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Produced by the NASA Center for Aerospace Information (CASI) NASA TECHNICAL MEMORANDUM NASA TM-75440 DESIGN OF A TRANSONICALLY PROFILED WING B. Kiekebusch N78-32052 DESIGN OF A TPANSCNTCAILY (NASA-TM-75440) PROFILED WING (National Aeronautics and Space Adrinistration) 62 p HC A04/MF A01 Unclas CSCL 01A
31612
G3/02 Translation of "Entwurf transsonisch profilierter Tragfluegel", Deutsche Gesellschaft fur Luft- and Raumfahrt, Jahrestagung, 10th, Berlin, West Germany, Sept. 13-15, 1977, Paper 77-026, 75 pages 3141515T B 9< Vol^rc^^^^o
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NATIONAL AERONAUTICS AND SPACE ADMINISTRATION WASHINGTON, D. C. 20546 AUGUST 1978 DESIGN OF A TRANSONICALLY PROFILED WING* / + B. Kiekebusch** SUMMARY During a design study, we examined to what extent the applica- tion of well-known design concepts with the combined use of thick transonic profiles would lead to solutions which are optimized in terms of weight and operational costs. From the point of view of optimizing the overall functions of the wing, we felt that the usual design criteria and concepts were too restricted, and did not suffi- ciently represent the physical processes over the wing. Suggestions have been made for improving this situation, and a design example was worked out. Compared with a wing designed according to previously- used criteria, the new design is found to be superior in the most important functions. We have drawn the conclusion that an isobar concept adjusted to the plan form in conjunction with an "organically" designed wing will lead to the weight optimum solutions of wing pro- files.
KEY WORDS: Transonic wing, isobar concepts, wing desi,, Sn criteria, "organic design".
*Lecture at the DGLR Yearly Meeting, September 13-15, 1977, Berlin.
Lecture Number 77-026.
**MBB-UH 12-77 (6), Hamburg Aircraft Division.
+ Numbers in margin indicate pagination in foreign text.
STANDARD TITLE PAGE 1. Report No. 2. Government Accession No.
2: Recipient's Catalog No.
NASA TM-75440
_T
4. Titleawsuk"tlo S. Roper#Dto Design of a Transonically August, 1978 Profiled Wing 6.
Performing Organisation Code P-1—mineOrsonisation Resort No.
7 • Aw " 1eds) B. Kiekebusch 10. Mork Unit No.
9. 11.
Performing Orgamaenon Name and Address Contract or Grant No.
NASW- 198 .SCITRAN 12. Type of Report end Period Cove ► BOX 5456 aA Santa Barbara, CA 93108 Translation 12. Sponsoring Agency None and Address National Aeronautics and Space Administration 14. sponsoring Agency Code Washington, D.C. 20546 13. Svpplamantery Naas tt Translation of Entwurf transsonisch profiliert-e Tragflueg2l", Deutsche Gesellschaft fur Luft- and Raumfahrt . , I 'Jahrestagung,._10th) Berlin, West Germany, Sept.
13-15, 1977, Paper 77-026, Pages q18 -- 2 4 4 ) 16. Abstract During a design study, we examined,to-what extent the applica- k tion of well-known design c.oncepts with the combined use of thi transonic profiles would lead-to solutions'which are optimized in terms of weight and operational costs. From the point of we felt view of optimizing the over t all functions of the wing, .- were too restricted that the usual design- criteria and concepts: and did;notsufficierrtly represent the physical processes over Suggestions have been made for improving- this situa- the wing...
tion, acid a design example was.worked cut.. Compared with a win designed according t.o previouslyrused criteria, the new design We is found to he superjor in the most important fanctions.
isobar concept adjusted to have drawn the • concluson that.an the plan form in conjuiction with ari "organically".designed wing will lead to the weight optimurr, ' solutions of wing; profiles 17. Kay words (>iNfKtM by Auther(s)) 16. Distribution Statement ,.,.
Unclassified — Unlimited 19. Security Classier (of Ntlo report) 20. Security Cla.sio. (of We page) 21. No. of Pages 22.
Unclassified 61 Unclassified ORIGMAL P A r i, 18.
OF POOR QUALITY NASA-110 TABLE OF CONTENTS Page 1. Introduction 3 2. The Design Problem 3 2.1 Preliminary Optimization of Aspect Ratio and Thickness 2.1.1 Results of a Project Design Variation 4 2.1.2 Structural Weight and Wing Geometry 5 2.2 Aerodynamic Considerations for Realization of Thick Wings (Profiles) 7 2.2.1 Orientation Aids for Thickness Limitations 2.2.2 Aerodynamic Profile Load and Profile Thickness 9 2.2.3 Design Check of a Profile Thickness 2.3 Tiling Concept 3. Aerodynamic Design 3.1 Design Example 15 B 10 - Design - A 300 B 16 3.2 Comparison of: 4.
Summary 17 5. References 17 6. Figures 1. INThODUCTION /1 Technical concepts must be examined for the further developments of the air bus, (A 300) within the framework of an aircraft family, and future new designs of commercial aircraft. These concepts must lead to a clear improvement of the overall economy of an aircraft.
Extensive market studies and ingi}iries from airlines regarding their ideas about fleet composition, have shown that there is a require- ment for short and medium range aircraft tykes. A sufficiently fine graduation of the passenger capacity is required. The commonality of components, service, and maintenance is another side condition. This means that aircraft manufacturers must restrict themselves to family concepts. Compared with previous requirements, this requires a larger design flexibility. This is especially true for a mission spectrum and the required aerodynamic design. It can be assumed that the economy of a commercial aircraft (a single design) is essentially determined direc- tly by takeoff weight, payload weight, fuel consumption, complexity of maintenance, reliability, procurement costs, capital costs, etc. In the following, we cannot clarify the sensitivity of aircraft economy to any of these variables. Instead, we will discuss the relationships 12 between aerodynamic wing design and the structural and project require- ments, and side conditions which have a direct influence on economy.
Design criteria and a simple design procedure will be developed for a base wing design, which allow a check of the aerodynamic design itera- tions with respect to the design requirements.
2. THE DESIGN PROBLEM We can assume that increasing the payload fraction (savings in dead weight) and/or reducing the drag for a specified takeoff weight, range, and Mach number will remain the main goal of a design optimi- zation for future commercial aircraft. In this sense, a design aero- dynamicist is required to find a wing/aircraft geometry having an aero- dynamically "optimum" pressure distribution (force distribution) within the constraints of the design requirements. In addition, it must satis- fy the minimum aerodynamic properties (construction principle).
When this problem is solved, this does not necessarily mean that /3 the wing design is optimized in the overall economic sense. Increases in the payload fraction require an optimization of the design weight for any specified force distribution over the wing (aircraft). The optimum combinations of geometric design parameters (aspect ratio, thickness distribution, sweepback, engine configuration, etc.) usually do not coincide for the aerodynamic and weight (structural) optimiza- tion processes. For the overall economic cptimization, only an opera- tional cost calculation can give the necessary information about the most important design parameters, and their optimal combination.
During an iteration optimization, the important design restric- tions are defined by the aerodynamic performance limits of the wing, and the design aerodynamics and project aerodynamics, which leads to the desirable optimum combinations of design parameters. In the pre- sent design situation, we expect substantial improvements in the over- all economy using a transonically-profiled wing (increase in the area loading, thickness increases). A transonically-profiled wing with
favorable aerodynamic properties has already been built for the A 300 B
[1]. The calculation procedures and the experimental results have led to much new information about transonically-profiled wings. We have gained more information about the useful performance range. We are certain that a further and new development of commercial aircraft
will take place during the beginning of the 1980's, and will result
in a substantial expansion of previously-specified or unclear perfor- /4 mance limits.
2.1 Preliminary Optimization of Aspect Ratio and Thickness 2.1.1 Results of a Project Design Variation The dependences between economy and aerodynamic functioning of a wing are the points of departure for all of the design work, which is specified by the overall project.
Here there is a direct connection between economy, wing aspect ratio and wing thickness, and quantitatively this has not yet been sufficiently clarified for the transonically-profiled wings of dif- fering thicknesses. During a project parameter study, we carried out a preliminary optimization of wing aspect ratio and profile thickness for a current aircraft type ((Airbus B 10-type), in order to obtain information about a cost optimum parameter combination [2, 31.
Starting with the basic design, we investigated the influence of aspect ratio and profiling of different wings on the resulting; de- sign. In addition to the engine position and the designed mission, we also fixed the takeoff and landing path requirements, so that dif- ferent aircraft result depending on size and payload capacity. The corresponding design weights and fuel consumption rates were related to the number of passengers. T _n this way, we obtained information about favorable and unfavorable wing concepts. By connecting the two /5 cost factors in an overall operational cost calculation, we can obtain information about economy. When transonically-profiled wings are used and which therefore results in possible average wing thicknesses of (D/L) = 15%, one finds that economic wing aspect ratios are between A = 10-11. Thinner profiles are less economical because for the spe- cified sweeprack (here, F S = 25 0 ) and area loading, cruise Mach numbers are possible which are not required here. The important results for aerodynamic design can be found in Figures 1-3. Figure 2 shows a sum- mary of the results of this investigation for the present design case with the aspect ratio = 9.5 and a sweepback of ,& 25 0 . We find T2S = from this that even if one assumes the same gains in operating costs, there is a savings in the operating empty weight/passenger ratio for large profile thicknesses for a wing with an average thickness of (D/L) > 0.135 using relatively conservative assumptions rega^ding the structural weight advantages.
For equal or slightly-increasing fuel consumption ratios per passenger, however, this maximum "economic" average wing thickness is between (D/L) = .15 (1200 nm) - .16 (500 nm) depending on range, which seems to be realistic if one considers the operational empty weight which can be used for large wing thicknesses.
2.1.2 Structural Weight and Wing Geometry The operational cost calculation of the previous section re- sulted in relationships between the wing aspect ratio and the average /6 wing thickness. However, this data is not sufficient for establishing differentiating geometric side conditions (for example, thickness dis- tribution) for a weight-optimum wing design. We are still missing in- formation forthe determination of the average wing thickness. The l'e- quired information is obtained for strength investigations for the spe- cified wing geometry using the load cases which determine the dimensions.
Figures 3-5 give the results of a strength analysis for a specified wing type which corresponds to the present design case.
Figure 3 [2] very clearly shows the strong dependence of wing weight on wing aspect ratio on average wing thickness. We can see the weight-optimum limiting thicknesses here. From strength calcu- lations, and for a specified wing geometry, we can define an average wing thickness, which is composed of wing segments which are repre- sentative of the structural complexity and have the corresponding weighting factors. For the wing planned form geometry of interest here, and for a representative load case, we have found that the fol- lowing definition of an average wing thickness (equivalent thickness) 151, is a useful one: (D/L = 4 6 (-*/Z ' '^` 0.3 091Z)^ F 0 7 (^/G ^R^T (1) riNk r /P For a specified "economic" wing thickness, the relationship (1) can be used as a first requirement for the thickness distribution as a /7 function of the span over the wing. From the weighting distribution of the representative wing thicknesses, it becomes clear that the weight savings is determined almost exclusively from the thickness distribution of the inner wing, because of the large height. The outer part of the wing has only a small influence, and also has the represen- tative aerodynamic profile. Substantial weight savings from the outer wing (sheared wing) will more likely come about by increasing the area loading there, by increasing the lift load of the profiles installed there, in conjunction with a reduction of the wing area. However, one mus t, 3ecjrl- :•.:,ether to exploit this possibility using the present wing d.Lan form and the selected design lift distribution. Up to now, we have discussed the average wing thickness. Here, we mean a thickness which is representative structurally for the entire wing. In addition to the thickness steps in the span direction, we also consider a distribution in the chord of the wing direction, which corresponds to the average spar height of the supporting wing box structure.
If the wing box structure position is known for a specified wing plan form geometry, by using the thicknesses to be determined as a function of span according to (1), one obtains a first impression lbout the distribution about the weight optimum box structure cross-sections.
However, one must have an idea about the aerodynamically-feasible limi- ting thicknesses (drop thicknesses).
The selection of suitable profile drops (profiles) for the spe- cified wing plan form must consider at least the feasibility of the main dimensions of the wing box structure cross-section (average spar height, box structure depth). At least in the wing areas which are most sensi- tive to structural weight (inner wing) when carrying out a weight opti- mization.
Wing cross-sections or profiles which do not conform to this /8 must be looked upon as non-"weight optimum" (Figure 6), as far as their thickness is concerned, even if they satisfy the desired largest profile thickness requirements.
Additional structural advantages result from this in addition to a direct influencing of the wing box structure weight by selecting a thickness distribution which is matched to the structure. This leads to further savings in structural weight of the wjng.
Figure 4 shows the most important structural advantages of a thick and transonically-designed wing. A table of the wing structure weights is given for a design example (B 10 X) with the various wing thicknesses which can be realized. Figure 5 shows various thickness distributions (D/L (n)) over the span for the design example already mentioned. The lowest curve assumes the first project assumptions.
The top curve considers the structural recommendations for saving weight. The broken curve indicates the compromise based on aerody- namic and other design limitations.
2.2 Aerodynamic Considerations for Realization of Thick Wings (Profiles We can roughly formulate the tasks of the design aerodynamicists resulting from the previous discussion as follows: for a specified lift requirement, a :wing must be designed with consideration of its flow-physical limiting regions and a realistic maximum thickness must be determined. This means a "thickness/lift optimizatiori'for the wing as far as the structural weight advantage is concerned (increase of the net lift equals payload increase) with the side conditions of the smallest possible drag. For the transonically-profiled wing, there is not yet sufficient quantitative information, and therefore the design aerodynamicist must base his work on empirical and intuitive methods.
In order to obtain an idea about a wing design, it is useful to consider the basic relationships between wing thickness, pressure dis- tribution, and the fluid dynamic limitations.
For the wing having an average or large aspect ratio, and for an overcritical profiling, we assume here again that the aerodynamic wing characteristics can be reduced to characteristic profile flows, for the most part.
The basic ideas about the influencing of thickness profiles by /10 an appropriate selection of the design pressure distribution are also applicable to the wing discussed here.
2.2.1 Orientation Aids for Thickness Limitations According to [9], it has been found practical to associate the suction side pressure distribution with a special transonic drop geo- metry, which also makes sense in regard to the usual isobar concepts [10, 11].
By locally changing the thickness of the profile underside, using conventional design techniques of subsonic profile theory, we can real- ize the desired lift requirements 171.
The problem of influencing the thickness of a transonically- designed profile can be approximately reduced to the design of a pro- file drop and a skeleton line [9, 12]. This clearly facilitates the definition of a suitable design pressure distribution in our design task.
The association of a drop pressure distribution and a suction side pressure distribution over the wing means a substantial influence on the thickness distribution of the wing. Also, there is a strong influence of this drop pressure distribution type on the fluid mecha- nical limiting loads on the wing (subsonic separation tendency, C Amax /11 without flaps, shock/boundary layer, separation tendency, etc.)
In order to achieve the desired profile thicknesses or to evalu- ate the selected pressure distribution type regarding its influence on the thickness distribution and the achievable limiting thicknesses, information is required about the influence of the individual pressure distribution parameters on these target values.
the most interesting pressure distribution According to Figure 7, types of transonic profiles can be described roughly using four charac- teristic ranges: the level of the pressure minimum, cpmin the setback of the point of beginninj; of recompression, xR/L -- the size of the local supersonic region cps, x sl' xs2 the trailing edge pressure cPHK It can be assumed that these pressure distribution parameters will give a. good description of the drop thickness of the type of thick- ness distribution which depends on the chord. Incollaboration with the DFVL,R [lj, 141, we were able to evaluate the results shown in Figure 8 for simple transonic drop pressure distributions and a simple case with lift. However, these are only the first rough relationships and can be used for selecting a suitable design pressure distribution. Addi- tional boundary layer variations for transonic profiles have been estab- lished by Boerstoel 1151, and are shown in Figure 9.
2.2.2 Aerodynamic Profile Load and Profile Thickness 112 The requirement for a large profile thickness and a large pro- file lift means a substantial load on the suction side, which is re- stricted essentially by the required working range limit (off-design behavior). The design pressure distribution which is important is the which in the final analysis one for the maximum speed design (MME ), also determines the base profile of the wing. In a study on optimum recompression, Sonnleitner [16] pointed to the basic research of A.
M. 0. Smith [17], etc.. He found a type of pressure distribution which is favorable for this range (as far as recompression and lift for the off-design behavior is concerned), which leads to a modified isobar concept when applied to the wing.
The analysis essentially proceeds from an aerodynamic optimi- However, zation of the glide coefficient for the profiles or the wing.
this is probably not sufficient for a consequent optimization with re- gard to economy (net lift). In order to obtain a realistic evaluation of the "glide coefficient" (for payload), in any case structural modi- fications which are required for improving aerodynamic performance of the wing should be taken into account in the calculation of the useful lift to total drag calculation. This is not so true for the high-speed range using a "clean wing", but is more true for a "low speed wing" Bielefeldt [18-20] systematically with its typJcal high lift ai_;.
evaluated a large number of high-lift measurements using wings with q flaps. He found a substantial dependence between the thickness of the /13 fast flight profile and the useful additional lift caused by a certain flap system (Figure 10, 11).
It was found that by selecting the profile thickness (thickness distribution) and the high lift aids (single, double, triple slotted flaps) the useful additional lift values become optimum in the direction of increasing profile thickness. Also, one can count on a substantial reduction in the weight of the flap installations. Our own measurements with a 17% thick transonic profile have confirmed this tendency [20].
For the high-speed range, we can dispense with minimizing the profile drag for optimum recompression, if the profile thickness distribution leads to better weight values.
The thickness distribution of a profile can be contrasted to the complexity of installing high-lift devices.
The additional weight in the payload weight is a factor propor- tional to the induced drag (square of the weight) in the calculation of the drag. The increase in the drag due to the thickness increase is linear, according to Truckenbrodt [21].
We define the following simple relationship between the lift and the drag as the "effective" glide coefficient: Aeff CA
(2)
W
o ^/ )
y CW? ^'1 f ^( f4z t1( (64CA)2 .
f Wr (CA f aCd)
where ACA is a. aerodynamically-required additional weigjit* (high lift /14 system), then we have not yet found a quantitative description of the problem, but we dan derive a design for the aerodynamicists: the aero- dynamic possibilities of a thick profiling must be exploited completely over the entire working range of the wing, in other words, an "organic" wing must be optimized [22].
2.2.3 Design Check of a Profile Thickness Once certain design criteria have been decided upon for a de- sign pressure distribution, the base profile geometry can be determined using well-known transonic design procedures [23, 241.
In the applications of the profile and in order to maintain the profile thickness, it is important to ensure that the required working *Translator's note: mehrgewicht equals "additional weight".
limits of the profile are satisfied (wing). We will examine this for the design example presented using a suitable recalculation method [25, 261 with a coupled boundary layer calculation. If the working limits are not reached, it is necessary to influence the variation of the recompression over the profile in the positive direction (pressure gradient, trailing edge pressure, trailing edge angle, profile thickness).
The profile can be modified in the trailing edge re g ion, during an iteration. When calculating; the limiting working range, a contour correction is derived from the variation of the boundary layer displace- ment thickness extended beyond the separation point on the profile upper side and its linear continuation to the downstream base point of the X15 sonic line. After smoothing it is applied to profile contours on the top side and the bottom side.
X ^ XR
Z Ck) = S, - & w u N
A (k )
with
S, (x)L
(S4 )" ` s, `x- '^ ^XR z oo c 2 2o +4 -2- L< k- Li Z- - it ^- <- See - .24 = When the trailing edge is redefined, with consideration of the contour filling, Az, one then uses the extension of a skeleton line.
2.3 Winp 'once pt
During an operational optimization of a wing, the design aero- dynamicists must consider structural weight gains during wing design; more than previously. The classical problem formulations for wing de- sign for fast flight such as maximum s p eed, "drag rise" limit, mission range, "buffet" limits, etc., are expanded here by the optimization parameter "wing thickness distribution". It may be advantageous during the first design steps to specify certain wing areas for positive gains in thickness, and to ar • .ume a realistic maximum value for the thickness distribution during wing preliminary design. The possibilities of de- veloping a weight-optimum high lift system from the specified wing should be ,just as important as the purely structural weight gains brought about by modifying the height in the wing box structure. This is very 116 important because the wing area is an important parameter which deter- mines the weight and is already specified by the given takeoff perfor- mance values. The special geometry of thick transonic profiles offers new possibilities compared with conventional and more slender profiles.
Considering the high lift investigations of Bielefeldt [18-20], we see that an optimum adjustment of the fast-flight profile to the desired high lift performances can be achieved by curving the top side of the profile. By matching; the fast flight performance and the low speed performance of a profile design, we can bring about an organic develop- ment of a high-lift system from a high-speed wing. This design possi- bility should be used always in transonic wing design; even subsonic.
Unfortunately, this ha3 not been done as much as for the fast flight per- formances. Assuming a "linear" development of the wing, from base pro- files, the basic requirements mentioned above will become involved in the basic profile design.
The following are areas of "potential" weight savings: - the entire inner wing*, in the chord and span direction (height at the wing root, tank volume, landing gear storage, high-lift system, etc.)
- the wing box structure region has an important supporting mem- ber over the entire span - the rear box structure in the flap field region - the nose box structure In the wing; topside region.
At this stare of development, we have consciously accepted dis- advantages in regard to the expected aerodynamic performances of the preliminary wing; design. By exploiting; geometric reserves, these can be equalized with only a slight modification to the wing design (pri- marily changes in the local thickness distribution in the front and rear box structure region).
For a weight optimum matching; of the wing to specified working ranges or performances, It is recommended to first specify the wing design from the "thickness", rather than to provide for high aerody- namic reserves to begin with, which later on could not be used.
- isobar concept The isobar concept used as the basis for wing design is very important for the expected aerodynamic performances of the wing and the weight, considering the relationships discusoed above.
Sonnleitner proved that a consequent application of the "straight isobar" concept to a pointed swept wing does not represent an optimum solution; espe- cially when good "off-design" properties are required. /18 This is especially true for the case where aerodynamic perfor- mances are required for a given wing planfurm and a specified lift dis- tribution, which in addition are to bring about a low-weight thickness distribution of the wing. The working range of the wing is then limited by flow separations which can no longer be controlled, cr can only be controlled to a limited extent. Large changes in the equilibrium state of the flow forces (inertia forces, friction forces, pressure forces) in the wing boundary layer will start a pressure increase if there are delays in the flow. Using the selected isobar concept, and for a spe- cified wing plan form, we can control the operating limits of the wing in the design stage with consideration of the three dimensional effects during recompression and boundary layer development.
Sudden separation phenomena are undesirable, which are associated with large changes in forces and moments, and will therefore lead to a strong reduction in aircraft stability and controllability.
As is well known, the outer wing "tip" region is an especially critical area. It is only possible to influence the separation phenomena during the design in the recompression region of the wing.
These can come about, either from a continuous development of the boundary layer or from a shock/ boundary layer interaction. The type of boundary layer development over the wing, the development of the pressure distribution as a function of span (first occurrence of shocks, changes in the shccks in the chord /19 direction and physically-possible trailing edge pressure (see Figure 14)) can therefore be directly influenced through the selected design pres- sure distribution and its characteristic behavior over a specified wing plan form. Wing plan forms of the type of interest, here, (commercial or transport aircraft with medium and large aspect ratios) are characterized by a trapezoid plan form with sweepback and a bend in the trailing edge (also leading edge). If one uses the previously-used "straight isobar" concept, which essentially assumes an aerodynamically-representative pressure distribution at the "sheared part" of the wing [8, 11, 27], by the the aerodynamic limiting load on the wing is then determined flow processes along the outer wing.
The pressure gradients become more steep with increasing span in proportion to Vie change in the chord.
There is also an increased tendency for separation in the boundary layer (small local Re-numbers, boundary layer migration). Due to the flow around the wing tip, there is a modification to the isobars at the outer wing. This leads to a flow collapse which is not repre- sentative for most of the wing. If one uses the "straight isobar" concept this limiting behavior will, of necessity, be a consequence of the selected design pressure distribution and therefore the expected wing profile (especially thickness distri-bution), if one conforms with specified operating limits. This then leads to a non-weight-optimized wing profiling. The isobar concept should then be designed so that the special characteristics of the variations of recompression in the span direction are completely exploited in conjunction with the permissible boundary layer load and shock development in order to achieve the operating limits of the wing, and to favorably exploit the thickness characteristics. Measures for influencing the pressure variation in the trailing edge region include the following: adaptation of the [161, setback of the subsonic recompression beginning point, and Cpmin.
matching of the trailing edge pressure (downflow angle, cutoff trailing edges, etc.) In order to improve the flow behavior in the region of reduced isobar sweep and to counteract a separation tendency induced by shocks, higher effective design Mach numbers (for shockless recom- pression) can be used for the profiles, compared to the regions which are not endangered. Figure 15 shows the basic possibilities for buil- ding up an isobar distribution matched with a profile plan form. By using the various possibilities for influencing the operational limits, and by exploiting recompression variations, matched to the wing plan form, as well as exploiting the correct set of parameters for the Xle C J 4 ) ^ KS4 pressure distribution type (Cp,y;n ^Cp fK ) , there is KSz sufficient leeway to maximize the thickness over the wing span, and also satisfy the aerodynamic requirements.
3. AERODYNAMIC DESIGN Satisfactory calculation methods are one of the most important tools for aerodynamic wing; design. Also, another important tool is the wind tunnel. The frequency of using these tools during a project design iteration will point out design uncertainties and gaps.
If calculation methods are not available, which would represent a clear cost savings during the design work, it is recommended to re- strict oneself to cost-saving standard methods, or simplified methods.
This for the most part will eliminate parameter adjustments which could lead to a falsification of the design result. The calculation methods shown in Figure 16 are adapted to the design of transonically profiled wings. We have checked their forecasting performance using our own tests. We feel that they are satisfactory. Figures 17-21 show the results of our own recalculations. Here we will not give a detailed account of the design cycle and the relationships between computer pro- grams and correction methods. Figure 17-21 shows a "linear" design pro- cess. It will be easy to notice the basic ideas. 122 3.1 Design Example For an actual design case, (Airbus B10) we attempted to use the design concept discussed above. In addition, to the project requirements given in Figure 31, and the design requirements, we wanted to carry out a consequent thickness optimization within the constraints. The pro- filing of the inner wing was examined with great care and we investi- gated the contribution of this profiling to the high lift characteristic.
Figures 26 and 27 showed the example of a sheared wing profile used here.
and gives the results of a thickness/lift optimization.
Because of the fixed wing connection, the shortened air frame and the defined control surface (family concept, commonality), we had to pay especial attention to the minimization of the longitudinal. moment.
The only solution we could find was.a drastic reduction in the "rear loading" of the inner wing and in the wing tip reg{on. The required lift values frcm the wing profile regions were equalized by higher over- critical contributions on the suction side, and by flattening the pro- file underside in the nose region (Figure 26). This led to a clear reduction in the longitudinal moment (Figure 28).
Even though we theoretically-determined the required operational limits (boundary of linear lift increase), the outer wing requires im- provement in its separation behavior in the range of low design Mach numbers. At high angle of attack angles, a "pitch-up" tendency is recorded (Figures 25 and 30), which is not desirable. The only re- /23 maining solutions were "Kuechemann-Tips" [11] or a further unloading of the wing tip from overcritical width contributions (reduction in width design of a tip profile for even higher Mach numbers).
Cpmin'
3.2 Comparison of: B 10 - Design - A 300 B.
Figure 31 shows a planform comparison of the two aircraft, and shows the important design data. Compared with the A 300 B, the B 10 has an increased aspect ratio and a clearly higher lift load.
Figure 32 shows the thickness distributions „^Qx j (.D/L)KASTEN) [kasten = box] of both aircraft. The B 10 has a thickness of - 'D7T ti .15, and this results in a very large improvement (42%), compared with the A 300 B (D7E_ _ .105). Operating limits can be compared using Figure We find that for about the same standard of the "sheared wing" 33.
profile of both aircraft, (Figure 34), substantially higher limiting lift values are achieved for the B 10 in the mission range of interest.
This was only possible by using a profiling which is matched with the flow in the span direction, that is, by introducing an isobar concept which is matched to the plan form. Figures 35 and 36 show the theo- retical pressure distributions and isobar variations for both wings.
From the dashed "critical" isobars (Cp*), we can see how the "straight isobar" concept was used for the A 300 B, with a subtantial overcritical unloading (thickness reductions) of the inner wing (Figure 35). Figure 36, on the other hand, gives the B 10 design, and shows an isobar varia- tion adapted to the wing plan form with a strong overcritical load on the inner wing.
Figures 37-40 show the development of the pressure fields along
o f ).. The comparison
both wings when approaching the operational limits (I + , H
of the wing was based on comparison of only a few important design charac-
teristics for the high-speed range. We can expect a clear improvement in the sense of higher economy for the "thick" transonic wing.
We assume that the increased design thickness will not only re- sult in more favorable weight characteristics compared with the high- speed design (wing box structure weight, Figure 4), but also by saving the weight of the additional high -lift devices, we will then achieve a "organically"-designed wing (Figure 13).
4. SUMMARY /25 In an actual design we examine to what extent the use of well- known design concepts could lead to weight-optimum and operating cost optimum solutions, exploiting the possibilities of thick transonic profiles. The usual design criteria concepts used for optimizing the overall function of the wing were considered to be too restricted and not sufficiently appropriate for the physical processes over the wing.
Suggestions have been made for improving the situation, and these have been examined on an actual design. Compared to previously designed wings according to conventional criteria, we find that the new design is superior in several aspects. We reached the conclusion that an iso- bar concept matched to the plan form in conjunction with a "organic" design will lead to a flight profiling resulting in optimum weight characteristics.
5. REFERENCES McRae, D. M.: The Aerodynamic Development of the Wing of the A 300 B.
1.
Aeronautical Journal, July, 1973.
MBB-UH Excerpt from: Low fuel wing - design variation for determi- 2.
ning a low-fuel wing design. TN-HE 23 -020/75. Sept., 1975.
3. MBB-UH Excerpt from: Low fuel wing - aerodynamic specifications.
TN-HE 23-020/75, Sept.
4. Scheerer, J.: BMFT-LFK 7512 ZKP "wing section" - summary of results - First Main Milestone, December 31, 1976.
5. Schneider, W.: Contribution to structural design of supercritical transport aircraft wings; VFW-Fokker, Contribution to the DGLR specialists meeting on "Fixed wj.ng aircraft", on November 19, 1974 5 Bremen.
Kuchemann, D., Weber, J.: The subsonic flow past swept wings at 6.
zero lift with and without body. ARC, R.u.M., 2908, 1956.
Weber, J.: The shape of the centerpart of sweptback wings with a 7.
required load distribution. ARC-R.u.M.
3098, 1958.
A method for predicting the pressure distribution on 8.
swept wings with subsonic attached flows. Royal Aeronautical Society (Transonic Aerodynamics Committee), Transonic data 6312, 1963• Memorandum, 9. Dira'i 3 O., Kiekebusch, B., Scheerer, J.: MBB-HFB 4.03 (463), Wing design for transonic flows, MBB-report UH 10-70 ZTL 1970 FAG 4 10. Lock, R. C., Rogers, E.W.E.: Aerodynamic Design of Swept Wings and Bodies for transonic speeds. Proc. 2nd Inter. Cong. Aero. Sci.
Zurich, 1960.
11. Kuchenmann, D.: On some three-dimensional flow phenomena of tran- sonic type Symposium Transonicum, IUTAM SYMPOSIUM Aachen, 1962.
12. Hansen, H.: Design of wing profiles for transonic flow using the integral method. Internal DFVLR report IB 151-75/4, Braunschweig, March, 1975.
13. Hansen, H.: Investigation of thickness distribution of profiles for flows without shocks and lift, Internal DFVLR Report iB-151- 77/9 Braunschweig, June 1977.
14.
Kiekebusch, B.: Preliminary study on the design of transonic profiles, MBB Working report TN-HE 212-34/76 (final report in preparation).
15. Boerstoel, J. W.: Review of the application of Hodograph Theory j to Transonic Aerofoil Design on Theoretical and Experimental Analysis of Shock-Free Airfoils. In: Symposium Tranonicum II K. Oswatitsch and D. Rues), Springer Verlag Berlin, (Publisher: Heidelberg, New York, (1976).
16. Sonnleitner, W.: MBB 4-23: Wing design using transonic profiles and a modified isobar concept; MBB Report UFE 1155 ZTL 1974/FAG 4 17. Smith, A. M. 0.: High Lift Aerodynamics (37th Wright Brothers Lec- ture, AIAA Paper No.
74-939 (1974).
18. Bielefeldt, E. A.: Limiting Lift of Slotted Flap Systems, MBB Report -05-75 UH(1975).
19. Bielefeldt, E. A., D,jermani, S.: MBB 4.21-1, Determination of In- stallation losses for Multiple Slot Flap Systems. MBB Report UH-17-73, ZTL 1973/FAG 4 20. Bielefeldt, E. A.: STOL-Aircraft with mechanical high lift systems, compared with mechanical STOL aircraft with blowing flap wings.
Lecutre at 5th yearly meeting of DGLR in Berlin. Lecture No.
72-057, Oct., 1972.
Aerodynamics of Aircraft, Volume I and II, 21. Schlichting/Truckenbrodt: [Goettingen], Heidelberg, (1960).
Springer Verlag Berlin, Hert- a l, H.: Structure and Motion - Biology and Technology, Kraus- 22.
Mainz (1963).
kopf-Verlag, Eberle, A.: Exact Photography Hodographic method for designing over= 23.
(o), critical Profiles, MBB Report UFE-1168 1975.
24.
Bauer, F., Garabedian, P., Korn, D.: Supercritical wing Sections, Lecture Notes in Economics and Mathematical Systems, Springer Verlag, Berlin-Heidelberg-New York, (1972).
25. Murman, E. A., Krupp, J. A.: The Numerical Calculation of Plane Steady Transonic Flows Past Thin Lifting Airfoils, Rep. No.
D-180-12958-1, Boeing, Aerodynamic and Marine Sciences.
26. Kiekebusch, B., Scheerer, J.: IMBB 4.02-3, Wing design for transonic flows, MBB Report UH-17-72, ZTL 1972, FAG 4.
27. Lock, R. C., An Equivalence Law Relating three- and two-dimensional pressure distributions, ARC, R.u.M., 3346, 1964.
28.
Gruschwitz, E.: Wing trailing edge of finite thickness on drag of a wing for subsonic speed. Dornier-ZTL-Report, 68/12 (1968).
29.
Korner, H.: Relation of Potential theoretical flow over wing/air frame combination in comparison with measurements. DFVLR Report 71/11, Braunschweig, 1971.
30. Loerke, J., Kiekebusch, B.: Development of the Simple Wing Design Procedure with Approximate Consideration of fuselage and Engine Interferences. MBB Report TN-HE 212-32/76 (1976).
31.
Loerke, J.: Plot program for 3D-calculations of wing/fuselage combi- nations. 1. Graphic Output of computer results. 2. Panelling of a wing fuselage transition with fairing and plotting output.
MBB report TN-HE 212-11/77, (1977).
32.
Vanino, R., Rohlfs, S., Kuehl, P.: Calculation of three dimensional transonic flow over wings with a relaxation method. Dornier Report 73/21 B ZTL 1973/FAG 4 Rohlfs, S., Vanino, R.: Calculation of three dimensional transonic 33.
potential flow around wing body combinations with a relaxation method. Lecture No. 74-101 Dornier, 7th Yearly meeting of DGLR in Kiel, 1974.
34. Fritz, W.: Program description TRA WeB. Dornier Report BF 30/P-0020- 75, ZTL 1915-FAG/4 Otte, F., Thiede, P.: Calculation of plane and rotational symmetric 35.
compressible boundary layers, based on integral conditions. VDI Z Research reports, series 7, No. 33, 1973.
36. Redeker, G.: Calculation of Shaking Limits of Swept Wings, DFVLR Report Number 0695, Braunschweig, 1971.
37. Kraus, W.: Further Expansion of panel method. Part 2: Expansion of panel method on wing control surface interference. MBB-UFE 1017/1973.
38.
Fingerhut, H. P.: Theoretical and numerical investigations of the aerodynamics of wing/body configuration with engine fairings (Airbus). MBB-UFE 1177/1975.
Laihad, M.: Use of the panel method on rotationally-symmetric en-
39•
gine flows. Diploma thesis at Institute for Aerodynamics and space flight of TU-Berlin,
1975•
40.
Goede, E.: Forces induced by Engine flow over VTOL-Aircraft during hovering flight. Working Report Mitt.
13(1975), Institute for
Aerodynamics and Space Flight TU, Berlin.
41. Eberle, A., Sacher, P.: MBB 4.02-4 Wing design for transonic flows, MBB-UFE 1058, ZTL-1973, FAG 4.
42.
Eberle, A.: Experimental Invesgigations over critical profiles and
wings for the high-speed range. MBB-UFE 1 -53, ZTL 1974, FAG 4
43.
Kiekebusch, B.: The state of development in design work of the ZKP with consideration of the results of our own processing work.
MBB Report TN-HE 212-21/76 (1976).
44. Bosch, H., Kiekebusch, B., Scheerer, J., Woelfer, G.: Theoretical and experimental investigations of noise shielding measures of ,jet engines. MBB Report UH -19-75 (1975). BMFT-Requirement LFF 29.
45. Bosch, H., Kiekebusch, B., Scheerer, J.: Theoretical and Experimen- tal investigations on noise shielding possibilities of jet engines.
Part II Measurement Appendix. MBB Report UH-
19-75, BMFT Require-
ment LFF
29/1975-
tz elative Operating Cost/Passenger Relative Operating Cost/Passenger o o CS, CI L9 `D o ui ^n C) Co - - I - Co I / • 0 0 0 0 cD
jNi
r
^o
^ μ O Q a ~ r ^ 0v J 0o r w ft rt n w W _ rt O
y
U1 O CD O O I O Profile thickness G) Profile thickness (,o) 1100d "
Linva?)
Fuel consumption/passen€er operating weight/passenger [kp] (k^] w w-• w r r CDw N O Ln O O Cn O O O O O O _ — _ --L CO X IQ1 CD — I O I (] C:> ^ W Ul r• o J o ro o ro w ^' C v m w m v N fD f) n rt Pt PI w rt rt F'• ^• o Profile thickness (Z) Profile thickness (Y_) R.
aso 3,6o177PJ 340' operating Empty Weight Per Passenger .941 .9. I \ ` 9Z Relative Operating Cost per Passenger 6, Fuel consumption per passenger Figure 2: Project Preliminary Optimization. Selection of "Most Economic" Profile Thickness.
ORIGINAL P lk"' '+'.)
& POOR Qum,", 22 ORIGINAL PAGE IS OF POOR QUALITY Reference wing area = 187 (m2) Sweepback angle - 25° ^ I ^ ^ lE u \ , 7 W w ^^^ f Q 1 mac. / Ar k^ s >> rJ 12- Figure 3: Dependence of Wing Weight on Relative Thickness and Wing Aspect Ratio. [2] STRUCTURAL ADVANTAGES OF THICK TRANSONIC WINGS Room for connecting wheels storing flaps therefore simp ler conc, lift gaining weight Stiffness increase with height.
more flutter safety margin reduced bending Bending stiffness, EA B -- k •H2 H = average spar box height k•1-1<G-1T<k•FH2 stiffness, Greater aspect ratio ,-,ithout [eight additional weight flight weight 2) m 1,P (0/. ) 16100 ? 9,5 13,35 hin 17400 10,5 9,5 lick 97 15650 9,5 15,0 100 18100 d 8,0 1015 zcture including central tank in fuselage if a structural investigation of the transonically wing with large aspect-ratio [4].
RELATIVE THICKNESS DISTRIBUTION 90 I3 recommended for B10Y -MBB weight saving ++ 15,0 15,0 `• 1 14,5 `•^ • I1.1310 ( Project Definition o,126 10 L 1,0 0,3 o,G 0,4 0 0,2 w Figure 5: Preliminary Design of the Limitations on Wing Thicknesses
N
Figure 6: Explanation of the Structural Exploitation of the Box Region from Profiles having equal thickness.
-CP Ik Figure 7: Simplified Description of a Transonic Pressure Distribution N pe" n22 r + l.'1.`
1°!T?
NX t r aia Xgr/ i r p4tt ^ ^X*/L --'00 t -- 4 .X air ..
j Cp ,r,s^' •^-Z--= ,.-;^: '9 :^. :j....
W2 profiles with Lift OJO i Figure 8: Influencing the Thickness Distribution of Transonic Profiles Using Pressure Dis- tribution Parameters 113, 141.
ORIGINAL PAGE IS OF POOR QUALM Cams H=35000 t; ^^^^^ 1 8— 1 1 . ♦ ; nom ^ 1 ♦ 1 1 ,1^^ ^ n ♦ j) H ='20000
f
Ma z ca= 254 Hs25COOf1 VX Design Requirements l•c a .00 (G/i:)tafV --G20 to i- J - v m2 12— f[i '/1.1^.1L If ^^ ^ i
t ° I
I 1 II I
s
o2s
MEC^,LgMMO 25 (D/L) maximum variations Desi4n Tianoe source: iTU, Boerstoel Figure 9: Lift/Thickness Limits of Transonic Profiles According to Boerstoel 1157.
W O triple slotted flaps (-4,-) ?0 double slotted flaps d1t- \ 0,17 simple slotted flaps Y 03 opt /` _ ► 'C ,.d Cl/`_
1 — 06 ^
nro / o,^! I -to '08 ^ oao °'' I approximations c7cvmcnclf Pn mn QS ,,,f ,,,2andp^^^2 according to Figures
4, 10
M, - 1,41 p3 - 6,38 O O If 02 05 os qp e = rough geometry parameter of flap system r + / ^ki Figure 10: Limiting Lift Values of Slotted Flap Systems. Dependence of Fast Flight Profile thickness and Usable Additional Lift Brought about by Flaps [18].
Figure 11: Explanation of the Various Topside Curvature Component of the Flap Wing System, Main wing-simple slotted flap [18].
CP ORIGINAL PAGE IS OF POOR QUAIXff 'PHK
I - \
(
I -^'^ dd,/L
( ^ XR \ dXIL
b
L /C-w I r^^ ) UN - (6+)XR t l dX^/XR (X-XR) I 1 '
I
42 S 1W -(64)LlN
i 2
A profile I For Profiles with Rear Loading Recommendation Zo ; Z +,&Z , Zu = H O <k is 1 for Zu- zu Figure 12: Measures for Influencing Recompression Variations.
ORIGINAL PAGE IS OF POOR QUALITY EXPECTED: BARGE SUCTION SIDE LIFT. AERODYNAMICALLY-EFFECTIVE _ Landing HIGH LIFT SKELETON. FAVORABLE High Lif t_ - -Takeoff FLOW SEPARATION. LARGE HEIGHT CONTROLLABLE LONGITUDINAL MOMENT Cruise REDUCED LIFT LOSSES. OVERALL: HIGH EFFECTIVE GLIDE COEFFICIENT.
+i I "Organic" Development of the High-Lift Skeleton from the "Topside" Curvature of the Fast Flight Profile.
LOW SUCTION SIDE LIFT. POOR CONTOUR TRANSITIONS TO THE HIGH LIFT SKELETON. THIS CAUSES FLOW LOSSES, INCREASED COMPLEX- ITY OF HIGH LIFT AIDS, LONGI- "additive" solution: TUDINAL MOMENTS DIFFICULT TO fast flight profile \ CONTROL. LIFT LOSSES. OVERALL: + flap wing
I LOW EFFECTIVE GLIDE COEFFICIENT
+ optimum installation losses ACA added weight +K 2'(C A + ACA)2 CKR ( 1 + Ko D/L) +K1(C A + AC, A ) 13: Explanation of a "organically"-designed wing profile.
Figure W
n
1.0
(^ L)Z
U^HK
^r
C14^
0.5 10
:^U
lU 15 ,^F+ 20
[oJ Figure 14: Dependence between Trailing Edge Pressure and Trailing Edge Angle, According to Gruschwitz [28].
Isobar Concept and Base Profile -CP - COs Mas-M a = Mo-Cos . Mo. = Mo - Coa7M ^Z
Cf,;n
MQa 1 , CP ' 1 1 / PHK design of base profile using, transonic theory [23, 24, 25, 26, etc.]
^t CP SIDE COMMON:: "GENTLE" SHOCK DEVELOPMENT DESIGN SUITABLE FO P THE MISSION Ca (71) M DESIGN MC
0 0 0
g^
MO.= Ma= MO ^ro 99^ tryy ^ Figure 15: Isobar Concept Matched to the Plan Form and Design of Base Profiles.
w
► C U Ul Figure 16 rn SUMMARY OF CALCULATION METHODS BOUNDARY LAYER SUBSONIC VERSIONS TRANSONIC VERSIONS SIMPLIFICATIONS Design Postcal- Design Postcal- culation culations Weber me- Weber method Hodograph Garabedian/Korn Integral method.
thod.
compressible method, ac- method, DFVLR Walz II in the "Semiinv- with boun- coring to version. Thiede/Otte ver- verse panel dary layer. Ebe2le sion.
method Panel method. Transonic, Difference method Compressible, Multibody subsonic, according to Murman/ laminar, and configuration analogy with Krupp coupled with turbulent boundary iteration G. S. and coupled layer. Extension control using subsonic approximate beyond separation transonic dif- calculation: for in- point for simula- ferential fluence of thickness ting weight with method and starting solution. simple semiempirical relationship for turbulent boundary layer c f = 0.
3-D Extended Reversal of Subsonic ana- Transonic difference Integral method ac- wing theory design with logy method method (small distri- cording to Cumpsty- (vortex- fuselage butions). Expansion Head. Compressible Iteration lattice) and engine of the program version version acc. to coupling of fuselage in- fairing of Dornier. Redeker turbine, subsonic de- fluence ac- compressible boun- sign and de- cording to dary layer up to sign transonic Koerner and separation point, postcalcula- (unknown) varied extension to tion method wings in sense of a with checking simple strip method of boundary (consideration of layer devel- average span - depen- opment.
dent isobar sweep and wing chord).
ORIGINAI, PAGE I5 OF POOR QUALITY `... X Figure 17: Example of surface discretization for the design and post- 311.
calculation according to 130, k LA) -_—..--- °tr° -.
1 .1 : ^O
Sz
o.r.n ^ MWV . 1i 11-• 1:[1 .0•sl,
a
°.+i ^^ 0.rn M/ O.SJ 0.'0 o.:n 0.1 n.n - %0.1^{0:_ - o.+o o.so 7.R0 11..
0.10 Figure 18: Results of a subsonic post calculation (linear theory, [291) for the A 300 B 1301.
(5 <5 b.03 :,:I 7.00 44 0.3 G1.
in ..09 1 i t QA 0.4 C . 7 C b 4^1 C-W w Figure 19: Results of a subsonic design and postcalculation (linear theory) for a B 10 x E301.
'D CD CZ .. :..._i-. .
measurement • a.
; I • •f 1.,.. i meas ur ement i I urement 1 ! ^ ^'"' I tv ff 0, 94S •) en. 6 transonic calculation , I a 1^? ^.•.w • • n • o. a,o I I .... transonic calculation i 3 .
yyy ^^/ ' 1 t ' I I I I N 1 swI!.,._ ..r,.:. _;•.,,.r... _:.,._. -
^^ .-^_ [illegible]
__ _ j^ I. - !
I ^ I ._. ^ .. r.. riv. .x: w; ^_^.=u: w:.ti e _ l^ - 7t ^•r— f ^ ^^^ • •• • 32 • L — —_— 1 — -^- ^ -- . t-`- '^^ •a a , ra:. i rc . ^ • __^ ^ . `t j 7t.wpf 3 ^ /^ I y i I ^ ^ 1 _ nn Arf 1t_^__.
_•'1pYuA6lr u:? 07 j i• -; Otl_`t:^ `i-or i Figure 20: Comparison of transonic postcalculation and measurement results for the A 300 B [HST/NLR].
CA 0.8 0.7 0.6 OIz 7-1 F7 aft I - -.1-__L ___ ---. 1. C ) • 0.3 A
,/
a2 -- -----1--
/
:A ro
` ' ^ J2 Calculation 0.1 I Heasurement i 1j, I .
'2 1' t: in in Pn C^ In Aerodynamic Note A-0011-50-11/1/36 Xz_ Figure 21: Comparison of theoretical and experimental linearity boundary for the A 300 B.
DESIGN PROCEDURE PROJECT REQUIREMENTS CA design range working limits CA = Const.
Na?
H-35.000 {t.
F^j
i j H-30,000{t.
i
Mc-i' Mcmox Ma basic mission M MC ' M C NI1\I0 G/F S1'ART GR/F i Wing plan form • D/L A, NI I\' Engine position, fuselage geometry D R , L Required Fuel Tank Volume Required Design Volume (fuel tank, landing gear, etc) SELECTION OF BASIC PRESSURE DISTRIBUTIONS FOR TOPSIDE ISOBARS SELECTION CRITERIA FOR: MAXIMUM THICKNESS TOP SIDE CURVATURE TRANSONIC OPERATION TENDENCY TO SEPARATE AS A FUNCTION OF SPAN LOW SPEED HIGH SPEED Figure 22: Design Procedure - Step 1 DESIGN PRESSURE DISTRIBUTION SUBSONIC ANALOGY: OVERCRITICAL WORKING IaINGS ('A!i BE DEVELOPED LINEARLY FROM PROFILE FLOWS, JUST LIKE WINGS IN PURE SUBSONIC FLOW I - III BASE PROFILES J - 5 Design Steps INSTALLATION OF BASE PROFILES INTO THE WING CROSS-SECTION LINEAR STRAKE AND INTERPOLATION OF SECTIONS PARALLEL TO THE FLOW POST CALCULATION OF THIS WING WITH SPECIFIED TWIST FOR DETERMINING THE DESIGN PRESSURE DISTRIBUTION SPECIFICATION OF THE TOP SIDE GEOMETRY AND THE WING SECTIONS IN SPE- CIFIED CONTROL SEGMENTS.
Zo(X,lt) FIXED Figure 23: Design Procedure - Step II.
DESIGN CALCULATION WITH A METHOD EQUIVALENT THEORETICALLY AND NUMERICALLY TO THE POST CALCULATION.
TWIST p(,j (ij) CURVATURE ZS (x,-I) DEFINITION OF WING UNDERSIDE I) = - Zu ( x . - 7o ( -x + 2 Zs (X,J) TRANSONIC POSTCALCULATION OF THE GEOMETRY FOUND TEST OF THE DESIGN GOALS. POST CORRECTION Ca(7) C4, Cxz Co' ( J) TRANSSON.
I coC ( Goal and Result of v Linear Subsonic Design I POST CORRECTION OF THE TWIST DISTRIBUTION OF USING LOCAL LIFT INCREASES FOR THE TRANSONIC CALCULATION.
Figure 24: Design Procedure - Step III ORIGINAL PAGE IS OF POOR QUALITY CHECKING AND DESIGN CORRECTIO_JS FOR "OFF-DESIGN" REQUIREMENTS TRANSONIC POSTCALCULATIONS PLUS BOUNDARY LAYER METHOD, THEORY OF DETERMINATION OF SEPARATION CHARACTERISTICS AND OPERATING LIMITS fd Ma l / DESIGN 0.1 i`A AC A linearity limit C A Ca Q
0- XA16(^)) dj
CA _ C « limit 0( cX ' 0alimit 1.4-« limit -^ PROCEDURE FOR POST CORRECTION, IF NECESSARY - SEE FIGURE [12] required limit CA CA aired limit Ma Figure 25: Design Procedure - Step IV 1j5 L U 1-0 - '
-----
--------~
-
profile top side • profile bottom side
•
Figure 26: Result of a "Profile Optimization" ("Sheared-Wing" Profile).
11- t T
IS ORIGINAL PAGE OF POOR QUALITY -1 Cf • -o a.c o.s CL u 1.0 1.5 profile top side • R33.
profile bottom side Fixture 27: Development of the Shock Position for "Off Design" PAGE iS 0 QUALITY 0FGpocg I I I S
!
i
i
i
I
O,p . L N ^ ^ 1.)J • I 1 - SO .5 } 1 J.
1 -SO a 1 1.1G C.iC Xr^'•i ^ ^-• i • ..^ .. .13: Vf 'l LIN ^^s...__—_^.•—•-----....-- V. V VJ V.^ u.5 u.l u.^ ^ V•J VJ IV X%L
---•---.-----•-.-•-.-.-•-•-.-•-.- •-
•-- L
Figure 28: Reconfiguring of the Differential Pressure Distribution for Minimizing the Moment of the B 10 X Preliminary Design }i' 1. ^i: :J.
-i - t[;: :i: I' t I' :ii Vii"
_
:I
i.:,: I•..I I
I :i: iii :1: ' :^: ,i .I.
^i is :ii i ;.
:f.: .I x :f_ rw :t.
, a^ .,.
^tQl.
.i.
:i , ti I r :I.
t + ....
i
^y e is
t a _ ^'. a ,.
r I^ 2 -}- 0 i :::i. I^ ,: 1 co mpletely turbulent ent m 1 u P Y I: .... i 1.
rr '..
i' is I ^1: f ^t^ :I . f f : ►
^i
..'ii
^.
t: t I r; :t. :+: t is ll I: :E: :i _::: O O t 'i: ,' :1.: I :t : .t f.
;;.
, ^i :f: 8 — - ii r• — :^i t > I: i' G^
^f. t
_ L I: ili ^. i^ ! is , ^I I _ I, A.
-,... :rte' ,-
:77; .i •r
t
t
.-
Figure 29: Theoretical Separation Characteristics for the B 10 Preliminary Design o b ^.J1
O
S
b
I I I^ ^j li I^ ^t ^f II it i +I CO I s o9 : . 9C } f I l ..Sp r^ 1 .tC I 7-SC r , .. p er" ..50 C.SC I I 1.50 -' i^'l h ^/ L / ^.q- GL G.7 ,;.9 G.d 0 G.I 9.: G.J ..< 75 G.G ,, .. G'.9 :.J l 0 ri X/ displacement thickness shape parameter H12 friction coefficient Figure 30: Results of a boundary layer calculation for the B 10 X wing
pAGElS
OBl~Q\l~
or
A 300 '8l
B-IoX H , 0.18
H" a18
~ £,.",) "R [~",] 2QoO
If (£11
'33000 H [f/J 35000 ~(~J 4lJ2.
,f30 G~ [l-J I
~ r~] 438
G [."'] i 42'
!
F La':J
2'0 F (..,~ :
20C)
, i;/F 530 (;/F '03 A..
1. ':13
q.o
A.
).
0.2' '
i\
0.2'
'PlS
l8· j
(D/L.) % 40.s /-I()'S
Figure 31: P1anform Comparison of A 300 B2 - B 10 X and Project Data N :(:.:. f: ,.: !
:f' —
y l - ^ :i
i^ 1.
, ^I...I^... .. .
: — D _ 0 6• t: t root r,v bend i h i. ..I: a t.
IF 7.
:i.
r i _-4 r.
.I. ,.
--000: i.
I.
.....
. 1
cc
t _ .I.
I^ :t f— I i^ I 8 ^, T + f.A x
^r
1: ;
Cb
_ 3 I
:.
.l.
is :t. - t.
I L L I: f.
I
t
f is :;. , :^ I
3D
A B
:I D 1 B1 :t.
0 X
{ 1 77 ( is f:
`! l-/L^,,,cx .149
i ( -.
^:: i 1 1 !
3^a• 093 .1 35 ! o raver .. a e b b ox h .^ ox
S eiht C /
^Xl Ox ll ^. f jj is is 0 x a e^ A3 a ra e b ox h ei
1. ht
(t:..
i s
.9 0+ I J..: 1— . .... ... .... ......... ..
.1 Figure 32: Comparison of king Thickness Distribution A 300 B1 - B 10 X pRIGIN AL P AGE IS OF POOR QU ALI'1 , }.
r ao _; _ . .. .^ _: _ .. _. . ^ ^`f i .. •^9M , .Bogy .. _ i a I ^ i (t^ Hg°),u^
e!.'a ,as i -1
u i l ^_ 1 \^ :.
61 R !j r.
LJ Evaluation of operational limit - - 9 estimate.
Theory: TSP + boundary layer integral method [32, 36].
I C A • .a buffet onset requirement _ Brox } I I `
I j^
FXP. BUFFET-aSer I ^ I A3008
^ \-35,000'
theoretical linearity limit y A 610 G^ _X ICA laats.Gw 30.000' '!
I I I I H57-NL P, I A300
I ^-
I
I
I 1 •^ .5
6 :7 .8 9
M0.
Figure 33: Operating Limit Comparisons, A 300 B -- B 10 X :n r przf Ile profile C^,r.0A5^^ ^^ • T hir F^-u1s 7a5- 4-2 AI-
J Ei,-^
'•.0 I ^^ L • mot ^.^^ f 1^ L ^ t t K O.E ^%
^C
^2
;P.
N p .1 f i{
r^
U
^s 1 ^ t .t .
0.4 < r { i Drag rise limit buffet onset limit 0,2
I
i
l - ► ct-------- i A N 0.7 0.8 Q^ a6 0.7 ac "_gure 34: Profile LiTi'^1-7 Curve Comparison A 300 B - B 10 X., Lasic Profile cver the "Sheared Part".
I .35 C A 9: ----- - — ----- oil, V. :3 14,— — - — — — — — — — — — — — — Z "j
j
illegible
Ul Figure B Isobar Variation in the Design Range (Transonic Theory) 35: A 300 ,s rn a ( 110 .785 1 d I C A z 44 . ..
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-- — — B 10 Isotar Comparison in the Design Range (Transonic Theory), Figure 36: o .785 .43 z C A 1 .3 \xK I d- .0.2
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Figure 37: A 300 B Isobar Variation, Transonic Postcalculation
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d Mo .786 U z L CA -59 v Is
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it
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Figure A B Isobar Variation, Transonic Postcalculation 39: 300 m C) .82 CA .625 it 5.
14 tj - - - - - - - - - - - - - - - - - - - - - - - - - - G -1: _ _._ _--- ----- --------- illegible Figure 40: B 10 Isobar Variation, Transonic Postcalculation