NASA/TM-2001-210867

HSCT4.0 Application

Software Requirements Specification

A. O. Salas, J. L. Walsh, B. H. Mason, R. P. Weston, J. C. Townsend,

J. A. Samareh, and L. L. Green

Langley Research Center, Hampton, Virginia

May 2001
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NASA/TM-2001-210867

HSCT4.0 Application

Software Requirements Specification

A. O. Salas, J. L. Walsh, B. H. Mason, R. P. Weston, J. C. Townsend,

J. A. Samareh, and L. L. Green

Langley Research Center, Hampton, Virginia

May 2001
Available from:

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Space Administration.
iii

 Table of Contents

Foreword..............................................................................................................................1

1.0 Introduction....................................................................................................................2

1.1 Purpose..................................................................................................................2

1.2 Scope.....................................................................................................................2

1.3 Acronyms, Abbreviations, and Nomenclature......................................................3

1.3.1 Acronyms and Abbreviations ...................................................................3

1.3.2 Nomenclature............................................................................................3

1.4 Overview...............................................................................................................5

2.0 Overall Description........................................................................................................5

2.1 Product Perspective...............................................................................................5

2.2 Product Functions and Constraints .......................................................................6

3.0 Specific Requirements ...................................................................................................6

3.1 HSCT4.0 Application Input and Output ...............................................................6

3.1.1 Optimization Data.....................................................................................6

3.1.2 Fixed Input Data .....................................................................................11

3.1.3 Generated Data........................................................................................13

3.2 Functions.............................................................................................................17

3.2.1 Optimization Process ..............................................................................21

3.2.2 Analysis Process .....................................................................................25

3.2.3 Geometry Process ...................................................................................26

3.2.4 Weights Process......................................................................................28

3.2.5 Nonlinear Corrections Process................................................................33

3.2.6 Rigid Trim Process .................................................................................34

3.2.7 Polars Process .........................................................................................35

3.2.8 Performance Process...............................................................................36

3.2.9 Ground Scrape Process ...........................................................................36

3.2.10 Displacements Process..........................................................................37

3.2.11 Loads Convergence Process .................................................................38

3.2.12 Stress and Buckling Process .................................................................40

3.3 Data Storage Requirements.................................................................................43

3.4 Performance Requirements.................................................................................43

3.5 System Design Constraints .................................................................................43

3.6 Software System Attributes ................................................................................44

Appendix............................................................................................................................45

4.0 References....................................................................................................................48
iv

 List of Tables

Table 1. HSCT4.0 Design Variable Data Summary..........................................................7

Table 2. Shape Design Variables.......................................................................................8

Table 3. Structural Design Variables.................................................................................9

Table 4. Geometry Constraints ........................................................................................10

Table 5. Weights Constraints...........................................................................................10

Table 6. Performance Constraints....................................................................................11

Table 7. Structural Constraints ........................................................................................11

Table 8. HSCT4.0 Fixed Data Summary.........................................................................12

Table 9. Load Condition Data..........................................................................................13

Table 10. HSCT4.0 Generated Data Summary..................................................................14

Table 11. Weight Types Assigned to Each Weight Mesh .................................................29

Table 12. Structural Weights Hierarchy ...........................................................................30

Table 13. Systems, Payload, and Fuel Weights Hierarchy...............................................31
v

 List of Figures

Figure 1. High-Speed Civil Transport. ...........................................................................50

Figure 2. Baseline HSCT4.0 Model................................................................................51

Figure 3. Optimization....................................................................................................52

Figure 4. Gradient-Based Optimizer...............................................................................53

Figure 5. Analysis. ..........................................................................................................54

Figure 6. Geometry. ........................................................................................................55

Figure 7. Weights............................................................................................................56

Figure 8. Nonlinear Corrections. ....................................................................................57

Figure 9. Rigid Trim. ......................................................................................................58

Figure 10. Polars. ..............................................................................................................59

Figure 11. Performance.....................................................................................................59

Figure 12. Ground Scrape.................................................................................................60

Figure 13. Displacements..................................................................................................61

Figure 14. Loads Convergence. ........................................................................................62

Figure 15. Stress and Buckling. ........................................................................................63

Figure 16. Shape Design Variables - Planform. ...............................................................64

Figure 17. Planform Control Points..................................................................................64

Figure 18. Shape Design Variables - Thickness, Camber, Twist, and Shear. ..................65

Figure 19. Structural Design Variable Zones. ..................................................................66

Figure 20. Composite Laminate Stacking Sequence. .......................................................67

Figure 21. Ply Orientations...............................................................................................67

Figure 22. Miscellaneous Geometry.................................................................................68

Figure 23. Airfoil Interior Thickness Constraints in Airfoil Cross-section......................68

Figure 24. Weights Meshes...............................................................................................69
1

Foreword

During the 1990s, the High Performance Computing and Communications Program (HPCCP)

sponsored a series of application projects that were based on the High Speed Civil Transport

(HSCT). With each new HSCT project, the application was made more complex by increasing

both the number and fidelity of the engineering analyses used. As the application complexity

increased, it became clear to the software developers that a more formal approach to software

development was needed in these projects.

This document presents the requirements for the HSCT4.0 application. The HSCT4.0 application

project was the only project in the HSCT series that documented the application requirements.

This was a much more difficult task than was anticipated by most project members, and not all

requirements were clearly documented before design and implementation; however, all project

members developed an appreciation for the benefits gained from documenting project requirements. The lessons learned from the HSCT4.0 requirements effort has formed an experience base

that will be applied towards future HPCCP projects.
2

1.0 Introduction

This document specifies the software requirements for the High Performance Computing and

Communication Program (HPCCP) High Speed Civil Transport (HSCT, fig. 1) application project

referred to as HSCT4.0. Information about the HSCT4.0 computing environment can be found in

references 1 and 2.

1.1 Purpose

This requirements document serves several purposes. First, it serves to establish an agreement

between the suppliers (Multidisciplinary Optimization Branch, Computational Modeling and

Simulation Branch, Analytical and Computational Methods Branch, and Computer Sciences Corporation) and the customer (HPCCP/Computational AeroSciences Team) as to what the HSCT4.0

application should do. Second, the document provides descriptions of the various functions (and

the relationships among them) that make up the multidisciplinary application. Any constraints on

the software design are included. The goal is to provide to the software developers the information

necessary to design and implement the system. Finally, the document provides a baseline for verification and validation activities and for later enhancements.

1.2 Scope

The objective of the HPCCP HSCT4.0 application project is to demonstrate the application of

high-performance computing techniques to the problem of multidisciplinary design optimization

(MDO) of a supersonic transport configuration, using high-fidelity analysis simulations. The

products of this project include a set of high-fidelity tools suitable for use in a conceptual to early

preliminary design environment. The use of a realistic baseline model will have the added benefit

that the results generated can be used to derive physically meaningful trends. The requirements

set forth in this document are for an HSCT configuration. (A different HSCT configuration will

require changes to the problem data defined later in this document.)

The project deliverable initially called for a software system capable of multidisciplinary analysis

and optimization of a typical configuration using shape and structural sizing variables. The system

was to provide the user a menu of options that include analysis, sensitivity analysis, and optimization for each contributing discipline as well as multidisciplinary analysis, sensitivity analysis and

optimization. The goals of the project were too ambitious for the project’s time period; therefore,

this document primarily covers the requirements for the multidisciplinary analysis that are suitable for an optimization process; this multidisciplinary analysis is the main project deliverable.

(The specific requirements can be found in section 3.0, in subsections 3.1.1, 3.2, 3.4, 3.5,

and 3.6.)

The HSCT4.0 application will be implemented within a framework. Although this document primarily focuses on the analysis capabilities, a set of requirements related to user interaction with

the framework were specified in early stages of the project. These requirements were later deemed

beyond the scope of the project and therefore were removed from the software requirements.
3

1.3 Acronyms, Abbreviations, and Nomenclature

1.3.1 Acronyms and Abbreviations

AIT Airfoil Interior Thickness

BC Boundary Condition

BLF Buckling Load Factor

CFD Computational Fluid Dynamics

CORBA Common Object Request Broker Architecture

FEM Finite Element Model

FIDO Framework for Interdisciplinary Design Optimization

GLW Gross Landing Weight

GTOW Gross Takeoff Weight

HPCCP High Performance Computing and Communication Program

HSCT High Speed Civil Transport

MDO Multidisciplinary Design Optimization

OEW Operational Empty Weight

SFI Stress Failure Index

SLP Sequential Linear Programming

c. g. center of gravity

1.3.2 Nomenclature

1-direction Fiber (0o) direction

2-direction Transverse to fiber (90o) direction

A direction Direction in which NA acts

B direction Direction in which NB acts

CL Coefficient of lift

CDi Coefficient of drag due to lift

CDv Coefficient of viscous drag

CDw Coefficient of wave drag

Cm Pitching moment coefficient

Dij Stiffness matrix terms (row i, column j)

F Approximate objective function

F0 Objective function

K0 FEM stiffness matrix for unloaded shape
4

KC FEM stiffness matrix for cruise shape

N Number of design variables

N11 In-plane normal stress resultant in 1-direction

N22 In-plane normal stress resultant in 2-direction

N12 In-plane shear stress resultant

NA Largest compressive normal stress resultant

NB Smallest compressive normal stress resultant

Nmn Bi-axial buckling load

NShear Shear buckling load

PM0 Ply mixture ratio for 0o plies

PM45 Ply mixture ratio for 45o plies

PM90 Ply mixture ratio for 90o plies

S Allowable shear stress in the principal material system

T Average thickness of upper and lower wing surfaces at a given

wing station

X Design variable vector

Design variable increment

XC Allowable compressive stress in the 1-direction

XT Allowable tensile stress in the 1-direction

YC Allowable compressive stress in the 2-direction

YT Allowable tensile stress in the 2-direction

a Length of the side of a finite element in the A direction

aC Aerodynamic cruise loads

aM Aerodynamic maneuver loads

b Length of the side of a finite element in the B direction

fC Cruise loads (aerodynamic + inertia)

fM Maneuver loads (aerodynamic + inertia)

g Approximate constraint vector

g0 Constraint vector

hmin Minimum AIT

r Distance between upper and lower wing surfaces (zUpper-zLower)

t0 Thickness of 0o ply

t45 Thickness of 45o ply

t90 Thickness of 90o ply

tCore Thickness of core

tFace Thickness of composite face sheet (t0+2t45+t90)

∆X
5

s0 Aircraft unloaded shape (FEM node location vector)

sC Aircraft cruise shape (FEM node location vector)

sM Aircraft maneuver shape (FEM node location vector)

u0 Cruise displacements using unloaded shape stiffness matrix (K0)

uC Cruise displacements using cruise shape stiffness matrix (KC)

uM Maneuver displacements using cruise shape stiffness matrix (KC)

x, y, z Principal coordinate axes (see fig. 2)

Vector of objective function gradients

Vector of constraint gradients

σ11 In-plane stress in 1-direction

σ22 In-plane stress in 2-direction

τ12 In-plane shear stress

1.4 Overview

The remainder of the document is organized as follows. Section 2 describes general factors that

affect the HSCT4.0 software requirements. Section 3 lists specific software requirements for the

HSCT4.0 application.

2.0 Overall Description

2.1 Product Perspective

The HSCT4.0 application is a natural continuation of earlier applications referred to as HSCT2.1

and HSCT3.5. The previous applications have made use of increasingly refined versions of the

Framework for Integrated Design Optimization (FIDO) system3, 4. The major components of the

FIDO system included the Parallel Virtual Machine based communications library, Data Manager,

Graphical User Interface, Executive module, and discipline modules.

During earlier stages of the project, the iSIGHT5, 6, 7 software was considered as an alternative

framework to FIDO for implementing the HSCT4.0 application. Because a number of difficulties

were encountered when applying the iSIGHT 3.0 software to the HSCT2.1 problem, a decision

was made to develop a follow-on to FIDO that would be based on Common Object Request Broker Architecture8 (CORBA) and Java. Specific requirements for the CORBA/Java framework,

referred to as CJOpt, are not included in this document. See references 1 and 2 for information on

CJOpt.

The HSCT4.0 application is a multidisciplinary system that is to be assembled from an existing

set of legacy codes; therefore, the software development focuses on the integration (rather than

internal details) of the legacy codes.

∂X

∂F

∂X

∂g
6

2.2 Product Functions and Constraints

The primary product of the HSCT4.0 application project is a multidisciplinary analysis that

includes the following capabilities (described in section 3.2):

geometric modeling and parameterization with consistent aerodynamic and structural models

(see fig. 2)

weights analysis

aerodynamics analysis (linear and nonlinear)

performance analysis

ground scrape analysis

structural analysis (displacements, stress, and buckling)

aeroelastic loads analysis

The HSCT4.0 application will execute in a distributed environment. In order to reduce the computation time, portions of the application will be executed in parallel.

3.0 Specific Requirements

3.1 HSCT4.0 Application Input and Output

In this section, the HSCT4.0 application data are described by three categories. First, the optimization data (design variables and constraints) are described. Second, the initial, fixed data (data

which does not change during the HSCT4.0 analysis) are described. Finally, the data generated

from an HSCT4.0 analysis are summarized. The design variables, initial and generated data items

are shown on the process diagrams, fig. 3 - fig. 15. These figures are described in detail in

section 3.2.

3.1.1 Optimization Data

This section describes the design variables and constraints to be used in the HSCT4.0 application.

The requirements for the optimization data are listed below. The requirements refer to the tables

that follow in this section.

Requirement #1 - Twenty-seven shape design variables defined in table 2 shall be used to

control the planform and airfoil shapes.

Requirement #2 - Two hundred forty-four structural design variables defined in table 3

shall be used to size the ply thicknesses and core thicknesses in 61 design variable zones.

Requirement #3 - The geometry constraints defined in table 4 shall be applied in the optimization.
7

Requirement #4 - The weights constraints defined in table 5 shall be applied in the optimization.

Requirement #5 - The performance constraints defined in table 6 shall be applied in the

optimization.

Requirement #6 - The structural constraints defined in table 7 shall be applied in the optimization.

3.1.1.1 Design Variables

The design variables to be used in the HSCT4.0 optimization include shape variables (table 2) and

structural variables (table 3). The HSCT4.0 application has 271 design variables for optimization

– 244 structural variables and 27 shape variables.

The design variables are updated by the Gradient-Based Optimizer process (fig. 4). Table 1 below

identifies the subprocesses that use the shape and structural design variables.

Shape Design Variables. All analysis geometry models (i.e., aerodynamics and structures) are

parameterized based on the locations of the shape design variables that are varied relative to the

reference geometry. Table 2 lists all of the shape design variables. Note that the ranges provided

are the initial estimates that can be used for optimization. The twenty-seven shape design variables consist of two sets. The first set contains the nine planform variables shown in fig. 16: the

root chord Cr , the outer break chord C2, the tip chord C3, the semispan distance to the outer break

B2, the leading edge sweep of the two outer wing panels SLE2 and SLE3, the total projected area of

the three wing panels At

, and the fuselage nose and tail lengths Ln and Lt. Note that the root chord

also sets the length of the center fuselage section, and that the wing semispan variable B3 is dependent on other planform variables, including the total projected area.

Table 1. HSCT4.0 Design Variable Data Summary

Data Description Used By:

design variables (shape)- 27 shape variables

Linear Aero Model Update,

Miscellaneous Geometry

Update, Nonlinear Aero

Surface Model Update, FE

Model Update

design variables (structural)- 244 structural variables

Section Property Update,

Structural Geometry, Buckling
8

Table 2. Shape Design Variables

Shape Design Variables (See Fig. 16)

Name Description (units) Estimated Range

Wing Planform Variables (See Fig. 16)

Lt

Tail length (distance from wing trailing edge to

the first tailframe) (inches) +5% of baseline value

Ln Fuselage nose length (inches) +5% of baseline value

Cr

Root chord (also panel 1 inboard chord)

(inches) +5% of baseline value

B2

Semispan distance to the outer break (panel 2)

(inches) +5% of baseline value

C2 Outer break chord (panel 2) (inches) +5% of baseline value

SLE2 Leading-edge sweep (panel 2) (degrees) +5% of baseline value

At total projected wing area (inches2) +5% of baseline value

C3 Tip chord (panel 3) (inches) +5% of baseline value

SLE3 Leading-edge sweep (panel 3) (degrees) +5% of baseline value

Airfoil Shape Variables (See Fig. 18a)

Thickness 1 (at 10% chord, 29.17% span) (inches) +10 inches

Thickness 2 (at 10% chord, 52.17% span) (inches) +10 inches

Thickness 3 (at 10% chord, 70.09% span) (inches) +10 inches

Thickness 4 (at 50% chord, 29.17% span) (inches) +10 inches

Thickness 5 (at 50% chord, 52.17% span) (inches) +10 inches

Thickness 6 (at 50% chord, 70.09% span) (inches) +10 inches

Camber 1 (at 10% chord, 29.17% span) (inches) +10 inches

Camber 2 (at 10% chord, 52.17% span) (inches) +10 inches

Camber 3 (at 10% chord, 70.09% span) (inches) +10 inches

Camber 4 (at 50% chord, 29.17% span) (inches) +10 inches

Camber 5 (at 50% chord, 52.17% span) (inches) +10 inches

Camber 6 (at 50% chord, 70.09% span) (inches) +10 inches

Airfoil Shape Variables (See Fig. 18b)

Twist 1 (at 52.17% span) (degrees) +5 degrees

Twist 2 (at 93.40% span) (degrees) +5 degrees

Twist 3 (at 100% span) (degrees) +5 degrees

Shear 1 (at 52.17% span) (inches) +10 inches

Shear 2 (at 93.40% span) (inches) +10 inches

Shear 3 (at 100% span) (inches) +10 inches
9

The changes in all planform locations under the influence of the planform design variables are

governed by a set of equations defining the locations of 22 control points (points 15 - 22 are used

for the engines). The control point locations are shown in fig. 17. For convenience, all points are

referenced to the aft end of the fuselage (point 0), because the fuselage end and the horizontal tail

will not change during the optimization.

The second set of shape design variables (see fig. 18) consists of airfoil control shape points that

define the wing thickness, camber, twist, and shear at a set of airfoil shape definition points. For

the HSCT4.0 application, the definition points for thickness and camber are identical (fig. 18a),

and the points for the wing twist line and the wing shear definition are identical (fig. 18b). The 18

airfoil shape variables are the vertical (z) perturbations of the camber, thickness, and shear from

the wing baseline shape and the wing twist perturbation from the baseline shape in constant y

planes. Note that the airfoil camber and thickness perturbations are smooth globally, while the

twist and shear perturbations are linear between the line definition points.

Structural Design Variables. The structural design variables are associated with the ply thicknesses and core thicknesses of the laminated composite finite elements in the skins of the fuselage

and the wing. Sixty-one design variable zones are sized by the design variables. As shown in

fig. 19, 39 zones are defined on the fuselage, and 22 zones are defined on the wing. The elements

in each zone are associated with a unique section property set. Each section property set is defined

as a 9-layer laminated composite (four ply sheets surrounding a layer of core material) as shown

in fig. 20. Four design variables are defined for each laminate. One design variable is the thickness

of the 0o plies in each face sheet. Another design variable is the thickness of the 45o plies in each

face sheet. The -45o plies have the same thickness as the 45o plies. The third design variable is the

thickness of the 90o plies in each face sheet. The last design variable in each design variable zone

is the thickness of the core. Local orientations for the composite laminate 0o ply direction on the

wing and fuselage are shown in fig. 21. The same ply thickness limits (given in table 3) are used

for all design variable zones.

Table 3. Structural Design Variables

Structural Design Variables per Zone (61 Zones)

Description (units) Minimum Thickness Maximum Thickness

0o ply thickness (inches) 0.00740 0.1000

45o ply thickness (inches) 0.00740 0.1000

90o ply thickness (inches) 0.00370 0.1000

Core thickness (inches) 0.20000 5.0000
10

3.1.1.2 Constraints

The tables in this section describe the geometry, weights, performance, and structural constraints

to be applied to the aircraft design.

For details on the calculation of the fuel volume, AIT ratios and ply-mixture ratios, see

section 3.2.3 “Geometry Process”. For details on the scrape lift constraints, see section 3.2.9

“Ground Scrape Process”.

For details on the weights constraints, see section 3.2.4 “Weights Process”.

Table 4. Geometry Constraints

 Geometry Constraints

# of type Description (units)

Range

Lower Bound Upper Bound

11 Fuel volume of tank (inches3) 0 NA

30 Airfoil Interior Thickness (AIT) ratio 0 NA

61 0o ply-mixture ratio 0.1 NA

61 45o ply-mixture ratio 0.4 0.6

61 90o ply-mixture ratio 0.1 NA

1 Takeoff scrape lift (pounds) Gross Takeoff

Weight (GTOW) NA

1 Landing scrape lift (pounds) Gross Landing

Weight (GLW) NA

Table 5. Weights Constraints

Weights Constraints

# of type Description (units)

Range

Lower Bound Upper Bound

14 Mesh Weights (pounds) 0 NA

9 Fuel Tank Weights (pounds) 0 NA

1 Operational Empty Weight (OEW)

(pounds) 0 NA
11

For more information on the performance constraints, see section 3.2.8 “Performance Process”.

The number of each structural constraint type is the number of sized elements (2260) multiplied

by the number of load conditions (7).

For details on the SFI and BLF calculations, see section 3.2.12 “Stress and Buckling Process”.

3.1.2 Fixed Input Data

Table 8 summarizes the fixed (would not change during a multidisciplinary optimization) input

data required for the various HSCT4.0 analysis processes. Each entry in the table briefly summarizes the data item and identifies the subprocesses that require the data. (Note that a different

HSCT configuration will require changes to the problem data defined in this document.)

Table 6. Performance Constraints

Performance Constraints

# of type Description (units)

Range

Lower Bound Upper Bound

1 Range (nautical miles) 5,000 NA

1 Balanced takeoff field length (feet) 0 10,000

1 Landing field length (feet) 0 10,000

1 Approach speed (knots) 0 155

1 Time to climb to cruise (hours) 0 1

1 Takeoff flyover noise (decibels) NA baseline flyover

noise level

1 Takeoff sideline noise (decibels) NA baseline sideline

noise level

1 Combined figure of merit noise (decibels) NA baseline figure of

merit noise level

Table 7. Structural Constraints

Structural Constraints

Range

# of type Description (non-dimensional) Lower Bound Upper Bound

15,820 Buckling Load Factor (BLF) for each element

and load condition in all design variable zones NA 1

15,820

Hoffman Stress Failure Index (SFI) for each

element (maximum layer-wise index) and load

condition in all design variable zones

NA 1
12

Table 8. HSCT4.0 Fixed Data Summary

Data Description Used By:

parameterized linear aero grids - linear aerodynamics grid resulting from the shape parameterization Linear Aero Model Update

parameterized miscellaneous grids - wireframe surface grid resulting from the shape parameterizationMiscellaneous Geometry

Update

parameterized nonlinear aero surface grids - nonlinear aerodynamics surface grid resulting from the shape parameterizationNonlinear Aero Surface

Model Update

parameterized FEM grid - set of finite element model (FEM) node

locations resulting from the shape parameterization FE Model Update

airfoil surface node data - paired upper and lower airfoil surface

FEM node numbers and minimum distance between them Structural Geometry

finite element data and BC’s - material properties, nonsized section

properties, element connectivities, rigid bars and elastic elements,

boundary conditions (BC’s)

Theoretical FEM Weight,

FEM Displacements, FEM

Stress, Buckling

reference weights data - as-built reference structural and nonstructural weights and weight distributions Built Up Weights

Mach number, angle of attack, tail deflection table - sets of values

used for the linear aerodynamics calculations; (different sets are used

for the Linear Aero subprocesses called from Nonlinear Corrections,

Rigid Trim, Polars, and Ground Scrape)

Linear Aero

aero reference data - reference span, mean aerodynamic chord, and

wing area

Linear Aero, Calculate CL ,

Nonlinear Aero, Performance, Scrape Lift

baseline nonlinear aero volume and surface grids - three distinct

computational fluid dynamics (CFD) volume grids that are used for

various load conditions and the surface grids that correspond to them

Volume Grid Adjustment

load condition data - See table 9

Calculate CL , Aero

Moment Equilibrium,

Induced Drag, Add Inertia

Loads

zero lift angle of attack - angle of attack at which no lift occurs for

the configuration Wave Drag

polars conditions - sets of CL, Mach, and altitude values at which the

drag calculations are evaluated

Wave Drag, Viscous Drag,

Induced Drag

performance reference data - engine, mission, and performance

analysis parameters Performance

scrape angle data - specified roll angle, minimum allowed clearance

distance, landing gear strokes Scrape Angle

augment loads data - internal cabin pressure, taxi forces, factor of

safety Augment Loads
13

3.1.2.1 Load Condition Data

Table 9 shows the load condition data used in the HSCT4.0 application. These eight load conditions represent critical design load conditions along with the associated wing flap settings, mass

case, load factor, Mach number, altitude, and equivalent air speed. Three flap settings are considered: (1) undeflected flaps set for flight at the cruise Mach number, (2) flaps set for flight at a high

subsonic Mach number, and (3) flaps set for flight at a low supersonic Mach number. The masses

are practical construction (i.e., realistic or “as-built”) weights that represent variations in payload

and fuel ranging from the OEW to maximum GTOW. These load conditions are used to define the

loads for structural analysis.

VC = cruise velocity; VD = dive velocity; VE = equivalent air speed; +HAA = positive high angle of

attack; -HAA = negative high angle of attack; A2 - A7 = load condition altitudes.

3.1.3 Generated Data

The following table summarizes the data generated by the HSCT4.0 analysis subprocesses. Each

entry in the table briefly summarizes the data item and identifies the subprocess that generates the

data and the subprocesses that require the data for input. Note that table entries are not included

for data items shown on the optimization process figures (figs. 3 and 4). Also, note that the Linear

Aero subprocess is used in several of the higher level Analysis processes (Nonlinear Corrections,

Rigid Trim, Polars, and Ground Scrape). The data generated by and used by Linear Aero are

determined by the process from which Linear Aero is invoked. If the data item is not applicable to

Linear Aero in all situations, the relevant parent processes are identified in parentheses.

Table 9. Load Condition Data

Load

Condition

 Number

VE Mass

Case

Load

Factor

(limit g’s)

Mach Number Altitude Wing Flap

Settings

1 Cruise Cruise Cruise Cruise Cruise Cruise

2 VC GTOW MIN High Subsonic A2 High Subsonic

3 VD GTOW MAX High Subsonic A3 High Subsonic

4 +HAA GTOW MAX High Subsonic A4 High Subsonic

5 VC GTOW MIN Low Supersonic A5 Low Supersonic

6 +HAA GTOW MAX Low Supersonic A6 Low Supersonic

7 -HAA GTOW MIN Low Supersonic A7 Low Supersonic

8 Taxi GTOW Taxi - - -
14

Table 10. HSCT4.0 Generated Data Summary

Data Description

Generated

By: Used By:

derived linear aero grids - grids (contained in the

wavedrag decks) that provide discrete representations

of the configuration surfaces in the form of coordinates

at each discrete point

Linear Aero

Model Update

Apply Linear Delta

Displacements, Linear

Aero (Rigid Trim,

Polars, Ground

Scrape), Wave Drag,

Viscous Drag

derived miscellaneous model - data for miscellaneous

processes

Miscellaneous Geometry UpdateFuel Geometry, Performance Geometry,

Scrape Geometry

derived nonlinear aero surface grids - surface grids

used to generate the derived nonlinear aerodynamics

volume grids

Nonlinear

Aero Surface

Model Update

Apply Nonlinear Delta

Displacements

derived FEM - finite element node locations which

define the cruise shape of the aircraft

FE Model

Update

Structural Geometry,

Theoretical FEM

Weight, Built Up

Weights, Loads Transfer, FEM Displacements, FEM Stress,

Buckling

derived section properties - sized element (composite)

section properties

Section Property Update

Theoretical FEM

Weight, FEM Displacements, FEM Stress

derived fuel tank geometry - coordinates of fuel tank

reference points

Fuel Geometry Built Up Weights

derived performance geometry - a coarse resolution,

wire frame geometry description

Performance

Geometry Performance

derived scrape geometry - number of airframe test

points, coordinates of landing-gear ground-touch points

and of selected airframe test points

Scrape Geometry Scrape Angle

ply mixture and airfoil interior thickness ratios -

data used for constraints

Structural

Geometry

Calculate Objective

and Constraints

FEM weight - theoretical FEM nodal weights Theoretical

FEM Weight Built Up Weights

fuel weights - weight of fuel in tanks (for available fuel

volume and tank fill ratios)

Built Up

Weights Performance

cruise weight (total) - total weight at cruise; cruise

weight with aft center of gravity (c. g.) limit (OEW +

payload + cruise fuel weight)

Built Up

Weights

Calculate CL , Calculate Nonlinear Corrections, Aero Moment

Equilibrium

cruise weight (nodal) - nodal weight at cruise Built Up

Weights

Add Inertia Loads
15

cruise c. g. - axial location of c. g. at cruise Built Up

Weights

Calculate Nonlinear

Corrections, Aero

Moment Equilibrium,

Linear Aero (Polars)

GTOW (total) - total weight at takeoff; maximum

GTOW with forward c. g. limit (OEW + payload +

GTOW fuel weight)

Built Up

Weights

Calculate CL , Calculate Nonlinear Corrections, Aero Moment

Equilibrium, Performance

GTOW (nodal) - nodal weight at takeoff Built Up

Weights Add Inertia Loads

GTOW c. g. - axial location of c. g. at takeoff Built Up

Weights

Calculate Nonlinear

Corrections, Aero

Moment Equilibrium

OEW (total) - the sum of structural, nonstructural, and

systems weights

Built Up

Weights

Calculate Objective

and Constraints

displaced linear aero grid - derived linear aerodynamics grid modified by the delta displacements

Apply Linear

Delta Displacements

Linear Aero (Nonlinear Corrections, Rigid

Trim)

displaced nonlinear aero surface grid - derived nonlinear aerodynamics surface grid modified by the delta

displacements

Apply Nonlinear Delta Displacements

Volume Grid Adjustment

displaced nonlinear aero volume grid - CFD volume

grid based on the displaced nonlinear aerodynamics

surface grids

Volume Grid

Adjustment Nonlinear Aero

target CL - required lift coefficient based on total

weight Calculate CL Nonlinear Aero

linear pressures, forces, and moments - table of linear aerodynamics surface pressure coefficients and total

force and moment coefficients for a set of angles of

attack

Linear Aero

(Nonlinear

Corrections)

Calculate Nonlinear

Corrections

nonlinear pressures, forces, and moments - nonlinear

aerodynamics surface pressure coefficients and total

force and moment coefficients

Nonlinear

Aero

Calculate Nonlinear

Corrections

nonlinear corrections - nodal surface pressure coefficient differences between the nonlinear aerodynamics

and the matching-force linear aerodynamics pressures

Calculate

Nonlinear

Corrections

Apply Nonlinear Corrections

linear pressures - table of linear aerodynamics surface

pressure coefficients for a set of angles of attack

Linear Aero

(Rigid Trim)

Apply Nonlinear Corrections

corrected pressures - table of linear aerodynamics surface pressure coefficients, modified by nonlinear corrections, for a set of angles of attack

Apply Nonlinear Corrections

Aero Moment Equilibrium

Table 10. (Continued) HSCT4.0 Generated Data Summary

Data Description

Generated

By: Used By:
16

trimmed CL , CDi (cruise)- trimmed cruise target CL

and resulting CDi from linear aerodynamics with nonlinear corrections.

Aero Moment

Equilibrium Induced Drag

trimmed aero loads - trimmed aerodynamics panel

forces generated for target CL, resulting from linear

aerodynamics with nonlinear corrections

Aero Moment

Equilibrium Loads Transfer

table of CDw - wave drag coefficients for a set of Mach

numbers Wave Drag Assemble Polars

table of CDv - viscous drag coefficients for a set of

Mach numbers and altitudes Viscous Drag Assemble Polars

table of CL , CDi , Cm - linear aerodynamics lift and drag

force coefficients and pitching moment coefficient for a

set of angles of attack and Mach numbers

Linear Aero

(Polars) Induced Drag

table of trimmed CL , CDi - linear aerodynamics lift

and drag force coefficients at the trim angle of attack

for a set of Mach numbers

 Induced Drag Assemble Polars

mission tables -CDi , CDv , and CDw at the polars conditionsAssemble

Polars Performance

performance metrics - range, balanced takeoff field

length, landing field length, takeoff speed, approach

speed, landing speed, time to climb to cruise, takeoff

noise (flyover, sideline, and combined)

Performance

Calculate Objective

and Constraints,

Scrape Lift

scrape angles of attack - computed angles of aircraft

at scrape conditions on takeoff and landing Scrape Angle Linear Aero (GroundScrape)

scrape CL - computed lift coefficients at scrape conditions on takeoff and landing

Linear Aero

(Ground

Scrape)

Scrape Lift

ground scrape responses - takeoff scrape lift, landing

scrape lift Scrape Lift Calculate Objectiveand Constraints

aero loads - aerodynamic forces distributed to FEM

nodes

Loads Transfer Add Inertia Loads

displacement loads - applied forces (combined aerodynamic and inertia) at FEM nodesAdd Inertia

Loads FEM Displacements

displacements - FEM nodal displacements FEM Displacements

Calculate Delta Displacements

delta displacements - delta displacements at FEM

nodes (displacements for maneuver conditions minus

cruise displacements)

Calculate

Delta Displacements

Apply Linear Delta

Displacements, Apply

Nonlinear Delta Displacements

converged loads (2-7)- converged displacement loads

for load conditions 2-7

Loads Convergence Augment Loads

augmented loads (2-8) - combination of converged

loads and augment loads data for load conditions 2-8

Augment

Loads FEM Stress

Table 10. (Continued) HSCT4.0 Generated Data Summary

Data Description

Generated

By: Used By:
17

3.2 Functions

The functional requirements for the HSCT4.0 application are defined in this section. In the subsections that follow, the application functions (or processes) are summarized with a series of process diagrams and diagram descriptions. These diagrams include fig. 3 - fig. 15. The diagrams

show the basic information flow among processes included in the multidisciplinary analysis and

optimization. A description is provided for each figure in the subsections to follow.

In the diagrams, circles are used to indicate processes (or functions) and arrows show the principal data that is passed between processes. A shaded circle refers to a process that may be further

expanded into a set of subprocesses. An unshaded circle represents a lowest level subprocess (or

function). A process outlined with dashes indicates a process that may or may not execute during

an analysis. By convention, this document will use italics for process names.

The data are distinguished several ways in the diagrams. Data items enclosed within two solid

lines indicate fixed data that do not change throughout the optimization. The data generated during each optimization cycle are labeled in two different notations on the diagrams. If the data item

is generated by another process that is not shown on an individual diagram, that data item is

enclosed within a shaded rectangular box. Otherwise, the data item is labeled beside the arrow

exiting the process that generated it. For example, in the Weights process diagram (fig. 7), the

“derived FEM” data item is computed by the Geometry process and therefore is enclosed within a

shaded box. The Analysis process diagram (see fig. 5) has been simplified to show only enough

data to indicate the sequencing among the highest level processes.

Note that fig. 3 gives an overview of the optimization process, where the two most significant processes are the Analysis and the Sensitivity Analysis processes. The details of the Sensitivity Analysis process are not covered in this document, because the final project deliverables did not include

the optimization. This document gives a description of the optimization process, but the focus of

the document is to describe the requirements for the Analysis process.

The following list summarizes the functional requirements for the HSCT4.0 application processes

and subprocesses. Each requirement refers to the sections that describe that requirement in more

detail. When appropriate, the existing engineering analysis code selected to perform a particular

function is identified. The appendix provides descriptions for each of the codes selected, except

for the optimization codes JOPT and CONMIN. If no codes are specified for a particular requirement, the code must be developed according to that requirement.

stress resultants - stress resultants on sized elements FEM Stress Buckling

buckling load factors - buckling load factors on sized

elements Buckling Calculate Objectiveand Constraints

stress failure indices - maximum layer-wise stress failure indices on sized elements FEM Stress Calculate Objective

and Constraints

Table 10. (Continued) HSCT4.0 Generated Data Summary

Data Description

Generated

By: Used By:
18

Requirement #7 - The HSCT4.0 optimization process (see section 3.2.1 “Optimization

Process”) shall minimize GTOW subject to the constraints and design variable limits

defined in section 3.1.1. This requirement has been deferred.

Requirement #8 - The Calculate Objective and Constraints subprocess (see section 3.2.1

“Optimization Process”) shall gather the responses from the analysis processes and calculate the objective function and constraints for the optimizer. This requirement has been

deferred.

Requirement #9 - The Accept Design and Set Move Limits subprocess (see section 3.2.1

“Optimization Process”) shall determine the move limit factor for the design variables.

The move limits will be determined manually based on the criteria for design acceptance

and rejection. This requirement has been deferred.

Requirement #10 - The Gradient-Based Optimizer process (see section 3.2.1 “Optimization Process”) shall determine the values for the set of design variables that optimize the

objective function, subject to the set of constraints. The JOPT and CONMIN codes shall

be used for these calculations. This requirement has been deferred.

Requirement #11 - The Linear Aero Model Update subprocess (see section 3.2.3 “Geometry Process”) shall deform the linear aerodynamics grids to incorporate the changes in the

shape design variables. The GP code will be used for this calculation.

Requirement #12 - The Nonlinear Aero Surface Model Update subprocess (see section

3.2.3 “Geometry Process”) shall deform the nonlinear aerodynamics grids to incorporate

the changes in the shape design variables. The GP code will be used for this calculation.

Requirement #13 - The Miscellaneous Geometry Update subprocess (see section 3.2.3

“Geometry Process”) shall deform the miscellaneous geometry grid to incorporate the

changes in the shape design variables. The GP code will be used for this calculation.

Requirement #14 - The FE Model Update subprocess (see section 3.2.3 “Geometry Process”) shall derive the FEM grid to incorporate the changes in the shape design variables.

The GP code will be used for this calculation.

Requirement #15 - The Scrape Geometry subprocess (see section 3.2.3 “Geometry Process”) shall derive the scrape geometry.

Requirement #16 - The Fuel Geometry subprocess (see section 3.2.3 “Geometry Process”) shall derive the fuel tank volumes.

Requirement #17 - The Performance Geometry subprocess (see section 3.2.3 “Geometry

Process”) shall derive the performance geometry.

Requirement #18 - The Section Property Update subprocess (see section 3.2.3 “Geometry

Process”) shall derive the laminated composite shell property sets for the sixty-one design

variable zones from the structural design variables.
19

Requirement #19 - The Structural Geometry subprocess (see section 3.2.3 “Geometry Process”) shall derive the ply-mixture ratios and AIT ratios.

Requirement #20 - The Theoretical FEM Weight subprocess (see section 3.2.4 “Weights

Process”) shall compute the theoretical FEM weights at the nodes. The GENESIS® code

(Vanderplaats Research & Development, Inc.) shall be used for this calculation.

Requirement #21 - The Built Up Weights subprocess (see section 3.2.4 “Weights Process”)

shall compute the as-built total weight, nodal weights, and the c. g. for the cruise and

GTOW mass cases.

Requirement #22 - The Nonlinear Corrections subprocess, Apply Linear Delta Displacements (see section 3.2.5 “Nonlinear Corrections Process”), shall deform the linear aerodynamics surface grid for a given load condition. The S2W code shall be used for this

calculation.

Requirement #23 - The Nonlinear Corrections subprocess, Linear Aero (see section 3.2.5

“Nonlinear Corrections Process”), shall calculate linear aerodynamics characteristics for

the current aircraft surface shape at a given load condition for specified flight conditions.

The USSAERO code shall be used for this calculation.

Requirement #24 - The Apply Nonlinear Delta Displacements subprocess (see

section 3.2.5 “Nonlinear Corrections Process”) shall deform the nonlinear aerodynamics

surface grid for a given load condition. The CSCMDO code shall be used for this calculation.

Requirement #25 - The Volume Grid Adjustment subprocess (see section 3.2.5 “Nonlinear

Corrections Process”) shall adjust the nonlinear aerodynamics volume grid for the new

derived surface grid. The CSCMDO code shall be used for this calculation.

Requirement #26 - The Calculate CL subprocess (see section 3.2.5 “Nonlinear Corrections

Process”) shall calculate the aircraft lift coefficient, CL , for a given aircraft weight and

load condition.

Requirement #27 - The Nonlinear Aero subprocess (see section 3.2.5 “Nonlinear Corrections Process”) shall solve the Euler/Navier-Stokes equations for a given load condition on

the derived nonlinear aerodynamics volume grid. The CFL3D code shall be used for this

calculation.

Requirement #28 - The Calculate Nonlinear Corrections subprocess (see section 3.2.5

“Nonlinear Corrections Process”) shall calculate the nodal-pressure difference (on the linear aerodynamics grid) between the nonlinear and linear aerodynamics calculations. The

L2NL code shall be used for this calculation.

Requirement #29 - The Rigid Trim subprocess, Linear Aero (see section 3.2.6 “Rigid Trim

Process”), shall calculate linear aerodynamics characteristics for the current aircraft sur-
20

face shape at a given load condition for specified flight conditions. The USSAERO code

shall be used for this calculation.

Requirement #30 - The Apply Nonlinear Corrections subprocess (see section 3.2.6 “Rigid

Trim Process”) shall add the nonlinear correction nodal pressures to the linear aerodynamics nodal pressures, resulting in a corrected pressure distribution. The TRIM_NLC code

shall be used for this calculation.

Requirement #31 - The Aero Moment Equilibrium subprocess (see section 3.2.6 “Rigid

Trim Process”) shall calculate the angle of attack and tail deflection that trim the aircraft

for a given load condition and weight. The induced drag coefficient and the loads are interpolated for these angles. The TRIM_NLC code shall be used for this calculation.

Requirement #32 - The Wave Drag subprocess (see section 3.2.7 “Polars Process”) shall

calculate the supersonic wave drag contribution to the total configuration drag coefficient.

The AWAVE code shall be used for this calculation.

Requirement #33 - The Viscous Drag subprocess (see section 3.2.7 “Polars Process”) shall

calculate the surface skin friction drag contribution to the total configuration drag coefficient. The CDF1 code shall be used for this calculation.

Requirement #34 - The Polars subprocess, Linear Aero (see section 3.2.7 “Polars Process”), shall calculate linear aerodynamics characteristics for the aircraft surface shape at

cruise for specified flight conditions. The USSAERO code shall be used for this calculation.

Requirement #35 - The Induced Drag subprocess (see section 3.2.7 “Polars Process”) shall

calculate the lift-dependent drag contribution to the total configuration drag coefficient.

Requirement #36 - The Assemble Polars subprocess (see section 3.2.7 “Polars Process”)

shall generate the drag polar mission tables.

Requirement #37 - The Performance subprocess (see section 3.2.8 “Performance Process”) shall perform a mission analysis. The FLOPS code shall be used for this calculation.

Requirement #38 - The Scrape Angle subprocess (see section 3.2.9 “Ground Scrape Process”) shall calculate the maximum pitch angle that can be attained for each specified

clearance, stroke and roll angle.

Requirement #39 - The Ground Scrape subprocess, Linear Aero (see section 3.2.9

“Ground Scrape Process”), shall calculate linear aerodynamics characteristics for the current aircraft surface shape at takeoff and landing conditions. The USSAERO code shall be

used for this calculation.

Requirement #40 - The Scrape Lift subprocess (see section 3.2.9 “Ground Scrape Process”) shall calculate the lift forces available at the maximum angles of attack for takeoff

and landing conditions.
21

Requirement #41 - The Loads Transfer subprocess (see section 3.2.10 “Displacements

Process”) shall transfer the z direction aerodynamic loads to the FEM using a method that

conserves the total force and moments. The A2S code shall be used for this calculation.

Requirement #42 - The Add Inertia Loads subprocess (see section 3.2.10 “Displacements

Process”) shall add inertia loads to aerodynamic loads for a given load condition. The A2S

code shall be used for this calculation.

Requirement #43 - The FEM Displacements subprocess (see section 3.2.10 “Displacements Process”) shall calculate displacements for a given load condition. The GENESIS®

code shall be used for this calculation.

Requirement #44 - The Loads Convergence subprocess, Apply Linear Delta Displacements (see section 3.2.11 “Loads Convergence Process”), shall add delta displacements at

aerodynamic grid nodes to the derived linear aerodynamics grid to produce the displaced

linear aerodynamics grid for the given load condition. The S2W code shall be used for this

calculation.

Requirement #45 - The Rigid Trim process invoked from the Loads Convergence subprocess (see section 3.2.11 “Loads Convergence Process”) shall generate trimmed aerodynamics pressures for a given load condition. Refer to section 3.2.6 “Rigid Trim Process”

for a description of the Rigid Trim process.

Requirement #46 - The Displacements process invoked from the Loads Convergence subprocess (see section 3.2.11 “Loads Convergence Process”) shall generate the FEM nodal

displacements for a given load condition. Refer to section 3.2.10 “Displacements Process” for a description of the Displacements process.

Requirement #47 - The Calculate Delta Displacements subprocess (see section 3.2.11

“Loads Convergence Process”) shall subtract the FEM nodal displacements for the cruise

condition from nodal displacements for a given load condition.

Requirement #48 - The Augment Loads subprocess (see section 3.2.12 “Stress and Buckling Process”) shall augment the converged loads for the FEM Stress subprocess.

Requirement #49 - The FEM Stress subprocess (see section 3.2.12 “Stress and Buckling

Process”) shall perform a finite element analysis to compute SFIs and stress resultants for

a set of augmented loads. The GENESIS® code shall be used for this calculation.

Requirement #50 - The Buckling subprocess (see section 3.2.12 “Stress and Buckling Process”) shall compute BLFs for FEM elements using stress resultants for a set of augmented loads.

3.2.1 Optimization Process

Although it is not required that optimization be implemented, it is described here to provide context for the HSCT4.0 analysis. The HSCT4.0 optimization problem is described as:
22

Minimize: GTOW

Subject to:

Side Constraints (upper and lower limits for design variables) (tables 2 and 3)

Geometry Constraints (table 4)

Weights Constraints (table 5)

Performance Constraints (table 6)

Structural Constraints (table 7)

The optimization procedure is shown in fig. 3. Refer to section 3.5 “System Design Constraints”

for a discussion on the optimization method choice for the HSCT4.0 application. The GradientBased Optimizer process and the subprocesses, Calculate Objective and Constraints and Accept

Design and Set Move Limits, are described in this section. The Analysis process is described in

section 3.2.2. No requirements for the Sensitivity Analysis process have been defined for this

project.

After an initialization process, the optimization proceeds using a Sequential Linear Programming

(SLP) technique, where the outer loop shown in fig. 3 represents a “design cycle”. A design cycle

uses the following processes: Analysis, Calculate Objective and Constraints, Accept Design and

Set Move Limits, Sensitivity Analysis, and Gradient-Based Optimizer. The Analysis process produces the multidisciplinary responses, which are used by the Calculate Objective and Constraints

subprocess to form the objective function and constraints. The Accept Design and Set Move Limits subprocess either accepts or rejects the current design and may adjust the design variable move

limits; this subprocess requires manual intervention by the designer. The Sensitivity Analysis process evaluates the gradients of the objective function and constraints, which are used by the Gradient-Based Optimizer process to compute an approximate objective function and approximate

constraints. Errors which may be introduced by use of the approximate analysis are controlled by

imposing “move limits” on each design variable during the iteration process. A move limit, which

is specified as a fractional change of each design variable value, is imposed as an upper and lower

design variable bound.

The remainder of this section briefly describes the overall Optimization process. Section 3.2.1.1

describes each subprocess in more detail. The HSCT4.0 optimization procedure is conducted as

follows. Prior to the first cycle, initial values for the design variables and move limits are set, and

the analysis, objective function, and constraints are calculated. Then this design is reviewed for

acceptance and possible move limit adjustments. (See criteria discussion in the next section for

more detail on decision making.) Note that on cycle=0, even if this first design is infeasible, the

design is “accepted” and the move limits are not adjusted.

If the design is accepted, the current (accepted) set of design variables along with the corresponding function and gradient data will be used in the next execution of the Gradient-Based Optimizer

process. The Accept Design and Set Move Limits subprocess may or may not adjust the move limits. The cycle number is updated and the solution is checked for convergence. If the optimization

process has converged, the HSCT4.0 application calculation is terminated. Otherwise, the cycle
23

continues with a gradient calculation. The gradients are used to form the approximate functions

that are used in the Gradient-Based Optimizer process.

On the other hand, if the design is rejected, the cycle number is not updated, the move limits are

decreased, and the most recently accepted design variables, along with the corresponding function

and gradient data, are used as input to the Gradient-Based Optimizer process. This process is

repeated until the optimization convergence criteria are met. The HSCT4.0 optimization procedure will be considered converged when the change in the objective function over three consecutive cycles is within a specified tolerance and all of the constraints are satisfied.

3.2.1.1 Optimization Subprocesses

The Calculate Objective and Constraints subprocess gathers responses from the Analysis process

to calculate the objective function, F, and the constraint vector, g. The constraints described in

section 3.1.1.2 are used to form g. The Sensitivity Analysis process computes the gradients of the

objective function and constraints.

The Accept Design & Set Move Limits subprocess is an interactive subprocess in which the

designer chooses whether to accept or reject the current set of design variable values and adjusts

the move limit values if necessary according to the criteria described below. Note that the software must have a stop and restart capability to perform this function.

The criteria for design acceptance and rejection involves the designer examining the current

objective function and constraints, the approximate objective function and constraints, and the

previous cycle’s objective function and constraints. Note that the term “current objective function

and constraints” refers to the values obtained from the Analysis process based on the current set of

design variables. The term “previous objective function and constraints” refers to the values

obtained from the Analysis process based on the previous set of design variables. The term

“approximate objective function and constraints” refers to the values obtained from the GradientBased Optimizer process based on the current set of design variables. The first priority for acceptance will be improved constraint satisfaction followed by reduction in objective function. The

objective function and constraint approximation values (equations 1 and 2 below) are compared to

the actual values and the move limits are adjusted according to the criteria for design acceptance

and rejection outlined below. (Recall that the objective function will be minimized.)

Assuming all constraints are satisfied at the beginning of the current cycle, then at the end of the

current cycle:

1. If all current constraints are satisfied and the current objective function decreases, then the current set of design variables is accepted, and the move limits are not adjusted.

2. If all current constraints are satisfied and the current objective function increases, then the current set of design variables is rejected, move limits are decreased, and the cycle is repeated

with the previous set of design variables.
24

3. If there are current constraint violations and the current objective function increases, then the

current set of design variables is rejected, move limits are decreased, and the cycle is repeated

with the previous set of design variables.

4. If there are small current constraint violations and the current objective function decreases, then

the violated constraints need to be examined in greater depth. If it is felt that it would be easy

for the optimizer to satisfy the violated constraints, then the current set of design variables is

accepted. The approximate objective function and approximate constraints are also examined

to see if the move limits need to be reduced.

Assuming some constraints are violated at the beginning of the current cycle, then at the end of

the current cycle:

1. If all current constraints are satisfied and the current objective function decreases, then the current set of design variables is accepted, and move limits are not adjusted.

2. If all current constraints are satisfied and the current objective function increases, then the current set of design variables is accepted, and move limits are not adjusted.

3. If there are current constraint violations and the current objective function increases, then if the

largest current constraint violations are less than at the beginning of the cycle, the current set of

design variables is accepted (even if the number of violated constraints increases), and move

limits are not adjusted.

4. If the current constraint violations are greater and more numerous than at the beginning of the

cycle, then the current set of design variables is rejected, the move limits are decreased, and the

cycle is repeated with the previous set of design variables.

Note that in the above criteria, in cases where move limits are not adjusted by the designer, the

designer may make a judgement call based on his previous optimization experience to decrease

the move limits. This is usually the case when the designer feels that the approximate constraints

and objective function are no longer “good” approximations of the current constraints and objective function.

The Gradient-Based Optimizer process, expanded in fig. 4, consists of a general purpose optimization program and an approximate analysis, which is used to reduce the number of full analyses

during the optimization procedure. The approximate analysis is used to approximate the objective

function and constraints with linear Taylor Series expansions using gradients of the objective

function and constraints (computed in the Sensitivity Analysis process in each design cycle). The

approximate objective function value and approximate constraint values are described by the following two equations, respectively.

(1) F F0 ∂Xi

∂F

0

∆Xi

i = 1

N

= + ∑
25

(2)

where F0 is the objective function (computed by the Analysis process), F is the approximate

objective function, g0 is the constraint vector (computed by the Analysis process), g is the approximate constraint vector, X is the design variable vector, is the design variable increment (controlled by the move limits), N is the number of design variables, is the vector of objective

function gradients, and is the vector of constraint gradients. The assumption of linearity will not

introduce a large error into the analysis, provided the changes are small. The loop shown in

fig. 4 represents an “iteration”.

3.2.2 Analysis Process

A high level view of the procedure required for HSCT4.0 multidisciplinary analysis is shown in

fig. 5. Descriptions of the Analysis processes appear in the sections to follow. For the HSCT4.0

analysis, there are eight load conditions (see table 9), but these are applied to only three distinct

geometry models. The models are distinguished by flap settings: cruise, high subsonic, and low

supersonic. These flap settings have been modeled for linear and nonlinear aerodynamics analyses; however, the FEM analysis uses only the cruise flap settings for all load conditions.

The primary engineering disciplines used in the HSCT4.0 analysis include geometry, weights,

aerodynamics, structures, performance, and ground scrape. All discipline models are derived from

a single CAD model. Weight is calculated using a combination of reference as-built weights and

theoretical FEM weights. The aeroelastic calculation uses a linear structural analysis coupled with

a variable-fidelity aerodynamics analysis. The variable-fidelity aerodynamics analysis uses a combination of linear aerodynamics with corrections based on nonlinear aerodynamics. Linear aerodynamics, without nonlinear corrections, are also used in both the performance and ground scrape

disciplines. The performance computation uses the linear aerodynamics calculations in addition to

empirical data to perform a mission analysis. The ground scrape computations are a simple algebraic computation based on the linear aerodynamics in ground effect.

The Analysis process begins with the Geometry process, which derives the updated geometries,

grids, and section properties from the baseline geometries and grids using the design variable values. Once the Geometry process has completed, the Weights process may proceed.

The Weights process computes the theoretical FEM weight, the total as-built weights, the nodal

weights, and the c. g. locations for the cruise and takeoff mass cases. These data are needed before

the Nonlinear Corrections and Rigid Trim processes can be executed.

The Nonlinear Corrections process is the first of two stages in what is called a variable-fidelity

aerodynamics analysis approach. For efficiency during the Analysis process, this approach uses

only one computationally intensive, nonlinear CFD calculation per load condition. A nonlinear

correction is then calculated relative to an appropriate linear aerodynamics calculation. In the second stage of the approach, this correction will be applied each time a linear aerodynamics calculag g0 ∂Xi

∂g

0

∆Xi

i = 1

N

= + ∑

∆X

∂X

∂F

∂X

∂g

∆X
26

tion is made during the subsequent Rigid Trim and Loads Convergence processes. Because of the

large time for the nonlinear CFD computation, the Nonlinear Corrections process will not be executed in every Analysis cycle after the first cycle. (This is indicated by the dashed lines in fig. 5.)

Using the most recent nonlinear corrections, the Rigid Trim process calculates trim conditions for

the cruise condition that will be used as reference conditions for subsequent calculations. The trim

conditions are the angle of attack and tail deflection that provide lift equal to weight and no net

pitching moment. (Note that the Rigid Trim process is used again for other load conditions in the

Loads Convergence process.) Once the Rigid Trim process has completed, the Analysis process

divides into two branches, which may be computed in parallel.

In the left branch of the Analysis process, the Polars process is followed by the Performance and

Ground Scrape processes. The Polars process uses the cruise shape for all of its aerodynamic calculations. The cruise results from Rigid Trim are augmented by a set of linear aerodynamics drag

polars calculated for a set of Mach numbers and lift coefficients. The Polars process provides

input for the range calculation in the Performance process. The Performance process also calculates the takeoff and landing speeds, in addition to other metrics. These speeds are used in the

Ground Scrape process to calculate the takeoff and landing lift that are achievable with the tail at

the minimum clearance from the runway.

In the right branch of the Analysis process, the Displacements process is followed by the Loads

Convergence and Stress and Buckling processes. The Displacements process calculates the FEM

displacements under the trimmed cruise loads for use in the Loads Convergence process. Then,

the Loads Convergence process performs the aeroelastic trim calculations for the six noncruise

load conditions (2-7). (Within the Loads Convergence process, the Rigid Trim and Displacements

processes are used again at each of these load conditions.) This resulting set of loads, along with

the load representing taxi, is used in the Stress and Buckling process to provide stress and buckling response values.

3.2.3 Geometry Process

The Geometry process is displayed in fig. 6. The Geometry process calculates the geometry constraints and provides shape parameterization for the HSCT4.0 application. An important feature

of any shape optimization formulation is the means to parameterize the geometry in terms of a set

of user-defined design variables that can be systematically varied during the optimization to

improve the design. The parameterization is done once after the shape design variables have been

selected. (Reference 9 provides a survey of shape parameterization techniques for multidisciplinary optimization and highlights some emerging ideas.) As shown in fig. 6, the Geometry process consists of nine subprocesses: Linear Aero Model Update, Miscellaneous Geometry Update,

Nonlinear Aero Surface Model Update, FE Model Update, Fuel Geometry, Performance Geometry, Scrape Geometry, Section Property Update, and Structural Geometry. Each subprocess is

described in the next section.

A discussion of the shape design variables is provided in section 3.1.1.1. The shape design variables and geometry constraints are listed in table 2 and table 4, respectively.
27

3.2.3.1 Geometry Subprocesses

The Linear Aero Model Update, Miscellaneous Geometry Update, Nonlinear Aero Surface Model

Update, and FE Model Update subprocesses, shown in fig. 6, use the approach described in reference 9 to modify the geometry of the analysis models. This approach provides internal FEM grids

consistent with aerodynamic surface grids. All analysis geometry models (i.e., aerodynamics and

structures) are parameterized based on the locations of the shape design variables that are varied

relative to the reference geometry. For each design cycle, the “derived grids/models” are generated by applying the shape design variable values to each of the parameterized grids. Recall that

there are three aerodynamic shapes, one for each flap setting.

The output from the Miscellaneous Geometry Update process, shown in fig. 22, consists of a set

of curves that defines a wire-frame description of the model for the various miscellaneous geometry subprocesses. The Fuel Geometry subprocess uses the locations of sets of points at the corners

of the fuel tanks to calculate the total and individual fuel volumes of the tanks. The Performance

Geometry subprocess uses discretized curves to calculate a wide variety of geometric information

needed as input for the Performance process; examples are the wing span, sweep angles, and

aspect ratio, the wing chords and maximum thickness at several span stations, and the fuselage

dimensions. The Scrape Geometry subprocess uses the location of selected points on the aircraft

surface to calculate the pitch angle for which one or more of these points touches the ground.

Two Geometry subprocesses generate the FEM data. The FE Model Update subprocess updates

the finite element node locations, and the Section Property Update subprocess updates the finite

element section properties. The FE Model Update subprocess uses the 27 shape design variables

to produce a set of finite element node locations. The Section Property Update subprocess uses

the 244 structural design variables (table 3) to produce 61 laminated composite shell property

sets.

Both the ply-mixture and AIT ratios are computed by the Structural Geometry subprocess. (Refer

to section 1.3.2 for definitions of the symbols used below.) The ply-mixture ratios are computed

at each of the sixty-one design variable zones (see fig. 19 and fig. 20) using equations 3 - 5.

(3)

(4)

(5)

The AIT ratios are computed at each of 30 wing stations (each with a corresponding upper and

lower airfoil surface node, see fig. 23) from the equation below:

(6)

where hmin = 0 for HSCT4.0.

PM0 t0 tFace = ⁄

PM45 2t45 tFace = ⁄

PM90 t90 tFace = ⁄

AIT 1

hmin – r

T = + -----------------
28

3.2.4 Weights Process

The Weights process is displayed in fig. 7. The Weights process computes the as-built nodal and

total weights, fuel weights, and the c. g. location of a given aircraft configuration.

A particular aircraft geometry is specified with the shape design variables (table 2), which define

the aircraft cruise shape. A particular mass distribution is defined using shape design variables,

structural design variables, and fuel loading. The term “fuel loading” implies both the weight and

the location of the fuel. The shape design variables may affect the takeoff and cruise fuel loadings

by changing the available fuel volume.

The total theoretical FEM weights represent only about 20 percent of the total aircraft as-built

weight. As such, the total theoretical FEM weight is incomplete for use as an optimization objective function, because the percentage change in the theoretical FEM weight is much greater than

the percentage change in the aircraft total as-built weight. Therefore, it is required that the Weights

process estimate other aircraft weights to provide a total as-built weight.

The Weights process uses as-built nodal weights for a reference aircraft and theoretical FEM

weights to provide a reasonable estimate of the as-built weight. The process uses a set of as-built

nodal weights for the reference airplane geometry, including the takeoff and cruise fuel loadings

that were generated by the process described in reference 10. The reference data includes fuel

weight, tank fill factors, c. g. locations for nine tanks, and two mass cases. The process also uses

the FEM for the reference aircraft geometry for the calculation of the theoretical FEM weight.

The weights process must yield the reference weight results for the reference airplane geometry,

using the appropriate reference aircraft fuel loadings.

The reference weights data are a set of fixed data files that assign as-built nodal weights to each of

the 14 weights meshes seen in fig. 24 for several types of weights. See table 11 for a complete listing of the weight mesh names and the types of weights assigned to each mesh. The as-built nodal

weights in this data set were defined using the reference weights process described in reference 10

for the specific geometry shown in fig. 24. All 14 meshes are assigned as-built structural nodal

weights. Some of the 14 meshes are also assigned nodal weight increments for nonstructural, systems, payload, and fuel weights.

The structural weights are understood to include a theoretical FEM weight, as well as as-built

structural weight increments for production splices, local pad-ups, side-of-body joints, adhesives,

paints, materials for damage tolerance, sealants, and fasteners essential in building the aircraft.

The nonstructural weights include weight increments for windows, landing gear doors, access

doors, seat tracks, fuel tank baffles, passenger doors, and system attachment fittings. As shown in

table 11, the nonstructural weights are applied only to the five meshes (1 through 5) representing

the primary aircraft structure. For the HSCT4.0 application, the systems weights are provided as

fixed nodal loads.
29

The as-built total weight of the aircraft can be considered to be a hierarchy of summations of

smaller weight groupings, as illustrated in tables 12 and 13. Mesh numbers are shown in parentheses. In general, moving from right to left in these two tables for each component, each vertical

bar in the table represents a summation of several items from the right column to form the item in

the left column. The fuel weight in table 13 is an exception; the fuel component is either cruise or

GTOW fuel.

For example, in table 12, nodal theoretical FEM weights for a given mesh are summed to find a

total theoretical FEM weight for the same mesh. The summation of nodal theoretical FEM

weights for a given mesh into a total theoretical FEM weight for the same mesh is defined as a

subassembly weight. Likewise, the summation of nodal as-built structural weight increments for a

given mesh to find a total as-built structural weight increment for the same mesh is also defined as

a subassembly weight. A similar subassembly weight is defined as the summation of nodal nonstructural weights for a given mesh (of meshes 1 through 5 only) to find a total nonstructural

weight for the same mesh.

Table 11. Weight Types Assigned to Each Weight Mesh

Weight

Mesh

Number

Weight Mesh

Name

Structural

 Weights

NonStructural

Weights

Systems

Weights

Payload

Weights

Fuel

Weights

1 Inboard Wing Yes Yes Yes No Yes

2 Outboard Wing Yes Yes Yes No No

3 Fwd-Fuselage Yes Yes Yes Yes No

4 Mid-Fuselage Yes Yes Yes Yes No

5 Aft-Fuselage Yes Yes Yes Yes Cruise

only

6 Vertical Tail Yes No Yes No No

7 Horizontal Tail Yes No Yes No No

8 Inboard Strut Yes No Yes No No

9 Outboard Strut Yes No Yes No No

10 Inboard Control

Surfaces

Yes No Yes No No

11 Outboard Control Surfaces

Yes No No No No

12 Rudder Yes No No No No

13 Elevator Yes No No No No

14 Nose Cone Yes No No No No
30

Table 12. Structural Weights Hierarchy

Component

Reference Aircraft Assembly

(Weight Mesh Number, fig. 24)

Reference Aircraft Subassembly

Wing

Inboard Wing Structure (1)

Theoretical FEM Weight

As-built Structural Weight Increment

Nonstructural Weight

Outboard Wing Structure (2)

Theoretical FEM Weight

As-built Structural Weight Increment

Nonstructural Weight

Inboard Strut Structure (8) Theoretical FEM Weight

As-built Structural Weight Increment

Outboard Strut Structure (9) Theoretical FEM Weight

As-built Structural Weight Increment

Inboard Control Surface Structure (10) Theoretical FEM Weight

As-built Structural Weight Increment

Outboard Control Surface Structure (11) Theoretical FEM Weight

As-built Structural Weight Increment

Fuselage

Nose Cone Structure (14) Theoretical FEM Weight

As-built Structural Weight Increment

Fwd-Fuselage Structure (3)

Theoretical FEM Weight

As-built Structural Weight Increment

Nonstructural Weight

Mid-Fuselage Structure (4)

Theoretical FEM Weight

As-built Structural Weight Increment

Nonstructural Weight

Aft-Fuselage Structure (5)

Theoretical FEM Weight

As-built Structural Weight Increment

Nonstructural Weight

Vertical Tail Vertical Tail Structure (6) Theoretical FEM WeightAs-built Structural Weight Increment

Rudder Structure (12) Theoretical FEM Weight

As-built Structural Weight Increment

Horizontal

Tail

Horizontal Tail Structure (7) Theoretical FEM Weight

As-built Structural Weight Increment

Elevator Structure (13) Theoretical FEM Weight

As-built Structural Weight Increment
31

* Fuel is either cruise or GTOW fuel; i.e., there is no summation.

The summation of the subassembly weights for a given mesh to find the total mesh structural and

nonstructural weight is defined as an assembly weight. For example, the summation of the total

theoretical FEM weight, as-built structural weight increment, and nonstructural weight, all for

mesh 1, is defined for the assembly known as the Inboard Wing Structure. Several assembly

weights are summed to find the total weight of aircraft components, such as the wing or fuselage.

The OEW is the summation of the weights for the wing, fuselage, vertical tail, horizontal tail,

engines, systems, and landing gear components. The cruise weight is the summation of the OEW,

payload weight, and cruise fuel weight. The GTOW is the summation of the OEW, payload

weight, and GTOW fuel weight.

3.2.4.1 Weights Subprocesses

The Weights process has two subprocesses, Theoretical FEM Weight and Built Up Weights (see

fig. 7). Both processes use data computed by the Geometry process. The Theoretical FEM Weight

subprocess computes the nodal theoretical FEM weights for both the reference (a one time only

Table 13. Systems, Payload, and Fuel Weights Hierarchy

Component

Reference Aircraft Assembly

(Weight Mesh Number, fig. 24)

Reference Aircraft Subassembly

(Weight Mesh Number, fig. 24)

Engines Engines (8 and 9) Inboard Engine Weight (8)

Outboard Engine Weight (9)

Systems Systems (1 through 10)

Inboard Wing Systems Weight (1)

Outboard Wing Systems Weight (2)

Fwd-Fuselage Systems Weight (3)

Mid-Fuselage Systems Weight (4)

Aft-Fuselage Systems Weight (5)

Vertical Tail Systems Weight (6)

Horizontal Tail Systems Weight (7)

Inboard Strut Systems Weight (8)

Outboard Strut Systems Weight (9)

Inboard Control Surface Systems Weight (10)

Landing

Gear Landing Gear (1 and 3) Body Landing Gear Weight (3)

Wing Landing Gear Weight (1)

Payload Payload (3, 4, and 5)

Fwd-Fuselage Payload Weight (3)

Mid-Fuselage Payload Weight (4)

Aft-Fuselage Payload Weight (5)

*Fuel Cruise Fuel (1 and 5) Inboard Wing Cruise Fuel Weight (1)

Aft-Fuselage Cruise Fuel Weight (5)

GTOW Fuel (1) Inboard Wing GTOW Fuel Weight (1)
32

calculation) and current aircrafts. The theoretical FEM weights are computed on an element-byelement basis from first principles relating the structural dimensions of elements in the FEM to

their volumes, densities, and weights. The theoretical FEM element weights are then translated to

nodal weights by using an element-to-node translation algorithm specific to the finite element

analysis code. The structural design variables size only the finite elements representing the skins

of the primary structural components (meshes 1 through 5). The shape design variables affect the

theoretical FEM weights of all meshes except for meshes 6, 7, 12, and 13.

The Built Up Weights subprocess computes the as-built nodal structural weight increments and

adds them to the theoretical FEM nodal weights. This subprocess also computes fuel weights, airplane total weight, and the c. g. location based on the design variable values and fuel fill factors.

Nodal as-built weights for the reference aircraft, computed by the reference 10 process, are provided to the Built Up Weights subprocess from the reference weights data set.

As-built structural weight increments are determined by subtracting the reference theoretical

FEM weight from the reference aircraft as-built structural weight at every corresponding node.

These as-built structural increments are then applied as a constant vector of increments to the theoretical FEM weights for the current aircraft. Systems and payload weights are applied as constant vectors to the theoretical FEM weights for the current aircraft. Three mass cases are

considered: 1) cruise weight, 2) GTOW, and 3) OEW.

The next step in the process is to calculate the fuel weight for both the cruise and the GTOW mass

cases. Because the exact location and geometry of the nine reference aircraft fuel tanks are not

known, they are modeled as a set of 11 six-faced, straight-edged polygons. These tanks are

defined as part of the HSCT4.0 geometry parameterization and are all contained within the aircraft wing and fuselage outer mold lines. The 11 tank definitions include all the locations of FEM

nodes of the reference aircraft for which fuel can be assigned, considering the different fuel loads

and distribution for the takeoff and cruise conditions.

Fuel volumes for each of 11 tanks are computed for the reference and current aircrafts. These fuel

volumes are multiplied by the density of JP-4 aircraft fuel to obtain 11 full fuel weights for each

of the reference and current aircrafts. These 11 full fuel weights for the reference and current aircraft geometries must then be associated with nine fuel weights provided as part of the reference

aircraft data. The association is done by comparing the reference geometry tank c. g.’s. Some of

the tanks may be combined or renumbered to associate with the nine reference geometry fuel

tanks.

The 11 tank geometries from the HSCT4.0 application parameterization and the nine fuel tank

weights and fill factors from the reference aircraft data must be reconciled so that the HSCT4.0

application fuel geometries contain the right amount of fuel weight for the reference geometry.

Three sets of scale factors are used to determine the correct fuel tank weights. The first two scale

factor sets are geometric factors and apply to any mass case. The third set of scale factors is mass

case specific, i.e., there is a scale factor set for both the cruise and the GTOW mass case. The first

set of scale factors is applied to the 11 HSCT4.0 application computed fuel weights to ensure that

the correct reference fuel weight is obtained for the reference geometry. The second set of scale

factors is applied to the HSCT4.0 application fuel weights to account for changes in the fuel volume between the current and reference geometries. The third set of scale factors is used to change
33

the full fuel weight within each tank, based upon the reference aircraft tank fill factors for each

tank between the takeoff and cruise conditions. When the current aircraft is geometrically and

structurally identical to the reference aircraft, the as-built weights computed by the Built Up

Weights subprocess identically reproduce the reference weights data set.

3.2.5 Nonlinear Corrections Process

The process for calculating nonlinear corrections is displayed in fig. 8. The purpose of the Nonlinear Corrections process is to compute a correction term to be added to each linear aerodynamics

surface pressure coefficient to account for nonlinear aerodynamics effects. This computation is

the first stage in the variable-fidelity aerodynamics process. The second stage applies this set of

correction terms each time a linear aerodynamics calculation is made during the Rigid Trim process.

Although the optimization requirements have been deferred as stated in section 3.2.1, for completeness, the role of the Nonlinear Corrections process in the optimization process is described

here. The computational time for calculating the nonlinear aerodynamics is much longer than the

combined computational time for all the other processes in the Analysis process. In an effort to

accelerate the overall computation time, the Nonlinear Corrections process shall be computed in

parallel with several cycles of the optimization process. The Nonlinear Corrections process will

be executed during the first optimization cycle using zero delta displacements. In subsequent optimization cycles, the most recently calculated nonlinear corrections will be used until the updated

nonlinear corrections are available. Note that the lag in computation will make the corrections

inconsistent with the current set of design variable values. In the later stages of the optimization,

the nonlinear corrections will be updated every cycle to increase accuracy. For the cycles in which

the nonlinear corrections are computed, the updated nonlinear aerodynamics volume grids and

linear aerodynamics grids are used in recalculating the nonlinear correction terms for each load

condition.

Calculations of the Nonlinear Corrections process are required for each load condition. Because

the process is independent for each load condition, these calculations can be performed in parallel. In addition, within each load condition calculation, the right and the left branches of this process (refer to fig. 8) are independent of each other and can be performed in parallel before

synchronizing at the Calculate Nonlinear Corrections subprocess.

3.2.5.1 Nonlinear Corrections Subprocesses

The right branch in fig. 8 calculates the nonlinear aerodynamics for a given load condition. To

produce the displaced nonlinear aerodynamics surface grid, the Apply Nonlinear Delta Displacements subprocess adds the delta displacements from the most recent Calculate Delta Displacements (shown in fig. 14) subprocess to the derived nonlinear aerodynamics surface grid. The

Volume Grid Adjustment subprocess then uses this displaced nonlinear aerodynamics surface grid

and the baseline nonlinear aerodynamics volume and surface grids to produce the displaced nonlinear aerodynamics volume grid, which is used as input to the Nonlinear Aero subprocess. The

appropriate altitude and the total weight (computed within the Weights process) are used by the

Calculate CL subprocess to determine the target CL that is input to the Nonlinear Aero subprocess.
34

The Nonlinear Aero subprocess calculates the nonlinear aerodynamics surface pressures, forces,

and moments for the input CL by iteratively solving the three-dimensional Euler equations with a

finite-volume formulation on the structured volume grid.

The left branch in the figure calculates linear aerodynamics for the same load condition. To produce the displaced linear aerodynamics surface grid, the Apply Linear Delta Displacements subprocess adds the delta displacements from the most recent Calculate Delta Displacements

subprocess to the derived linear aerodynamics surface grid. Independent executions of the Linear

Aero subprocess are made for a predetermined set of angles of attack and tail deflections. The

angles are preselected by the aerodynamics specialist to bracket the range of expected angles for

the given load condition. The Linear Aero subprocess provides surface pressure distributions,

forces, and moments to the Calculate Nonlinear Corrections subprocess.

The Calculate Nonlinear Corrections subprocess determines the linear aerodynamics angle of

attack that generates the same configuration normal force that was calculated in Nonlinear Aero.

The normal force was chosen as the matching condition, rather than lift force, because only the

normal force components are used in the aeroelastic Loads Convergence process. The linear pressures are interpolated at the angle of attack that matches the configuration normal force. The nonlinear pressures are transferred to the linear aerodynamics grid using a method that conserves the

total forces and moments. The nonlinear corrections are then computed as the panelwise difference between the resulting linear pressures and nonlinear pressures. The integral of these corrections over the entire configuration is zero because of the imposed normal force matching

condition. As a result, there is no net normal force contributed when the corrections are applied in

the Rigid Trim process; however, there will be a net pitching moment for the configuration. This

moment is accounted for in the Rigid Trim process.

3.2.6 Rigid Trim Process

The Rigid Trim process is shown in fig. 9. The Rigid Trim process represents the second stage in

the variable-fidelity aerodynamics analysis approach. The purpose of this process is to provide

surface pressures and total aerodynamic forces at a trim condition. The Rigid Trim process executes within two different processes; both of these process executions involve different load conditions. The first execution of Rigid Trim occurs after the Weights and Nonlinear Corrections

(when computed) processes have completed; during this execution, the aircraft is trimmed for the

cruise load condition only. The Rigid Trim process is also executed from within the Loads Convergence process for each of the noncruise load conditions two through seven.

3.2.6.1 Rigid Trim Subprocesses

The Rigid Trim process computes the trimmed aerodynamic loads independently for each load

condition. The input grid for the Linear Aero subprocess is the current geometry for the load condition being considered (i.e, the derived grid for the cruise load condition or the displaced grids

for the noncruise load conditions). The Linear Aero subprocess computes the surface pressures

for a prescribed set of angles of attack and tail deflections for this load condition. The table of

angles of attack and tail deflections is preselected by the aerodynamics specialist to bracket the

range of expected angles for each load condition.
35

In the Apply Nonlinear Corrections subprocess, the most recent nonlinear corrections for the current load condition are added, node-by-node, to the linear aerodynamics pressures. These corrected pressures provide input to the Aero Moment Equilibrium subprocess, which computes

trimmed aerodynamic loads for the load condition. The trimmed aerodynamic loads and total

force coefficients are interpolated using the calculated angle of attack and the tail deflection that

together yield the target CL with no net pitching moment about the c. g. location. (The input

weight and c. g. are calculated in the Weights process and depend on the specific load condition.

This target CL is calculated from this input weight and the specific load condition.) The trimmed

aerodynamic loads will be used in the subsequent Displacements process executions. The

trimmed force coefficients (CL and CDi), for the cruise load condition only, will be used in the

Polars process.

3.2.7 Polars Process

The Polars process is shown in fig. 10. Aircraft drag polars are calculated for the current set of

design variable values over a range of flight conditions. The Polars subprocesses calculate the liftdependent and lift-independent drag components. All of these subprocesses use the derived linear

aerodynamics grid for the 1g cruise shape (from the Geometry process) and the polars conditions.

These conditions are preselected by the performance specialist and consist of a fixed set of Mach

numbers, altitudes, and lift coefficients. No nonlinear corrections are used in the Polars process.

3.2.7.1 Polars Subprocesses

The right side of fig. 10 shows the lift-dependent drag subprocesses. First, the Linear Aero subprocess is executed for combinations of angle of attack and tail deflection. These combinations

are preselected by the aerodynamics specialist at Mach numbers matching those from the polars

conditions table. Then, in the Induced Drag subprocess, for each Mach number and angle of

attack, the trimmed drag due to lift is interpolated at the tail deflection that produces no net pitching moment. This produces an intermediate table of lift and trimmed drag coefficients at the specified angles of attack. This table is extended by including the trimmed cruise condition data

computed within the Rigid Trim process. Finally, the data in this table are interpolated at the

polars conditions CL values to provide the lift-dependent drag coefficient (CDi) table.

The left side of fig. 10 shows the lift-independent drag subprocesses, Wave Drag and Viscous

Drag. The Wave Drag subprocess is executed at the zero-lift angle of attack for the specified

Mach numbers; the computed wave drag coefficients (CDw) are only non-zero for supersonic Mach

numbers. The Viscous Drag subprocess calculates all viscous drag components (CDv) including

skin friction, roughness, and profile (form) drag. The Viscous Drag subprocess is executed for the

specified Mach numbers and altitudes.

The Assemble Polars subprocess produces the mission tables of drag coefficients, which will be

used by the Performance process. First, the lift-independent drag coefficient tables are assembled

from the wave drag and viscous drag coefficients. Then the lift-dependent drag coefficient table is

combined with the lift-independent drag coefficient tables to produce the mission tables.
36

3.2.8 Performance Process

The Performance process shown from the Analysis process (Fig. 5) contains no subprocesses.

However, a more detailed view of the inputs and outputs of this process are shown in fig. 11. The

Performance process calculates the aircraft range and several other performance metrics (see definition, table 10).

The Performance process requires numerous inputs from a variety of sources. The derived performance geometry (a coarse resolution, wire frame geometry description) is obtained from the

Geometry process. The wing and fuselage fuel weights and GTOW are obtained from the Weights

process. Mission tables of drag coefficients are obtained from the Polars process. A variety of

other reference aircraft data (engine, mission, and performance analysis parameters) are obtained

from prior analyses of the reference configuration.

Given these inputs, the Performance process repeatedly solves the equations of motion until a

mission analysis is obtained that is consistent with the input geometry, weights, aerodynamics,

and engine tables. The mission analysis considers the takeoff, landing, climb, cruise, descent, and

reserve portions of a specified mission profile, while requiring that the various Federal Aviation

Regulations (FAR) and Federal Aviation Agency (FAA) flight operational procedures, required

for certification, are satisfied. These regulations are summarized in references 11-13.

3.2.9 Ground Scrape Process

The Ground Scrape process is shown in fig. 12. The purpose of the Ground Scrape process is to

calculate the maximum available lift forces at ground scrape conditions on takeoff and landing.

These forces will be used in the formulation of the ground scrape constraints (see table 4). The

takeoff lift force must be greater than the GTOW, and the landing lift force must be greater than

the GLW (usually defined as GTOW minus one-half takeoff fuel weight). Weights exceeding

these maximum available lift forces would require higher angles of attack, resulting in the aircraft

tail scraping the ground. Although the implemented Ground Scrape process is not realistic in fully

constraining the aircraft design to avoid all ground scrape conditions, it is included as a simple

model of more realistic ground scrape processes that may be used by industry.

3.2.9.1 Ground Scrape Subprocesses

The Ground Scrape process consists of three subprocesses. The first subprocess, Scrape Angle,

calculates the takeoff and landing pitch angles with the landing gear just touching the runway at

zero roll angle and the aircraft tail at the specified minimum ground clearance (6 inches) to avoid

tail strike. For the takeoff condition, the landing gear is assumed to be at the static length (-6

inches stroke), and for the landing condition, the gear is at the fully stroked length (-24 inches

stroke). The tail strike point comes from the derived scrape geometry, which is produced by the

Geometry process.

The second subprocess, Linear Aero, computes the lift coefficients at the maximum angles of

attack for takeoff and landing (the pitch angles just calculated) at a low subsonic Mach number.

For simplicity, the Linear Aero process uses the 1g cruise shape (the derived linear aerodynamics
37

grid from Geometry) for the aircraft, ignoring realistic takeoff and landing flap and tail deflections.

The third subprocess, Scrape Lift, uses standard atmosphere data for a high altitude airport (5000

feet) and the takeoff and landing speeds from the performance metrics (generated by the Performance process) to convert the lift coefficients into the maximum available takeoff and landing lift

forces.

3.2.10 Displacements Process

The Displacements process is shown in fig. 13. Structural displacements due to displacement

loads are generated by the Displacements process. When Displacements is called from within the

Analysis process, the displacements are calculated for the cruise load condition only. When Displacements is called from within the Loads Convergence process, the displacements are calculated for load conditions two through seven. In this section, background for the cruise

displacement calculations is presented. Refer to section 1.3.2 for the definitions of symbols used

in this section.

Both the geometry of the aerodynamics model used in the Rigid Trim process and the geometry of

the FEM used in the Displacements process are based on the 1g cruise shape (sC, see sketch

below), which is described by the shape design variables.

In order to obtain the correct stresses from a structural analysis, the displacements must be computed relative to the unloaded shape, s0 (see sketch below). The unloaded shape is the aircraft

shape that deforms to the cruise shape when cruise loads (fC) are applied.

The cruise loads are computed from the following equation:

(7) f C = aC – nodal cruise weight
38

where aC represents the aerodynamic cruise loads. The inertia loads (load factor, which is 1.0 for

the cruise case, multiplied by the nodal cruise weight) are subtracted from aC, because the weight

acts in the -z direction.

The shape change (displacements, u0) from the unloaded shape to the cruise shape is given by the

following equation:

(8)

The stiffness matrix of the unloaded shape (K0) is unknown. Assuming that the FEM is geometrically linear, the differences between K0 and the stiffness matrix of the cruise shape (KC) are negligible. Using this assumption, fC can be applied to KC to produce a set of cruise displacements (uC).

(9)

thus, the unloaded shape is given by equation 10.

(10)

3.2.10.1 Displacements Subprocesses

As shown in fig. 13, the Displacements process uses data calculated in the Weights process (nodal

cruise weight and nodal GTOW) and the Geometry process (derived FEM and derived section

properties). In the first step of the Displacements process, the Loads Transfer subprocess transfers

the z direction aerodynamic loads to finite element nodes. Loads Transfer is executed once for the

cruise condition (when Displacements is called from within the Analysis process) and once per

iteration for load conditions two through seven in the Loads Convergence process (fig. 14).

The Add Inertia Loads subprocess calculates the displacement loads by subtracting the inertia

loads (acting in the -z direction) from the aerodynamic loads. The final subprocess to be executed

is FEM Displacements, which computes structural displacements at the finite element nodes due

to the displacement loads. For the HSCT4.0 application, the FEM Displacements subprocess performs a linear static finite element analysis.

3.2.11 Loads Convergence Process

The Loads Convergence process is shown in fig. 14. Before the Loads Convergence process is discussed, it is necessary to explain the need for an iterative aeroelastic convergence process. In this

section, load conditions two through seven are referred to as maneuver conditions, and loads are

considered to be forces acting on nodes. Refer to section 1.3.2 for the definitions of symbols used

in this section.

At maneuver conditions, the aircraft has maneuver shape sM and is subjected to maneuver loads fM

(illustrated in the following sketch).

sC s – 0 u0 K0 [ ]–1 f = = C

uC KC [ ]–1 f C K0 [ ]–1 f === C u0

s0 sC – u0 s = = C – uC
39

The maneuver loads are computed from the following equation:

(11)

where aM represents the aerodynamic maneuver loads, and LF represents the maneuver load factor. The inertia loads (LF multiplied by nodal GTOW) are subtracted from aM, because the weight

acts in the -z direction. Two unknowns, sM and aM, are determined using the Loads Convergence

process. The maneuver shape is the net vehicle shape used for the aerodynamic analysis and is

consistent with the deformed structural shape produced by the aerodynamic loads.

The Rigid Trim process is used to compute aM using sM as input. The aerodynamic grids used in

Rigid Trim are based on sC (see following sketch).

To compute aM, an aerodynamic grid based on sM is required. The aerodynamic grid for sM is computed by deforming the sC grid by , the delta displacements. The delta displacements are

computed from equation 12:

(12)

Recall that equation 9 is used to compute uC. The other unknown in computing is (the

maneuver displacements), which is computed using equation 13:

(13)

(The uM is computed from a finite element analysis.) The maneuver displacements are thus a function of the maneuver loads, and the aerodynamic loads (a component of the maneuver loads) are a

function of the maneuver shape of the aircraft.

f M = aM – LF nodal ⋅ GTOW

δuM

δuM sM s – C sM s – 0 ( ) sC s – 0 == = – ( ) uM – uC

δuM uM

uM K0 [ ]–1 f M KC [ ]–1 = = f M
40

(14)

(15)

Because of this mutual dependency between aerodynamic maneuver loads and maneuver displacements, a converging iterative process is used to determine the converged maneuver loads for

load conditions two through seven. This process is called the Loads Convergence process in the

HSCT4.0 application.

3.2.11.1 Loads Convergence Subprocesses

As shown in fig. 14, the Loads Convergence process uses data calculated in the Weights process

and the Geometry process. In the first step of the Loads Convergence process, the Apply Linear

Delta Displacements subprocess uses the delta displacements (see equation 12) to modify the

derived linear aerodynamic grids, generating displaced linear aerodynamic grids. For the first iteration in the loads convergence loop, a vector of zero delta displacements is used, and the resulting

displaced aerodynamic grids represent the cruise shape of the aircraft.

In the next step, the Rigid Trim process uses the displaced linear aerodynamics grids and the

GTOW and c. g. to compute trimmed aerodynamic loads for load conditions two through seven.

The Rigid Trim process is explained in detail in section 3.2.6 “Rigid Trim Process”.

The Displacements process uses the trimmed aerodynamic loads and the nodal GTOW to compute new displacements for load conditions two through seven. The Displacements process is

explained in detail in section 3.2.10 “Displacements Process”.

The Loads Convergence process iterates until convergence. Convergence is achieved when the net

vehicle shape used for the aerodynamic calculations is consistent with the structural displacements caused by the structural loads.

For each load condition, the Calculate Delta Displacements subprocess computes the using

equation 12 above. This subprocess is only invoked if the convergence criterion is not met. When

the convergence criterion is met, the final set of delta displacements corresponds to the net vehicle

shape that was used for the final aerodynamic calculations.

The output of the Loads Convergence process is a set of converged loads and converged delta displacements.

3.2.12 Stress and Buckling Process

The Stress and Buckling process is shown in fig. 15. Refer to section 1.3.2 for the definitions of

symbols used in this section.

The structural responses are listed in table 7 and include SFI and BLF for each quad element and

triangle element in each design variable zone for each load condition. As shown in fig. 19, there

uM uM f M KC ( ) , uM aM nodalGTOW KC = = ( ) , ,

aM aM uM uC sC = ( ) , ,

δuM
41

are 61 design variable zones. All 61 design variable zones contain quad elements, and 35 of these

zones also contain triangle elements.

The Augment Loads subprocess prepares load conditions two through eight (see table 9) and

assembles them into augmented loads. The FEM Stress subprocess then calculates an SFI, stress

resultant, and stress for each quad and triangle element in the design variable zones for each load

condition. The stress resultants are used to calculate the BLF for each load condition in each quad

and triangle element in the design variable zones.

3.2.12.1 Stress and Buckling Subprocesses

The Augment Loads subprocess generates a set of seven augmented loads to be used to calculate

the SFI’s and BLF’s. The first six augmented loads (based on load conditions two through seven)

are obtained from the converged loads generated by the Loads Convergence process. Internal

forces representing a cabin pressure of 10.78 psi are added to selected nodes on the fuselage for

all of the trimmed loads from the Loads Convergence process. The seventh augmented load is

based on the taxi condition (load condition 8). The forces for the taxi condition were obtained by

multiplying the inertia forces (nodal masses multiplied by -1.0) by the appropriate load factor

(given in table 9) and adding reaction forces at two nodes. The values for these two reaction

forces were determined by the following rationale. The aft landing gear is attached to the wing at

three locations. If all three points were constrained in the upward z direction, there is the possibility of getting unrealistic reactions at these three points because of the redundancy of the supports

as the wing displaces. For example, as the wing stiffness changes there is the possibility that a

force at the gear point could be in the downward instead of upward direction; therefore, only one

of the three gear points was constrained and forces equal to one-third of the total gear load were

applied to the other two nodes. The seven augmented loads are then multiplied by a factor of

safety (1.5) and are then assembled into the augmented loads for the FEM Stress subprocess.

Three in-plane stresses (σ11, σ22, and τ12) are computed from a linear static finite element analysis.

An SFI is used to normalize these stresses by material stress allowables (XC, XT, YC, YT, and S)

defined by the material properties. An SFI is also used to reduce the output from three values per

element to one value. The Hoffman SFI is computed for all layers in the composite face-sheets (a

total of eight layers) for each of the 2260 elements in the design variable zones for each of seven

load conditions. For the constraints, only the maximum layer-wise SFI in each element is

retained. The equation used to compute the SFI is given below14:

(16)

For the in-plane stresses, the 1- and 2-directions correspond to the 0o and 90o ply orientations in

fig. 21, respectively.

The Buckling subprocess uses analytical solutions for the buckling load in simply-supported

square plates. This is referred to as a local buckling constraint, as opposed to a global (eigenvaluebased) buckling constraint. The BLF is computed for each element in the design variable zones

using the equations below:

SFI σ11

1

XT

------ 1

XC

+ ------     σ22

1

YT

------ 1

Y C

+ ------     σ11

2

XTXC

------------- σ22

2

YT Y C

------------- τ12

2

S2 -------- σ11 σ22 ⋅

XTXC

= + – – + + -------------------
42

(17)

(18)

(19)

In the above equations, the in-plane stress resultants (N11, N22, and N12) are computed from a linear static finite element analysis. NA is the largest compressive (negative) normal stress in the element. If both N11 and N22 are in tension (positive), then NA is zero, otherwise, it is positive. The

buckling allowables (Nmn and NShear) are computed from the material properties and the element

dimensions.

The bi-axial buckling load (Nmn) is obtained from the non-trivial solutions for stability of a simply-supported rectangular plate under uniform bi-axial compression15, as given in the equation

below (the Nmn used is the lowest of the 25 combinations of m, n=1 to 5):

(20)

Assuming the elements are square, then a is equal to b, and equation 20 becomes:

(21)

A constant value (30 in.) is used for the element edge length (a). This edge length represents a

standard aircraft frame spacing. The element bending stiffness matrix terms (DAA, DBB, D12, and

D66) are computed from the material properties and the structural design variables.

The NShear term in equation 22 is obtained from the shear buckling interaction equation16:

(22) for

(23) for

BLF

NA

min N mn ( ) ------------------------ N12

Nshear

--------------    2

= +

NA = –1 ⋅ min N( ) 11, N22, 0

NB –1 max N11 N22 = ⋅ ( ) ,

N mn

π

2 DAAm4 2 D12 + 2D66 ( )m2 nb

a

-----    2

DBB

nb

a

-----    4

+ +

a

2

m

2 nb

a

-----    2 NB

NA

+ ------    

= -----------------------------------------------------------------------------------------------------------------------

N mn

π

2 DAAm4 2 D12 + 2D66 ( )m2

n

2 DBBn4 [ ] + +

a

2

m

2

n

2 NB

NA

+ ------    

= -------------------------------------------------------------------------------------------------------

Nshear

32.5 DAADBB 10.1 2 D12 + 2D66 + [ ] ( )

b2 -------------------------------------------------------------------------------------------- DAA

DBB

= 4 --------- DAA ≥ DBB

Nshear

32.5 DBBDAA 10.1 2 D12 + 2D66 + [ ] ( )

b2 -------------------------------------------------------------------------------------------- DBB

DAA

= 4 --------- DBB > DAA
43

3.3 Data Storage Requirements

Specific data storage requirements have been deferred to the HSCT4.0 application project design

phase.

3.4 Performance Requirements

Because the HSCT4.0 application project is a high-performance computing project, the following

requirement applies:

Requirement #51 - The HSCT4.0 application shall demonstrate high-fidelity analysis calculations using high-performance techniques, exploiting coarse-grained parallelism where

appropriate.

3.5 System Design Constraints

The requirements phase for the HSCT4.0 application project included selecting a set of existing

codes to perform the computations described earlier in section 3.2. In the remaining portion of

this section, the reasons for the major discipline code selections are briefly stated. Additional

codes selected are briefly described in the appendix. The functional requirements indicated where

these codes would be used. The project’s requirements phase also selected the approach for implementing distributed computing.

Requirement #52 - The HSCT4.0 application shall be designed, using the legacy codes

described in the appendix, to execute in a distributed, heterogeneous Unix environment

using the Java programming language and CORBA-compliant software. If a cost-effective

CORBA based product is not available for a target architecture, the Java remote method

invocation language feature will be used to facilitate distributed computation.

The conventional multidisciplinary feasible formulation17, which requires a complete multidisciplinary analysis for each function evaluation, was chosen as the HSCT4.0 optimization approach.

The SLP technique (using the CONMIN18 feasible directions optimizer and piecewise linear

approximations) was chosen as the specific optimization algorithm. An important factor in the

decision to use SLP was the amount of past team experience accumulated using this approach.

During the requirements phase of the project, the decision was made to use the GENESIS® software for structural analyses (see ref. 19). Among the other finite element codes considered for use

were MSC-NASTRAN20, COMET-AR21, and EAL22. GENESIS® and MSC-NASTRAN were

considered top choices primarily due to derivative computation features. At the time the decision

was made, the team considered MSC-NASTRAN to be superior in several factors (flutter analysis,

eigenvalue and buckling analysis, team member familiarity, industry acceptance and use); however, GENESIS® was chosen due to the code’s additional derivative capability and parallelism.

(At the time this decision was made, MSC-NASTRAN did not have parallel capability.)

The USSAERO code23, 24 was chosen as the linear aerodynamics analysis code for calculating the

pressure distribution and aerodynamic characteristics of wing-body-tail combinations in both sub-
44

sonic and supersonic potential flow. The USSAERO code provides a unified approach to the aerodynamic analysis of wing-body-tail configurations in both subsonic and supersonic flow. This

code permits the analysis of noncircular bodies, provides a more accurate representation than

other linear aerodynamics codes of the rounded wing leading edges, and allows the determination

of wing interference effects in the presence of the body.

For nonlinear aerodynamics analysis, the CFL3D25 code was chosen. This code has a very general

structured-grid capability for complex geometries and has been used extensively within NASA

and in industry for analysis of high-speed flows. The particular version used has been processed

through the automatic differentiation tool ADIFOR26 to provide aerodynamic sensitivities and can

run on both sequential and parallel processors.

The FLOPS27 mission analysis code was chosen as the performance code for a variety of reasons.

First, the code executes quickly. Second, it has been used in prior NASA-industry studies. Third,

its accuracy for mission analysis has been validated against similar analysis codes.

3.6 Software System Attributes

This section defines several requirements related to numerical precision and error handling.

Requirement #53 - All analysis codes shall be compiled as double precision, unless otherwise specified.

Requirement #54 - All exchange of data between analysis codes shall be in double precision format, unless otherwise specified.

Requirement #55 - All analysis codes shall indicate if errors have occurred. If an error

occurs, the code shall report the cause of the error by returning an integer flag. A negative

flag shall indicate a fatal error. A positive flag shall indicate a warning. A flag set equal the

number 0 shall indicate normal execution.

Requirement #56 - The integrated HSCT4.0 system shall report any analysis code errors

and take the appropriate actions.
45

Appendix

This appendix briefly describes the codes that have been selected for implementing HSCT4.0

application functions. The codes and the functions that they implement were identified in the summary of functional requirements, listed in section 3.2.

A2S. The Aerodynamics-to-Structures, A2S, code transfers the aerodynamic loads to the structural elements using a distribution process that preserves the total aerodynamic normal (z-component) force and moments. The surface pressure on each aerodynamic panel is first converted into a

single force normal to the panel at its center. Only the configuration normal component of each

panel force is then distributed among the nodes of the closest structural element. The distribution

is done so that the total normal force and the total x-moment and y-moment at the structural nodes

is the same as that of the aerodynamic panel force. This process is repeated for all the aerodynamic panels to transfer all the aerodynamic loads to the structure.

AWAVE. The AWAVE code computes the cross-sectional area and volume distributions as functions of the axial distance along the fuselage for an aircraft configuration input to the code in wave

drag format. From the computed area and volume distributions, the wave drag coefficient is computed for the input configuration and also for an optimized, equivalent body of the same volume.

The wave drag computations are performed at the configuration zero-lift angle of attack for a set

of specified Mach numbers. The resulting wave drag is zero for subsonic Mach numbers and is

some positive value for supersonic (greater than 1.0) Mach numbers. The user of the code inputs

information to control the fidelity of the area and volume computations.

CDF1. The CDF1 program calculates several aircraft configuration viscous drag coefficient components, including the friction, form, and roughness drag coefficients, at user-specified Mach

numbers and altitudes. The aircraft geometry is specified as a series of wetted-area segments, each

with distinct viscous drag characteristics. The friction drag is computed by a strip theory method.

The form drag is calculated as a function of friction drag and the roughness drag as a function of

both friction and form drag.

CFL3D25. The CFL3D code solves the three-dimensional, time-dependent Euler and thin-layer

Navier-Stokes equations with a finite-volume formulation on structured grids. The equations are

advanced in time implicitly with the use of 3-factor approximate factorization. It can employ grid

sequencing, multigrid, and local time-stepping to accelerate convergence to steady state. It can

also utilize a wide variety of grid multiple block connection strategies-including point matched,

patched, and overset grid connections-in order to handle complex geometric configurations. Second-order upwind-biased spatial differencing is used for the inviscid terms, and flux limiting is

used to obtain smooth solutions in the vicinity of shock waves. Viscous terms, if present, are centrally differenced. Several turbulence models of varying complexity are available. The particular

version of the code used here is known as CFL3dv4.1hp. This version has been ported to parallel

computer architectures via the use of MPI message passing protocols. Furthermore, the automatic

differentiation tool ADIFOR26 has been applied to this version of the CFL3D code. The resulting

code is able to provide a numerical solution to the Euler (or Navier-Stokes) equations as well as

consistent derivatives of the numerical solution with respect to shape design variables.
46

CSCMDO28. The Coordinate and Sensitivity Calculator for Multidisciplinary Design Optimization (CSCMDO) code is a general purpose multi-block three-dimensional volume grid generator

which is suitable for MDO. The code is fast, robust, highly automated, and written in ANSI “C”

for platform independence. Algebraic techniques are used to generate and/or modify block face

and volume grids to reflect geometric changes resulting from design optimization. Volume grids

are generated/modified in a batch environment and controlled via an ASCII user input deck. This

allows the code to be incorporated directly into the design loop. Volume grids have been successfully generated/modified for a wide variety of configurations.

FLOPS27. The Flight Optimization System (FLOPS) code is a multidisciplinary system of computer programs for conceptual and preliminary design and evaluation of advanced aircraft concepts. It consists of nine primary modules: Weights, Aerodynamics, Engine cycle analysis,

Propulsion data scaling and interpolation, Mission performance, Takeoff and landing, Noise footprint, Cost analysis, and Program control.

The FLOPS code may be used to analyze a point design, parametrically vary certain design variables, or optimize a configuration with respect to these design variables (for minimum gross

weight, minimum fuel burned, maximum range, minimum cost, or minimum NOx emissions)

using nonlinear programming techniques. The configuration design variables are wing area, wing

sweep, wing aspect ratio, wing taper ratio, wing thickness-chord ratio, gross weight, and thrust

(size of engine). The performance design variables are cruise Mach number and maximum cruise

altitude. The engine cycle design variables are the design point turbine entry temperature, the

maximum turbine entry temperature, the fan pressure ratio, the overall pressure ratio, and the

bypass ratio for turbofan and turbine bypass engines. The aircraft configuration, engine cycle and

size, and the flight profile may be optimized simultaneously.

GENESIS19. The GENESIS® code is a fully integrated finite-element analysis/design software

package. Analyses are available for static, normal modes, direct and modal frequency analysis,

and heat transfer. Shape, sizing and topology optimization are the design options available to the

user. Sensitivity derivatives can also be computed.

GP9. The GP code is a parameterization tool for complex shapes suitable for a multidisciplinary

design optimization application. The approach consists of three basic concepts: 1) parameterizing

the shape perturbations rather than the geometry itself, 2) exploiting Soft Object Animation algorithms used in computer graphics, and 3) relating the deformation parameters to aerodynamics

shape design variables such as thickness, camber, twist, shear, and planform. The GP code formulation is independent of grid topology, which makes it suitable for use with a variety of analysis

codes such as CFD and computational structural mechanics. This algorithm is suitable for lowfidelity (e.g., linear aerodynamics and equivalent laminated plate structures) and high-fidelity

analysis tools (e.g., nonlinear CFD and detailed finite-element modeling). The analytical sensitivity derivatives are available for use in a gradient-based optimization.

L2NL. The L2NL code calculates the nonlinear corrections as the nodal difference between the

nonlinear aerodynamics surface pressures, transferred to the linear aerodynamics grid, and the linear aerodynamics surface pressures that have been interpolated at a matching condition. The lin-
47

ear pressures are interpolated at the angle of attack at which the configuration normal force

matches that from the nonlinear aerodynamics calculation.

S2W. The Structures-to-Wavedrag, S2W, code transfers the computed displacements from the

structures grid to the linear aerodynamics grid. The transfer is accomplished by infinite-plate

splines. This method is based on a superposition of the solutions for the partial differential equation of equilibrium for an infinite plate. The details of the method can be found in reference 29.

TRIM_NLC. The TRIM_NLC code adds the nonlinear corrections, node by node, to the linear

aerodynamics surface pressures for a prescribed set of angles of attack and tail deflections. The

code interpolates to determine the angle of attack and tail deflection angle that together yield the

target lift coefficient with no net pitching moment about the c. g. location.

USSAERO23, 24. The Unified Subsonic and Supersonic Aerodynamic analysis (USSAERO) code

is a linear aerodynamics panel code that has incorporated a symmetrical singularity method to

provide surface pressure distributions on a fuselage and wings in subsonic and supersonic flow.

This method extends the range of application of the program to include the analysis of multiple

engine nacelles or finned external stores. In addition, nonlinear compressibility effects in high

subsonic and supersonic flows are approximated by using a correction based on the local Mach

number at panel control points.

.
48

4.0 References

1. Sistla, R., Dovi, A. R., Su, P., and Shanmugasundaram, R.: “Aircraft Design Problem Implementation Under the Common Object Request Broker Architecture.” 40th AIAA/ASME/

ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Exhibit, St.

Louis, MO, 1999, pp. 1296-1305B.

2. Sistla, R., Dovi, A. R., and Su, P.: “A Distributed Heterogeneous Computing Environment for

Multidisciplinary Design & Analysis of Aerospace Vehicles.” 5th National Symposium on

Large-Scale Analysis, Design and Intelligent Synthesis Environments, Oct 12-15, 1999, Williamsburg, VA.

3. Weston, R. P., Townsend, J. C., Eidson, T. M., and Gates, R. L.: “A Distributed Computing

Environment for Multidisciplinary Design.” 5th AIAA/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Panama City Beach, FL, AIAA-94-4372-CP, Sept.

1994, pp. 1091-1097.

4. Krishnan, R., Sistla, R., and Dovi, A. R.: “High-Speed Civil Transport Design Using FIDO,”

NASA CR-1999-209693, Oct. 1999.

5. Engineous Software, Inc.: iSIGHT Developer’s Guide, Version 3.1, Morrisville, NC, Apr.

1998.

6. Engineous Software, Inc.: iSIGHT Advanced Designer’s Guide, Version 3.1, Morrisville, NC,

Apr. 1998.

7. Engineous Software, Inc.: iSIGHT Designer’s Guide, Version 3.1, Morrisville, NC, Apr. 1998.

8. Vinoski, S.: “CORBA: Integrating Diverse Applications Within Distributed Heterogeneous

Environments.” IEEE Communications Magazine, Vol. 14, No. 2, 1997, pp. 46-55.

9. Samareh, J. A.: “A Novel Shape Parameterization Approach.” NASA / TM-1999-209116, May

1999.

10. Mitchell, P. M.: “Advanced Finite Element Weight Estimation Process on the High Speed

Civil Transport.” SAWE Paper No. 2169, Presented at the 52nd Annual Conference of the

Society of Allied Weight Engineers, Inc. May 24-25, 1993, Biloxi, MS.

11. Roskam, J., and Lan, C.-T. E.: Airplane Aerodynamics and Performance. Design, Analysis,

and Research Corporation (DARcorporation), Lawrence, KS, 1997.

12. Roskam, J.: Airplane Design, Part I: Preliminary Sizing of Airplanes. Design, Analysis, and

Research Corporation (DARcorporation), Lawrence, KS, 1997.

13. Nicolai, L. M.: Fundamentals of Aircraft Design. METS, Inc., Distributor, Xenia, OH, and E.

P. Domincone Printing Services, Fairborn, OH, 1975.

14. Haftka, R. T., and Gurdal, Z.: “Elements of Structural Optimization.” Third revised and

expanded edition, Kluwer Academic Publishers, Boston, 1992, pp. 416-420.

15. Whitney, J. M.: “Structural Analysis of Laminated Anisotropic Plates.” Technomic Publishing

Company, Inc., Lancaster, PA, 1987, p. 104.
49

16. Stroud, W. J., Agranoff, N.: “Minimum-Mass Design of Filamentary Composite Panels Under

Combined Loads: Design Procedure Based on Simplified Buckling Equations.” NASA TN D8257, 1976, Table III.

17. Dennis, J. E., and Lewis, R. M.: “Problem Formulations and Other Optimization Issues in

Multidisciplinary Optimization.” Center for Research on Parallel Computation, Rice University, CRPC-TR94469, Houston, TX, Apr. 1994.

18. Vanderplaats, G. N.: “CONMIN—A Fortran Program for Constrained Function Minimization.” NASA TM-62282, Aug. 1973, plus addendum, May 1978.

19. Vanderplaats, G. N.: GENESIS User's Manual, Version 4.0. Colorado Springs, CO, 1997.

20. Moore, G. J.: “MSC/NASTRAN Design Sensitivity and Optimization User's Guide.” The

MacNeal Schwendler Corp., April 1994.

21. Stanley, G., Hurlbut, B., Levit, I., Loden W., Stehlin, B., and Swenson, L.: “Computational

Mechanics Testbed with Adaptive Refinement User's Manual.” Lockheed Palo Alto Research

Laboratory, Feb. 1995.

22. Whetstone, W. D.: EISI-EAL Engineering Analysis Reference Manual. Engineering Information Systems, Inc. July 1983.

23. Woodward, F. A.: “An Improved Method for the Aerodynamic Analysis of Wing-Body-Tail

Configurations in Subsonic and Supersonic Flow, Part I -Theory and Application.” NASA

CR-2228, Part I, May 1973.

24. Woodward, F. A.: “USSAERO Computer Program Development, Versions B and C.” NASA

CR-3228, April 1980.

25. Krist, S. L., Biedron, R. T., and Rumsey, C. L.: “CFL3D User’s Manual (Version 5.0).” NASA

TM-208444, June 1998.

26. Bischof, C., Carle, A., Hovland, P., Khademi, P., and Mauer, A.: “ADIFOR 2.0 User’s Guide

(Revision D).” CRPC-TR95516-S, March 1995, Rev June 1998.

27. McCullers, A.: “Aircraft Configuration Optimization Including Optimized Flight Profiles.”

Proceedings of the Symposium on Recent Experiences in Multidisciplinary Analysis and

Optimization, Sobieski, J., ed. NASA CP-2327, Hampton, VA, April 1984, pp. 396-412.

28. Jones, W. T., and Samareh-Abolhassani, J.: “A Grid-Generation System for Multidisciplinary

Design Optimization.” Proceedings of the 12th AIAA Computational Fluid Dynamics Conference, San Diego, CA, 1995, pp. 657-669.

29. Harder, R. L., and Desmarais, R. N.: “Interpolation Using Surface Splines.” Journal of Aircraft, Vol. 9, No. 2, 1972, pp. 189-191.
50

Figure 1. High-Speed Civil Transport.
51

a) Linear aerodynamics grid

b) Finite element model

Figure 2. Baseline HSCT4.0 Model.

X

Y

Z
52

Figure 3. Optimization.

GradientBased

Optimizer

design variables

responses

F0; g0; design variables

(optimized)

F0

; g0

F0; g0; design variables

(cycle = 0)

yes no

Analysis

Converged?

Accept

Design

and Set

Move Limits

Sensitivity

Analysis

Calculate

Objective and

Constraints

(design not accepted)

(design accepted,

cycle = cycle +1)

F; g; design variables

∂F0

∂x

∂g0

; ∂x
53

Figure 4. Gradient-Based Optimizer.

design variables

design variables

(updated)

objective; 

constraints

(approximate)

Optimizer

Approximate

Analysis

objective; 

constraints;

gradients
54

Figure 5. Analysis.

Geometry

Loads 

Convergence

Stress and

Buckling

cruise weight (total) and c.g.

trimmed aero loads

(cruise)

trimmed

CL, CDi 

(cruise)

stress failure indices;

buckling load factors

performance metrics

converged loads

(2–7)

derived FEM;

derived section properties;

derived fuel tank geometery

mission tables displacements

(cruise)

derived nonlinear

aero surface grids;

derived linear

aero grids

cruise weight (total) and c.g.;

GTOW (total) and c.g.

nonlinear

Rigid Trim corrections

Displacements

Nonlinear Corrections

Weights

Polars

Performance

Ground

Scrape

ground scrape responses

design

variables
55

Figure 6. Geometry.

airfoil surface

node data

parameterized 

linear aero grids

parameterized 

miscellaneous

 grids

parameterized 

nonlinear aero 

surface grids

derived 

performance

geometry 

derived nonlinear

aero surface grids derived linear

aero grids

derived

miscellaneous

model

ply mixture and 

 airfoil interior

thickness ratios

Linear

Aero Model

Update

Nonlinear

Aero Surface

Model 

Update

Miscellaneous

Geometry

Update

FE Model

Update

Section

Property

Update

Structural

Geometry

Performance

Geometry

Fuel

Geometry

Scrape

Geometry

derived 

fuel tank

geometry 

derived 

scrape

geometry 

parameterized FEM grid

derived 

FEM derived 

section

properties

design variables

(shape) design variables

(structural)

 
56

Figure 7. Weights.

fuel weights;

cruise weight (total, nodal);

GTOW (total, nodal);

cruise c.g.; GTOW c.g.; 

OEW (total)

Theoretical

FEM Weight

Built Up

Weights

reference weights data

FEM weight

derived section 

properties

finite element 

data and BC's

derived fuel tank

 geometry

derived FEM
57

Figure 8. Nonlinear Corrections.

baseline nonlinear

aero volume and

surface grids

displaced

nonlinear aero

surface grid

Apply Linear

Delta

Displacements

Linear

Aero

Nonlinear

Aero

Calculate

Nonlinear

Corrections

Volume Grid

Adjustment

Apply

Nonlinear

Delta

Displacements

Calculate CL

target CL

displaced nonlinear

aero volume grid

derived linear

aero grid

displaced linear

aero grid

nonlinear

corrections

linear pressures,

forces, and moments nonlinear pressures,

forces, and moments

aero reference data;

load condition data

*delta displacements *delta displacements

 

 

 The process is performed for load conditions 1–7.

**weight (total)

derived nonlinear

aero surface grid

aero reference data

Mach number, angle of attack,

tail deflection table;

aero reference data

* For design cycle one, delta displacements are zero.

** For load condition 1, weight (total) and c.g. are "cruise".

 For load conditions 2-7, weight (total) and c.g. are GTOW.

**weight (total) and c.g.
58

Figure 9. Rigid Trim.

Apply

Nonlinear

Corrections

Aero Moment

Equilibrium

Linear

Aero

linear

pressures

corrected

pressures

trimmed aero

loads

trimmed CL

, CDi

(cruise)

load condition data

*linear

aero grid

nonlinear

corrections

**weight (total)

and c.g.

Mach number, angle of attack,

tail deflection table;

aero reference data

* From Analysis, linear aero grid is "derived". From Loads Convergence, the grid

 is "displaced".

** From Analysis, weight (total) and c.g. are "cruise" for load condition 1.

 From Loads Convergence, weight (total) and c.g. are GTOW for load conditions 2-7.

 In Loads Convergence, this process is performed for load conditions 2-7.
59

Figure 10. Polars.

Figure 11. Performance.

Wave Drag Viscous Drag Linear Aero

Induced Drag

table of

trimmed CL

, CDi

table of CL

, CDi , Cm

Assemble

Polars

Mission tables

polars conditions;

load condition data

table of

CDw

table of

CDv

derived linear aero grid

polars conditions

cruise c.g.

trimmed CL

, CDi (cruise)

zero lift angle

of attack Mach number, angle of attack,

tail deflection table;

aero reference data

Performance

performance

metrics

derived performance

geometry 

GTOW (total);

 fuel weights

mission tables

performance reference data;

aero reference data
60

Figure 12. Ground Scrape.

ground scrape

 responses

scrape angles

of attack

scrape CL

Scrape

Angle

Linear Aero

Scrape

Lift

scrape angle data

derived linear 

aero grid

aero reference data

derived scrape

geometry

performance

metrics

Mach number, angle of attack, 

tail deflection table;

aero reference data
61

Figure 13. Displacements.

Loads

Transfer

Add Inertia

Loads

FEM

Displacements 

aero loads 

displacement

loads

displacements

finite element 

data and BC's

load condition data

derived FEM, derived section properties

trimmed aero

loads

*weights (nodal)

derived FEM

* In Analysis, weight (nodal) is "cruise" for load condition 1.

 In Loads Convergence, weight (nodal) is "GTOW" for load conditions 2-7.

 

 In Loads Convergence, this process is performed for load conditions 2-7.
62

Figure 14. Loads Convergence.

converged loads

 (2–7)

displacements

(loads 2-7)

displaced linear aero grids

Apply Linear

Delta

Displacements

Converged?

Calculate

Delta

Displacements

no

yes

*delta 

displacements

delta displacements

delta displacements

trimmed aero 

loads

(loads 2–7)

derived linear

aero grids

Displacements

GTOW (total)

and c.g.

GTOW (nodal)

Rigid Trim

displacements (cruise)

* For design cycle one, delta displacements are zero.
63

Figure 15. Stress and Buckling.

Augment

Loads

FEM Stress 

stress

resultants

design variables

(structural)

buckling load factors stress failure indices

Buckling

finite element

data and BC's derived FEM

converged 

loads (2-7)

augment loads data

augmented

loads (2-8)

derived section properties
64

Figure 16. Shape Design Variables - Planform.

Figure 17. Planform Control Points.

Panel 3

Panel 1

Panel 2

Ln Cr Lt

C3

SLE3

SLE2

B3

B2

C2

At

1 2

3 4

5 6

7 8

9 10

11

12

13

14 0

1

2

3

4

5 6

21

18 17

22

16 15

20 19
65

Figure 18. Shape Design Variables - Thickness, Camber, Twist, and Shear.

!!!!!!!!!

!!!!!!!!!

!!!!!!!!!

!!!!!!!!!

!!!!!!!!!

!!!!!!!!!

1

2

3

4

5

6

(a) Thickness and Camber Locations

1

2

3

(b) Twist and Shear Locations
66

Figure 19. Structural Design Variable Zones.
67

Figure 20. Composite Laminate Stacking Sequence.

Figure 21. Ply Orientations.

Face Sheet

Face Sheet

Core

T0 ̊

T0 ̊

T–45 ̊

T–45 ̊

T45 ̊

T45 ̊

T90 ̊

T90 ̊

Tcore
68

Figure 22. Miscellaneous Geometry.

Figure 23. Airfoil Interior Thickness Constraints in Airfoil Cross-section.

Finite Element Node

T Lower

T Upper

r

Airfoil

interior

thickness
69

Figure 24. Weights Meshes.

11

2

10

1

14

3

4

6

12

5

8

9

13

7
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May 2001 Technical Memorandum

HSCT4.0 Application

Software Requirements Specification 725-10-11-01

A. O. Salas, J. L. Walsh, B. H. Mason, R. P. Weston, J. C. Townsend, J. A.

Samareh, L. L. Green

L-18072

NASA/TM-2001-210867

The software requirements for the High Performance Computing and Communication Program High Speed Civil

Transport application project, referred to as HSCT4.0, are described. The objective of the HSCT4.0 application

project is to demonstrate the application of high-performance computing techniques to the problem of multidisciplinary design optimization of a supersonic transport configuration, using high-fidelity analysis simulations.

Descriptions of the various functions (and the relationships among them) that make up the multidisciplinary application as well as the constraints on the software design are provided. This document serves to establish an agreement between the suppliers and the customer as to what the HSCT4.0 application should do and provides to the

software developers the information necessary to design and implement the system.

Software requirements, High Speed Civil Transport, High performance computing,

Multidisciplinary design optimization

77

A05

NASA Langley Research Center

Hampton, VA 23681-2199

National Aeronautics and Space Administration

Washington, DC 20546-0001

Unclassified–Unlimited

Subject Category: 05 Distribution: Nonstandard

Availability: NASA CASI (301) 621-0390

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