. The optimum rib spacing is approximately 4 8 in. for the inboard area and 50 in. for the outboard areas. However, as in the case for the tubular panels, rib spacing between 43 and 52 in. can be used without appreciable weight increase. For a @-in. rib spacing, 0.016-in. gage thickness panels are required for the upper surface and minimum gage (0.015-in.)
for the lower surface. A radius of 1 . 5 0 i n . is required to provide adequate stiffness and strength to transmit the design loads f o r the respective panel For a rib spacing of 46 in. minimum-gage panels can be used for both designs.
the upper and lower surface mnel designs.
Weight optimization of the trapezoidal-corrugation concept is presented in figures 13-22 and 13-23, indicating both wing component and total cross- sectional equivalent thickness. The results indicate rib spacing requirements of approximately 30 in. for both the inboard and outboard areas of the wing.
Both upper and lower surface thickness requirements exceed the minimum gage criteria established, with 0.024-in. and 0.020-in. material thickness required, respectively.
The goal of the intermediate screening was the selection of the two lightest-weight semimonocoque spanwise structures for final sizing. These are The trapezoidal corrugation the tubular and beaded-skin concepts (table 13- 5 ) is seen to be about 30 percent heavier than the beaded skin and about 13 per- cent heavier than the tubular concept. aowever, a further intermediate screen- ing of the trapezoidal-corrugation concept was conducted using the final semi- monocoque spanwise loads presented in section 8 . The results were compared with the final beaded and tubular weights (presented later), and the trapezoidal- corrugation concept was still heavier than the other two spanwise concepts. The details of the further intermediate screening of the trapezoidal corrugation are presented below.
The trapezoidal-corrugation primary structure with heat shields on both upper and lower surfaces was assessed on t i n e basis of coybinei! loadings (com- pression, shear, and bending), material capability (Rene 4 1 ) , practicality of Thermal- design for the given wing cross-section, and detailed thermal analyses.
protection arrangements with no insulation and with insulation at the lower surface outboard of the one-third wing chord were considered. (Insulation reduces the spanwise thermal gradients and enables a better match between the gradient through the depth of the wing and the fuselage.)
Insulation was placed so as to maintain the 1600~~ material limit and to minimize thermal gradients in the spanwise direction and to provide gradient matching between the wing and fuselage, thereby reducing thermal stresses.
Figure 8-18 of section 8 shows typical reductions in thermal stresses resulting from proper insulation placement.
Optimum rib and spar spacings were determined by considering sizrface pancls, rib and spar caps and webs, heat shields, closeouts, fasteners, in- The surface panels were sulation, oxidation penetration, and vertical posts.
analyzed for their most critical flight condition, the t2.0-g maneuver.
The 60" circular-arc (sine wave) spar webs were analyzed for total minimum 'G across the three wing areas (A, B, C) for critical shear stability.
A n optimum spar spacing of 90 in. allowed minimutn-gage webs of O,Ol'j=in Rene'41 in the center (A) and ovtboard (C) wing areas and 0 . 0 1 8 in. in the (B) section.
inboard 13-10 I From the optimum W-in. spar spacing, t o t a l wing cross-section and various win/: element effective thicknesses were determined as a f’unction o f r i b spacing.
The opt.imization r e s u l t s for t h e center area (A) f o r the insulated arrangement are summarized i n figure 13-24 and indicate an optimum r i b spacing of 30 in.
This same type of r i b spacing optimization was accomplished for the re- maining areas (B and C ) of the insulated arrangement and f o r the three areas f o r the uninsulated arrangement, as shown i n figures 13-25 t o 13-29, In a l l cases, the r i b spacing f o r minimum wing E was low enough for minimum-gage (O.Ol5-in. ) r i b webs.
As a r e s u l t of t h e heat-shield evaluation (described later), the ref’urbish- able corrugated heat shield w i t h multiple supports w a s used i n t h i s analysis.
Oxidation weight was based on a depth of oxide penetration commensurate w i t h the exwsure t i m e and temperature. The fastener weight represents the head, or nut, section of the fastener.
The summary of optimum r i b spacing and u n i t weights shown i n table 13-21 indicates t h a t t h e insulated arrangement (lower surface outboard) i s cf l e a s t weight as w e l l as being t h e minimum thermal s t r e s s design.
A summary of the trapezoidal-corrugation panel geometrics is presented i n tables 13-23 and 13-23.
The compnent thicknesses and weights f o r t h e minimum we2ght trapezoidal corrugation (insulation outboard) are shown i n table 13-24.
Semimonocoque Chordwise The results f o r spanwise stiffening eliminated both corrugation-stiffened O f t h e remaining semimonocoque panel skin and trapezoidal-corrugation concepts.
concepts, tubular and beaded, only the tubular buckling analysis had been veri- f i e d by tests at the t i m e the selection of a panel concept w a s made for t h e chordwise weight analysis. Therefore, the tubular concept was selected for intermediate weight analysis. A variation of t h e tubular concept (convex-beaded) t h a t does not require an aerodynamic f a i r i n g on t h e upper surface and t h a t reduces t h e exposed bead depth t o provide a smoother surface was a l s o considered, This variation permitted a comparison of the least-weight chordwisc tubular concept with the least-weight spanwise tubular concegt. A s a r e s u l t of t h e l a t e r a l pressure loads and excessive temperatures when unshielded, tubular panels instead of convex-beaded panels were necessary on the lower surface.
The rib-spar spacing weight results, including t h e substructure, are shown in table 13-6. On the basis of these results, t h e lightest-weight structure con- sists of tubular lower surface and canvex-beaded upper-surface .panels, and t h i s construction was selected for Sinal chordwise evaluation. However, a further intermediate screening of chordwise concepts was conducted t o evalu- ate thermal-protect ion arrangements.
13-11 The following tubular and convex-beaded priinary- structure and thermal- protection arranyements were assessed on the basis of combined loadings, material capability (Rene 41), pr , c t i c a l i t y of design for the wing crosa-section, and detailed thermal analysis data.
Insulation Primary structure and Remarks Arrangement heat- shield arran@ement(a) ~ ~ N o Heat shields required Upper: tubular Lower: tubular
Yes (b) (4
N o Upper surface structural temp Jpper : convex beaded increased Lower: tubular I I i Ekcessive structural temp NO Upper : convex beaded Lower: convex beaded
I I
N o Heat shields reduced structural Upper: convex beaded Inboard lower: convex bea6-9 Outboard lower: txbulas
1 Yes
Tubular upper surface under fuselage for a l l arrangements.
(a) Convex beaded: no heat shields.
Tubular: heat shields required.
Insulation on lower surface outboard.
( b ) bwer outboard insulation reduced the spanwise thermal gradient.
(c) Since the chordwise-stiffened panels are oriented i n the direction of the airflow, the convex-beaded primary structure was used without heat shields.
Therefore, thermal gradients f o r the arrangements investigated varied from small t o very large.
13- 12
section 8 were used f o r evaluating the various configurations; however, a plane-
The chordwise redundant-model internal loads 5hown in L9ble 8-17 of section 8 were used f o r evaluating the various configurations; however, a plane- strain analysis as presented in section 8 was conducted t o determine thermal.
loads for each arrangement.
Optimum rib and spar spacings were determined from data on the surface pa,iels, rib and spar caps and webs, heat shields, closeouts, fasteners, insula- tion, oxidation penetration, and vertical posts. The surface panels were analyzed for their most critical flight condition.
The 60" circular-arc (sine wave) rib webs were analyzed for the total minimum % across the three wing areas (A, B, C) for vertical shear stability.
A rib spacing of 60 in. in the center (one-half fuselage) and 7 5 in. in the inboard (B) and outboard ( C ) areas allowed minimum-gage webs of O.Ol5-in. Rend 41 to be used.
From the optimum rib spacing, total wing cross-section and various wing- element effective thicknesses were determined as a function of spar spacing (figures 1-3-30 to 1 - 3 - 5 0 ) . The optimization results for inboard area B (BL 120- 212) summarized in figure 13-40 indicate an optimum spar spacing of 24 to 28 in.
for the arrangement with a convex upper surface and a tubular lower surface and with lower surface insulation outboard.
The minimum-weight spar spacing for wing areas A, B, and C was 24 in. for this concept. Identical spar spacing optimization was accomplished f o r all chordwise arrangements and for the three areas (A, B, C) of the wing investigation section as shown in figures 13-30 to 13-50. In all cases, the spar spacing for minimum wing F was low enough for minimum-gage (0.015 i n . ) spar webs to be used.
The tubular semiapex angle and the convex-beaded inner semiapex angle were held constant at 77.5'. The bead height-to-width ratio for the unshielded convex-beaded surfaces was held constant at 0 . 1 0 to reduce performance (aero- dynamic drag) penalties. A summary of the panel geometrics for the various chordwise arrangements is presented in tables 13-25 to 13-31.
As a result of the neat-shield evaluation described ?.s;ter,the refurbish- able corrugated heat shield with multiple supports was used in this analysis instead of the corrugated-skin, hat stiffened, clip-supported heat shield design that was used on most of the other intermediate weights. Oxidation weight was based on a depth of oxide penetration commensurate with the exposure time and temperature. The fastener weight represents the head, or nut, section of the fastener.
The summary of optimum spar spacing and unit weights for the chordwise candidates, shown in table 13-32, indicates the importance of insulation placement. The reduced thermal gradients and thermal stresses resulted in weight savings of 1 0 percent o r more for the two minimum-weight arrangements.
Also, table 13-32 indicates that the unshielded and uninsulated convex-beaded arrangement is the heaviest. Since the convex-beaded upper surface and tubular lower surface arrangement (with LOWET surface insulation outboard) was of the least weight (6.89 lb/ft2), it was selected for the final structural analysis.
However, at this point in the chordwise investigation, the stiffnesses resulting from the least-weight chordwise structural arrangement were observed to differ from .he stiffnesses usrd for the redundant-model analysis. Ike primary differences encompassed the shear stiffnesses, the 3xtensional stiff- nesses for the upper and lower surface spanwise direction (affecting spar cap geometry), and the extensional stififnesses for the upper surface chordwise Therefore, a new redundant direction (affecting upper surface panel shape).
analysis was conducted with the actual stiffnesses of the least-weight chord- wise structural arrangement of table 13-32, and these results were used for the final structural anaiysis.
FINAL STRUCTUFAL WEIGHTS I During final structural sizing of the Rene 4 1 primary structure, various thermal-protection arrangements were considered to determine the most compatible arrangement of wing-fuselage temperatures and temperature gradients and to determine the structure with the lowest weight. With respect to the heat shields and insulation, the major objective was to minimize weight and to reduce thermd stress by limiting .'.hermaI.-stressprimary-structural temperatures to a maximum of 1600"~.
Monocoque Waffle Coricept Thermal-protection arrangements for the 45" x 45" waffle primary structure were assessed on the basis of lowest reight, practicality of design for the given ding cross-section, and detailed th.,mal analysis data. These arrange- ments were for (1) no heat shields and no insulation, (2) lower surface heat shields outboard of one-third wing chord with and without insulation and, (3) heat shields on entire lower surface with icsulation outboard of one-tlijrd chord and without insulation.
Final redundant-analysis average internal loads and thermal strains are shown in table 8-4 of section 8 for the thermal-protection arrangement with lower surface heat shields outboard and no insulation. l ' h e redundant-model airloads were used for all the thermal-protection arrangements; however, the thermal loads were obtained for other arrangements by plane-strain analyses, which, for the same thermal-protection arrangement, indicated genexiallygood agreement with the redundant-model results of table 8-4, as shown in section 8 .
The thermal-analysis data included transient effects on structural tem- peratures and isotherms generated for the candidate thermal-protection arrange- ments as presented in section 9. The transient effects were based on a general thermal model, which included effects of heat-shield placement, lower surface insulation, and spar and rib size.
13-14 Optimum r i b and spar spacing f o r wing inboard area B (BL 120 t o BL 212) was determined for the thermal-protection arrangement with outboard lower surface heat shield and insulation. Forty upper and lower surface panels were optimized for panel-aspect r a t i o s of 0.5, 1.0, 2.0, 3.0, and 4.0 and panel widths of 10, 20, 30, and 40 in. As shown i n figure 13-51, the optimum pans1 width i n the inboard area was 20.0 in. and t h e optimum panel aspect r a t i o w a s 1.0 for wing area B. However, f i n a l selection of optimum r i b and spar spacing was based on a comparison of average un5t weights f o r the e n t i r e wing investi- i n whlch a panel spanwise width of 20 in. and panel aspect g a t i m section, r a t i o s of 1.0 and 2.0 were considered. Average unit weight f o r aspect r a t i o s of 1.0 was 10.764 lb/ft2 and for 2 . C was 10.494 lb/ft*. Consequently, a waffle panel spawise width of 20 in. and panel aspect r a t i o of 2.0 (20 in. x 40 in. ) was selected for f i n a l sizing of the five waffle arrangements.
A summary of average unit weights f o r the various arrangements of lower The arrangement w i t h the surface thermal protection i s shown i n table 13-33.
lowest weight has heat shields w i t h insulation on the lower surface outboard Deleting the outboard insulation resul%s i n of t h e wing one-third chordline.
a 3 percent weight penalty and decreasing the panel aspect r a t i o from 2 to 1 causes a 2.6 percent weight penalty. &tending the heat shield over the e n t i r e lower surface results i n a 5.6 percent weight penalty (higher wfthout outboard I d and insulation rrtsults i n an 11 percent insulation). Deleting both heat s h ' weight penalty. The lowest-weight wing w a s achieved when t h e thermal-protection arrangement imposed temperatures thak resulted i n a temperature gradient %rough the depth of the wing t h a t nearly matched the temperature gradient through the fuselage depth, both a t the same station.
A summary of the waffle panel c o n f i w a t i o n geometries f o r the various thermal protection arrangements is presented in tables 13-34 t o 13-37 f o r the center, inboard, and outboard areas of the wing section investigate&, Xotation for the panel dimensions is presented i n figure 13-52. The waffle-cdcept component weights shown i n tables 13-39 t o 13-43 include those of panels, single shear cap and closeouts, r i b and spar webs, web intersection, Dynaflex-insulated corrugated heat shield, oxidation losses, and fasteners. A spanwise weight distribution was used to obtain an average unit weight f o r the e n t i r e wing cross-section. %"hewaffle panels a r e seen t o represent appraximately 55 percent of the t o t a l wing weight f o r the minimum-weight arrangement of table 13-40.
The f i n a l structural design offering the lowert weight waffle thermal- protection arrangement are shown i n figures 13-538 and B. Center, inboard, and cutboard areas (designated A, B, and C) were used for determining t o t a l wing weight and cost. A r i b spacing of 22.30 in. (in area B) and a spar spacing 41.05 in. was used so t h a t the one-third wing chord lies .?.long the panel of This arrangement provides maximum uniformity of panel design.
diagonal.
Out-of-plane loads at the one-third chordline were resisted by full-depth webs along the panel diagonal. A minimum gage (0.015 j . n . ) 60" circulw-arc corrugation was used for r i b and spar webs. Flush Hi-Lnk fasteners were used t o attach the upper surface panels t o the r i b and spar caps. For attachment of lower surface panels, countersunk screws and nut plates were used.
(Renoval of the upper surface primary structural panels is accomplished by first removing the lower surface panels. ) A t web intersections, combinations of bentup flanges and separate angles were joined by resistance spotwelding. Dynaflex insulation, varying from 0.25 in. i n thickness near the leading edge t o 0.125 in. inboard, w a s packaged in Inconel X-750 f o i l .
Leading edges and heat shields were attached by externally accessible flush screws. Cross-sections of the corrugated heat shield with multiple supports and t h e segmented leading edge are shown i n figure 13-53.
Monocoque Honeycomb- Core Sandwich Concept The honeycomb-core sandwich primary structure was evaluated with lower surface heat shields and insulation outboard of the one-third wing chord, since t h i s arrangement has the lowest weight f o r the monocoque waffle -nncept.
A f t e r detailed evaluation, it was detemlned t h a t Rene' 41 honeycombcore sandwich could not be adequately brazed by using existing techniques. Therefore, resistance spotwelding was selected for welding the cellular-shaped foil-ribbon core t o the face sheets.
The honeycomb-core venting problem was approached i n two ways: (1) com- plete venting t o the atmosphere, and (2) sealed panels, evacuated t o a low pressure, and f i l l e d w i t h helium. Honeycomb-core vented t o the atmosphere simplifies heat-shield attachment and fabrication. However, t h i s approach permits oxidation ana corrosion (from condensation of water vapor) of core and interior-skin surfaces. Honeycomb-core sealed, evacuated, and f i l l e d w i t h hel5.m at 2 psia eliminates oxidation and corrosion of the panel interior, but using existing fabrication techniques the panel pressure seal i s extremely d i f f i c u l t t o achieve (adequate welding of closeouts). However, since honeycomb sandwich offers a low weight potential and adequate sealing techniques may be developed for future application, the sealed approach was used for t h i s investigation.
Table 8-8 of section 8 shows the f i n a l internal loads, resulting from the redundant-model analysis, used f o r the f i n a l structural sizing.
Optinlum r i b and spar spacing were determined as shown i n figure 13-54, considering surface panels, r i b and spar caps and webs, heat shields, closeouts, fasteners, insulation, oxidation penetration, and v e r t i c a l posts. To assure that no weight decrease occurs due t o the relieving effect of l o c a l thermal gradients, weights were determined w i t h and without thermal. gradients. Fifty- four panels were optimized f o r panel aspect r a t i o s of 1.0, 1 . 5 and 2.0. Panel widths of 40, 50, and 60 in. were considerea. l'ne effective design condition for the center and outboard upper surface p e l s was cruise and -1/2g maneuver, respectively. All. other pcnels were desigxd by the +2.0-g raaneuver condition.
13-16 As indicated in f'igure 13-54 and table 13-44, a panel aspeci; r a t i o of 2.0 and panel w i d t h o r 40 in. ( 4 0 in. x 80 in.) provides minimum weight, This i s in ap-eemenb witah t h e panel size selected f o r f i n a l redundant-model loads and I;herraal analysis. A comparison between the shear and extensional thickness used for I,he honeycomb redundant-model load analysis and t h e f i n a l panel stiff- nes::es indi cated excellent agreement.
A summary of t h e honeycomb sandwich panel design temperatures and geom- e t r y is presented i n t a b l e 13-45 indicating t h a t the height h varies from 0.71 t o 0.96 in. with internal face thicknesses varying from 0.012 t o 0.015 in. and external face thicknesses varying from 0 . 0 1 5 t o 0,019 in. The tnaximum face sheet temperatures of table 13-45 were conservatively used t o determine mate- rial properties f o r both face sheets and t h e core. The honeycomb-sandwich component weights shown i n t a b l e 13-46 include weights of panels, closeouts, caps, webs, web intersection, Dynaflex insulation, corrugated heat shield, oxidation losses, and fasteners. A spanwise weight distribution was used t o obtain an average unit weight of 6.47 lb/ft2 f o r t h e e n t i r e wing cross-section.
The panels represent approximately 59 percent of t h e wing weight.
A drawing of the f i n a l honeycomb-sandwich structural arrangement i s shown i n figures 13-55 A and B. Center, inboard, and outboard areas (designated A, R i b spacing B, and C ) were used f o r determining t o t a l wing weight and cost.
of' 40 in. and spar spacing of 80 in. were used. A minimum gage (0.015 i n . ) 60" circular-arc corrugation was used for the r i b and spar webs. Flush Hi-Zlok fasbeners were used t o attach the upper surface panels t o the r i b and spar For. atAachment of lower surface panels, countersunk screws and nut caps.
plal.es wet*@ used. Removal of the upper surface primary structural pafiels i s accutnpl i slied by L'irsl. removirq: the lower surface panels. A t web intersections, cotti1)irial.j cms O S 1)ent.up rlanges and separate angles were Joined by resistance spo I.wc:ld Lni:.
Dynaflex insulation, varying from 0.25 in. i n thickness near the leading Heat shields edge t o 0.125 in. inboard, was packaged i n Inconel 750 f o i l .
and leading edges were attached by externally accessible flush screws.
Semimonocoque Spanwise Concepts Two spanwise primary-structure concepts were considered during t h e f i n a l Tubular and beaded-skin primary structures with heat shields structural sizing.
on both upper and lower surfaces were assessed on the basis of combined loadings, material capability (Rene' 41), practfcality of design f o r the given wing cross- section, and detailed thermal analyses. Thermal-protection arrangements with no insulation and with insulation at the lower surface outboard of the one-third wing chord were considered. (Insulation reduces t h e spanwise thermal gradients. )
Tubular. - The internal loads resulting from t h e spanwise redundant-model
These loads were used f o r eval- analysis are shown i n t a b l e 8-9 of section 8.
uating both spanwise structures.
Good agreement between assumed and actual stiffenesses were noted.
Plane-strain analyses were conducted t o determine thermal loads f o r each thermal-protection arrangement.
13-17 Insulation was placed so as to maintain the 1600"~ material limit and to minimize thermal gradients in the spanwise direction and to provide a match between gradients through the wing and the fuselage depth, thereby reducing thermal stresses.
Optimum rib and spar spacings were determined by considering surface panels, and webs, heat shields, closeouts, fasteners, insulation, oxi- rib and spar caps dation penetration, and vertical posts. The surface panels were analyzed for' their most critical flight condition, the i-2.0-g maneuver.
The 60" circular-arc (sine wave) spar webs were analyzed f o r total mini- mum% across the three wing areas (A, B, C) for critical shear stability. A n optimum spar spacing of 90 in. allowed minimum-gage webs of O.Ol5-in. Rene'41 in the center (A) and outboard (C) wing areas and 0.018-in. in the inboard (B) section. The The redundant-model shear loads were used for sizing the webs.
determination of the web shear strength was based on the optimization procedure presented in section 11, and subjected to the stated manufacturing constraints in that section. Shear allowables are presented in figures 13-56, 13-57, and 13-58 for temperatures of 1300°F, 14OO0F, and S500"P. The rib and spar cap weights were determined from figures 13-59 and 13-60. Figure 13-60 also in- cludes the basic geometry of the caps.
From the optimum W-in. spar spacing, total wing cross-section and various wing-element effective thicknesses were determined as a function of rib spacing.
The optimization results for center area (A), summarized in figure 13-61, indi- cz';e an optimum rib spacing of 50 in. for the tubular concept with insulation.
This same type of rib spacing optimization was accomplished for all three areas (A, B, and C) of the wing investigation section and for both thermal protection arrangements as shown in figures 13-61 to : i 3 - 6 6 . In all cases, the rib spacing f o r ninimum wing % was low enough f o r mini:aum-gage (O.Ol5-in. ) rib webs.
To provide heat-shield support-oli;: attachment surfaces, the flats between tubes were set at 0.50 in. The tubular panel semiapex angle was held constant at 77.5", as in the intermediate sizing.
As a result of the heat-shield evaliaation (described later), the refurbish- able corrugated heat shield with multiple supports was used in this analysis.
Oxidation weight was based on a depth of +txidepenetration commensurate with the exposure time and temperature.
The summary of optimum rib spacing and unit weights shown in table 13-47 for the tubular concepts with and without insulation indicates that the insulated arrangement (lower surface outboard) is the lower weight and lower thermal-stress design.
A summary of the panel geometry cf the final tubular structure is pre- sented in table 13-48 for the center, inboard, and outboard areas of the wing sect-Jn investigated. A s indicated in table 13-48, the panel geometry is near minimum gage ( t = 0.010 in, ) for the tkree wing areas.
23- 18 The component thicknesses and weights a r e shown i n table 13-49 for primary s t r u c t u r a l panels, panel closeouts, r i b and spar caps, webs, and posts, Dynaflex
insulation, corrugated heat shields, oxidation losses, and fasteners . A span-
wise weight distribution w a s used t o obtain an average unit weight f o r .the e n t i r e wing cross -section.
The primary-structure panels are approximately 45 percent of t h e t o t a l wing weight.
The f i n a l s t r u c t u r a l design of t h e tubular concept is shown in figures 13-67 A & B. The tubular concept has panel dimensions of 90 by 48 i n . , 90 by 40 i n . , and 90 by ~ c O in., respectively, for t h e three sections from center t o Outboard The v e r t i c a l rib and spar webs are of 6 0 ' circular-sLrc corrugation f u l l - depth Rene'41 construction melt-through-welded t o t h e r i b and spar caps. The caps are of sheetmetal with flanged edges (channels). A t the web intersections, the posts a r e formed from conibimtions of angles and bentup flanges, joined by resistance spotwelding.
The heat-shield attachment c l i p s are spatwelded t o the shield and panel on Since the heat shield is s l i g h t l y smaller t b n the s t r u c t u r a l both surfaces.
are attached mechanically t o t h e spars. Foil- panel, corrugated cover s t r i p s packaged Dynaflex insulation placement and thickness a r e indicated in figure 13-67.
Beaded Skin. - T h e m 1 protection arrangements with and without insulation
at the lower surface outboard of t h e one-third chordline were considered t o eval- uate t h e r m 1 stresses. The loads of table 8-9 of section 8 were used t o evalu- ate t h e beaded structure. The tubular structure's optimum g0-in. spar spacing was used t o determine total,wtng cross-section and optimization r e s u l t s f o r the center area ( A ) , s m r i z e d in figure 13-68, indicate an optimum r i b spacing of 50 in. for t h e beaded concept with insulation.
This same type of rib spacing optimization, as shown in f i s a e s 13-68 t o 13-73, was accomplished f o r a l l t h e three areas (A, B, and C ) of t h e wing inves- In a l l cases, t h e tigation section and both therml-protection arrangements.
r i b spacing f o r minimum wing t was low enough f o r minimum-gage (O.Ol5-in.) r i b Webs e To provide heat-shield support-clip attachment surfaces, the f l a t s between The beaded-panel semiapex angle was held constant beads were set at 0 . 5 0 i n .
a t 77.5', as i n the intermediate sizing.
The refurbishable corrugated heat shield with multiple supports was used i n t h i s analysis. Oxidation weight was based on a depth of' oxide penetration commensurate with t h e exposure time and temperature.
13-19 The sumnary of optimum r i b spacing and u n i t weights shown i n table 13-50 for the spanwise candidates indicates t h a t t h e insulated arrangement (lower surface outboard) is the lower-weight and lower-thermal-stress design.
A summary of t h e f h a l b e a d e d - p e l geonetry is presented i n table 13-51 f o r t h e center, inboard, and outboard areas of t h e wing section investigated.
The panel gages shown i n table 13-51 range from a minimum gage of t = 0.015 t o t = 0.022; that is, although lower weight than the other concepts, mini- mum gage is not required.
The component thicknesses and weights are shown in t a b l e 13-52 f o r p r i m r y structural panels, panel closeouts, rib and spar caps, webs, and posts, Dynaflex insulation, corrugated heat shields, oxidation losses, and fasteners. A span- wise weight distribution was used t o obtain an average unit weight f o r the en-
tire w i n g cross-section. me primary-structure panels are approximately 45 per-
cent of the t o t a l wing weight.
The f i n a l structural design f o r t h e beaded concept is shown i n figures 13-74 A and B . The panel dimensions a r e 90 by 50 in., 90 by 50 in., and 90 by Other 40 in., respectively, f o r the three sections from center t o outboard.
design aspects of figure 33-74 f o r the beaded concept are the same as discussed earlier f o r ' t h e tubular concept.
Semimonccoque Chordwise Concept The weight of t h e semimonocoque chordwise concept, consisting of tubular panel with heat shields on t h e lower surface and convex-beaded upper surface without heat shields, was determined with insulation on t h e lower surface out- board of the one-third chordline. The chordwise redundant-model internal loads shown in table 8-39 of section 8 were used. Detailed transient therm1 analyses were conducted t o determine l o c a l stresses and deflections caused by temperature gradients through the panel structure as presented i n section 9.
The 6 0 ' c i r c u l a r e r c (sine wave) r i b webs were analyzed f o r the t o t a l mini- mum t across the three wing areas (A, B, C ) f o r v e r t i c a l shear s t a b i l i t y . A r i b spacing of 60 in. i n the center (one-half fuselage) and 75 in. in ;he inboard (B) and outboard (C) areas allowed minimum-gage webs of 0.035-in. Rene 41 t o be used.
From the optimum r i b spacing, t o t a l wing cross-section and various wing- element effective thicknesses were determined as a function of spar spacing as presented i n figures 13-75 t o 13-77. The optim3.zation results f o r center area
A (E t o BL QO), summarized i n figure 13-75, indicate an optimum spar spacing of
25 i n . The minimum-weight spar spacing f o r wing areas A, B, and C was 24 in.
for t h i s concept. In all cases, the spar spacing f o r minimum wing weight was low enough for minimum-gage (0.015-in.) spar webs t o be used.
13- 2.0 The tubular semiapex angle and t h e convex-beaded inner semiapex angle were held constant at 7 7 . 5 ' . The bead height-to-width r a t i o f o r t h e unshielded convex-beaded upper surface panels wa" Leld constant at 0.10 t o reduce perform- ance (aerodynamic drag) penalties .
As a result of t h e heat-shield evaluation described later, the refurbish- able corrugated heat shield with multiple supports was used i n t h i s analysis.
Oxidation weight was based on a depth of oxide penetration commensurate with the exposure t i m e and temperature.
A sumnntry of the f i n a l panel configuration is presented i n t a b l e 13-53 f o r the center, inboard, and outboard areas of the wing-section investigated.
As indicated, t h e t u b u l a r - p n e l configumt,ion f o r t h e lower surface and upper surface under t h e fuselage is near minimum gage ( t = 0.010 in.) f o r the three w i n g areas. The convex-beaded prtnel gages are a l s o near minimum gage ( t upper = O.Ol5 in. and t lower = 0.010 in.).
The convex-beaded tubular concept component thicknesses and weights &re shown i n table 13-54 f o r primary-structure panels, end closeouts, r i b and spar caps, webs, and posts, Dynaflex insulation, corrugated heat shield, oxidation losses, and fasteners. A spanwise weight distribution was used t o obtain an u n i t weight f o r the e n t i r e w i n g cross-section. "he primary-structure average penals a r e seen t o represent approximately 40 percent of the t o t a l w i n g weight.
The final structural design f o r the chordwise concept shown i n figures 13-78 A and B has panel dimensions of 60 by 24 in. and 75 by 24 in. Figure 13-78 also shows p e l cross-section f o r each wing area. The v e r t i c a l rib and spar webs and caps are identical t o those of the spanwise concept.
The lower surface, which is the only surface requiring thermal protection, is shielded from aerodynamic heating by a corrugated heat shield supported on multiple truss-type clips. Dynaflex insulation, packaged in f o i l , is located on t h e lower outboard w i n g surface.
S t a t i c a l l y Determinate Concept The s t a t i c a l l y determinate structure is a series of spanwise-stiffened beams, decoupled at the chordwise-rib intersections. The s l i p joints at the beam-rib intersections provide v e r t i c a l shear continuity only, thereby main- taining the wing contour (shape) but providing ne2ther bending nor a x i a l load paths. Thus, the l e a s t -weight semimonocoque spanwise-stiffened panel construc- t i o n was t h e logical choice f o r the detail s t a t i c a l l y determinate analysis.
The least-weight beaded p r i m r y structure was evalmted on the basis of com- bined loadings, weight, p r a c t t c a l i t y of design f o r the specified wing cross- section, and detailed thermal analyses. Heat shields covered a l l exposed surfaces and three t h e m l - p r o t e c t i o n arrangements were considered: (1) no insulation, (2) insulation on the Lower surface at t h e center and inboard areas, and (3) insUhtion at the lower surface outboard of the one-third wing chordline .
13-21 The second thermal-protection arrangement (insulation on the center and inboard areas) was t o investigate s t r u c t u r a l temperatures even lower than 1600% t o provide minimum-gage panel designs, since the spanwise loads were low. Because of nonccntinuous ribs and the allowable wing rotation at t h e fuselage, wing4o-fuselage temperature and temperature gradient compwbibility i r not important i n this concept.
Internal loads were used, as shown h table 8-40 of section 8, f o r the no-insuhtion armngement.
Good agreemem between the assumed and the actus1 f i n a l stiffnesses calcu3ated were noted. Because the ribs are discontinuow f o r t h i s concept, t h e chordwise airloads and thermal loads are zero, as indi- cated i n t a b l e 8-40. Also, the spanwise thermal loads are small, providing a minimum-theml-stress w i n g concept .
therm1 analyses were conducted f o r t h e thermal- Detailed transient prokection arrangements t o determine local stresses and deflections from temperature gradients through the panel structure, as presented i n section 9.
y I n determining optimum rib and spar spacings, surface panels, caps, w e , heat shields, closeoubs, fasteners, oxidation penetration, v e r t i c a l posts, m14 s l i p j o a t asset&lies at each r i b and spar intersection were considered. Sur- face panels were analyzed f o r t h e most c r i t i c a l condition, the +2.O-g maneuver.
A spar spacing of 90 in. was used, with minimum-gage webs of O.Ol5-in. thick- ness. However, t h e spar spacing could be increased since twice as many spars are used t o carry the shear as the semimonocoque concept, thus allowing a lower wing weight.
With spar spacing fixed, t h e rib spacing0 were varied t o determ5ne el-- ment sizes and wing weights (figures 13-79 t o 13-81). The optimization r e s u l t s
f o r the inboard area (BL 120 - 212) shown in figure 13-80, indicate an optimum
This same r i b spacing of 50 in. f o r the beaded concept with no insulation.
type of rib-spacing optimization was accomplished f o r t h e instdated arrange- ments and f o r the three areas (center, inboard, and outboard) of the wing in- All r i b spacings resulted i n the use of minimum-gage vestigation section.
rib wsbs (0.035 in.).
The beaded-panel semiapex angle was held at 77.5', the same as f o r t h e spanwise concept. To pravide heat-shield support-clip attachment surfaces, the The refurbishable heat; shield with flats between beads were set at 0 . 5 0 in.
in f o i l was used i n t h i s multiple supports and Dynaflex insuJ.at9on packaged analysls 13-22 Structural sizing was not conducted f o r t h e t h i r d thermal-protection arrangement, with insulation only on t h e lower surface outboard area, since t h e outboard panels f o r t h e no-insubtion arrangement were minimum gage (t = 0.015 in.) f o r the lower surface and near minimum gage (0.016 in.) f o r the upper surface. Therefore, t h e use of insulation, w i t h its required packaging, would increase the wing weight above the saving of 0.001 i n . on the upper surface.
A summary of unit weights f o r no-insulation and two thicknesses of insula- tion inboard, presented i n t a b l e 13-55, indicates a s l i g h t weight advantage f o r the no-insulation arrangement. Therefore, the f u l l y shielded s t a t i c a l l y deter- minate concept with no insulation was selected f o r d e t a i l cost, performance, and r e l i a b i l i t y evaluation.
A summary for the selected configuration is presented i n t a b l e 13-56 f o r As the center, inboard, and outboard areas of t h e wing-investigation section.
is minimum gage except f o r the center (A) and inboard indicated, t h e beaded panel (B) upper surface panels. These are not minimum gage because of larger compres- sion airloads.
The s t a t i c a l l y determinate component thicknesses a r e shown i n t a b l e 13-57 f o r p r i m r y s t r u c t u r a l panels, p a e l closeouts, r i b and spar caps, webs, and posts, corrugated heat shield, exidation losses, and fasteners. A spanwise weight distribution was used t o obtain an average unit weight f o r t h e e n t i r e wing cross-section. As indicated, t h e average unit weight of t h i s configuration is 5.55 lb/ft2, and the primary-structure panels represent approximately 35 per- cent of t h e t o t a l wing weight. The s t a t i c a l l y de-kerminate fuselage weight in- curs a 10 percent penalty Over the semimonocoque and monocoque concepts due t o additional fuselage skin, l o c a l f i t t i n g s , and concentrated loads. The d e t a i l s of t h e t o t a l f u s e h g e weight penalty a r e presented i n section 22.
The final s t r u c t u r a l design for the s t a t i c a l l y determinate beaded concept is shown i n figures 13-82 A and B . Panel dimensions are 90 by 60 in. from centerline t o BL 320, and 90 by 40 in. from BL l20 outboard. A b a l l s l i p joint, providing wing-surface continuity, is located at each spar-rib intersection, with adequate tolerance t o permit unrestrained thermal expansion i n t h e chordwise direct ion .
R i b and spar webs are of 60° c i r c u l a r e r c corrugation (sine-wave) con- m e sheetmetal flanged rib and spar caps, struction, fabricated from Rene 41.
which a r e a l s o fabricated. from Rene”41, a r e melt-through welded t o t h e v e r t i c a l webs 13-23 Primry-Strmcture Weight Summary Table 13-58 presents a swamary of t h e concept weights and associated m r - gins of safety established f o r each 0.6 the s i x s t r u c t u r a l concepts.
A s indicated i n the table, the margins of safety were determined f o r t h e c r i t i c a l ultimate flight-load condition, panel f l u t t e r , vehicle f l u t t e r , sonic fatigue, load fatigue, and creep.
Ultimate load analysis. - The margins of safety f o r t h e ultimate f l i g h t load
are zero or eear zero f o r minimum-weight design. However, as shown in t a b l e 13-58, is as high as Q.30 because of t h e the load m r g j n of safety f o r the beaded concept use of minimum-gage materials.
Panel f l u t t e r . - A detailed panel-flutter analysis of the concepts indicates
t h a t t h e p n e l s a r e stable and substantially exceed t h e f l u t t e r factor-of-safety are shown in table 13-58.
The panel-flutter mrgins of safety requirement of 1.3.
Vehicle f l u t t e r analysis . - Vehicle f l u t t e r was investigated by applying
the results of the redundant ane2yses t o the' maximum-weight climb and acceleration region of t h e trajectory. %%e investigation showed t h a t an adequate margin on airspeed and dynamic pressure (beyond the required 1 . 3 f a c t o r ) 2s available over the design f l i g h t path and t h a t t h e concepts are not c r i t i c a l i n f l u t t e r . The mrgins of safety f o r vehicle f l u t t e r a r e large, as presented i n t a b l e 13-58.
-Analyses conducted t o determine the e f f e c t s of Sonic fatigue analysis.
random sound pressures on the si.x concepts indicate %hat t h e allowable sound- pressure l e v e l (dB/Hz) is greater than the maximum predicted sound-pressure l e v e l of t h e 0,007-q c r i t e r i o n f o r upper and lower surfaces f o r both concepts.
The application of t h e 0.002-9 c r i t e r i o n on t h e lower surface during cruise a l s o r e s u l t s i n root -mean-square stresses l e s s than fatigue-limit allowable stress.
The resulting margins f o r sonic fatigue a r e shown i n table 13-58.
This analysis provides an interim basis f o r determining t h e fatigue resistance of the structure or? an empirically derived nominal vibratory s t r e s s of t y p i c a l f l i g h t hardware. However, f o r t h e p r i m r y structures of t h i s study, further sonic -fatigue t e s t i n g is necessary t o determine t h e a c t u a l boundary conditions and the detailed design refinements f o r the primary structure and its attachments.
Fatigue analysis . - Fatigue analysis was conducted t o establish allowable
design stress levels f o r p r i m r y structures t o meet the l i f e requirements speci- The load-fatigue margins of safety are presented i n t a b l e 13-58 f o r the fied.
tension load surfaces.
13- 24
Creep analysis. - Creep margins of safety were established f o r t h e most
The effect. of compressive ther!-d s t r a i n s on c r i t i c a l area f o r each concept.
creep buckling and t e n s i l e thermal s t r a i n s on t o t a l p l a s t i c deformation can be stress relaxation.
neglected, due t o Thus, only airlads were used t o determine appllcd stresses for creep at elevated temperatures .
The allowable compressive stresses under creep conditions were determined by w i n g isochronous s t r e s s - s t r a i n curves. The resulting margins of Psfety a r e shown in table 13-58. The c r i t i c a l f a i l u r e mode f o r a11 concepts is creep buckling,
Primary-structure weight comparison. - The wing-section weight investiga-
t i o n resulted i n t h e following ranking of s t r u c t u r a l conceFts: semimonocoque spanwise beaded, semimonocoque spanwise tubular, s t a t i c a l l y determinate monocoque honeycomb sandwich spanwise beaded, semimonocoque chordwise eubular, and mono- cogue waffle. However, when t h e t o t a l wing weight is considered (as presented i n section 2 2 ) , the honeycomb sandwich is lower i n weight than t h e s t a t i c a l l y determinate concept. This is because the hoEeycomb sandwich has b e t t e r efficiency i n the high-load area of t h e aft wing. es The double-sheet tubular concept is heavier i n weight than t h e single-sheet for the upper surface where bending (due t o normal pressure) and beaded concept inplane compression loads a r e c r i t i c a l . O n t h e lower surface, where bending due t o n o n a l pressure and tension a r e the design modes, t h e beaded concept (minimum gage or near minimum gage) is consfderably lower i n weight than t h e tubular con- cept. Therefore, it is concluded t h a t caution should be applied in using on!y inplane compression weight/strength data f o r concept selection, since such data show the tubular panel t o be lighter than t h e beaded panels which is not t h e case f o r combined loads.
The spanwise-stiffened concepts a r e lower i n weight than the chordwise, because the t h e r m 1 s t r e s s a r e h i e e s t i n t h e chordwise direction, and the principal airloads a c t spanwise and added spar cap material is required f o r chordwise stiffened panel concepts, The high thermal stresses a r e imposed on t h e panels of the chordwise concept, whereas only t h e r i b caps of t h e szanwise concepts are designed f o r chordwise thermal stresses. When t h e spanwise t u b u h r concept was compared t o t h e chordwise tubular conce'p;t;, it was found t h a t a convex- beaded upper surface f o r chardwise stiffening was l i g h t e r than a tubular uppez surface. While panel configurations are about equal i n weight f o r t h e 7 d .d. con- ditions, the convex-beaded concept does not involve the weight of heat '.Ids . I . r surface as does the tubular concept. !The net result is t h a t t h e convex-beaded is lighter.
In comparing t h e s t a t i c a l l y determinate and chordwise concepts, t h e stakically determinate design permits a different gradient and a different mean temperature This concept provides no between the w h g and fuselage without t h e m 1 stress.
no resistance t o d i f - resistance t o thermal bowing i n t h e chordwise direction and While t h e s t a t i c a l l y determinate f e r e n t i a l expansion between wing and fuselage.
concept requires additional fuselage and f i t t i n g weights, t h e weight is s t i l l less than the chordwise-stiffened concept because of spanwise stiffening and thzrmal- stress alleviation provided by $he s t a t i c a l l y determinate concept,. However, t h e s t a t i c a l l y determinate concept is not iowest in weight because t h e semimono- coque spanwise concepts also have low taermal stress, require no f i t t i n g 3 , and requtre no added fuselage stiffening.
Results show t h e waffle t o be about 4.0 lb/f't* heavier than honeycomb structures. I n i t i a l screening (see table 13-1) indicated honeycomb t o be i n i t t a l screening was based only on inplane heavier than waffle. Iiowever, the compressive loads for an a r b i t r a r i l y selected panel size.
These factors yielded minimum gage f w both waffle arid honeycomb panels with t o t a l honeyco;.:, weight less favorabl. recause of more edge-member weight. Moreover, waffle is con- sidered t o bc -' more state-of-the-art cofistraction. Therefore waff.ie was
considered for detail analysis . However, later analysis with optimum-size
panels (including effects of pressure), show that the honeycomb structure has half the substructure weight of the waffle-panel structure. In addition, when air-pressure loads were included in t h e analysis, t h e waffle panels were shown t o be less e f f i c i e n t than honeycomb. Consequently, the honeycamb-core sandwich structure is considerably lighter than the waffle monocoque structure.
'Phis result indicates that i n i t i a l screening should include effects of sub- structure and presswe loads.
Since monocoque panels support b i a x i a l loads, %hey might be expected t o be of minimum weight. However, two factors r e s u l t i n t h e spnwise semimono- The span- coque structures having Xes;; weight than the monococpe stxuctures.
wise semimonocoque beaded ar:d tubular concepts are new and were found t o be more e f f i c i e n t than the honeycomb-sandwich concept. Another reason t h a t semi- monocoque structure is lighter than the monocoque is that chordwise t h e m 1 loads are imposed only on the r i b caps nfl t h e spanwise concept. Monocoque structure, however, provides chordwise ciffening ( l i k e the chordwise-stiffened semimonocoque structure) which offers bending resistance t o the moment derived throUgh the wing and fuselage. A better from mismatched ternperahre gradients m t c h of temperatures arid gradients might be achieved by using thermal pro- tection on the upper surface, but t h i s would negate Yne smooth surface offered by monocoque concepts. Also, bas& on seminonmoque choidwise stiffen- re- sults, the reduction i n primary-structure weight m a y be less than t h e added thermal-protection system weight, The two spanwise semimonocoque concepts each require shields t o provide a r e l a t i v e l y smooth surface, so t h e beneficial t h e r m 1 e f f e c t s of shields are inherent i n t h e concepts .
13- 26 TABLE 13-1 INITIAL PANEL WEIGHT SCFWNINC a OFMONOCOQUE PRIMARY STRUCTURE
-
- I -
- -
-
endidate
- -
tton -
Pruiel -
Materia I# ‘Basic height D p t ~ ~ tilent tPancl tT*t,t Totn onfiguratic factor, shfelc in.
ill.
NOF in.
i l l . a i l l .
lb/t’t
- - -
- -
-
grit Uaffle Red 51 .03N .3Y1 1 . 2 4 .0302 0 .OI.L’ 1 .hi unflangea llaynes 25 .400 . 0 3 1 i 1 . a i .03~2 0 .03u3 1 .a3 ; 5 0 x 450 U a f f l e grit Red bl 241 1 . 3 0 -0354 .Oh60 0
. O t 6 0
1 . 9 7
*la& -
Haynes 25 .243 1 . 3 0 ,0462 -0356 0 .0162 2 . 2 0 450 x 450
F unflanged Uaffle 00 x 900 * rll . 41
.547 .0310 .0128 1 - 3 8 0 .0t28 f .& Haynes 25 -530 -0310 .0428 0 ,0423 1.38 2 . 0 4 Waffle grit Red 4 1 . 3 1 2 -0370 1 .GO .0518 0 .0518 2 . 2 2
flanged - Haynes 25 1 . 4 0
- 9 1 0 370 -0518 0 . 0 5 1 8 2 . 4 6
Honeycomb aene’ $1 .0308 *l97 1.80 0 2 . 3 8 -0555 -0555 sandulch Haynes 25 -197 . 0 3 @ 1 . 8 0 0 2 . 6 ; -0555 a0555 Truss-core Red 41 -193 -0362 1 . 5 0 .OS62 0 -052 2.33 IInynes 25 -0362
- 1 9 3 1 . 5 0 .Os42 0 .0542 2 . 5 8
- -
- - - - -
Uaffle grit .TOT .051& 1 . 2 ; 0 0637 -0637 2 . 7 3
unflanged - .lo40 1 . 2 4 .la0
. e 5 9 0 1290 6 . 1 3 450 x 450 Uaffle grit . : ? 5 .Ob99 1 . 3 0 .0636 0 -0636 2 . 7 3 (NA) flanged - (NA) 1 . 3 0 (NA) 0 (NA) (NA) 450 x r50 Uaffle grid .OL59 e734 1 . 3 8 ,0634 0 ,0631 2 . 7 2
unflanged - ,011 .lo18 1 . 3 8 .1404 0 . 1 Got
6.68 00 x 900 Waffle grid ,643 . O i b 1 .so ,061 5 3 .0615 2 . 6 ;
flanged -
1 . : o ,1360 0 1 360 -973 0970 6 . 4 6 0 ’ x 90° Honeycomb 1 . 8 0 ,0654 0 . a 5 8 1 * 709 -0363 2 . 8 0 sandwich 1 . 8 0 ,1710 0 .?640 1755 -0953 7 . 8 0 Trusseore ,514 ,0606 1 . 5 0 ,0910 0 .a910 3*% sandwich L 678 1.50 ,1470 0 .1570 7 . 0 0
-
- -
- -
-
a Compression panel; aspect ratio, a/b = 2, b - 20 in.
__ - d d d d d d 0'0' d d o ' d d d d d mc- lnb lnF mLn r l r l r l r l cucu
a 0 0 0 0 0 0
d d 0 0 d d d d d b 0 0 d d d d
-
9 .i
Pi o ' d d d d d d d d d d d d d d d w l n l n o o 0 0 FF Lnlnoo 0 0 bb r l r l c u c u c u c u r l d r l r l c u N c u c u r l F I . . . .
2 ; r i r i r l r l r l r l cncha3a3 r l r l r l r l cncna3a3 r l r l F I F I c u c u c u c u N N c u c u m m cum cucu 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d d d d d d d d d d 0'0' d d d d lnln lnln Inn n L n 0 0 c u c u c u c u 0 0 0 0 c u c u c u c u 0 0 0 0 a3a3 m a 0 0 0 0 ma3 wv3 0 0 (u'd d d d d d d d d do' d d d d h E m E l - 13-28
I I
T - 1 a Ur-i .
c, c .
b D c dcl a , X I 4 d .rl k a , -P
k
TABLE 13-4 MANUFACTURIXG PRCJCESSES FOR CANDIDATE MONOCOQUE PANEL CONFIGURATIONS ~ ~~ ~
-
Panei configuration Manufacturing process
-
Unfl Anged waffle grid Electro-chem-milled waffle grid Flanged waffle grid Electro-chem-milled waffle grid Diffusion bonded flanges Brazed face sheets and core Honeycomb sandwich Resistance welded core Diffusion-bonded face sheets Truss-core sandwich and core 13-30 0 0 0 0 O O O O O O O 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 3 2 2 s232z2s 2 3
0 0 0 0 0 0 0 0 0 e o 0 0 0 0 0 0 0 0 0 0 0
rl+d = ( O W 23zzs4 z s
0 0 0 0 0 0 0 0 0 0 0
* * * a m m m m m m a
3 %
R
13-31
ii .i
T -
L
J3-33
I ,', I TABL?Z 13-8 Inplane loads plus Unit pwnel Inplane loads only normal pressure weight, l b / f t 2 -45' x 45O oo x goo -45O x 4 5 O oo x goo W a f Ele waffle waffle waffle Upper surface 1.68 1.59 2 . 2 3 2 . 1 3 Lower surface 1.94 2.26 2 . 5 9 3-03 T o t a l 3.62 3.85 4.82 5 . 1 6 3-3-34.
13-35
\
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0 3
I ?- m
n w s r-
In f cu M
ch 4
9 9 ?
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r - l o o o o o o o o
I
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I F 6
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0 c- % 8 f =I-
In M 0 f "9 . ? (u. .
0 0 cu r-l 0 C 0 N O O d O O O O O cu 0 .
;t:
d 2 .!I
d .i .A .a'
n :.
d R I$
13-36 crc
w
rl I 1 m o o r 1 o o o f d
n d
co 2
a , In
C d 8 cu
?
?
k k 0 0 0 k
a , cg %
Ln cv)
iK I-l Ln
3 In
0 In Tu 3 rl M ? ?
0 9 (u 0 0 0 In
k
M (3\ c n
%
d
rl d d ! & 0 cu cu 00 rl 00. ?
? ? '0.
~ 0 0 d 0 0 0 0 0 I1 a , % k a ,
@
a , 4J n k (3\ a , C U M Ln
! 3
a
v ? ? 9 i - l o o r l o o o o o 13-37 I rl m rl 9 .
A M m m m .
kChr10 m a 0 N
2 .a
? ? e ?
0 0 0 0 0 0 0 0 0 0 0 0 N h .
cc cr)
P P .a
a3044 n .
f P - l C - 0 c 1 d CU ma3 CU Q - r l 9 9 9 : 0 0 0 0 4 Ln cu , cu % i-4 m 3 cu cu I 4
9 9 9
I 9
0 0 0 , 0
- -
% a .
m 3 w a c 3 J c P -rl 9 9 9 9 0 0 0 0 mcua cu m c u b a a C 0 0 m on000 rl cu tnrn 4 4 - 0 3 rn
9 9 5 9 9 9 9 9
0 0 0 0 0 0 0 0 cu cu 4- c!
0 d
--
. \ .
P* 2
0 0 0 0 k . . .
a a k 0 0 0 0
2 4 W S cd rlcuMA-
O II II II I I e II II I 1 It
I3 P P P P 6 P P P P
$ P P P P
I
13-39
i'
TABLE 13-14 MONOCOQUE WAFFIX COMFONEPI' WING WEIGHTS, INBOARD AREA, a/b = 2.0 Panels Between BL 120-220, N o Heat. Shield
-
Equivalent panel thickness, t, in.
Item b = 10 in. b = 20 i n . b = 30 in. b = 40 in.
0 . 08093
Upper surface 0 03750 0.05294 0.06707 Lower surf ace Panels 0.04566 0.06211 0.08265 0.10537 Total 0.08316 0.1305 0.14972 0.18630 Upper surface Caps and 0.02351 0.01835 0.01750 0.01769
Lower surface closeouts, 0 . 03168 0.01944
0 . 01763 0.01745
single shear 0.03514 0.05519 0 03779 0.03513 a
Rib and spar webs 0 109 0.0546 0.0354 0 . 0272
Total 0.2474 0 . 2074 0.2213 0 . 2486
a 600 Circular-arc corrugation: thickness, t = 0.015 in.
average depth, h = 40 in.
13-40 TABU 13-15 MONOCOQUE WAFFU COMPONENT WING WEIGHTS, OUTBOARD AREA, a/b = 2.0 Panels Between BL 220-350, Heat Shields on Lower Surface Only
-
Equivalent pcznel thickness, t, in.
b = 40 in.
Item b = 10 in. b = 20 in. b = 30 in.
~ 0.05158 o ,06606 0.08138 Upper surface 0 03789 0.0 5489 0.08 589 0.11927 Panels Lower surf ace 0 9 06733 0.09278 0.20065 0.11891 0 15195 Caps and 0.01718 Upper surf ace 0 02379 0 801795 0.01755
0.03164 0.01878 0 . 01838
closeouts, 0 901597 Lower sufrace single shear 0.05543 0 03673 0 -03315 0.03593
(4
0.0545 0.0270 0.0182 0 . 0136
iiib and spar webs Heat shield (b ) 0.0157 0 8 0157 0.0157 0.0157 -.- 0.2190 0.2659 T o t a l 0.2184 0.1383 a 600 Circular arc corrugation: thickness, t = 0.015 in.
axerage depth, h = 20 in.
bCircular arc corrugation: skin thickness, ts = 0.010 in.
13-41 TABLE 13-16 M)NOCOQVE WAFFLE PANEL ASPECT RATIO OPTIMIZATION MATRIX
Panels between BL 120 - 220
H e a t shield on lower surface only -
. ?
Upper surf ace Lower surface T = lbOO°F T = 145OoF It a/b = 1.0, 1.5, 2.0, 2.5 a/b = 1 . 0 , 1.5, 2.0, 2.5 Lo ads
-
Pressure and inplane loads Edge eccentricity, e = + 0.02 in.
I n i t i a l deflection due t o bowing, 6max = 0.01 x b in.
13-42 TABLE 13-17 MONWOQUE WAl?FLE COMPONENT WING WEIGHTS, INWARD AREA, b = 20 INCHES Panels Between B.L. 120-220, Heat Shields on Lower Surface Only ~-~~ ~ ~ ~ ~
-
Equivalent panel thickness, t, in.
a/b = 1.5 a/b = 2.0 a/b = 2.5 Item a/b = 1.0 0.0522 Upper surface 0.0422 0.0478 0.0553 Lower surface 0.0547 0.0545 0.0530 0.0534 Panels
0.1023 0.1052 0 . 1087
Total 0.0969 0.0206 0.0202 0 0207 0.0206 Upper surface Caps and 0.0175 0.0152
Lower surface closeouts, 0.0246 0 . 0204
0.0452 0 . 0406 0 . 0382 0.0358
single shear a 0.0605 0.0545 0.0508
Rib and spar webs 0 . 0726
b 0 0157 0 00157 0.0157 0.0157 Heat shield
o . 2191 0 . 2137 0 . 2110
Tot a1 0.2305 a 600 Circular arc corrugation: thickness, t = 0.015 in.
average depth, h = 40 in.
bCircular arc corrugation: thickness, t = 0.010 in.
13-43 HONEYCOMB-CORE SANDWICH PAN& CLOSEOUT COMPARISON
I
Smooth Aero drag pmalty Str. wt.
Wing wt. (9774 f t 2 ) wt.
Weight saving TABLE 13-20 WING UNIT WEIGHTS FOR MONOCOQUE HONEYCOMB-CORE SANDWICH PANELS, INCLUDING SMOOTH CLOSEOUT& Equivalent thickness E, in.
Item Center Inboard Outboard.
- 0.0415 0.0440 0.0400 0.0438 0.0522 0.0348 0.0893 0.1002 0.0788 Smooth cap and 0.00807 0.00787
Upper, * 0.00793
closeout 0.00403 Upper, Y 0.00397 0 00393 Total 0.0119 0.0118 0 0095 Iower, x 0.00787 0.00787 0 00753 Lower, y 0 9 00393 0.00393 0 00 377 T o t a l 0.0118 0 . 0 ~ 8 0.0113 Total 0.0237 0.0198 0.0231 R i b and spar R i b w e b 0.0182 0.0091 webs Spar web 0.0091 0.0046 Total 0.0137 0.0273 W e b s intersection Total 0.000281 0.000563 - Dyna f l e x Insulation 0.00146 insulation Packaging 0.00202 Total 0.00348 Corrugated heat Corrugation 0.01660 shield Clip 0.00485 Total 0.02145 Oxidat ion Total 0.005664 Fastener T o t a l 0.00403 0.00453
-
T o t a l equivalent thickness, in. 0,156991 0.150505 T o t a l u n i t weight, l b / f t 2 6.250 6.458 6.737 Average unit weight, l b / f t 2 6.442 -- ahsulation and heat shield a t outboard lower surface, ba = 80 in., b = b in., d b = 2.
‘Includes brazing a l l o y (te = 0.002 in./panel).
13-46 h h P 3-3-48 h .
*.a
n 13-49 I' TABLE i3-24 CO1\IPONE!NTS WEIGHTS F O R SEMIMONOCOQUE SPANWISE STIFFENED TAAPEZOIDAL CORRUGATION PAlJELs Center Inboard Outboard Item t, in. t, in.
t, in.
Panels upper 0336 0356 .0244
Lower ,0242 . c y 6 0215
Caps Spar
Upper 0 0011 . 0011 . 0011
L o w e r L 0011 . 0011
. 0011
Rib Upper .0042 0031 Lower .0045 0040 .0050 - Closeouts .0074 0079 .0087 Webs spar 0084 .OO% 0047 R i b .0252 0 0240 .0230 Posts .0007 0007 .0006
-
-
h s u l a t ion 00685 Heat rhields .0131 .0263 Fasteners 0036 .0036 0050 -- Oxidation .00234 .00213 .00676
e : : l
Totajl ( i n . ) .P2 7 * 1527
_.- - .-. ..--.-- -
Unit w t . (lb/ft2) 6.45 5-55 6.55 Average unit w t . (1b/ftt2) 6.17 Q)
3 k
w w cu V (u
-
(u
\D 9
c!
$ cu A-
-
h .
&2 z: 0 . r I M h .
. o c '?
-. I
i l \ r- 03
ill .$
0 1 :7 li' d .I I (r) I 1 \ f2' d 0 .I I I-l (u (u w s d I-l rl F l .rl 0 0 0 13-52 13-53
+
I ...
I' 5 13-54 I \o m S R ri oi In In 0 e;
s
I r i ~ \I) 0 rl
'@
I n t - d (3 ;t.
rl I 0 0 In d a .
.
-&
+
c ! d 13-55 a0 v:
T
I
L
.
E . @ 0 ln
s ?
m m d m 6-4 m (u n (u (u 9 9 ? 9
-
M 02 Yi m ?
g: P
x
m
6 h
u(u 13-56
L . < @
t - t- "-57 . . e . .
r- E - u E - E - t - c - I 13-58 Q)
x
i 13-59
i
TLBLl3 13-34 DESICII TEPDPERATUIIES AND GE)3I"RY FOR I'43NOCOQW WAJ?FLE PANELS, PAFQIAL HEAT SHIELD AT OUTBOARD A E X E A JLM3R SURFACE Center Inboard Outboard
-
--
Lower Lower Lower Upper
-
1550 1330 1500 1530 1385 ,
-
3.084 W, lb/ft2 2.859 3.159 2.425 3 519 3.313
-
0.06662 0.07360 0.05651 0.08200 0.07186 t, in. 0 .OW21 0.5944 0.7186 0.7488 0.6622 h, in. 0.6744 0.5797 1.051 1.036 0 9196 1,0143 1.087 1.023 . P, in.
0.02641 0.0200 ts, in.
0.02043 0.02296 0.0200 0.02724 tw, in.
0 a03789 0.04025 0.02814 0.04410 0.04483 0.04030 0.05227 0.08653 0.09842 0.06674 0.07957 0.04955 e l l ' i n .
0.1492 0 2275 0.1423 0.2520 0 2093 0.1851 e339 in.
0.2569 0.3021 0.2265 0.3276 w in. 0.2571 0 3307 0' TABLE 13-35 DESIGN TEMPERATURES AND GEOMERRY FOR MONOCOQUE WAFFIX PANEIS, PAFULAL HEAT SHIELD AT OUTBOAFEI W LOWER S W A C E , WITH INSULATION Center Outboard Lower Lower Lower Upper
-
. Temp., 1260 Item . OF 1450 1530 1500 1330 1370 2.821 3.392 3.529 3 039 1.942 2.935 0.07904 0.08224 0,07082 0 06840 0 06 575 0.04525
0.7143 0.6213 0.7078 0.6436 0 . 4642
0.7259 1.031 1.022 1.076 1.105 0.7991 0.8305 0.02015 0.02683 0.0200 0.0210 0 .02001b 0 .om0 0.04205 0.03097 0.04395 0.03975 0.04375 0.02395 0.09274 0.07582 0.06969 0.08106 0.03582 0.07457 0.2065 0.1870 0.2162 0.1982 0.1052 0.2395 0,2544 0.2994 0.2877 0,3222 0.3319 0 1339 TABLE l3->6 DE::ICII TEMPERCITURES AND GEOMETRY F O R MONOCOQUE W A J ? F T 8 PANEIS, HEAT SHIELD ON ENTIRE M W E R SURFACE Center Inboard Outboard
-
Upper Lower Upper Lower c r c
- - -
1075 1265 1200
1390 1385 I 1550
-
-
3.792 2.352 3.350 2.628 2.728 3 - 9 5 .
0 . 08836
0.05482 0.07806 0.06125 o .09100 0.06357 0.7909 0.6235 0.5742 0.6222 0,8176 0.7155 1.008
1.194 1.081 1 . 185 1 122
0.9755 0.02012 0.02708 o ,02129 ObO2!j85 0.3293 0.02538 0.04565 0.02810 0.04514 0 .03200 0 -04368 0.04746
0.1084 0.04150 0 . 08730
0 . 04702 0.06801 0.09820
0.2740 0.1255 0.2286 0 . 1364
0 . 1838 0.2584
0.3503 -0 2328 0.3425 $0 3088 0.208 0,3537
- -
TABLE 13-37 DESIGH TEMPEFtATUFBS AND GEOMETRY FOR J!X)NOCOQ~ WAFFIX PANELS, HEAT S H I E L D ON ENTIRE LOWER SUIIFACE, WITH INSULATION AT OUTROARD ABEA . _ _ u Outboard
Center I Inboard
-
Lower Lower Lower upper Upper -.
1265 1200 1075 1390 1365 -r 2.120 3.689 2.792 2.780 3.253 3.009 0.04941 0.07581 0.06507 o ,06478 0.07011 0.7082 0.7668 0 5927 0,6248 0.6269 0,5985 1,122 1.021 1.184 1.197 0.9779 0.02016 0.02597 0.025g7 0.02204 0.02619 0.0200
0.02475 0,04487 0.04605 0 e03415 0 . 04467
0,03945 0.03619 0.08243 0 1033 0 e05125 0.06938 0.05917
0.1113 0.2188 0.2625 0.1468 0,1866 0 . 1660
0.2851 0.2668 0.3186 00.2563 0.3775
-
- ----- - - 13-61 TABU3 13-38 DESIGN T.EMPERATURE8 AND GEOMETRY FOR MINOCOQUE W A F F L E PANELS, A 0 HEAT SHIEL33 AND NO INSULATION ~ I Inboard out Center oard l m I Upper Lower Upper Lower UPPe r Upper I 1534 1420 1504 I
-
I
' I 3 . 6 1 1 3 133 2 . 9 6 4 ' 5,228
W, lb/ft* 3 -267 2.295 -
0 . 0 8 1 4 4 0.07301 0 . 0 6 9 0 8 t, in. 0 . 0 7 6 1 4 0 . 0 5 3 4 7 G . 1218
0.7604 0 . 6 5 1 2 0 . 6 6 2 L . h, in.
0 7303 0 5 7 0 7 1.1177 1 . 0 6 2 1.065 0 . 9 5 8 2 1 . 1 5 : 1 . 1 8 9 p, in. 2 . 4 2 6 0.02123 3 . 0 2 5 6 3 0 . 0 2 1 0 4 0 . 02124 0 . 02817 ts, in.
, 0 . 0 6 0 3 9 0.04633 0 . 0 3 7 0 1 0 . 04410 0 . 0 4 1 9 6 0 . 0 2 8 0 7 tw, in.
0 0 ' 7 1 5 3 0,09782 0 . 0 6 4 7 2 0,07433 0 . 0 8 7 C 3 0 . 0 3 4 4 4 0.07418 e 1 1 ' in.
0 . 2 3 0 6 e 3 3 ' in.
0 . 2521 0 . 1 7 9 3 0.1994 0.1060 0,2244
0.3455 0.1423 0.2823 O 3106 -0 2991 w in.
0 . 1013
0 ' I I 23-62 TABLE 13-39 Equivalent thicknes
I
- in.
-
Item Center Inboard Outbo ai- d
I
J P P r 0.0736@ 0 .oaao 0.07186 Panels
Lower 0.05651 0 . 07721
0.06662 Total 0.1301i 0.15921 0 0 13848 0.02052 0 ,01797 I cap m m a Vpper, spar I diwction 0 . 0 0 9 1 1 3 0.01026 0 00898 closeout, Tot a1 0.02829 0.03078 0,02695 single shew .Cower*, rib direction 0.013f9 0.01657 0 , 0 1 1 1 4 0 Lawer, spar direction 0.00659 o.ooa2g
Total I O.Oig78 0.02486
0.05564
+ ? + Rib a n d
0.0363 spar webs 0,0182 0.0132 0 -0545 i’eb Total 0.00225 o ,001125 intersect ion Insulation
Paclcaging --
insulation --
I --
-0 no
I Total I --
-- Cor1 U C J ~ t ed
Corrugation 0.01660
heat shield Clip --
--
I 0.02145 0000485
Total I
~~ ~
Oxidation Total 0.00097 0.000216 I
0.005552 . - Fastener Total 0.00541 Total equivalect thiclcness , in.
0.21 131
u. -
TotaL unit weight, l.b/ft Average utiit d.:ight, I b / f t XI. 8x1 TABLE 13-10 BREAKDOWN OF WING WEIGHTS FOR MONOCOQUE W A F n E PANELS
WITH LOWER SURFACE OUTBOARD HEAT SHIELD AND INSULATION^
Equivalent thickness x, in.
Item Center, A
' Outboard, C Inboard, B
I
-
0.0708 0.0684 0.0790 Panels 0.0452 0.0658 0.0822 0.00173 8.00173 0.00173 Spar, lower 0.00173 0.00173 0.00173 (minimum Rib, upper 0.00345 0.00345 0.00345 gage) Rib, lower 0.00345 0.00345 0.00345 0.0222 0.0245 0.0207
Closeouts I = 0.0180 0.0217
0.0108 I 1 I Rib web 0.0363 0.0363 0.0182
I Webs
I Spar web 0.0182 0.8182 0.0091
0.00225 0. GO225 0.00112
E:rsections 1
I I - - 0.00348 Insulation - - 0.0166 Corrugation Heat shields
1 - -
0.00485 I Clip
0.00047 0.00050 0.00566 I Oxidation I Total
~~
0.00541 0.00541 0.00541 I Fasteners I Total
~ ~ ~~ ~ -~
Total equivalent thickness, in. I 0.2498 I 0.2804
I 0.2199
-- Total unit weight, Ib/ft 12.03 0.44 aa = 40 i n . , b = 20 i n . , a/b -- 2.
13-64 TABLE 13-41 COMPONENT WEXGm FOR MONOCOQUE W A F F I X CONCEPT, HEAT SHIELD ON EXPIRE IOWER SURFACE Equivalent thicknes in.
Item Inboard (B) (Outboard (C ) Center(A) 0.08836 0.07806 Uppe 1- o .06357 Panels Lotre * 0.05482 0.06125 0.09100 Total 0.14318 0.13931 0.15457 Uppei., r i b ilirect ion 0.02X)l 0.01927 o .01653 Uppel-, spai.
Cap and sire c t ion 0 .on01 0.00964 0.00826 closeout, Total 0.03302 0.02891 0.02k('9 single shear Lower, r i b direction 0.01325 0.01330 0.02161 Lowe?, spar direction 0.00662 0.00665 0.01080 Total 0.01987 0.032k1 0 01995 Total - * - ! .- 0.05289 0.04886 0.05720 Rib auld R i b web 0.018s 0.0363 0.0363 spar webs Spar web o .0182 0.0182 o .0091 Tot a1 0.05kj 0.0273
1 0.0545
W e b intersection
Totai o .00225 0.00225 0.001125
-- -- -_
Dynaflex -.lsulat ion
-- insulation -*e
Packaging -I Total Corrugation 0.0105 Corrugated 0.0105 0.0166 0.00448 0 .ook85 Clip 0.00448 heat shield 0.01498 0.02145 Oxid.& ion o .00098 0.005552 - 4 1 0.00541
A ? . . 0.27461!- 0.26629 0.27261
Total unit weight, lb/i't 11.785 11.427 11.698
-
Abei-age u n i t weights, lb/f; 11.670 A
-
13-65
f
TABLE 13-42 COMPONENT WEIGHTS FOR MONOCOQa WAFFU3 CONCEPTS, HEAT SHIELD ON ENTIRE IXlWER SURFACE, WITH INSULATION AT OUTBOARD A m a Equivalent thickness, i n .
Item Outboard (C)) Center (A) Inboard (B)
0.061178 0 08597 o .07581
Upper 0.01~341 0.06507 Lowe? Panels Total 0.11!088 0 13538 Uppe;., r i b direction 0.02131 0.01878 o .01671!- Upper, spar direction 0.01065 cap an1
o .00837
0 .00939 Total 0.03196 closeout, 0.02817 0.02511 Lower, r i b single shear direct ion 0.01229 0.01398 Lower, spar
direction 0.0061~!. o .006gg
0.00770 Total 0.01843 0.02097 0.02311 Total
0 A5039 0 . 04914 0 .ob822
0.0363 Rib and R i b web 0.0363 0.0182 0.0182 0.0182 spar webs Spar web 0 .oog1 0.0545 0.0545 Total 0.0273 W e b intei-sect ion Total 0.00225 0.001125
--
Dynaflex Insulation 0.00146 insulrtt ion Packaging O*OOx)2
--
Total 0.00348 Corrugation Corrugated 0.0105 0.0166 0 . 0 1 0 5 Clip 0.00485 heat shield 0.00448 0.001!-48
Total 0.01A98 0.01498 0 . 0 2145
~ 0.00143 Oxidat ion
o .00098 0.0053116 Total
0.00541 0.00541 Fastener Totol 0.00541 Total equivalent thickness,
0 . 26814 i n e 0.26434
0.211.723 10.609 Total u n i t weight, 1b/rt2 11.343 11.506 Totol unit weight, lb/f-b 1 1 . 0 8 1 1 .
--
a a = 40 in., b = 20 in.
13-66 TABU 13-43 COMPONENT WEIGH!l'S FOR MONOCOQUE WAFFLE CONCEIT, NO HEAT SHIELJX AND NO INSULATIONa Sauivalent t h i ckness in.
~ .~ Item Outboard Inboard Center uppel- 0.07616 0.081%~ 0.06308 Lower 0 .Ori3O1 0.1218 Panels 0 -05347
Total 0 . 12961 0.15445 0.1W88
Upper, r i b direct ion 0.02080 0.01923 0.01753 Upper, spai- direct ion 0.00962 Cap and 0.01040 0.00877 Tot31 0.02885 0.02360 closeout, 0.03120 Lower, r i b single shear direct ion o .01225 0 -01586 0.03186 Lowef, spar dii*ection 0.00613 0.01591~ Total o .01838 o .oh782 Total 0.04723 0.07lk12 R i b and liib web 0.0363 0.0363 0.0182 spar webs Spa]: web 0.0182 0.0182 0 .oog1 Tot a1 0.05&5 0.05h5 0.0273 W e b intersection 0.00225 Total 0.00225 0,001125 Dynaflex Insulation insulation Packaging Total Co;.;.ugat ea Cos;.ugat ion heat shield. c1 i p Total ~~ ~ Oxidat ion Tot a1 0.000976 0.000224 Fastener Total 0.00541 0.0054-1 , Total equivalent thickness, i n .
0.27182 0.23998 I ..II I Total u n i t weight, lb/ft io. 298 I
-
Average u n i t weighi, lb/ft;' Average u n i t weighi, lb/ft;' " ( a = 40 in., b = 20 in,) " ( a = 40 in., b = 20 in,) 13-67 13-67 TABLE 3.3-4& AVERAGE WING UNIT WEIGHTS FOR VARIOUS PANEL WIMIHS AND ASPECT RATIOS, MONOCOQUE HONEYCOMB- CORE SANDWICH PANEIS Average wing unit weight, lb/ft2 Average wing unit weight, lb/ft2 m Panel width, b, in.
39 40 50 60 39 40 5 0 60 Aspect ratio, a/b
1 . 0 - 6.959 6.782 6.822
- 6.608 6.576 6.805
1 . 5 2.0 6.712 6 . 4 7 3 6. go8 13-68 TAE3LE 13-45 FINAL TEMPERATURES AND GE0ME;TRY FOR MONOCOQUE HONEYCOMB-CORE SANDWICH PANELS WITH OUTBOARD LOWER SURFACE HEAT S H E L D AND INSULATION a,b Cciitcr ~ llppcr Lower Uppcr Lo W'CL r Lo we 1 '
I
1003 1 2(i 3 1 33 5 Max. fiwr -0.5-g 1313 1595 1412
-
shcct t2.0-g 1026 1534 1245 1572 1408
- -
- -
temp. , OF Cruise 1277 1927 1130 1340 1123 1315
-
w@), ll)/ft2 1.820 1.800 1.760 1.070 1. 990 1.520
I tdrt 3 7. (io0 7.120 (i . (i 90 7.070 5. 740 (i. l(i0
W '
-
0.042 0.042 0.041 0.04(i t, in. 0.046 0.035 0.935 0.898 0.950 0. 937 0.963 0.714 h, in.
tl, in. 0.015 0.015 0.015 0.018 0.018 0.015 t2, in. 0.014 0.015 0.014 0.015 0.018 0.012 0.002 0.002 tc, in. Q. 002 0.002 0.002 0.008 0.294 0.35tl 0. 334 S, in. 0.271 0.291 0.308 0.450 0.449 0.461 0.420 0.492 0.319 Z, in.
w ! ' ) , in. -0.970 1.610 -0.820 0.230 1.160 -0.950
:I a 80 in., b 40 in., ;Lib 2.0.
I3 Effective dc sign condition under1incd.
c' Nominal, docs not includcb core flanges and corrug:itions.
dMidpancl deflc!ction.
Chordw i se a -4 t i (Exterior) 1 '2 f = panel equivalent thickness w = panel equivalent unit weight 4 = density 13-69 .quivalent thickness, f, in.
Item Center, A Inboard, B Outboard, C Uppera 0.0449 0.0434 0.0480 Panels Lowera 0.0443 0.0482 0.0372 Caps 0.00097 0.00097 0.00097 Spar, upper (minimum Spar, lower 0.00097 0.00097 0.00097 gage) Rib, upper 0.001 95 0.00195 0.00195
Rib, lower 0.00195 -1 0.00195 0.00195
0.00878 0.00888 0.00888 Upper Closeouts 0.00868 0.00878 0.00848 Lower ~-
- 0 . 0 0 9 1 -1
0.0182 0.0182 Rib web Webs
~~ I 0.0046 0.0091 I - - 0.0091 Spar web
Web
-1
intersections 1 0.00056 1 0.00056 1 ~ 0.00028 I
Insulation Total -
1 - 1 0.00348 1
~ Corrugation - -.
0.01660
Heat shields Clip - -
0.00485 Oxidation Total 0.00110 0.00077 0.00599
i --
1 Fasteners Total 0.00417 0.00421 0.00404
Total equivalent thickness, in. 0.1456 0.1479 0.1573 6.25 6.35 6.75 Total unit weight, lb/ft I Average unit weight, lb/ft2 6.47 aIncludes weight due to core corrugation and flanges.
13-70 TABLE 13-48 FINN, GEOMETRY’ FOB SENIMONOCOQUE SPANWISE-STIFFENED TUBULAR PANELS I,, in. Pilch, in.
50 3.429 r 0.950 40 2.355 Upper 0.0287 0.011 1 3 (120-212) Lower 0.0284 0.011 0.800 40 2.062 0.010 0.750 40 1.964 UPPLT 0.0258 C (212-350) Lower 0.0254 0.010 0.600 40 1.672 b 2 - - panel equivalent thickness.
1, panel length (rib spacing).
I> Critical Pitch - - Plight 0.5 centcr-to-center in. condition flat. all of wing stifher.
arcws +2.0 g .
( 7 ) I \
13-73 TABLE 13-43 BREAKDOWN OF WING WEIGHTS FOR SEMIMONOCOQUE SPANWISE STIFFENED TUBULAR PANELS G T H FULL €EAT SHIELDS AND LOWER SURFACE OUTBOARD INSULA T I O N a Item Equivalent thickness, ^t, i n .
Center, A ---_ -. - Pancls 0.0292 0.0287 0.0258 0.0258 0.0284 0.0254 I- ~ Caps 0.0011 0.0011 0.0011 Spar, lower 0.0011 0.0011 0.0011 Rib, upper 0.0027 0.8028 0.0032 Rib, lowcr
0.0032 0.0034 I- 0.0028
c10sc0uts Upper 0.0032 0.0029 O . 0024 Lower 0.0020 0.0025 0.0021 - _ - - -
w cbs
Rib web 0.0151 0.0180 0.0120 Spar web
0.0084 0.0096 1 0.0047
Web Total intersections 0.00042 0.00050 0.00029
Total - - 0.00685
Lisulation
1 0 . 0 1 3 1 . - : - 0.0263 1 0.0358
Heat shields Total __L_____
-
Oxidation Total 0,00453 0.00246 0.00633
- - - - --. - --
Total 0.00254 0.00294 0.00294 Fasteners
-
Total cquivalent thickness, in.
0.1124 0.1307 0.1328 l l - - l - - l - - - . - _- Total unit weight, Ib/ft 4.82 5.61 5.70 . _ - I - - L- --
i Average unit weight, lb/ft2 I 5.38
'Area A: a = 90, b = 60, a/b = 1 . 8 .
Area B and C: 2 = 90, b = 40, a/b = 2 . 2 5 .
13-73 % Ln v = panel equivalent thickness.
I ; = panel length (rib spacing).
b = 0.5 in. flat.
Pitch = center-to-center of stiffener.
Critical flight condition all wing areas = +2.0 g.
13-75 I___- - - - -
-
Equivalent thickness, t , in.
Item -- I -- --__ -- _--- -.--- --
Center, A Inboard, B Outboard, C
- . - -- _--I” -- - ---
Panels lJpper 0.0263 0.02G2 0.0221 LOWC k- 0.0196 0.0224 0.0197 caps 0,0011 0.0011 0.0811 Spar, Upper 0.0011 0.0011 0.0011 Spar, Lower 0.0027 0.0028 0.0032 Rib, Upper Rib, Lower 0.0032 0.0034 0.0028 Closeouts 0.0037 0.0038 0.0030 Upper Lower 0.0040 0.0053 0,0036 Webs 0.0084 0.0096 0.0047 spar Rib 0.0151 0.0180 0.0120 Posts 0.00042 0.00050 0.00029
- - 0.00685
Insulation Heat shield 0.0131 0.0263 0.0358 Oxidation 0.00254 0.00173 0.00602
Fasteners I 0.00254 I 0.00294 I 0.00294
Total, in. 0.1039 0.1253 0.1252 Unit wt. , lb/ft2 4.46 5.38 5.37 a Area A: a = 90 in., b = 50 in.
Area B and C: a = 90 in., b = 40 in.
13-76 13-77 ‘l’AI3LE 13-54 I N l ’ A l L l ! l W K D O W N O F WING hUIGHTS FOH SIQlIMONOCOQU& CHORDWISE- :Yl”l’PFENED T U n U I ; A R / C r ) N ~ X - ~ ~ A D E D PANELS WITH WLT, L O m R SURFACE IEAT SJIIELI) AND OUTROARD LOWER SURFACZ INSULATION a ____ ___- __ - . - - . . - -. ..__ -_--
-
[ Item
Inboard, B Center, A 1
Outboard, C Panels
I
0.0292 0.0286 0.0381 Upper Lower 0.0337 0.0261 0.0254 I___I_ -.- Caps 0.0070 0.0069 Spar, Upper 0.0051 0.0070 0.0083 Spar, b w e r 0.0041 0.00167 Rib, Upper 0.00163 0.00115 0.001G7 0.00163 Rib, Lower 0.00145 Closeouts 0.00865 0.00420 0.00491 Lower 0.00805 0.00613 0.00348 -I 0.0329 0.0300 0.0176 0.0150 0.0155 0.0056 Posts 0.00131 0.0010 0.00058
- -
Insulation 0.00685 -__ Heat shields 0.0145 0.0143 0.0230 ~ _--_--___- -I-_- - Oxidation 0.00525 0.00173 0.00588 - - ll.--._-l___.__ Fasteners 0.0044 0.0041 0.0041 Total, in,
0.1619 0.1584 0.1476 I
Unit wt, lb/ft2 6.33 6.67 aArea A: a = 24 in,, b = 60 in.
Area B and C: a = 24 in., b = 75 in.
\ I d ( c u In (0 In VJ m VJ (D
s
Q, cu l-l I", d d
7-
-...!!I-
o , d 23-79 TABLE 13-56 FINAL GEOMFtTRY FOR LOWEST WEIGHT STATICALLY DETEPMINATE PANELS
-
'"w su dit(!(! 1 , in. t , in. R, in. L , in, Pitch, in.
:t J'c'a A Upper 0.. 0314 0.024 1.000 (i 0 4.90s
q, - 120
1.200 GO 5.686 Lower 0.02 1 1 0.016
-
0.022 1.300 50 6.077 I3 Upper 0.0291 BI. 120- 1.600 50 7.248 212 Lower 0.0253 0.019 C Upper 0.0206 0.016 0.750 40 3.929 131, 212- I 0,015 1.350 4 0 6.278
:m Lowcr 0.0199
- t = panel equivalent thickness.
L = panel length (rib spacing).
b = 0.5 in. flat, Critical flight condition on all wing areas = +2.0-g 13-80 TABU 13-57 BREAKDOWN OF WING WEIGHTS FOR STATICALLY DETERMINATE PANELS WITH F'ULL HEAT SHIELDS ANL, NO INSULATIONa -. Equivalent .---- ..--. thickncs: Item Center, A Inboard, B I__- . - _. . . -- ~ -_-.- Panels Upper 0.0314 0.0291 0.0206 Lower 0.0211 0.0253 0.0199 --_I_- l--._l_--l__ I_-_ -.I_- -_ _ _ - __ -. ..-.____ -. .
Caps Spar, upper 0.0022 0.0022 0.0022 Spar, lower 0.0022 0.0022 0.0022 Rib, upper 0.00135 0.0020 0.0025 Rib, lower 0.00165 0.0020 0.0085 -- I~ 1_..---- Closeouts Upper 0.00338 0.00408 0.002G
Lower o. 00387 0.00482 0.0041
.------I -._I_.___I Webs Rib webs 0.0126 0.0144 0.0120 Spar webs 0.0157 0.0147 0.0084
-- - - I - _ _ l - . _ . - - _ - - l - l l l _-..I____-
Web intersections Total 0.00039 0.00044 0.00032 I _ _ --- Insulation
-
Total -.-- -- __.-_.-- €Isit shields 0.0131 0.0263 0.0369 .---- I Oxidation Total 0.0023 1 0.00162 0.007 14 --_*--.--. -.
Fasteners Total 0.00226 0.00254 0,00294 - - Vertical shear 0.0076 0,00819 0.00594 fittings - Total, in. 0.1214 0.1399 0,1292 Unit wt, lb/ft2 5.21 6.00 5.54
2 1 5.55 I Average unit wt, lb/ft
- . --I_- 'Area A: a = 90 in., b = 60 in.
Area B: a = 90 in., b =: 50 in, Area C: a =: 90 in., b = 40 i n .
_ _ 13-81 - ----I------- 00 W 00 s: W v3 W
4 6i j " rl rl d
I -___I__
-+-
0 00 0 00 dt b N W rl
N 6i 1 : & rl
+ + + +
m m m .
4 r.l 1 : 4
0 0 0 0 0 0 m o o 0aCQ 0 0 0 0 0 0 q m m r l 0 w - l d d d d o ' d d d d d d d z g 2 d d d
I
f c,
u
? . 3-8 2 I Waffle grid -.- Electro-chem-milled closeout ; Honeycomb sandwich
,- Chemmilled facing
1 1
L Sheet metal close-off zee
*
Truss -core sandwich Fi {ure 13-3. Typical edge closeouts SOP candidate mmcxoque panel c o n f i g m t i o n s . _ 13-83
i
2 13-84 rl
H
k k X al ?
r-l
r : E !
P
. --
/ 13-84
13-87
Material I
Rend41 S .T .A. @ 1400°F Applied loads - *.I .
p = 2.85 psi (ult)
I
AT = lW0F 1 -
-
.032 '
T = 14000F il-
I
Temperature = 1 4OO0F .028 .024' t .- I-- .020 cn' v) Q) E Y V .- f o) .018 w .- c V Q) Y Y W .012
.om
.004 10 20 30 40 50 60 Length, L, in.
Effective thickness versus length of semimonocoque spanwise- Figure 139.
stiffened beaded panels, lower surface, BI; 120 - BL 220
13-89
.om
R = S O E .- I+- vi .040.
E Y u .- .-E 0, > .032- Y w .024 i .016.
.om:
I
0 20 40 60 80 100 120 1 40 Length, L, in.
. I_ -.
Effective thickness versus length of semimonocoque spanwise- Figure 13-10.
stiffened beaded panels, upper surface, centerline t o BL 220 13-99
I i
Material Rene'41 S . T . A . 5 1400°F .
- Applied loads
p = .975 psi (ult) .08 .07
.G .06
I 2 s I n In Q) c Y .U .05 -f Q) > .- 4- u a 3 Y Y UJ .04 .03 .02 .01
0 20 ' 40 60 80 100 120
Length, - - L, - - -. in. - Figure 13-11. Effective thickness versm Length of semimonocoque spanwise- stiffened tubular panels, upper surface, centerline t o BL 220 Applied loads p = 2.85 psi (ult.)
AT = 100°F
I Temperature = 140OoF
c .- I+- .
VI VI a C Y U .- - c 0.
c C
-
> .- U w 0 20 40 60 80 100 120 140 Length, L, in.
Effective thickness versus length (Upper surface spanwise stiffened)
* ' * t Material - R e d 4 1 (S.T.A. @ 140OOF)
Material
I I Rene‘41 S.T.A. fd 1400’F I
I Applied loads
I I I
2 . 0 .14 .12 s : . a + v .10 I t’ .04 .02 0 20 40 60 80 100 120 140 Length, L, in.
-- ...-..- I -_
Materia I
i I I
500 Ib/in ( u l t ) I ; , * : : .14 .12 t .- I+& .
v) g .10 C Y U .- f 0 ) > .- i=j .08 0 ) cc cc w . 0 6 .04 .02 0 20 40 60 80 100 120 Length, L, in.
Effective thickness versus length of sen;2monocoque spanwise- Figure 13-15, trapezoidal corrugated panels, upper surface, centerline t o BL 220 13-95
2 .o
I .6 1.6 1.4 1.2
1 .o
F
.-
c
d
0.8 0.6 0.4 0.2 0 10 20 30 40 50 60 70 80 9 Semi-central anglel deg .
-_ Figure 13-16 Optimum semimonocoque spanwise-stiffened headed concept 13-yb 30 34 38 42 46 50 54 58 62 66 70 - Rib spacing,; b, in.
Figure 13-18. Weight optimization of semimonocoque spanwise-stiffened tubular panels, BL 120 t o BI, Y I P \ 2 - ( l { \ .12 Panel concept: tubular -_ .~ _ _ Aspect ratio (panel): a/b = 2.0 .10 Tbar (panel): 2.61 t Web height: 20 i n .
Material: Rene'41 S .T .A. 1400'F .06 .04 .02 30 34 38 42 46 50 54 58 62 66 70 Rib spacing, b, in.
- - - - ...
Weight optimization of semimonogue spanwise-stiffened tubular Figure 13-19 e panels, BL 232 t o BL 350 &',, ) Aspect ratio (panel): a/b = 2.0 Tbar (panel): 1.306 t .14 Web height: 40 in.
.12
I I I I I I I
c .- I ; .08 ui In a c Y .- -E a > .- +- u a
z
w 30 34 38 42 46 50 54 58 62 66 70 b, Rib spacing, in, Figure 13-20, Weight optimization of semimonocogue spanwise-stiffened beaded panels, BL 1-20 t o BL 222 .
I 1 I I I 1 I I 1 1 1 1
Pane I concept: -___ Beaded .- Aspect ratio (panel): a/b 2.0 Tbar (panel): 1.306 t Web height: 20 in.
Material: Ren6 41 S .T .A. 140OOF .12 .10 c .- I--
. .08
v) v) 0 ) C Y U .- -f a l > .- c .06 U Q) Y Y w .04 .02 30 34 38 42 46 50 54 58 62 66 70 b, Ribspacing, in.
Figure 13-21. Weight op.1;imiza.t;ion of Gemimonocoque spanwise-stiffened beaded paneb, BL 212 to BL 350 12-I')l C .- I+- Q) > .- c V Q) Y Y w Figure 13-23. Weight bptimization of semimonocoque spanwise trapezoidal- cormgated panels, BL 212 to BL 350 .
.
C
.-
IC’
-
In u) al c Y
.-
al >
.-
.I- o
d
Lu 0 10 20 30 40 50 R i b spacing, b, in.
Figure 13-24, Weight optimization of wing area A (8 2;o BL U O ) of semimonocogue
spanwise trapezoidal-corrugated panels, insulation outboard lower surface 13-134
. 16
. 14
.
S
.-
,z: b u)
z 010
t Y
.-
f a l >
.-
t .08 L E re w
. 04
0 10 20 30 40 50 Rib spacing, b, in.
Figure 13-25. \4eigLt optimization of wing area B (3L 120 t o BL 212) of semi- monocoque spanwise tra~e~ofdal.-corrugated panels, I naul.utj on out- boalad lotrer :jurf;Lce
. 16
. 14
' 2 .12
.-
I+ 4' v) V I a , S Y .10
.-
a , >
.-
+
. $ ' .08
Lu .06
. 04
.02 0 10 20 30 40 50 R i b spacing, b, in, Weight; o p t i m i z n t l o n of Iring area C (RL 212 t o BL 350) of semi- FiGure 13-26, twnrx oque opanwioe trupezoidwl-corrugated pane Is, . L n s u l a t i o n oub- b o m l 1 owcr surface
I Rib spacing, b, in. 1
- - 8 -- - -- - - - I Figure a 1327.- Weight optimization of wing area A ( t o BL 120) of setnimonoc oque , - spanwise trapezoidal-corrugated pane no insulation - - - - -- - e t
.-
1 . 2
- .10
m v) Q) C Y
.-
f .08 a- +
i!
Lu . 0 6 .02 - Rib spacing, b, in, _._ Figure 13-28, WeSgiit 0ptZmi.cation of wing Area B (BL l . 2 0 t o BL 2E) of' semi- monocoque spanwise _. tmpezoldallcorrugaked pant-ls, no inauiatioii 13-~08 L 0 16 .14 0 12 c
.-
\
'* .10
.
Q,
I
C Y Upper panels .
I-
' .08
a l > . 0 6
lower punels 1
4 , Heat shields
. 0 2 Closeouts e Rib webs I
4 I
I 1 0 20 30 40 50 Rib spacing, b, in.
I- . ___--.- .
Figure 13-29. Weight optimization of w i n g C (BL 212 to BL 350) of semimono- coque spanwise trapezoidal-corruga.t;ed panels, no insulation 1.3-1W .18 .16 .14 1 2 .10 .08 e 06 .04 .02 0 10 20 30 40 50 60 - - - Spar spacing, a, in.
__. - - - - - - - - - - - - - -p-plfup
Figure 13-30. Weight o p b i ~ z a t i o n of wing area A (E t o $ 1 ; 120) of semimono-
coque chordwise-stiffened tubular panels, no insulation . .
,-
lSpar spacing, a, in. j
- - - , A -- Weight o p t i m i ~ t i o n - of wing a r e a B ( B L 120'to B L 2l2) ' of semi- Figure 13-31.
monoc oque chordwig e -st i f f ened tubular pmels , no insulation
-- - 0 10 20 30 40 50 60 70 Spar spacing, a, in, -_ I- - . - - .
Figure 13-32. Weight optimization of w i n g ai C (BL 212 to BL 350) of semi- rnonocoque chordwise-st iff ened tubular panels, no insulation .1c 14.
.10 .08 .06 .04 20 30 50 60 70 40 0: _ . . - - . _ .
- .
Length, L, in.
Figure 13-33. Weight optimj-zationbf wing area A (p! t o BL 120) of semimono- coque chordwise-stiff ened tubular panels, with insulation .18 .16 9 .12 C
.-
IC t n ;6./ 9 .10
.-
r4 9) >
.-
c 9 . 0 8 Le1 w . - - a 06 0 10 20 30 40 50 &I 70 Length, L, in. , - - - - .
Figure i3-34. Weight optimizP.tion of wing a%a B (BL 120 t o BL 2l2) of semi- monocoque cLordwise-stiffened tubular panels # with insula€ion 13- 11 )I 0 2 0 .16
.- : -12
I * v)
f
S *10
.-
f 0, >
.-
c 0 .
$ .08 Lu .06 0 : 10 20 30 40 50 60 70 . . .
- Length, L, - in. - __
Figure 13-35. Weight optimiza'tion of wing area C (BL 232 t o BL 350) of semi- monocoque chordwise-stiffened tubular panels, with insulation C
.-
$ C Y
.-
f 9) >
.-
c $ W 10 20 30 40 50 60 70 Spur spacing, a, in.
Figure 13-36. Weight optimization ‘of wing area A (E t o BL E O ) of semimono-
I coque chordwise-st iff ened convex-beaded upper/tubuhr lower panels, no insulation i I 13-116 .18
. 12
.
t
.-
.
I+ 3 010 v) c 3 ’ L) .C
9 .08
.-
c c) L L Lu . 0 6 a 02 0 10 20 30 40 50 60 Spar spacing, a, in.
Figure 13-37. Weight optimization of wing area B (BL 520 to BL 212) of semi- rflonocogue chordwisc-st iffened convex-beaded uppcr/tubular lowcv ~ i ~ c l . s , no inoixla1,ion 1 . 5 - 1 l’i .24 ,24 .2c C *- . 1 9 G-
i C
Y
.$ , i o
f a l >
.-
c u
8 .w
e 0 6 .04
. 0 2
c
0 10 20 30 40 50 60 70 Spar spacing, .. -. . a, - in. - Figure 13-38. Weight optimization of wing area C (BL 212 to BL 350) of semi- monocoque chordwise-st if f ened convex-beaded uppez?/tubular lower panels, no insulation 13 -3.18 .20 .18 .16 .14 C
.-
b ' .12 z
b
C r)
2 010
0) >
.-
4-
d
- .res
.04 0 02 0 10 20 30 40 50 60 70 Spar spacing, a, in.
Figure 13-39. Weight optimization of wing area A ($ to BL 120) of semimono- coque chordwise-st iffened convex-beaded upper/tubular lower panels, with insuhtio!
1.3-I 1.9
t
.20 . l a o l d , 1 4 .12 .1c
. o E
spar webs 0 O d 0 0 4 Spar C"'85 .02
Uk. f. "-T- x i -
Fasteners C 10 20 30 40 50 60 70 Spar spacing, a, in.
Figwe 13-40.
Weight optimization of w i n g area B (BL E O to BL 232) of semi- monocoque chordwise-stif f ened convex-beaded upper/tubular ? nwer, with i n s u b t ion ~ 3 - 1.23 0 20 .16 .14 S
.-
I-’ . -12
C
yo
.-
f *lo 9) >
.-
c
d
Lu .08 .06 . 0 4 Shield .02 0 10 20 30 40 50 60 70 Spar spacing, a, in.
Figure 13-41. Weight optimization of w i n g area-C (BL 2 U to BL 350) of semi- tnanocoque chordwise-stiff ened convex-beaded upperitubular lower panels, with i n s d a t i o n - - ~ - _ .I_.
.. 1 - 1 13-121 .20 -18
.? 6
.14 v) .12 E c Y u
.-
f
: .10
.-
c k ! !
LLI i.
14- .08 -06 .04 .02 0 10 20 30 40 50 60 70 Spar spacing, a, in.
__I--__.
Figure 13-42. Weight optimization of wing area A (5 t o BL E O ) of semimono-
coque chordwise-stiff ened convex-beaded panels, no insula.tl.OkI 40L 1.3-322 .20 .18 .16
. 14
r 012 .- I+- cn' v) 0, c "0 .10 .- f Q) > .- c Q) Y -08 .06 0 04 .02.
G 10 20 30 40 .SO 60 70 Spar spacing, a, in, - .
Figure 13-43. Weight optimization of wing area B (BL I20 t o BL 2 l . 2 ) of semi- monocoque chordwfse-stiffened convex-beaded panels, no insuktion Figwe 13-44. Weight optimization of wing area C (BL 2l2 to BL 350) of semi- monoccque chordwise-stiffened convex-beaded panels, no insulation I 23-22b I .24 .22 -20 .14 C
.-
I - '
-
v) v) C Y .10 U
.-
al > .- c U a l Y Y .08 W .06 .04 .02 10 20 30 40 50 60 70 Spar spading, a, in. * Figure 13-45.
Weight optimization of ving area A (E to BL 120) of setnimonocoque
chordwi se -s tiffened convex-beaded/tubular lower outboard no 1 . nsulati on c 13-125 I a 2 0 ,18 -16 -14 E .- I ; ui a12 In 9) E Y u .- f 9) >
.-
.. 10
c 9) Y Y w -08 .06 e . 0 4 ..02 ieat ihield :ib caps 20 30 40 50 0' 10 60 70 Spar spacing, a, in.
Figure 13-46. Weight optimization of wing area B (BL 1-20 t o BL 2 ~ ) of semi- monocoque chordwise-stiff ened convex-beaded/tubUr Lower outboard, no insulation
-_ -
13-126 .20 .18 .16 .14 C .- I*' .
v) v) 0) e .12 Y u .- f > .- c V 2 .10 Y W . 0 8 0 . 0 6 .04 .02 0. 10 ;20 .30 50 660 70 \ Spar spacing, 11, in.
-- .
Weight optirmlza%ion of wing area C (BL 212 t o BL 350) of semi- Figure 13-47.
monocogue c hordw is e -st Iff ened convex-beaded/tubular lower c.rtboard, no insulation 13-127 .26 .24 .22 .
.14 C .- .12 I+- .
u) u) P) C Y u
z .10
a > .- + u a Y Y w .08 .06 . 0 4 .02 0 10 2 0 30 40 50 60 70 Spar spacing, a, in.
.-
Weight optimization o f , wing area A (e t o BL E O ) of semimono-
Figure 13-48.
coque chordwise-st iffened convex-beaded/tubular lower outboard, with insulation Spar spacing -__t_- i n 9 - - - - - - - - - - - - - - -- -=====I
Figure 13-49. Optimization of wing area B (BL 120 to BL 212) of semimonocoque '
chordwise-stiffened convex-beaded/tubular lower outboard, w i t 1 insulation - - - - - - -- - - - - - - - .lI . I ( .1, .
C 0 1
...)
G
% C Y 0 1 .-
s
a# >
.-
4- .O
d
w .O 0 10 20 30 40 50 60 70 Spar spacing, in.
Figure 13-50. Weight optimization of wing area C (BL 23-2 t o BL 350) of semi- monocoque chordwise-st if f ened convex-beadedltubulr lower outboard, with i n s u h t i o n Panel dimensions : (AZI dimensions i n inches (Spanwise) Waffle dimensions:
h - cvarall waffle height
p -- pitch of stiffeners
tB - skin thickness
tw - stiffene? thickness
5 - panel equivalent thickness
Mtscellaneous:
eU - extensional. ecceutsicity
- shear eccentricity
@33
w - maximum panel deflection
Figure 13-52 Notation Zi.i* monocoque waffle pariel design data 13-133 - m c 40 50 Spanwire panel dimension, b, in.
FLgure 13-54 Iioneyconib-core sandwich psrlel s i z e requ: rements m
t
h c 0 - W n u U D L L m i i a .
n c .- e a
Material: Rene 41 (ST& A. @ 14!10°F) I
I h/t= 2670 .- v)
T = &'
u 40 T = 1.21t m' L ai.
-
= 30
L O al z v) I Local instabi I i ty
o m atian radius,, , (R/+)
% i m - k E -
Shear allowable versus R / t of vertical circular-arc webs at 1 3 0 0 ' Figure 13-56.
13-138 .- Y" 40 .
L V VI L .
a
-
n O 30 :
- -
0 ) -c m 50 I 100 150 2oG 250 300 Corruaa ti on radius ( W t ) t Web thickness Figure 3-3-57. Shear allowable versus R / t of vertical circular-arc webs at 1400% 13- 133 - = 1250 t I
I s = l
50 106 150 200 2 3 I 300 I- xruaation radius I W t ) Web thickness Shear allowable versus R/t of vertical circuIar*rc webs at Figure 13-58.
i500oF 1.3-140 -- -r -- .
Cap thickn@sf t cf in.
I - &
- -- of rib - aid Gr c z l 13-59. - - - ~ l e w a b l e - compression stress versus - %hichess - , ~ i g u r ? - * 040 .050 Cop thickness, tc, in.
~ Figure 13-60. Cap area. vs thickness of rib and spar caps 13-14?
i
0 2 0
I I
AREA: s T O B L 1 2 0 ~~ TOTAL m E R PANEZS L O W E R PANELS R I B CAPS 0 10 50 60 SPACING, I N .
R I B Figure 13-61 Optimum r i b spacing f o r center area of semimonocoque spanwise- stiffened tubular panels with heat shields and p a r t i a l i n s u l a t i o n outboard .1a .16 . I 4 .12 .10 . O f
.a
.04 .0; Q 10 50 70 20 30 40 Rib spocing, in.
Ff Gure 1-3-62 Optimum rib spacing for spanwise-stVfened tubular panels with partial insulation outboard .20 -18 . 1 4 . 1 2 . 1 0
. 08
.06 .04 e 0 2 Figure 13-63 Optimum r i b spacing f o r outboard area of semimonocoque spanwise- stiffened tubular panels with heat shields and partial insulation outboard
. 14
.12 C
.- .10
I r
-
YI c Y u *- .08 f 0) >
.-
4- 2i .06 .04 0 0 2 30 40 50 lo
Q
- - . ..
- - .-. . .
Rib spacing, in.
Optimum rib spacing for center area of semimonocoque spanwise- Figure 13-64.
stiffened tubular panels with no insulation
1 3 . . 1.46
;
!. 14
0 12 .
.-
. - I C
2 . i o
Y u
.-
f 9,
.- > .oa
$ w . 0 6
. 04
- - . Rib spacing, in.
Figure 13-65. Optimum rib spacing for inboard area of semimonocoque spanwise- stiffened tubular panels with no Lnsulatton . 2 0
. 18
. 16
. 14
c
.-
I C '
I .10
Y L)
.-
f P) >
.-
c
" .08
rc w . 0 6 .04 . 0 2 ' 0 10 20 30 40 50 Rib spacing, in.
.-. - _-_ . .I-___ .-.
Figure 13-66. O p t i m u m r i b s p c i n g for oubboard area of semimonocoque spanwise- stiffened tubular panels with no bsuhtion
I
13-49 n .- 1.3-150 R I B SPACINGS I N , Figure 13-68 O p t i m u m r i b spacing f o r center area of semimonocoque spanwise- stiffened beaded panels with heat shields and p a r t i a l insulation outboard 1 ,
i
I
I
I ,.: [ .
Figure 13-70 Optimum rib spacing f o r outboard area of semimonocoque spanwise- stiffened beaded panels with heat shields and p a r t i a l insulation outboard .20
. 18
. 16
. 14
_ .
C
.-
I 3 4 lo a , C yo
.-
' .08
a , >
.-
c t i !
w . 0 2 Rib spacing, in.
P i m e 13-71. OI2rt;imum rib- spacing f o r center area of semimonocoque spanwise- stiffened beaded panels with no ineuWsSon
13 . . 1 . 5 4
.14 .12 ..
C .
*- .
I2 \ .10 b S 2i U
.-
-r +!
.06 3 Rib spacing, in.
0yut;irnum r i b spacing for outboard area of sendnlonocoque spanvise- Figure 13-73.
stkPPened beaded panels with no insulation .
AREA A : E T 0 BL 120 UPPER PANELS L O W E R PAImIS
-
cm3EouTs
RIBWEBS I I A
HE4T SHIEXJlb SPAR C A P S FASTENERS R I B CAPS 10 20 3 0 40 50 60 SPAR SPACING, I N .
Figure 13-75 Opthum spar spacing f o r center area o f semimonocoque chordwise- stiffened tubular lower surface andconvex-beaded upper surface with lower heat shields and partial insulation outboard .18 -14 c
3 .04
> .- U w .03 .02 .01 10 20 30 40 50 Spor spacing, in, Figure 13-76 Optimum spar spacing for semimoncoque chordwise sti f fcned concept .20 .18 .16 .14
Fi
I +;' @ = -
E
8 .05
X E-c
E
[ . 0 4
.02 0 1 .
I I I I I I C 0 10 20 30 40 5 0 60 SPAR SPACING, M o Figure 13-'77 op tinium spar spacing f o r outboard area of semimonocoqae chordwise-s tj.ffened tubular panels with lower surface heat shield and p a r t i a l insulation outboard 13-162
a
.a
T-rr
. ?O
. 13
.It; .14
>
.02 .01 0 10 20 30 40 50 60 RXB SPACING, I N .
n a c 13-168 PANEL FLWTER ANALYSIS bY G . W . Davis, La E . Fogg, and C . C . Richie CONTENTS Page PANEL FLUTTER ANALYSIS 4-1 CRI!TIERIA 14-1 PRIMXRY STRUCTURAL PANFZS 14-2 HEAT SHIEW) CANDIDAT@ ANALYSIS
J-4-4
REFEEENCE 4-6 Tzble Page zlr-1 Waffle closeout spring constants 3.4-7
1L- : Heat shield c l i p spring constants
3-44 i - 3 Panel spring constant for shielded areas u-9 Monocoque w a f f l e panel f l u t t e r parameters a - 1 0 3.4-4 Monocoque honeycomb spring constant equations
3 - 4 -5
(unshielded ) 14-12 Honeycomb sandwich panel flutter evaluation 4 - 1 3 Panel f l u t t e r requirements - semimonocoque, tubular 14-15 Panel f l u t t e r requirements - sesnimonocoque, spanwise, beaded 14-16 Semimonocoque, chordwise closeout spring constant
14-9 11-17
llr-10 Panel f l u t t e r requirements - semimonocoque, 14-18 chordwise
a - 1 1 Panel f l u t t e r requirements - s t a t i c a l l y
determinate 14-19 4 - 2 0 l4-12 Summary of heat shield panel f l u t t e r analysis 14-v SYMBOLS Panel geometqy parameters Panel dimension i n x and y coordinates a, b BL Butt l i n e C Stiffness coefficients of governing d i f f e r e n t i a l equations D1JD2’D12 E Modulus of e l a s t i c i t y I Moment of i n e r t i a Deflectional spring constant per unit length K Deflectional spring constant, W’/&~ ’ii I Length M Mach number Pitch o f panel s t i f f e n e r s and beak shield c l i p s P Dynamic pressure of airstream Temperature T
(M2 - 1 ) 1 ’ 2
B
Dynamic pressure parameter h Value of dynamic pressure parameter at flutter
Section 1 4 .
Section 1 4 .
PANEL FLUTTEB ANALYSIS The results of the analytical flutter investigation indicate a l l wing surfaces exposed t o t h e aerodynamic enviroment remain s t a b l e throughout the e n t i r e f l i g h t trajectory.
CRITERIA The surface panels were analyzed by use o f t h e method presented by Bohon
and Anderson (ref . a-l), which includes t h e influence of spring-supported
edges.
A factor of safety of 1.3 on the dynamic pressure and a test correlation f a c t o r of 2.0 is used. This results i n t h e theoretical c r i t i c a l dynamic pressure t o cause f l u t t e r being greater than 2.6 times t h e actual dynamic pressure at the c r i t i c a l point of t h e f l i g h t trajectory.
The c r i t i c a l p r i n t of the f l i g h t t r a j e c t o r y was evaluated from t h e maximum value of the q / , E parameter, where q = dynamic pressure, p s i
= [(Mach No.)* - 1]1’2
E = Young*s modulus of t h e structure a t the temperature corresponding t o the point of the f l i g h t trajectory being evaluated was evaluated a t 7, 20.6, and 40 minutes into the f l i g h t , This parameter and t h e c r i t i c a l point of t h e f l i g h t t r a j e c t o r y was determined t o occur a t 7 minutes into the flight. Consequently, t h e s t i f f n e s s of i h e unshielded primary structural panels was based on a temperature of 500 F, and f o r t h e shiglded ageas the hegt shield, support clip, and panel temperatures were 500 F, 350 F, and 200 F, respectively.
Where refurbishable heat shields are used, the spring constants include the f l e x i b i l i t y of the heat shield edge closeout, the support clip, and t h e primary structural panel. The primary s t r u c t u r a l panel i s regarded as shielded from the aerodynamic environment when the refurbishable heat shield is employed.
However, where modular o r permanently attached heat shields a r e used, both t h e heat shield and the primary s t r u c t u r a l panel a r e required t o be f l u t t e r free.
Unshielded primary structural panels a r e analyzed and required t o be f l u t t e r frec with edge spring supports based on the f l e x i b i l i t y of t h e panel edge closeout and the structure t o which it is attached.
PRIMARY STRUCTURAL PANELS Monocoque Waffle The waffle concept has heat shields on t h e lower outboard surface only.
i s subjected t o the aerodynamic In a l l other areas the structural panel environment. The panels have an aspect r a t i o of 2 and dimensions of 20 inches by 40 inches, with the long dimension p a r a l l e l t o the airstream. The edge of the panel is attached t o t h e spar and r i b flanges.
The effective spring constant of the unshielded panels is based on t h e flexibility of t h e spar/rib flange, t h e panel edge thickness, and t h e panel edge closeout. A schematic
drawing f o r t h i s closeout area is shown i n table a-1. The spar/rib flange
was assumed t o be cantilevered from a point halfway between t h e centerline and the edge of t h e corrugated web, with an inflection point occurring a t t h e panel- to-flange attachment point. The s t i f f n e s s of the tapered panel edge closeout was assumed t o vary according t o t h e square of t h e tapered length. On the basis of these assumptions and by use of the s t r a i n energy of bending f o r this system, the equation f o r the spring constant was determined. The spring constant equation, spring constants, and related s t i f f n e s s e s for the panel edge closeout a r e summarized i n t a b l e 14-1.
It was assumed t h a t t h e leading and t r a i l i n g edges were simply supported and the streamwise edges were e l a s t i c a l l y supported with the aforementioned spring constant.
The heat shield on the lower surface of the out.board segment of the wing is corrugated i n the streamwise direction and is supported on hat-shaped c l i p s spaced at 1C inches in the streamwise direction. The effective spring constant i s based on the combined flexibility of the support c l i p s and t h e waffle primary structural panels. The equations f o r t h e spring constants, stiffnesses, and geometry for the c l i p s and the primary s t r u c t u r a l panels are shown i n t a b l e s The c r i t i c a l dynamic pressure parameter as defined 14-2 and 4-3, respectively.
i n the c r i t e r i a section occurs a t 7.0 minutes i n t o the f l i g h t . A t ;his time the temgerature of t h e heat shield, t h e clip, and the panel are 500 F, 350°F, and 200 F, respectively.
A l l areas of the wing are stable and exceed t h e f l u t t e r f a c t o r of safety
requirements as defined i n t h e c r i t e r i a section. Table 4-4 summarizes t h e
principal f l u t t e r parameters and results. The minhum fact;or of safety of 6.77 occurs on the lower surface heat shield between SL 304 and $0.
Monocoque Honeycomb The honeycomb concept has the i d e n t i c a l thermal protection arrangement
a s t h e waffle concept - heat shields on t h e lower surface outboard area of t h e
The panels have an aspect r a t i o o f 2 and dimensions of 40 inches by wing.
80 inches, with t h e long direction p a r a l l e l t o the airstream. The panel has a channel closeout stiffening the two face sheets, with an upper-surface splice plate fox load transfer between adjacent panels. The lower face sheet i s attached t o the spar and r i b flanges.
14-2 The effective spring constants ?or the unshielded panels a r e based on the combined f l e x i b i l i t y of t h e spar/rib flange, panel edge thicknesses, and t h e panel closeout. The closeout geom=Gry and the assumptions made f o r the
solution of the spring constant are shown i n table 14-5. The spring constants
f o r these unshielded areas a r e summarized i n table 14-6.
The heat shields on the lower surface of the outboard segment a r e corrugated i n the streamwise direction and attached t o t h e primary s t r u c t u r a l panels by c l i p s spaced approximately l l . 4 inches. The heat shield spring constants, which are composed of the heat shield c l i p and primaqy structure panels, are shown i n tables l k - 2 and a-3.
A l l areas of the wing a r e stable, with t h e minimum factor of safety of 5.31 occurring on +.he shielded lower surface between BL 212 and 304. The principal f l u t t e r parameters and r e s u l t s are showti i n table 14-6.
Semimonocoque Spanwise The tubular and beaded concepts have refurbishable heat shields on both upper and lower surfaces. These heat shields are t h e corrugated concept with multiple supports. The shield is stiffened i n the streamwise direction and attached t o the primary s t r u c t u r a l panels by c l i p s spaced approximately 13.1 inches i n t h e spanwise direction. The panel width is equal t o t h e r i b spacing, which is 50 inches, 40 inches, and 40 inches from center t o outboard areas, respectively, f o r both concepts.
Since these concepts are completely shielded, t h e spring constants are based on the combined f l e x i b i l i t y of t h e heat shield support c l i p s and t h e primary structure panels. These equations and spring constants are shown i n tables 14-2 and a-3. The heat shields for a l l wing areas f o r both t h e tubular and beaded concepts are stable and meet t h e required f a c t o r of safety, The principal flutter parameters and results are shown i n t a b l e s 14-7 and 14-8.
The minimum factor of safety f o r both concepts occurs on t h e lower surface heat shield located between t h e centerline and RI, 120, h c r / ~ = 2.69 for the tubular and Acr/A = 3.0 f o r the beaded conoept.
Sernimonocoque P,hor&wh e The chordwise concept has tubular rx9,m2y7,' s t m c t u r e panels on t h e lower surface and convex beaded panels on t h e IQ~W surface. The lower surface requires heat shield f o r thermal protectio- q.nd aerodynamic smoothness. The shields, which a r e stiffened i n the spanwise direction, are attached t o the primary structure by c l i p s spaced 13.1 inches i n t h e streamwise direction.
The panel dimensions f o r both upper and lower surface primary structure panels a r e 75 inches by 25 inches spanwise and chordwise, respectively.
The spring constants on the lower surface heat shields are based on the combined f l e x i b i l i t y of the heat shield c l i p and tubular panel. The c l i p spring constants are summarized i n table 14-2. The spring constant equation and stiffnesses f o r the lower surface panels are shown i n table 14-3 The unshielded upper surface spring constants are based on the combined fl-exibility of t h e spar flange thickness and panel closeout geometry.
The spar flange was assumed t o be cantilevered from a point halfway between the centerline and the edge of the corrugated web. The s t i f f n e s s of the panel edge closeout was assumed t o vary according t o t h e square of the tapered length. The closeout spring constants f o r the upper exposed panels are shown i n table 14-9. The related dimensions and stiffnesses as well as the spring constant equation are contained i n t h i s table.
Both upper and lower surfaces are stable and have factors of safety against f l u t t e r , h,,/h , t h a t exceed the required factor of safety of 2.6.
The minimum factor of safety of 12.4 occurs on the lower surface between the centerline and BL 120. The principal f l u t t e r parameters and r e s u l t s of the analysis are summarized i n table l4-lO.
S t at ica !.ly Determinate This concept has refurbishable heat shields on both upper and lower surfaces with corrugations i n the streamvise direction. The heat shields are attached t o the primary s t r u c t u r a l panels by c l i p s spaced 13.1 inches i n the streamwise direction. The primary s t r u c t u r a l panels used on t h i s concept are t h e spanwise stiffened beaded configuration.
The panel widths are equal t o t h e r i b spacing and are 60, 50, and 40 Since a l l surfr3es are inches from center t o outboard area respectively.
shielded, the effective spring constant xas calculated from the combined f l e x i b i l i t y of the heat shield support c l i p s and the primary s t r u c t u r a l panels. These spring contaxu.’ calculations are shown i n tables 14-2 and 14-3 The heat shields are stable and have factors of s a f e t y Pgains‘t f l u t t e r t h a t exceed the required factor of safety of 2.6. The minimum factor of safety occurs on the lower surface heat shield between the centerline and BL 120.
The principal f l u t t e r parameters and r e s u l t s are summarized In table 14-11.
HEAT SHIELD CANDIDATE ANALYSIS A detailed panel f l u t t e r analysis of each of the candidate heat shield concepts w&s conducted by use of t h e method and c r i t e r i a discussed i n the Both refurbishable and permanently attached heat shields c r i t e r i a section.
The heat shield designs investigated are described i n Section were analyzed.
20. The effective spring constant is based on the combined f l e x i b i l i t y of the support clips and the prbnary s t r u c t u r a l panel.
14-4
A typical tubular panel was assummed with a radius of 1.0 inch, a thickness of 0.010 inch and a pLtch of 2.4526 inches.
For the analysis of the panel with permanently attached heat shields, t h e effective spring constant was based on the combined f l e x i b i l i t y of the r i b flange, the panel edge thickness (including doubler), and the tapered end closeout of the tube. The c r i t i c a l dynamic pressure parameter occurs at 7.0 minutes into the f l i g h t .
The refurbishable heat shields are stable and have factors of safety against f l u t t e r , &/A t h a t exceed the required value of 2.6. However, the primary structural' panel of the permanently attached (modular) concepts has an allowable f l u t t e r parameter t h a t is l e s s than the applied dynamic pressure; consequently, it would f l u t t e r . The principal f l u t t e r parameters and results are summarized i n t a b l e 14-12.
14 -5
REFERENCE 14-1 Bobon, Herman; and Anderson, Melvin 5 . : The Role of Boundary Conditions on Flutter of Orothotropic P a a d s . AIAA Journal, Vol. 4, No. 7, R.4.l-l248, July 1966.
14-7 A d d 0 N a d, d,
H B
d o ' - 1 - I
$ 8 0 0
0 0 0 0 0 0 x x x x x x d .d h \ co .
m m h 3 2 rd -d 0.4 a L_ cu h u3 rl rl h .
cot x aa-4 P \o h . d o
w gd
w 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c u c u c u N c u c u c u c u c u c u c u ( v c u c u c u
I
n a , 14-9
TABLE 14-4
4- MONOC0QL.Z WAFFLE PANEL FLlPTTER PARAMETERS Location Center Inboard Outboard Lower Upper Lower Surface WPer 47 400 47 100 32 350 124 500 124 700 85 400 D129 lb-in. (b )
i o 240 8 920
6 840 68.8 70.1 72.4
2.625 2.649 2 . 636
-
-A 21.0 21.2 21.1 X (A’ c r Ill3 3.4 3.4 3.4 495 498 340 135 92 (a) Flexural s t i f f n e s s = D = D 1 + 2 D (b) Twisting stiffness, D 1 2 33 3 = K b 3 3 /n D2, where b = 20 inches (c) (d) C = D12/(D1D2) 1/2
(e) -xx = 2 (a/b)2 D12/Dl, where a = 40 inches
(f) (Acr) ’ 1 ’ 3 = (2q$/,~,)”’ (D1/g2)’I2; from figure 4 , reference 14-1; (C = 7.07 and = 5 0 ) (g) q / , = 3.68 psi at 7.0 minutes 14-10
TABLE l4-4 (Concluded)
-
EL 212-30h BL 3oL-350 10 680 10 680 9 . 2 n.2 2 376 1 560 6.100 Loo5 3.098 lr.72IJ o.o00lI$2 ~.000U3 28,180 18,576 9.1 9.07 1 . 0 5 6 0.693 25 32 8.4 6.n
- 30.3 x lo6 psi ( R e n t W clip8 T - 3 5 0 ° F ) x Ecllp - 20 x 1 8 pi
(8) %lip
(TD N i C r clips e T - SSOOF)
(h) 1 -1.1 KPanel %lip
(i) - 3 I[ ( b 3 ~ 2 ) H s
( 3 ) kCr from Figura 2, reference U-1.
(k) Heat shield panels and clips; R e d W between BL 212-3018; TD N i C r between EL 3a-350.
TABLE a-5 MONOCOQUE HONEYCOMB SPRING CONSTANT EQUATIONS Assumptions 7 No dofomtion
E
(1) Cap and closeout have same slope, 0, due t o clamping by shoulder
I
bolt. I . .
Head of shoulder bolt permits inward movemen but resists outward movement.
clos.out -1Rne1
m 8 I 8' + 6 " Closeout deflection equation: 8 Total Panel deflection equation: Spring constant : 14-12 TABLE lb-6 HOWYCOMB SANDWICH PANEL FLUTTER EVALUATION ~ ~ ~~ - Location Center Inboard Outboard Lower Surface Lower
D 1 = D2 = D12, in.-lb 231 goo
209 770 265 000 K, lb/in./in. 1210, 34 1210.34 1210.34 118909 10.773 98427 C 1.0 1.0 1.0
-
-A 8.0 8.0 8.0 X 4.7 4.7 4.7 170.15 188.10 2fi. 95 46.20
51. 07 58.36
(a) Flexural and twisting s t i f f n e s s ( b ) Deflectional spring constant per unit width = Kb 3 3 /R D2, where b = 40 i n .
(c) (g) q/,, = 3.683 p s i a t t = 7.0 minutes TABU 4 - 6 (Concluded) tocation 212-34 U6 197 39.809 5.9768 be7125 O.ooalil8 llr07.0 38.7llr 0.7898 2s 5.3% TABLE 1L-7
PANEL F " T E R REgUIREMENTS - SEMIMONOCQUE, TUBULAR
laver
-
- - -
120-212
p - 120 120-212 212-304
- -
-
0.10 0.mi 0.010 0.010 0,OlL 0.019 1.22 1.52 1.22 1.22 1.88 2.50 1.15 0.91 0.91 0.91 l.bG 1 . 9 0 0.35 0.3 0 . 3 0. Y 0 . U 0.a 22 x 106 lr3 x 104 2 .,lo+ 80 x 104 22 x 1 0 4 72 I lod 1277.1 653.4 653.L 653.4 2138.4 3 5 1 0 . 0 1.971 3.b5C 1.911 1.971 5.LO7 9.017 O.O(n92 O . O M 7 C 0.00292 0.00292 0.0025) 0.OMS7 13.1 13.1 13.1 13.1 13.1 13.1 12.96 25.32 25.32 25.32 7.72 h.7lL LO hC 50 LO ha LO O.ax1626 O.oooS80 ~.oOollOl 0.000626 0.m5L2 o.cao551 l O h . 0 u . 0 1056.0 1056.0 lW7.0 1119.0 82.b h3.B 90.9 55.2 26.5 26.5 76.118 L?.511 20.494 53.360 26.010 25.887 8.47 2.u 1.27 5.92 0.882 0.535 180 68 7 5 llr0 30 20 7.11 5.79 2.69 5.53 L A 3.88
-
- -
4-15 TABLE 14-8
PANEL FLUTTER REQUIREMEXl'S - SEXIMONOCOCIUE, SPANWISE, BEADED
I sAvfao* buer or
- -
-
212-350 tocation stations, 8L fi - 120 120-212 120-212 212-3u4
-
0 . 0 1 2 o.ma 0 . 0 1 0 0 . 0 1 0 0 . 0 1 1 r 0 . 0 1 9 1 . 5 2 1 . 2 2 1 . 2 2 1 . 2 2 1 . 8 8 2 . 5 0 1 . 1 5 0 . 9 1 0 . 9 1 0 . 9 1 1 . 4 0 1 . 9 0 0 . 31 0 . 3 1 0.h8 0 . 3 9 0.P 0.a 3 x 1 0 ' 6 22 x 1 0 ' 6 22 x 1 0 ' 6 1 x 1 6 12 x 10-6 80 x 104 1 5 1 0 . 0 1 2 7 7 . 1 6 5 3 . 1 653.b 6 5 3 . k 2138.8 3A5O 1 . 9 7 1 1 . 9 7 1 1 . 9 7 1 5 . b W 9 . 0 1 7 0.00270 0 . 0 0 2 9 2 0 . 0 0 2 9 2 O . O W 2 9 2 0 . 0 0 2 5 ) 0 . 0 0 2 5 7 1 3 . 1 1 3 . 1 1 3 . 1 1 3 . 1 1 3 . 1 1 3 . 1 1 2 . % 25.32 2 5 . 3 2 25-12 7 . 7 3 8 b . 7 & b0.0 5 0 . 0 bo. 0 bO.0 bO.0 bO.0 o.owg~o o.mm 0.000626 D . M 1 0 6 2 6 O.oo05b2 0.ooo551 UL.0 102.0 1 0 5 6 . 0 l l l 9 . 0 1 0 5 6 . 0 lJJW.0 5 6 . b 7 2 8 . 7 2 1034 l l 6 . 1 85.11, 8 5 . U s.35 * 2 ? . % 9 b . w 1 4 1 . 6 8 0 . 5 5 79.9 3 . 1 0 1 0 . b 3.06 U . p l 2 . 7 3 I.& 7h 16 2 w 220 68 b 6 5 . 7 1 3 . 0 0 7 . 9 0 6 . 6 9 6-79 9 . 7 6
- -
4-16 \
* m
n
1 0 0
c\1 d
+
0 0 0 0 0 0 -\
9 b
H H 4
m
0 @
0 0
8 0
m do \n m I a l 0
. 9
H a - 0 0 % I 3 c u
d
*rl - 1 :
.a 3
cv
2 r-l
ce
9 .
9 .
si +
H lY\
s 0
9 .
9 .
0 "3 I " "
I
s
H II 14-17 r Y h e r
__I - - - -
120-212 112-350
e - 120 120.212 212-3-h Y21-350'~
- -
- -
-
0.012 0 . 0 1 2 0 . 0 1 5 0,019
-
1 . 2 1 1177 I.'/? 2.611
-
0 . 9 1 0 . 9 1 112 1 . 9 2
-
0. P 0.9 OA9 0 . 6 7 Irm x 104 23 x 1 0 ' 6 23 x loa BO x 10'6 203 x 10-6 119 OOO 683.1 6 d .I. L 2 3 7 6 . 0 3900.0 57 m 3.m 3 . 1 % 6 . 6 1 5 8 - 8 9 0 . 1 8 1 0.oOllpe O . W l 9 8 0.&?78 0 . 0 0 2 2 7 2 1 . 0 1 3 . 1 1 3 . 1 1 3 . 1 1 3 . 1 0.855 2t.22 2 1 . 2 2 6 . % h 8.2L3 75 60 15 75 -5 .WE5 . m 7 5 .Urn170 JNIIJlfl .m*
-
8 9 . 3 1003.0 Mlfl.0 2 0 9 1 . 0 52.1 5 7 8 . 5 5 1 7 . 0 2 1 6 . 7 Z ( 6 . 7 $ 2 . 1 U.1 1 3 5 . 8 1 9 1 . 2 370.3 1.3 %*2 3 9 . 3 5 . 6 7 3.5s I6 )oo Y O 130 90 53.e 1 2 . 1 1 2 . 8 1 8 . 7 21.2
-
14-18 TABU 14-11
PANEL FLUTTER REQUlREMlWS - STATICALLY DEJXRHINATE
m 2 l 2 2lZ-350 f - 120 2lZ-pr *-,S@
lo-zlz
- - -
in. o m 0 0.012 o . m o 0.010 o.oY, 0.019 In. 1.22 1.52 1.2- 1.22 1 . 0 8 2.50 0.91 1.15 0.91 0 . 9 1 l.LO 1 . 9 0 in.
Ill. 0.39 0.31 0 . L 8 0.61.
0.3 0.9 22 x 10-6 ha I 10-6 12 a 1 0 ~ .eo 10-6 1 n . h . 22 x 104 22 x 10-6 lb-ln. 1 2 1 7 . 1 15io.o 6 5 3 . h 653.h 653.L 21384 Ib-In. 1.971 3 . 1 5 0 1.9?1 1 . 9 7 1 5.101 9.017 0.0492 0.00270 O.QC252 0.00292 0.00253 O.WZS7 in. 13.1 13.1 13.1 13.1 13.1 13.1 12.96 1 . 7 a 6.32 25.32 25.32 7.738 In. 50 LO 60 so 10 h0 o.oocGo O.go05B 0 . W b o.oocyro Qmoszl 0.00055 lh/tn./tn. - 3S.J l W . 0 lU9.0 l u . l o 5 6 . 0 IlrO7.0 Ib/ln./In. 67.1 19.8 121.2 K.L 90.' l 2 1 . 2 109.0 Ib/ln./ln. 63.0 9l.5 19.b 83.h 111.6 1 . 9 6 2.11 6.W 9.25 3.78 2.25 60 66 lb5 185 92 66 5.72 1.a 2.61 7 . P ll.9 U8.L _I_ 4-19 I t" rm
Section 15
Section 15 VEHICLE FLUTTER bY R . F . O'Connell CONTENTS Page VEHICLE FLWTS 15-1 ILLUSTRATIONS Figure 15-1 vs Mach number f o r vehicle t r a j e c t o r y cLa 15-2 Damping coefficient and frequency vs equivalent airspeed monocoque waffle concept 15-4 Damping coefficient and frequency vs equivalent 15-3 airspeed semimonocoque spanwise concept 15-5 Damping coefficient and frequency vs equivalent airspeed semimonocoque chordwise concept 15-6 15-5 Damping coefficient and frequency vs equivalent airspeed s t a t i c a l l y determinate concept 15-7
% Lift coefficient
g Gravitational acceleration M Maah number ’ k e a s Equivalent ahspeed a Angle .of attack 35-V
Section 15
Section 15 VEHICLE F'LUTTER F l u t t e r analysis of t h e hypersonic cruise vehicle was conducted t o assure t h a t the s t r u c t u r a l concepts w e r e not flutter c r i t i c a l . This inves- t i g a t i o n was limited t o symmetrical modes in keeping with the redundant analyses. Previous studies of flutter response of long, slender vehicles have indicated t h a t asymmetric flutter is not l i k e l y t o be c r i t i c a l f o r the overall vehicle (configurations having t i p f i n s may require l o c a l s t i f f e n i n g t o avoid asymmetric f l u t t e r ) .
The critical flutter condition is expected t o occur during t h e heavy weight climb/acceleration phase of t h e t r a j e c t o r y as maxixnum %,q is attained. The variation of the parameter aaq with Mach number during climb is shown i n figure 15-1. Symmetric flutter response at Mach 2.75, 520 000 pounds vehicle gross weight, was analyzed using piston-theory aerodynamics f o r the wing and slender-body aerodynamics f o r t h e forebody.
The level of aerodynamic forces was modified t o give a C, q of 0.0215 lb/deg- o !
s q ft based on the w i n g reference area.
Using the computer program of reference 15-1, vehicle f l u t t e r analyses were performed f o r the monocoque, semimonocoque spanwise, semimonocoque chordwise, and s t a t i c a l l y determinate s t r u c t u r a l concepts. The resultant damping coefficients and frequencies versus equivalent airspeed for the first three modes are shown i n figures 15-2 through 15-5. (Higher order modes were included i n the analyses but were determined t o be of l i t t l e significance. ) I n general, the vehicle modes exhibit the low frequencies typical of long slender configurations.
The first mode is comprised primarily of fuselage bending, while the second node p i n c i p a l l y indicates wing bending about the longitudinal axis.
The t h i r d Response frequencies of both f l u t t e r evaluations are similar.
mode shape, consisting of combined second fuselage bending and outer wing bending, exhibits a s l i g h t l y lower frequency than the t h i r d mode resulting from the preliminary f l u t t e r analysis. This mode displays negative damping No positive damping was indicated throughout the velocity range investigated.
throughout the speed range investigated. The speed range considered extends well b vmd the required 1.3 factor on dynamic pressure. Therefore, it is ",at high margin on airspeed and dynamic pressure is available conclu over t, ... uesign f l i g h t path and t h a t the s t r u c t u r a l concepts are not critical It was not required t o conduct a vehicle f l u t t e r analysis f o r i n f l u t t e r .
This concept was investigated the mono2oque honeycomb sandwich concept srfter tne f i n a l analysis of a l l the other concepts was complete. Since the wing s t i f f n e s s of the honeycomb sandwich concept was similar t o the other concepts, which provided high margins on airspeed and dynamic pressure, it we.s concluded t h a t t h i s concept was not critical i n f l u t t e r .
15-1 REFERENCES 15-1 Lockheed F l u t t e r and Matrix Algebra System (FpMAs).
15 -2 a , rl k k k a , @ E: I 1 I Figure15-3.Dmping coefficient and frequency vs equivalent airspeed semi-monocoque spanwise concept
15 -5
t.02 a 0 ' p -.02 rs Fmqwncy vt oinped N 3 I u ' 100 500 700 "kea, Figure 15-&.Damping coefficient and frequency vs equivalent airspeed semi-monocoque chordwise concept 15-6
Section 16
Section 16 SONIC FATIGIE AMALYSIS B . C . Wollner, I. F . Sakata, H . He Armstrong, C. C. Rkhie, G . W. Davis CONTENTS Page 16-1 SONIC FATIGUE PNALYSIS 16-1 BOUNDARY LAYER AM) NOISE C R I Y E B ~ 26-3 LAMINAR-TIRBULEUT TRANSITION CRT?XEtIA 16-3 METHOD O F ANALYSIS 16-4 SPRUCTURAL RESPONSE 16-4 SEtUCTURAL DAMPING 16-4 RESPONSE FREQUEXCY 16-5 NORMALIZED STRESS 16-5 FLANGE STRESS 16-6 FATIGUE CURVES AND A L L O W A B L E S 16-7 SCATTER FACTOR AND DESIGN LIFE 16-8 DESIGN NOMOGRAPHS AND SEENICE LIFE CURVES 16-9 VALIDATION O F ANALYSES 16-10 FATIGUE ANALYSIS RESULTS 16-10 MONOCOQUE PRIXWY STRUCTURE 16 -12 SEMIMONOCOQUE AND STATICALLY D l i T m W E PRSM4RY STRUCTURE 16-13 HEAT SHIELD SONIC FATIGUE 16-13 m T SHIELD CLIPS 16-iii \ TABLES Table Page 16-1 Acoustic fatigue criteria 16-15 16-2 Sonic fatigue allowables f o r TD N i C r -lower outboard heat shield 16-15; 16-3 Monocoque waffle sonic fatigue analysis, primary structural panels 16-17 16-4 Monocoque honeycomb sandwich sonic fatigue analysis, primary structural panels 16 -17 16-5 Primary structure sonic fatigue analysis, semi- monocoque and s t a t i c a l l y dekcnninate panels 16 -19 16-6 Rib and spar cap sonix -atigue, monmoque concepts 7 1-21 16 -7 Rib cap sonic fatigue, beaded concept 16-22 16-8 R i b and spar cap sonic fatigue, tubular primary structure 16-23 16 -9 Rib and spar cap sonic fatigue concept, chordwise critical, spar caps 16-24 16-10 Rib and spar cap sonic fatigue concept, s t a t i c a l l y deteminaf - c r i t i c a l caps, r i b caps 16-25 16-11 Heat shield sonic fatigue 16-27 16-29 Heat s h i e l d clips sonic fatigue 16-12 ILLUSTRATIONS Figure Page 16 -1 Variation of boundary layer noise during design trajectory 16 -30
16 -2 l i n g area applicable t o the 0.022 q criteria 1 6 - 31
16-3 Random-loading fatigue curves - Renel 11 16 -32
16-h TD N i C r fatigue analysis 16-33 16-vii SYMBOLS Panel cross section area; effective moment arm A x and y distances between simply supported edges of plates a, b B Panel width BL Butt l b e C End f i x i t y coefficient; empirical constant used f o r calculating r m s flange stress D Directivity correction used i n calculating the overall sound pressure level Stiffness coefficients of governing differential equation Decibels Modulus of e l a s t i c i t y Factor of safety Resonant frequency Gravitational accelemt ion Hertz Height 1 Moment of inertia K 187.61, emperical constant used i n equation 16-6 EtemP/EwI, w t e r i a l correction factor
Kt
L Panel length M Bending moment; k c h number N Number of loading cycles P Pressure PSd Power spectral density 16-ix Dynamic pressure Reynolds number; reduction factor u;?d i n equation 16-5; radius Root mean square Thickness Flange thickness Equivalent panel thickness Def lecticn Distance from leading edge; distance from sound source Rectangular Cartesian coordinates Distance from "neutral" axis t o extreme fiber Boundary layer thickness Damping r a t i o Root mean square pressure density bhterial density Root mean square flange stress Normalized stress Allowable root mean square stress U l l i t pressure stress Root mean square stress 16-x
Section 16
Section 16 SONIC FATIGUE ANALYSIS Adequate resistance of t h e wing s t r u c t u r e t o t h e acoustic loading f o r t h e l i f e cycle span (10 000 hours) was determined by t h e o r e t i c a l methods of analysis supplemented by empirical data.
BOUNDARY LllYER AND NOISE CRITERIA Boundary layer and engine noise l e v e l s are considered t o e s t a b l i s h acoustic (sonic) f a t i g u e e f f e c t s . For t h e wing study area, t h e boundary l a y e r noise i s t h e primary condition contributing t o sonic f a t i g u e for t h e wing s t r u c t u r a l concepts.
Estimated o v e r a l l sound pressure levels (OASPL) f o r boundary l a y e r noise were determined, based on t h e c r i t e r i o n (ref. 16-1) that o v e r a l l root mean square pressure is 0.7 percent of f r e e stream dynamic pressure for laminar and turbulent flow conditions. For t r a n s i t i o n from laminar t o turbulent flow, t h e c r i t e r i o n i s based on an o v e r a l l root mean square pressure that i s 2.2 percent of t h e freestream dynamic pressure. The r e s u l t a n t values, as shown i n f i g u r e 16-1, are found t o be 1G Jb higher than those f o r 0.7 percent q. The 0.022 q c r i t e r i o n is based on recent f l i g h t test data from t h e X-15 program, which indicated t h e p c s s i b i l i t y t h a t a higher r e l a t i o n between noise l e v e l and dynamic pressure than found i n reference 16-1 may e x i s t .
Boundary l a y e r thickness (A) i s computed using a n extension of t h e method suggested i n reference 16-2.
( 16 -1) where X = t h e distance f r o m t h e leading edge M = t h e Wch number at t h e edge of t h e boundary l a y e r R = t h e l o c a l Reynolds number
Maximum octave . nd pressures occur i n the 2400 - 480C Hz octave band f o r body
Since fwdamental panels and i n t h e 4800 - 9600 Hz octave band for wing panels.
panel frequencies were a n t i c i p a t e d t o f a l l within t h e 37.5 - 3-50 Hz octave band, sound pressure levels within t h i s range were determined as shown i n f i g u r e 16-1.
Sound pressure levels from engine noise were determined using t h e t h r u s t and flow relationships f o r t h e P r a t t and Whitney STF-219 t u r b o j e t engine. An overall power l e v e l (FWL) of 186 dB r e l O ' l 3 watts is produced. The o v e r a l l sound pressure l e v e l (OASPL) is determined as: OASPL = PWL + D -10 2nX2 (16 -2) where D = a d i r e c t i v i t y correction, -15 dE3 a t 150% from t h e jet a x i s X = t h e distance f r o m t h e exhaust nozzle, 52 feet t o t h e aft edge of t h e wing st.udy a r e a The most severe sonic environment on t h e wing study a r e a due t o engine noise is thus defined by an OASPL of 123 dB. The sound pressure l e v e l i n t h e octave band corresponding t o fundamental panel frequency (37.5-150 Hz) is 122 dB at takeoff. This decreases rapidly as speed i s increased, with t h e influence a t s t a t i o n s forward of t h e exhaust disappearing as sonic speed is a t t a i n e d . The v a r i a t i o n s of OASPL with t i m e due t o boundary l a y e r noise i n d i c a t e values i n excess of those due t o engine noise ( f i g . 16-1). Therefore, t h e l a t t e r are not considered c r i t i c a l f o r design, and t h e acoustic environment due t o boundary l a y e r is used t o d i c t a t e design requirements.
A comparison of acoustic f a t i g u e e f f e c t s due t o boundary l a y e r noise for t h e 0.007 q and t h e 0.022 q c r i t e r i a are contained i n t a b l e 16-1. For ease of computation, t h e vehicle l i f e is conservatively considered t o be composed of t h r e e loading levels: one based on maximum pressure during t h e basic mission, one a t maximum dynamic pressure (2200 p s f ) during t h e p o s i t i v e maneuver, and a t a nominal dynamic pressure (2000 p s f ) during t h ? s p e c i f i c maneuver one excursion. Except f o r t h e lower outboard area, t h e win is conservatively analyzed for t h e maneuver (2200 p s f ) a t an OASPI, f o r loB0 loading cycles.
Using t h e maneuver sonic c r i t e r i a i s conservatjve s i n c e t h e maneuver pertur- bation requires only 16 hours of t h e 10 000-hour life. The 0.022 q c r i t e r i a i s v a l i d only during cruise, as discussed. below. Root mean square (rms) pres- sure and power s p e c t r a l density (psd) i n both t h e second and t h i r d octave bands are included. Pressure increases by a f a c t o r of 3 a r e produced under t h e more severe c r i t e r i o n and power s p e c t r a l density l e v e l s a r e increased by a f a c t o r of 10.
LAMINAR 4"JFWJlXNT TRANS I T I O N C RITERLA Transition from laminar t o t u r b u l e n t flow a% t h e wing leading edge is assumed t o occur a t a freestream Reynolds number of 130 000 based on leading edge diameter. Flow over both t h e wing upper and lower s u r f a c e is assumed turbulent whenever t h e leading edge is t,urbulent. For laminar leadjng edge I'Iow, t r a n s i t i o n on the wing lower s u r f x e is assumed t o be6f.n when t h e r a t i o of momenturn thickricss Reynolds number t o l o c a l Mach number equals 150. Trans- i t i o n on windward upper surfaces occurs under t h e same conditions as f o r t h e lower surface. Flow over leeward upper s u r f a c e s is assumed t u r b u l e n t f o r all f l i g h t conditions.
Flow f i e l d a n a l y s i s f o r t h e design t r a j e c t o r y i n d i c a t e d t h a t leading edge flow is t u r b u l e n t throughout climb and through t h e t r a j e c t o r y perturbations.
Immediately after t h e 2.0-g maneuver, t h e leading edge Reynolds number drops below 130 000 and decreases u n t i l t h e end cf c r u i s e . F l i g h t angle of a t t a c k remains above 8 O , however, s o a l l wing upper surfaces are leeward and flow t h e r e remains t u r b u l e n t . Since t u r b u l e n t flow is a stable condition and laminar flow is unstable, it is impossible t o p r e d i c t e x a c t l y when flow at t h e leading edge w i l l s h i f t f r o m t u r b u l e n t t o laminar, if at a l l . If leading edge flow does become laminar as soon as possible, a laminar-to-turbulent t r a n s i t i o n l i n e w i l l occur on t h e lower surface within t h r e e feet of t h e leading edge, measured along t h e wing chord l i n e during t h e c r u i s e portion of f l i g h t . The area of a p p l i c a b i l i t y of t h i s c r i t e r i a is shown i n f i g u r e 16-2, i n d i c a t i n g only a small region of t h e panel a f f e c t e d . The analyzed area is l o c a l i z e d n e a r t h e end closeout of t h e p n e l s adjacent t o t h e leeding edge s t r u c t u r e .
METHOD OF ANALYSIS Fatigue e f f e c t s of random sound pressure on t h e wing s t r u c t w e are determined by a n a l y t i c a l and empirical approaches of references 16-3, -4 and -5.
The following basic assumptions are postulated f o r t h e s t r u c t u r a l response, r e s u l t i n g stress l e v e l s , and f a t i g u e damage : 1 . S t r e s s e s t h a t contributed t o t h e sonic f a t i g u e damage are s i g n i f i c a n t only i n t h e primary s t r u c t u r a l resonanf modes.
2. Lightly damped s t r u c t u r e w i l l respond s i g n i f i c a n t l y i n only one mode when exposed LO random e x c i t a t i o n .
The f a t i g u e failure r e s u l t i n g from random sound p r e s s u r e e x c i t a t i o n 3.
can be i n t e r p r e t e d as a quasi-sinusoidal response whose frequency is t h a t of t h e s i g n i f i c a n t mode and whose amplitude has a random v a r i a t i o n .
The peak p r o b a b i l i t y d i s t r i b u t i o n i s Rayleighian (ref. 16-5).
4. The randomness of t h e pressure input can be defined s t a t i s t i c a l l y as t h e p r o b a b i l i t y rate of occurrence of instantaneous pressure. The instantaneous d i s t r i b u t i o n is Gaussian (ref. 16-5).
5 . For s i n g l e mode response, the sound pressure c o r r e l a t i o n is unity; i.e., t h e pressure everywhere on t h e s u r f a c e under t h e random pressure load is i n phase.
6 . Fatigut.
zmace is accumulated at a l i n e a r r&e (ref. 16-5).
S t ruc t u r a l Res pons e The response of t h e s t r u c t u r e , when excited by random sound pressure, may i n many instances be complex and i s due l a r g e l y t o the s t r u c t u r a l con- f i g u r a t i o n i t s e l f where t h e s k i n panels and support s t r u c t u r e are dynamically coupled. For these ar,alyses, it is assumed t h a t t h e s t r u c t u r e under study w i l l respond as a s i n g l e degree-of-freedom system. S t r u c t u r a l response tm random sound pressure levels can t h e r e f o r e be expressed by Miles' theory ( r e f . 16-6). This assumption may not be r e a l i s t i c i n many instances, but, it Serves q u i t e w e l l i n estiinating f o r more complex s t r u c t u r a l configurations t h e lowest resonant frequencies. This approach has g r e a t p r a c t i c a l value i n t h a t t h e v i b r a t o r y motion of a complex s t r u c t u r e g e n e r a l l y e x h i b i t s its maximum displacement and stress amplitude a t its lowest resonant frequency.
Miles' theory is dependent on s t r u c t u r a l damping r a t i o s , response frequency, and normalized stress response, which are discussed b r i e f l y i n t h e following paragraphs.
S t r u c t u r a l Damping The zmplitude of t h e displacement and dynamic stress i n t h e s t r u c t u r e , when excited at any resonant mode, is dependent on t h e damping r a t i o . Most of t h e f a t i g u e damage can be expected t o accumulate when t h e response is i n t h e least damped mode. Damping r a t i o ( 6 ) i n t h e range of 0.010 t o 0.020 is usually considered f o r t h e s e analyses; here, t h e conservative value of 0,010 is used.
Response Frequency Determination of t h e s t r u c t u r a l response frequency i s another important consideration i n sonic f a t i g u e analyses. It i s assumed t h a t t h e niaxj tiiutn sonl c w ' i l l be accumul. ?d i n t h e lower frequency modes of tlie struc- f a t i g u e damage tural configuratior, and, the1 are, it is important t o determine a c l o s e approximatton of t n e s e resonan frequencies. For a n a l y t i c a l purposes, t h e response freqEency is determinr l a n d t h e n t h e sound p r e s s u r e level is chosen t o be t h e octave band l e v e l cc respondinc t o t h i s frequency. Due t o t h e complexity of t h e s t r u c t u r e and t h e i n t e r a c t i o n between members, it is very d i f f i c u l t i n many instances t o p r e d i c t t h e exact resonant frequencies; h : s t o r i c a l t e e t data and/or response t e s t s are required t o better d e f i n e ul;ructural response. For a n a l y t i c a l purposes, response frequencies f o r t h e various s t r . - c t u r a l members are determined from beam and p l a t e t h e o r y (ref. 16-7).
Normalized S t r e s s As noted previously, s t r u c t u r a l response t o random pressure f l u c t u a t i o n s is expressed by Miles' theory w i t h t h e rms ,';ress as: where:
-
Q = rms s t r e s s d = t h e damping r a t i o fO = Tesonant frequency of t h e system
o0 = root mean square pressure density (psi2/Hz)
00 = normalized stress The normalized stress response t o a unit pressure c l o s e l y approximates t h e s t a t i c s t r e s s response t o a u n i t pressure; therefore, basic p l a t e and beam theories a r e used i n determining t h i s parameter f o r s t r u c t u r a l sizing. In addition, t h e normalized s t r e s s (ao) is e q u d t o 90 percent os, r e s u l t i n g from a u n i t pressure loading. Bending s t r e s s e s i n p l a t e s and supports and a x i a l s t r e s s e s i n members &re determined from basic theories. Through Miles' equation, rms s t r e s s e s due t o t h e various random conditions are determined f@r f a t i g u e l i f e predictions.
Flange S t r e s s Adequate support s t r u c t u r e s i z i n g i s esserxkiai, s i n c e t h e prying a c t i o n of t h e a t t a c h flange on its f a s t e n e r s causes Etre%es i n t h e flapze. This is sometimes c r i - t i c a l i f t h e thickness of t h e flange is l e s s than t h e skin thick- as shown below, is out of proportion r e l a t i v e t o ness or if t h e moinerii; arm, A, panel width, as may be t h e case w i t h a large bend radius or overhang of t h e cap flange due t o corrugated webs ( r e f , 16-5).
Test Data Web The rms flange s t r e s s r e s u l t i n g from a w i i t load is determined from t h e following empirical equation: c = (16-4) f t: where: of = rms flange stress B = panel width A = e f f d , i v e moment arm tfl = flange thickness $?&= rms sound pressure, p s i C = empirical constant = 21.3 for dodble flange = 42.6 f o r s i n g l e Flange
I
Fatigue Cuives and Allowables ir, f i g u r e 16-3 a r e used f o r The Rend 41 random f a t i g u c curves presented t h e sonic f a t i g u e analyses. These data w e r e s u l t s of narrow-bm$ rqdoln amplitude bending f a t i g u e tests conducted on sharply notched Rene )'I specimens Theoretical l i f e pi-ed'ctions were made for t h e random loading t e s t s by using t h e Palmgren-Miner zumulative damage r u l e and two d i f f e r e n t peak stress d i s t r i b u t i o n s , t h e d i s t r i b u t i o n determined from t h e tests and t h e c l a s s i c a l Rayleigh d i s t r i b u t i o n . The data i n d i c a t e t h a t , f o r s h o r t l i v e s , a procrcssive For l-orit., l i v e s , loss of f a t i g u e strength occurred with increase i n tempt:mture.
f a t i g u e strength decreased from room temperature t o r(OO?, l)iii, did nol. tl(:(:rcanc* "be Rend 11.1 heat ailield p m c l d,rc;m:cs wc?rc: (!oiii[uLr'(,ii 1 . 0 Llu: f u r t h e r at 1400Ol?.
10 000 psi f a t i g u e a11 owabl-c (cnilumncc l i m i t S I ; ~ C U G ) .
The lower outboard surface heat shield TD N l C r allowahles were based on t h e analpis discussed i n section 17 (fatigue). Figure 14-4 shows a t o t a l strain versus cycles t o failure f o r TD N i C r from 1600~ t o 2400% f o r three factors of safet;y. The methods of reference 16-8 were employed t o derive the curves an3 a factor of safety (P.S.) of 1 . 5 is recommended (ref. 14-8) t o assure that a l l test resul%s fall above the curve. Table 16-2 shows the allowable stresses for factors of safety (on stress) of 1.0, 1.5, and 2 . 0 .
The 953C psi allowable at P.S. ZF: 1 . 5 is conservatively used i n t h e analysis for TD-NiCr shields and heat shield clips.
Scatter Factor and Desrgn L i f e A scatter factor of 2.0 is used t o bracket the normal spread i n fatigne life. This factor accounts f o r scatter fatigue data, f o r tolerances in mnufacturing and materzals, f o r unknowns i n analysis techniques, and for scatter i n environment .
The anaJysis presented is based on a R e d 41 allomble r m s stress of
10 OOO psi at TOO0 t o 1400% (fL . 16-3) which corresponds t o an extrapolated
endurance l i m i t greater than 10 18 cycles. Should a conversion from cycles t o time be desirable, the following equation is appropriate, where: R = reduction factor = 0 . 5 0 (for scatter factor = 2.0) N = cycles
fo = fundamental panel frequency, Hz
Design Nornographs and Service L i f e Curves Results of sonic fatigue development tests and full scale tests o i ' seveial types of aircraft structures are compiled and are used t o produce acoustic fatigue design charts f o r aluminum and titanium a l l o y (re$'. :LO-3 and l<%h). These data are combined with applicable thcory t o clurivc. the r c h t i o n s h i p that yicxlds t h c capability of a panel t o wiI.hstcltic1 s o n i c j.'al,jf:iitx due t o inndotn acoustic cxcitation. This cmpi r i c a l rclai.ionsh i p rc?.la-l.cs 1.11~: allowable spcctrurii lcvcl (dR/IIz) t o the gcoinctric and tnal.crial pr.cit!irti.r.r:i Ly t h c rollouing equation: where Rend 41 TD N i C r K = empirical constant = 187.61 arms = allowable rms stress (psi) 10,000 9530 8 = structural damping r a t i o (C/Co) 0.01 0.01 E = modulus of e l a s t i c i t y (psi) 31.6~10~ 21XlOG P = mterial density (lb/cu in.) 0.298 0.306 g = acceleration of gravi.ty (in./sec2) A = panel cross sectional area (in.*/in.)
I = p n e l moment of i n e r t i a (in. /in.)
Z = distance t o extreme f l b e r (in.)
L = panel length (in.)
16 -8 For both the R e d 4 1 and TD N i C r constants shown above, equation 16-6 becows
A1lowabl.c dB/€Iz = 195 - 5 log Kt -C 20 log p$3'4)
( 1 6 -7) where K = t E temp/ E Validation of Analyses Since a sonlc fatigue preventior, prrya-: in-irolves many varlables d i f f i c u l t t o model analytically, labomtory developmerit tests are necessary t o complement analyses. These development t.ests are required t o support the detail desi@, evaluate new design concepts and materials, and substantiate analytical- fatifpc l i f c predictions; a l l of these are aimed at developing minimum weight and tni nitnuni cost structures.
16-9 FATIGUE ANALYSIS RESULTS Margins of safety are shown f o r primary s t r u c t u r a l panels, r i b and spar caps, heat shield panels, and heat shield clips.
Monocoque Primary Structure The monocoque primary structure results are shown f o r waffle and honey- comb sandwich panels. The flexural r i g i d i t i e s , D1, D2, D3, and other constants are discussed in reference 16-9.
Waffle - The natural frequency (f,) of t h e waffle panels is solved
The basic d i f f e r e n t i a l using orthotropic p l a t e theory (ref. 16-10).
equation is ( 16 -8)
-
where q = -& % (load term) g Q) m .
mnx nnY
and the deflectLon, s i n - w = Qmn s i n -
b a m = l n=l the solution is where leading t o for the lowest frequency, and a = 20, b = 40 in.: ( 16 -10) I 16-10 Tkle rms stress (cq. 16-3 ) is solved using 6 = 0.01 and t h e normalized stress of the maximum unit pressure s t r e s s (as) in the skin (ao) equal t o 90 percent o r t h e stiffener.
The results are summrized i n table 16-3, where margins of safety based 011 the 10 000 p s i allowable are also shown. All margins are high, w i t h the lowest (1.16) based on the 2.2 percent q.
Honeycomb sandwich panels - The natural frequency (lowest mode) of
honeycomb sandwich panels are given by reference 16-11: ( 16 -11) for a = 40, B = 80, R e d 41 ( 16 -12) M stress: The normalized stress (a ) is equal t o 90 percent of the unit pressure stress : (O.9)M 146.45 O o = - = - htmin htmin -where
GX = 0.1017(40) = 162.72 in.-1b (ref. 16-52)
tlnin = thinnest face thickness RIG stress, ref eq. (16-3), 1 1
- 112
for 6 = 0.01, o = 8.86 co(fo40)
16-11 The results arc? summarized i n t a b l e 16-11, where margins of s a f e t y are showii f o r rms stress bascd on the 10 000 p s i allowable. EZtrgins of safety above 5.0 a r e seen t o exist except on t h e lower outboard p n e l s , where use of t h e 2.2 percent (1 c r i t e r i a r e s u l t s i n M.S. = O.%, which is s t i l l large.
Semimonocoque and S t a t i c a l l y Determinate Primary Structure The sonlc f a t i g u e r e s u l t s f o r the spanwise and chordwise s t i f f e n e d primary structural. panels a r e shown i n t a b l e 16-5. The margins of s a f e t y are based on rms stress predictions and the 10 000 p s i endurance l i m i t allowable.
The lowest margins for each construction occur on t h e lower surface outboard where t h e high t r a n s i t i o n l i n e sound pressure level (0.022 q) is considered applicable. The minimum margin of 0.0 for t h e "sheet-metal" constructions occurs on t h e tubular panels where minimum gages and low moments of inertia ( l i g h t s t a t i c loads) tmke t h e designs more susceptible t o f a t i g u e damage.
The first mode bending frequency, fo, from reference 16-7 is: i
-
1 % EIg *
fo = c[x] HZ
where C = 1.57 for pinned ends $ = a temperature correction = Etemp/ErCr L = panel width, i n .
Rib and Spar Caps The margins of s a f e t y f o r t h e r i b and spar caps a r e shown f o r each s t r u c t u r a l concept.
Monocoque waffle - The maximum rectangular panel reactions on t h e r i b
and spar caps due t o Lateral ;?ressure sonic loading are approximately equal on t h e long and short s i d e ( r e f . 16-12) : where a is t h e s h o r t s i d e of t h e panel. Equation (16-4) can then be used f o r both spar and r i b caps, provided t h e s h o r t s i d e panel dimension i s used f o r B The outboard 8 inches i n equation (16-4). The results a r e shown i n t a b l e 16-6.
of the spar and t h e leading edge beam require 0.033-inc'h thicknesses t o meet t h e 0,022 q c r i t e r i a , 16-12
Monocoquc honeyconh sandwich - The waffle methods are pertinent, using the
1iO-iri(:t-b short sick tiimcnsion for thc honeycomb panels. The r e s u l t s arc a l s o showri in table 1G-6, but, here t h e last d inches of the spar and t h e leading edge, beam thickness requirement is O.043-inch t o s a t f s f y t h e 0.022 sonic requirement .
Semimonocoque spanwise - For spanwise stiffening, t h e sonic f a t i g u e pres-
sure loadings are reacted by t h e r i b caps. The r i b cap designs are i d e n t i c a l for t1.e beaded and tubular and t h e r e s u l t i n g margins of s a f e t y are shown i n t a b l e s 16-7 and 16-8. The leading edge beam cap thickness is g r e a t e r for t h e beaded because t h e higher panel n a t u r a l frequencies cause a higher r m s stress.
Semimonocoque chordwise - Chordwise sonic f a t i g u e pressure loadings are
reacted by t h e wing spars. The spar cap margins are shown i n t a b l e 16-9. U s e of t h e 0.022 q c r i t e r i a results in large flange stress i n t h e l a s t 6 t o 8 inches outboard adjacent t o the leading edge. A l o c a l 0.010-inch doubler is s u f f i c i e n t t o provide positive margins of safety.
S t a t i c a l l y determinate - The c r i t i c a l r i b cap margins of s a f e t y f o r t h e spanwise stiffened, s t a t i c a l l y determinate concept are shown i n t a b l e 16-10.
The leading edge beam cap requires a thickness of 0.049 t o meet t h e 0.022 q c r i t e r i o n .
Heat Shield Sonic Fatigue Analyses were conducted t o determine t h e effects of random sound pressures on t h e multisupport corrugation heat shield and t o define t h e requirements imposed by t h e established criteria. The a n a l y t i c a l approach presented i n t h e semimonocoque primary s t r u c t u r e evaluation was used t o determine estitmted allowable sound pressure l e v e l s (dB/Hz) and panel/clip s t r e s s e s due t o t h e random sound pressures. The heat shield panel n a t u r a l frequencies were based on a '[-span beam analysis and stresses determined.
The heat s h i e l d is Rend 41 except for t h e BL 304 t o 350 lower surface which is fabricated of T D Nidr.
The maximum moment ( M ) , due t o a 7-span beam is equal t o 0.10 p f o r calculating oo, t h e normalized s t r e s s due t o a u n i t of loading (1.0 p s i ) .
The r e s u l t i n g margins of s a f e t y are shown i n tabl-e 16-11 where t h e following values were used f o r rms stress allowable (0)- Rene' 41 10 000 p s i TD N i C r 9 530 Psi Positive m r g i n s a r e noted throughout.
Heat Shield Clips The heat shield c l i p s are analyzed using t h e equation (16.4). The r e s u l t - ing margins of safety a r e shown i n t a b l e 16-12 f o r t h e allowables noted above.
16-13 REFERENCES 16 -1 Dyer, I.; Franken, ?.A.; and Ungar, E. E.: Noise kvironments of F l i g h t Vehicles, Noise Control, January-February 1960.
16 -2 Eldred, K.; Roberts, W.; and White, R.: S t r u c t u r a l Vibrations i n Space Vehicles, WADD TR 61-62.
16 -3 Lockheed C a l i f o r n i a Company: S t r u c t u r a l L i f e -Assuranc e Manual (SLM No. $, Sonic Fatigue Prevention).
1 6 -)I 16 -5 Lockheed Georgia Company: Ix; lVS58-1-3 C5A F l n a l Sonic Fatigue Analysis, February 1968.
16 -6 Miles, J.W.: On S t r u c t u r a l Damge Under Random Loading, Journal of t h e Aeronautical Sciences, Volume 30, No. 11, November 1954.
16-7 Fredberg, C.R.; and Kemter, E.N.: Elements of Mechanical Vibration, John Wiley and Sons, I n c . , New York, 1949.
Thermal S t r e s s and Low-Cycle Fatigue, McGraw Hill Co. 1966 16 -8 b n s o n , S.S.: 16 -9 Hubka, R.E.: S t r u c t u r a l Optimization of S i x Different Types of Rectangular Plates Subjected t o Combined and Biaxial-Compressive Loading, LockheedCalifornia Company, LR 21662, 1968.
16 -io Timoshenko, S.; and Gere, J.: Theory of E l a s t i c S t a b i l i t y , McGraw Hill Co., Second m i t i o n , 1 9 6 1 .
16 -11 Timoshenko, S . : Vibration Problems i n Engineering, Van Nostrand Co Third Edition, 1955.
Theory of P l a t e s and S h e l l s , 16 -12 Timoshenko, S; and Woinowsky-Kreiger, S . : Second Edition, McGraw H i l l Co,, 1959.
16-13 Philips, E. P.: Fatigue of Rend 41 Under Constant and Random Amplitude Loading a t Room and Elevated Temperatures, NASA TN D3075, Iangley Research Center, November 1968.
16-14 I TABLE 16-1 ACOUSTIC FATIGUE C R I T E R I A 1 0 000 HOUR LIFE
37.5 < fo< 150 HZ
r--- Leading
Overall Sound Pressure Level, O S P L _--_- T i m e L C V L . 1 P = 0.022(") ? = o.oo7q
RIG PSD R 4 3 psc
seconds pressure, P ( p s f ) (ps5)2/fIz prcssul.e, ( psi ) ' / H Z p s i p s i
1500(b) 35.98 x 1 0 ' 9.0080 1 . 7 0 7 x lo4 0.0251 1.680 x
10.92 x 103 0.0095 2.43 x 2000(C) 2200(d) 11.1~0 1 0 0 3 0.0100 2.67 x "Valid only during cruise.
b B s c d on rtaxi t w n pressure during t h e basic mission.
C Based on nominal pressure during maneuver excursion.
%sed on maximum dynamic pressure during p o s i t i v e nlaneuver* Table 16-2
SONIC FATIGUE ALLOWABLE3 FOR TD R i C r - LOWER OUTBGARD HEAT SHIELD
a
Total r e v e r s i b l e strain f o r one cycle for lo7 cycles ( f ~ g . 16-4)
-4 I
c .- baz a
___+ . - -
ith jj
&" "
@
0 0 0 0 0 0
- -
!- &--e?(\!
OLU - .
16-17 ! - .- h ' P 11 d .I S a 0" 16-19 i t-l I
9-"-
'9
rf d rt k
2 4 2 k
u 16-21 I . .
rl c h I oco 0 0 M O M 0 ? ? 3 - ? ? -'.a=.
0 0 0 r l d 0 4 L n m C n ; t m m 2 A - l n m o m ; J -
o q o 0 0 0 0
. . . .
A \c) \ o v ) r l r l W r- &i co u 3 d \ d d rl cd .rl r- - + a .
-PIP-
0 - * d
.rl k u 16-22
s 2 p
0 0 0 0 0 . . . 0 .
& G l i b
4 . I
* . . . . . *
h r- >k
d o d
16 -24 n h I a r l w m r l A - c u o m o r l w o o a 0 0 0 0 ? ?
d d d d d 0 0 . . . . . . .
0 0
2 3 3 w w O 0 lnln
I rl 0 0 c u ( u 1 7 d I I 16-25 16-27
I
I n n
5 2 3 2 i r l C U
? ? ? ? 9 ?
0 0 0 0 0 0 n 0 *rl t - - e m
2 G
v CU CU n a rl a ,
- I
.ri
E
O N X -$ v j B L 212
I
Rib Rib -$BL 258
%. Rib
-fBL 298 +BL 338
\
Figure 16-2. Wing area applicable t p the 0,022 q criteria 1 6 - 3 2 . .
s
N b
P
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I I I I I I l l I I 1 1 1 I l l Figurn 16-4. TD NICr Fatigue Allowables 16-33 1.1,
Section 17
Section 17 FATIGUE ANALYSIS by: I . F, Sakata, C . C. Richie, H. H. Armstrong, B. C . Wollner C O N T r n S Page N o .
FATIGUE SPECTRA 17-1 WING FATIGUE SPECTRA DEVEZOFMENT 17-2 ALIOWABLE DESIGN FATIGUE STRESS OETERMINATION 17- 3 Monocoque Waffle 17- 4 hbnocoque Hbneycomb Sandwich 17- 4 Semimonocoque and Statically Determinate 17- 5 Spar and Rib Cap Fatigue 37-5 REFERENCES 17-6 TABLES Table Page 17-1 Time segments for spectra definition 17-7 17-2 Discrete loading spectra derived from cumulative loading spectra for Sm = constant 17-8 Life utilization r a t i o for Kt = 4.0 17-9 17-3 Allowable tensile stresses, Rene' 41 17-10 17-4 Monocoque waffle fatigue l i m i t loads, cruise and +2.0g 17- 5 17-11 conditions 17-6 Monocoque waffle unit stresses 17-12 Monocoque waffle fatigue analysis 17-12 17-7 17-8 Monocoque honeycomb sandwich fatigue l i m i t loads, cruise and +2.0g conditions 17-13 17-14 Monocoque honeycomb sandwich fatigue analysis 17-9 17-10 Semimonocoque and s t a t i c a l l y determinate primary structure fatigue analysis, cruise condition 17-15 Semimonocoque and s t a t i c a l l y determinate primary structure 17-11 fatigue analyses, 2g maneuver l i m i t loads 17-16 17-12 R i b cap fatigue, semimonocoque spanwise tubular and semi- monocoque spanwise beaded cruise l i m i t loads and tempera- tures 17-17 17-13 Spar cep fatigue semimonocoque chordwise cruise l i m i t l c s d s end temperatures 17-18 17-v 17-1 Hypersonic cxuise airplane design trajectory Frequency of exceedance of c.g, load factor 3 . 7 - 2 Fsequency of exceedaoce of longitudinal bending moment 17- 3
a t ; statior: 2364 - 10 000-hour l i f e 17-21
17- 4 Fatigue spectra for wing structure life determinekion 17-22
Constant l i f e diagram - Rene‘ 41 (Kt = kO), room
17- 5 t emperatme 17-23
17- 6 Constant l i f e 8iagmm - Rene’41 (Kt = LO), 70O0F
17-24
Constant l i f e diagrlram - Rene’41 (Kt = 4 . 0 ) , l l O O ° F
17-7 17-25
17-8 Constant life d f a g m - Rend41 (Kt = LO), 1kO0F
17-26 S/M curve for R a e 4 1 at l b O ° F (Ke = 4 . 0 ) 17-9 17-27 SYMEOIS Butt line BL C Distance from neutral axis to extreme fiber Center of gravity c. g .
D Calculated life utilization ratio E Modulus of elasticity Fatigue allowable stress for operational load condition Fatigue allowable stress Fatigue allowable stress for ultimate load condition Tensile ultimate strength Tensile yield strength Alternating stress Mean stress Gravitational acceleration H Altitude Moment of inertia, in.
I K Fatigue quality index Stress concentration factor Kt k Number of stress levels L Length Calculated life LC Life span in hours represented in the spectra L1 M Fuselage body bending moment; Mach number M S Margin of safety N Number of cycles Number of loading cycles t o failure f o r the ith stress level from the relevant constant-life diagram Btensional forces and shear force i n xy coordinate system Nx, NY, N xy per unit length n Cumulative number of occurrences Number of loading cycles at the ith stress level n i n b a d factor in. z direction P Pressure Dynamic pressure R Reduction coefficient used t o assure a specified probability of obtaining a test l i f e equal t o o r greater than the calculated l i f e RT Room temperature T Temperature t Time; thickness
e Equivalent thickness
Z I/C section modulus a Angle of attach Differential pressure AP E Strain
c Summations
c
Cumulative nunber of occurrences n 17-x
Section 17
Section 17 FATIGUE ANALYSIS Analyses were conducted t o establish allowable dcoigo s t r e s s levels f o r fatigue evaluation of primary structure and heat chisld concepts t o meet the specified l i f e requirements of 10 000 hours. The factors considered f o r selection of the design stress levels included operational utilization, corresponding loading spectra snd environmental conditions, temperature, and structural fatigue quality (ref. 17-1).
The loading epectra, including the ground-air-ground cycle effect, were combined t o obtain a t o t a l spectra for cumulative damage evaluation. Constant l i f e diagrams f o r Rene'41 a t room temperature, and a t various elevated t e m - peratures using a K t = 4.0 (stress concentration factor) were used. Although the design goal i s t o achieve the lowest practical fatigue quality index, a minimum value of 4.0 vas selected based on previous experience. Early service failures are characterized by K values greater than 4 ; whereas, parts which have demonstrated adequate service l i f e invariably give K values l e s s than 4.
Ekperimental evaluation of designs with reasonable simulation of the loading spectra i s essential t o demonstrate acceptable fatigue quality, i n addition t o care given t o details during design and fabrication of structural elements.
A fatigue scatter factor of 1.5 w a s used f o r the nominal vehicle design.
FATIGUE SPECTRA A fatigue spectrum was established for detemination of cyclic loadings on the vehicle with the specified maneuver perturbation occurring every tenth f l i g h t for the 10 000-hour vehicle life.
The altitude-Mach number schedule (fig. 17-1) was divided into seven segments (table 17-1) consisting of three during ascent, two during cruise, and two during descent, so that typical load levels could be defined within each segment. A spectrum of load occurrence was developed fur each segment.
The vehicle altitude within each segment was related t o load factor, thus defining the frequency of exceedance of a given load level within each seg- ment ( f i g , 17-2). These individual spectra were summed t o obtain a cumulative frequency of exposure t o cyclic loading.
A frequency of exceedance of cog. load factor was established f o r each segment of the design traJectory as shown i n figure 17-2. These spectra were based on previous studies for a supersonic transport (ref. 17-2) with an Since the SST airplane operates in i n i t i a l aecent along a similar profile, a lower Mach-altitude environment, extension of the load factor experience t o the hypersonic cruise vehicle is conservative.
17-1 The spectra for inflight cyclic loading (fig. 17-2) was used to construct The spectra were obtained for a cumulative flight loading spectra (fig. 1 7 - 3 ) .
the three flight regimes (ascent, cruise (including maneuver), and descent) so that pertinent temperature effects could be properly taken into account.
Cumulative frequencies in excess of the defined l3ad factor excursions were based on Maneuver b a d Spectrum C of MILA=8866(ASG), Application of this portion of the flight loading spectra for determination of the fatigue strength is complicated by the requirement that the limit load is considered to occur 10 percent of tho time, which precludes a single-occurrence load level, A ground-handling cycle (taxi considerations) is included in figure 17-3, to permit definition of forces on the vehicle throughout the contemplated ground-air-ground cycle. Since design loads on the vehicle are defined by flight loading conditions at cruise altitudes, it was necessary to adjust vehicle loads associated with ground-handling/landing criteria to satisfy the limit load envelope.
Ianding criteria were selected as 2-g acceleration at the nose gear for 0.33-g for a single occurrence per flight. a single occurrence per life and The criteria set forth in the foregoing paragraph were considered as limit.
The cruise diagram of figure 17-3 includes the -0.5-g and the +2.0-g maneuvers with 1.0-g cruise represented by the apex (Le., M = -30 x 106 i n . - l b , n = 1 0 0 0 0 0 ) . The +2.0-g maneuver condition is represented by the point de- scribed by the intersect'on of the cruise line with the extreme left vertical
line ( i .e . , M = -60 x 1 0 i; in.-lb; n = 8 1 1 ) . The -0.5-g maneuver condition
is represented by the cruise-line intersection with 811 cumulative number of occurrences which corresponds to -18 x 1 0 6 in.-lb of bending moment.
WING FATIGITE SPECTRA DEVEZOPMENT The spectra for fatigue evaluation of the wing was assumed to be similar to that described for fuselage bendiw (figure 1 7 - 3 ) . Initially, the assump- tion was made that the wing stresses we e proportional to the bending moments presented in figure 17-3 (i.e . , 30 x 1 0 8 in.-lb = 30 000 psi for cruise).
Based on this proportionality, maximum, minimum, and mean stresses were established for ascent, cruise (including maneuver), descent, and taxi. The corresponding applied cycles were compared with the allowable cycles using the appropriate constant life diagrams and, through the theory of linear cumulative damage, the service life was determined. The initial results yielded a calculated life greater than 19 000 hours (with a scatter factor of 1 . 5 ) ; therefore, the stresses were increased until the specified life was obtained. The cumulative spectra used to determine the allowable fatigue design stress are presented in figure 17-4, indicating representative values of mean stress (fm) and alternating stress (fa) that result in 1 0 OC3 hours of 1s.fe.
Applied stress relationahips (air plus thermal stresses ) greater than those specified, result in less life and correspondingly smaller stresses will result in increased life.
1 7 ' - 2 ALLOWABLE DEBIGN FATIGUE STRESS DETERMINATION Discrete loading spectra were derived based on the established cumulative loading spectra and usee for cumulatP.2 damage evaluation (fig. 17-4; Constant l i f e diagrams for R F L ~ ' , I a t room temperature, TOOOF, table 17-2).
1100"F, end l b O ° F (figs. 17-5 through 17-8) and appropriate S-N curves (fig. 17-9) for a $ = 4.0 were used.
The Palmgren-Miner theory of linear cumulative fatigue damage was used t o determine the required service l i f e . The basic equation is expressed as follows : n n n ni
. . . +- k = h - i A+%+* + - +
D = N 1 . N 2 Ni Nk i = 1 Ni where D = calculated l i f e utilization r a t i o ni - - number of loading cycles applied a t the ith stress level Ni - - number of loading cycles t o failure for the ith stress level from the relevant constant-life diagram.
The relevant constant-life diagram is the one which applies t o the material and fatigue quality index of the section under consideration n i - - - cycle r a t i o I$ k = number of stress levels considered The method of analysis using the above equation as a basis is as follcws: 1, Select a fatigue quality index K for the section under consideration (Kt = 4.0).
2 . Obtain loading spectra end temperakures associated with applicable phase of spectra.
Obtain constant-life diagi-ws ?as Q = K for Rend 41 at 3.
applicable temperatures (fig@. L705 throllgh 17-8).
4. Convert applied l i m i t loads t o stresses (since constant-life diagrams are presented as percent of room temperature strength, loads are converted t o streases as a percentage of the room- temperature ultimate tensile strength).
Calculate the cycle r a t i o of each loading case and add the 5.
cycle ratios t o obtain the l i f e utilization r a t i o I'D" (table 17-3).
17- 3 Calculate the life in hours for the section under consideration 6 , by L1 LC =-" D = calculated life where LC
5 = the life span in hours represented in'the spectra
used in the analysis R = a reduction coefficient used to assure a specified probability of obtaining a test life equal to or greater than the calculated life Using a reduction coefficient of 0 . 6 6 7 (which corresponds to a scatter factor for nominal design equal to 1 . ! 5 ) , a calculated life of 1 0 000 hours was determined (table 1 7 - 3 ) . This life-time corresponds to the total life requirement of the vehicle and indicates that for the assumed alternating stress levels and the number of applied cycles and temperatures, the operating lg stress level ( f , ) during cruise is 46 000 psi. The basic material allow- ables, as well as allowable tenaile stresses for fatigue for both cruise and The operational stresses maneuver conditions are presented in table 17-4.
(Ffo) reflect allowables applicable for service ,life calculations. The ultimate value for Ffn is an eq.uivalent value for comparative purposes, with the minimum value (underlined) governing the design. Reduction of design stresses to the minimum values provides a structured system which meets the specified life requirement of 1 0 000 hours.
Mono co que Waffle The 45" x 45" waffle panel limit eLr and thermal loads are summarized in table 17-5 for both the cruise and 2g maneuver conditions. & i t inplane loads ( N , and Ny) were input into the computer program (Section 10) to determine unit internal stresses (table 1 7 - 6 ) . Also, unit pressure @P) lateral loads were input and the resulting stresses are show in table 17-6.
The tensile inplane loads and the limit pressure loads for the 2g and cruise conditions are summarized in table 17-7 where they are multiplied by the unit cases and summed to arrive at the predicted fatigue levels for the wing study area. These stresses are compared to the appropriate fatigue allowables to arrive at margins of safety. The minimum margins are tabulated; the lowest being 1 . 5 0 on the upper skin outboard for the cruise condition.
Monocoque Honeycomb Sandwich The limit air and thermal loads for the 2-g maneuver and cruise condition Table 17-9 summarizes the fatigue e,nelysis, including are shown in table 17-8.
margins of safety. The stress resultants for unit cases of pressure and inplane loads for the 40 x 8 0 in. panels are given. These are multiplied by the tensile 1 7 - 4 hplane loads and predicted pressures, also shown. The stresses are summed and compared with the appropriate fatigue allowablee t o obtain margins of safety. The minimum margin (0.36) is seen t o occur on the upper outboard surface for the cruise condition.
Semimonocoque and Statically Determinate The fatigue analysis r e s u l t s and margins of safety f o r the foul* "sheet" metal" wing constructions a r e shown i n tables 17-10 (cruise) and l7-:!1 (2-g The air load inplane loads, N , a r e the c r i t i c a l "x" o r "y" maneuver).
direction loads, as are the thermal strains. The three s t r e s s components a r e : inplane stress: fl = N/% thermal stress: f2 = E:
bending stress: f3 = - M Z where M = %
I The sum of these stresses a r e compared with the appropriate fatigue allowables (table 17-4) t o determine the margins of safety. The minimum margin (0.003) occurs on the s t a t i c a l l y deteiminate center lower surface (E t o BL 120), for the 2-g condition.
The 60-in. rib spacing causing large bending stresses due t o lateral pressures was t h e major s t r e s s contributor in this analysis.
Spar and Rib Cap Fatigue The caps for spxs and r i b s a r e subject t o fatigue analysis whers they must support primary thermal loads and air loads WiChout panel support. That is, for the spanwise-stiffened concepts the rib caps a r e considered, and f o r chordwise stiffening the spar caps a r e considered. The lowest margins of safety occur during cruise and a r e shown i n tables 17-12 and 17-13. The combined air and thermal stresses a r e not applicable when the net s t r e s s is compression. large margins, i n excess of 1.0, exist f o r a l l concepts.
REFERENCES 17-1 Structural Ufe Assurance Manual. bckheed-California Company, 1968, 17-2 Airframe Design. luckhoed- California Company, Volume 11-C, w9839.
TABLE 17-1 TJME SEGMENTS FOR SPEECRA DEFINITION Angle of attack, Time, Altitude Mach NG, a !
M t, H , Ft degrees min 1 . 6 4-3 6 . 0 2 . 8 3 . 8 5 1 3 . o 6 . 5 0 4 . 3 5 1 9 . 9 8.00 630 9 . 3 1 36.0 8.00 530 9 . 6 52.2 u2 500 9 . 7 7 . 1 5 4 7 5 6 2 . o 84 ooo 390 5.75 3. 45 7 2 . 4 27-7 TABLE 17-2 DISCRETE LOADING SPECTRA DERIVED FROM CUM[TLATNE LOADING SPECTRA FOR % = CONSTANT Given cumulative Derived discrete loading spectrum loading spectrum ~~ Alternating Cumulative Alt ernet ing No. of cycles stress level, No. of stress level, applied at fa, Condition cycles , fay %, n psi psi C n ~~ 100 000 2 500 9 6 000 4 000
5 om
3 820 7 500 Taxi 10 000 180 12 500 loom temp 15 000 8 16 750 18 500 1 ~~ 10 000 5 000 2 500 3 650 Ascent , 700" F 10 000 13 7 500 337 14 000 1 12 000 12 0 100 000 2 500 67 ooo 5 000 33 000 21 500 7 500 10 000 ii 500 12 500 7 500 Cruise,
1 5 ooo 4 000
2 700 1400°F 17 500 2 G 000 i 300 21 e50 22 500 1 000 22 500 22 500 0 1400 1 250 2 500 5 000 Descent, 7 500 133 10 000 l l O O ' F 12 500 15
15 ooo 2
15 850 16 700 1
-
17- 8 TABLE 17-3 LIFE W I L I W I O N RATIO FOR K t = 4.0 c Applied Allowable Cycle *a’
cycles, cycles, ratio, r% I
No. Condition n N % Ftu at RT 1.47 107 .010 9.6~10 4 Ttixi, 35 =7 3 . 8 ~ 1 3 5x105 .008 2 Room (60 700 psi) 4.41 1 . 7 2 ~ 1 0 ~ 5xlO4 Temp 7.35
7 3 .6x104 - .018
9 *85
I
~ Ascent, 1.47 9.65xl03 107 0001 2 700”F 4.41 3.37~2.0~ 5x105 .001
7.06 12 105 - .002
1 27 01 Cruise,
2 1400”F (46 ooo psi)
27.1 6 mneuver Descent, 2 1 l O O O F
I
Re& 41; Ftu = 170 000 lb/in.2, room temp R $ (.667)(10 000) % = - - = 10 000 hours D - (.666) where Lc = calculated l i f e (hours) R = reduction coefficient = 0.667 (scatter factor = 1 . 5 ) L1 = l i f e span represented i n spectra (hours) D = l i f e utilization ratio 17-9 U l t i m a t e L i m i t Operational
Temp -
Reference GJ? Ftu,(&) Ffu, Fty, (b) 2/3 Ftu, p s i P s i psi p s i psi %sic Material RT 1 7 0 ooo 130 ooo 113 333 46 ooo
Cruise 1400 1 s ooo go ooo 108 ooo 86 ooo
46 ooo &newer 14eo 1 s 000 133 400 108 ooo 86 000 68 500 a, = ( 0 . 7 6 ) ( 1 7 0 000) = 129 000 p s i (min.)
- t u 1 4 0 0 ? l ?
= (0.83)(130 000) = 108 000 p s i (min.)
bFty 1400% fatigue design allowable stress : C = Operational stress.
Ffn, For cruise, Ffo = ((27.1)(170 000) * (loo)] = 46 000 p s i
For maneuver, Fro = [(27.1 3. 13*2)(170 000) I (100)
= 68 000 psi Equivalent allowable ultimate stress : Ffu = 1 . 3 x 1 . 5 Ffo 17-10 TABLE 17-5 MONOCOQUE WAFFLE FATIGUE LIMIT LOADS, CRUISE AND +2.0-g CONDITIONS Center Inboard Outboard Upper L o w e r Upper Lower Upper Iower
Nx, Air - 39 -120 - 36
-109 - 17 - 69
Nx, Thermal -436 -415 440 546 -226 -289 404 -3.30 4- -475 -535 529 -295
C N X
N , Air -198 189 -187 - 82 85
Y
- 62 - 45
-105 - 23 - 83 69
-260 144 -292 151 -165 154 Z Y r n e - l
- 10 1 N Air
- 9 0 73 - 77 68
XY’
N Thermal - 38 - 26 82 - 9 106 - 9
XY’ - 4 8 - 2 5
- 8 64 29 59
C N X Y Center Inboard Outboard Upper Lower Upper L o w e r Upper Lower
Nx, A i s - 78 -261
- 74 -235 - 13 -116
Nx, Thermal 360 -289 616 -493 395 -437 282 -550 542 ‘ -728 382 -553
C N X
N , Air - 439 412 394
-414 -203 197 Y
- 88 40 -152 98
N , Thermal - 50 45
-502 434
65 -489 457 -355 -295
N Air - 29 10 -2l2 143
-179 1.63 XY’
Nxy, Thermal 0 7 118 - 18 - 52 - 12
- 29 17 - 94 -231 151
C N X Y “ L i m i t loads 17-11 m
-7-
L P A 8
+
0 0 0 0 0 0 0 0
-
+
2 % 6 4
5 %
m a m n * a n w I n 3 rl I 1 I I , I 2 %
5 %
M a a s n w I , 1 .
-
I I
+
I
X I I 42 '
5 2 8
17- 12 I TABLE 17-8 MONOCOQUE HONEXCOMB SANDWICH FATIGUE LIMIT LOADS, CRUISE AND +2.0g CONDITIONS Center k b
I hwer
Upper Upper Nx, Air
- 21
-96 - 73
- 78
Nx, Thermal - 506
-903 t688 +429 -400 +io36 410 -999 +408
- 579
C N X
N , Air
+I32 +a46 -136
- 57 -157
I- 5 6 Y Ny, Thermal -125 -158 -177 +io9
+ 31 - 99
- 2 6 +165
+ 7 c " Y I -315 - 31 -235
N Air
+ 44 + 4 - 12
+43 - 67 + 37
X Y ' N Thermal
+ 266 +220
- 71 + 50 + 49 + 3 6
XY' + 28
+ 310 + 54
+ 3 7 - 31 +257
Z N X Y Cen !r Outbj rrd Iower Lower %Per Upper Lower Upper Nx, Air -205 -152 -170
-198 - 52
Nx, Thermal +518 -181
- 593 6 9 2 -738 +348
+522 +296 -214 +313 -745 -936 cm, N , Air
+301 - 302 +287 -124 +124
-334 Y N Thermal -120
- 65 +134
+ 5 7 - 74 + 77
+364 -244 +258
- 399 353
- 376
siy
N Air + 2
+ 13 -155 - 99 - 9 8 - 76
X Y ' N Thermal
- 12 + 84 +132
- 35 +139 - 9 8
X Y ' + 1 + 4 0
- 33 - 71
-196 + 5 6 C N X Y
- - -
a L i m i t loads bpositive value tension, negative value compression I ( 17-13 m m k f c, 17- 14
E ; l a
17-15 d w *I Y 0 d k %
4 4 q
17-16 d r l 1 1 -- 17-17 17-18 .4*olhruJw Hypersonic cruise airplar? design trajectory Figure 17-1.
maneuver +2. O g maneuver Fuselage bending moment (in, =lb ) '\ Figure 17-3. Frequency of exceedance of longitudinal bending
moment a t s t a t i o n 2364 - 10 000-hour l i f e
I Representatitve value of mean stress, fm, l i m i t 35 200 700 46 000 1400
ii
Maneuver 46 000 1400 . ?
% i d
E
+J +>
8 1 5
a ,
3 10
1 10 102 103 105 Cumhtivc number of occurances, Z n Fatigue spectra for wing structure l i f e determination Figure 17-4.
17-22 . . I .
c n t - u) I n .f % cu
/ 17-23
4 3-
a
d
r l
I I
/
I lo2 106 10 Allowable nuuiber of cycles, N S/N Curve for Rene' 41 at 1400 F(Kt = 4e0) FIGURE; 17-9 ..- . -. ._ __ -I 19-27
Section 18
Section 18 CREEP by C. C. Richie 18-i PRECEDING PAGE BLANK NOT RLMED.
CONTENTS Page 18-1 CREEP 18-1 CREEP DESIGN CKCTEIUA 18-3 CREEP EVALUATION RESULTS 18-5 REFERENCES .
18-iii TABLES Page Analysis of creep bucding; .t; = 6680 hours 18-6 18 -1 10-7 10-2 Analysis o f permanent creep deformationa9b 18-3 Beam cap creep buckljng; t = 6680 hours 18-9 18 -4 Cap plastic strain analysis 18 -5 Analysis of creep buckling; t = 30 hours 18-v ILLUSTRATIONS Page 1 . 8 -11 18-1 Semiiiionocoque chordwise thermal stress relaxation Typical stresz-§%rain states f o r t = 3 O h r and t-6680 h r 18 -12 18-2 18-3 Typical isochronous sf -ess-strain diagram f o r 1400°F 18-13 aged Rene' 41 sheet (0.020-0.080), T = l3OOOF 18 -h Isochronous plas &city reduction factors f o r Rene 41, sta 11OO0F, T = 1300°F, t = 668C hr 18-5 Isochronous p l a s t i c i t y reduetion factors f o r Rene'bl, 18 -15 sta lh@G°F, T = 1300°F, t = 30 h r .
18 -16 18 -6 Zocal a r c buckling, t = 6680 hr Local a r c buckling, t , = 30 hr 1 6 -17 18-7 18 -18 18-8 I n i t i a l bhckling of r i b cap Cap t : Suckling analysis 1.8 -19 18-9 18-vii f!&ECEDING PAGE MkNK NOT FILMED.
BL Butt line b Wldth of panel flat E Mulus of elasticSty Elastic modulus of elasticity % l Compressive yield strength CY Compressive stress f C Compressive crippling stress %c Compressive buckling stress f c,cr Thermal stress for lower surface of center area fl,th Thermal stress for upper surface of center area fu, t h Extensional stresses and shear stress in xy C O O r d i a a t e system fx’ fy’ fxy g Gravitational acceleration Ms -gin ef safety &tensional forces and shear force in xy coordinate system per
ax, Ny’ Nxy
unlt length of section M a t e r i a l constante used in creep equations, also n is shape n , no pameter determined Fman stress-&rain curve of the material P Pressure R Radius T Temperature t Time; material thickness Cap thickness tc E Strain 18-Sx &tensional strains and shear strain i n xy coordinate system € x 9 € ? Y Y Equivalent uniaxial strain based on octahedral shear stress theory ‘equiv.
0 Stress Material constants “0’ “c
- ES
Secant plasticity factor ? 9 E ’ E t
-
Tangent plasticity factor qT E ’ 18 -X
Section 18
Section 18 CREEP CREEP DESIGN CRYYERIA Creep design criteria considered creep buckling and permanent deformation To evaluate creep effects, of 0 . 5 percent f o r a vehicle l i f e of 10 000 hours.
the following assumptions were made: 1. The allowable compressive stresses under creep conditions can be apFroximated by using the isochronous stress-strain curves as if th. y were actual stress-strain curves (ref. 18-1).
2 . Stress relaxation of thermal strains can be approximated using the theory of t o t a l creep deformation presented i n reference 18-2.
The creep material properties are based on the average temperature 3.
during cruise and the t o t a l time at cruise (6680 hours, including a scatter factor of 1 . 5 ) for a vehicle l i f e of 10 000 hours.
% b e criteria used for evaluating stress relaxation is based on the theory of t o t a l creep deformation presented i n reference 18-2. In this theory, the assumptions are as follows: (1) Elastic defomations are considered small campared with plastic or creep 4eformations.
(2) Plastic (slip) deformation with strain hardening, measured by the plastic strain c in the gresence of stress c r , can be expressed i n the form: where a . and no are material constants (3) The viscous flow under constant uniaxial stress, a, during the secondary stage of creep can be represented i n the form of a power law: where ac md n are material constante.
18 -1 Based on assumptions (1) through ( 3 ) , the total. creep rate can be expressed i n the form: n (18-1)
at -
Integration gives t (18-2) assuming andU>O. For a = constant, equation (18-2) can be expressed in the form:
€ = Jo) i . v t
where v = ($-r is the corresponding creep rate i n secondary creep.
Stress relaxation due t o creep of R e n 6 41 was evaluated by considering a constant thermal s t r a i n and gradually dimi.nishing the- stresses.
Based 8n
creep data presented i n reference 18-3 for Rend 41 at a temperature of 1300 F, the material constants for the creep power law are: n = no = 1.0 o = 41.44 x 10 psi o = 9.615 x 10’ psi C Thus, from equation (18-1) 18 -2 Stress relaxation for the chordwiae semimonocoque concept is shown i n figure 18-1. Based on equation (18-3), these results show that the upper sur- face panel thermal stress decays exponentially frcs al = -36 000 psi t o C J ~ = -100 psi i n 1360 hours a d the lower surface panel thermal stress de- creases from a = -29 000 psi t o cr2 = -100 psi i n 1320 hours. From t h i s example, the fo i lowing conclusions are evident: 1 . Thermal stress relaxation of R e d 41 a t temperatures near 1300°F i s very significant.
2 . Creep effects produce redistribut5on of thermal stress.
Residual stress buildup due t o creep significantly reduces thermal 3.
stresses.
An exact determination of the redistribution of thermal stresses i n transient creep due t o cyclic variation of stresses and temperature i n a com- plex redundant structure is beyond the scope of t h i s study. Hence, the fore- going simplified c r i t e r i a w a s used for evaluation of creep effects.
CREEP EVALUATION RESULTS Creep evaluation of primary structural concepts encompassed monocoque panels and semhonocoque panels and rib/spar caps. Creep design c r i t e r i a included creer buckling and permanent deformation of 0 . 5 percent. Compressive in-plane loa& only were u s e d t o determine creep buckling margins of safety.
Factors of safety were f o r l i m i t loads and a scatter factor of 1 . 5 was applied t o creep design l i f e . The wing location selected f o r creep evaluation w a s the This area w a s selected because of center area under the fuselage (BL 0-120).
maximum compressive loads and temperatures during cruise. Equations used f o r s t r e s s analysis of the Qonocoque and semimonocoque concepts are presented in sections 10 md 11, respectively. Isochronous stress s t r a i n curves f o r the average temperature under the fuselage during cruise, T = 13OO0F, were used t o determine creep buckling strengths and plastic creep deformation.
Since creep was twmmed t o occur predominantly during cruise, the cruise in-plane loads, thermal strains, and pressure loads were selected for the a e e p evaluation.
Only steady-state aerodynamic pressures were considered f o r the creep evaluation.
Wing vent pressures are transient pressure loads occurring during a small fraction of the vehicle l i f e and, therefore, are not considered.
Because of thermal stress relaxation, two elapsed times were considered f : the creep buckling criteria. All structural concepts were evaluated f o r the time a t cruise, including the scatter factor of 1 . 5 , t = 6680 hours, based on 8. vehicle 1. .e of 10 000 hours, corresponding t o the minimum difference 18-3 between the isochronous yield strength and the time-dependent themal stress (see fig. 18-1). Typical stress-strain states f o r 30 hours and the design creep l i f e are shown i n figure 18-2.
Since thermal stress relaxation produces permanent creep deformation, figure 18-1 shows that maximum permanent deform- ation and minimum themal stress occur at t = 6680 hours.
Results of the creep evaluation indicate that the monocoque and semi- monocoque primary structural concepts are aaequate with respect t o creep buck- ling analysis of monocoque and semimonocoque panels for the creep design l i f e , t = 6680 hours. The lower surface panel for the s t a t i c a l l y determinate concept has the minimum panel =gin of safety of 1.42. Results of the permanent creep deformation analysis of the primary structural panel concepts for the creep design l i f e are shown i n table 18-2. The minimum panel margin of safety of 2.16 occurs for the upper surface panel of the semimonocoque chordwise concept.
Comparison of tables 18-1 and 18-2 shows that creep buckling i s the governing panel c r i t e r i a for a l l but the upper surface panel of the semimonocoque chord- wise concept a t t = 6680 hours.
Creep bucklsng and plastic s t r a i n analysis - results for t h e semimonocoque beam cap concepts are shown i n tables 18-3 and 18-4, respectively. Minimum margin of safety of 0.37 occurs f o r the upper
-
surface spar caps f o r the stAmonocoque chordwise concept. The s t a t i c a l l y determinate concept has no chordwise stiffness and, therefore, no evaluation was required.
Results of the creep buckling analysis of the semimonocoque chordwise concept for a time of 30 hours, corresponding t o the minimum differ- ence between isochronous yield etrength and time-dependent yield stress, are shown i n table 18-5. Comparison of tables 18-1 and 18-5 shows that the mini- mum creep buckling margin of safety f o r the chordwise semimonocoque concept occurs for a time of 30 hours.
Typical creep materials data and creep buckling allowables required for
-
the creep evaluation are shown i n figures 18-3 through 18-9. Isochronous stress strain curves for Rene' 41 a t the 1300°F design temperature are shown i n figure 18-3. Isochronous p l a s t i c i t y reduction factors f o r the creep design t i m e of 30 hours are shown i n figures 18-4 and 18-5, respectively.
l i f e and a b c a l creep buckling strength of a circular-arc f o r timeo of 6680 hours and F-igure 18-8 presents 30 hours is shown i n figures 18-6 and 18-7, respectively.
i n i t i e l creep buckling of semimonocoque rib caps for the design temperature of 1300°F and t i m e of 6680 hours. A comparison of seslimonocoque cap crippling and i n i t i a l buckling stresses is shown i n figure 18-9. fa-itial creep buckling of the caps is seen t o be the governing allowable compressive stress.
REFERENCES 18-1 Gatewood, B. E. : Thermal Stresses. McGraw-Hi11 Book Co,, 1957, page 134.
18-2 Falke, K. G . Wqvist: Mathematical Theory of Creep and Creep Rupture.
Oxford, 1966.
18- 3 AarneE, M. N.; Tuttle, M. M.: Presentatjm of Creep Data for Design Purposes. ASD TR-61-216, June 181.
Manson, S. S.: 18- 4 Thermal. Stress and Low Cycle Fatigue. 1966.
1t -5
k
7 "
I E;i I rl m - I rl n l
+
1.8-6 L n a 3 co al I
0 b i ho
M
rl a
3 Ln In 03 a, c- rl rl t - M I
J
TABLE 18-3 Wing Concept It e m fc,cr M S L x a t ion psi p s i
Semimonocoque, Q - 120 R i b -14 700 24 000 to. 63
spanwi se (upper caps
- 120 Rib -18 500 28 ooo a. 5 1
Bower) caps Semimonocoque,
g, - 120 Spar -21 200 29 000 .to. 37
chorciwise (upper caps
9, - 120 Spar -19 loo 29 ooo a. 52
(lower ) caps
S t a t i c a l l y 9 , - 120 Rib
determinate
(upper 1 caps
No chordwise cap s t i f f n e s s -
not c r i t i c a l i n creep buckling
a - 120 Rib
(lower) caps 18 -8 TABLE 18-4 CAP PLASTIC STRAIN ANALYSIS €air' € t o t a l 9 in. /in. t o t a l ' Wing in./in.
in. /in.
1 m a t ion % ( p l a s t i c x 10-6 ) ,: 10 -6
Semirnonocoque, - 120 -1490 -14 700
spanwi sea
(upper 1
( r i b caps)
c , - 120
-1570 -18 500 (lover) Semimonocoque,
CL - 120 1 -21 200 -0.0895
-550 -895 chordwise (upper) (spar ce;s)
% -120 -19 LOO - 450 752 -0.075
(lower) _I S t a t i c a l l y determinete "NO CHORDWISE STIF'FNFSS" ( r i b cays) 1 - -.-- --.
a Semirmnocoque, spailwise. tubular & beaded have i d e n t i c a l caps and loads.
bplasi ic s t r a i n .
c
- 1 , where E = 0.5%. MS =
maJEtota1 max 18 -9 TABLE 18-5 ANALYSIS OF CREEP BUCKLING, a ' b t = 30 HOURS (Concept: semimonocoque, chordwise) Surface (BL 0-120) Lower upper ?L OF NX ,Airload -130
- 915
Nx , Thermal -663
-73 NAX, %tal
-988 -793
p, psi(") 0 - 0 . 2 3 -41 105
T ~ , psi(c)
-34 550 f 74 000 69 000 c , cr MS 1 . 1 4 0 . 6 8 a Material: Rene 41, sta 1k0OoF, T = l3OO OF, t = 30 hr bkXresses based on limit in-plane and pressure loads for cniise condition.
C Not including vent pressure.
dcompression only.
18-19
-
lo00 -
-
..
-
-
XWS :
-
1. FCy k Isochronous compressive y i e l d stress, Red 4 1 , - aged 140O3F, tmqerature, T = 1 3 0 0 9 2. f p ~ ~ ~ - l ' h e r a d stress, v;pper surface panel, center area - 3. fl,'ITI--Thermal Stress, l a w surface panel, center area Time, hr _I_- ~ Figure 18-1 Semimonocoque chordwise t h e m 1 stress relaxation 28-11 thermal
I 1 ///
f t
airload ) F f t = 6680 h r Figure 18-2 Typical stress-strain states f o r t = 30 hr and t r: 6680 hr 18-32 0 0 -1 0.2 0.3 0.4 0.5 0.7 Strain, porcmt Figure 18-3 TypiFel isochronous stress-strain diagram for l b O ° F aged Rene 41 sheet (0.020-0.080), T = 1 3 0 0 ' F 18-13 1 . 0 0 . 8 0.7 0 . 6 k 0 . 5 l d k b P rl c, 0.4
A
PI 0.3 0 . 2 0 . 1 0 5 10 1 5 20 30 f , P s i - - Figure 18-4 Isochronous plasticity reduction factors for Hene'41, eta 1400°F, T = 1300°F, t = 6680 hr 18-14 0 20 40 60 80 100 f , P s i - - _I .-- .
.-- Figure 18-5 Isochronous plasticity reduction factors for Rene' 41, eta l b O ° F , T = 13009, t = 30 hr 18-15 II II II II 11 I1 v) w \o c) I co rl (Y c *) 0, X .- a b U . m .
0 100 200 300 400 500 R /t Figure 18-7 h c a l arc buckling, t = 30 hr d (II P4 r i
.=I- 4
c4 u 0 'U x 0 d M 4 d II II II II II II Q f .E!
H cu I I u
-
k I I II II II E
Section 1 9
Section 1 9 OPTIMIZATION PROCEDURE FOR HEAT SHIELDS bY C . C . Richte PRECEDING PAGE BLANK MOT FILMED.
CONTENTS Page 19-1 OPTIMIZATION PROCEDURE FOR HEAT SHIELDS 19-1 PANEL LOADING 19-3 STRESS ANALYSIS 19-4 LOAD BUCKLING ANALYSIS 19-6 CLOSED F O R M EQUATIONS 19-iii Table Page 19-1 Reaction, moment, and deflection coefficients due t o 19-13 pressure f o r the corrugated heat shield 19-2 Moment coefficient due t o nonuniform thermal deflection 19-14 of the supports for the corrugated heat s h i e l d Deflection and moment coefficients due t o pressure f o r 19-3 various coordinates of post-supported isotropic sandwich of figure 19-2 19-15 Deflection coefficients due t o pressure and thermal gradient 19-4 and moment coefficients due t o pressure f o r least moment designs of table 19-1 19-16 f&ECEDING.PAGE BLANK MOT FIU.,L:J.
ILLUSTRATIONS Figure Page 19-1 Cross s e c t i o n of flat skin, dimple-stiffened heat s h i e l d 19-15 19-2 Grid of f i n i t e difference s o l u t i o n of reference 19-1 f o r post-supported sandwich plate. F i c t i t i o u s g r i d points along bo-mdaries a r e omitted 19-16 19-3 Cross s e c t i o n of corrugated s k i n heat s h i e l d 19-17 19-4. Heat s h i e l d support c l i p geometry 19-18 19-vii SYMBOLS Width of flat for corrugated heat. shields; width of flat b plate f o r buckling analysis Modulus of elasticity E Deflect ion; elongation e 0.7 E Stress corresponding t o modulus of e l F0.7 f Stress h Height I Moment of I n e r t i a Compressive bucking coefficient k L Length Bending moment M N Extensional forces per unit of length Shape pnrameter n Pitch P Radius R r Radius of curvature t Thickness
-
t Equivalent panel thickness Rectangular Cartesian coordinates Panel deflection W Distance from neutral axis t o exbreme f i b e r .
Semi-apex angle f o r corrugation stiffened heat shields ;
a
r a t i o of M ~ / I ~ ~ Parameter as defined by equation 19-25 Parameter as defined by equation 19-14 P l a s t i c i t y f a c t o r Ratio as defined by equation 19-17 V Poissons r a t i o Subscripts b Denotes bending c r denotes critical. o r minimum value e l Elastic I Denotes quantity at inner f i b e r 0 Denotes quantity at outer f i b e r sec Denotes Secant values t a n Denotes tangent value t h Abbreviation f o r thermal Denotes direction i n rectangular Cartesian coordinates 19- x
SECTION 19
SECTION 19 OPTIMIZATION PROCEDURE FCrl JBAT SHIELDS Equations of the computer programs which were used t o determine ininimum weight configurations i n the evaluation of refurbishable and permanently attached heat shields are presented i n t h i s section. The refurbishable heat shield concepts are :
Corrugated skin , hat-se c t ion st i f f m e d , c l i p supported
Corrugated skin, simply supported Corrugated skin, multiple supports Flat skin, dimple-stiffened, c l i p supported.
The permanently attached concepts which are of the corrugated skin con- figuration are : Modular, simply supported Modular cantilevered The heat shield panels are assumed t o be separated by flexible j o i n t s which a l l e v i a t e inplane loading.
The function of the heat shields is t o protect the primary structure i n a high-temperature environment due t o asrodynmic heating and t o provide a smoother aerodynamic surface than afforded by some of the s t r u c t u r a l panel concepts. Even though they are vented, the heat shields are subjected t o pressure loading due t o fluctuation of the pressure.
The analysis, which is formulated f o r the closed-form rasthod of opti- mization, is discussed i n fqur categories: (1) panel loading, (2) stress analysis , ( 3 ) l o c a l buckling analysis, and ( 4 ) cldsed-form equations.
PANEL LOADING The aerodynamic pressure is assumed t o a c t positively and negatively on the heat shields.
19-1 Corrugated Heat Shield Bending moments of t h e corrugated s k i n heat s h i e l d , produced by t h e pressure loading, are dependent on t h e type of supports and on t h e spacing of t h e supports.
The heat s h i e l d reaction, moment, and deflection indices due t o pressure loading are pre snted i n t a b l e 19-1. These results can be obtained by using any one t h e loads and deflections of con- of the many methods available f o r calculating tinuous beams; i.e. , area-moment, moment d i s t r i b u t i o n , e t c . I n addition, t h e corrugated heat s h i e l d with multiple supports is subjected t o bending moments produced by nonuniform thermal deflection of t h e supports and bowing of the s t i f f e n e d panels of t h e primary s t r u c t u r e under loading. The heat s h i e l d is moment due t o nonuniform thermal deflection of the supports bending shown i n t a b l e 19-2. These data, which are presented as a moment index, are f o r heat shields with 3, 4 , and 5 supports.
The bending moment on t h e corrugated heat s h i e l d with multiple support due t o bowing of t h e s t i f f e n e d panels of t h e primary s t r u c t u r e under loading is as follows: A conservative approximation of t h e primary-structure panel deflection due t o thermal bowing is %.:iere t h e deflection due t o thermal bowing eth is defined i n s e c t i o n 12 by equation 12-4, and as indicated i n t h e above equation a beam column magni- f i c a t i o n f a c t o r is used.
Assuming t h e heat s h i e l d is subjected t o t h e same deflection as t h e primary s t r u c t u r e due t o t h e continuous supports between s h i e l d and pri- mary s t r u c t u r e , the radius of t h e curvature r f o r t h e heat s h i e l d is L2 r = (19-2
G
where t h e length L is measured i n t h e heat-shield s t i f f e n e d direction, chordwise. The heat s h i e l d bending moment can then 5e written as E1 M = - ( 19-3) r 19-2 F l a t Skin, DimpleStiffened Heat Shield The flat skin, dimple-stiffened heat s h i e l d ( f i g u r e 19-1) has four symmetrically located d i s c r e t e supports (posts). Approximations of t h e moments and deflections of t h e heat s h i e l d are determined with t h e f i n i t e difference solution of reference 19-1. Moment and deflection indices due t o pressure loading are presented i n t h e reference for various coordinates of t h e The deflection indices were used f o r e7.%luations of t h e p l a t e ( f i g u r e 19-2).
heat shield performance penalty.
STIiESS ANfiYSIS The stresses of t h e corrugated s k i n heat s h i e l d ( f i g u r e 19-3) are I Y where t h e subscripts 0 and I denote q u a n t i t i e s at t h e outer and inner ex- t r e m i t i e s of t h e corrugation, neglecting the thickness t. The moment is considered positive when it produces a compressive stress i n t h e outer surface of t h e heat shield.
The stresses f o r t h e hat-section stiffeners and support c l i p s used were determined as follows: The hat-section f o r the corrugated heat s h i e l d stresses are evaluated by equation 19-4 at t h e maximum-moment location, mid- way between support c l i p s . The hat-section s t i f f e n e r c r o s s s e c t i o n is shown i n figure 19-4. The stress f o r t h e support c l i p s is N (19-5)
f = T
The and the maximum stress l e v e l occurs on t h e upright member of t h e c l i p .
support c l i p geometry is shown i n f i g u r e 19-4..
The stresses f o r t h e truss-type continuous c l i p s used on both t h e simply supported and multiple supported corrugated heat s h i e l d concepts are evaluated by equations 19-4 and 19-5. This c l i p design is shown i n figure 19-4.
19-3 : : t , r ~ - z s ~ ~ s 0 1 ’ t,tic> I’lat skin, dimple s t i f f e n e d heat s h i e l d a r e
( e = 0,L)
The moments are positive when they produce compressive s t r e s s e s i n t h e outer skin. The stresses f o r t h e support c l i p s used on t h e flat-skin, dimple-stiffen- ed heat s h i e l d a r e evaluated by equation 19-5.
LOAD BUCKLING ANALYSIS Corrugated Skin Heat Shield “he buckling stress of t h e circular-arc segment is approximated by equation (12-14) of SectioQ 12, which i s i n which and T r e a t i n g t h e p l a t e element as a long, simply supported p l a t e , t h e expression o f t h t buckling stress is wherc.6, = - f ) , c j ~ , which i o given by equation ( l O - l % , ) of s e c t i o n 10.
F l a t Skin, Dimple S t i f f e n e d Heat S h i e l d Spacing of t h e dimples,which are i n the i n n e r s k i n of t h e flat s k i n dimple-stiffened h e a t s h i e l d , i s t h e same i n t h e x and y d i r e c t i o n s . The o u t e r and inner s k i n s are tnen t r e a t e d as square p l a t e s with post supports a t t h e f o u r corners, and t h e heat s h i e l d is analyzed f o r l o c a l i n s t a b i l i t y with t h e buckling equation
( a = 0,I)
(19-9 1
i n which t a n and with t h e i n t e r a c t i o n equation
( Q = 0,I) c 19-10]
The p l a s t i c i t y c o e f f i c i e n t ?.tan i s based on t h e stresses fx and YY, t h e equivalent s t r e s s of which is determined with octahedral shear stresr; theory.
NASA s t a t e d t h a t buckling c o e f f i c i e n t s obtained from some of t h e i r t e s t data ranged f'rom 1.0 t o 1.5. = k1 = 1 was used f'or t h e pi-cscrit Hence, investigation.
19-5 CLOSED FORM EQUA'fIONS Corrugated Skin Heat Shield I n t h e formulation of t h e closed-form equations of optimization f o r t h e corrugated s k i n heat shield, t h e maximum momen% (r,bsolute value) is applied positively and negatively and t h e l o c a l buckling stresses o f t h e arc and t h e flat are equal and ar ? based on t h e extreme f i b e r stresses. The analysis i ; simplified by assumj,g t h a t t h e stress gradient through +he ci-oss section is linear. I n additior ,he geometry is constrained so t h a t t h e maximum stresses a t t h e t o p and bottou of the corrugation are equal; i.e., t h e centroid of t h e cross section is at t h e mid-height of t h e corrugation. Hence, when b, R, and t are eliminated from equations (19-6) and (19-8), an expression f o r t h e o p t h . m stress is obtained as i n whici-, and 19-6 The geometry of the corrugated '?at shield can now be defined as
( 19-13 I
1 1 where I n which 2(1 + A ) sin cy 41 = s i n CY
o 2 = 1+x,-
(19-15 sin o - -
- c o s 0
+3 - Q The equation of the average thickndss is Aemdynamic requirements require t h a t a constraint be imposed on t h e height/pitch r a t i o of the corrugation, (h/p) = 0.10. Hence, f o r a specified value of (h/p), the angle of equations (19-11) through (19-16) can be obtained from the expression
1 - cos a - 2 ( s i n u + h s i n a) (E) = 0
and equation For a given moment and material, t h e dimensions of t h e (19-12).
minimum weight design of t h e corrugated heat shield are now defined within t h e constrained geometry.
When the last of equations (19-13)yielded a stress which w a s less than the minimum gage, t h e spacing of t h e supports was increased u n t i l t h e f u l l strength potential of the optimum configuration of minimum gage was utilized.
The allowable stress f o r t h e hat-section s t i f f e n e r i s based on t h e cross section element t h a t has t h e minimum crippling stress. The thickness of t h i s element was varied u n t i l crippling failure mcurred.at t h e same stress l e v e l as the applied bending stress. The crdppling stress w a s determined from Stress M e m o 80 of reference 19-2.
The allowable stress f o r t h e support c l i p s is based on t h e column buckling stress of the upright member (see figure 19-41 This stress is evaluated i n section 12 by equation 12-8. The same procedure as described f o r the hat section s t i f f e n e r is u t i l i z e d t o a t t a i n minhum thickness clips.
The weight of the truss-type support clips, which are used on the s h p P j supported and multiple supported heat shield conceptg w a s determined by varying the shield-to-support attachment flange thickness u n t i l the allowable stress, the bendingmoduius of rupture, is equal t o the applfed bending stress, equation The upright member was analyzed f o r bending and compression stresses, 19-4.
equations 19-4 and 19-5. I n a l l cases, the designing element f o r the c l i p was the attachment flange. The thickness determined from t h e flange analysis provided The c l i p height sufficient c l i p stiffness f o r heat shield flutter analysis.
h is determined so t h a t sufficient clearance is provided between the deflected shield and the primarj structure.
Flat Skin, Dimple Stiffened Heat Shield I n designing the f l a t skin, dimple-stiffened heat shield, a constraint Assuming t h a t was imposed on the elongation due t o dimpling of the inner skin.
is a cone (r = 0), the elongation is defined as the dimple 19-8 2 2 T ~ R /sin (Y - n R e = lTp2/h or (19-17 To obtain expressions of the thickness and stress ratios of the two faces, let (19-18a)
MO
where the quantities of equation (19-18a) are buckling moments of the outer face and those of equation buckling moments of the inner face.
(19-18b), Using equations ( 1 9 - 9 ) , ( 1 9 - l o ) , and ( 1 9 - 1 8 ) , the thickness ratio can be expressed as in which
( a = 0,I)
From equations (19-8) and ( l 9 - 1 8 ) , f , (19-21 ) i*irc.t; eliminating Y and then X f'rom equations (19-19) and (19-211 yields N d . t \ that. t h c s t r c w e c arid fI are d i r e c t rcsu.1t.r. of t h e m o t n c r i t s Mi, a n d MI.
The expression f o r t h e average thickness -is (r = 0 ) Solving equation (19-17) for (h/p), s u b s t i t u t i n g t,he r e s u l t i n g cquat,i on arid equation (19-22) i n t o equation (13-24) and then usin@ eqimtjons 19-5, 19-9, 1 9 -19, and 19 -22 gives where AS already s t a t e d , t h e loading of t h e heat s h i e l d s is applied p o s i t i v e l y and negatevely. Hence, W/MI = y = 1 . The average thickness of t h e optimum con- figuration is then determingd by minitnfzing equation (19-25) with respect t o f1 4 Note t h a t equation (19-25) can be expressed i n terms of Mo with t h e use Of equation ( 1-3 -. l8c ). .
19-10 1 I . i th thc s t r e c r fI known, dimensions 01’ t h e minimum weight conl’iguration :irp r l r ~ t , r t r m l n c t d w i t h t l w I’ollowing equations : 0 3 - 2 6 ) The weight of t h e c l i p supports f o r t h i s h e a t s h i e l d is determined by t h e same procedure as described f o r t h e hat-section s k i n - s t i f f e n e d corrugated heat s h i e l d concept.
19-11 19-1 Plank, P. P.; and MacMiller, C. J.: Anal.yl;ical I n v e s t i g a t i o n of Candidate Thermal-Structural Concepts Applicable t o Wing, Fuselage and I n l e t Struc- t u r e of a Manned Hypersonic Vehicle, AFFDL-TR-66-15(Gonfident ial ) ‘1966.
19-2 Lockheed-California Company, Engineering Stress Memo Manual $0.
19-12 I
32Kl
r ! O ?
00'0 c u c u c u mln Lc II I 1 I 1 I 1 II I 1 m
+
*El
k = J m
:-
a a
2 t u
h 3 * I
k m B
T 7 '
0 -P Q4 .#-I k a ,
2 k
a
E - 0
a 8 0
m
* I 2
c 19-34.
1 A I- \. lrrner skin Dimple I Figure 19-1 Cross section of fl& skin, dimple- Yt iff3r:e.i !:est s h i e l d 13-15 X
T c It
s
x- 19-16 Figure19-3 Cross section of corrugated skin heat shield 19-17 Croas Section
A - 6bt +
I 1 . 1 6 7 2 = 2 . 3 % Hot-section stiffener aaPau-seotion f o r the post-supported aomgated heat shield Support o l i p geaaetry for the post-mpp~Ft@d oormgated and tlat-skln dimple-atlffsned heat rahield concept8 Heat shield support c l i p geomet-ry Figure 19-4 19-18 t . 1 0 Support o l i p gumat* for tha ri.pty mrpportod and multiple nqrported cormgatd b a t &old figure 19-4 Heat shield support c l i p geometry (Concluded) 19-19
Section 2 0
Section 2 0 HEXI' SHIEID WEIGHT ANALYSE bY W . A. Clam, C . C . Richie, F. T . Bevan 20- i &@CEDING PAGE BLANK NOT'FIMED.
CONTENTS J & 20-1 INITIAL FJEIGEPT EVALUATION 20-2 R e furb i shable Heat Shield Concept 20-5 Permanently Attached Heat Shield Concept 20-6 Heat Shield Thermal Analysis 20-3 Summary of b i t i a l Weight Waluation 20-9 FINAL HEAT S H I m STRUC- SIZING 20-iii TABLES Page Table 20- 1 20- 1 0 Heat shield material comparison summary Temperature for direct attachment of corrugated heat 20-2 shield to semimonocoque tubular panels 20-11 20- 3 Temperature diffemntial across multiple clip support for corrugated heat shield 20-12 20- 4 Temperature differential from heat shield to semi- 20-13 monocoque panels 20- 5 Temperature differential from crest of corrugation 20- 14 on heat shield to adjacent clip attachment point 20-6 Temperatures for flat skin dimple stiffened heat shield concept 20- 15 Temperatures for corrugated heat shield derived from 20-7 semimonocoque primary structure isotherm analysis 20-16 20-17 Summary of heat shield data 20- 8 Typical heat shield and clip design data, spanwise 20- 9 20-18 semimonocoque concept Heat shield and support weight summary, typical heat 20- 1 0 shields on semimonocoque spanwise concepts 20-19 20- 11 Typical heat sh3.eld and clip design data, chordwise 20-20 semimonocoque concept 20- 12 Heat shield and support weight summary, typical heat 20- 2 1 shield on semimonocoque chordwise concept Heat shield and support weight summary, typical heat 20-13 shields on monocoque concepts 20- 22 Page 20-3 Heat-shield tenpera‘uure vs spanwise distance from leading edge along station 2360 20123 20-2 Heat-shield material mmparison 20-2& 20-3 Corrugated heat shield concept, hat section stiffened and c l i p supported (refurbishable) Corrugated heat shield concqt, b a t suctioii stiffened and c l i p su2ported (refurbishable) 20-26 P a n e l size vs 3 for oorrugated heat shields with 20-5 hat sections and c l i p support 20-21 2 0 4 Panel, size vs total deflection f o r corrugated heat shields w i t h n a t section =and clip su:.!:>orfas 20-27 20-7 Temperature vs f o r corrugated heat shields with hat sections and c l i p s u p p r l s 20-28 2 0 4 corrugated heat shield concept with simply supported ends ( refurbishable) 20-29 Effective thickness and deflec-bn for cormgated 20-9 heat shield with simple supports 20-30 Corrugated heat shield concept %nth multiple 20-10 ( ref ur bishable ) 20-31 20-32 Heat shield with multiple supports ( refurbishable) 20-lJ.
Span length vs 5 for multisupported corrugated heat shield 20-12
20-33 20-13 Span length vs deflection f o r multisupported corrugated heat shield 20-34 F l a t skin dimple stiffened heat shield concept with c l i p supports (refurbishable) 20-35 Heat shields, fkt skin, dimple stiffened with c l i p supports (refurbishable) Panel size vs for dimpled concept heat shields 2 0 . 1 6 2047 Deflection vs panel size for dimpled concept heat shields 20-18 Simply supported modular heat shield concept with interlocking joint (permanently attached) 20-39 20-3.9 Heat shield, modular, simply supported and cantilevwed (permanently attached) 20-20 Simply supported modular heat shield cam@, ( permanently attached) 20-21 Length vs 3 for modular heat shield concept with simple supports 20-41 20-22 Length vs 6 for modular heat shield concept with simple supports Candlevered modular heat shield (permnentLy attached) 20-23
M- 2rr Length v8 t for cantilevered modular heat shield
Length vs 8 for cantilevered modular heat shield 20-25 Temperatures a t lower surface attaehent point for 20-26 corrugated heat shieldwith hat sections and d i p supports 20-lk x and y distances between simply supported edge of panels Aspect r a t i o of t h e panel Butt l i n e Flat width of heat shield corrugation Pitch Diameter Fuselage stat ion Gravitational acceleration g h Height L Length of span Pressure; pitch Dynamic pressure Radius T Tempemt ure t Thickness Thickness of corrugated heat shield t C
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t Equivalent p n e l thickness Deflection Surmnation of e q u i v a l a t p n e l thickness
cs
Subscripts chan Indicates quantity pertains t o cap c l i p Indicates quantity pertains t o c l i p corr Indicates quantity pertains t o corrugated h a t shield hat Indicates quantity pertains t o hat h s Denotes quantity associated with heat shields m x Denotes maximum value oxid Denotes quantity pertains t o oxidation panel Denotes quantity pertains t o panel t r u s s Denotes quantity pertains t o truss-type c l i p s
Section 20
Section 20 mT-SBIEGO WEIGHT ANALYSIS The heat-shield welght analysis consisted of an i n i t - a l weight b v e s t i - gation (including cost, perf’ormce, and r e l i a b i l i t y ) of several concepts and a f i n a l structural sizing of t h e most promising heat -shield concept.
INITIAL WEIGHT EVALUATION The i n i t i a l heat-shield weight analysis f o r both refurbishable and per- mnently attached shields was -de i n terms of temperature requirements, mate- rials, aspect ratio, and width, and was based on a multiple of t h e overall primary load-carrying dimensions of a typical semimonocoque spanwise tubular panel The refurbishable heat -shield concepts considered were as follows : Corrugated skin, hat section stiffened with c l i p supports (1) Corrugated skin with simple supports (2) Corrugated skin with multiple supports ( 3 ) Flat double skin, dimple stiffened with c l i p supports (4) The permnently attached heat-shield evalwtions included t h e following concepts : (1) Modular, simply supported (2) Modular, cantilevered Figure 20-1 shows h a t - s h i e l d temperature versus distance from t h e
me data are f o r a
leading edge along FS 2360 (wing investigation section).
typical semimonocoque spanwise concept with insulation on t h e lower surface outboard of the one-third chordline. The upper surface tempemtures of figure 20-1 are f o r t h e -0.5-g condition. As indicated i n the figure, t h e lower sur- face tempemture varies from 1 9 4 5 ’ t o 1555% with a reduction t o lgOO’?F after 5 inches. The upper surface heat-shield temperatures range from 1785% t o l 2 8 0 % .
I n view of the temperature range, Haynes 25, Rene’ 41, and TD N i C r were evaluated as candidate materials Equivalent thicknesses o r weights were determined f o r the corrugated concept, using a maximum bending moment of 17 in.-;Lb/in.
These weights f o r various temperatures a r e shown in figure 20-2 w i t h t h e corresponding corruga- t i o n geometry shown in table 20-1.
The results indicate .chat Rene'41 is t h e most suitable m t e r i a l f o r heat-shield application below 1800%. Rene' 41 was selected f o r heat -shield applications below 1800% and TD N i C r was selected f o r temperatures above 18009. TD N i C r is used on t h e first 71 inches of t h e lower surface. The welding of TD NiCr is d i f f i c u l t ; therefore, riveted con- struction was considered.
Using Rene' 41, t h e evaluation of both refurbishable and perrnanently attached heat shields was conducted by providing a n arrangement of heat shields t o protect a t y p i c a l spanwise tubular panel (46 inches by 92 inches) The design temperature was 1 6 0 0 % for transient pressures of 1 . 0 p s i (ultimate). However, i n addition t o t h e pressure loading, t h e cormgated multiple-support concept included Lending due t o nonuniform thermal deflection of t h e multiple supports and bowing of t h e panel due t o thermal gradie.Its, pressure, and inplane loading.
Minimum gage f o r t h e corrugated and modular heat shields is 0,010 inch.
For the flat skin dimple stiffened heat shield, t h e minimum gage of the outer skin is 0.015 inch and of the innerformed skin 0.010 inch, The basic data obtained f o r each cand-idate heat shield included a plot of versus panel size, mximum deflection versus panel size, and drawings showing s t r u c t u r a l arrangement and t y p i c a l dimensions.
Refurbishable Eea-t Shield Concept
Corrugated hat section stiffened, c l i p supported heat shield. - The
heat shield shown i n figures 20-3 and 20-4 is formed by a corrugated sheet supported by a hat section s t i f f e n e r a t %bout one-tenth of t h e corrugation length from each end of t h e shield. Corrugation amplitude i s one-tenth the corrugation pitch. A f l a t between corrugation arcs enables the hat sections t o be attached. The attachment is mde by resistance spotwelding. The sup- port c l i p is a l s o attached t o t h e hat section by resistance spotwelding.
Mounting of t h e shields is performed from outside t h e shield through A flanged nut i s an access hole at each of t h e four attachments per shield.
resistance spotwelded t o the p r i m r y s t r u c t u r a l panel, a super mica washer is used, the shield i s installed, and a scqket head screw fastens t h e standoff support c l i p t o t h e nutplate. Each access hole is located a t t h e center of a corrugation at about one-quarter spm of t h e shield, and each hole I s closed a f t e r assembly with a pronged cap.
The effect of several support locations cn t h e maximum heat shield The optimum support location f o r bending moment is presented i n section 1,90 equal magnitude of bending moment at t h e supports and mid s s n is 20.7 per- cent of the span. However, t o s t i f f e n the corrugation near t h e "overhang" 20- 2 edges and prevent flattening of the ends, the support location selected was 10.0 percent of t h e span.
!Ibis support location increases t h e maximum bending moment by a factor of 3.5.
"he support c l i p s are rotated so as t o place the plane of the web normal t o a l i n e joining opposed attach points.
This orientation of t h e support c l i p s allows f u r bidirectional thermal expansion and gives shear stiffness t o t h e supports i n any direction.
A summary of design data f o r the corrugation, hat section, and support c l i p is shown i n figure 20-3.
The lowest weight shield has a minimum gage corrugation thickiiess of 0.030 inch, aspect r a t i o of 1.0, and width of 15.3 inches. Minimum gage f o r t h e hat section s t i f f e n e r is 0.020 inch. Figures 20-5 and 20-6 show panel s i z e versus effective thickness and panel s i z e versus deflection, respectkely. The deflection consists of corrugation and hat section deflection and uoes not include t h e r m 1 deflections, For an aspect r a t i o of 1.0 and width of 15.3 inches, t h e maximum deflection is 0.380 inch. Figure 20-7 shows a parametric study of effective thickness versus temperature f o r a panel aspect r a t i o of 1.0 and width of 23.0 inches.
Corrugated heat shield with simple supports. -The short corrugated heat shield sham in figure 20-8 consists of a corrugated sheet supported by simple supports a t about one-tenth of t h e corrugation length from each end of each shield. Shields overlap a t t h e trailing edge forming shingles. Cor- rugation amplitude is one-tenth the corrugation pitch. A f l a t is provided between corrugation a r c s t o enable attachment of t h e truss-type support c l i p .
The support The attachment is mde by at least two spotwelds at each flat.
c l i p is a l s o attached. t o tkc primry-structure panel by resistance spot- welding. The support c l i p is stamped from f l a t sheet and rlibber formed. Sup- port c l i p s at one end of a shield are stiffened by gussets i n t h e shield length wise direction t o transmit drag shear t o the p r i m r y structure.
Mounting of t h e heat shields is performed before the primary structural panel is installed. If necessary, removal of t h e shiel.ls is accomplished by: (1) removing cover plates between adjacent primary-structure panels, (2) re- moving primary-structure panel, and (3) d r i l l i n g out spotwelds attaching the To replace t h e heat shield, rive%s support c l i p s and primary structure panel.
are installed i n place of t h e drilled-out spotwelds .
Spanwise t h e r m 1 expansion due t o thermal gradients between t h e heat shield and primary-structure panel is allowed by bending of the c i r c u h r - a r c portion of t h e corrugated skin. Chordwise thermal expansion i s permitted by Gusset c l i p s are deflection of t h e support c l i p s at one end of t h e shield.
provided a t t h e other end of t h e shield t o resist inplane shear i n the short dimension of the p n e l .
A surmtlary of design data f o r the corrugation. and support c l i p is shown i n figure 20-8. The support clips are sized one the basis of eccentrically The lowest weight shield h : 3 a applied compressive loads due t o pressure.
minimum gage corrugation thickness of 0.010 inch and length of 15.3 inches.
20- 3 Figure 20-9 shows heat s h i e l d length versus e f f e c t i v e thickness and heat s h i e l d length versus maxixum deflection. For a length of 15.3 inches, t h e maximum de- f l e c t i o n i s 0.360 inch.
Corrugated heat shield with multiple supports. -The heat s h i e l d shown i n figures 20-10 and 20-11 consists of a corrugated skin supported by multiple rows of truss-type supports. I.ie corrugated skin i s of t h e same size as t h e primary-structure panel. S p u s between the supports are a multiple of t h e primary-structure panel s i z e .
Other d e t a i l s of rlesign and i n s t a l l a t i o n are similar t o those for t h e simply supported heat s h i e l d concept discussed i n t h e preceeding section.
In addition t o pressure, loads f o r the muhisupported heat s h i e l d includt- bending due t o nonuniform t h e m l deflection of t h e supports and bowing of panel substructure due t o t h e m l gradients, pressure, and i n p l m e loading.
Provisions for differential inplane thermal expansion between t h e heat shield and primary-structure panel are similar t o those f o r t h c simply supported heat s h i e l d concept discussed i n t h e preceeding section, except t h a t one row of c l i p s a t t h e panel centerline is perpendicular t o t h e others t o r e s i s t inplane shear i n the long dimension of the panel.
I
A s m r y of design data for the corrugation and support c l i p is shown i n f i g u r e 20-10. Sizing of t h e support c l i p s is based on e c c e n t r i c a l l y a p p l i s l compressive loads due t o pressure. The lowest deight s h i e l d has a minimum gage corrugation thickness of 0.010 inch, a span of 1 3 . 1 inches, and 8 rows of sup- port c l i p s . Figures 20-12 and 20-13 show support span versus e f f e c t i v e t h i c k - ness and support span versus maximum deflection, respectively. For a span of 13.1 inches, t h e maximum deflection i s 0.242 inch.
c l i p supported heat shield. -The heat s h i e l d F l a t skin, dimple stiffened, shown i n f i g u r e s 20-14 and 20-15 c o n s i s t s of a flat s k i n stiffeneri i s o t r o p i c a l l y m e formations i n the sheet are truncated cones and each by a formed sheet.
cone is resistance spotwelded t o the flat sheet. Support c l i p s a r e located i n t h e P l a t s of t h e primry s t r u c t u r a l panel and a r e near as possible t o t h e loca- '-e*t s h i e l d deflection (section 19) .
t i o n f o r minimum Mounting of the s h i e l d s is perfortled f s o m t h e outside by means of f l u s h socket head screws a t each of t h e four a t t a c h points. The socket head screws then fasten t o flanged nuts which are resis-kmce spotwelded t o t h e support c l i p s .
The support c l i p s ,',re resistance spotwelde; i,o t h e primary s t r u c t u r a l panel.
The support c l i p s are rotated so as k~ place t h e plane of t h e web normal This o r i e n t a t i o n of t h e suppoJrt c l i p s t o a l i n e joining opposed a t t a c h poilnts.
allows f o r b i d i r e c t i o n a l thermal expansion and gives shear s t i f f n e s s t o t h e supports i n any direction.
I-
[.; A summary of design data f o r the heat shielc? i s shown i n figure 20-14.
The lowest weight shield has a minimum gage flat ski.n thickness of 0.015 inch, a m i n i m u m gage dimpled skin thickness of 0.010 inch, aspect r a t i o of 1.0, and width of 15.3 inches. Figures 20-lb and 20-17 show panel size versus effective thickness and panel s i z e versus maximum deflection, respectively.
For an aspect r a t i o of 1.0 and width of 15.3 inches, the maximum deflection is 0.173 inch.
Permanently Attached Heat Shield Concept
Modular, simply supported, interlockilig joint heat shield. - The heat
shield shown i n figures 20-18 and 20-19 consists of corrugated sheets t h a t are
ZI
simply supported at t h e ends and shingled with rearward facing steps.
@ . I the forward end of the corrugated sheet, a joggle is formed and finger s l o t s a r e cut. In t h e flats of t h e aIX end of t h e corrugated sheet, standoff supports are provided. Various types of standoff supports were considered, including: (1) Truncated conical dimples drawn i n t h e corrugated sheet (2) Flanged cups spotwelded t o t h e shield Spacers projection welded t o the shield.
( 3 )
I'
were selected f o r the standoff supports.
Truncated conical dimples The shield is mounted by sliding the joggle? end under the adjacent upstream shield and resistance spotwelding the dimpled end t o the primary- r -; e . structure panel.
t. 3 At joints between shields, the joggle minimizes aerodynamic drag. Fin- ger slots on the joggled end permit chordwise d i f f e r e n t i a l thermal expansion Spanwise d i f f e r e n t i a l between the heat shieid and primary-structure panel.
thermal expansion is allowed by bending of the circular-arc portion af the corrugated sheet.
A surmuary of design data f o r t h e corrugation i s shown in figure 20-20.
The lowest weight heat shield has a minimum gage corrugation thickness of 0.010 inch and maximum allowable length of four times t h e pitch (i.e., 10.44 The maximum allowable length i s due inches) of the primry-structure panel.
t o high bendtng i n the w i n g p e l tube w a l l from reactiorls at the heat shield Figure 20-21 shows heat shield length versus effective thick- simple supports.
Figure 20-22 shows heat shield ness, including t h e effect cf overlapping joints.
For a length of 10.44 inches, t h e mximum length versus maximum deflection.
deflection is 0.195 inch, not including thermal or support deflection, Modular, cantilevered heat shield. -The heat shield shown i n fi,ures 20-23 and 20-19 consLs5s of corrugated sheets t h a t are cantilsvered at the %'he forward end of the forward end and shingled with rearward facing steps.
corrugated sheet is curved Lo fit the c i r c u l a r a r c portion of the primry- structure panel. The c w i 4 end of the heat shield is attached d i r e c t l y t o the circular-arc portion of the primry-structure panel by at l e a s t two re- sistance spot, ;Ids located i n t h e f l a t s of t h e corrugated sheet.
20- 5 . .
Spanwise differential therm1 expansion due t o therml gradients between t h e heat s h i e l d and primary-structure panel is allowed by deformation of the circular-arc portion of t h e corrugated sheet.
Since t h e shingled heat shield is only attached at t h e forward end, chordwise thermal expawion is permitted by t h e rearward facing overlapping joints.
A surmnary of design data f o r the corrugation is shown i n figure 20-23.
The lowest weight heat shield has a minimum mge corrugation thickness of 0.010 inch and tmximum allowsble length of one pitch (i.e., 2.61 inches) of the primary-structure panel. The maximum allowable length is due to high bending i n the wing p n e l tube w a l l from the cantilever moment and shear.
Figure 20-24 shows heat shield length versus effective thickness, including the effect of overlapping joints. Figure 20-25 shows heat shield length versus maximum deflection. For a length of 2.61 inch, t h e maximum deflection i s 0.0073 inch, not including therml o r support deflection.
Heat Shield Thermal Analysis Heat shield isotherms at t h e three specified f l i g h t conditions (-0.5-g, +2.0-g, and cruise) have been shown i n section 9 with the isotherm presentations f o r the different primary-structure concepts.
Mean temperatures f o r t h e heat shields were derlved assuming a single flat sheet with an equivalent mass thick- ness The effect of corrugations was neglected but i s assmed of 0.011 inch.
small because boundary layer flow is nearly parallel t o t h e corrugations. The start of t h e corrugations at t h e leading edge experiences higher l o c a l heating effect of t h e corruga,tion closeout. An estimate of 25-percent due t o t h e ramp increase in t h e l o c a l heat transfer coefficient due t o a 3-degree maximum chord- w i s e slope yields a local temperature increase of 90% at peak heating condi- tions on the upper and lower surfaces.
Various heat shield attachment methods were examined t o determine l o c a l effects on heat shield and panel temperatures. Table 20-2 shows temperatures derived f o r a direct attachment method i n which t h e heat s h i e l d is spotwelded The analysis was or riveted d i r e c t l y t o t h e circular+rc stiffened panel.
performed at one wing locatfon ( F S 2366, BL 270) f o r upper and lower surfaces without insulation. Panel and heat shield temperatures were found t o be un- affected except at t h e attachment point, where direct aerodynamic heating occurs through t h e heat shield. A l o c a l "hot spot" of approximately 85OF above norm1 panel temperature is shown for t h e upper panel at t h e -0.5-g condition and f o r t h e lower panel a t t h e +2.0-g condition. For a l l conditions, t h e attachment point temperature is between the p n e l and heat shield temperatures. Applica- t i o n of these results t o t h e modular heat shield concepts is direct; i.e., temperatures a t th.e attachment points are between heat shield and Wnel temperatures.
Two methods of attaching t h e heat shield t o the panel with standoff c l i p s were a l s o investigated. The first method holds t h e heat shield i n place with clips which connect a flat portion of t h e panel t o a continuous hat section on the inside surface of the heat shield. The lower wing surface with no insulation Figure 20-26 shows temperatures was analyzed at one 1oca.tion (FS 2366, BL 270).
20-6 a t t h e attachment point f o r t h r e e f l i g h t conditions f o r t h i s first attachment method. Temperature differences are 155OF across t h e hat and 115% across t h e c l i p at t h e +2.@-g condition.
Differences are under 100°F f o r t h e other f l i g h t conditions.
Temperature f o r t h e section of heat s h i e l d enclosed by t h e h a t is seen t o vary by l e s s than 10%' from t h e temperature f o r t h e heat s h i e l d away from t h e hat. Where t h e hat section i s attached t o t h e shield, t h e higher ther- m a l capacity and conduction t o t h e i n t e r i o r at these poinfs cause temperature lag during t h e t r a n s i e n t s and reduced temperature a t cruise, compared t o t h e normal heat shield temperature.
The higher inner s t r u c t u r e temperatures shown for t h e -0.5-g condition are caused by rapjdly reduced heating rates, hence lower temperatures, on t h e heat s h i e l d when t h e lower surface is a t negative angle of attack. S t r u c t u r a l panel temperatures are unaffected by t h e presence of t h e hat and clip, except during t h e +2.O-g condition, when reduced exposure t o t h e heat s h i e l d a t peak temperature reduces l o c a l panel peak temperatures by about 50%.
The second c l i p attachment method examined assumes t h a t t h e c l i p d i r e c t l y c o n e c t s the heat shield t o t h e flat portion of t h e panel, as with t h e multiple The analysis was p e r f o r m e d f o r upper and lower surfaces a t an support concept.
inboard location (BL 166) and a t an lnsulated outboard location (BL 3OO), and f o r t h e lower surface under t h e fuselage (BL 60). Table 20-3 shows temperature differences across t h e support c l i p derived f o r t h e three f l i g h t conditions f o r t h i s method of attachment. The 535OF d i f f e r e n t i a l shown f o r t h e outboard lower surface a t t-2.0-g is due pritnarily t o the insulation which i s o l a t e s t h e primary s t r u c t u r e and forces t h e shield t o high temperatures during t h e peak heating condition. Thermal : sistance through t h e c l i p from shfeld t o panel w a s c a l - culated t o be about four times t h e normal therm1 resistance through t h e insula- t i o n and radiation air space a t t h i s location. Thus the e f f e c t of t h e c l i p on l o c a l s h i e l d and panel tempemtures is minor. This is evidenced by comparing t h e derived d i f f e r e n t i a l s across t h e c l i p , Shawn i n table 20-2, with t h e tern- pemture differences from heat s h i e l d t o panel, based oa the detailed panel model, shown i n t a b l e 20-4. Agreement is good, considering t h a t the a d d i t i o n a l thermal capacity and conduction path of the c l i p are not included i n t h e d e t a i l e d panel analysis. The e f f e c t of t h e c l i p on t h e heat s h i e l d at t h e s e locations is shown i n t a b l e 20-5, which l i s t s '"*le temperature difference from t h e c r e s t of a corru&ion on t h e heat s h i e l d t o an adjacent c l i p attachment point. Except for the surfaces experiencing peak heating during t r a n s i e n t s , t h e temperature difference i s not more than 5OOF. The higher d i f f e r e n t i a l s a t t r a n s i e n t con- d i t i o n s a r e caused by t h e thermal l a g a t t h e attachment point, due t o a higher mass per exposed area cornpared t o t h e corrugation skin.
An analysis was a l s o conducted t o detertrdne temperatures of the flat skin, dimple stiffened heat shield concept f o r compxison with corrugated heat s h i e l d Table 20-6 shows t e a p r a t u r e s f o r t h e upper and lower h e a t shields temperatures.
at four locations on t h e wing f o r t h r e e flight conditions. The outboard loca- t i o n s are shown with and without insulation on t h e lower surface. Temperatures are presented f o r t h e external skin [ T ( 1 ) f o r upper surface and T ( 6 ) f o r lc-*reT surface], f o r t h e t o p of t h e dimple at t h e attachment point with t h e external s k i n [ T ( 2 ) f o r upper surface and T ( 5 ) f o r lower surface], and for t h e i n t e r n a l skin [T(3) f o r upper surface and T ( 4 ) f o r lower surface]. Temperature d i f f e r - ences from t h e t o p of t h e dimple t o the inner skin, T(2) t o T ( 3 ) and T ( 5 ) t o 20-7 T ( 4 ) , a r e l e s s than 10°F except during t h e transient, conditions, when t h e differences f o r surfaces undergoing peak heating (upper surface a t -O.5-g, lower surface a t 2.0-g) are on t h e order of 50°F.
Peak temperature differen- tials from external t o internal skin, T ( 1 ) t o T ( 3 ) and T ( 6 ) t o T(4), f o r lo- cations without lower surface insulation occur a t t h e -0.5-g condition on the
upper surface (looo t o 150%); at t h e 4-2.0-g condition on t h e lower surface
( l l O o t o 1609); and at t h e cruise condition on t h e upper surface ( 130°F).
With insulation, the peak temperature d i f f e r e n t i a l occurs on the upper surface (2209) a t t h e -0.5-g condition. Tne peak d i f f e r e n t i a l s for all other condi- tions, upper cr . Jer surface, with or-without insulation, are not more than 70%.
Teiiiperatures f o r t h e corrugated heat shisld derived from t h e isotherm analysis f o r structu-a1 p i n e b are presented i n t a b l e 20-7 f o r direct compari- son with t h e dimple stiffened heat shield tclnperatures i n t a b l e 20-6.
Temperatures f o r t h e external skin of t h e dimple stiffened heat shield a r e generally 0 ' t o 7 0 9 cooler than corrugated heat shield temperatures, ex- cept f o r t h e lower surface a t -0.5-g and cruise conditions. For these condi- A comparison of t h e tions, t h e corrugated heat shield is up t o 4 0 9 cooler.
effects of both heat shield concepts on semimonocoque s t r u c t u r a l panels showed t h a t peak panel temperatures are about t h e same (within 100%) with either heat shield concept, except f o r t h e outboaril locations w i t h insulation. A t these locations, peak panel temperatures are l S O o t o 2OOOF lower with t h e dimple stiffened heat shield than with t h e corrugated heat shield.
Summary of I n i t i a l Weight Evaluation O n t h e basis A s u m r y of hzat shield data is presented i n t a b l e 20-8.
the data show that t h e corrugated heat shield with of weight and deflection, multiple siqports is the leading candidate f o r t h e refurbishable shield; f o r is lover t h e permanently attached shield, t h e simply supported modular shield Also, the multiple-supported shield is of large single-piece con- i n weight.
s t r u c t ion and af f ordc appreciable cost advantages.
the flow For t h e refurbishable shield, t h e flat-skinned concept reduces disturbances and l o c a l heating due t o cross flow from t h a t of t h e corrugated concepts, but it e n t a i l s a weight penalty.
Panel f l u t t e r analyses of the heat shields were a l s o conducted (as pre- sented i n section 14). When refurbishable heat shields were considered, t h e sprixig constants included t h e f l e x i b i l i t y of t h e heat -shield edge closeout, panel the support clip, and t h e primary-structure panel. The primary-structure is regarded as shielded fromthe aerodynamic environment when the refurbishable h a t shield is employed. However, when modular, or permanently attached heat shields were considered, both t h e shield and t h e primary-structure panel were required t o be f l u t t e r free.
20-8 The refurbishable shields are stable; they have panel f l u t t e r factors of s a f a y exceeding the required 1.3. On the other hand, the permanently attached shields are f l u t t e r c r i t i c a l , because the primary-structure panel has an allowable f l u t t e r parameter that i s l e s s than the applied dynamic pres- sure. This is because the chordwise stiffness of the spanwise-oriented tubu- l a r concept i s low. Iu decreasing the r i b and spar spacing t o overcome t h i s condition, the t o t a l wing substructure weight i s increased significantly be- yond that of the refurbishable shield (additional ? = 0.204 inch or 8 . 7 lb/ft2L Results of analyses t o determine effects of random sound pressures indi- cate that the upper surface and lower surface inboard heat shields and support 0.022-q c r i t e r i a a s required.
clips satisfy the 0.007-q and Considering the weight results shorn i n table 20-8, and cost, perform- and r e l i a b i l i t y data presented i n later sections, the corrugated heat ance, shield with multiple supports was selected for application t o the several primary-structure concepts.
FINAL HEAT SHIESD STRUCTURAL SIZING The corrugated heat shield concept w a s applied t o the various primary structure concepts i n obtaining t o t a l concept weight. Typical heat shield design and weight data f o r the spanwise semimonocoque concept are shown i n tables 20-9 and 20-10, respectively.
For the chordwise semimonocoque concept, typical heat shield design and weight data are shown i n tables 20-11 and 20-12, For the monocoque concept, typical heat shield weight data are respectively.
shown i n table 20-13. For each primary-structure concept, the effect of oxi- dation i s included i n the t o t a l heat shield weight. TD N i C r i s used on the lower surface outboard area between BL 304 and BL 350, and R a e 41 is used on the remaining upper and lower surface areas. Since a support spacing of 13.1 inches was determined l e a s t weight a t a location where minimum gage Re& 41 shields were required for least weight, and since t h i s spacing was used f o r a l l concepts requiring shields, not all heat shields are minimum gage nor least weight. For shields thicker than minimum gage, a weight reduction is achievable by reducing the support spacing; actually a l l analyses conducted indicate that support spacing should be reduced u n t i l the shield i s minimum gage t o result i n least weight. However, the reduction i n spacing would have t o be i n multiples of the pitch of the primary-structure panel configuration (tubular and beaded) and hence maximum spacing for minimum gage shield (least weight) might not be attainable. Also closer supports mean more fasteners, welding, and labor, so fabrication cost must be considered; but t o t a l system cost i s not a s sensitive t o fabrication cost as t o weight, so i n the f i n a l analysis the maximum support spacing (compatible with the primary-structure configuration) i n which a minimrm gage shield can be utilized is probably the optimum weight design.
20-9 20- 10 TABLE 20-2 DIRECT ATTACRMEVT OF CORRUGATED HEAT SHIELJ, FOR
sEMIMoI?ocoQuE TUBULAR PANELS TO
Reat s h i e l d Panel a 0
I Temperature, F
- Condition
2.06 Cruise I
- 0 . 5 ~ Location Heat shieldb T ( l ) 1650 1350 Upper surf ace Attach pint T ( 2 ) 1010
1500 1 os0
Panel e x t e r i o r T ( 3 ) 1400 t Panel i n t e r i o r T ( 4 ) 1lt20 11 30 ~
L
Panel i n t e r i o r T(lt) 1230 141 5 1485 Lower surf ace
Panel e s t e r i o r T ( 3) 11t15. I Goo
I Attach point T(2) 1630 1400 ‘b
IIea.1; shield A 1 420
T ( 1 ) 1-11 5 13iO a - - TemperatGes at FS 2366, BL 270.
b ~ o insulation.
- 20- 11 I T(1) s h i e l d a t attachment point 'Heat s h i e l d Clips . .
flat of panel T(2), panel at attachment point
Temperature differential, T(1) - T(2), OF
P- Condition Locat ion BL 6oa BL 166a BL 300ajb
-
- *5g Upper surface
0 +275 Lower surface +115 + 85 +175
-
2.0g Upper surface
- 50 +110
Lower surface +295 , 4-280 +535
-
Cruise Upper surface -250 -130 Lower surf ace -5 +130 +295 20-12 T ( 1 ) , heat s h i e l d - - c y
f -
T ( 2 ) , f l a t of panel .
L
Temperature differential, T(1) - T ( 2 ) , OF
[ ::-
F Condition Location BL 6oa BL ~ 6 6 ~ BL 300ajb
-0 *5r: Upper surface - +125 +260
Lower surf ace +135 - 20 + 80
-
- 20 2 .og Upper surface
- 75
Lower surface +275 +225 +440
Cruise Upper surf ace - -165 - 90
Lower surface 0 + 90 +3 70
u
With insulation at lower surface I -- I
I * '
20-13 , I ' T(l), s h i e l d a t corrugation T(2), s h i e l d a t attachment point _ I . _ - - Heat s h i e l d Clips F l a t of panel ______. - --.
/Temperature differential, T(1) - T ( 2 ) , OF
R
BL Goa BL 166" BL 300a'b
Condition Locat ton
- +115 +145
Upper surface - 0 * 5 g
-40 - 50 + 40
Lower s u r f ace
- - 40
2.0g Upper surface
- 50
Lower s u r f a c e 4-80 + 75 + 55
-
- 50 - 25
C r u i s e Upper surface Lower surface 0 + 10 + 50 -_ 20-14 TABLE 20-6 TEMpERATuIiFs FOR FLAT SKIN DIMPI;E STlFFENED HEp3c SH33T.D CONCEF'S Upper s h i e l d
. L L - - r . - Upper panel
, r ::;: r - 7 I : t I r d , Lower panel . , . .- . - - - - - - - . , . . .. I n s u l a t i o n ( i f used) Lower h e a t s h i e l d -
Temperatures , F
BL 60 BL 1 6 6 BL 258 BL 258 BL 350 BL 35( LocxtJon
None Condition t - I n s u L n t i on
None None 2 5 i n . None .5O i n
-
-0.5s External skin, T ( 1 ) 1305 1585 1550
-
Attach point, T ( 2 ) 1675 1475 1220 1470 1370 1565
-
I n t e r n a l skin, T(3) 1200 1435 1325 1530 14-27 1190 1300 1400 1465 1480 1540 I n t e r n a l skin, T(4) Attach point, T(5) 3300 1400 1460 11-95 1480 1535 External skin, T(6) 1300 1375 1405 1235 1450 1475
-
?.Q; External skin, T ( l j 1.155 1355 1305 1420 1375 c 1190 1275 Attach point, T ( 2 ) 1380 1460 1365
-
I n t e r n a l skin, T(3) 11-95 1385 12 70 1465 1355 134C I n t e r n a l skin, T ( 4 ) 1445 1550 1640 1645 a725 Attach point, T(5) 15 90 1660 1385 1485 16 go 1750 External skin, T(6) 1605 1685 1710 1775 1545 1795
-
:mise Exkcrnal s k i n , T ( l ) 835 1005 875 885 950
-
1000 1065 86 0 Attach point, T(2) 1125 8 90
-
I n t a r n a l skin, T( 3) 1010 10'75 860 1140 3 90 1340 I n t e r n a l skin, T ( 4 ) 1285 1350 1445 1415 1525 Attach point, T(5) 1295 1365 145 0 1435 1345 1530 1340 1340 1410 1445 148 0 1520 External skin, T(6) .. .
- - aTempemtures at Es 2366, semimonocoque primry structure.
TABLE 20-7 TEMPERAT= FOR CORRTJGATFD HEAT SHIELD DERNED F R O M SEBUWNWOQUE PRLMARY 3TRUCIURE ISOTHERM ANALY3IS --^I-
-01)- Lower panel
- -.- -I_
I n s u l a t i o n ( i f used) Lower s h i e l d /--- I Locat ion BL 60 BL 166 BL 258 B L 258 BL 35C BL 350 ondition I n s u l a t i o n none none none .25 in. none .50 i n .
-
Upper s h i e l d , T ( 1 ) - 1370 1620 1590 1700 1675
-0 54 Lower s h i e l d , T ( 2 ) 1245 1280 1360 I 1-36!? 1430 ~~
2.0g Upper s h i e l d , T ( 1 ) - 1335 1320 1425
1180 1380 1555 1600 1685 1745 1845 Lower s h i e l d , T ( 2 ) 1775
Cruise Upper s h i e l d , T ( 1 ) - 945 990 910 1050
9 3 5
Lower s h i e l d , T ( 2 ) 13hO 1325 1385 1415 1500
.- -
20- 16 E -4 29- 17 TABLE 20-9 TYPICAL HEAT SHIELD AND CLIP DESIGN DATA, SPANWISE SEMEMOIVOCOQUE C O N C m S O in.
eu N
3 0
VJ cD d d rl (0 dc d 0 0 I- 0 0 t: a , m s l N 0 0 0 c; d o ' @¶ u 3 b VJ 0 0 0 0 V J N 0 0 0 0 0 0 0 0 d d d d m
8 0
rl 4 0 0 0 0 0 0 0 0
T PI rl CD (0
F 4 rl
- t -
cu 0 0 rl In v) cu m m O U 0 G u 0 N ev cu r4 rl N k k Q, 0
P E t 8
20-1.3 TABLE 20-11 TYPICAL HEAT SHIED AND CLIP DESIGN DATA, CHORDWISE SEMIMONOCOQUE CONCEPT . W i n . , L -
. .. ! s I i n f : -
. I in.
b . 10 in.
t - _ _ _ I -
c1 : - ) I
.SO in.
Geometry: r Surface BL a, b , h , t, R, bs, bf t C in. in. .
in. i n i n . i n . i n . i n .
Upper 120-212 .40 1 . 2 2 .31 . o n
. Y j 1 . 1 8 3 . o s .gl Upper 2l2-350 . 4 0 1 . 1 8 3 .032 i.i~ 1 . 5 8 .40 .014 h e r 0-1x1 . 3 0 -66 1 . 4 3 9 1 . 2 2 . 3 1 ,012
.ov .gi
Lower 120-212 . 6 6 1 . 4 3 9 .027 1 . 2 2 -30 .gi . 3 1 .012 Lower 232-304 1 . 4 3 9 . 0 3 6 1 . 4 2 1 . 9 2 -30 .66 . 4 9 . 0 1 5 Lowera 304-350 .66 1 . 4 3 9 .044 1 . 9 2 2 . 6 0 .67 .oig .3C a T D - N i C r heat shield and clips, 20-20 I m L n cr) Ln \o '0.
rl m f- (\1 cu a 3 co 3 Ln rl rl rl 9 .
Ln 4 - 5 Q
--I z
--I 0 0 0 9 .
In \D v3 Ln 0 0 0 0 0 0 c\l
4 Ln R
cu cv) ri I I I I cu
d Fz
cu rl c 20- 21 v) \D '9.
rl cr) Ln m Ln ln
rl \R" rl
0 0 0 03 03
5 %
3 -3
0 0
? 9 "
9 9
0 0 0 0 Ln n ln ' 0 .
zi
3 : rl 9 9 0 0 \D rl G I a 20-22 oL 1700
i
+ t
c
0 5 10 15 20 25 30 35 Sponwise distance from leading edge, ft _- Figure 20-1.. Heat-shield temperature vs spanwise distance from leading edge along s t a t i o n 2360 20- 23 .03( I I I 1
I
Support spacing = 13.1 constant
0 TD-NiCr
0J T = corrugation only, no support clips A Haynes 25 ,
I1 0 Rent
.02( C .- I+- .01( - 0 - 4
T
I a Temperature, "F Heat shield material comparison Figure 20-2.
20-24 C l i p : 1 at cach
support point 7.A
f
,t point) .207L (Suppoi
. I L (Support point)
Con ugatioii sc-ction Hat scction D = 3/16 in.
/ - , Connect to wing panel CI ip Connect to hat section (heat shield)
-
Hoot section Panel data c l i p data Weight data Deflectibv data L
Panel -
length, bf' bS' tC R, that# hhat' Dclip' hclip' ',lip# ZIPi)sld"clip' ZT, ' m , in, in. in. in. in. 1 in, in, in. in. in. ' in. in. in. i n .
- -~ ~ -~ - ,039 .0151 .0014 -0165 - 3 8 0 15.3 .32 1.24 ,010 .910 .020 .250 1.30 1.31 -044 -0198 90008 e0206 -557 23.0 -47 1.84 ,016 1.360 e020 ,320 1.30 1.49 - - Figure 20-3. Corrugated heat shield concept, hat section stiffened and c l i p supp~. fed ( refurbishable) ------..- 20-25 .
2 0 - 26 0 0.5 I .o I .5 2.0 2.5 3.0 3.5 4.0 Panel *pati ratio, o/b
Figure 20-5. &ne1 size YS t ’ for corrugated heat shields
with hat sections and clip support 2.0 1.6 .4 Figure 2 0 6 . Panel s i z e vs t o t a l deflection f o r corrugated heat shields with hat section and c l i p supports .02n .E .016 I’ n r’ 012 f 0 1150 I 2 5 0 1350 1450 1550 1650 1750 Temperature, OF ..-- Figure 20-7. Temperature vs for corrugated heat s’?ields with hat sections and c l i p supporta Geometry:
Panel -
-
-
length bp bs* *e * R, h. t, 'chan, 'shield' t. 6mmox, in.
in. in. in. in. in. in. in.
in. in. in.
1.172 .023 0.0042 .0105 0.0147 ,360 15.3 .32 1.25 A10 0.910 23 .47 1.85 a016 1.360 1.362 SO23 0.00294 -016 0.0189 e483 Figure 20-8. Corrugated heat shielcl concept with simply supported ends ( refurbishable) .u7 . .
0 10 30 40 50 60 70 80 90 100 Hear ihleid Ian&, L, in.
Panel Length vs t
Panel length vs deflection Figure 20-9. Effective thickness and deflection f o r corrugated! heat shield with simple supports 20-30
-
U.
C C c F w a C a P . I + a
I-=-
!
c!
L!
u c a z "
-
0 v) I n a
L j
0 u) 20-32 Pressure: p = t 1.0 psi I - 92 in.
-
Shield temperature: 16OOOF -040 Channel temperature: 1500OF Material: Rene' 41
-032 - 4 L l -
c .- IC- ui In spans 9, e -0 .024 f + t a ,
-
> .- a W -016 .008 Figure 20-12. Span length vs f o r multisupported corrugated heat shield Span length, L, in.
- -- - - Figure 20-13. Span length vs deflection f o r multisupported corrugated heat s h i e l d n l ..(I. --I -- - - - - - - --.--
-
-
Lf P a R i h l t,, fSf 6 , tpanelt shie Id 1 in. in.
in. in. . in.
in. in. in. in.
.01Q .015 .173 ,0284 .02,98 15.3 .250 .063 .063 I- ,017 .480 .035 ,0353 23.0 ,310 .077 ,077 . O 17 & J 0 Material: Rene'41 Design temperature: 16OO0F
-
0 <hieid - - tpanel + T,.lip (from corrugated concept)
~- .- - Figure 20-14, F l a t skin dimple stiffened heat shield concept with c l i p supports (refurbishable) ,
---t--lt 1 -
- - - .I- .. . -__- 20-36 Pressure: p = f 1.0 psi Temperature: 16OO0F Material: Rene.41 S.T.A.
0 0 16 24 32 40 Q P o d width, b, in.
Figure 20-16. Panel s i z e vs for dimpled concept heat shields 1 .o
.- d . 6
L a .2 Figwe 20-17. Deflection vs panel size f o r dimpled concept heat s h i e l d s 20-38 !
'u
Section A 4
+2.61 in.--+ Spotwelds
cc P
Section A 4 Geometry: Figure 20-20. Simply supported modular heat shield concept (pernaanently attached) /’
. /
\ I
1 I
- cd Design data: Pressure: p = t 1.0 psi Minimum gage
Temperature: 160OOF -
Material: Rend41 S.T.A.
at 140OoF I , .I 6 10 14 18 26 30 34 Figure 20-21. Length vs f o r modular heat shield concept with simple supports .a0
. . 6 0
C .- co c .- 2 .40
-
c E l a .20 4 8 12 16 20 24 32 Heat shield length, L, in.
Figure 20-22. Length vs 6 f o r modular heat s h i e l d concept with simple supports Section A 4 in.
Moximum allowable length due to h:gh bending in wing 0 .
pone1 tube wall from cantilever mootent.
Does not include thermal deflection or support daflection.
b.
Figure 20-23. Cantilevered modular heat s h i e l d (permanently attached) .048 I I Design data: Pressure: p = f 1.0 psi Temperature: 1600°F / .040 Material: Rens' 41 S.T.A.
C .- 1 2 Maximum length allowed
- i s 2.61 in. due to hIgh
.032 beding in wing panel .u tube fran cantilever i- moment t
.- -
p .024 W .016 .
.wa 0 4 e 12 16 20 24 Heat thldd length, 1, In.
Figure 20-24. Length v s t for cantilevered modular heat shield
I 1 Design data: Prarsure: p f 0.5 psi Temperature: 1600aF 1 .o Material: Rene'41 S.T.A.
o t 14OOoF 0.8 Maximum length allowed C .- - i s 2.61 in. due to high 1
- 0 . 6
bending in wing panel b tube from cantilever
i moment .- s
,'
* U = & 0.4 0.2 0 4 8 12 16 20 24 28 32 Heat shield length, 1, in.
Length vs 6 for cantilevered modular heat s h i e l d Figure 20-25.
-0.59 Condition . - 'I 385 2.09 Condition
\
* 1710 2 L- 1715 Cruise condition Note: iemperotures T F ) at FS 2366, BL 270, lower surfa-ce'ofi semimonocoque primary structure, - with-upper and l w e r
--
- I - - - .. . I- shields, no insulation Figure 20-26. Temperatures a t lower surface attachment point for corrugated herk shield with hat sections and clip supports Sectiok 21 LEADING EDGE WEIGHT A&%LYsIs bY C . C . Richie CONTENTS p%e PARAMEXRIC THERMAL ANALYSIS AND MATERIAL SELECTION 21- 1 EVALUATION OF CANDIDATE LEADING EDGE CONCEPTS 21- 3 Continuous Concept 21- 3 21- 5 Segmented Leading Edge Concept b w Cycle Fatigue 21- 12 Selection of Leading Edge Geometry SUMMARY O F DESIGN AND WEIGW DATA 21-13 21- iii TABLES 21- 1 Leading edge pressures 21- 16 21- 2 Leading edge design pressures 21- 3 Monocoque leading edge evaluation, continirous hot load carrying concept without leading edge spar, 4-2.0-g maneuver condition 21- 18 21- 4 Monocoque leading edge evaluation, continuous hot load carrying concept including leading edge spar, +2.0-g maneuver condition 21- 1 9 21- 5 Spanwise semimonocoque leading edge evaluation, continuous heat shielded and insulated concept; nose thickness = 0.12 in., +2.0-g maneuver condition 21-20 21- 6 Detail temperatures f o r heat- shielded and insulated leading edge concept; nose thickness = 0.125 in. 21- 21 21-7 Detail temperatures f o r heat-shielded and insulated = 0.375 in. 21- 22 leading edge concept; nose thickness 21-8 Detail temperatures for heat-shielded and insulated 21-23 leading edge concept; nose thickness = 0.625 in.
21-24 21- 9 Continuous leading edge evaluation matrix 21-10 Spanwise semimonocoque leading edge evaluation, continuous heat shielded and insulated concept; nose thickness = 0.625 in., f l a t thickness = 0.060 in. 21-25 21-26 21- 1 1 Summary of continuous leading edge data 21-27 21-12 Segnented leading edge evahation matrix 21- 28 Summary of segmented leading edge data 21-13 21-14 Summary of thermal deflections, segmented leading edge concept 21-29 21-15 Spanwise semimonocoque leading edge evaluation segmented heat shielded and insulated concept; nose thickness = 0.125 in., flat thickness = 0.03 in. 21- 3 0 21-v Page 21-16 Spanwise semimonocoque leading edge evaluation, segmented heat shielded and insulated concept; nose thickness = 0.125 in., flat thickness = 0.06 in. 21- 31 21- 17 Spanwise semimonocoque leading edge evaluation, segmented heat shielded end insulated concept; nose thickness = 0.625 in., flat thickness = 0.06 in. 21- 32 21- 18 b w cycle fatigue evaluation for selected leading edge concepts 21- 33 21-19 Leadiilg-edge design and weight data for selected concepts 21-34 21-vi ILLUSTRATIONS Page 21-1 Wing leading edge pressure v a r i a t i a c during maneuver 21- 35 21-2 Peak temperature at leading edgn stagnation l i n e vs material thickness and emmittance 21- 3 6 21- 3 Monocoque leading edge evaluation, continuous hot load carrying concept, without leading edge spar 21- 37 21- 4 Monocoquc leading edge evaluation, continuous hot load carrying concept, including leading edge spar 21- 3 8 Spanwise semimonocoque leading edge evaluation, 21- 5 continuous heat shielded and insulated concept; leading edge thickness = 0.120 in.
21- 39 21-6 Spanwise semimonocoque leacling edge evaluhtion, continuous heat shielded and insulated concept; leading edge thickness = 0.625 in., f l a t thickness = 0.060 in. 21- 40 21-7 Spanwise semimonocoque leading edge evaluation, segmented heat shielded and insulated concept; leading edge 21- 41 thickness = 0.125 in.
21-8 Sign conventions and notation used i n analysis of the 21- 42 end effect for the segmented leading edge concept 21- \ ' Thermal s t r a i n reduction factor at center of leading edge segment, segmented heat shielded and insulated 21- 43 concept lyclic s t r e s s and s t r a i n pattern involving zero mean 21- 10 sL-ess and alternating plastic s t r a i n 21 Relaticq between t o t a l strcrin range and cyclic l i f e 21-11 for TD N i ? r 21- 45 21- 46 21-12 Deflection o t segmented leading edge 21-13 Optimum length of segnented leading edge for monocoque concept 21- 47 21-vii Optimum length of segmented leading edge, semimonocoque 21-14
corxept 21- 4 a
21-15 Leading edge nose section, continuous 21- 49 21-16 7egmented leading edge 21- 50 21-t’iii A Cross section area D I h c t i l i t y Modulus of e l a s t i c i t y E Ultimate tensile strength Ftu G Shear modulus Gravitational acceleration Rmoer of stress levels considered Fatigue quality index KQ 1 Length M Material constant used i n equation 21-1 Cyclic l i f e Nf Number af loading cycles t o failure at the ith stress level 'i n Number of loading cycles applsed at the ith stress level i Pressure P Shear f l o w R. A. Reduction i n area T Temperature t Thickness
-
t Equivalent panel t h i c h e s s U Strain energy z Material constant upa-7 i n equation 21-1 01 Linear coefficient of thermal e-* --WAX: Y Material constant used i n equation 21-2 AT Temperature difference A€ Total strain range AU Stress range corresponding t o t o t a l s t r a i n range (A€) E Strain (T Stress Subscripts e l Denotes e l a s t i c value f Denotes f i n a l value 0 Denotes i n i t i a l value P Denotes plastic value 21-x
Section 21
Section 21 LEADING EDGE WEIGHT ANALYSIS The leading-edge analysis consisted of a parametric thermal analysis, selection of the leading candidate material, structural evaluation of the candidate arrangements f o r the segmented and continuous concepts, design, and weight data.
Plasma- j e t t e s t r e s u l t s {presented i n section 4) indicated that although the porous tantalum metal concept results i n improvements by a factor of 2 over previously tested concepts, a sheetmetal concept w i t h an oxidation- resistant coating showed marked improvement and therefore satisfies b e t t e r the leading-edge oxidation-protection requirement.
The coated sheetmetal concept was selected f o r detailed evaluation.
The leading-edge pressures used f o r the investigation a r e presented i n table 21-1 and the design pressures, which a r e based on the net difference between internal and aerodynamic pressures, are shown i n table 21-2. The leading edge pressure variation during maneuver is presented i n figure 21-1.
PARAMFPRIC THERMAL ANALYSIS AND MATERIAL SELECTION O n the basis of radiation equilibrium temperatures, the tantalum alloy Ta-1OW was originally considered the leading candidate. However, a two- dimensional thermal analysis, the lower curve i n figure 21-2, indicated lower temperatures which would allow use of the superalloy TD N i C r as presented i n d e t a i l l a t e r i n the discussion. Figure 21-2 i s a plot of temperature versus material thickness f o r Ta-1OW (tantalum alloy), Cb-752 (columbium alloy), and TD N i C r (dispersion-strengthened alloy). I n i t i a l l y , only internal radiation effects were evaluated f o r a hot load carrying leading edge (no insulation a t the Rene' 41 leading edge spar). Later, conduc- tion and internal radiation effects were determined using TD N i C r and an insulated concept (insulation at the Rene' 41 leading edge spar).
The transient-temperature analysis of figure 21-2 indicates that a maximum of 2200°F is achi.eved by increasing the leading-edge thiclmess t o TD N i C r does not about 0.125 in., thus permitting the use of T D N i b .
require an oxidation-resistant coating. The d e t a i l s of t h i s selection are presented i n the following discussion.
A preliminary thermal analysis of the wing leading edge was conducted f o r three structural arraneements, which include two hot load carrying concepts (with and without a leading edge spar) and an insulated concept. Three leading edge materials were considered: preoxidized TD N I C r , s i l i c i d e coated Ta-low, Temperatures determined f o r the stagnation l i n e and s i l i c i d e coated (3-752.
on the leading edge and f o r the attachment point8 of the leading edge section 21- 1 t o the s u p p r t i n g structLrc are shown i n tables 21-3, 21-4, and 21-5 for t h e +2.0-g condition. These temperatures were used t o determine thermal s t r a i n s f o r t h e various material arrangements at t h e maximum dynamic pressure condi- tion. A material thickness of 0.12 inch at the radius was assumed, and radiation was the only mode of heat transfer accounted for within t h e struc- ture. Table 21-3 sk-ows Lemperatures f o r the hot load carrying concept without a leading edge spar (figure 21-2) f o r Ta-1OW and f o r TD N i C r . Table 21-4 prcsents temperatures f o r the hot load carrying concept with a leading edge spar (fig. 21-4). Fcx t h i s concept, the nose beam and the panels immediately behind it were TD P;"Cr, with the leading edge shown f o r Ta-low, TD N i C r , and Cb-752. Temperatures f o r t h e iilsulated concegt (fig. 21-5) a r e presented i n table 21-8 f o r Ta-lOh and Cb-752. The leading edge spar i n , t h i s case was protected by inm!.atiun and was assumed t o be made from Rene 41.
hown i n Tables 21-3 and 21-4 f o r TD N i C r at t h e stagnation Temperatures l i n e are representative of temperature accounting f o r radiation, lateral con- The effect of lateral conduc- duction, and an elri-ssivity of 0.75 (Section 5).
t i o n at locations oth3r than the stagnation l i n e is much smaller because teta2er- ature gradients aloug the structure become insignificant behind t h e leading edge The emittance value determined by t e s t f o r TD N i C r was used i n a later radius.
analysis of t h e insulated leading edge concert.
The results of the preliminary a.nalysis of the hot load carrying concept are summarized t o show the difference i n peak temperature due t o material and thickness at the leading edge radius. Figure 21-1 shows peak temperatures at the leading edge stagn:ticii l i n e f o r the three materials and a, range of material thickness. 3esults f o r TD N i C r are presented f o r surface emittances c,f 0.75 and 0.90. The temperature increase of 95°F f o r the lower emitta.nce i s f a i r l y constant over the range of material thickness shown (0.04 t o 0.20 inch!.
A change i n emittance from 0.80 t o 0.70 f o r Ta-lOW r e s u l t s i n a 6 5 " ~ increase i n peak temperature. As the structure at the leading edge becomes thinner, hea,t cap:ic:ity effects diminish 2nd peak temperatures vary inversely with sur- face emittance, regardless of material.
Tables 21-6, 21-7, and 21-8 show r e s u l t s of t h e thermal analysis of the in:;ulated Zca,di.ng edge concept f o r "1) N X r , with material thicknesses a t tho ra,di.us of O.l.25, 0.375 and 0.625 inch, respectively. Temperatures are zho-~rri a t three f l i g h t conditions f o r three locations on the radius (including t,h.lc :,t,agnatLon l i n e ) and f o r the supporting structure behind the r:tdiur,.
Conduction was included i n the anaLysis, and the 0.75 emittance was used f o r Til ITi.Cr. The leading edge section immediately behind the radius w a s assumed fsak with an equivalent mass thickness (%FLAT) of e i t h e r 0.03 or 0.06 inch.
- Thickness of the section connecting the radius with the flat section is double Peak temperatures a t tPe stagnation Line, T ( 4 ) , a r e not more than tFIAT.
The effect of increasing material thick- 2200 v for any of the concepts shown.
nes:; at t h e radius i s minor f o r the flat sections of the leading edge, where tcmper4xrcs a t :211 flight conditions change by less than 30°F as material thicknc:::: is increased from 0.125 t o 0.625 inch. A t the radius, temperatwes .ire reiluscd by 50" t o 1 0 O " l ' for the s m e thtckness increase. Temperature gradj.cnt through the material at the stagnation l i n e (temperature difference ' r ( 4 ) t o ' l ' ( f ~ ) ) i s a maximum of 6 5 " ~ at the 2.0g condition f o r the 0.625-inch Differences a t the stagnation l i n e f o r the other f l i g h t conditions thickness.
and material thicknesses are under 50°F. Differences through other locations on the radius, T ( 3 ) to T ( 8 ) and T ( 5 ) t o T(10), are under 25°F f o r the three material thicknesses a t any f l i g h t condition.
EVALUATION OF C A N D I D A m LEKOING EDGE CONCEPTS Continuous Concept The continuous leading edge concepts consist of relatively long segments t h a t are attached t o adjacent structure by sealed, nonslip joints. Cross sections of the four structural arrangements used i n the continuous leading edge concepts evaluation are shown i n figures 21-3, 21-4, 21-5, and 21-6.
From the preceding parametric thermal analysis data involving four structural arrangements, three materials and thicknesses ranging from 0 . 0 3 t o 0.625 inch (the resulting eight variation of the continuous leading edge concept given i n table 21-9) were further evaluated. Included i n the eval- uation were : Analysis of thermal strains Reusability requirements (refurbishment ) a . depth of oxide penetration b. coating l i f e c. low cycle fatigue Analysis of local buckling Thermal strains were obtained based on a plane strain analysis (section 7, case three, bending about one axis) of the entire vehicle cross-section for Idealizing the leading edge and vehicle cross- each leading edge concept.
section by discrete elements, the actual values of coefficient of expansion (a), e l a s t i c modulus (E), and temperature (T t 80°F) were used a t each node point. Results of the plane strain analysis are shown i n tables 21-3, 21-4, The plane strain results indiccte that the failure mode for 21-5, and 21-10.
the coated refractory metal systems (i.e., Ta-low, Cb-752) is tension, due t o the lower a A T (i, e., product of the coefficient of thermal expansion and 21- 3 corresponding temperature of the refractory metal) i n comparison with the ad- jacent Rene 41 structure and its associated thermophysical properties.
For the superalloy (TD N i C r ) leading edge, compression is the failure c r i t e r i a due CXAT of the TD N i C r i n comparison t o the Rene 41 structure and t o the higher i t s AT.
Reusability requirements were evaluated a s follows. For TD N i C r , depth w a s based on data taken from figure 4-18 of section 4.
of oxide penetration For coated Ta-low, coating l i f e data of section 5 were used.
Low cycle fatigue data are presented later.
To analyze local buckling of the leading edge, the following procedure was used. Using the elastic thermal strain from a plane strain analysis, the corresponding stress level i s obtained from the stress-strain curve for the given temperature. The compressive buckling stress for the curved leading edge nose i s obtained using cylinder buckling theory from reference 21-1.
Buckling allowables for the stiffened leading edge f l a t s are based on ortho- tropic plate theory from reference 21-2.
A summary of results for the continuous leading edge concepts i s pre- sented i n table 21-11 w i t h the exception of weight and low cycle fatigue data which a r e presented later.
For the tension c r i t i c a l coated refractory metal concepts, the local buckling problem i s eliminated; however, other problems exist. Coating l i f e for the Cb-752 concepts i s 500 hours a t cruise conditions (stagnation temp "his coating l i f e i s based on a compilation of 2300°F and p = 1.00 psi).
t e s t data for 1-hour time cycles a t pressures l e s s than one atmosphere, see section 4, fig. 4-19. Another reference, 21-3, reports a coating l i f e for the cruise condition environment of approximately 200 hours; these data represent a more stringent environment of 1-hour time cycles a t a pressure of one atmos- It can be seen from either of these references that the columbium coat- phere.
ing l i f e i s much l e s s than the required coating l i f e of 4460 hours. To repair the coating of a refractory metal ieading edge, the component must be removed and recoated. No other practical mesns exists at present for repairing the damaged disilicide coating. Also, t o prevent eutectic reaction a t the inter- face between the coated refractory metals and the adjacent Rene 41 structure, ceramic spacers are required. Thus, because of the unsatisfactory reusability evaluation, the coated refractory metal leading edge concepts were excluded from further consideration.
For the compression c r i t i c a l TD N i C r leading edge, the hot load carry- ing concepts, I-A-2 and I-€?-2, proved unsatisfactory because of local buckling.
However, further increase i n thickness and corresponding reduction i n tempera- ture and thermal gradient were pursued. This approach led t o the insulated concept, 11-B-1, which possesses adequate buckling strength. h c a l buckling i s precluded i n the curved nose section because of the thickness and, i n the flats, corrugations relieve the compressive stresses. Also, maximum cxide penetration for the TD N i C r concepts, based on stagnation point temperatures and a vehicle l i f e of 10 000 hours, is l e s s than 2 m i l s . Thus, the i n s d a t e d concept was 21- 4 selected as the best continuous leading edge concept and was further evaluated as indicated i n the material on low cycle fatigue.
Segmented Leading W.ge Concept The segmented leading edge evaluation matrix is shown i n table 21-12.
Three concepts involving different nose and f l a t thicknesses were evaluated.
A typical cross sect5on i s shown i n figure 21-7. B e superalloy, TD N i C r , was selected a s the leading candidate material for reasons given i n the pre- ceding discussion.
Evaluation procedure for the segmented leading edge is identical w i t h that for the continuous leading edge. Results of t h i s evaluation are shown i n table 21-13 w i t h the exception of low cycle fatigue and weight data which are presented i n subsequent sectic,is.
strAns were obtained based on a plane-strain analysis (sec- Thermal tion 7, case two, bending about two axes). To accommodate thermal expansion and bowing, the leading edge segment was attached t o adjacent wing structure i n the manner of a simply supported beam. Thus, the segment i s free t o expand the leading edge and i s free t o deflect i n t h e plane i n a direction parallel t o and normal t o the plane of the main wing structure. A parametric analysis of thermal deflections i s shown i n table U-14. A summary of thermal strains from the plane strain analysis i s shown i n tables 21-15, 21-16, and 21-17. Before the plane-strain data can be used for the evaluation of low cycle fatigue, it i s necessary t o %ccount for end effects which w i l l be considered next.
To account for secondary thermal stress (or strain) near the stress free end of the segmented leading edge, the procedure presented i n reference 21-4 w a s used. In t h i s procedure, a self-equilibrating force group i s applied t o the end of the structure t o liquidate the elementary stresses (section 7, case one, bending about two axes and axial loading) and so satisfy the boundary conditions for stress. The r a t e of decay of t h i s force group i s determined by a m i n i m u m The problem is made as simple a s possible by assuming that energy principle.
the temperature distribution over a cross-section does not vary along the length of the leading edge segment and that the segment contains closely spaced r i g i d ribs. The notations and sign conventions of figure 21-8 apply.
of a The force i n any discrete element i s assumed t o be the product function of the cross section times a function of x The distribution of (uA) . i s given by the elementary analysis, J 21- 5 The shear flow around the section i s where g . i s the shear flow determined from an elementary analysis i n which the a s s h p t i o n i s made that 'L'lie decay function + ( x ) can be detem5.ncd from the principle of m i n i m u m complc- !Che t o t a l s t r a i n energy can be expressed i n terms of Cp as mentary energy.
follows : The variation of the s t r a i n energy i s then determined and s e t equal t o zero; the result Is The strain energy i s a m i n i m u m if 6 satisf'-es the following differential e quat ion : where 21- 6 With t h e coordinate system of f i g w e 21-8 and a segment of length 21, the folloxing solution of the differential equations s a t i s f i e s the boundary condi- x = 1 :
t i o n s of 9 = 0 when x = 0 and + = 1
dx cosh Kx
' cosh K 1
The reduction i n thermal strain a t the center of the leading edge seg- ment i s shown i n figure 21-9 for concept I - A - 1 of table 21-12. These results show that thermal stresses for short segments are considerably different from those predicted by elementary theory. Experimental evidence supporting t h i s conclusion i s given i n reference 21-5 based on t e s t s of ring stiffened cylinders.
The least weight insulated concept, I-A-1 of table 21-12 was selected as the best segmented leading concept and was further evaluated as indicated i n the section on low cycle fatigue.
b w Cycle Fatigue t h i s section i s based on the Manson The method of analysis presented i n theory of low cycle fatigue (ref. 21-6). While it i s recowized that t h i s method of analysis i s not precise, it w i l l yield reasonable estimates of cyclic l i f e based on very limited data. In t h i s method, the relation between t o t a l strain arid cyclic l i f e is separated into plastic and e l a s t i c components which can be represented as straight lines on log paper. Relations f o r the slopes and intercepts of these lines are obtained by correlation w i t h t e s t data for a relatively 'Large number of materials.
The relation between plastic strain and cyclic l i f e Nf i s related t o the plastic strain per cycle e p by a power law i n the form z E = M N f (21-1)
r
where M and z are material constants.
The relation between elastic strain and cyclic l i f e is: (21-2) 21-7 i s the e l a s t i c - s t r a i n range per cycle corresponding t o t h e c y c l i c where F C 1.
l i r c PI[., 14 i s I;he e l a s t i c modulus, and G and y a r e other material constants, The r e l a t i o n between t o t a l s t r a i n range and c y c l i c l i f e i s E + E (21- 3 ) P e l G
= M N f Z + -
E Nfy where h a i s the s t r e s s range corresponding t o thz t o t a l strain range AE.
Tensile d u c t i l i t y ( i n t h i s discussion, p l a s t i c s t r a i n i s taken as t h e "true" o r "logarithmic" value, based on measurement of reduction i n area ill t h e t e n s i l e test) is given as: (21-4) are t h e i n i t i a l and f i n a l areas of t h e where D i s the d u c t i l i t y , A, and A f fracture cross section i n the t e n s i l e t e s t , and R.A. i s the c o n v u t i o n a l reduction i n area = (A - Af)/Ao.
Tensile f r a i t u r e s t r e s s i s determined by dividing -<he load j u s t p r i o r t o f r a c t u r e by t h e area measured j u s t a f t e r A n approximate r e l a t i o r f o r t h e f r a c t u r e s t r e s s i s fracture.
ir (1 + D) (21- 5 ) Of u where (J- i s the ultimate t e n s i l e s t r e s s .
U 21-8 The correlation between p l a s t i c s t r a i n a t l i f e of 10 cycles and d u c t i l i t y i s
The c o r r e h t i o n of s t r e s s range at lo5 cycles w i t h
ultimate t e n s i l e strength i s The correlation o f s t r e s s range at 1/4 cycle with fracture stress i s (21-8) The correlation of e l a s t i c and p l a s t i c s t r a i n components a t 10 4 cycles is Relations between t o t a l s t r a i n and cyclic l i f e involving ductjl.'.ty, ultimate t e n s i l e strength, and fracture s t r e s s a r e pre- senter; as follows: The two l i n e s constituting e l a s t i c and p l a s t i c components of s t r a i n range can be determined by using relations The two components involved i n equations (21-1) through (21-9).
then yield t h e t o t a l s t r a i n range i n terms of cyclic l i f e and pro- These relations p e r t i e s determined from the uniaxial t e n s i l e t e s t .
for M, z, G and Y i n terms of D, oU, and of are given as follows: 22- 9 where (21-11)
y = -0.083 - c.166 log (21-12)
4 3 @ 179
M = 0.827 D [l - 82 (2) (")
W U
]
0.179
z = -0.92 - l/lC log D - 1 . 1/3 log [. 82 (%) (%)
(21-14) W U Comparisons of' predicted t o t a l strain t o raeasurd t o t a l s t r a i n on a relative1.y large number of ma-berials, show t h a t the method can be made predominantly conservative by dividLig the pre- dicted s t r a i n by a s c a t t e r factor of 1.5.
The e f f e c t of mean strain i s shown in figure 21-13 which indicates the situation which develops wheri the completely reversed stress exceeds the yield strength, ( r e f , 21-6.) A mean s t r a i n de- velops during t h e f i r s t cycle (or early cycles) and i s followed by a
r e p e t i t i v e cyclic-strain range AE, of which cp i s the p l a s t i c strain
per cycle. Since the p l a s t i c s t r a i n is cyclic, the mean s t r e s s be- comes equal t o zero, the magnitude of the t e n s i l e stress equal t o the compressive stress. Since u represents the stress f o r one occurrence, it i s evident t h a t : one cycle = 2 occurrences The effect of complex loading 2s based on the Palm&Ven- Miusr theory of l i n e a r cumulative fatigue damage (ref. 21-7).
The basic equation i s n
9 s 2 - %
- I - - = 1 - I - . . . , + - N1 N2 *k 21-10 where = number of loading cycles applied a t the ith stress level n i Tii = number of loading cycles t o f a i l u r e for the i t h atrezs level from t h e relevant con::tant l i f e diat-:ram n i
- : cycle r a t i o
Ii i K = number of s t r e s s levels considered Since -die number of cycles n n2, . . ., at each stress l e v e l i s j i t 1 0 \ ~ 1 2 , t . h ~ proporiicn
of tile total lig; that w i l l be consumed a t each stress lcvel can
be determined. Thus, i f N i s the resultant l i f e -
= C Y * n = o l N , n2 - a2 N, . ., nk
k substitution i n equation (U-15) gives "1 " 2 a k -
- - I - - + . . . . + - - -
(21-16) N ti2 *k T h i s equation can be written (ref. 21-8) E = *l "2
- f - + . . . . f -
N1 N2 Nlr The relation between the t o t a l strain range and cyclic l i f e of TD N i C r shown i n figure 21-11 was obtained from computer program using equations (21-10 The figure shows that temperatures between 1600 t o 24000F through (21-14).
have practically no influence on the low cycle fatigue of TD NiCr. This be- havior indicates that the plastic component of the t o t a l s t r a i n range has a dominant effect on the low cycle fatigue strength of TD NiCr between 1 and The plastic strain component depends on ductility, which i s 105 cycles.
constant (R.A. = 5 percent) i n the range between 1600 t o 24000F f o r TD N i C r .
21-11 The results of the low cycle fatigue evaluation f o r the selected con- tinuous and segmented leading edge concepts are shown i n table 21-18. A fatigue equality index, KQ = 2.0, was applied t o the l i m i t e l a s t i c thermal strain.
A nominal scatter factor of 1.5 was applied t o the low cycle fatigue strain allow- able. For the cumulative fatigue damage analysis, -0.5-g and 2.0-g conditions are assumed t o occur for one of ten flights. Because of high thermal strains, t h e low cycle fatigue l i f e of the continuous leading edge concept i s only 12 flights.
However, f o r a segment length of 20.0 inches (optimum length as discussed l a t e r ) , the thermal strains for the segmented leading edge concept were reduced t o very low values. Thus, low cycle fatigue l i f e for the segmented leading edge concept i s very large, and f a r exceeds the required vehicle l i f e of 8110 flights o r 10 000 hours.
Selection of Leading Edge Geometry Because of the high thermal strains of the continuous concept, the lov- cycle fatigue l i f e w a s below the acceptable level, thereby requiring early re- placement. However, the maximum thermal strains a t the nose of the segmented leading-edge segment are quite l o w , a d fatigue l i f e substantially exceeds the requirement of 8110 flights. Therefore, the length of the segmented leading edge was optimized by considering the weight, strength, performance, and aerodynamic heating. Since proportions of the segmented leading-edge cross- section (nose thickness of 0.125 inch and flat thickness of 0.030 inch) were selected t o enable use of TD N i C r rather than coated refractory metal t o mini- mize weight and thermal stresses, the optimum segment length was determined by holding cross-section dimensions constant and varying only the length.
Maximum stresses and deflections due t o pyessure occw on %he lower Attach- surface of the leading edge segment a t the a f t edge support member.
20.7 percent of the segment length t o minimize ment f i t t i n g s are located a t Maximum segment bending moments i n the a f t end of the leading edge segment.
Based on the pressure load- length based on ultimate strength is 20.0 inches.
ing for the J-2.0-g condition, the maximum bending stress i s 1 1 863 psi (ulti- mate). The corresponding temperature T = 20000F and ultimate strength Ftu = 12 000 psi.
Performance evaluation of the segmented leading edge was based on fuel increments due t o the expansion joint between segments, attachment screws, joint between leading edge segment and adjacent heat shields on wing panels, and overall deflection of the leading edge segment under thermal and pressure For example, for a segment length of 20.0 inches, the maximum over- loading.
all deflections (see fig. 21-12) on the upper and lower surfaces f o r the cruise condition were 0.022 inch (inward) and 0.120 inch (inward), respectively.
A t the nose of the leading edge segment, the overall outward deflection Difference i n thermal expansion parallel t o the leading edge was 0.053 inch.
for the +2.0-g and cruise conditions leaves a net gap between segments of 0.075 inch during cruise (not considering deformatim of adjacent wing structure. ) 21- 12 As shown in figures 21-13 and 21-14, the optimum lengths of the leading-edge segments for the monocoque and semimonocoque concept:; (based on minimum structural weight and drag penalty) were 2 0 . 0 inches and 2'2.5 inches, respectively. However, consideration of ultimate strength limits the semi- monocoqw segmerlt length to 2 0 . 0 inches, and this length was selected. ? ' h e drag pentLlty (fuel increment due to deflactions, joints, and fasteners) shown is based on an equivalance between fuel a d structure weight of 1.5 to 1 . 0 , respectively. This ratio was determined from results of the vehicle- performance interaction evaluation. Since fewer attachment fittings are re- quired, the veight of the leading-edge segment decreases with increasing seg- ment length.
Additional aerodynamic heating occurs because of local changes in flow angle resulting from the segmented leading-edge distortions. For example, based on a leading edge segment length of 2 0 . 0 inches, forward deflection of the segmented leading edge stagnation line increases stagnation temperature by l5'F. Net inward deflection at the center of the lower surface aft edge of the segment due to pressure and thermal effects for the - I - ' 2 . 0 - gcondition decreases the temperature 8 0 O ~ . Corresponding net deflection of the extreme ends of the aft lower surface of the loading edge is outward relative to the wing reference surface, and the local temperature is increased 70'F.
SUMMARY OF DESIGN AND WEIGHT DATA A summary of design and weight data for the selected continuous and segmented leading-edge concepts is shown in table 21-19. Because of the high thermal scrains, the low cycle fatigue life of the continuous leading edge is very deficient (only 12 flights). The selected segment length of 20 inches leads to low strains and long life for the segmented leading edge. As shown, unit weights for the continuous and segmented leading edges are 8 . 3 1 lb/ft2 and 4 . 8 9 lb/ft2, respectively. The unit weights include insulation and the effects of oxidation.
The nose section of the continuous leading edge structures (figure 21-15) used in detailed analyses is machined from bar stock and the flats are formed from sheet and attached to the nose section with flush rivets. The nose assembly is attached to the ma5n wing structure with brackets located between the heat-shield beads. The attachment brackets are spotwelded to the leading edge spar cap on one side and fastened to the removable leading edge assembly with screws on the other side. Sealed, nonslip, overlapping joints are provided between the leading edge and heat shield and also between the relatively long segments. Washout of the heat-shield corrugations, carried into the flats of the leading edge to relieve compressive thermal strains, are symmetrical about a median contour to minimize aerodynamic drag and local heating.
The integrally stiffened nose section of the segmented leading edge, shown in figwe 21-16 is chem-milled from 0.125 inch shpet prior to forming.
The removable leading edge is screw-attached to the main wing structure hinges.
Overlapping joints are provided between the leading edge and heat shield and 21-13 also between adjoining segments. Experiments t o determine the effect of hot a i r leakage through the lap joints are warranted. Heat-shield corrugations are washed out adjacent t o the leading edge joint. This approach results i n maximum uniformity and also reduces the cost of the leading edge.
The segmented leading edge was selected for f i n a l design primarily because it met the desired l i f e requirements without refurbishment, assuming Additionally, it was lower i n hot a i r leakage proves t o be insignificant.
weight than the contintdous design, as shown i n table 21-19.
The t o t a l weight of the leading edge for the entire wing is: Primary structure Leading edge weight, l b Monocoque 1700 Semimonocoque 1956 Statically determinate 1956 21- 14 21-1 NASA Space Vehicle Design Criteria, Buckling of Thin-Walled Circular Cylinders, NASA SP-8007, September 1965.
Timoshenko, Stephen P.; and Gere, James M.: Theory of Elastic 21-2 Stability, Second Ed., McGraw-Hill Book C o . , Inc., 1961.
Personal Communication, L. Sama, Sylvania t o J. W. L e w i s , 21-3 Lockheed-California Co., October 1967 Heldenfels, R. R. : The Effect of Nonuniform Temperature 21- 4 Distributions on the Stresses and Distortions of Stiffened- Shell Structures. NACA TN 2240, November 1950.
Anderson, M. S.; and Card, M. F.: Buckling of Ring-Stiffened 21- 5 Cylinders Under A Pure Bending Moment and A Nonuniform Temperature Distribution. NASA TN D-1513, November 1962.
Manson, S. S.: Thermal Stress and Low-Cycle Fatigure. McGraw 21- 6 Hill Book Company, 1966.
21-7 Lockheed- California Company, Structural L i f e-Assurance Manual, SLM No. 4, Methods of Fatigue Analysis.
Spotts, M. F.: Design For Ekpected Efe. Product bgineering, 21- 8 7 June 1965.
21- 15 TABU 21-1 LEADING EDGE PRESSUFBS 2g Cruise -0 5k3 Nose 2.25 3 -25 0.93 Internal 0.30 0.35 0 . 1 0 Upper surface 0.2c 0.08 0.02 Lower surface 0.0 0 . 8 8 0.54 ~~ ~~~ 21- 16 TABLE 21-2 LEADING-EDGE D E S I G N PRESSURES
I Limit A p ? psi
y n d i t i o n I I I
Surface -0. 5-g 12.0-g Cnrisc AP Upper
Ap Nose I 1 . 9 5 I 2.9 I 0 . 8 3
A p Nose (Ti
AI, Upper -0.1 -0.27 -0. 08 Ap Lower - 0 . 3 0.53 0 . 4 4 Ap Lower Positive pressure shown 21-17 I TABLE 21-3 MONOCOQUE W I N G EDGE EVALUATION, CONTINUOB HOT IfiAD CARRYING CONCEPT WITHOUT LEADING EDGE SPAR, +2.0-g MANEWER CONDITION No spar Stagnation point ~ ~ BIean l i n e a r L i m i t L i m i t thermal 2lastic e l a r t i c c oe f f i c i e n t thermal thermal E l a s t i c of expansion, moJulus, stress, strain, -6
r
0- C r X l O , t '
E x l o
ks i i n . / i n .
point i n . / i E . /OF p s i G 6 1 Ta- 1OW 3.68 x 10- 20.2 x 10 0.0053 2 T a- 1OW 28.6 0.0021 13.3 3.96 0 0045 Ta- 1OW 18.9 85.8 3.76 ~~~~ ~ -18.8 1 TD N i C i ' 8.6 11.8 -0.0015 1575 * .> L. ? 1 y G -0.0069 TI) N i C y 8.72 7.G 4 9 . 1 -0.0028 TJ) N i C r 8.65 1 0 . 0 -28.5 3 1715 a Emissivity of TD N i C r assmed t o be 0.9 21- 18 TABLE: 21-4 MONOCOQUE IXADING EDGE EVALUATION, CONT3NUOUS HOT lxlAD CARRYING CONCEFT INCLUDING W I N G D G E SPAR, +2.0-g MANEWER CONDITION Leading edge spar Stag nation point
-
Mean linear L i m i t L i m i t thermal
I
e l a s t i c e l a s t i c coefficient t he:cmal the m a l Elastic: of expansion, stress, s t r a i n , modulus, a x Temperature, t’ =t, E x 10 N0d.e Mater i a l ks i ks i I ?
in./in. /OF point p s i
( 4
-
1 TD NiCi- 8.65 x 1 0 . 0 x 106 1711 -29.8 -0 .oo2gE 2 Ta- 1OW 19.6 1711 98.8 0.00501 3.73 Ta- 1OW 3 13.2 2308 30.2 0.0022: 3.97 1) Ta- 1OW 3.81 1888 76.1 0.0042: 17.9 TD N i C r 8.65 8.0 1888 -36.0 -0.OOlI5C
- ~~ ~
1682 -0.00 25 7 1 Td NiCi- 8.65 10.5 -27.0 2 10.5 1682 -27.0 -0.0025: TD N i C r 8.65 TD N i C r 2207 -0.0072E 3 8.73 5.4 -39.3 -0 .ool-n: 4 TD N i C r 8.65 8.4 1863 -34.7 8.11 1863 -34.7 -0.0041: TD N i C r 8.65
-
-0.0028: 1 TD N i C r 8.65 LO. 2 170 2 -29.1 2 12.1 170 2 0 . 0 0 4 l t C b -75 2 1!. .33 50.3 12.2 0.0011; Cb -75 2 10.4 3 4.53 2290
4 .40 0.0032f
4 C b -75 2 11.9 39.0 -0 0043; TD N i C y 8.65 8.2 1879 -35 8
-
a Emissivity of TD N i C r assumed t o be 0.9 21- 19 TABLE 21-5 SPANWISE SEMIMONOCOQUE LEADING EDGE EVALUATION, CONTINUOcFi HEAT SHIELDED AND INSULATED CONCEPT; NOSE THICI(NEsS = 0.12 I N . , +2.0-g MANEUVER CONDITION - --*.
- Primary structure Stagnation 2 - point
Heat shields .-A 3
Mean linear L i m i t = L i m i t thermal e l a s t i c e l a s t i c coe i'ficient Elastic theimal thermal of e q a n s ion , modulus, stress, s t r a i n c ( x 'emperature at) e t N o de Material E x 10 ks i in. /in.
point p s i F ~~ ~
-
1 Ta- 1OW 3.70 x 20.0 x 1 0 1654 08.2 0,004h1 2 T a- 1OW 12.0 16.2 o ,00125 3.98 T a- 1OW 16.4 44.5 0.00271 3 3.87 2x3 25
- -
42.1 0.003b5 1 Cb -75 2 h . 32 12.2 16118 0.0000959 2 Cb-752 4.54 LO. 2 2311 0 378 4.411 19.8 1,0016~ Cb-75 2 11.7 a02
-
21- 20 DETAIL "ERATURES FOR HJNT-SHIELDED AND I L N S U L A T E D LEADING EDGE CONCEPT; NOSE THICKNESS = O e E 5 I l l * 6 , stagnation-line location Moterial, TO NiCr (€=0.75) Thermal model of cross-section normal to Ieoding-edge sweep Temperature, F ~- -0.5-g 4-2.0-g Cruise Condition
-
- __I_
Temp
0.03 I 0.06 0 . 0 3 0.06 0.06
0 . 0 3 location
- -- I -
1925 1860 1795 1785 1340 1340 1940 1890 1875 1365 1480 1405 1975 1960 2005 1985 1625 1615 2055 2045 2200 2190 1795 1790 1920 1910 2135 2115 1770 1760 1845 1860 2065 201 5 1630 1645 1985 1515 1515 1765 1770 2025 5 5 0 0 0 10 10 10 10 5 0 5 5 0 5 5
L _ I I - - -
21- 21 TABU2 21-7 DETAIL TEMF'ERATUFW FOR H2XTSHSEI;DED AIVD INSULA'LED W J N G EDGE CONCEFT; NOSE THICIQWS = 0.375 IN.
6 7 8 I stagnation line locytion Material I ?D NiCr (e = .75) - ..
Cross section normal to leading edge sweep , .. - . . .. - - . .
Temperature, OF ' - 1 Condition Cruise -0.5s
- - _L_1 - -
' .03 .06 . 0 6 .06 .OS .03 1335 1775 1780 1335 1920 1855, 1855 1860 0 495 1935 1885 1660 1675 1955 1940 1970 1985 1 760 2090 21 00 1770 20G0 1990 1915 2055 2070 1760 1640 3045 1630 1840 1850 2000 1515 1515 1975 J.015 1760 1765 0 0 4 10 5 20 40 20 15 15 5
-
--
21- 22 'i WBLE 21-8 rlEiTAIL TEMpERATlTREs FOR HEAT.SHIELDED AND IC?SuLATED LEADING EDGE CONCEM'; NOSE THICKNESS = 0.625 IN.
! \
3 j_
48 -
L-
TnsllLat ion t~~~~ at leading edge spar 8 stagnation line location Material, TD N i C r (E = .75) Cross stction normd to leading edp? sweep Cruise Condition 4.59 . 0 6 .06 .06 .03 .03 -03 lccation
--
1_1 1335 1775 1920 1850 1770 1335 1520 1850 1930 1875 1845 1500 1940 1925 1965 1950 1690 1755 2060 1970 1965 2050 1765 1900 2035 1755 1910 2020 1640 2035 1835 1840 1990 1630 1765 2015 1515 1755 1975 I -1 0 0 -10 15 15 0 30 65 30 40 45 65 10 -5 - 5 25 10
* - -
21-23 TABLE 21-9 CONTINUOUS IXADII!IG EDGZ EVALUATION MATRIX I. Monoccque leading edge evaluation: (Nose tl-iiclmess = 0.12 in.; P l a t thickness = 0.032 i n . ) A . Hot load carrying conccgt witliout ;Lose beam 1. Wozc scction material: !ki-l.O~i 2 . Nosc section m a t w i d . : TD W i C r a B. Hot 3.ad carrying concept w i t h nose beam 1. Nose sectiofi material: Ta-10N 2. Rose section material: 'I!D Micra 3 . Nose s e c t i o n material: Cb-752 Spanwise semlmonocoque leading edge evaluation: 11.
A. Heat shielded and insulated concept (fiosc tliiclmess = 0.06 in.; flat tliickicss = 0.06 i n . ) 1. Nose section material: Ta-1Oli 2. Nose scction material: Cb-752 B. Heat shielded and insulated concept (PJose thiclmess = 0.625 in.; flat thickness = 0.060 i n . ) b 1. Nose section material: TD N i C r ~ ~~ a Bnissivity = 0.90 bEmissivity = 0.75 1 l t 1 1 1 1 1 1 1 1 1 1 1 . . ~ .
1 1 1 1 1 -??-??.“o.?cu.
cn cn L - u l Q t - b k V .ri z 5 - M) cu 21- 25
d c
*ri v i k rr A h a , -P Fc 21- 26 S E G W LEADEVG EDGE EVAWATION M A T m I . Spanwise seuimonocoque leading edge evaluation: Heat shielded and insulated concept A.
(nose section material: TD NiCra) 1. Nose thickness = 0.125 in.; flat thickness = 0.03 in.
2. Nose thickness = 0.125 in.; flat thickness = 0.06 in.
Nose thickness = 0.625 in.; flat thickness = 0.06 in.
3 .
a Emissivity = 0.75 21- 27 21- 28 TABIE 21-14 SUMMARY O F THERMAL D E F J X T I O N S , SE)GMHvTED W Y N G EDGE CONCEPT J X Thennol deflection t nora = .125 in., t flat = .03 in., t nose =.&25 in., t flat - .O&in.
l d condition I, in. 6th (z), in. 6th (r), in. 6 th (z), in. 6 th ( y ) , in.
. M ) 6 .007 .002 .006 4.59 10 20 ,026 .028 .a09 .025 .058 8 6 3 ,020 .057 29 10 .016 .006 .013 .007 20 . O M .037 .051 .028 .144 ,084 .115 .062 CNire 10 ,015 ,013 .014 .014 . O S .058 30 .129 ,131 ,119 i cnri0U)d-m mcuCUomr--<r\ wA- m4-co rl
O L n O 3 c o N r - s; A-a3coP--rlal
3 m r l c - 3 3 % m o m c o o a 3 3 MLnCUA-r-04- m c u r - l c u m r l m o o o r l o o r l rlrlocu000 r l ~ O c u r l O 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
9 9 9 9 9 9 9 9 9 9 9 9 9 9
I I I I l l ..
n Q r l x In r- I 1 k V . . - I
a R
E
k h
x
*
*rl rn r n
P
22- 3 0 m o 0 Fri r n f 4 U 3 r i O ( u r - d r-i r l o m o d rl r i o m r i 0 0 0 0 0 0 0 0 0 ? ? ? ? ? ? ?
I I I I I n k k V V . d .rl 7 : a FI E-l r-i (u m 3 m a cc w Ln tQ
B (u
a a M r l do03 c u r i c r ) r - - c ~ c o d 0cr)corlcuoo c u b O c o L n r l 0 c u ? i r i r l c u o L n r l c r ) c u 0 oul (u o o o r l o o r l d d O r l 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
9 9 9 9 9 9 9
9 9 9 9 9 9 9
I l l I I I I l l d 0 O c - O'C', cu d c h r - r i M rl I I I x k V .rl
-
t X rl cu MA- na E- M Ln .
I 21-32 TABU 21-18 LOW CYCLE FATIGUE EVALUATION FOR SELEX2TED KEYDING EDGE C O N C E F T S Scatter f a c t o r = 1.5
I
I Continuous leading Segmented leading edge concept edge concept I I Main wing primary ci;ructurc S l b Slb c oncep-l; TD N i C r TD N i C r NOSC area m a t e r i a l \
Nose thickness , i n . 0.625 0.125
Flat thic1:ness , i n . 0.060
0.930
-
Scgmcn-l; lcngtli , i n . 20 .O
Limit e l a s t i c -0.006363 -0.000616 1 ; lie r m a l -0.0061170 -0 .om850 s t r a i n , CT, -0 -005305 i n . / i n -0 e000539 -0.5g condition 8 15.0 105 Leading edge l i f e at CT, 2g c o r d i t i o n 6 2.4 105 f l i g h t s c r u i s e condition 18 2.8 x lo6 'Jotal leading edge l i f e , 12 11.9 105 f l i g h t s ~~ ~~ a Including end effect 21-33 TABLE 21-19 LEADING-EDGE DESIGN A N D WEIGHT DATA FOR SELECTED CONCEPTS Selected leadir -edge concept I tem Continuous leading- Segmented leading- edge concept edge concept ~ Nose area material TD NiCr TD NiCr Nose thickness, in. 0.625 0.125 Flat thickness, i n . 0.060 0.030 Segment length, in. 20.0 Maximum temperature, OF 2050 2200 (stagnation point, +2-g condition) Maximum limit elastic thermal -0.00647 -0.000850 strain, e T , in./in.
Maximum dept?s of oxidation, 0.00151 0.00165 6, irn. /side (stagnation point, 10,000-hr vehicle life) Local buckling margin of High 0.43 safety Low-cycle fatigue life, 12
11.9 lo5
flights 8.31 Unit weight, lb/ft2 4.89 21-34 surface
-
I
Nose lower R = .75 surface
I 1
.-
b
t
H H t 0, 12 16 20 24 28 Time, mfn Figure 21-1. Wing leading edge pressure variations during maneuver ~~ ~~ 0 .04 .08 .12 .16 .20 k t e r i o l thickness ct stagnation line, in.
Figure 21-2. Peak tmpemture a t leading edge stagnation l i n e vs m t e r i a l thickness and emittance 21-36 .
C Y h.
m
-
9)
.-
f c I 21-37 21-38
-
w Q) C OL c n a l U S U
-
K X 0, Q
.'
-
c .
+ U a t VI x
J
t i E .- L n -- , C
.-
21-39 ...
C Z Y
/
X Figure 21-8. Sign conventions and notation used in analysis of the end effect for the segmented leading edge concept 21-42 29-43 e Cyclic stress and s t r a i n p a t t e r n Involving zero mean s t r e s s Figure 21-10.
and a l t e r n a t i r -, plastic s t a i n 21-44 k R
@
k k Figure 21-l.2. Deflection e : segmented leading edge
- -
Notes: I
1 .. Equivalence between fuel and structure weight assumed 1 .s to 1.0
2. LMAX = Maximum segment length based on ultimate strength I
\
1 14 18 22 26 30 Segment length, 1 (in.)
- - .. - .- ... I . . - .. - Figure 21-14. Optimum length of segmented leading edge, semimonocoque concept
_- -- - _ _ __. ._ ~_-___-- ---- ~ - ---- -
2I.48 a , c In i-l I
Section 22
Section 22 T C Y T A L WING AND BASELINE V E H I C U WEIGHT ANALYSLS by I. F. Sakata, R. D. Kjares 22-i CONTENTS J%3e 22-2 IiEDuNDAIvT mDEL IDAIE 22-2 FORWARD DEIlllA WING STRUCTURE WEIGHTS 22- AET DEUPA WING STRUCTURE WEIGHTS 22- 4 TOTAL WING WEIGH'IS FOR BASELINE VMICIIF: 22- 5 BASELIIUE VEHICUZ DATA 22-6 V W I C I E WEIGHT AND S I Z I N G 22-iii TABLES Table h g e 22-1 Wing forward delta weights 22-8 22 -2 Nominal wing weights f o r baseline airplane 22-9 22 -3 Statically determinate fuselage combined stresses,
"Ultimate stresses, flight condition - +2g 22-10
22-11 22-4 Fuselage temperature sunmary 22-5 Primary variables and coefficients f o r weight/sizing 22 -12 procedure 22-15 22 -6 Sample calculation of baseline vehicle data 22-17 22-7 Input data f o r interaction analysis ILLUSTRATIONS Page . ..
22-1 ning geometry - baseline airplane
22- 18 22 -2 Redundant model loads monocoque waffle c onc ept (upper ) 22- 19
22 -3 Redundant model loads - monocoqlie
waffle concept (lower) 22-20 22-4 Redundant model loads ,monocoque honeycomb concept (upper) 22-21
22-5 Redundant model loads - monocoque
honeycomb concept (lower) 22-22
22 -6 Redundant model laads - seniimonocogue spanwise concept (upper) 22-23
22-7 Redundant model loads - semimonocoque spanwise concept (lower)
22-24 22 -8
Redundant model loads - semimonocoque chordwise concept (upper)
22-25
22-9 Redundant model loads - semimonocoque chordwise concept ( lcwer)
22- 26
22 -10 Redundant model loads - s t a t i c a l l y determinate concept (upper
and lower) 22-27 22-11 Forward delta geometry and weights 22- 28 22-12 Wing forward delLa structure 22-29 22 -13 Forward delta structure at various fuselage stations 22- 30
22 -14 Wing scaling factors - monocoque concept 22- 31
22-15 Wing scaling factors - spanwise stiffened concepts 22- 32
22 -16 Wing scaling factors - chordwise stiffened concept
22- 33 22-17 Redundant model idealized fuselage 22-34 22-18 Corrugated stiffened concept 22- 35 22-19 Decking and longitudinal stiffeners required f o r s t a t i c a l l y determinant concept 22-35 22 -20 Vehicle scaling 22-j6 22-21 Wing scaling comparison 22-37 22-vis SYMBOLS A Area BL Butt l i n e Fuel f r a c t i o n designation used i n vehicle weight and s i z i n g CMR program.
Wing weight c o e f f i c i e n t used i n vehicle weight and s i z i n g program CWING Fs Fuselage s t a t i o n f S t r e s s Gravitat ional acc e1era.t ion f 3 L Length N O F Nonoptimum f a c t o r for panels P Axial load i n pounds S Wing planform area, t Thickness t Equivalent thickness W Weight of tozal wing Wing loading
w / s
Unit wing weight expressed i n lb/f’t W 22- ix
Section 22
Section 22 TO. AL WIXG AND BASELINE VMTCIE WEIGHT ANALYSIS Total wing weights for each of the s i x structural concepts were deter- mined, as w e l l as t h e component weights f o r %he remaining portion of the base- l i n e vehicle (550 000 pounds). These data were used as input f o r the interac- t i o n analysis of section 26.
Comprehensive an&l.yr;es tiere conducted as p e s e n t e d i n section 13, t o determine f i n a l concept weights for t h e center are3 (centerline of vehicle t o t h e intersection of the wing and fuselage), inbawd area (intersection of t h e wing and fuselage t o t h e wing one-third chordline), and outboard area (one- t h i r d chordline t o t h e wing leading edge) of t h e selected wing section of 22-1.
figure To obtain the t o t a l wing weights f o r concept evaluation these unit weights (of t h e sele-ted wing section) were related t o t h e other areas of t h e wing by a multiplier. These m * . t i p l i e r s were based on t h e analysis of t h e wing structural elements at selected locations using t h e i n t e r n a l loa& data from t h e redundant analysis O f each concept. The basic substructure arrange- ment ( r i b and spar spacrag) was maintained identical t o t h e study area, except f o r slight variation i n the forward delta. In general, element weights were related t o the detailed weight summary f o r each concept, with incremental
changes determined through analysis of thc s t r u c t u r a l elements ( i .e ., rib/spar
caps, webs). The analyses were i n sufficient depth t o provide material t o transmit the spccffied loads at axeptable stress levels. In areas where loads are solall, minimum gage caps and panels are used. The panel require- ments are determined through comparison with areas of similar loading and temperature The designated zones (A, B , and C ) of t h e selected wing section are shown i n figure 22-1. This designation was carried t o the balance of the total wing, as indkated, using t h e same philosophy t h a t was used f o r t h e detailed analysis area. By selection of t h e basic zones on t h e basis of common-type structures, a multiplier could readily be determined.
22- 1 The zones include: Zone General Ty-pe of Structure Locat ion
-
Wing Center Section A Under-Fuselage WSng Outboard Section C H e a t Shielded o r Insulated Wing Inboard Section B Balance of AB Delta (Basic Wing) Wing Forward Section D Combined Under-Fuselage and Outboard Section of t h e Forward Delta Trailing Edge E Elevon To provide a rational basis f o r determining t h e t o t a l w i n g weight f o r each concept, t h e internal loads data from t h e redundant analysis were used.
The aft wing loads f o r each concept is presented i n figures 22-2 through 22-10. The lumped cap areas used as input t o t h e redundant analyses are given w i t h each figure for the spanwise and chordwis- elements. To obtain the distributed in- plane loads and associated stresses, t h e extensional s t i f f n e s s used f o r input The increment&!! area t o t h e redundant model is also presented for each concept.
required t o bring the stress level t o design values of t h e selected wing area is accomplished by direct r a t i o of t h e given value of extensional s t i f f n e s s to the required value.
FORWARD DEUPA WING STRUCTURE WEIGm A weight summary f o r t h e wing forward delta structure is presented i n Review of loads data and t h e requirements of table 22-1 and figure 22-11.
similar structural areas indicates t h a t minimum gage panels and substructure are adequate. Nonoptimum factors t o account f o r panel edge-closeouts, attach- ments, and oxidation effects are determined from t h e selected wing section analysis. The unit weights vary between 4.12 &id 6.11 psf between the minimum weight semimonocogue, spanwise beaded-skin concept, and t h e monocoque waffle concept, as indicated. These weights are used f o r determination of the t o t a l wing weight f o r each concept.
Formed sheet The basic type of structure varies as shown i n figure 22-5-2.
metal segments are used between Stations 790 and 1075; machined frame segments are assumed between Stations 1075 and 1345; and spanwise wing beams that extend under t h e fuselage with a fairinglheat shield structure Ls assumed from Sta- t i o n 1345 art; t o Station 1932. The type of structure is absumed constant f o r a l l the concepts between Stations 790 and 1345. The average unit weight f o r t h i s area is 3.51 psf or 3779 pounds, as previously shown in figure 22-11. This corresponds t o a unit weight of 3.24 l b s / f t 2 for t h e forward area (487 square f e e t ) and 3.73 psB f o r t h e aft area (590 square feet). The unit weight of t h e structure between Stations 1345 and 1932 varies with each concept. The 22- 2 mder-fuselage structure unit weight w r i e s from 4.04 t o 7.80 psf, and t h e outboard area varies between 5.20 t o 7.79 p s f .
Station 790 t o 1075. - The chine is attached t o the body structure by
formed sheet metal bulkheads, as indicated i n figure 22-13. The chine i s assumed non-structural i n this area with respect t o body bending loads and transmits l o c a l pressure loads only. The skin is segmented t o provide f o r thermal expansion.
Station 1075 t o 1210. - Machined f r a m e segments are used t o attach t h e
chine t o t h e body structure and transmit the pressure loads t o the body struc- t u r e (fig. 22-13). The fuselage i n t h i s area is essentially a barrel-section with these frames externally attached. Sheet metal extensions are used t o make up t h e remaining structure. Radial and tangential loads are introduced t o t h e basic f r a m e at t h e pinned attachment j o i n t .
Station 1210 t o 1375. - Wchined f r a m e segments with integra: chine sup-
port elements are used i n t h i s area ( f i g . 22-13}. Transition of t h e side s h e l l from a circular shell (forward) t o v e r t i c a l pnnels is mde i n t h i s region. The f i t t i n g at Station 1210 provides support f o r t h e resulting change i n load paths and introduces an additional moment loading on t h e frame. A sheet metal struc- t u r e i s provided between the machined f r a m e and the leading edge attachment points .
Station 1345 t o Station 1932. - The wing (forward delta) i n t h i s region
passes beneath the fuselage, as shown i n figure 22-13. A separate fairinglheat shield is assumed on the lower surface as indicated. The basic arrangement is assumed similar t o t h e study area. Mtnimum gage panels are used i n a l l cases with associated non-optimum factors.
The fuselage f r a m e s terminate at t h e wing- f o r bookkeeping purposes, t h e f a i r i n g weight i s fuselage intersection; however, assumed t o be contained i n the fuselage unit weight; thus, t h e calculated wing unit weights are directly applicable f o r t o t a l wing weight determination.
AET DEUPA WING STRUCTURE WEIGNTS Several areas of the aft delta wing structure were selected f o r analysis t o determine unit weight changes required t o transmit t h e applied loads a t acceptable s t r e s s levels. Using the detailed weig-ht -breakdown for each concept as t h e basis, t h e incremental weight changes determined were added t o t h e basic values t o obtain the unit weight of each area evaluated.
The center area (Zone A) weights increase aftward t o accommodate t h e increase i n spanwise shears and bending moments. No increase i n t h e chordwise elemental weight is required, since the maximum loading i n t h i s direction occurs i n t h e study area.
The inboard area (Zone B) weights a l s o increase aftward t o accommodate the The combined effect of elevon increase i n spanwise shears and bending moments.
forces (chordwise bending) and increased spanwise bsnding moments i n t h e a f t area 22- 3 between Fs 2800, and t h e control surfaces r e s u l t i n t h e highest unit weights on t h e t o t a l wing.
The outboard area (Zone C ) wing weights are assumed t o be constant f o r each concept except i n t h e area of t h e elevons where t h e chordwise loads at BL 488 define these requirements. I n addition, increase i n t h e spanwise s t i f f n e s s is reqiiired t o transmit these loads inboard.
The elevons a r e assumed t o weigh 10 psf f o r a l l concepts, with t h e calcu- lated leading edge weights used with t h e appropriate concept.
The r e s u l t s of t h e s e analyses are presented i n f i g u r e s 22-14 through 22-16.
The monocoque concept scaling relationships are presented i n figure 22-14. The scaling relationshfp for t h e aft wing indicates t h a t t h i s concept r e s u l t s i n t h e l e a s t weight change, since panel s t f f f e n i n g (i.e., waffle grfd, honeycomb core) can be adjusted t o accommodate t h e higher loading i n t e n s i t i e s wzthout l a r g e weight changes. Since t h e weight changes f o r t h e waffle g r i d p l a t e and honeycomb core sandwich were very similar (waffle s l i g h t l y higher), the waffle concept scaling relationships were used f o r both concepts. For t h e semimonocoque, spanwise s t i f f e n e d concepts and f o r t h e s t a t i c a l l y determinate, spanwise s t i f f e n e d con- cept , the d i s t r i b u t i o n f a c t o r s were esseritially t h e same (semimonocoque s l i g h t l y higher). The wing of spanwise elements (i.e., panels and spars) were increased t o transmit t h e higher inplane loads. The higher spanwise loads i n t h e aft wing area a r e comparable t o t h e chordwise (tubular) design data, and t h e r e f o r e were used f o r determiriation of t h e wing weights i n t h a t area.
The chordwise concept requires an increase i n spar weight t o accommodate t h e increase i n spanwise bending moments and shears. Since -the maximum chordwise loads occur i n t h e study area, panel designs a r e adequate t o transmit t h e loads i n t h i s area.
TOTAL WING WEIGHTS FOR BASELINE VMICLF: T o t a l wing weights were determined f o r each concept, using t h e wing-section weights and t h e sca!-ing relationships discussed previously. The wing average weights ( p s f ) f o r the baseline (550 000 l b ) vehicle, including elevon and leading- edge weights, a r e shown i n t a b l e 22-2. The s t a t i c a l l y determinate concept incurs a fuselage w i g h t penalty, over t h e other concepts, of 3 685 pounds. This is equivalent t o a 0.365 psf of wing u n i t w e i g h t , based on t h e planform area, and must be added t o t h e s t a t i c a l l y determinate weights t o obtain a t r u e weight com- parison.
The resdts of t h e t o t a l wing-weight investigation provided t h e following ranking of s t r u c t u r a l concepts : sercimonocoque spanwise beaded, semimonocoque spanwise tubular, monocoque honeycomb sandwich, s t a t i c a l l y determinate spanwise beaded, semimonocoque chordwise, and monocoquc waffle. A s indicated i n t a b l e 22-2, the t o t a l wing weight of t h e honeycomb sandwich concept is lower than ihat f o r the s t a t i c a l l y determinate concept, which i s a change from t h e wing investigation section analysis ranking discussed e a r l i e r . Honeycomb i s l i g h t e r f o r the t o t a l wing because of b e t t e r efficiency f o r t h e high b i a x i a l load area of t h e aft w i n g .
22- 4
BASELINE VnrICm DATA I n addition t o the wtng weights, weights f o r all elements of t h e baseline vehicle were determined and used i n t h e interaction analysis of section 26.
Except f o r t h e s t a t i c a l l y determinate concept, which requires additional fuse- lage weight, identical weights were used f o r the remaining portion of t h e vehicle, f o r each structural concept.
Additional Fuselage Weight f o r S t a t i c a l l y Determinate Concept The s t a t i c a l l y determinate concept incurs a fuselage weight penalty Over the other structural concepts f o r fuselage skin, decking (rzquired t o close out lower portion of fuselage), longitudinal stiffeners, and f r a m e members.
The assumed baseline vehicle fuselage prit-cary structure weight is 36 850 l b
with an average mss distribution of 2.5 psf ., This fuselage design uses bulk-
heads, rings, and longitudinal stiffened Bene 41 panels with a p n e l t = 0.038 in.
and conventional fuselage t o wing attachments.
The s t a t i c a l l y determinate fuse- lage has a weight of 3685 lb (10 percent) increase over t h e baseline vehicle fuselage w e i g h t , as shown below.
It e m
-
Skin panels (corrugation-stiffened) 1646 Decking (beaded skin) Longitudinal s t i f f e n e r s Frame members 320 Contingency (5%) (Fittings, fasteners, e t c .)
Total Weight Penalty 3685 The weight increase of the s t a t i c a l l y &?terminate fuselage was based on t h e redundant model loads (model e1emer;l;s an.-! dtresses a r e presented i n figure 22-17 and t a b l e 22-3, respectlvely) 8.ld temperatures (table 22-4). Using these loads and temperatures, t h e incre;r.se i l l skin panel weight over t h e base- l i n e vehicle, in which minimum gage ( t = ,038) corrugation stiffened panels were adequate, was determined using t h e vide column curve presented i n figure 22-18, To provide thermal protection f o r the tankage, fuselage decking was pro- vided as shown i n figure 22-19, This decXng (beaded concept) is stiffened i n t h e spanwise direction so t h a t it is not strained with t h e fuselage body loads.
Longit1 i n a l stiffeners of 1-beam configmation are provided t o support the 22- 5 decking and carry the longitudinal body loads. Figure 22-19 indicates t h e applicable plariform area and support system (longitudinal s t i f f e n e r s ) f o r t h e fuselage deck. The same type of I-beam u t i l i z e d for t h e longitudinal supports was used for connecting t h e frames at t h e lower portion of t h e fuselage.
VMICLF: W E I G H T AND SIZING A weight s e n s i t i v i t y and vehicle sizing procedure ( r e f . 22-1) was used t o synthesize and compute vehicle s i z e and weight f o r t h e interaction analysis of section 26. While the procedure is used i n t h e section 26 analysis, a sum- mry of t h e primary variables and coefficients a r e given i n table 22-5 of t h i s section so t h a t t h e baseline vehicle weight input; requirements m y be provided.
Using t h e information of t a b l e 22-5, a sample calculation of weights f o r t h e baseline vehicle was performed and is shown i n table 22-6, using t h e mass f m c - t i o n data presented i n section 1 ( i n i t i a l l y used f o r obtaining loads).
For t h e interaction analysis of section 26, a l l data of table 22-6 remains t h e same except f o r the wing weight, f u e l fraction and weight, payload weight, and fuselage w e i g h t of t h e s t a t i c a l l y determinate concept. These inputs a r e presented i n t a b l e 22-7 f o r each wing s t r u c t u r a l concept and f o r t h e three levels of r e l i a b i l i t y (low, nominal, and high).
The s t a t i c a l l y determinate concept payloads of t a b l e 22-7 include t h e effect of t h e additional fuselage The CWING values of table 22-7 are t h e wign weight coefficients used weight.
i n the vehicle sizing procedure of reference 22-1, as presented i n t a b l e 22-5.
A parametric investigation f o r t h e e f f e c t of scaling the baseline vehicle (wing loading W/X = 66.8 psf) was conducted and is shown i n figure 22-20 f o r various wings (CWING), payloads and f u e l fractions (CMR). The relationships between t h e coefficients CWING for t h e baseline vehicle weight can be deter- mined from figure 22-20, as shown i n t h e tabulation below.
Easeline vehicle
CWING wing weight - lb
-
o .006 48 420 0.008 64 560 0 .OlO 80 700 0.012 96 840 The d i ference between scaling t h e wing using S (wing area) and S1*$ versus S l o g is shown i n figure 22-21. Typically, t h e monocoque concept has x) percent of its structure proportional t o S, which r e s u l t s i n almost no difference. The semimonocoque concept may run t o about 30 percent, which could result in a weight difference of only 3 percent. Therefore, t h e scaling factor of S l . 5 was used for t h e interaction evaluation o f section 26.
22- 6 22-1 Jones, R. : Weight Synthesis and Sensitivity Programs, Iockheed-California Company, LR 21205, 1967.
22-7 22-8 8 8 8 8 8 d
4 rl d d 3 rl
I -
22-9 TABLE 22-3 STATICALLY D - A T E FUSELAGE COMBINED STRESSES ‘‘WIMATE STRESSES FLIGHT CONDITION +X Element no. A (in. ) Fuselage station ’comb (Ib) ~~ ~~ 1 6 2 . 2 6 -462 384 +27 600 4 . 4 7 +27 500 17 4-122 953 -106 832 -32 470 3 0 2 9 1 . 4 6 -53 800 -78 585 +26 960 2058 2 6 2 . 2 6 + 6 ~ 000
+180 ooo +40 415
4 . 4 6 28 -120 000 -36 450 3 *29 -56 200 2 . 1 6 -121 000 151 500 +21 580 2.38 5 1 4 . 7 2 +198 000 4 1 960 -89 000 3 070 -23 970 4.11 -161 000 -39 140 61 +48 500 +20 249 2-39 62 4 . 7 2 +180 000 +38 070 -64 000 -16 929 63 3 078 -44 270 64 -164 000 3 071 22- 10 22-11 TABLE 22-5 PRIMARY VAIIIABLES AND COEFFICIENTS FOR WEIGHT/SIZING PRXEDURE Primary Coefficient Item Variable Aerodynamic Surfaces: Wing Constant 6 8 WG. SW.
Wing Vertical t a i l SVT Body group: Pressurized crew cmpartment Constant 2000 Body structure SBDY 2, e456(b Tankage structure SBDY ( SpYE)1/2 0.081044 Induced environment protection: Thermal protection (tankage insulation) SBDY 1.129 Launch, recovery, and docking: Landing gear WG 0.030 M a i n pr opul s i on :
Main engine - airbreathing
Constant -6132
Main engine - airbreathing TTOT 0.146826
A i r induction system CSAP 201.3
Propellant distribution - fie1 TTOT
0.0098 Orientation controls, separation and ullage: Reaction control system 0.0020 Aerodynamic control system Aerodynamic control system 0.010 Power conversion and distribution: Electrical Constant 1400 Electrical 0.0040 WG Hydrau1.i~and pneumatic WG 0 0050 - P - (a) varies with each wing structural concept, Note: cwing = 1.239 x wing weight (b) The value i s 2.4702 for s t a t i c a l l y determinate concept 22-32 TABLE 22-5 PRIMARY VARIABLES AND COEFFIClXXITS FOR WEIGH?/SIZIPlG PROCEDURE (Continued) Primary It om Var i ab le C c e Sf f c i c n i; - .- Guidance and navigation Constant; 1060 Instrumentation Const ant; 1100 Communication Constant 2 40 Environmental L,.lCrol:
ECS - personnel Constant
5 50
ECS - equipment
Constant 1180 Personnel provisions Constant Crew s t a t i o n control and panels Constant 200 Design reserve z;Wi .020 Empty weight Crew NCREW( =3) Pay 1 . oad (WAY ) 1:nput; D r y weight Res idual s ( unusable ) WFTOT Zero fael weight Reserve WFTOT 0.050 Landing weight c-= WLW S BDY I n f l i g h t Lc, sses 0.660 L J i t e r fuei WLW Burnout weight Performance propellant
Liftoff Weight c = WTJO
Taxi f u e l (WTF) W I ; 0 00225
(wc; - Wl.1~~)
Run-up fuel 0,00765
Maximum gross weight x = WG
TABLE 22-5 - Concluded
PRlMARY VARIABLES A X 2OEFFICTENTs FOR wEIGRp/SIZING PROCEDURE ~~ Primary It em Variable Coefficient volume (VTOT '1 required): Available body (VBDY) 0.096572 Fuel 0.23702 Crew compartment Cargo cmpartment (Variable density ) VBDY -VTuT Equipment bay 0.0050 WG 0.500 Structure and insulation SBDY Miscellaneous V ! W T o.o6!so Area : wing area (SW) 0.0149705 WG Vertical t a i l (SVT) s w 0.0995 * Body cross-section (SPYY) 0.1805 ( vBDY)2/3 I n l e t capture area (CSAP) Constant
Body wetted area (SBDY) ( VBDY) 2l 3 9 . 4 8 0
Total thrust (TTO!T) WG 0.510 TABLZ 22-6 SAMPLE CALCULATION OF BASELINE VECIICLE DATA VOLUMES (cu ft) 52 144
Fuel - 220 000 (0.23702) =
Crew
Cargo - 72 088 to 68 073 = 4 015
EQuipment - 550 000 (0.005) =
2 750
Structure and Insulation - 16 '*?O (0.50) = 8 210
Miscellaneous - 72 088 (0.062) =
4 469 VTOT = 72 088 A R E A S (sq ft): 8 234
Wing - (550 000/66.7978) =
818.8
V . T . - 8234 (0.0995) =
Body c-s - (72 088)2/3 0.1805 = 3 1 2 . 6
Inlet
b a y Wet - (72 088)~'~ 9 . 4 8 = 16 420
WEIGHTS (lb): 60 500
Wing - 500 f (550 OOO)o*6 ( 8 2 3 4 ) 0 ' 8 (0.01590729) =
Vertical Tail - (818.8) 8.54 =
6 990 81 030 Body and Insulation: Crew Compartment 2 000 Body Structure (16 420) 2 . 2 5 = 3 6 950 Tankage (16 420) (312.6)1/2 0.081044 = 23 530 Insulation (16 420) 1.13 = 18 550
Landing Gear - (550 000) 0.030 = 16 500
Propulsion: 82 $9
Main Ehgine - 550 000(0.510) 0.146826 - 6132 =
35 050
Inlet - (222) 201.3 = 44 690
Fuel System - 550 000 (0.510) 0.009 =
2 750 Note: a varies with each wing structural concept f increases 3 685 lb for statically determinate concept 22-15
TABLE 22-6 - Concluded
SAMPLE CALCULATION O F BASELINE VEHICLE DATA
Orient. Controls - 640 c (550 000) 0.012 =
7 240
Power Conv/Dist - 1 400 + (550 000) 0.009 =
6 350 Miscellaneous System 6 780 Design Reserve (267 880) 0.02 = 5 360 h p t y Weight 273 240
Crew - 3 (220) =
Payload -
55 ooo(a)
Residuals - 220 000) 0.005 =
1 100 Zero Fuel Weight 330 000
Reserve - (220 000) 0.05 =
11 000 Landing Weight 341 000
Irlflight bsses - (16 420) 0 . 6 6 =
io 8 4 0 ( ~ )
b i t e r Fuel - (341 000) 0.007455 = 2 5 4 O ( 4
Burnout Weight 354 380
Performance Propellent - 220 000 - 29 050) =
190 950(a) Liftoff Weight 545 330
Taxi Fuel - (550 000) 0.00225 = 1 2 4 0
--up Fuel - (550 000 - 1240) 0.00765 =
3 430 Maximum Gross Weight 550 000 22-16 TABLE 22-7 IX" DATA FOR IN'I'mCTION ANALYSIS
(Baseline Vehicle - 550 000 pounds)
CWING CMR WAY Primary R e l i a b i l i t y Structure (1239 x
I IIW.el
(Fuel Concept x Wing (Payload ) Fraction) Weight ) 0.01191 19 412 Monocoque I;oW 0.01298 i?ormal 10 714 Unflanged 0 399398 0.01389 Waffle High 3 4r( Mono coque 0.00805 50 5 i 5 L N Honeycomb 0.00824 0 399824 49 023 Sandwich H 0.00848 47 044 L 0.00782 Semimono, 52 430 Spanwise N 0.00817 0.399504 49 563 Tubular H 0.00860 46 126 L Semimono, 0.007275 5 6 791 Spanwise N 0.007752 0.399518 52 943 Beaded H 0.008268 48 778 Semimono, L 0.008545 46 544 Cho rdw i s e N 0 009272 0.402624 40 677 36 802 Tubular H 0.009752 S t a t i c a l l y L o.008000 47 250 Determinate, N 0.008468 0.399873 43 477 Beaded H 0.008887 40 094 aIncludes the ef feet of increased body weight.
For nominal r e l i a b i l i t y (47162 - 3685) = 43 477 lb.
22-17'
3 0
I 22- 18 Lumped cop areas Sponwise Chordw ite I -.
’ Redundant model grid 2 = 2.40 in.
A27a0 = 2.76 in, A48. 5 2 = 1.64 in.
Azss0 = 2.82 in. A1 20
= 1.84 in.
A3030 = 1.41 in.
. - -27,345 0 -28,400
- BL488
(1 4,980) (-1,419)
1 1 181,340 I 93,700
-. BL 394 c I t I . . I ,- BL 212
(111,465) - (53,570) 8
c * -. 5 8
. .$
.m ,a
E 3 I 3
R 1 4,922 !b 11,5601 I
- BL120
(86,080) (43,775)
I 1 31,130 1 14,660
- BL48.5
(14,785)
, (5,855)
I 1
A B L *
Jb
XXX = Air loads (XXX) = h e m a l loads 0 Condition: 29 maneuver 0 T, extensional = 0.020 in.
Figure 22-2. Redundant; model loads - monocoque waffle concept; (upper)
22- 19 Spanwise Chordwise %730 = 3.14 in.
= 3.00 in.
A48.5 A2880 = 4.23 in.
= 2.04 in.
Al 2 0
1 - BL488
- B L 396
I_ BL 3w-
27,412 21,020
- BL 48.5
-r (-22,680) (-11,880)
XXX = Air loodr 1 ut timate Notes: 0
(XXX) = thermal loads 0 Condition: 29 maneuver 0 7, extensional = 0.025-0.030 in,
Figure 22-3. Redundant model loads - monocoque waffle concept (lower)
22- 20
--
I Lumped cap areas
Spanw i se Chordwise
I
A2730 = 4.58 IN. 2 A48.5 = 1.97 IN2 A2880 = 4.81 IN. 2 Redundant model grid A120 = 3.53 I N 2 A3030 = 4.81 IN. 2 A212, 304 = 3.24 IN?
I
A396, 4188 = 3.01 IN2
Ti
tBLS6
BL304 L.
BL212 G ch
-
9 . Y h .
x R
s q c)
c - c !
$ 5 (3
I
-72,980 1 - -67,104
BL 120 ( 1 70, ~ 6 7 ) (88,759)
c
16,699 1 , 370 (47,9 19) (l9,414) Figure 2 2 - 4 . Redundent model loads Q mmcocpsg honepomb mneept (upper)
Lumped cap arec I
Spanwise
Chordwise I
~~ - r - - - ~ ~~ = 220 IN2
A2730 = 5.17 IN2 (c - 120)
6.49 IN2 (120-212) A120 = 4.43 IN2 4.28 I N 2 (212 -OB) A212 = 3-44 *;.;
r Redundant model grid
= 5.38 IN2 (e - 120)
A304 = 3.07 IN2 6.68 IN2 (120 - 212) 4.52 IN2 (212 -08) I BL488
t
BL396
t I BL304
F 52580 FS2730 F 52880 FS3030 xxx = Air loads Notes: ) ultimate (xxx) = Thermal loads Condition: 2g maneuver 22-22 Lumped cap areas Spanwise C hordw ise a 4.07 in.
A7730 4.07 in, *2880 A3030 = 2.06 in.
-28,340
1- BL 488
(-6,011)
I
I I , -62,017
- BL396
c 1 -42,745 I
- BL304
I -=y
I.-
I 1 -22,450
-7,790 1 1
B L 212
r
e
s 11,706 I
5,203 !- B L 120
0 1
B L 48.5
I-
r
B L 0 FS 2580 FS 2730 FS 2880 FS 3030
XXX = Air loads lultimate
Notes' (mx) = thermal loads 0 Condition: 29 maneuver
-
0 T = 0.028 in, tchord = 0,005 in.
span
Figure 22-6. Redundant model loads - semimonocoque spanwise concept (upper)
22-23
Lumped cap areas I
-~ Spanwite Chordwise 2 2 A2730 = 4.07 in, = 0.60 in.
A48.5 2 2 A2880 = 4.07 in. = 0.41 in,
- 61488
5 1 396 B l 304 BL 212 hlo V Q O O
-
BL 120
(-14,136) ' (-13,418)
12,405 9,365 BL 48.5 (-1,536) (-1,061) BL 0 d XXX Air loads t ultimate (XXX) = thermal loads I 0 Condition: 2g maneuver
-
= 0.028 in 2 - *tchard = 0.005in.
tspan
Figure 22-7. Redundant model loads - semimonocoque spanwise concept, (ldwer)
22-24 Lumoed COD areas
Span w i se 1 Chordwi sc
Redundant model grid 2.42 IN2 (120-212) 1.87 I N 2 (212-@3'
n
8 L 488 BL396 BL304 BL212 BL 120 I 24,180 10,965 BL48.S (2,523) (-624) F S2580 FS2730 FS2880 FS3030 xxx = Air loads }ultimate Notes: (XXX) = Thermal loads 0 Condition: 2g maneuver 53,355 21,085 8L396
- (-29,857)
m 5 i
(-6,734) ./
t
st8 z. 2.
R ?
0 ' 6 2 3 h I -J. Y 57,45 1 29,794 BL304 (-1 1,788) (-5,06 1 )
~1 t
25,165 50,126 BL212 (-8,462) (-4,541) c-
R 8
83 v)h
-3
'PG.
- 0 3 P N,
3 - a;: 0-
p s!2
C Y u I 48,866
tBLlal
(14,063) .!. (1 24,059 1,931) 14,882 12,768 mBL48.5 (8,3071 (3,680) BLO 0.60 in. 2 %730 = 4.07 in.
A40,S = 0.41 in.
BL 488 BL 396 F 3 n ", c I BL 304 n BL212 n c3 c c .
% Y 3 v
!
!- BL 120
- BL48.5
I
FS 2580 FS 2730 FS 2880 FS 3030 xxx = Air loads I~~~~~~~~ Notes: (xxx) = thermal loads I 0 Condition: 2g maneuver 0 Upper surface shown, lower surface i s opposite sign
Figure 22-10. Redundant model loads - statically deteminate concept
(upper and l o w e r ) -
22- 27 Sta
270 -
T87 I
Remrks Assume c o n s t a n t f o r a l l c onc ept s - - . .
Refer to table 22-1 for weight v a r i a t i o n Figure 22-11.
Forward delta geometry and weights 22- 28 i d 22-29 22-31 I I
r I
I I 22-32 22-33 Hori zonta I t a n g e n c y
/ point
-I
Model lumped stringers 3rd point Wing root
/-
I I______(
--e
-
I- + % BL 120 &del element numbers I _ r
Location 1700 FS 2058 FS 2320 I FS 2472
Upper 16 26 51 6 1 2nd paint 17 27 52 62 3rd point 18 28 53 63 Wing root 19 29 54 64 ~- Figure 22-17. Redundant model idealized fuselage 22-31, J 0. -I
.t! .O1
1 4 0 001 10 000 10 LOO 1000 Nx/L, psi Figure 2-18. Wide column curve f o r s i z i n g fuselage skin p n e l s , stat i c a l l y determinate concept FS FS Spanwise Decking and longitudinal s t i f f e n e r s required f o r Figure 22-19, s t a t i c a l l y determinate concept 22-35 c P
+ I
22-37