"wrap"or "glance"solutions for the nacelle pressure field,as shown in figure 3.6-3.(The far-field wave drag program uses essentially the "wrap" solution). Available experimental data do not make it clear whether a "wrap"or "glance" solution is more correct.Since the nacelle-on-wing interference term is substantial,both solutions are available in the program (controlled by an input code). 3.7 Wing Design and Lift Analysis The wing design and lift analysis programs are separate lifting surface methods which solve the direct or inverse problem of: ● Design to define the wing camber surface shape required to produce a selected lifting pressure distribution.The wing design program includes methods for defining an optimum pressure distribution. ● Lift analysis -to define the lifting pressure distribution acting on a given wing camber surface shape,and calculate the associated force coefficients. The lift analysis program contains solutions for the effect of fuselage, nacelles,canard and/or horizontal tail,and wing trailing edge flaps or incremental wing twist.Using superposition,the program solves for drag-due-to-lift,lift-curve slope,and pitching moment characteristics of a given configuration through a range of angles of attack at a selected Mach number. The wing design program is more limited in scope,since it is used to solve for the wing shape required to support a design pressure distribution at a specified flight condition.The program also contains,however,a number of optional features for identifying the design pressure distribution.This is a demanding solution,because it requires that: ● Drag-due-to-lift of the wing be minimized at a given total lift, subject to an optional pitching moment constraint. ● Constraints be applied to the design pressure distribution to provide physical realism. ● Effects of fuselage upwash,nacelle pressure field,etc.,be reflected in the design solution. As a special case,the optimization feature of the wing design program may be bypassed and the wing designed to support a single input loading definition. This may be done either with or without including the effects of fuselage upwash,nacelle pressure field,etc. 17
"wrap" or "glance" solutions for the nacelle pressure field, as shown in figure 3.6-3. (The far-Field wave drag program uses essentially the "wrap" solution). Available experimental data do not make it clear whether a "wrap" or "glance" solution is more correct. Since the nacelle-on-wing interference term is substantial, both solutions are available in the program (controlled by an input code). 3.7 Wing Design and Lift Analysis The wing design and lift analysis programs are separate lifting surface methods which solve the direct or inverse problem of: Design to define the wing camber surface shape required to produce a selected lifting pressure distribution. The wing design program includes methods for defining an optimum pressure distribution. Lift analysis - to define the lifting pressure distribution acting on a given wing camber surface shape, and calculate the associated force coefficients. The lift analysis program contains solutions for the effect of fuselage, nacelles, canard and/or horizontal tail, and wing trailing edge flaps or incremental wing twist. Using superposition, the program solves for drag-due-to-lift, lift-curve slope, and pitching moment characteristics of a given configuration through a range of angles of attack at a selected Mach number. The wing design program is more limited in scope, since it is used to solve for the wing shape required to support a design pressure distribution at a specified flight condition. The program also contains, however, a number of optional features for identifying the design pressure distribution. This is a demanding solution, because it requires that: Drag-due-to-lift of the wing be minimized at a given total lift, subject to an optional pitching moment constraint. Constraints be applied to the design pressure distribution to provide physical realism. • Effects of fuselage upwash, nacelle pressure field, etc., be reflected in the design solution. As a special case, the optimization feature of the wing design program may be bypassed and the wing designed to support a single input loading definition. This may be done either with or without including the effects of fuselage upwash, nacelle pressure field, etc. I?
S31733VN 18
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Wing Design and Optimization Given a wing planform and flight condition,the wing design program solves for an optimum (least drag)pressure distribution and the corresponding wing shape,subject to specified constraints on: ● Total lift ● Pitching moment at zero lift ● Upper surface pressure coefficient level and/or streamwise gradient ● Ordinate at defined planform locations Basically,the method of the wing design program is that of references 4 and 5.For use in the integrated design and analysis system,however,the program has been expanded to provide the following capability: ● Use of any combination (or all)of ten basic lifting pressure loadings,in an optimum fashion. Optional imposition of pressure level and pressure gradient constraints on the wing upper surface,to prevent occurrence of unrealistically low pressure coefficients. Optional consideration of three configuration-dependent loadings (fuselage upwash and buoyancy,and nacelle pressure field). ● Optional consideration of three wing camber-induced loadings which are proportional to the three configuration-dependent loadings,This introduces camber-related terms to modulate the configuration related loadings (Example:trailing edge reflex for nacelle buoyancy loading). Optional identification of a small planform region (e.g.,trailing edge flap)for special incremental loading. Optional constraints on camber surface ordinate at specified planform locations. The presentation of the wing design results,for selection of an optimum pressure distribution,is in the form of drag-due-to-lift versus zero-lift pitching moment (Cmo Cmo).A typical presentation is shown in figure 3.7-1, illustrating the effect of increasing the number of design loadings and adding the nacelle-buoyancy loading.Selecting a CL and Cr Cmo combination for the wing defines a corresponding pressure distribution which may then be used to generate the associated wing camber surface shape.(The bucket plot is not used with ordinate constraints,however,and only the solution corresponding to the design point values of CL and Cmo is printed. 19
Wing Design and Optimization Given a wing planform and flight condition, the wing design program solves for an optimum (least drag) pressure distribution and the corresponding wing shape, subject to specified constraints on: m Total lift • Pitching moment at zero lift • Upper surface pressure coefficient level and/or streamwise gradient • Ordinate at defined planform locations Basically, the method of the wing design program is that of references 4 and 5. For use in the integrated design and analysis system, however, the program has been expanded to provide the following capability: Use of any combination (or all) of ten basic lifting pressure loadings, in an optimum fashion. Optional imposition of pressure level constraints on the wing upper surface, unrealistically low pressure coefficients. and pressure gradient to prevent occurrence of Optional consideration of three configuration-dependent loadings (fuselage upwash and buoyancy, and nacelle pressure field). Optional consideration of three wing camber-induced loadings which are proportional to the three configuration-dependent loadings, This introduces camber-related terms to modulate the configuration related loadings (Example: trailing edge reflex for nacelle buoyancy loading). Optional identification of a small planform region (e.g., trailing edge flap) for special incremental loading. Optional constraints on camber surface ordinate at specified planform locations. The presentation of the wing design results, for selection of an optimum pressure distribution, is in the form of drag-due-to-lift versus zero-lift pitching moment (Cmo). A typical presentation is shown in figure 3.7-1, illustrating the effect of increasing the number of design loadings and adding the nacelle-buoyancy loading. Selecting a CL and Cm_ combination for the wing defines a corresponding pressure distribution whi_ may then be used to generate the associated wing camber surface shape. (The bucket plot is not used with ordinate constraints, however, and only the solution corresponding to the design point values of CL and Cmo is printed.) 19
M=2.7 CLdesign =.1 Note: At the design points denoted by circular symbols, Cpupper ≥0.7 Cpvacuum surface Wing thickness pressures included Two and three loading combinations are the first two and first three loadings in Table 1 Uniform loading and nacelle buoyancy loading Uniform Flat wing- loading 0070 Two loadings and nacelle buoyancy loading Two loadings Three-loading optimum 0060 Optimum combination .0050 of three-loadings and nacelle buoyancy loading .0040 Nine-loading optimum Optimum combination of nine loadings and nacelle buoyancy loading .0030 -.02 -.01 0 .01 .02 03 04 Cmo FIGURE 3.7-1.-EFFECT OF NUMBER OF LOADINGS ON WING DESIGN 20
Note: M=2"7 CL = At the design points denoted by circular symbols, _>0.7C Cpupper Pvacuum surface Wing thickness pressures included Two and three loading combinations are the first two and first three Ioadings in Table 1 -1 "O Q .0070 - .0060 - .0050 - .0040 -- .0030 -.02 Uniform loading and nacelle buoyancy loading Flat wire Uniform loading Two Ioadings and nacelle buoyancy loading Two Ioadings Three-loading optimum I ! Optimum combination of three-loadings and nacelle buoyancy _ loading I I I I -.01 0 .01 .02 .03 Nine-loading optimum Optimum combination of nine Ioadings and nacelle buoyancy loading I .04 Cm o FIGURE 3. 7- 1.-EFFECT OF NUMBER OF LOADINGS ON WING DESIGN 2O
Pressure constraints.-The use of a large number of basic wing loadings permits great flexibility in identifying a theoretically optimum lifting pressure distribution.Such an optimum may be physically unrealistic, however. Linear theory contains no limitations on allowable surface pres- sures,i.e.,"optimum"pressure distributions may well involve upper surface pressure coefficients lower than vacuum Cp.To avoid this possibility,a pressure constraint formulation has been added to the solution.This functions by limiting the total wing upper surface pressure coefficient to be equal to or.greater than an input Cp:and by limiting the longitudinal gradient of this upper surface pressure to be less than or equal to an input gradient level. By superposition,the total upper surface pressure coefficient is the sum of wing thickness pressure (from the near-field wave drag program,as noted in Section 3.6),fuselage pressure field,and the upper surface lifting pressure. The effect of constraining the allowable design pressure distribution for a basic wing planform (no fuselage)is illustrated in figure 3.7-2.For a given planform and set of loadings,the program cycles to find an optimum pressure distribution (least drag)subject to input constraint conditions.First an optimum loading combination is found,then the corresponding peak pressure level and gradient are located.If either violates the input limits,a new optimum loading is found with a pressure constraint applied at the location of the max imum pressure violation.The new optimum is then examined,etc. Gradient is everywhere satisfied before level is constrained,as described in the theory document,volume 1. The cyclic operation continues until the wing pressure distribution everywhere satisfies the pressure constraints.In the example case shown,the effect of adding pressure constraints shifts the drag minimum from the bucket plot level to the level indicated by the flagged symbol. It can occur that the input pressure gradient constraint cannot be satisfied within the other constraint bounds of Cmo,wing thickness pressures and/or Z constraints.In this case,the program automatically increases the input acceptable gradient level by 20 percent and tries again.This process will continue until the gradient level is satisfied.No similar option is applied to the pressure level constraint,however;if pressure level cannot be satis- fied,the program halts. A further discussion of pressure constraint application is given on page 32. Loading definitions.A tabulation of the pressure loadings available within the design program is given in Table 1 on page 23.The configuration depen- dent loadings may be used both as a superimposed,independent effect and also as a definition of a loading which may be varied (by wing camber)in the optimization process. 21
Pressure constraints. - The use of a large number of basic wing loadings permits great flexibility in identifying a theoretically optimum lifting pressure distribution. Such an optimum may be physically unrealistic, however. Linear theory contains no limitations on allowable surface pressures, i.e., "optimum" pressure distributions may well involve upper surface pressure coefficients lower than vacuum Cp. To avoid this possibility, a pressure constraint formulation has been added to the solution. This functions by limiting the total wing upper surface pressure coefficient to be equal to or greater than an input Cp, and by limiting the longitudinal gradient of this upper surface pressure to be less than or equal to an input gradient level. By superposition, the total upper surface pressure coefficient is the sum of wing thickness pressure (from the near-field wave drag program, as noted in Section 3.6), fuselage pressure field, and the upper surface lifting pressure. The effect of constraining the allowable design pressure distribution for a basic wing planform (no fuselage) is illustrated in figure 3.7-2. For a given planform and set of loadings, the program cycles to find an optimum pressure distribution (least drag) subject to input constraint conditions. First an optimum loading combination is found, then the corresponding peak pressure level and gradient are located. If either violates the input limits, a new optimum loading is found with a pressure constraint applied at the location of the maximum pressure violation. The new optimum is then examined, etc. Gradient is everywhere satisfied before level is constrained, as described in the theory document, volume 1. The cyclic operation continues until the wing pressure distribution everywhere satisfies the pressure constraints. In the example case shown, the effect of adding pressure constraints shifts the drag minimum from the bucket plot level to the level indicated by the flagged symbol. It can occur that the input pressure gradient constraint cannot be satisfied within the other constraint bounds of Cmo, wing thickness pressures and/or Z constraints. In this case, the program automatically increases the input acceptable gradient level by 20 percent and tries again. This process will continue until the gradient level is satisfied. No similar option is applied to the pressure level constraint, however; if pressure level cannot be satisfied, the program halts. A further discussion of pressure constraint application is given on page 32. Loadin 9 definitions. - A tabulation of the pressure loadings available within the design program is given in Table % on page 23. The configuration dependent loadings may be used both as a superimposed, independent effect and also as a definition of a loading which may be varied (by wing camber) in the optimization process. 21