Ashwin Shah

Sest, Inc., Middleburg Heights, Ohio

Enhancement/Upgrade of Engine Structures

Technology Best Estimator (EST/BEST)

Software System

NASA/CR—2003-212126

March 2003
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Ashwin Shah

Sest, Inc., Middleburg Heights, Ohio

Enhancement/Upgrade of Engine Structures

Technology Best Estimator (EST/BEST)

Software System

NASA/CR—2003-212126

March 2003

National Aeronautics and

Space Administration

Glenn Research Center

Prepared under Contract C–76751–J
Available from

NASA Center for Aerospace Information

7121 Standard Drive

Hanover, MD 21076

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22100

The Propulsion and Power Program at

NASA Glenn Research Center sponsored this work.

Available electronically at http://gltrs.grc.nasa.gov
NASA/CRó2003-212126 1 

Foreword

 This report represents a summary of the technical work performed during the entire contract 

period for the Order No. C-76751-J entitled ìEnhancement/upgrade of the EST/BEST (Engine 

Structures Technology Benefits Estimator) Software System.î ALCCA module has been 

integrated with the EST/BEST software system and the documentation for the work performed 

has been completed. Also, the EST/BEST software system package has been prepared and 

delivered along with. 

SUMMARY OF ACTIVITIES:

The following sections of the report describes the work performed during the contract period 

and the capabilities included in the EST/BEST software system. The developed EST/BEST 

software system includes the integrated NESSUS, IPACS, COBSTRAN and ALCCA computer 

codes required to perform the engine cycle mission and component structural analysis. Also, the 

interactive input generator for NESSUS, IPACS and COBSTRAN computer codes have been 

developed and integrated with the EST/BEST software system. The input generator allows the 

user to create input from scratch as well as edit existing input file interactively. Since, it has 

been integrated with the EST/BEST software system, it enables the user to modify EST/BEST 

generated files and perform the analysis to evaluate the benefits. Appendix A gives details of 

how to use the newly added features in the EST/BEST software system. 

Highlights of the added capabilities and further testing of the EST/BEST software system are 

as follows: 

(I) INTEGRATION OF THE NESSUS COMPUTER CODE WITH EST/BEST 

SOFTWARE SYSTEM: 

The NESSUS computer code and the developed interactive input generator modules have 

been integrated with the EST/BEST software system. The existing capabilities in the in the 

integrated EST/BEST software system have been enhanced as well as improvements on the 

results have been made. The highlights of the capabilities are summarized below: 

• User can generate the following input required to perform the probabilistic structural analysis 

using NESSUS: 

♦ Nodal Coordinates 

♦ Element connectivity 

♦ Boundary conditions 

♦ Mechanical loads such as point loads, nodal pressures, distributed pressure load, 

centrifugal forces 

♦ Thermal loads. Each layer temperature can be interpolated by providing top and bottom 

surface temperatures and specifying the interpolation method. 

♦ Analysis options: static, frequency with and without stress stiffening and buckling 
NASA/CRó2003-212126 2 

♦ Primitive random variables related geometry, boundary conditions, mechanical and 

thermal loads, etc., their probability distributions and perturbations. 

♦ Probabilistic analysis methods: mean value first order analysis (MVFO) and advanced 

mean value first order analysis (AMVFO). The user can perform both non-iterative as 

well as iterative probabilistic methods. MVFO provides faster solution whereas the 

AMVFO can be used for structures with non-linear responses where convergence of 

probability needs iterations. 

♦ Output request definitions. 

• The entire input can be prepared using default options and/or non-default options. 

• The geometry can be generated using the integrated COBSTRAN computer code. User can 

generate the coordinates and connectivity for complicated structures like blades with a 

minimal input. 

• User can edit the COSMO generated NESSUS file and enhance the input data for other 

NESSUS features. 

• Input can be prepared in one or more sitting sessions (for larger problems). 

• Each individual input set can be created through direct keyboard entry or by importing files 

containing the respective input set e.g. thermal loads can be read from the file also. 

• Program checks for consistency of the input and eliminates possible general errors made by 

the user. 

• Previously available options related to NESSUS have been kept intact. 

Additional capabilities were demonstrated by performing the probabilistic analysis of the 

high-pressure compressor blade. Static, frequency (with and without stress stiffening) and 

buckling analyses were performed for the High Speed Civil Transport engine blade. The 

problem details of the results were submitted in the monthly progress reports and are attached in 

Appendix B. 

Graphical User Interface (GUI) in the EST/BEST system was modified/updated to enable the 

use of additional NESSUS features. The typical updated GUI screens are given in the Appendix 

C. 

(II) INTEGRATION OF THE IPACS COMPUTER CODE WITH EST/BEST SOFTWARE 

SYSTEM: 

The IPCAS computer code (with FORTRAN 77 features) received from Mr. Chuck Putt was 

debugged and tested for static, frequency with and without stress stiffening, and buckling 

analysis capabilities. Several problems related to these analyses options were fixed and verified. 

The IPACS code is made available as stand alone as integrated computer code with EST/BEST. 

The IPACS computer code and the developed interactive input generator modules have been 

integrated with the EST/BEST software system. The existing capabilities in the in the integrated 

EST/BEST software system have been enhanced as well as improvements on the results have 

been made. The highlights of the capabilities are summarized below: 
NASA/CRó2003-212126 3 

• User can generate the following input required to perform the probabilistic structural analysis 

using IPACS: 

♦ Nodal Coordinates 

♦ Element connectivity 

♦ Boundary conditions 

♦ Mechanical loads such as point loads, nodal pressures, distributed pressure load, 

centrifugal forces 

♦ Thermal loads. Each ply temperature can be interpolated by providing top and bottom 

surface temperatures and specifying the interpolation method. 

♦ Analysis options: static, frequency with and without stress stiffening and buckling 

♦ Composite properties uncertainty definitions of the constituents, fabrication and geometry 

variables. The mean values of the constituents are retrieved directly from the material 

property database based on the constituent keyword name. Thus, the user input is 

minimized. 

♦ Ply group and arrangement definitions on the structure. 

♦ Primitive random variables related geometry, boundary conditions, mechanical and 

thermal loads, etc., their probability distributions and perturbations. Thermal loads can 

be fully or partially correlated random variables. 

♦ Perturbation magnitude definitions. 

♦ Ply response table and structural response definitions for the desired output. 

♦ Output request definitions. 

• The entire input can be prepared using default options and/or non-default options. 

• The geometry can be generated using the integrated COBSTRAN computer code. User can 

generate the coordinates and connectivity for complicated structures like blades with a 

minimal input. 

• User can edit the COSMO generated IPACS file and enhance the input data for other IPACS 

features. 

• Input can be prepared in one or more sitting sessions (for larger problems). 

• Each individual input set can be created through direct keyboard entry or by importing files 

containing the respective input set e.g. thermal loads can be read from the file also. 

• Program checks for consistency of the input, and eliminates possible general errors including 

those related to inter dependence of different input cards. 

• Previously available options related to IPACS have been kept intact. 

Additional capabilities were demonstrated by performing the probabilistic analysis of the 

COBSTRAN generated hollow blade. Static, frequency (with and without stress stiffening) and 

buckling analyses were performed for the hollow engine blade. The problem details of the 

results were submitted in the monthly progress reports and are attached in Appendix D. 

Graphical User Interface (GUI) in the EST/BEST system was modified/updated to enable the 

use of additional IPACS features. The typical updated GUI screens are given in the Appendix C. 
NASA/CRó2003-212126 4 

(III) INTEGRATION OF THE COBSTRAN COMPUTER CODE WITH EST/BEST 

 Additional capability of generating mesh for complicated structures like hollow engine blade 

with and without spars was added and made operation in the COBSTRAN computer code. The 

input can be created or modify the existing input interactively. Also the mesh can be generated 

interactively and corresponding output files can be imported by NESSUS as IPACS computer 

codes. Such a capability minimizes the mesh data input in NESSUS and IPACS. 

 Inputs for the hollow blade with and without spars were generated using the integrated 

COBSTRAN computer code in the EST/BEST software system. Graphical User Interface was 

developed to integrate the COBSTRAN computer code and its interactive input generator 

module. The typical updated GUI screens are given in the Appendix C. 

Added capabilities have been demonstrated by generating the input for a typical composite 

hollow blade with and without spars for an engine structure using the integrated COBSTRAN 

and the interactive input generator in the EST/BEST software system. The details of these 

capabilities were reported in the previous monthly reports. 

Also, GUI programming to integrate ALCCA computer code in a modular fashion with the 

EST/BEST software system has been completed and analysis for a test problem has been done. 

The ALCCA module augments the existing FLOPS cost-analysis computation for the engine 

cycle missions and component/structures using new cost models. Further testing is in progress 

and is expected to be complete during the next reporting period. 

(IV) INTEGRATION OF THE ALCCA COMPUTER CODE WITH EST/BEST 

 The ALCCA (Aircraft Life Cycle Cost Analysis) computer code to perform the cost analysis 

of composite structure was integrated with the EST/BEST software system. Graphical User 

Interface required to integrate the code was developed. A sample problem to perform the cost 

analysis was run and the typical cost analysis results are listed in Appendix E. The ALCCA 

computer code can be used as a substitute to the FLOPS (Flight Optimization Code) for the 

engine cycle analysis. However, the current effort of integration is limited to the standalone 

version of ALCCA analysis. ALCCA computer code has cost analysis based on newer and 

advanced models. 

(V) PROBABILISTIC FATIGUE LIFE ANALYSIS OF COMBUSTOR LINER: 

 Probabilistic fatigue life cycle analysis of the combustor liner was performed as required by 

the NASA project manager. The NESSUS capability for the harmonic loads was used to 

compute the probabilistic responses of a combustor liner subject to high temperatures. Material 

properties were input using the elasticity matrix coefficients. The probabilistic analysis input file 

was received from Dr. S. Pai of the NASA Glenn Research Center. Several NESSUS analyses 

runs were made for different degraded D-matrix coefficients due to the cyclic loads. Material 

degradation of these coefficients was performed using the multi-factor-interaction-model 
NASA/CRó2003-212126 5 

(MFIM). Probabilistic cyclic stresses and respective sensitivity factors were computed using 

NESSUS computer code. 

 Also, the material strength cumulative distribution function using the Weibull distribution 

was computed for different cyclic load cycles. The strength degradation was achieved using 

MFIM. Degradation due to both the temperature as well as cyclic load effects was accounted in 

the computation process. CDF of strength under different load cycles was computed. The life 

cycle curves at different probability levels generated using the results of probabilistic strength 

and stress. Also, the probability of failure as well as survival probability curves for different load 

cycles were developed. The details of the analysis were reported in the March 1997 monthly 

progress report and are attached in the Appendix F. 

NASA/CRó2003-212126 7 

APPENDIX A: USERíS GUIDE TO THE UPDATED EST/BEST SOFTWARE SYSTEM 

A.1 Interactive Input General Information 

The structure of the IPACS input file reflects the modularity of each module. The structured 

format helps the user locate specific input data and manually enter or edit it. The IPACS input 

file can have any user-specified filename, but must have a .DAT extension. The input file may 

consist of up to six input data blocks; the data blocks must be separated by delimiters beginning 

with the $ character. If multiple sections are desired, they must be arranged in the following 

order: 

 $COB 

 - Automatic Mesh Generation Input - 

 ï 

 ï 

 ï 

 $PIC 

 - Material Property Uncertainty Input - 

 ï 

 ï 

 ï 

 $NES 

 - Finite Element Input - 

 ï 

 ï 

 ï 

 $RAN 

 - Structure Level Random Variable Input - 

 ï 

 ï 

 ï 

 $FPI 

 - Probabilistic Output Request Input - 

 ï 

 ï 

 ï 

 $EXE2 

 -Execution Control Input 

 ï 

 ï 

 ï 

The delimiters may be abbreviated to the first four characters (i.e. $COB, $PIC, $NES, $FPI). 
NASA/CRó2003-212126 8 

 The structure of the NESSUS input file is same as that is described in the NESSUS 

manual. 

 During interactive processing of NESSUS input blocks, scratch files may also be created 

with the following extensions and formatting: 

IPACS/NESSUS Body Force Block Card 1: *BODY, IBODY(I) 

input filename.BODY Card 2 (IBODY=1): X-COMP(F), Y-COMP(F), Z-COMP(F) 

 Card 2 (IBODY=2): X1(F), Y1(F), Z1(F) 

 Card 3 (IBODY=2): X2(F), Y2(F), Z2(F) 

IPACS/NESSUS Boundary Conditions Block

input filename.BOUND Cards 1 thru N: NODE #(I), DOF #(I), DISP(F) 

NESSUS Material Properties Block

input filename.prop Cards 1 thru N: NODE #(I), NODE(J) ,(PROP(I),I=1,5) 

NESSUS Layer Temperature Block

input filename.temp Cards 1 thru N: NODE #(I), NODE(J) ,(TEMP(I),I=1,5) 

IPACS/NESSUS Element Connectivity Block

input filename.CONN Cards 1 thru N: ELEM #(I), INODE(I), JNODE(I), KNODE(I), 

 NODE(I) 

IPACS/NESSUS Nodal Coordinates Block

input filename.COORD Cards 1 thru N: NODE #(I), X(F), Y(F), Z(F), TH(F) 

IPACS/NESSUS Random Variable Coordinates Block

input filename.CRDxxx Card 1: MEAN(F), STD DEV(F), DIST TYPE(I) 

 Cards 2 thru N: NODE #(I), X-SDF(F), Y-SDF(F), Z-SDF(F), 

TH-SDF(F) 

IPACS/NESSUS Distributed Loads Block

input filename.DIST Cards 1 thru N: BEG ELEM(I), END ELEM(I), ICODE(I), 

TRAC(F), PRESS(F), BODY FORCE(F) 

IPACS/NESSUS Random Variable Distributed Loads Block

input filename.DSTxxx Card 1: MEAN(F), STD DEV(F), DIST TYPE(I) 

 Cards 2 thru N: BEG ELEM(I), END ELEM(I), ICODE(I), 

TRAC SDF(F), PRESS SDF(F), BODY 

FORCE SDF(F) 

IPACS/NESSUS Duplicate Nodes Block

input filename.DUPL Cards 1 thru N: MASTER NODE(I), SLAVE NODE(I) 
NASA/CRó2003-212126 9 

IPACS/NESSUS Nodal Forces Block

input filename.FORCE Cards 1 thru N: NODE #(I), DOF #(I), FORCE(F) 

IPACS/NESSUS Random Variable Forces Block

input filename.FRCxxx Card 1: MEAN(F), STD DEV(F), DIST TYPE(I) 

 Cards 2 thru N: NODE #(I), DOF #(I), FORCE SDF(F) 

IPACS Material Orientation Block

input filename.orie Cards 1 thru N: BEG NODE(I), END NODE(I), X-COMP(F), 

 Y-COMP(F), Z-COMP(F) 

where xxx is a three-digit number identifying the random variable and where (I) indicates integer 

and (F) indicates floating point numbers. 

 The IPACS/NESSUS scratch files are useful in recovering data following a program abort 

or a system failure. To recover data, use the "Input Existing File" options found on many of the 

menus, after reentering the input module using a filename different than the one used in the 

previous run. The quantities found in each of these files are written in free format consistent 

with the IPACS/NESSUS convention. This feature also allows users to import their own mesh, 

boundary conditions, and loads from outside the input module. To import this data, use the 

scratch file naming convention described above and simply have the data read into the program. 
NASA/CRó2003-212126 10 

A.2 Detailed Description of the Interactive Input Module 

 As described in section 3.1, the IPACS/NESSUS input file consists of five separate 

sections including automatic mesh generation module, a module to compute probabilistic 

composite material properties, probabilistic finite element analysis module, and probability 

algorithm module. 

 The IPACS code contains an interactive input module that allows the user to interactively 

create or edit an IPACS input file and submit it for processing. Interactive module enables an 

inexperienced user to prepare the input in a user-friendly manner in a short time without making 

common mistakes. This module allows creating or editing the input file with little or no 

knowledge of the file's structure and format, and thus allows an inexperienced user to run the 

code and come up to speed more quickly. 

 The interactive input module is designed for ease of use. An input session need not be 

completed in one sitting: once an IPACS input file has been created it can be saved and returned 

to later for further editing, or in order to enter the execution mode and run the code. (For 

example, the user can enter or change the finite element mesh inputs, save the entries or edits, 

exit the IPACS program, and return later to add or edit the material specifications.) 

 An input session is begun at the main menu, which offers six options that allow the user 

quick access to input functions (refer to Figure 3.2.1of the IPACS manual). The six input 

options may be selected and run in any order. The options access a series of menus in which the 

user is prompted for information to enter or change. 

A.3 Batch Input

 IPACS input can be prepared manually or by using any other preprocessor and processing 

it in a batch mode. The procedure to prepare the input is described in the following section. 

 As described in section A.1, the input file is divided into several different blocks. The 

block pertaining to the automatic mesh generation data should not be used in the batch mode. 

Each of the material property uncertainty input and finite element input data blocks are divided 

into parameter and model data groups. The parameter group of a data block defines the size of 

the problem, whereas the model group of the data block contains the actual model data. In both 

the data blocks, the model group always follows the parameter group. Also, a ëENDí card marks 

end of the parameter group in a data block. The $PIC input data block contains the data related to 

the material properties and the lay-up configuration of composites in the structure. The $NES 

input data block contains the actual finite element data. Detailed input information on each block 

is discussed below: 

A.3.1 Material Property Uncertainty Input Data Block: 

 The material property uncertainty input data block begins with a '$PIC' card. The 

composite lay-up configuration and material property uncertainties are defined in this block. 
NASA/CRó2003-212126 11 

Normally, the $PIC data block ends with the beginning of the $NES data block (i.e., with a 

'$NESSUS' card). Different key words (a key word always begins with an '*'; asterisk) used in 

the material property uncertainty data block are discussed below: 

A.3.1.1 Material Property Uncertainty Parameter Input Data Group:

CFEM 

 The above card is used to flag ifemx (MV) analysis 

$PICn 

 where n = 0 is used if material properties PDF computation is desired 

 = 1 is used material properties PDF computation is to be bypassed 

*PROSOL 

 The keyword PROSOL is used to define the probabilistic structural analysis solution 

method. The general format is 

 *PROSOL 

 NSOL 

 NMCS 

 where NSOL is the probabilistic solution method. Different available probabilistic 

solution methods and their NSOL values are given below: 

 NSOL = 21 PV Based method using fast probability integrator 

 = 22 Monte Carlo simulation technique for material property related 

 uncertainties 

 NMCS = No. of samples for Monte-Carlo simulation (required for NSOL = 22) 

*INDZON 

 The keyword INDZON is used to define the total number of statistically independent 

zones in the structure. The general input format is 

 *INDZON 

 NDZON 

 where NDZON is the total number of independent zones in a composite structure. 

*PLYGRP 

 The keyword PLYGRP is used to specify the total number of ply groups in each 

independent zone. The general input format is 

 *PLYGRP 

 INDI(1) NLGRP(1) 

 INDI(2) NLGRP(2) 

 INDI(3) NLGRP(3) 

 . . 

 . . 

 . . 

 INDI(n) NLGRP(n) 
NASA/CRó2003-212126 12 

 Where INDI is the independent zone no. NLGRP is the total number of ply groups in an 

independent zone. 

 There will be NDZON number of lines under this keyboard. 

 Note: *INDZON key word card must precede *PLYGRP key word card. 

*NODGRP 

 The above keyword is used to specify the total number of node groups. A node group 

used to identify the common independent zone and the common layer group for all the nodes in a 

group. The general format is: 

 *NODGRP 

 NGRP 

 where NGRP is the total number of node groups. 

*PLIES 

 The keyword PLIES is used to specify the maximum number of plies that exists in an 

independent zone. The general input format is: 

 *PLIES 

 INDI(1) NMAXPL(1) 

 INDI(2) NMAXPL(2) 

 INDI(3) NMAXPL(3) 

 . . 

 . . 

 . . 

 INDI(n) NMAXPL(n) 

 where INDI is the independent zone No., and NMAXPL is the maximum number of plies 

in an independent zone. The maximum number of plies for all the independent zones must be 

defined. 

 Note: *INDZON key word card must precede *PLIES key word card. 

*MATSYS 

 The keyword MATSYS is used to specify the total number of material systems in a 

structure. The general input format is: 

 *MATSYS 

 NMAT 

 where NMAT is the total number of material systems in a structure. 

*ORISYS 

 The keyword ORISYS is used to specify the total number of orientation systems in a 

structure. The general input format is: 

 *ORISYS 

 NORI 
NASA/CRó2003-212126 13 

 where NORI is the maximum number of orientation systems in a structure. 

*THKSYS 

 The keyword THKSYS is used to specify the total number of thickness systems in a 

structure. The general input format is: 

 *THKSYS 

 NTHK 

 where NTHK is the total number of thickness systems in a structure. 

*RNDGRP 

 This key word is used to specify the maximum number of random field groups related to 

material properties for each independent zone in a structure. 

 The general input format is: 

 *RNDGRP 

 INDI(1) NRFT(1) 

 INDI(2) NRFT(2) 

 INDI(3) NRFT(3) 

 INDI(n) NRFT(n)

 where INDI is the independent zone number NRFT is the total number of random field 

groups (*CORTAB) related to the constituent material properties in an independent zone. 

 The number of random field groups related to the constituent material properties for all 

the independent zones must be defined. 

 Note: *INDZON key word card must precede *RNDGRP card. 

*RANTEM 

 This key word is used to specify the maximum number of random variables related 

thermal loads and corresponding number of perturbation sets. 

 The general input format is: 

 *RANTEM 

 NRTEM NTPER 

 where NRTEM is the number of temperature related random variables and NRPER is the 

total number of perturbations related to the temperature related random variables. 

 The number of random variables related to the temperatures for all the independent zones 

must be defined.

*END 

 This key word card is always required to terminate the parameter data block input. It 

must always be put at the very end of parameter data input block. The general input format is 

 *END

A.3.1.2 Material Property Uncertainty Model Input Data Group:

*NODGRP 
NASA/CRó2003-212126 14 

 The keyword NODGRP is used to specify the node numbers that belong to a specific ply 

group of a specific independent zone. The general input format is shown below: 

 *NODGRP 

 IG 

 NODB(IG) NODE(IG) INDZ(IG) ILAY(IG) 

 where IG is the node group number 

 NODB(IG) is the beginning node number of a series of nodes in group IG, 

 NODE(IG) is the end node number of a series of nodes in group IG, 

 ILAY(IG) is the ply group number to which NODB(IG) through NODE(IG) 

 belongs 

 INDZ(IG) is the independent zone number to which NODB(IG) through 

NODE(IG) belongs 

 Remember that the node groups for all the ply groups and all the independent zones must 

be specified. 

*RESTAB 

 The keyword RESTAB is used to specify the plies and their responses for which the 

probabilistic simulation is desired. The response table for all the plies within an independent 

zone must be specified. The code used to specify the computational request is 0(zero) or 1(one). 

0 means the probabilistic ply response computation is not desired and 1 means the probabilistic 

ply response computation is desired. The general input format is: 

 *RESTAB 

 IZ 

 NPB, NPE 

 IEX(1) IEXE(2) Ö (EX(23) 

 where 

 IZ is the independent zone number 

 NPB is the beginning ply number of independent zone IZ 

 NPE is the end ply number of independent zone IZ 

 IXE(I) is the code to request ith probabilistic ply response 

 Following is the list of ply responses for which the probabilistic analysis can be 

performed. 

 1 Longitudinal strain 

 2 Transverse strain 

 3 Shear strain 

 4 Longitudinal stress 

 5 Transverse stress 

 6 Shear stress 

 7 Longitudinal tensile strength 

 8 Longitudinal compressive strength 

 9 Transverse tensile strength 

 10 Transverse compressive strength 

 11 Shear strength 
NASA/CRó2003-212126 15 

 12 Modified distortion energy failure criterion 

 13 Hoffmanís failure criterion 

 14 Interply delamination failure criterion 

 15 Fiber crushing criterion (compressive strength) 

 16 Delamination criterion (compressive strength) 

 17 Fiber micro buckling criterion (compressive strength) 

 18 Failure in longitudinal direction 

 19 Failure in transverse direction 

 20 Failure in Shear strength 

 21 Out of plane Shear 13 

 22 Out of plane Shear 23 

 23 Sigma zz 

*PLYTAB 

 The keyword PLYTAB is used to specify the ply configuration of a laminate in a ply 

group of any independent zone. The ply configuration of a laminate is specified by the existence 

of a ply. The code used to specify the existence is 0(zero) or 1(one). 0 means the ply does not 

exists and 1 means the ply exists. The general input format is: 

 *PLYTAB 

 IZ, LG, 

 NPL(1,IZ,LG), NPL(2,IZ,LG), ... NPL(NMAXPL(IZ),IZ,LG) 

 where 

 IZ is the independent zone number 

 LG is the ply group number of independent zone IZ 

 NMAXPL(IZ) is the maximum number of plies in an indpendent zone IZ 

 NPL is the ply existence code, either 0 or 1. Code zero indicates that 

 the ply does not exist and 1 indicates that the ply exists 

*MATSYS 

 The keyword MATSYS is used to specify the uncertainties of a specific material. The 

general input format is: 

 *MATSYS 

 I 

 'KEY(I)KEYS(I)' FVRM(I) VVRM(I) FRS(I) FVRMS(I) VVRMS(I) 

 C(1,I) C(2,I) C(3,I) ... C(29,I) 

 CF(I), CVV(I), CFRS(I), CFS(I), CVVS(I) 

 CS(1,I) CS(2,I) CS(3,I) ... CS(29,I) 

 IM(1,I) IM(2,I) IM(3,I) ... IM(29,I) 

 IF(I), IV(I), IFR(I), IFS(I), IVS(I) 

 IMS(1,I) IMS(2,I) IMS(3,I) ... IMS(29,I) 
NASA/CRó2003-212126 16 

 where I is the material system number KEY(I) and KEYS(I) are the acronyms defining 

the I th primary and secondary composite material system . The acronym must be specified in 

quotes ('). The acronym is used to pull the mean values of composite material properties from 

the data bank. Refer to Table 3.4.1.1 and Table 3.4.1.2 of the IPACS manual for the description 

of composite material acronyms. FVRM(I), VVRM(I), FRS(I), FVRMS(I), and VVRMS(I) are 

mean values of the primary system fiber volume ratio, the primary system void volume ratio, 

fraction of secondary system, the secondary system fiber volume ratio and the secondary system 

void volume ratio respectively of the I th material system. C(n,I) is the coefficient of variation 

for the nth primary material property random field of the I th material system. The list of the 

random field numbers is given in section 3.5 of IPACS manual. CF(I), CVV(I), CFRS(I), 

CFS(I), CVVS(I) are the coefficient of variation for the primary system fiber volume ratio, the 

primary system void volume ratio, fraction of secondary system, the secondary system fiber 

volume ratio and the secondary system void volume ratio respectively of the I th material system. 

IM(n,I) is the distribution type for the n-th material property random field number of I th primary 

material system. IF(I), IV(I), IFR(I), IFS(I), IVS(I) are the distribution types for the primary 

system fiber volume ratio, the primary system void volume ratio, fraction of secondary system, 

the secondary system fiber volume ratio and the secondary system void volume ratio respectively 

of the I th material system. 

IMS(n,I) is the distribution types for the nth secondary system material property number. No 

more than ten integer numbers and eight real numbers in a given line can be specified. If there 

are more numbers for a particular data type, then their input should continue in the subsequent 

lines. 

*ORISYS 

 The keyword ORISYS is used to specify uncertainties of the ply orientations. The 

general input format is: 

 *ORISYS 

 OM(1) OM(2) ... OM(NORI) 

 OC(1) OC(2) ... OC(NORI) 

 IO(1) IO(2) ... IO(NORI) 

 where OM(i), OC(i) and IO(i) are the mean, a constant to specify standard deviation 

(standard deviation = 90 x constant), and the distribution type respectively of the ith orientation 

angle system. NORI is the total number of orientation systems. 

*THKSYS 

 The keyword THKSYS is used to specify uncertainties of the ply thickness. The general 

input format is: 

 *THKSYS 

 TM(1) TM(2) ... TM(NTHK) 

 TC(1) TC(2) ... TC(NTHK) 

 IT(1) IT(2) ... IT(NTHK) 

 where TM(i), TC(i) and IT(i) are the mean, the coefficient of variation and distribution 

type respectively of the ith thickness system. NORI is the total number of orientation systems. 

NTHK is the total number of thickness systems. 
NASA/CRó2003-212126 17 

*MATTAB 

 The keyword MATTAB is used to specify the material of each ply of a laminate in an 

independent zone. The material property uncertainty specification of a ply in an independent 

zone corresponds to a material system id. All the plies of an independent zone must have a 

material system id defined, and the material property uncertainty for that id must also be defined 

in 

*MATSYS card. The general input format is: 

 *MATTAB 

 IZ 

 NMT(IZ,1) NMT(IZ,2) NMT(IZ,3) ... NMT(IZ,NMAXPL(IZ)) 

 where IZ is the independent zone number. NMT(IZ,n) is the material system number of 

the nth ply of independent zone IZ, and NMAXPL(IZ) is the maximum number of plies in 

independent zone IZ. 

*ORITAB 

 The keyword ORITAB is used to specify the uncertainties of each ply orientation of a 

laminate in an independent zone. The orientation uncertainty specification of a ply in an 

independent zone corresponds to an orientation system id. All the plies of an independent zone 

must have an orientation system id defined, and the orientation uncertainty for that id must also 

be defined in 

*ORISYS card. The general input format is: 

 *ORITAB 

 IZ 

 NOT(IZ,1) NOT(IZ,2) NOT(IZ,3) ... NOT(IZ,NMAXPL(IZ)) 

 where IZ is the independent zone number, NOT(IZ,n) is the orientation system number of 

the nth ply of independent zone IZ, and NMAXPL(IZ) is the maximum number of plies in 

independent zone IZ. 

*THKTAB 

 The keyword THKTAB is used to specify the uncertainties of each ply thickness of a 

laminate in an independent zone. The thickness uncertainty specification of a ply in an 

independent zone corresponds to a thickness system id. All the plies of an independent zone 

must have a thickness system id defined, and the thickness uncertainty for that id must also be 

defined in 

*THKSYS card. The general input format is 

 *THKTAB 

 IZ 

 NTT(IZ,1) NTT(IZ,2) NTT(IZ,3) ... NTT(IZ,NMAXPL(IZ)) 

 where IZ is the independent zone number and NTT(IZ,n) is the thickness system number 

of nth ply of independent zone IZ, and NMAXPL(IZ) is the maximum number of plies in 

independent zone IZ. 
NASA/CRó2003-212126 18 

*CORTAB 

 This key word is used only in case of a primitive variable based method to specify the 

correlation of a particular random field between different plies (correlation table) of a composite 

material. Refer to Appendix A for the definition of a correlation table. The general input format 

for the primitive variable based method is: 

 *CORTAB 

 IZ 

 NRFi NRFj 

 ICOR(1) ICOR(2) ... ICOR (NMAXPL(IZ))

 Where IZ is the independent zone number 

 NRFi is the beginning material related random field number. NRFj is the 

end material related random field number (Legal list of material related 

random field numbers are given in Appendix A, Section A.3). 

 ICOR(i) is the correlation id number for the ith ply 0<= ICOR(i) <=NMAXPL(IZ) 

 NMAXPL(IZ) is the maximum number of plies in independent zone, IZ. 

 The cards (NRFi NRFj) and (ICOR(1), ... ,ICOR(NMAXPL(IZ)) can be repeated for 

additional random fields in independent zone, IZ. For additional independent zones the data 

should be specified in the same order discussed above. 

 Remember that the correlation table for all the material related random fields of all the 

independent zones should be specified. The random field automatically becomes deterministic if 

its correlation table is not defined. 

*MEANTM 

 This key word is used to specify mean ply temperatures at different nodes. The 

temperature groups and the number of node groups must be exactly same. The correlated 

temperatures at different nodes can be specified using the *RELPER card. The standard 

deviations for the temperatures are specified in the *STDVTM card. The first ply is the bottom 

ply based on the local z-definition. The general input format for the definition of the mean ply 

temperatures is: 

 *MEANTM 

 NODi NODj 

 PT1 PT2 Ö PTn

 NODi is the beginning ply number. 

 NRFj is the last node number in a group. 

 PTi is the mean ith ply temperature 

 The cards (NODi NODj) and (PT1, ... ,PTn) can be repeated for additional nodes. 

*STDVTM 

 This key word is used to specify standard deviation of the ply temperatures at different 

nodes. The temperature groups and the number of node groups must be exactly same. The first 

ply is the bottom ply based on the local z-definition. The general input format for the definition 

of the ply temperature standard deviation is: 
NASA/CRó2003-212126 19 

 *STDVTM 

 NODi NODj 

 PSTD1 PSTD2 Ö PSTDn

 NODi is the beginning ply number. 

 NRFj is the last node number in a group. 

 PSTDi is the ith ply temperature standard deviation 

 The cards (NODi NODj) and (PSTD1, ... ,PSTDn) can be repeated for additional nodes. 

*RELPER 

 This key word is used to specify the autocorrelation matrix for random temperature 

variables. Basically, it represents the eigen-vectors of the correlation matrix. The general input 

format for the definition of the ply temperature standard deviation is: 

 *RELPER 

 NR 

 NODi NODj 

 EG1 EG2 Ö EGn

 NODi is the beginning ply number. 

 NRFj is the end lst ply number. 

 EGi is the ith ply autocorrelation coefficient 

 The cards (NODi NODj) and (EG1, ... ,EGn) can be repeated for additional nodes. 

*IRVPER 

 This key word is used to specify the perturbation of particular temperature random 

variables. Any random variable can be perturbed for any number of times. It also signifies in 

what order the variables shall be perturbed. Input entry in this card must be used in conjunction 

with the *ABSPER card which specifies the corresponding perturbation magnitude. Basically, it 

represents the eigen-vectors of the correlation matrix. The general input format for the definition 

of the temperature random variables perturbation definition is: 

 *IRVPER 

 NP(1) NP(2) Ö NP(n) 

 where NP(i) represents the ith perturbation of random variable NP(i). 

 The cards (NPi NPn) can be repeated for additional variable perturbations. 
NASA/CRó2003-212126 20 

*ABSPER 

 This key word is used in conjunction with the *IRVPER input card. It is used to specify 

the magnitude of the perturbation for the corresponding random variable in the *IRVPER card. 

The general input format for the definition of the perturbation magnitude is: 

 *ABSPER 

 PV(1) PV(2) Ö PV(n) 

 where PV(i) represents the mangitude of the ith perturbation of random variable NP(i) 

specified in *IRVPER card. 

 The cards (PVi PVn) can be repeated for additional variable perturbations. 

*REFTEM 

 This key word is used to specify the reference temperature of the material. The general 

input format for the definition of the reference temperature is: 

 *REFTEM 

 IZ 

 REFTM 

 where IZ represents the independent zone and the REFTEM the reference temperature in 

o

F units. The cards IZ and REFTM can be repeated for additional independent zones. 

A.3.2 Input for Probabilistic Output Request: 

 This section of input always begins with $FPI card. The response locations on the 

structure and the type of probabilistic analysis are defined in this section of input. The input 

details are given in the following card: 

 *STRU 

 ISTAT NTYPE NODN IDUMP IDUMP NCOMP 

 where 

 ISTAT = 1 for the Static Analysis 

 = 2 for the Buckling Analysis 

 = 3 for the Frequency Analysis 

 NTYPE = 1 for Displacement Response 

 = 2 for Ply Strain/Stress Response 

 NODN Node Number where probabilistic output is requested 

 IDUMP Reserved for future use 

 NCOMP displacement or stress/strain component in static analysis 

 mode number in case of buckling or frequency analysis 
NASA/CRó2003-212126 21 

A.3.3 IPACS Execution Control Input: 

 The input to this section always begins with $EXE2 card. The IPACS execution control 

is defined in this section. The input to this section is as follows: 

 IX1 IX2 IX3 IX4 IX5 

 

 where the variables IX1, IX2, IX3, IX4 and IX5 could be either 0 (zero) or 1. 0 means 

suppress the execution of the analysis type discussed below. 1 means perform the analysis. 

 IX1 = 1 Compute the perturbed material properties at every scale. 

 IX2 = 1 Prepare the input file for the probabilistic finite element analysis. 

 IX3 = 1 Perform the probabilistic finite element analysis. 

 IX4 = 1 Extract desired structural responses as indicated in $FPI section. 

 IX5 = 1 Compute the CDF of desired structural responses 

A.3.4 Output

 The user generally controls IPACS output. However, by default IPACS provides minimum 

necessary output required for the probabilistic assessment of composite structure. The minimum 

output consists of the following: (i) an echo of the input, (ii) CDF of the material properties and 

the desired structural response, (iii) the sensitivity factors of the primitive variables for the 

material properties and the desired structural response. The important output files are 

xxx21.fpimov, xxx21.nesout and xxx21.rantab. The names of these files and their respective 

contents are listed in Table A.3.4.1, on the next page. 

 Several other output files are created at intermediate computation stage or at the end of the 

computations. Some of these files provide an interface between different modules or serve as a 

database system. These files contain information for the user to study the overall problem 

behavior in greater detail. 
NASA/CRó2003-212126 22 

 Table A.3.4.1 List of Output Files

 jn - jobname 

 IZ - Independent Zone No. 

 LG - Ply Group No. 

 IPM - Method No. 

 $$ - A unique job number assigned by the computer 

File Name File Contents 

jn.msp-IZ-LG Mean value and standard deviations for ply material 

properties. 

jn.cpp-IZ-LG CDF of ply material properties 

jn.cpl-IZ-LG CDF of laminate material properties 

jn-IZ-LG-IPMIC.PIC 

If IC = 0 Mean Values of material properties. Perturbations 

of A, C, and D matrices terms for primitive variable based 

method 

jn-IZ-IPM.dat Data required for finite element analysis. The file contains 

the data supplied by the user and that generated by the 

program 

jn-IZ-IPM.pdb Perturbation database. 

jn-IZ-IPM.datu Perturbation data for each desired response. 

jn-IZ-IPM.dist Statistics of Primitive Variables for each independent zone. 

jn-IPM.datu FPI input file. 

jn-IPM.dist Statistics of primitive variables required for the probabilistic 

analysis of structural response. 

jn-IPM.fpinp Input file prepared by program to perform fast probability 

integration. 

jn-IPM.fpimov Sensitivity factors of primitive variables at cumulative 

probability levels of 0.001 and 0.999. 

jn-IPM.fpibin FPI logfile 

jn-IPM.nesout Discretized CDF of a structural response. 

jn-IZ-IPM.out Echo of FEM input and Results of Unperturbed Solution. 

jn-IBM.FPIMOV Sensitivity factors for independent random variables at 

probability levels 0.001 and 0.999. 
NASA/CRó2003-212126 23 

SAMPLE INPUT FILE:

CFEM 

$PIC1 

*INDZON 

 1 

*NODGRP 

 1 

*PROSOL 

 21 

*PLYGRP 

 1 1 

*PLIES 

 1 8 

*RNDGRP 

 1 2 

*MATSYS 

 1 

*ORISYS 

 4 

*THKSYS 

 1 

*RANTEM 

 1 4 

*END 

*NODGRP 

 1 

 1 9 1 1 

*RESTAB 

 1 

 1 8 

c o-skip fpi 1-with fpi 

 0 0 0 1 1 0 0 0 0 0 

 0 0 0 0 0 0 0 0 0 0 

 0 0 0 

*PLYTAB 

 1 1 

 1 1 1 1 1 1 1 1 

*MATSYS 

 1 

'AS--EPOXAS--EPOX' 0.60 0.02 0.000001 0.60 0.02 

 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 

 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 

 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 

 0.05 0.05 0.05 0.05 0.05 

 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 

 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 

 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 

 2 2 2 2 2 2 2 2 2 2 

 2 2 2 2 2 1 1 2 2 2 

 2 2 2 2 1 1 1 2 2 

 2 2 2 2 2 

 2 2 2 2 2 2 2 2 2 2 

 2 2 2 2 2 1 1 2 2 2 

 2 2 2 2 1 1 1 2 2 

*MATTAB 

 1 

 1 1 1 1 1 1 1 1 

*ORISYS 

 -45.0 0.0 45.0 90.0 

 0.02 0.02 0.02 0.02 

 2 2 2 2 

*ORITAB 

 1 

 3 1 2 4 4 2 1 3 
NASA/CRó2003-212126 24 

*THKSYS 

 0.020 

 0.050 

 2 

*THKTAB 

 1 

 1 1 1 1 1 1 1 1 

*CORTAB 

 1 

 1 1 

 1 1 1 1 1 1 1 1 

 33 33 

 1 1 1 1 1 1 1 1 

*MEANTM 

 1 9 

 200.0 200.0 200.0 200.0 200.0 200.0 200.0 200.0 

*STDVTM 

 1 9 

 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 

*RELPER 

 1 

 1 9 

 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 

*IRVPER 

 1 1 1 1 

*ABSPER 

 -2.0 -1.0 1.0 2.0 

*END 

$NES 

*FEM 

*DISP 

*FORC 1 

*ELEM 4 

 75 

*COMPOSITE 

*TEMP 

*PERT 

*NODES 9 

*BOUN 18 

*CONS 0 

*PRIN 

*END 

*INC 

 0 

*ITER 

 100 0.0001 0.0001 0.0001 0.0001 

*COOR 

 1 0.000 0.000 0.000 1.0 

 2 1.000 0.000 0.000 1.0 

 3 2.000 0.000 0.000 1.0 

 4 0.000 1.000 0.000 1.0 

 5 1.000 1.000 0.000 1.0 

 6 2.000 1.000 0.000 1.0 

 7 0.000 2.000 0.000 1.0 

 8 1.000 2.000 0.000 1.0 

 9 2.000 2.000 0.000 1.0 

*ELEM 75 

 1 1 2 5 4 

 2 2 3 6 5 

 3 4 5 8 7 

 4 5 6 9 8 

*BOUN 

 1 1 0 

 4 1 0 

 7 1 0 

 1 2 0 

 4 2 0 
NASA/CRó2003-212126 25 

 7 2 0 

 1 3 0 

 4 3 0 

 7 3 0 

 1 4 0 

 4 4 0 

 7 4 0 

 1 5 0 

 4 5 0 

 7 5 0 

 1 6 0 

 4 6 0 

 7 6 0 

*FORC 

 5 3 1000.0 

*ORIEN 

 1 9 1.00 0.00 0.00 

 1 9 0.00 0.00 1.00 

C*LAMI 

INCLUDE 

*PRINTOPTION 

 REACTION 

 STRESS 

 STRAIN 

 TOTALDISPLACEMENT 

*END 

$RAN 

*DEFI 1 

 1000.0 100.0 2 

 FORCE 

 5 3 1.0 

$FPI 

*STRU 

 1 1 5 0 0 3 

$EXE2 

 1 1 1 1 1 

NASA/CRó2003-212126 27 

APPENDIX B: 

The probabilistic stress, frequency and buckling analysis for a typical engine structure was 

created and the analysis was performed. The probabilistic analysis of an engine fan, highpressure compressor blades was performed using the integrated EST/BEST software system. 

The uncertainties assumed for the blade are listed in the Table I. Figure 1 shows the cumulative 

distribution (CDF) of the total displacement at the tip of the blade. Figure 2a and Figure 2b 

shows the sensitivity of the total displacement to the primitive variables. The sensitivity of the 

displacement is controlled by the length, modulus, thickness, temperature and coefficient of 

thermal expansion at probability level of 0.001 whereas modulus controls at the probability of 

0.999. Figure 3 shows the CDF of the first natural frequency and figure 4 shows its sensitivity to 

the primitive variables. The scatter of the frequency range between 900 to 1280 cps. The natural 

frequency of the high-pressure compressor (HPC) blade is found to be sensitive to the modulus, 

thickness and mass density at probability level of 0.001 whereas the order of sensitivity changes 

to mass density, modulus and thickness at probability level of 0.999. Figure 5 and figure 6 shows 

the CDF and sensitivity of the critical buckling load for the HPC blade stage 4. The modulus and 

the thickness dominate the critical buckling load at all probability levels. Thus, the critical load 

is thus controlled by the stiffness. 

Table I. Primitive variable uncertainties used for the engine blade

Fan Blade Stage 1 (Stress analysis) 

Variable Scatter (%) Distribution 

Temperature 10.0 Normal 

Length 4.0 Log Normal 

Thickness 2.5 Log Normal 

Modulus of Elasticity 7.0 Weibull 

Coefficient of thermal Expansion 7.0 Normal 

High pressure compressor Stage 2 (Frequency analysis) 

Length 4.0 Log Normal 

Thickness 2.5 Log Normal 

Modulus of Elasticity 7.0 Weibull 

Mass density 7.0 Normal 

High pressure compressor Stage 4 (Buckling analysis) 

Length 4.0 Log Normal 

Thickness 2.5 Log Normal 

Modulus of Elasticity 7.0 Weibull 

Poissonís ratio 5.0 Weibull 
NASA/CRó2003-212126 28 

Figure 1.—Cumulative distribution function of the total

 displacement at the tip of the blade stage 1.

0.0

0.2

0.4

0.6

0.8

1.0

Cumulative probability

0.10 0.16 0.20 0.24 0.12 0.14 0.18 0.22

Total displacement node 5 to component 1 to 6

Figure 2.—Sensitivity of total displacement at the tip of the fan blade stage 1 to the primitive random variable

 for (a) 0.001 probability and (b) 0.999 probability.

–0.75

–0.25

–0.50

0.00

0.25

0.50

0.75

Sensitivity

C

length

C

thickness

M

E M

Alpha T

temperature

(a)

0.75

–0.25

0.00

0.25

0.50

1.00

Sensitivity

C

length

C

thickness

M

E

M

Alpha

T

temperature

(b)
NASA/CRó2003-212126 29 

Figure 3.—Cumulative distribution function of the first

 natural frequency—high pressure compressor blade

 stage 2. 

0.0

0.2

0.4

0.6

0.8

1.0

Frequency, cps 

Cumulative probability

900.0 1000.0 1100.0 1200.0 1300.0

Figure 4.—Sensitivity of first natural frequency to the 

 primitive variables—high pressure compressor blade

 stage 4. 

–1.0

–0.8

–0.6

–0.4

–0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.001 Prob.

0.999 Prob.

Thickness Modulus

Mass density 

Sensitivity
NASA/CRó2003-212126 30 

Figure 5.—Cumulative distribution function of the 

 critical buckling load—high pressure compressor 

 blade stage 4. 

0.0

0.2

0.4

0.6

0.8

1.0

Buckling load, lbs

Cumulative probability –300.0 –350.0 –400.0 –450.0 –500.0 –550.0 –600.0

Figure 6.—Sensitivity of the critical buckling load to 

 the primitive variables—high pressure compressor

 blade stage 4. 

–1.0

–0.8

–0.6

–0.4

–0.2

0.0

0.2

Sensitivity

Length

Thickness Modulus

Poisson's

ratio

0.001 Prob.

0.999 Prob.
NASA/CRó2003-212126 31 

APPENDIX C: EST/BEST GRAPHICAL USER INTERFACE SCREENS 
NASA/CRó2003-212126 32 
NASA/CRó2003-212126 33 
NASA/CRó2003-212126 34 
NASA/CRó2003-212126 35 
NASA/CRó2003-212126 36 
NASA/CRó2003-212126 37 

NASA/CRó2003-212126 39 

APPENDIX D: IPACS/COBSTRAN DEMONSTRATION PROBLEMS 

The epoxy-graphite laminate with configuration (0/45/-45/90)2 was used for the blade. The 

uncertainties in the constituents such as fiber, matrix, and fabrication variables were considered 

at the material level. Pressure loads were considered in the assessment process. Initially 

uncertainties in all the material variables were included in the analysis. However, the significant 

variables have been listed here for the sake of brevity. All the uncertainties considered for the 

probabilistic analysis of a blade are listed in the Table I. Figure 2a thorough 4a respectively 

show the cumulative distribution function (CDF) of the longitudinal, transverse and shear 

stresses at the root of blade for a 0o ply. Correspondingly, the Figures 2b through 4b show their 

respective sensitivities to the primitive variables. It is seen that the longitudinal, transverse and 

shear stresses in the 0o

 ply at the root are mainly sensitive to the ply thickness indicating the 

stiffness control. However the transverse and the shear stresses are sensitive to the additional 

primitive variables such as fiber modulus, matrix modulus and fiber volume ratio. Similarly 

Figures 5a through 7a show the CDF of longitudinal, transverse and shear stresses for a 45o

 ply 

and Figures 8a through 10a for the 90o

 ply. Respective sensitivities are shown in Figures 5b 

through 10b. Trends similar to the 0o ply are also observed for the 45o and 90o plies except the 

fact that matrix modulus and shear modulus participation becomes obvious. The shear stress in 

the 90o

 ply shows stress reversal since it is controlled by the ply mis-alignment. Nonetheless, the 

stiffness controls stresses in all the plies. Therefore, the uncertainties in the thickness as well as 

ply mis-alignment must be controlled to reduce scatter in the stresses. Uncertainties in the 

displacements, ply strains, strengths can also be simulated in an exactly identical manner. 

Figure 11a show the cumulative distribution function of the first natural frequency of the 

hollow blade and the Figure 11b show its sensitivity to the primitive variables. The scatter in the 

frequency is 1000 cps to 1350 cps. The Fiber modulus, fiber density, matrix density, fiber 

volume ratio and the ply thickness are the most significant variables to the scatter in the 

frequency. The variable sensitivity shows that the stiffness controls at the low probability level, 

whereas the mass dominates at the higher probability level. 

A distributed point load at the tip of the blade in its axial direction was applied to evaluate 

the probabilistic buckling analysis. Figure 12a shows that first critical buckling load scatter 

range is 5 Lbs. to 18Lbs. (compressive). The critical load magnitude is quite small since it is 

controlled by the stiffness as evidenced by sensitivities shown in Figure 12b. At low probability 

level the most significant variables are fiber modulus 11, ply thickness and the fiber volume ratio 

(FVR) whereas the ply thickness, FVR and fiber modulus 11 are sensitive at the high probability 

level. Permissible scatter in these variables should be reduced to minimize the scatter in the 

buckling load. 
NASA/CRó2003-212126 40 

Table I. Primitive variable uncertainties used for the composite engine blade

Composite Hollow Blade 

Variable Scatter (%) Distribution 

Graphite Fiber (AS--):

Modulus 11 7.0 Weibull 

Modulus 22 7.0 Weibull 

Modulus 12 8.0 Log Normal 

Density 5.0 Normal 

Epoxy matrix (EPOX)

Modulus 4.0 Weibull 

Density 5.0 Log-Normal 

Fabrication variables

Fiber volume ratio 5.0 Normal 

Thickness 6.0 Log-Normal 

Ply mis-alignment 2.0 Degrees Normal 

Figure 1.—(a) Finite element model of the hollow engine blade. (b) Finite element model

 of the hollow engine blade with spars.

y

x

z

y

x

z
NASA/CRó2003-212126 41 

0.999 Prob.

0.001 Prob.

Ply misalignment 

Ply thickness

Figure 2.—(a) Cumulative distribution function of the longitudinal stress at root in a 0 degree ply. (b) Sensitivity

 of longitudinal stress in 0 degree ply at root to the primitive variables 

–0.2 0.0 0.2 0.4 0.6 0.8 1.0

Sensitivity

0.0

0.2

0.4

0.6

0.8

1.0

10.0 30.0 50.0 70.0 90.0

Longitudinal stress (ksi)

Cumulative probability

0.999 Prob.

0.001 Prob.

Ply misalignment 

Ply thickness

-0.2 0.0 0.2 0.4 0.6 0.8 1.0

Sensitivity

Matrix MOD. 

FVR

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.2 0.4 0.6 0.8 1.0 1.2 1.4

Transverse stress, ksi

Cumulative probability

Fiber MOD.

Fiber MOD. 22

Figure 3.—(a) Cumulative distribution function of the transverse stress at root in a 0 degree ply. (b) Sensitivity

 of transverse stress in 0 degree ply at root to the primitive variables. 
NASA/CRó2003-212126 42 

0.999 Prob.

0.001 Prob.

Ply misalignment 

Ply thickness

Figure 4.—(a) Cumulative distribution function of the shear stress at root in a 0 degree ply. (b) Sensitivity of

 shear stress in 0 degree ply at root to the primitive variables.

–0.2 0.0 0.2 0.4 0.6 0.8

Sensitivity

Fiber MOD. 11 

Matrix shear MOD. 

0.0

0.2

0.4

0.6

0.8

1.0

0.2 0.4 0.6 0.8 1.0 1.2

Cumulative probability 

Shear stress, ksi

Figure 5.—(a) Cumulative distribution function of the longitudinal stress at root in a 45 degree ply. (b) Sensitivity

 of longitudinal stress in 45 degree ply at root to the primitive variables.

–0.7 –0.5 –0.3 –0.1 0.1 0.3 0.5 0.7 0.9

Sensitivity

0.0

0.2

0.4

0.6

0.8

1.0

16.0 27.0 38.0 49.0 60.0

Logitudinal stress, ksi

Cumulative probability

0.999 Prob.

0.001 Prob.

Ply misalignment 

Ply thickness
NASA/CRó2003-212126 43 

Figure 6(a).—Cumulative distribution function of the transverse stress at root in a 45 degree ply. (b).Sensitivity

 of transverse stress in 45 degree ply at root to the primitive variables. 

–0.2 0.0 0.2 0.4 0.6 0.8

Sensitivity

0.999 Prob.

0.001 Prob.

Matrix MOD. 

FVR

Ply misalignment

Ply thickness 

0.0

0.2

0.4

0.6

0.8

1.0

2.0 3.0 4.0 5.0 6.0 7.0

Transverse stress, ksi

Cumulative proability

Fiber MOD. 22

Fiber MOD. 11

Figure 7.—(a) Cumulative distribution function of the shear stress at root in a 45 degree ply. (b) Sensitivity

 of shear stress in 45 degree ply at root to the primitive variables.

–0.4 –0.2 0.0 0.2 0.4 0.6 0.8 1.0

Sensitivity

0.999 Prob.

0.001 Prob.

FIB. MOD. 11 

FIB. MOD. 12

Matrix MOD. 

Ply misalignment 

Ply thickness

0.0

0.2

0.4

0.6

0.8

1.0

1.0 2.0 3.0 4.0 5.0

Shear stress, ksi 

Cumulative probability
NASA/CRó2003-212126 44 

Figure 8.—(a) Cumulative distribution function of the longitudinal stress at root in a 90 degree ply. (b) Sensitivity

 of longitudinal stress in a 90 degree ply at root to the primitive variables.

-0.5 -0.3 -0.1 0.1 0.3 0.5 0.7 0.9

Sensitivity

0.999 Prob.

0.001 Prob.

FIB. MOD. 11

FIB. MOD. 22

Matrix MOD.

FVR

Ply misalignment 

Ply thickness 

0.0

0.2

0.4

0.6

0.8

1.0

1.0 3.0 5.0 7.0 9.0

Longitudinal stress, ksi

Cumulative Probability

0.999 Prob.

0.001 Prob.

FIB. MOD. 11

FIB. MOD. 22

Matrix MOD.

FVR

Ply thickness 

-0.7 -0.5 -0.3 -0.1 0.1 0.3 0.5 0.7 0.9

Sensitivity

0.0

0.2

0.4

0.6

0.8

1.0

6.0 9.0 12.0 15.0 18.0

Transverse stress, ksi

Cumulative Probability

Figure 9.—(a) Cumulative distribution function of the transverse stress at root in a 90 degree ply. (b) Sensitivity 

 of transverse stress in a 90 degree ply at root to the primitive variables.
NASA/CRó2003-212126 45 

Ply thickness 

Figure 10.—(a) Cumulative distribution function of the shear stress at root in a 90 degree ply. (b) Sensitivity 

 of shear stress in a 90 degree ply at root to the primitive variables.

–1.0 –0.8 –0.6 –0.4 –0.2 0.0

Sensitivity

Ply misalignment 

0.0

0.2

0.4

0.6

0.8

1.0

–2.0 –1.5 –1.0 –0.5 0.0 0.5 1.0

Shear stress, ksi

Cumulative probability

0.999 Prob.

0.001 Prob.

0.999 Prob.

0.001 Prob.

Figure 11.—(a) Cumulative distribution function of the first natural frequency. (b) Sensitivity of the first natural

 frequency to the primitive variables.

0.0

0.2

0.4

0.6

0.8

1.0

1000.0 1100.0 1200.0 1300.0 1400.0

Cycles/sec

Cumulative probability

–1.0 –0.8 –0.6 –0.4 –0.2 0.0 0.2 0.4 0.6

Sensitivity

Matrix density 

FVR

Fiber density 

Fiber MOD. 11 

Ply thickness
NASA/CRó2003-212126 46 

0.999 Prob.

0.001 Prob.

Figure 12.—(a) Cumulative distribution function of the critical buckling load. (b) Sensitivity of the critical buckling

 to the primitive variables.

0.0

0.2

0.4

0.6

0.8

1.0

Cumulative probability

Ply thickness

Fiber density 

Buckling load, lbs Sensitivity

–1.0 –0.8 –0.6 –0.4 –0.2 0.0

FVR

Fiber MOD. 11 

–8.0 –10.0 –12.0 –14.0 –16.0 –18.0
NASA/CRó2003-212126 47 

APPENDIX E: ALCCA SAMPLE OUTPUT 

 ************************************************* 

 ** ALCCA ** 

 ** Aircraft Life Cycle Cost Analysis ** 

 ** IBM RS/6000 FLOPS Module Version ** 

   

 **  Aerospace Systems Design Laboratory ** 

 ** Georgia Tech, Atlanta GA 30332 ** 

 ************************************************* 

 ============ UNIT PRODUCTION COSTS == 1992. DOLLARS ============ 

 Breakdown of Manufacturing Cost Inflated from 1970 base dollars at 8.00% rate 

 AMPR Weight/Takeoff Gross Weight (lbs) 200132./ 735187. 

 Monthly Production Rate (ac/mon) 7.00 

 Group CF EF % W Weight Cost 

 STRUCTURE 149735.000 195.336 

 WING 55012.766 89.187 

 Aluminum 1.00 1.00 0. 0.0 0.000 

 Titanium 1.51 1.00 70. 38508.9 42.088 

 Composite 0.50 1.23 30. 16503.8 47.100 

 EMPENNAGE 5936.420 9.283 

 Aluminum 1.00 1.00 0. 0.0 0.000 

 Titanium 1.51 1.00 85. 5046.0 7.207 

 Composite 0.50 1.23 15. 890.5 2.076 

 FUSELAGE 59940.355 76.697 

 Aluminum 1.00 1.00 0. 0.0 0.000 

 Titanium 1.42 1.00 100. 59940.4 76.697 

 Composite 0.35 1.31 0. 0.0 0.000 

 LANDING GEAR 28845.453 20.169 

 Aluminum 1.00 1.00 50. 14422.7 10.084 

 Titanium 1.00 1.00 50. 14422.7 10.084 

 Composite 1.00 1.00 0. 0.0 0.000 

 NACELLES/PYLONS 0.000 0.000 

 Aluminum 1.00 1.00 0. 0.0 0.000 

 Titanium 1.00 1.00 100. 0.0 0.000 

 Composite 1.00 1.00 0. 0.0 0.000 

 ENGINES 3.00 66788.000 77.256 

 AIRFRAME PROPULSION 4938.445 1.662 

 THRUST REVERSER 1.00 1.00 0.000 0.000 

 FUEL SYSTEM 1.00 1.00 4938.445 1.662 

 ENGINE ACCESSORIES 1.00 1.00 0.000 0.000 

 FIXED EQUIPMENT 59659.789 60.749 

 AERODYNAMIC CONTROLS 1.00 1.00 10778.502 23.439 

 HYDRAULIC 1.00 1.00 4787.303 7.059 

 ELECTRICAL POWER 1.00 1.00 5518.508 7.871 

 AIR CONDITIONING 1.00 1.00 8682.571 3.455 

 ANTI-ICING 1.00 1.00 377.509 0.472 

 AUXILIARY POWER SOURCE 1.00 1.00 0.000 0.000 

 PASSENGER ACCOMMODATIONS 1.00 1.00 29515.398 18.453 

 INSTRUMENTATION 1.00 1.00 2004.900 11.358 

 EQUIPMENT 10.518 

 INSTALLATION 0.839 

 AVIONICS 1.00 1.00 3058.248 17.325 

 EQUIPMENT 16.044 

 INSTALLATION 1.280 

 LOAD AND HANDLING 1.00 1.00 0.000 

 FINAL ASSEMBLY AND CHECKOUT 18.380 

 VEHICLE TOTAL 286184.375 382.065 

 Manufacturing - First Unit Cost (FUC) ( 382.065) Spares not included 

 Airframe ( 257.747) 

 Avionics & Instrumentation ( 28.682) 
NASA/CRó2003-212126 48 

 Propulsion ( 77.256) 

 Assembly ( 18.380) 

 ============ PRODUCTION AND RDT&E COSTS == 1992. DOLLARS ============ 

 ***** Millions of U.S. dollars ***** 

 RESEARCH,DEVELOPMENT,TEST,AND EVALUATION 22399.066 

 AIRFRAME DEVELOPMENT (Eng. labor $65./hr) 5932.594 

 CONCEPT FORMULATION ( 150. man-yrs) 15.210 

 CONTRACT DEFINITION ( 500. man-yrs) 67.600 

 AIRFRAME ENGINEERING ( 43268. man-yrs) 5849.784 

 SUBSYSTEMS DEVELOPMENT 1396.944 

 AVIONICS DEVELOPMENT (1.00x Factor) 1142.428 

 PROPULSION DEVELOPMENT ( 53.% Spares) 5098.428 

 DEVELOPMENT SUPPORT 4066.667 

 GROUND TEST VEHICLES (1. aircraft) 257.747 

 GROUND TEST SPARES (10.0% of GTV) 25.775 

 FLIGHT TEST SPARES (20.0% of FTV) 76.413 

 TOOLING EQUIPMENT (Tooling labor $55./hr) 3162.146 

 FLIGHT TEST OPERATIONS (1. aircraft) 183.005 

 GROUND SUPPORT EQUIPMENT 353.940 

 TECHNICAL DATA 7.641 

 FEE (27.0% profit) 4762.006 

 AIRCRAFT PRODUCTION 165535.984 

 OPERATIONAL VEHICLES ( 504. aircraft) 80723.586 

 SPARES - Airframe ( 6.0% of Afrm) 7388.542 

 - Engines (23.0% of Engs) 8955.563 

 FACILITIES 0.000 

 SUSTAINING ENGINEERING 14660.934 

 SUSTAINING TOOLING 4394.380 

 GROUND SUPPORT EQUIPMENT 12108.538 

 TECHNICAL DATA ( 2% of OV) 1614.472 

 MISCELLANEOUS EQUIPMENT 32.945 

 TRAINING EQUIPMENT 0.000 

 INITIAL TRAINING 0.000 

 INITIAL TRANSPORTATION 464.325 

 FEE (27.0% profit) 35192.691 

 TOTAL COST ( 504. aircraft) 187935.047 

 AVERAGE UNIT AIRPLANE COST (including spares) 372.887 

 AVERAGE UNIT AIRPLANE COST (excluding spares) 331.702 

 ============ PRODUCTION COST VS. QUANTITY == 1992. DOLLARS ============ 

 

 Aircraft Cost Versus Quantity 

 Learning Curve Percentages 

 FIRST LOT SECOND LOT 

 Airframe 86.5 86.5 

 Avionics 86.5 86.5 

 Propulsion 100.0 100.0 

 Fixed Eqpm. 86.5 86.5 

 Integ. & Assembly 86.5 86.5 

 Production Line Learning Curve Breaking Point 200. 

 Propulsion based on production of 2500. engines 

 ***** Average Manufacturing Costs ***** RDT&E Sustaining Average 

 Number Airframe Propulsion Avionics Unit Cum. Costs Costs Cost 

 1 257.747 77.256 28.682 485.223 485.223 16071.595 1146.7317703.551 

 2 222.951 77.256 24.810 432.964 865.927 16303.068 2535.31 9852.153 

 3 204.817 77.256 22.792 405.728 1217.185 16479.281 3485.78 7060.750 

 4 192.853 77.256 21.461 387.759 1551.036 16623.479 4237.33 5602.961 

 5 184.056 77.256 20.482 374.547 1872.736 16746.535 4871.97 4698.249 

 6 177.167 77.256 19.715 364.201 2185.205 16854.475 5428.56 4078.039 

 7 171.544 77.256 19.089 355.756 2490.290 16951.008 5928.82 3624.302 

 8 166.818 77.256 18.563 348.657 2789.258 17038.600 6386.25 3276.764 

 9 162.757 77.256 18.112 342.559 3083.026 17118.967 6809.88 3001.319 

 10 159.208 77.256 17.717 337.229 3372.288 17193.365 7206.03 2777.168 

 20 137.715 77.256 15.325 304.949 6098.972 17744.881 10307.89 1707.587 
NASA/CRó2003-212126 49 

 30 126.514 77.256 14.079 288.126 8643.771 18121.723 12647.44 1313.764 

 40 119.124 77.256 13.256 277.026 11081.045 18416.236 14630.96 1103.206 

 50 113.690 77.256 12.651 268.865 13443.259 18661.566 16400.89 970.114 

 60 109.435 77.256 12.178 262.474 15748.459 18873.750 18025.81 877.467 

 70 105.961 77.256 11.791 257.258 18008.051 19061.869 19544.60 808.779 

 80 103.042 77.256 11.467 252.873 20229.859 19231.615 20981.66 755.539 

 90 100.534 77.256 11.187 249.106 22419.547 19386.811 22353.48 712.887 

 100 98.342 77.256 10.943 245.814 24581.400 19530.154 23671.72 677.833 

 200 85.066 77.256 9.466 225.875 45174.941 20591.379 35130.90 504.486 

 300 78.147 77.256 8.696 215.483 64645.000 21321.711 44998.68 436.551 

 400 73.582 77.256 8.188 208.627 83450.906 21897.609 54083.55 398.580 

 500 70.225 77.256 7.815 203.586 101793.148 22381.166 62680.83 373.710 

 600 67.597 77.256 7.522 199.639 119783.211 22802.270 70937.05 355.871 

 700 65.452 77.256 7.283 196.417 137491.594 23177.857 78937.31 342.295 

 800 63.648 77.256 7.083 193.708 154966.547 23518.555 86736.18 331.527 

 900 62.099 77.256 6.910 191.381 172243.109 23831.504 94371.16 322.717 

 1000 60.745 77.256 6.760 189.348 189347.750 24121.773 101869.24 315.339 

 ============ MANUFACTURERS CUMULATIVE CASHFLOW == 1992. DOLLARS ============ 

 Production Size = 504. 

 Average Aircraft Price = $ 298.3 M 

 Year Annual Cumulative Costs Income Net 

 Deliveries Deliveries RDT&E Manufacturing Sustaining Cashflow 

 2000 0.0 0.0 1019.7 0.0 0.0 348.3 -671.4 

 2001 0.0 0.0 4157.4 0.0 0.0 1336.0 -2821.3 

 2002 0.0 0.0 8311.7 0.0 0.0 3080.4 -5231.3 

 2003 0.0 0.0 12466.1 0.0 0.0 5636.8 -6829.2 

 2004 0.0 0.0 16620.4 2790.3 8258.2 9084.3 -18584.6 

 2005 24.0 24.0 17637.1 9798.5 17734.6 18760.5 -26409.7 

 2006 48.0 72.0 17637.1 19241.6 24514.6 34458.2 -26935.1 

 2007 60.0 132.0 17637.1 29527.6 29972.1 53287.5 -23849.2 

 2008 66.0 198.0 17637.1 40379.1 34816.0 72530.9 -20301.2 

 2009 72.0 270.0 17637.1 51341.5 39198.1 92309.2 -15867.5 

 2010 72.0 342.0 17637.1 62403.9 43291.8 111213.7 -12119.0 

 2011 78.0 420.0 17637.1 74187.2 47409.3 130586.4 -8647.2 

 2012 84.0 504.0 17637.1 80723.6 49619.7 150348.2 2367.9 

 Totals 504.0 17637.1 80723.6 49619.7 150348.2 2367.9 

 ============ MANUFACTURERS ANNUAL CASHFLOW == 1992. DOLLARS ============ 

 Production Size = 504. 

 Average Aircraft Price = $ 298.3 M 

 Year Annual Cumulative Costs Income Annual 

 Deliveries Deliveries RDT&E Manufacturing Sustaining Cashflow 

 2000 0.0 0.0 1019.7 0.0 0.0 348.3 -671.4 

 2001 0.0 0.0 3137.7 0.0 0.0 987.8 -2149.9 

 2002 0.0 0.0 4154.3 0.0 0.0 1744.4 -2410.0 

 2003 0.0 0.0 4154.3 0.0 0.0 2556.5 -1597.9 

 2004 0.0 0.0 4154.3 2790.3 8258.2 3447.4 -11755.4 

 2005 24.0 24.0 1016.7 7008.2 9476.4 9676.2 -7825.1 

 2006 48.0 72.0 0.0 9443.1 6780.0 15697.7 -525.4 

 2007 60.0 132.0 0.0 10286.0 5457.5 18829.3 3085.9 

 2008 66.0 198.0 0.0 10851.5 4843.9 19243.4 3547.9 

 2009 72.0 270.0 0.0 10962.5 4382.1 19778.3 4433.7 

 2010 72.0 342.0 0.0 11062.3 4093.7 18904.6 3748.6 

 2011 78.0 420.0 0.0 11783.3 4117.6 19372.6 3471.8 

 2012 84.0 504.0 0.0 6536.4 2210.4 19761.9 11015.1 

 Totals 504.0 17637.1 80723.6 49619.7 150348.2 2367.9 

 ============ MANUFACTURERS CUMULATIVE CASHFLOW == 1992. DOLLARS ============ 

 Production Size = 504. 

 Average Aircraft Price = $ 335.6 M 

 Year Annual Cumulative Costs Income Net 

 Deliveries Deliveries RDT&E Manufacturing Sustaining Cashflow 

 2000 0.0 0.0 1019.7 0.0 0.0 391.8 -627.9 

 2001 0.0 0.0 4157.4 0.0 0.0 1503.0 -2654.3 

 2002 0.0 0.0 8311.7 0.0 0.0 3465.4 -4846.3 

 2003 0.0 0.0 12466.1 0.0 0.0 6341.4 -6124.6 

 2004 0.0 0.0 16620.4 2790.3 8258.2 10219.8 -17449.1 
NASA/CRó2003-212126 50 

 2005 24.0 24.0 17637.1 9798.5 17734.6 21105.5 -24064.6 

 2006 48.0 72.0 17637.1 19241.6 24514.6 38765.2 -22628.1 

 2007 60.0 132.0 17637.1 29527.6 29972.1 59947.9 -17188.7 

 2008 66.0 198.0 17637.1 40379.1 34816.0 81596.6 -11235.6 

 2009 72.0 270.0 17637.1 51341.5 39198.1 103846.9 -4329.8 

 2010 72.0 342.0 17637.1 62403.9 43291.8 125114.4 1781.7 

 2011 78.0 420.0 17637.1 74187.2 47409.3 146908.5 7675.0 

 2012 84.0 504.0 17637.1 80723.6 49619.7 169140.6 21160.3 

 Totals 504.0 17637.1 80723.6 49619.7 169140.6 21160.3 

 ============ MANUFACTURERS ANNUAL CASHFLOW == 1992. DOLLARS ============ 

 Production Size = 504. 

 Average Aircraft Price = $ 335.6 M 

 Year Annual Cumulative Costs Income Annual 

 Deliveries Deliveries RDT&E Manufacturing Sustaining Cashflow 

 2000 0.0 0.0 1019.7 0.0 0.0 391.8 -627.9 

 2001 0.0 0.0 3137.7 0.0 0.0 1111.2 -2026.4 

 2002 0.0 0.0 4154.3 0.0 0.0 1962.4 -2191.9 

 2003 0.0 0.0 4154.3 0.0 0.0 2876.0 -1278.3 

 2004 0.0 0.0 4154.3 2790.3 8258.2 3878.4 -11324.5 

 2005 24.0 24.0 1016.7 7008.2 9476.4 10885.7 -6615.5 

 2006 48.0 72.0 0.0 9443.1 6780.0 17659.7 1436.5 

 2007 60.0 132.0 0.0 10286.0 5457.5 21182.8 5439.3 

 2008 66.0 198.0 0.0 10851.5 4843.9 21648.6 5953.1 

 2009 72.0 270.0 0.0 10962.5 4382.1 22250.3 6905.8 

 2010 72.0 342.0 0.0 11062.3 4093.7 21267.5 6111.5 

 2011 78.0 420.0 0.0 11783.3 4117.6 21794.1 5893.3 

 2012 84.0 504.0 0.0 6536.4 2210.4 22232.0 13485.3 

 Totals 504.0 17637.1 80723.6 49619.7 169140.6 21160.3 

 ============ MANUFACTURERS CUMULATIVE CASHFLOW == 1992. DOLLARS ============ 

 Production Size = 504. 

 Average Aircraft Price = $ 410.2 M 

 Year Annual Cumulative Costs Income Net 

 Deliveries Deliveries RDT&E Manufacturing Sustaining Cashflow 

 2000 0.0 0.0 1019.7 0.0 0.0 478.9 -540.8 

 2001 0.0 0.0 4157.4 0.0 0.0 1837.0 -2320.3 

 2002 0.0 0.0 8311.7 0.0 0.0 4235.5 -4076.2 

 2003 0.0 0.0 12466.1 0.0 0.0 7750.7 -4715.4 

 2004 0.0 0.0 16620.4 2790.3 8258.2 12490.9 -15178.0 

 2005 24.0 24.0 17637.1 9798.5 17734.6 25795.6 -19374.5 

 2006 48.0 72.0 17637.1 19241.6 24514.6 47379.7 -14013.5 

 2007 60.0 132.0 17637.1 29527.6 29972.1 73269.8 -3866.9 

 2008 66.0 198.0 17637.1 40379.1 34816.0 99729.3 6897.1 

 2009 72.0 270.0 17637.1 51341.5 39198.1 126924.2 18747.5 

 2010 72.0 342.0 17637.1 62403.9 43291.8 152917.8 29585.1 

 2011 78.0 420.0 17637.1 74187.2 47409.3 179555.1 40321.5 

 2012 84.0 504.0 17637.1 80723.6 49619.7 206727.6 58747.3 

 Totals 504.0 17637.1 80723.6 49619.7 206727.6 58747.3 

 ============ MANUFACTURERS ANNUAL CASHFLOW == 1992. DOLLARS ============ 

 Production Size = 504. 

 Average Aircraft Price = $ 410.2 M 

 Year Annual Cumulative Costs Income Annual 

 Deliveries Deliveries RDT&E Manufacturing Sustaining Cashflow 

 2000 0.0 0.0 1019.7 0.0 0.0 478.9 -540.8 

 2001 0.0 0.0 3137.7 0.0 0.0 1358.2 -1779.5 

 2002 0.0 0.0 4154.3 0.0 0.0 2398.5 -1755.9 

 2003 0.0 0.0 4154.3 0.0 0.0 3515.1 -639.2 

 2004 0.0 0.0 4154.3 2790.3 8258.2 4740.2 -10462.6 

 2005 24.0 24.0 1016.7 7008.2 9476.4 13304.8 -4196.5 

 2006 48.0 72.0 0.0 9443.1 6780.0 21584.1 5361.0 

 2007 60.0 132.0 0.0 10286.0 5457.5 25890.1 10146.7 

 2008 66.0 198.0 0.0 10851.5 4843.9 26459.5 10764.0 

 2009 72.0 270.0 0.0 10962.5 4382.1 27194.9 11850.4 

 2010 72.0 342.0 0.0 11062.3 4093.7 25993.6 10837.6 

 2011 78.0 420.0 0.0 11783.3 4117.6 26637.3 10736.4 
NASA/CRó2003-212126 51 

 2012 84.0 504.0 0.0 6536.4 2210.4 27172.5 18425.7 

 Totals 504.0 17637.1 80723.6 49619.7 206727.6 58747.3 

 ============ MANUFACTURERS CUMULATIVE CASHFLOW == 1992. DOLLARS ============ 

 Production Size = 504. 

 Average Aircraft Price = $ 447.5 M 

 Year Annual Cumulative Costs Income Net 

 Deliveries Deliveries RDT&E Manufacturing Sustaining Cashflow 

 2000 0.0 0.0 1019.7 0.0 0.0 522.4 -497.3 

 2001 0.0 0.0 4157.4 0.0 0.0 2004.0 -2153.3 

 2002 0.0 0.0 8311.7 0.0 0.0 4620.6 -3691.1 

 2003 0.0 0.0 12466.1 0.0 0.0 8455.3 -4010.8 

 2004 0.0 0.0 16620.4 2790.3 8258.2 13626.4 -14042.5 

 2005 24.0 24.0 17637.1 9798.5 17734.6 28140.7 -17029.4 

 2006 48.0 72.0 17637.1 19241.6 24514.6 51687.3 -9706.0 

 2007 60.0 132.0 17637.1 29527.6 29972.1 79931.3 2794.6 

 2008 66.0 198.0 17637.1 40379.1 34816.0 108796.4 15964.2 

 2009 72.0 270.0 17637.1 51341.5 39198.1 138463.8 30287.1 

 2010 72.0 342.0 17637.1 62403.9 43291.8 166820.6 43487.9 

 2011 78.0 420.0 17637.1 74187.2 47409.3 195879.6 56646.0 

 2012 84.0 504.0 17637.1 80723.6 49619.7 225522.3 77542.0 

 Totals 504.0 17637.1 80723.6 49619.7 225522.3 77542.0 

 ============ MANUFACTURERS ANNUAL CASHFLOW == 1992. DOLLARS ============ 

 Production Size = 504. 

 Average Aircraft Price = $ 447.5 M 

 Year Annual Cumulative Costs Income Annual 

 Deliveries Deliveries RDT&E Manufacturing Sustaining Cashflow 

 2000 0.0 0.0 1019.7 0.0 0.0 522.4 -497.3 

 2001 0.0 0.0 3137.7 0.0 0.0 1481.6 -1656.0 

 2002 0.0 0.0 4154.3 0.0 0.0 2616.5 -1537.8 

 2003 0.0 0.0 4154.3 0.0 0.0 3834.7 -319.6 

 2004 0.0 0.0 4154.3 2790.3 8258.2 5171.2 -10031.7 

 2005 24.0 24.0 1016.7 7008.2 9476.4 14514.3 -2987.0 

 2006 48.0 72.0 0.0 9443.1 6780.0 23546.5 7323.4 

 2007 60.0 132.0 0.0 10286.0 5457.5 28244.0 12500.6 

 2008 66.0 198.0 0.0 10851.5 4843.9 28865.1 13169.7 

 2009 72.0 270.0 0.0 10962.5 4382.1 29667.4 14322.8 

 2010 72.0 342.0 0.0 11062.3 4093.7 28356.8 13200.8 

 2011 78.0 420.0 0.0 11783.3 4117.6 29058.9 13158.1 

 2012 84.0 504.0 0.0 6536.4 2210.4 29642.8 20896.0 

 Totals 504.0 17637.1 80723.6 49619.7 225522.3 77542.0 

 ============ MANUFACTURERS CUMULATIVE CASHFLOW == 1992. DOLLARS ============ 

 Production Size = 504. 

 Average Aircraft Price = $ 484.8 M 

 Year Annual Cumulative Costs Income Net 

 Deliveries Deliveries RDT&E Manufacturing Sustaining Cashflow 

 2000 0.0 0.0 1019.7 0.0 0.0 565.9 -453.8 

 2001 0.0 0.0 4157.4 0.0 0.0 2171.0 -1986.3 

 2002 0.0 0.0 8311.7 0.0 0.0 5005.6 -3306.1 

 2003 0.0 0.0 12466.1 0.0 0.0 9159.9 -3306.2 

 2004 0.0 0.0 16620.4 2790.3 8258.2 14761.9 -12906.9 

 2005 24.0 24.0 17637.1 9798.5 17734.6 30485.7 -14684.5 

 2006 48.0 72.0 17637.1 19241.6 24514.6 55994.2 -5399.1 

 2007 60.0 132.0 17637.1 29527.6 29972.1 86591.9 9455.3 

 2008 66.0 198.0 17637.1 40379.1 34816.0 117862.7 25030.5 

 2009 72.0 270.0 17637.1 51341.5 39198.1 150002.5 41825.8 

 2010 72.0 342.0 17637.1 62403.9 43291.8 180722.6 57389.9 

 2011 78.0 420.0 17637.1 74187.2 47409.3 212203.3 72969.7 

 2012 84.0 504.0 17637.1 80723.6 49619.7 244316.3 96336.0 

 Totals 504.0 17637.1 80723.6 49619.7 244316.3 96336.0 
NASA/CRó2003-212126 52 

 ============ MANUFACTURERS ANNUAL CASHFLOW == 1992. DOLLARS ============ 

 Production Size = 504. 

 Average Aircraft Price = $ 484.8 M 

 Year Annual Cumulative Costs Income Annual 

 Deliveries Deliveries RDT&E Manufacturing Sustaining Cashflow 

 2000 0.0 0.0 1019.7 0.0 0.0 565.9 -453.8 

 2001 0.0 0.0 3137.7 0.0 0.0 1605.1 -1532.6 

 2002 0.0 0.0 4154.3 0.0 0.0 2834.6 -1319.8 

 2003 0.0 0.0 4154.3 0.0 0.0 4154.2 -0.1 

 2004 0.0 0.0 4154.3 2790.3 8258.2 5602.1 -9600.7 

 2005 24.0 24.0 1016.7 7008.2 9476.4 15723.7 -1777.5 

 2006 48.0 72.0 0.0 9443.1 6780.0 25508.5 9285.4 

 2007 60.0 132.0 0.0 10286.0 5457.5 30597.8 14854.3 

 2008 66.0 198.0 0.0 10851.5 4843.9 31270.8 15575.3 

 2009 72.0 270.0 0.0 10962.5 4382.1 32139.9 16795.3 

 2010 72.0 342.0 0.0 11062.3 4093.7 30720.1 15564.1 

 2011 78.0 420.0 0.0 11783.3 4117.6 31480.6 15579.8 

 2012 84.0 504.0 0.0 6536.4 2210.4 32113.0 23366.3 

 Totals 504.0 17637.1 80723.6 49619.7 244316.3 96336.0 

 ============ MANUFACTURERS CUMULATIVE CASHFLOW == 1992. DOLLARS ============ 

 Production Size = 504. 

 Average Aircraft Price = $ 372.9 M 

 Year Annual Cumulative Costs Income Net 

 Deliveries Deliveries RDT&E Manufacturing Sustaining Cashflow 

 2000 0.0 0.0 1019.7 0.0 0.0 435.3 -584.4 

 2001 0.0 0.0 4157.4 0.0 0.0 1670.0 -2487.3 

 2002 0.0 0.0 8311.7 0.0 0.0 3850.5 -4461.2 

 2003 0.0 0.0 12466.1 0.0 0.0 7046.0 -5420.0 

 2004 0.0 0.0 16620.4 2790.3 8258.2 11355.4 -16313.5 

 2005 24.0 24.0 17637.1 9798.5 17734.6 23450.6 -21719.5 

 2006 48.0 72.0 17637.1 19241.6 24514.6 43072.7 -18320.5 

 2007 60.0 132.0 17637.1 29527.6 29972.1 66609.4 -10527.3 

 2008 66.0 198.0 17637.1 40379.1 34816.0 90663.6 -2168.5 

 2009 72.0 270.0 17637.1 51341.5 39198.1 115386.4 7209.7 

 2010 72.0 342.0 17637.1 62403.9 43291.8 139017.1 15684.4 

 2011 78.0 420.0 17637.1 74187.2 47409.3 163232.9 23999.3 

 2012 84.0 504.0 17637.1 80723.6 49619.7 187935.1 39954.8 

 Totals 504.0 17637.1 80723.6 49619.7 187935.1 39954.8 

 ============ MANUFACTURERS ANNUAL CASHFLOW == 1992. DOLLARS ============ 

 Production Size = 504. 

 Average Aircraft Price = $ 372.9 M 

 Year Annual Cumulative Costs Income Annual 

 Deliveries Deliveries RDT&E Manufacturing Sustaining Cashflow 

 2000 0.0 0.0 1019.7 0.0 0.0 435.3 -584.4 

 2001 0.0 0.0 3137.7 0.0 0.0 1234.7 -1903.0 

 2002 0.0 0.0 4154.3 0.0 0.0 2180.4 -1973.9 

 2003 0.0 0.0 4154.3 0.0 0.0 3195.6 -958.8 

 2004 0.0 0.0 4154.3 2790.3 8258.2 4309.3 -10893.5 

 2005 24.0 24.0 1016.7 7008.2 9476.4 12095.2 -5406.0 

 2006 48.0 72.0 0.0 9443.1 6780.0 19622.1 3399.0 

 2007 60.0 132.0 0.0 10286.0 5457.5 23536.7 7793.3 

 2008 66.0 198.0 0.0 10851.5 4843.9 24054.2 8358.8 

 2009 72.0 270.0 0.0 10962.5 4382.1 24722.8 9378.3 

 2010 72.0 342.0 0.0 11062.3 4093.7 23630.7 8474.7 

 2011 78.0 420.0 0.0 11783.3 4117.6 24215.7 8314.9 

 2012 84.0 504.0 0.0 6536.4 2210.4 24702.3 15955.5 

 Totals 504.0 17637.1 80723.6 49619.7 187935.1 39954.8 
NASA/CRó2003-212126 53 

 ============ MANUFACTURERS RETURN ON INVESTMENT == 1992. DOLLARS ============ 

 Production Size = 400. 

 Monthly Rate = 1.6 3.2 4.0 4.4 4.8 4.8 5.2 5.6 0.0 0.0 0.0 0.0 0.0 0.0 0.0 

 Aircraft Price (Mill. $) ROI Manufacturing (%) Profit (Mill. $) Breakeven Unit # 

 411.404 1.40 2590.609 390. 

 462.829 12.40 23162.453 234. 

 514.254 22.20 43732.078 154. 

 565.680 31.60 64301.672 110. 

 617.105 40.90 84871.500 82. 

 668.531 50.40 105441.375 62. 

 Production Size = 800. 

 Monthly Rate = 3.2 6.3 7.9 8.7 9.5 9.510.311.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 

 Aircraft Price (Mill. $) ROI Manufacturing (%) Profit (Mill. $) Breakeven Unit # 

 292.467 1.70 3685.859 779. 

 329.026 14.50 32928.750 449. 

 365.584 26.70 62177.719 280. 

 402.142 39.20 91427.188 195. 

 438.701 53.30 120669.375 147. 

 475.259 70.50 149918.937 109. 

 Production Size = 504. 

 Monthly Rate = 2.0 4.0 5.0 5.5 6.0 6.0 6.5 7.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 

 Aircraft Price (Mill. $) ROI Manufacturing (%) Profit (Mill. $) Breakeven Unit # 

 298.309 1.30 2367.922 491. 

 335.598 10.90 21160.250 319. 

 372.887 19.60 39954.828 211. 

 410.175 27.80 58747.281 155. 

 447.464 35.80 77542.000 118. 

 484.753 43.80 96335.984 93. 

 Return on Investment = 12. % 

 Aircraft Price = 340.313 

 ============ DOC, IOC, & TOC == 504. UNITS == 1992. DOLLARS ============ 

 Airframe Cost (millions $) 232.218 

 Engine Cost (per engine) 17.627 

 Spares Cost (airframe and engine) 41.185 

 Number of First Class/Coach Passengers 0./292. 

 Annual Utiliz., Sup. Cruise Mach # and Alt. 4000.0 hrs at M = 2.40 and 57840. ft 

 Subsonic Cruise Mach # and Alt. M = 0.90 and 35000. ft 

 Trips per year 668. 1102. 756. 1161. 

 Stage Length (sm) 6621. 3682. 5754. 3452. 

 Stage Length (nmi) 5754. 3200. 5000. 3000. 

 Block Speed (mph) 1105. 1015. 1087. 1002. 

 Time (hr) 5.991 3.630 5.294 3.445 

 Ground Time Idle/Maneuver (hr) 1.500/0.180 

 Flight Time (hr) 5.811 3.450 5.114 3.265 

 Climb + Descent Time (hr) 0.857 

 Cruise Time (hr) 5.134 2.773 4.437 2.588 

 Block Fuel (lb) 379098. 213591. 330295. 200595. 

 Block Fuel (gal/hr) 9374. 8718. 9243. 8627. 

 Direct Operating Costs $/Trip 

 Flying Operations Costs: 3. person crew 

 Flight Crew ($ 828./Blk hr) 4961. 3397. 4499. 3274. 

 Fuel and Oil ($0.65/gal) 37242. 20983. 32448. 19707. 

 Total 42203. 24380. 36947. 22981. 

 Direct Maintenance Costs: Labor rate $ 19.50/hr *** Engine Removal Rate (/1000 EFH) 0.100 

 Airframe Labor (1.00 Complexity) 1620. 1110. 1469. 1070. 

 (Man hr/Flight hr) 14.3 16.5 14.7 16.8 

 Burden (200.% of Labor) 3240. 2220. 2939. 2141. 

 Material 2803. 1958. 2553. 1892. 
NASA/CRó2003-212126 54 

 Engine Labor Total (1.00 Complexity) 156. 93. 138. 88. 

 Line Maint. Labor Cost 37. 22. 33. 21. 

 (Man hrs per Installation) 71.9 71.9 71.9 71.9 

 Shop Maint. Labor Cost 56. 33. 49. 31. 

 Basic Eng. Maint. Labor Cost 82. 49. 73. 46. 

 (Man hrs for QEC build-up) 791.4 791.4 791.4 791.4 

 Outside Service Labor ( 0. % Labor) 0. 0. 0. 0. 

 Burden (200.% of Labor) 313. 186. 275. 176. 

 Engine Material Cost 4577. 2717. 4028. 2571. 

 Line Maint. Material Cost 75. 44. 66. 42. 

 Shop Maint. Material Cost 135. 80. 119. 76. 

 Basic Eng. Maint. Material Cost 4368. 2593. 3844. 2454. 

 Outside Service Material Cost 0. 0. 0. 0. 

 Total 12709. 8284. 11402. 7938. 

 Investment Costs: averaged 

 Depreciation (20. years,10.% residual) 22937. 13896. 20268. 13188. 

 Financing (100.% @ 8.00% interest) 26430. 16012. 23354. 15196. 

 Hull Insurance (.35% aircraft cost) 1784. 1081. 1576. 1026. 

 Total 51151. 30988. 45198. 29409. 

 Total Direct Operating Cost 

 $/Trip-DOC 106062. 63652. 93548. 60328. 

 $/Flight hr 18252. 18453. 18293. 18480. 

 $/Block hr 17703. 17537. 17671. 17514. 

 $/Aircraft Mile 16.02 17.29 16.26 17.47 

 $/ASM .054856 .059197 .055679 .059845 

 DOC per Aircraft Trip Equation = $ 10515.77 + $ 14.43/sm 

 DOC per available seat trip = $ 36.01 + $ 0.0494/sm 

 OliverDOC = .059197 

 Indirect Operating Costs $/Trip 

 Coach Passengers/Flight Attendents 38.0 

 First Class Passengers/Flight Attendents 11.0 

 Passenger Trip Distance (sm) 6621. 3682. 5754. 3452. 

 Departures/Trip 1.000 1.000 1.000 1.000 

 Coach Load Factor 0.650 

 First Class Load Factor 0.650 

 Maintenance - System ( 0.5000) 888. 602. 804. 579. 

 Maintenance - Local ( 5.2000) 3823. 3823. 3823. 3823. 

 Aircraft Servicing - Aircraft Cont ( 215.00) 1288. 780. 1138. 741. 

 Passenger Service - Cabin Crew ( 63.55) 2926. 1772. 2585. 1682. 

 Passenger Service - Food and Bev ( 2.0000) 2274. 1378. 2010. 1308. 

 Traffic Servicing - Passenger Hand ( 11.00) 2088. 2088. 2088. 2088. 

 Traffic Servicing - Bag and Cargo ( 80.00) 1028. 1028. 1028. 1028. 

 Passenger Service - Comm/Publ/Res ( 0.0214) 26895. 14957. 23370. 14022. 

 Cargo Service - Comm/Publ/Resrv ( 0.0120) 0. 0. 0. 0. 

 General and Administrative ( 0.0703) 10353. 6332. 9166. 6017. 

 Total Indirect Operating Expense 51562. 32760. 46012. 31287. 

 Total Indirect Operating Costs 

 $/Trip-IOC 51562. 32760. 46012. 31287. 

 $/Flight hour 8873. 9497. 8997. 9584. 

 $/Block hour 8606. 9026. 8691. 9083. 

 $/Aircraft Mile 7.79 8.90 8.00 9.06 

 $/ASM .026668 .030467 .027386 .031037 

 IOC per Aircraft Trip Equation = $ 9202.12 + $ 6.40/sm 

 IOC per available seat trip = $ 31.51 + $0.0219/sm 

 Total Operating Costs 

 $/Trip-TOC 157624. 96412. 139559. 91615. 

 $/Flight Hour 27125. 27950. 27290. 28063. 

 $/Block hour 26310. 26563. 26362. 26597. 

 $/Aircraft mile 23.81 26.18 24.26 26.54 

 $/Available Seat Mile .081524 .089663 .083066 .090882 

 TOC per Aircraft Trip Equation = $ 19717.89 + $ 20.83/sm 

 TOC per available seat trip = $ 67.53 + $0.0713/sm 
NASA/CRó2003-212126 55 

 Breakeven Required Yield ($/RPM) .125422 .137944 .127793 .139819 

 at Load Factors of .650 and .650 

 Base ticket price for 6621.sm distance = $ 1854.01 

 Based on Average Yield $/ASM of .140000 and .140000 

 OliverIOC = .030467 

 OliverTOC = .089663 

 ============ AIRLINE RETURN ON INVESTMENT == 1992. DOLLARS ============ 

 Trips/Year = 1102. Trip Distance = 3682.(sm) = 3200.(nmi) 

 Average Yields: First Class .130000 Coach Class .130000 $/RPM 

 Price (Mill. $) ROI (%) Total Operating Direct Operating ($/ASM) 

 340.313 5.600 .089663 .059197 

 374.344 4.100 .093212 .062512 

 408.375 2.700 .096761 .065828 

 442.406 1.500 .100310 .069144 

 476.438 0.400 .103859 .072459 

 Average Yields: First Class .140000 Coach Class .140000 $/RPM 

 Price (Mill. $) ROI (%) Total Operating Direct Operating ($/ASM) 

 340.313 9.100 .089663 .059197 

 374.344 7.300 .093212 .062512 

 408.375 5.800 .096761 .065828 

 442.406 4.500 .100310 .069144 

 476.438 3.300 .103859 .072459 

 Average Yields: First Class .150000 Coach Class .150000 $/RPM 

 Price (Mill. $) ROI (%) Total Operating Direct Operating ($/ASM) 

 340.313 12.100 .089663 .059197 

 374.344 10.300 .093212 .062512 

 408.375 8.700 .096761 .065828 

 442.406 7.200 .100310 .069144 

 476.438 6.000 .103859 .072459 

 Average Yields: First Class .160000 Coach Class .160000 $/RPM 

 Price (Mill. $) ROI (%) Total Operating Direct Operating ($/ASM) 

 340.313 14.400 .089663 .059197 

 374.344 12.800 .093212 .062512 

 408.375 11.300 .096761 .065828 

 442.406 9.800 .100310 .069144 

 476.438 8.400 .103859 .072459 

 Manuf. Return on Investment = 12. % 

 Airline Return on Investment = 12. % 

 Aircraft Price Mil $ = 340.313 

 Average Yield/RPM = .149500 

 Production Quantity = 504. 

 ============ RETURN ON INVESTMENT, OPERATIONS == 1992. DOLLARS ============ 

 Stage Length (nmi) = 3200. Utilization = 1102.08 trips/yr 

 Initial Aircraft Price = 340.313 Tax Rate = 34.00 % 

 Initial Investment = 340.313 Interest Rate = 8.00 % 

 Average Yield: Coach = .140000 First Class = .140000 $/RPM 

 Year (1-5) 2001. 2002. 2003. 2004. 2005. 

 Annual Revenue 107.838 107.838 107.838 107.838 107.838 

 Operating Cost 115.833 115.238 114.595 113.901 113.152 

 Interest 27.225 26.630 25.988 25.294 24.544 

 Depreciation 15.314 15.314 15.314 15.314 15.314 

 Earnings Before Tax -7.995 -7.400 -6.758 -6.064 -5.314 

 Income Tax 0.000 0.000 0.000 0.000 0.000 

 Net Earnings -7.995 -7.400 -6.758 -6.064 -5.314 
NASA/CRó2003-212126 56 

 Net Cash Flow -305.769 34.544 34.544 34.544 34.544 

 Discount Factor 1.000 0.772 0.708 0.650 0.596 

 Discounted Cash Flow -305.769 31.692 29.075 26.674 24.472 

 Year (6-10) 2006. 2007. 2008. 2009. 2010. 

 Annual Revenue 107.838 107.838 107.838 107.838 107.838 

 Operating Cost 112.343 111.468 110.524 109.505 108.404 

 Interest 23.735 22.861 21.917 20.897 19.796 

 Depreciation 15.314 15.314 15.314 15.314 15.314 

 Earnings Before Tax -4.505 -3.631 -2.687 -1.667 -0.566 

 Income Tax 0.000 0.000 0.000 0.000 0.000 

 Net Earnings -4.505 -3.631 -2.687 -1.667 -0.566 

 Net Cash Flow 34.544 34.544 34.544 34.544 34.544 

 Discount Factor 0.547 0.502 0.460 0.422 0.388 

 Discounted Cash Flow 22.451 20.597 18.897 17.336 15.905 

 Year (11-15) 2011. 2012. 2013. 2014. 2015. 

 Annual Revenue 107.838 107.838 107.838 107.838 107.838 

 Operating Cost 107.214 105.930 104.543 103.045 101.427 

 Interest 18.607 17.322 15.935 14.437 12.819 

 Depreciation 15.314 15.314 15.314 15.314 15.314 

 Earnings Before Tax 0.623 1.908 3.295 4.793 6.411 

 Income Tax 0.212 0.649 1.120 1.630 2.180 

 Net Earnings 0.411 1.259 2.175 3.163 4.231 

 Net Cash Flow 34.332 33.895 33.424 32.914 32.364 

 Discount Factor 0.356 0.326 0.299 0.275 0.252 

 Discounted Cash Flow 14.502 13.136 11.883 10.736 9.685 

 Year (16-20) 2016. 2017. 2018. 2019. 2020. 

 Annual Revenue 107.838 107.838 107.838 107.838 107.838 

 Operating Cost 99.679 97.792 95.754 93.553 91.175 

 Interest 11.072 9.184 7.146 4.945 2.568 

 Depreciation 15.314 15.314 15.314 15.314 15.314 

 Earnings Before Tax 8.158 10.046 12.084 14.285 16.662 

 Income Tax 2.774 3.415 4.108 4.857 17.236 

 Net Earnings 5.384 6.630 7.975 9.428 33.458 

 Net Cash Flow 31.770 31.128 30.435 29.687 51.339 

 Discount Factor 0.231 0.212 0.194 0.178 0.023 

 Discounted Cash Flow 8.722 7.840 7.033 6.293 9.985 

 Total 

 Annual Revenue 2156.752 

 Operating Cost 2125.076 

 Interest 352.920 

 Depreciation 306.282 

 Principle 340.312 

 Earnings Before Tax 31.677 

 Income Tax 38.180 

 Net Earnings 27.528 

 Net Cash Flow 346.416 

 Discounted Rate of Return on Investment 9.1 % 

 ************************************************* 

   

 **  End of ALCCA Economic Analysis ** 

   

 ** *********************************************** 

1 
NASA/CRó2003-212126 57 

APPENDIX F: PROBABILISTIC LIFE CYCLE ANALYSIS OF COMBUSTOR 

The NESSUS capability for the harmonic loads was used to compute the probabilistic responses 

of a combustor liner subject to high temperatures. Material properties were input using the 

elasticity matrix coefficients. Several NESSUS analyses runs were made for different degraded 

D-matrix coefficients due to the cyclic loads. Material degradation of these coefficients was 

performed using the multi-factor-interaction-model (MFIM). Probabilistic cyclic stresses and 

respective sensitivity factors were computed using NESSUS computer code. Hoop stress 

cumulative distribution function (CDF) for different load cycles at a critical node are plotted in 

Figure 1 and its sensitivity to the respective primitive random variables are shown in Figure 2. 

The temperature gradient at the location under study has been found most sensitive to the hoop 

stress. 

Also, the material strength cumulative distribution function using the Weibull distribution was 

computed for different cyclic load cycles. The strength degradation was achieved using MFIM. 

Degradation due to both the temperature as well as cyclic load effects was accounted in the 

computation process. Figure 3 shows the CDF of strength under different load cycles. Using the 

results of probabilistic strength and stress, the life cycle curves at different probability levels 

generated as shown in Figure 4. Also, the probability of failure as well as survival probability 

curves for different load cycles were developed as shown in figures 5 and 6 respectively. 

N/Nf = 0.0

N/Nf = 0.3

N/Nf = 0.5

N/Nf = 0.7

N/Nf = 0.9

Figure 1.—CDF of hoop stress at a critical location for different load cycles. 

0.0

0.2

0.4

0.6

0.8

1.0

–20 –10 0 10 20

Hoop stress, psi

Cumulative probability
NASA/CRó2003-212126 58 

Figure 2.—Sensitivity of random variables to the hoop stress at different load cycles at 0.01 probability.

–0.4

–0.2

0.0

0.2

0.4

0.6

0.8

1.0

Sensitivity

N/NF = 0.0

N/NF = 0.3

N/NF = 0.5

N/NF = 0.7

N/NF = 0.9

Near side field Far side field Thickness

Hoop

stiffness

Stress

location

Figure 3.—CDF of Hoop strength for different load cycles.

0.0

0.2

0.4

0.6

0.8

1.0

0 10 20 30 40 50 60 70

Hoop strength (ksi)

Cumulative probability 

N/Nf = 0.0

N/Nf = 0.3

N/Nf = 0.5

N/Nf = 0.7

N/Nf = 0.9
NASA/CRó2003-212126 59 

Figure 4.—Strength vs stress at different load cycles.

0

2

4

6

8

10

12

14

16

18

20

0.0 0.2 0.4 0.6 0.8 1.0

N / NF

Strength/stress, ksi

Strength 0.001 Prob.

Stress 0.001 Prob.

Strength 0.01 Prob.

Stress 0.01 Prob.

Figure 5.—Probability of failure.

0.000

3.50–04

7.00–04

1.05–03

1.40–03

0.0 0.3 0.5 0.8 1.0

N / Nf

Probability of failure 

Figure 6.—Survival probability.

0.9984

0.9988

0.9992

0.9996

1.0000

0.00 0.25 0.50 0.75 1.00

N / Nf

Probability of survival
This publication is available from the NASA Center for AeroSpace Information, 301–621–0390.

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Available electronically at http://gltrs.grc.nasa.gov

March 2003

NASA CR—2003-212126

E–13778

WBS–22–708–90–53

C–76751–J

63

Enhancement/Upgrade of Engine Structures Technology Best Estimator

(EST/BEST) Software System

Ashwin Shah

Computer codes; Structural analysis; Aerodynamic analysis; Probabilistic evaluations;

Damage tolerance; Systems evaluations

Unclassified -Unlimited

Subject Categories: 05, 07, and 39 Distribution: Nonstandard

Sest, Inc.

18000 Jefferson Park Road

Middleburgh Heights, Ohio 44130

Project Manager, Christos C. Chamis, Research and Technology Directorate, NASA Glenn Research Center, organization

code 5000, 216–433–9173.

This report describes the work performed during the contract period and the capabilities included in the EST/BEST

software system. The developed EST/BEST software system includes the integrated NESSUS, IPACS, COBSTRAN,

and ALCCA computer codes required to perform the engine cycle mission and component structural analysis. Also,

the interactive input generator for NESSUS, IPACS, and COBSTRAN computer codes have been developed and

integrated with the EST/BEST software system. The input generator allows the user to create input from scratch as

well as edit existing input files interactively. Since it has been integrated with the EST/BEST software system, it

enables the user to modify EST/BEST generated files and perform the analysis to evaluate the benefits. Appendix A

gives details of how to use the newly added features in the EST/BEST software system.