Weight Penalty Methods for Conceptual Aircraft Design

Linköping University | IEI – Department of Management and Engineering Master thesis, 30 hp | Master of Science in Aeronautical Engineering

Spring term 2018 | LIU-IEI-TEK-A--18/03188—SE

Weight Penalty Methods for Conceptual Aircraft Design

Ludvig Franzén Erik Magnusson

Supervisor: Ingo Staack Examiner: Christopher Jouannet

Linköpings Universitet

SE-581 83 Linköping, Sverige

013- 28 10 00, www.liu.se

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Ludvig Franzén

Erik Magnusson

http://www.ep.liu.se/

iii

Abstract

This report addresses a project conducted at Saab Aeronautics during the spring of 2018. The goal of the

project was to investigate aircraft weight estimations in the conceptual design phase. The work was divided

into two major parts: finding new weight estimation techniques and implementing an existing technique

called the Berry Weight Estimation in to the Pacelab APD software. Several weight estimation techniques

were found during an extensive literature review but in the end, only one was chosen for further

investigation. The chosen technique was the NASA Wing Weight Build-Up which proposed calculations

for wing weights based on aircraft statistics. It contained material data tables for determining so called K-

factors that were used to essentially scale the individual wing weight formulas. The data tables did not

include K-factors up to a load factor of 9 which was a requirement from Saab. Extrapolations of the material

data tables were done to approximate the missing values. The NASA wing weight build-up showed

promising results with little deviation from the actual wing weight for a few chosen aircraft. This weight

estimation technique was consequently chosen as a worthy candidate for a future implementation in the

Pacelab APD software.

The task of implementing the Berry Weight Estimation in Pacelab APD was divided into a fuselage- and a

wing part. This was done to ease the implementation since it would resemble the original description of the

method. The wing and fuselage weights were both calculated in two steps. The first step was to calculate a

gross shell weight. This is the weight of an idealized structure without cut-outs or imperfections. The second

step was to add so called weight penalties for various components within the wing or fuselage. Typical

aircraft components had associating weight penalty functions described in the Berry Weight Estimation.

Most of the implemented calculations used Pacelab APD to get involved parameters automatically.

However, some of the needed parameters had to be user specified for the implemented Berry Weight

Estimation to work. Once the implementation task was finished, several sensitivity studies were made to

establish a perception about the involved parameters impact on the Berry Weight Estimation results. The

new implementation gave benefits compared with the Berry Weight Estimation in Bex. One of these was

the ability to perform extensive trade- and sensitivity studies. The sensitivity studies gave verdicts on the

most influencing parameters of the implemented code and guide lines on future improvements of the

calculations. These sensitivity studies show, among other things, that is recommended to increase the

number of wing and fuselage stations significantly in order to get a converged result for the Berry Weight

Estimation.

Keywords:

Aircraft

Weight estimation

Concept development

Weight penalty

Structure

iv

Acknowledgement

We want to express our gratitude to our Saab-supervisor Kristian Amadori who has assisted us with all

aspects of the project. We would also like to thank our examiner Christopher Jouannet for his great support

and knowledge within this field of science. Our supervisor at Linköping University, Ingo Staack, has given

us great feedback which we are very grateful for. The feedback from our opponent Lukas Johnson has been

of good quality and has helped us in the improvement of this report, for this we are thankful. Our fellow

colleagues at Saab should receive special mentioning for great conversations and discussions during the

coffee breaks, they have given us much joy during the hard times of this project. We thank our new friends

Jacob and Johan for great entertainment during long work days. Last but not least, our deepest gratitude

goes to our Pace contact Lars Grabe who has help us with the extensive implementation task. His knowledge

in Pacelab APD and the C#-coding language has been a most important asset in this project.

Linköping in June 2018

Ludvig Franzén

Erik Magnusson

v

Nomenclature & Abbreviations

C# Programming language

SAWE Society of Allied Weight Engineers

CFD Computational Fluid Dynamics

FEM Finite Element Methods

DOE Design of Experiments

S Area

SWing Wing reference area

SWing,exp Exposed wing area

SWbox Wing box area

SWbox,exp Exposed wing box area

SMLGD Area of Main Landing Gear Doors (on wing)

STEFlaps Area of Trailing Edge flaps

SLEFlaps Area Leading Edge flaps

croot,exp Exposed wing root chord length

ctip Wing tip chord length

troot,exp Exposed wing root thickness

ttip Wing tip thickness

b Wing span

bexp Wing span (excl. width of fuselage)

bfolded Folded wing span

40% Wing sweep at 40% chord

LDGW Landing Design Gross Weight

TOGW Take-off Gross Weight

MZWFW Max Zero Wing Fuel Weight

WWstores Weight of wing stores

n Ultimate load factor

nLDG Ultimate load at LDGW

vmax Limit speed

vstall Stall speed

Ttot Total engine thrust

LE Leading edge (of wing)

TE Trailing edge (of wing)

Structure: in this thesis, the structure is regarded as the load bearing parts of the fuselage and wing

necessary for the aircraft to withstand loads during operation. It is defined, based on Torenbeek [1], as:

Wing – spars, ribs, skin/stringer panels, leading edge devices and structures, flight controls and their

supports and (if wing mounted engines) engine pylons. Fuselage – frames, longerons, stringers, skin, doors

and hatches, the necessary structures for mounting of actuators and mechanism for doors, pressure

bulkheads and engine pylons for fuselage attached engines. Fuel, hydraulics (fluid and actuators), engines,

electrics, furnishings, flight systems are not considered part of the aircraft structure.

vi

Table of Contents Introduction ................................................................................................................................. 1

1.1 Background ......................................................................................................................... 1 1.2 Purpose of Project ............................................................................................................... 2 1.3 Project Aims........................................................................................................................ 2 1.4 Research Questions ............................................................................................................. 2 1.5 Delimitations ....................................................................................................................... 3

2 Project Methodology ................................................................................................................... 5 2.1 Project Planning .................................................................................................................. 5 2.2 The Scrum software development methodology ................................................................ 7 2.3 Calculation Analyses and Impact Studies ........................................................................... 8

3 Theoretical Framework .............................................................................................................. 9 3.1 Aircraft Design Process ...................................................................................................... 9 3.2 Weight Estimation ............................................................................................................ 10 3.3 Aircraft Structures ............................................................................................................. 12 3.4 The Berry Weight Estimation ........................................................................................... 14 3.5 The NASA Wing Weight Build-up Method ..................................................................... 21 3.6 Pacelab APD Framework .................................................................................................. 22

4 Project Results ........................................................................................................................... 27 4.1 Literature review and Statistics gathering ......................................................................... 27 4.2 The NASA wing weight build-up ..................................................................................... 27 4.3 Comparison between the Berry and NASA wing weight estimations .............................. 32 4.4 Result of Implemented Berry Weight Estimation code structure ..................................... 33 4.5 Additional results for the Pacelab APD implementation .................................................. 37

5 Discussion ................................................................................................................................... 43 5.1 Project Methodology ......................................................................................................... 43 5.2 The NASA wing weight build-up ..................................................................................... 43 5.3 Comparison between the Berry and NASA wing weight predictions ............................... 45 5.4 Implementation in Pacelab APD ....................................................................................... 46 5.5 Research Questions and Project Aims .............................................................................. 48 5.6 Recommendations for Future Work .................................................................................. 49

6 Conclusions ................................................................................................................................ 51 7 References .................................................................................................................................. 53 8 Appendix .................................................................................................................................... 55

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List of Figures Figure 1. The planned project structure. The proposed aims (numbers) and research questions are believed

to be answered at their corresponding locations within the project plan. The aim-numbering is in the

chronological order of the stated project aims. ............................................................................................. 5 Figure 2.The work flow of the used Scrum methodology employed during the software development

process. Original image by Marekventur, used under CC BY-SA / Edited from original. .......................... 7 Figure 3. Example of a schedule for development phases for a commercial aircraft. Modified from

Torenbeek [1] with estimation classes visualised at corresponding phases in the development. ................. 9 Figure 4. A weight breakdown of an aircraft based on a breakdown in Torenbeek [1]. Airframe Structure

is the only detailed group since structural weight is the focus for this report. ........................................... 12 Figure 5. Schematic illustration of three common types of fuselage structures. Left: Semi-monocoque

structure with stringers. Middle: Semi-monocoque structure with longerons. Right: Monocoque structure.

.................................................................................................................................................................... 13 Figure 6. Illustration of two common types of wing structure. 1: Multi-rib wing structure with a front,

centre and rear spar. Original image by Dtom, used under CC BY-SA / Edited from original. 2: Multi-

spar wing structure with a single rib for external load. [13] ©Saab AB .................................................... 13 Figure 7. The Berry Weight Estimation loop. The specified error is the convergence error...................... 15 Figure 8. The fuselage of a Boeing 737 divided into a number of stations along the fuselage length. The

forward and rear wing-attachment points are marked as solid/green stations. Original image by Julien

Scavini, used under CC BY-SA / Edited from original. ............................................................................. 16 Figure 9. The fuselage visualized as a bending beam, with different loads at various locations along the

fuselage length resulting in individual shear forces and bending moments. Original image by Julien

Scavini, used under CC BY-SA / Edited from original. ............................................................................. 16 Figure 10. The perfect fuselage structure referred to in the fuselage gross shell weight (top) and a fuselage

with cut-outs (bottom). Original image by Julien Scavini, used under CC BY-SA / Edited from original.

.................................................................................................................................................................... 17 Figure 11. An example of weight penalty relationships for fuselage mounted speed brakes and gun bays

from Hammit [5]. ........................................................................................................................................ 18 Figure 12. The wing seen as a bending beam with a typical load distribution for a civil aircraft. Original

image by Julien Scavini, used under CC BY-SA / Edited from original.................................................... 19 Figure 13. Relations for aileron weight (right) and slat weight (left) from Hammit [5]. ........................... 20 Figure 14. Principle of the wing weight build-up method and the required input parameters needed for the

method. ....................................................................................................................................................... 21 Figure 15. The interface of the Pacelab APD Engineering Workbench. .................................................... 23 Figure 16. An example of dependencies for the calculation of a horizontal stabilizer mass and centre of

gravity. The colour of the involved blocks denotes their individual type. Input parameter boxes are white,

outputs are green and functions/formulas are shown in cyan. [21]. ........................................................... 23 Figure 17. The Pacelab APD Portfolio. ...................................................................................................... 24 Figure 18. The wing reference area definition with included results. Original image by Kaboldy, used

under CC BY-SA / Edited from original .................................................................................................... 28 Figure 19. The definition of different geometrical lengths and angles. Original image by Kaboldy, used

under CC BY-SA / Edited from original. ................................................................................................... 29 Figure 20. The extrapolations made for a multi-rib wing with aluminium cover with Y-stiffeners and

integral stiffeners. ....................................................................................................................................... 30 Figure 21. Comparison between upper and lower cover for Aluminium and Titanium Z and Hat stiffeners.

The Titanium comparison show that the trendline equation type with the best fit differs between upper

and lower cover. ......................................................................................................................................... 31 Figure 22. Trendline fitting and extrapolation of temperature K factor for an upper cover made from

titanium (top) and composite (bottom). ...................................................................................................... 32 Figure 23. The weight comparison between the Berry, NASA and actual wing weights are shown for the

F-16A, F-18A, SK-60 and the Hawk Mk.1 Aircraft. The F-22A wing weight is only estimated with the

NASA Wing Weight Build-Up................................................................................................................... 33

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Figure 24. The overall view of the Knowledge Designer with the implemented Berry Weight Estimation.

Dashed lines represent exchanges of information between blocks. A legend for the different blocks are

shown in the lower right corner. ................................................................................................................. 34 Figure 25. The structure of the implemented Berry Fuselage Estimation .................................................. 35 Figure 26. The Multidimensional Data Table for Cut-outs. The available types of defined cut-outs are

shown in the upper right corner. ................................................................................................................. 36 Figure 27. The ProductionJoints MDT with example of input values. ...................................................... 36 Figure 28. The structure of the implemented Berry Wing Weight Estimation. .......................................... 37 Figure 29. A sensitivity study of total wing weight difference against the number of wing stations......... 38 Figure 30. A sensitivity study for the fuselage gross shell weight difference against the number of

fuselage stations.......................................................................................................................................... 39 Figure 31. The aspect ratio and number of wing stations effect on wing mass at T/C=8%. 300 stations is

chosen as maximum limit for visualisation purposes, minimal variation to results above this value. ....... 39 Figure 32. The aspect ratio and number of wing stations effect on wing mass at T/C=12%. 300 stations is

chosen as maximum limit for visualisation purposes, minimal variation to results above this value. ....... 40 Figure 33. The aspect ratio and number of wing stations effect on wing mass at T/C=15%. 300 stations is

chosen as maximum limit for visualisation purposes, minimal variation to results above this value. ....... 40 Figure 34. Wing mass sensitivity to number of wing stations and aspect ratio. ......................................... 41 Figure 35. Wing mass sensitivity to number of station and aspect ratio. Normalised against end value

(1000 station) to visualise difference between estimations. ....................................................................... 41 Figure 36. How the chord length (i.e. inter-spar distance) at the fuselage centreline affects the fuselage

mass (1000 stations). The different series represent different location (x, lengthwise) of a Type 3 cut-out

with dimensions 2x0.5x0.5 m (LxWxH). ................................................................................................... 42

1

Introduction This report covers the thesis work conducted at Saab Aeronautics during the spring of 2018. The report

is primarily structured in the chronological order of the work, some general background is described,

along with the purpose and methodology of the thesis. Together with the theoretical framework they

form the foundation for the presented results and discussion at the end. Some conclusions are made and

suggestions for future work are given. Parts of the work contain sensitive material, consequently some

data and figures are altered for publication.

1.1 Background

Estimating the weight of a new aircraft can be a challenging task in a preliminary design phase. It is

nevertheless important to have a good approximation of the weight since it affects the aircraft structure,

performance and ability to carry out its intended mission among other things. Decent weight estimates

early in the development will aid the design selection process so that more informed decisions can be

made. Development costs can also be reduced by gaining greater knowledge of the chosen concept early

in the design process with the help of preliminary design tools. Weight estimations can allow the aircraft

engineer to explore possible designs and get a broader picture about the available design space. The

following parts of this subchapter gives some background for different companies and organizations

connected to the project and aircraft preliminary design.

1.1.1 Society of Allied Weight Engineers

The Society of Allied Weight Engineers (SAWE) is an international organisation that was formed in

1939 by a group of aircraft weight engineers, with the aim of gathering and sharing experience and

knowledge within the field of weight engineering. These days SAWE has members from all industries,

though military and civil aviation are still the main focus of the organisation. SAWE has through the

years collected an extensive arsenal of shared information. These consist of technical reports, papers,

documents and reference books within the subject of weight engineering. The SAWE paper database is

constantly growing and contains information ranging from weight analysis for American civil war naval

ships to weight and structural optimization in aircraft and space design. [2]

1.1.2 Saab AB

Saab is a Swedish defence and aerospace company founded in 1937 and currently has around 15000

employees. Saab supplies governments, authorities and corporations around the globe with products

within defence, security, services and solutions. Today, Saab consists of six business areas: Aeronautics,

Dynamics, Surveillance, Support and Services, Industrial Products and Services and Kockums. The

thesis is done at the Aeronautics division which conducts advance development of aviation technology

and is responsible for the Gripen system. The division also conducts long-term future studies of manned

and unmanned aircraft as preparation for the future. Responsible for this thesis assignment is the section

Overall Design and Concepts, which work mainly with a holistic perspective during development of

new and existing airborne systems. Furthermore, the section also develop new concepts for future

aircraft systems and it is within this field the thesis is done. [3]

1.1.3 PACE GmbH

Pace is a German company that specializes in aerospace engineering and information technology, their

main area is to develop software for the aerospace and aviation industries. The different software from

Pace ranges from aircraft design to aircraft market and operations. The software for preliminary and

conceptual design is Pacelab Aircraft Preliminary Design (APD) which aims at analysing preliminary

aircraft designs in order to make new, more effective and innovative aircraft. The Pacelab APD platform

enable the evaluation of performance and economics of new or existing aircraft configurations in a

relatively easy way. By this, the impact of different design choices can be determined early in the overall

design process of a new aircraft. [4]

2

1.2 Purpose of Project

One of many available methods for weight prediction was introduced by Hammit in 1956 [5]. This

method was later evaluated and modified by Berry and Jouannet [6], and is currently one of the methods

used at the Saab for estimating the weight during conceptual design. The modified method will hereafter

be referred to as the Berry Weight Estimation. The original method proposed by Hammit [5] is lacking

some newer materials and modern design variants and configurations. The method is partially based on

weight data from military aircraft of the ‘50s. The derived statistical values are compiled in graphs with

trend lines for different component weights and sizes. Saab have previously made comparisons of

estimates with true weights which showed that the accuracy varies and need improvement, especially

the wing and fuselage weight. Furthermore, the data basis and trend lines for component weights could

be verified for existing company designs. They could also be revised to reflect advancements in materials

technology.

Weight estimation methods are heavily dependent on the intended aircraft type, a method intended for

a civil airliner will give inaccurate results for a military fighter aircraft. Weight data for aircraft are often

considered classified information and weight estimates are consequently more difficult to verify.

Preliminary design of an aircraft is a complicated procedure full of compromises as multiple

interdependencies between design areas exist [7]. To get an easier overview of all design aspects,

software are often used to aid the design process. Saab currently uses a proprietary software but plans

to evaluate the commercial tool Pacelab APD during the coming year.

1.3 Project Aims

The following aims were established from the project purpose:

1. Implement the Berry Weight Estimation with an object oriented programming approach in

Pacelab APD and expand the software with required parameters.

2. Update the Berry Weight Estimation based on newer aircraft statistics and materials.

3. Investigate other possible weight estimation methods, their validity, accuracy and potential

usage at Saab.

4. Add new weight data where possible to Saab’s aircraft weight database and implement new

weight estimation functions in the Pacelab APD software.

5. Compare the resulting modified weight estimation functions against known aircraft data.

1.4 Research Questions

The research questions that will be addressed during the project are:

RQ1. How can the Berry Weight Estimation be improved to get more accurate estimates?

RQ2. How sensitive is the Berry Weight Estimation to the number of fuselage- and wing

stations used?

3

1.5 Delimitations

To keep the thesis work at a manageable level and within reasonable scope and timeframe, some

delimitations are made:

• Limited statistical basis.

Due to the confidential nature of the component weight data, available statistics and databases

will be used to validate or build a new weight estimation method. Only public data and to

some extent internal company statistics will be used. All credible weight data will be used to

some degree, to increase the statistical basis for the update. The amount of statistical data may

therefore vary between different weight functions and some may be more representative than

others.

• Fuselage and wing structure weight estimation and weight penalties only.

Only the structural weight estimation and associated possible penalty functions for the fuselage

and wing will be analysed. Several other subsystems (see chapter 3.2) could be included in the

weight estimation, but these would benefit to be subject of their own report due to complexity

and scope.

• Software implementation.

The updated and/or new methods will be implemented into Pacelab APD, since this is the

software that will be tested at Saab in the near future. Though, as the program is written in C#,

the code is useable after some modification in other software if necessary.

1.5.1 Later Delimitations

The project was after a literature review further delimited. The aim of investigating other possible weight

estimation techniques were narrowed down to only an investigation about one found method for wing

weight estimations. One of many reasons for this was that the found weight estimations were based on

collections of already investigated or used techniques at Saab. More focus was instead put on trying to

improving the found method. The aircraft statistics gathering was, as a consequence, also delimited to

wing weights focus only. The aim of implementing the Berry Weight Estimation in Pacelab APD was

prioritized over all other specified aims. An aftereffect of this was that the aim of updating the Berry

Weight Estimation with relevant statistics and new material data was altered. It was instead deemed as

desirable to identify where updates in the Berry Weight Estimation were most needed. This would allow

Saab to update the areas of interest with relevant statistics in the future if desired. Finally, the aim of

expanding the Saab aircraft weight database was slightly delimited as described above to only a

collection of wing weights.

5

2 Project Methodology A successful project is characterised by delivering value with the intended functionality, on time and on

budget. This could be achieved by a clearly defined scope, method and good planning. The team during

the project was small, and some parts of the method of project management suggested by Turner [8] are

more applicable to larger projects. This suggested method was used more as a guide and support rather

than a recipe that had to be followed to the letter. This decision was made to not be hindered by a large

method and keep the work moving forward.

2.1 Project Planning

Planning the project at an early stage, when the scope is not yet defined can be problematic. Estimating

the time consumption of different probable tasks and project management is an own subject in its entirety

and not within scope of the thesis. The thesis is nevertheless conducted in the form of a project and needs

planning and structure to ensure a worthwhile outcome. The decision was made to create an initial

overall project plan with major phases and deadlines outlined. The proposed schedule will be evolved

during the project and adapted when necessary. Figure 1 show the overall schematic plan with major

phases for the project.

Figure 1. The planned project structure. The proposed aims (numbers) and research questions are believed to be

answered at their corresponding locations within the project plan. The aim-numbering is in the chronological

order of the stated project aims.

6

The intention of the Problem Definition phase is to define the problem, aims and goals with the project.

For practical reasons, this is closely connected with the Literature Review and Statistics Gathering

during the initiation of the project at Saab. Internal documents and current software (Bex and

proprietary) will be extensively studied to gain more knowledge about the problem and current issues.

The literature review will also cover library and database searches for relevant and promising material

on the subject and new methods. Some informal interviews will also be held to narrow the scope of the

project. The next major phase in the project will be to test any discovered structure weight estimation

from the literature review against several aircraft with known weights. This will also involve some

statistics gathering to get weight data for as many aircraft as possible, which also is desirable for the

future update of some parts in the Berry Weight Estimation. The initial testing of found weight

estimations will be done in Matlab and Excel, as these are considered as quick and easy ways of

evaluating if a weight estimation technique is promising or not. The improvement of the possible weight

estimations selected for further work is planned to be done based on statistics from known, newer

aircraft.

Available data from Saab’s earlier military aircraft together with the Gripen fighter are supposed to be

collected and compiled for usage in updating the weight estimations. The acquired data will be used to

either update subcomponents of methods or as a base for creating a fudge factor (compensation factor)

for use at the end result of a weight estimation. A fudge factor can be calculated by dividing the actual

weight with the estimated weight [9]. The usage of a fudge factor is a brute force, but an easy way of

aligning a method’s estimated result to real values. Fudge factors can be used if the weight estimation

exhibits trends in over or under estimation of the weight, i.e. consistently under estimating the weight

of a certain type of aircraft. Using such a fudge factor for a similar type of aircraft should improve the

weight estimate. During the improvement attempts, the results of the methods will be continuously

monitored and compared against real values to ensure that a better estimate is actually achieved.

The later phases of the project will be more focused on software, coding, verification and validation.

Pace suggests the Scrum approach when working with coding and implementation. As the project team

has limited experience in software and code development, this approach will be adopted and used. In

order to properly implement, verify and validate the code some knowledge of the Pacelab APD software

is also needed. The software familiarisation will be conducted with the aid of tutorials and workshops

provided by Pace. The same is true for the code language familiarisation. Tutorials and workshop

specific to the software, but also C# coding language tutorials will be used to get more accustomed

before the upcoming implementation.

The final block from Figure 1 before the Project End is Verification and validation. This will consist of

comparisons for the found and modified weight estimation techniques against the Berry Weight

Estimation and known aircraft weights. If the results are similar (within 10 %), the implementation will

be considered as a success. The Verification and Validation will also include a comparison between the

Pacelab APD implemented Berry Weight Estimation and Bex. This will be done to ensure that the base

code for the calculation is correctly implemented. As the Berry Weight Estimation is available in Bex,

this will be used as a base for the implementation in Pace, and the code will be critically reviewed during

this phase.

7

2.2 The Scrum software development methodology

The Scrum methodology was chosen as the approach for the software development and implementation

of the Berry Weight Estimation. Scrum is a variant of the agile software development methodology and

was introduced by Jeff Sutherland and Ken Schwaber in the early 90’s. Scrum presents a way of dividing

the software development work in numerous time intervals called sprints. The sprints are four-week

(maximum) intervals where a specific development task is solved within a predefined framework. This

means that certain specifications of the intended task are fixated during an interval and should not be

changed. Future tasks and specifications outside of the current sprint can still be changed and remain

open until that sprint is started. After a sprint is ended, the results are checked to see if the intensions

were met. The benefits Scrum is that changes can take place without disturbing the overall workflow

and deviations from the original planning can be avoided. Immediate changes can also be avoided by

the locked sprints/intervals. The underlying Scrum framework consists of different Scrum-roles that the

software-development team should be divided into. Each Scrum-role serves a specific purpose and their

combined effort drives the intervals forward. The minimum number of Scrum-roles are the following

three:

• A product owner, who sets up the development work and look over the achieved and fulfilled

tasks.

• A development team, that drives the software development during each sprint and delivers the

requested results at the end of each sprint.

• A Scrum master, who ensures the compliance of the Scrum methodology. The Scrum master

serves as the leader of the Scrum team.

Scrum is often used by larger development teams, where the roles of the Scrum methodology are divided

between the software developers involved in the project [10] [11]. In order to apply the Scrum

methodology to the implementation of the Berry Weight Estimation, some minor alterations had to be

done to better suit a smaller group of only two individuals. The methodology was changed by shortening

each sprint time to a maximum of two weeks due to the limited project time. It seemed suiting to divide

the implementation according to the structure of the calculations presented by Berry and Jouannet [6].

The different sprints were therefore specified as different implementation tasks within the Berry Weight

Estimation as can be seen in Figure 2. The Scrum-roles were not explicitly followed since the work was

conducted by only two individuals. The roles were instead combined and equally distributed in the team.

The used Scrum plan as well as its individual sprints can be seen in Figure 2.

Figure 2.The work flow of the used Scrum methodology employed during the software development process.

Original image by Marekventur, used under CC BY-SA / Edited from original.

8

2.3 Calculation Analyses and Impact Studies

An additional desired step in the project was to investigate the impacts of individual parameters on the

weight estimation results. The sensitivity of parameters was to be check for both the Berry Weight

Estimation and other weight estimation techniques found during the literature review. Parameters that

were of the most interest for the different techniques were to be selected in collaboration with the

company supervisors. These investigations are closely tied to the proposed research questions and will

give a better understanding about different weight estimation parameter’s sensitivity. Parts of the weight

estimations that would benefit from updates can be easily identified as a consequence. That is,

parameters which give large impacts on the end-result are more critical to update than parameters with

lesser significance according to the sensitivity study.

9

3 Theoretical Framework This section describes the theoretical framework of the thesis. Some general theory about aircraft design

is given for a greater understanding of aircraft weight estimations. The basics of the Berry Weight

Estimation and the weight estimation technique discovered during the literature study (which is tested

to improve the weight estimations) are described. The theoretical framework also includes basic

information about the Pacelab APD software.

3.1 Aircraft Design Process

There are some disagreements on exactly when a development process actually starts, but many

designers see the conceptual design phase as the start of a product development. An example of an

aircraft development process can be seen in Figure 3, though the process differs from company to

company. The phases could overlap and the stages deviate, the distinction made in this chapter should

be seen as an example. Torenbeek [1] breaks down the product design process into the stages

specification, conceptual design, preliminary design and detail design. From the requirements from the

market analysis, a specification for the design is developed. The conceptual design stage then aims to

size the most promising overall aircraft design and prove its feasibility. The preliminary design stage

aims at specifying the design concept at the main component layer. The detail design stage goes down

to specify individual component layer.

Figure 3. Example of a schedule for development phases for a commercial aircraft. Modified from Torenbeek [1]

with estimation classes visualised at corresponding phases in the development.

10

3.1.1 Conceptual Design

The conceptual design phase is normally a creative and imaginative phase, during which the design

space is explored. Different novel designs are evaluated against more traditional designs, new layouts

are tested and evaluated to create a technically superior and economically viable design. A typical

character of the conceptual design phase is its iterative procedure. The major components such as wing,

fuselage, propulsion, empennage, landing gear and other systems are sized provisionally to result in a

baseline design. A baseline design is not necessarily an optimised aircraft, but the combined constraints

will normally give an adequate approximation to a feasible design. A difficult task in this phase is to

find the ideal aircraft design while several aspects of the design parameters contradicts each other. This

can for an example be if a wing is enlarged, the lift increases but also the weight. This consequence is

usually unwanted. The design tools are semi-empirical and the methods used are of low and medium

fidelity, geometry is provisional and some trade-off studies and basic optimisation is used. A

comprehensive design optimisation is of little value since the design will still change too much for it to

be useful. Proprietary tools developed by the company are calibrated with statistics, handbooks and

historical trends, leading to a typical prediction inaccuracy of roughly 5%. [1]

3.1.2 Preliminary Design

When the baseline design has been chosen, the preliminary design phase kicks in and focus shifts to

defining sub-systems and make component trade-offs and optimisation. Specialists help redesign the

baseline design in more detail to set goals for the following extensive detail design phase. The design is

subject to detailed analysis and sensitivity studies to determine the balance between geometry aspects,

performance and weight distribution. The design team usually expands significantly when entering this

phase, as more departments become involved and possibly sub-contractors as well. The aircraft

geometry, lifting surfaces, fuselage and their aerodynamic properties are detailed with the help of

extensive simulations and wind tunnel tests. Mass breakdown with centre of gravity (CG), load

restrictions and moments of inertia are detailed expanding the design database. The layout of the basic

flight control, control surfaces and devices along with the flying qualities are calculated from the

optimisation results. Economic analysis of operating costs, determining buy-out components and

analysis of environmental aspects prepare the design for the market. The amount of generated data for

the design is significant resulting in prediction inaccuracies around a few percent. The result of the

preliminary design phase is an optimised and verified design, detailing possible prototypes or tests to be

made and the type specification of the aircraft. If the design is given a go ahead, the design is frozen

since a significant change in a later phase would incur high costs. Consequently, the iterative procedure

is brought to an end. [1]

3.1.3 Detail Design

As evident by its name, this phase focus on specifying details for all the components of the aircraft. All

components of the aircraft are specified to geometry with technical drawings, a plan for manufacture

and assembly instructions. This phase is very time consuming and the development team expands

substantially while the concept design team’s participation is usually scaled back and limited to

addressing any new issues which affect the aircraft’s technical specification. An appropriate example is

if the empty weight has increased notably which needs to be addressed by a weight reduction

programme. Following the detail design, manufacture, assembly, test flight and certification ensues. [1]

3.2 Weight Estimation

Weight estimation is an important but difficult area of the preliminary design phase. Nikolai and

Carichner [7] even goes as far as saying “estimating weight at the conceptual design level is an art and

it will never be a science”. Beside the critical total weight, the weight estimations also result in system

and component weights. The more refined weight result in an estimated initial centre of gravity for the

aircraft, which determines important flight characteristics. The estimation is used and needed in the

design process in several aspects. Positioning of certain components such as the wing, main landing gear

11

or the size of horizontal tail are all affecting the CG. An adversely located CG could make the aircraft

unflyable. Since most weights are estimations, the actual weight may differ from the finished product.

It is important to account for this difference between preliminary design and finished aircraft weight in

some way to avoid an unwanted weight growth. Consequently, aircraft design projects usually have a

weight margin to allow for some growth. Too large difference between the preliminary design estimate

and later stages in the aircraft development may put an end to the project if the weight growth is too

high. [7]

The used prediction method differs during the stages of development, as the development progresses

more details are known about the design and can be included in the weight estimation. A typical

classification of the different methods, as presented by Torenbeek [1], are:

• Class I – Pre-conceptual studies

A Class I weight estimation typically uses the aircraft certification category, technology level

and one or more combinations of payload and range as inputs. The weight is based on the top

level requirements and a database of existing aircraft data and weight fractions. It rarely takes

any geometry aspects into account.

• Class II – Conceptual design

At this stage the basic geometry, performance and general characteristics of the aircraft is

determined and the weight estimation is refined with medium-fidelity methods. Inputs are

generally data from Class I estimations, a provisional three-view drawing and engine power or

thrust. The weight prediction has evolved into group weights with CG for each system which

produces new design weights. Structural weight estimates are determined by quasi-analytical

and analytical methods using geometric information. They are also improved with statistics for

similar aircraft. Some initial studies can also be made at this point, i.e. weight sensitivity to

different wing geometry or engine power.

• Class III – Preliminary design

A more developed design and an increased knowledge about it enables more complex and

detailed weight estimation. Several departments with specialist engineers cooperates to make a

weight breakdown of structures, systems and equipment into subsystems. In order to get the

refinement of the design that is the goal for this stage, the used methods need to accurately

predict the effects of design variations. Some high-fidelity analysis methods are also used at this

stage, such as CFD for lift and drag and FEM for loads and structural analysis. Weight statistics

are still used at this stage for calibration of the results which are used for performance, flight

dynamics analysis, and as a base for the flight control system development and the detailed

design phase.

• Class IV – Detail design

The thousands of components used in the aircraft are catalogued and detailed in order to get

accurate masses and moments of inertia. The catalogue is monitored by the weight engineers

which also compare the results to the aircraft specification. At this stage the discrepancy between

the catalogued weight and actual weight should be small, but a weight reduction programme at

this stage could be employed in case of excess weight.

An aircraft weight is usually divided into different categories. These are often the aircraft empty weight,

fuel weight, payload weight and crew weight. The empty weight can be detailed further, and include the

aircraft structure, systems and much more (see Figure 4). The weight breakdown can of course be further

detailed down to individual components, but at an early design stage these details are usually not known.

The structural weight can be divided into a number of aircraft components, where the largest ones

usually are the wing and fuselage.

12

Figure 4. A weight breakdown of an aircraft based on a breakdown in Torenbeek [1]. Airframe Structure is the

only detailed group since structural weight is the focus for this report.

Preliminary weight estimation formulas such as the ones presented by Torenbeek [1] and Roskam [12]

are based on statistical data from previously made aircraft. As a consequence, Nikolai and Carichner [7]

call for the calibration of estimation formulas against similar type of aircraft, preferably previous

company designed aircraft, to improve the estimates. The weight of additional aircraft components, such

as stabilizers, landing gears and landing gear attachment etc. can be estimated with various techniques

from [1], [7] , [12] among others. The propulsion system is usually a component that need to be taken

in to account in the structural weight estimation. The intended engine/engines for a new aircraft is often

determined before the preliminary design stage and the weights for the engine are obtained from the

engine manufacturer.

3.3 Aircraft Structures

A brief overview of the general structure of an aircraft fuselage and wing is presented. As with most

constructions the design differs between manufacturers, but three design types have emerged as more

popular than others.

3.3.1 Fuselage

Modern aircraft fuselages are often of monocoque or semi-monocoque design. A monocoque

construction in an aircraft is usually built up by a thick sandwich skin and circumferential frames. A

semi-monocoque fuselage normally have a thin skin, circumferential frames and either stringers or

longerons. An overview of these types of fuselage structures can be seen in Figure 5 where basic

illustrations are shown for simplicity. The frames are designed to keep the general shape of the fuselage

and provide attachment-points for wings, landing gear etc., as well as increase the buckling capability

of the stringers and longerons. The main difference between stringers and longerons are their dimensions

and how many that are used in the structure. Both work together with the skin to carry longitudinal

tension and compression loads. They also serve as a support to increase buckling capabilities of the skin.

The skin carries torsional, vertical and horizontal loads. As previously mentioned it also counteracts

fuselage bending. If a sandwich skin construction is used, stringers or longerons are usually not needed

as the skin has better compression buckling capabilities. [7]

13

3.3.2 Wing

Wing structures are typically built up of spars (spanwise) and ribs (usually chordwise) and a thin or thick

sheet skin (see Figure 6). Together, these structure component forms the wing box – the torsional load

bearing structure of the wing. A multi-rib wing usually has two spars (front and rear, and occasionally a

third centre spar), together with several ribs. The spars main function is to carry vertical shear loads and

part of the spanwise bending load, while the rest of the bending load is carried by the skin. The skin is

supported by the ribs to increase the top cover’s buckling capabilities while the lower cover experience

tension loads. Stiffening structures are often used on the inside of the skin to increase buckling stability.

A multi-rib wing is a common construction in commercial transport aircraft as the certification and usage

bending loads (spanwise) on such aircraft are moderate. A multi-spar wing usually has a thicker skin

cover and due to the many spars, ribs are seldom required. However, ribs are commonly used for

attachment-points for external stores or for extra structural support and attachment for the control

surfaces and high lift devices. The thicker skin and tighter spar spacing also generally eliminate the need

for skin stiffeners. This type of construction is common in high performance and fighter aircraft as the

wings are usually thinner and the loads higher. [7]

Figure 6. Illustration of two common types of wing structure. 1: Multi-rib wing structure with a front, centre and

rear spar. Original image by Dtom, used under CC BY-SA / Edited from original. 2: Multi-spar wing structure

with a single rib for external load. [13] ©Saab AB

Figure 5. Schematic illustration of three common types of fuselage structures. Left: Semi-

monocoque structure with stringers. Middle: Semi-monocoque structure with longerons. Right:

Monocoque structure.

https://commons.wikimedia.org/wiki/File:Wing_structure1.JPG

https://creativecommons.org/licenses/by-sa/3.0/

14

3.3.3 Materials

The structural design of an aircraft is not the only thing driving the aircraft weight. Building materials

are also of great importance in the production and design of an aircraft. As the weight is closely coupled

to the aircraft performance, the lowest possible weight is desired in the aircraft industry. Light aircraft

weight does often mean light and strong materials that usually come at a high cost. Thus, the design of

an aircraft is among other things a balance between weight and production cost. The material selection

has further influences on the aircraft, as maintenance and service shall be possible to perform during the

aircraft’s operational life. There have been many aircraft materials throughout the time of aviation,

reaching from wood to advanced metal alloys. The typical modern materials used in the aircraft

industries are:

• Aluminium (7075-T6, 7050, 2024)

• Composites (Carbon fibre, etc.)

• Steel (Stainless 301 Full Hard, and Carbon steel 4130)

• Titanium (6A1-4V)

Each of these materials have different properties and are commonly used within certain areas of an

aircraft. Properties such as specific strength, stiffness, environmental aspects, toughness against

fractures, limitations on minimum gage thickness, availability and manufacturability are important

factors when choosing materials for an aircraft [7]. The ability to withstand high temperatures is also an

important characteristic for materials in the aircraft industry. Fast flying fighter jets are exposed to

aerodynamic heating at high Mach numbers and their structural materials should be able to withstand

these temperatures [9]. Fighter jets are also subject of high G-forces which require strong structure and

materials. Modern fighter jets usually combine all the above listed materials in some way to achieve the

intended specifications of the aircraft. The use of composites has shown a positive trend in the past years

and aircraft manufactures tend to follow the trend due to the many benefits of composites. Composites

are very versatile and resistant to fatigue, they also show lower coefficients of expansion due to

temperature as well as resistance to corrosion. Composites also have the ability to be custom-made for

certain stiffness and strength characteristics. Finally, composites allow for different aircraft structures

than metals ones such as a carbon fibre monocoque design instead of an older truss structure. Composites

are however complicated materials, since their mechanical properties are dependent on many factors.

The mechanical properties are essentially determined during the manufacturing of the component, as the

properties are dependent on fibre type, direction, resin type, curing time, curing pressure and more. The

reader is strongly advised to seek material data tables and more detailed information about the different

material properties and their manufacturability. [7] [9] [14]

3.4 The Berry Weight Estimation

The Berry Weight Estimation is a way of estimating the structural weight of an aircraft in an iterative

process that uses obtained results for a next iteration of calculations. The procedure itself is a

combination of two other techniques for aircraft weight estimations [6]. These involved techniques were

presented in Torenbeek [1] & Hammit [5] and calculate the weight of a wing and fuselage in similar

ways. The calculation procedure for both techniques starts by obtaining a so-called fuselage gross shell

weight. This is a description of the fuselage weight as a “perfect” shell structure without imperfections

or cut-outs for windows and the like. The next step in the calculations is to add structural weight for

various components and cut-outs in the fuselage. These added weights are referred to as weight penalties.

The gross shell weight with the added weight penalties yields an estimate for the fuselage structural

weight. The wing weight is calculated in a similar fashion to the fuselage procedure. The wing is first

assumed as a “perfect” structure in a wing gross shell weight step, penalties for wing components such

as landing gears and their cut-outs are then added to obtain a structural weight for the wing. Both the

fuselage and wing procedure uses results from each other, which makes the calculations iterative. The

difference between the techniques presented in Hammit [5] and Torenbeek [1] are mainly that Hammit

focuses on military aircraft while Torenbeek describes the weight estimations for civil applications. This

difference is most noticeable in the weight penalties since the configurations and structures between

military and civil applications can vary quite a lot. The Berry Weight Estimation describes a combination

15

of these two techniques where the different weight penalties have been combined to allow for a weight

estimation of an aircraft regardless of the aircraft type. An implementation of the resulting estimation

have been implemented in an Excel-document, known as Bex. Figure 7 below describes the overall

procedure of the Berry Weight Estimation.

After a calculation has been made based on the guessed weight and if the specified error is too large, the

latest calculated weight is specified as the new guessed weight. The process is then repeated until the

specified error is attained. The final fuselage weight is then used to calculate the wing weight in the

same manner. Each box in this iterative method contains several weight estimation formulas for various

components. The initial guessed empty weight usually consists of known weights, such as the intended

engine, landing gears, and possibly tail and/or canard surfaces. Other structural parts of an aircraft apart

from the wing and fuselage are mainly calculated with estimations from Torenbeek [1] in the Berry

Weight Estimation. All such additional components are in the end added to the resulting weight from

the estimation loop which gives a final estimated weight of the aircraft structure.

The penalties in weight for aircraft can appear in several ways. The previously mentioned weight

penalties for various cut-outs are just a few examples that require additional structure weight. Weight

penalties are, among several other things, dependent on both position and size of the intended cut-outs.

The positioning will determine the loads and stresses that the structure need to withstand while the size

is directly coupled to the weight and strength of the surrounding structure. Overall weight for an aircraft

also include manufacturing related penalties in form of joints between structures and surfaces. Weight

penalties are the summation of every part that is included beyond the optimized shape (a shape with no

cut-outs or imperfections) for any loadbearing structure. Other things that generate weight penalties are

various aero-elastic effects that needs to be avoided and load criterions which must be fulfilled. These

penalties cannot be ignored when making accurate prediction of an aircraft weight. Weight penalties are

often applied as relations, formulas or fudge-factors for aircraft components.

The following sections of this chapter describes the Berry Weight Estimation more in detail, it is

however recommended to read the original documents from [1], [5] and [6] for more details and clarity.

3.4.1 Fuselage Gross Shell Weight

The fuselage gross shell weight is as previously mentioned a “perfect” fuselage structure weight without

any imperfections or cut-outs. The proposed fuselage gross shell weight methodology from Berry and

Jouannet [6] suggests that the fuselage shape is divided into several stations along the fuselage length

(see Figure 8). This allows for individual weight calculations of each station and unconventional

fuselage shapes can therefore be handled. In the end, the total fuselage gross shell weight is the sum of

all specified station weights. The stations are distributed in front, between and rear of the wing-

attachment points which are two fixed stations. Stations are desirably positioned so that eventual cut-

outs in the fuselage are captured either between or at a station. There is no information about the

distribution or number of stations besides that they should be almost equally spaced. [6]

Figure 7. The Berry Weight Estimation loop. The specified error is the convergence error.

16

Figure 8. The fuselage of a Boeing 737 divided into a number of stations along the fuselage length. The forward

and rear wing-attachment points are marked as solid/green stations. Original image by Julien Scavini, used

under CC BY-SA / Edited from original.

The fuselage itself can be seen as a bending beam suspended on two supports, these supports are the

front and rear wing-attachment points on the fuselage. According to Berry and Jouannet [6], these

attachment points corresponds to the front and rear spar of the wing for a civil aircraft, while the mean

aerodynamic chord position is used in combination with the heaviest loaded spars for a military aircraft.

The weight of the fuselage is mainly determined by the load applied to the structure. The load that needs

to be withstood is determined by the aircraft ultimate load factor, which corresponds to the ultimate load

that the aircraft is designed to be exposed to. Typical loads are generated by the fuselage structure and

items such as systems, engines, landing gears, etc. installed in the fuselage. These components are seen

as widespread loads, partly distributed loads or point loads at different positions along the assumed

fuselage bending beam. The size and position of these loads will determine the generated shear and

moment for the fuselage. Figure 9 below shows some examples of the loads applied to the fuselage

bending beam.

Figure 9. The fuselage visualized as a bending beam, with different loads at various locations along the fuselage

length resulting in individual shear forces and bending moments. Original image by Julien Scavini, used under

CC BY-SA / Edited from original.

https://commons.wikimedia.org/wiki/File:B737v1.0.png




17

The widespread load shown to the right in Figure 9 is due to the fuselage structure itself. This is one of

the values which makes the procedure iterative (see Figure 7), an initial guess of the fuselage structure

weight is thereby needed for the fuselage gross shell weight calculation. The fuselage structural weight

is however what is being calculated in this method and the resulting weight is therefor used after the first

iteration. The generated total bending and shear for each fuselage station is determined to give an

overview of the forces acting on the aircraft fuselage. The next step is to determine each fuselage stations

width, depth and perimeter. These measurements are then used in combination with the previously

obtained shear and bending for each station to determine the required fuselage skin thickness. The

fuselage skin thickness is in short sized by the total bending and shear determined at each station. The

skin thickness is increased in accordance with the distribution of loads along the fuselage towards the

wing-attachment points. The result of this procedure is a weight per fuselage station calculated with a

material density for the fuselage. The total gross shell weight for the fuselage is then, as previously

mentioned, simply the sum of all fuselage stations weight.

3.4.2 Fuselage Weight Penalties

The obtained results from the fuselage gross shell weight procedure is now used to add the penalties in

weight due to various cut-outs and components within the fuselage structure. Figure 10 shows the

difference between the assumed fuselage shell calculated in the fuselage gross shell weight procedure

and a fuselage with examples of added cut-outs.

Figure 10. The perfect fuselage structure referred to in the fuselage gross shell weight (top) and a fuselage with

cut-outs (bottom). Original image by Julien Scavini, used under CC BY-SA / Edited from original.

The typical fuselage weight penalties presented in Torenbeek [1] and Hammit [5] were shown as simple

relationships between weight, size and position of penalty-required components. Examples of weight

penalty relations taken from Hammit can be seen in Figure 11.



18

Figure 11. An example of weight penalty relationships for fuselage mounted speed brakes and gun bays from

Hammit [5].

These relationships for penalty-required components are based on statistics of various aircraft fuselages.

Typical components that generate fuselage weight penalties are presented in accordance with Torenbeek

[1] and Hammit [5] in the item list below:

• Landing gears

• Canopy, windshield and operating mechanism

• Cockpit

• Catapult (ejection seat)

• Arresting gear

• Speed brakes

• Gun bay and rocket bay

• Engines

• Fuel

• Production joints

• Tail support

• Wing support

• Equipment

• Tail bumper and barrier crash

• Miscellaneous

One of the main parameters for weight penalties in the fuselage are the positions of the structural cut-

outs, which are connected to some of the components listed above. The position of a cut-out is directly

coupled to the size of the weight penalty. The fuselage stations from the gross shell weight procedure

and their skin thickness are used once again for determining the size of the weight penalty. A cut-out in

a region with higher fuselage skin thickness will therefore be more weight demanding than a cut-out in

a station with thinner skin thickness. Typical cut-outs at different positions along the fuselage on a civil

airliner are for an example windows. The Berry Weight Estimation has combined the weight penalties

from Torenbeek [1] and Hammit [5] for a more versatile weight estimation approach. The results for all

weight penalties are in the end summed up to a total weight and are added to the previously calculated

gross shell weight. This yields an approximated value for the total fuselage weight [6].

3.4.3 Wing Gross Shell Weight

The wing gross shell weight is calculated by the same assumptions as the fuselage gross shell weight.

The wing is like the fuselage seen as a bending beam but with its supports at the fuselage sides. The

19

breakdown into stations and their subsequent calculations are only done for the wing box since it is the

structural part of the wing. These stations are distributed span wise along the wing. The bending and

shear for each station is used to obtain the wing gross shell weight as in the fuselage approach. The loads

that generate bending and shear are once again the structural weight of the wing itself, systems within

the wing, landing gears and wing mounted engines etc. These loads can as previously be point- , partly

distributed- or widespread loads. Figure 12 below shows the wing as an assumed bending beam as well

as a typical load case for an aircraft wing. The weight is calculated for half of the wing during the process

and the total weight for the wing with penalties is in the end multiplied with 2 according to Berry and

Jouannet [6].

Figure 12. The wing seen as a bending beam with a typical load distribution for a civil aircraft. Original image

by Julien Scavini, used under CC BY-SA / Edited from original.

It can be seen in Figure 12 that the load due to the wing lift is considered. This load is opposite to the

loads imposed by engines and structure etc. The lift force is dominant in the wing load case and all forces

opposite to the lift is seen as relieving. The generated lift in combination with the ultimate load factor is

therefore directly coupled to the maximum loads acting on the wing. The obtained bending and shear

due to loads determines the required skin thickness of each station similar to the fuselage calculations.

The required skin-thickness will increase in accordance with the load distributions and resulting

moments closer to the wing root. The total wing box weight is now obtained by calculating the weight

of each wing station with a material density and add up all station results. In order to acquire the total

wing gross shell weight, additional wing parts and weight correlations needs to be added to the wing

box weight. A sweep correction is added to the wing box weight to account for the necessary increment

in material at the wing-fuselage attachment due to a possible wing sweep angle. Finally, the weight of

the leading and trailing edges of the wing are determined by relations specified in Hammit [5] and added

to the wing box weight. This yields a total weight for a “perfect” wing structure without imperfections,

a wing gross shell weight.

3.4.4 Wing Weight Penalties

Similar to the fuselage weight penalties, the wing penalties consists of wing related components that

require additional weight. Cut-out penalties are not calculated as in the fuselage weight estimation and

no specific calculation for these are mentioned in Berry and Jouannet [6]. Component specific cut-out



20

penalties are instead included in the overall penalty for the intended component. A wing mounted speed

brake cut-out weight is for an example already included in the correlation for the speed brake weight

penalty proposed in Hammit [5]. The reason for this is that the correlation has been acquired from aircraft

statistics of wing speed brake weights. Other typical components that generate weight penalties on an

aircraft wing are the following, in accordance with Torenbeek [1] and Hammit [5]:

• Ailerons

• Flaps

• Slats

• Speed Brakes

• Wing Fold Mechanism

• Wing – Fuselage Attachment

• Wing Splices

• Supporting Structure for Actuating Equipment

• Airload Bulkheads

• Landing Gear

• Nacelle attachments

• Joints

• Stiffness Requirements

• Miscellaneous

Each presented component has its own relation in Torenbeek [1] and Hammit [5] obtained from aircraft

statistics so that the weight penalties for other aircraft can be estimated. Examples of such relations can

be seen in Figure 13. The sum of the wing weight penalties is in the end added to the wing gross shell

weight which yields an estimate of the total wing structural weight.

Figure 13. Relations for aileron weight (right) and slat weight (left) from Hammit [5].

The operational empty weight of the aircraft is finally determined by adding the total fuselage weight

with the total wing weight together with the weights of remaining aircraft components, such as landing

gears, engine, tail etc. The Berry Weight Estimation presents a quick and fairly accurate method of

weight predictions for aircraft. Further details of the original calculation are found in [6].

There is a proposed penalty for a “wing stiffness criteria” in Berry and Jouannet [6] which is included

in the Stiffness Requirements from the list above. It is however substituted with a formula from

Torenbeek [1] as it was never completed and evaluated [13]. An interpretation of the intended “wing

stiffness criteria” is presented in Appendix A.

21

3.5 The NASA Wing Weight Build-up Method

A study funded and published by NASA in 1980 suggests another method to calculate the wing weight.

Made by York and Labell at Grumman Aerospace [15], the method was derived from analysis of around

50 different aircraft. The aircraft used in the study varied from commercial transport to bomber and

fighter aircraft where some of the aircraft had special features ranging from foldable wings to variable

wing geometry. This section will give an overview of the method, more details can be found in [15].

The method is simpler compared to the Berry wing weight estimation as no iterations are necessary in

its calculation. In short, different wing components are calculated separately and then summed up for

the total weight of the wing (see Figure 14). With the help of the sample aircraft, the study derives a

simplified beam model for estimating the wing box and adding factors for materials and construction

methods used in the wing.

Figure 14. Principle of the wing weight build-up method and the required input parameters needed for the

method.

The procedure of calculating the wing weight with this method is to first calculate the weight of the wing

box and the wing box substructure. Different penalty weights are then added due to cut-outs for storages,

landing gear, fuel, folding and sweepable wings. Engine penalties are added if the aircraft has engines

installed on/in the wing. Additional penalties for control surfaces are added to the wing weight

depending on the aircraft’s control surface configuration. Each type of control surface present on the

wing is represented by different factors (hence called k-factors) for each control surface type. The factors

have different values depending on the type of control surface. The penalty weight for roll-control

surfaces are for example determined by different values of a particular k-factor which specifies if the

aircraft uses ailerons, elevons, flaperons or decelerons. Other things besides the k-factor that influence

the weight penalty for a roll-control surface are the area, total wing area and TOGW. Trailing Edge

Flaps and the item Sec. Structure LE, TE & Misc. also have their own k-factor depending on what is

present on the wing. The other items do not have a separate factor, but their impact on the wing weight

is governed by their surface areas. As an example, if no wing speed brake is present on the aircraft the

input SSpeedbrakes is set to zero and the formula will not give a weight penalty. After calculating the material

and temperature factors as per chapter 3.5.1, all the components are summed up to the total wing weight.

22

The equations from York and Labell [15] which are used to build up the wing weight are show in

Appendix B with corresponding k-factors.

3.5.1 Material, construction, temperature and load driven factors

The method utilizes material and construction data to derive correlations between different weight

driving factors. These factors are used in the weight estimation and are chosen depending on the aircraft

construction, material and design load.

In order to get an accurate estimate, the method requires the calculation of two material constants, which

are based upon tables within [15]. Material/structural and temperature factors for aluminium (7075-T6),

titanium (6AL-6V-2SN Ann.), stainless steel (PH15-7M0) and carbon fibre/epoxy (no detailed

specification provided) are given at different load factors ranging from 2.5 to 7.5. The factors vary

depending on type of construction, skin stiffeners used, materials and upper or lower skin cover. Both

the material factor and the temperature factor are calculated as an average of their constituents. By this,

different materials can be used on the wing and the method take this into account. As an example, a

multi-spar wing rated for a load factor of 5 with 12 inch spar spacing. The wing is constructed with a

carbon fibre lower skin, aluminium upper skin, centre-section upper and lower panels of titanium results

in the following:

𝐾𝑙𝑜𝑤𝑒𝑟 = 1.059 𝐾𝑢𝑝𝑝𝑒𝑟 = 1.786 𝐾𝑐𝑒𝑛𝑡𝑟𝑒,𝑢𝑝𝑝𝑒𝑟 = 2.430 𝐾𝑐𝑒𝑛𝑡𝑟𝑒,𝑙𝑜𝑤𝑒𝑟 = 2.319

𝐾𝑀𝑇𝐿𝐶𝑉𝑅 =(𝐾𝑙𝑜𝑤𝑒𝑟 + 𝐾𝑢𝑝𝑝𝑒𝑟 + 𝐾𝑐𝑒𝑛𝑡𝑟𝑒,𝑢𝑝𝑝𝑒𝑟 + 𝐾𝑐𝑒𝑛𝑡𝑟𝑒,𝑙𝑜𝑤𝑒𝑟)

4= 1.8985

The material tables for the NASA wing weight build-up method can be found in [15] and Appendix D.

3.6 Pacelab APD Framework

According to Pace, the software is an “Interactive aircraft preliminary design tool for the development

of conventional and unconventional aircraft in the conceptual and preliminary design phase” [16]. It

provides the user with an interface and an ability to customize the software. Pacelab APD offers the

ability to expand the software with user-defined parts. This means that the user can expand the software

by implementing own solutions and calculations which later can be used in the aircraft design process.

Geometrical representations to implemented components can also be defined and parameter controlled.

It features a user-interface where a geometrical representation of the intended aircraft for analysis is

shown. The geometrical representation is continuously updated with changed parameters. The

layout/configuration of the aircraft is easy to change and allows for quick changes of landing gear and

engines arrangements for an example. The user can specify and create own aircraft missions as well as

sizing scenarios which can be used to generate graphs and reports intended for the preliminary design.

An example of the APD user-interface can be seen in Figure 15.

23

Figure 15. The interface of the Pacelab APD Engineering Workbench.

The software comes with many predefined methods and functions for aircraft preliminary design and

can be used as it is for extensive aircraft analysis. It also comes with a number of predefined aircraft

which can be altered and analysed based on the user needs. The Pacelab software has a generic solver

which tracks updates to the model and handles numerical iterations. The entire software is built on

dependencies which are registered by the underlying Pacelab core code. This is done in a pre-analysis

before the entire system is solved by the generic solver. These dependencies of parameters can be shown

and gives the user an overview of the system mapping (Figure 16).

Figure 16. An example of dependencies for the calculation of a horizontal stabilizer mass and centre of gravity.

The colour of the involved blocks denotes their individual type. Input parameter boxes are white, outputs are

green and functions/formulas are shown in cyan. [21].

24

The input or output state of a parameter can be toggled as the calculation systems is dynamic. The users

can investigate the impact of all involved parameters in their analyses. The users do however need to

keep in mind that the system needs to be mathematically valid, i.e. the same number of unknown

parameters as equations and formulas. Pacelab APD has a built-in trade-study tool and numerical

optimization capabilities. This allows the users to explore the design space for an intended aircraft and

see the impact of different parameters as well as getting optimized values. In short, Pacelab APD offers

a structured view of the entire aircraft design process from which reports, tables and graphs of results

can be extracted.

The expansion of the software with own implementations is done in the Pacelab Knowledge Designer

which is a part of the Pacelab APD portfolio (Figure 17). The Knowledge Designer contains all

underlying equations and the core components for Pacelab APD. The Knowledge Designer permits

implementation of user created components, calculation cases, solutions and methods etc. The

underlying structure of Pacelab APD can also be adapted and changed to better suit the users need. User

implemented parts from the Knowledge Designer are called components and are after completion

available within a Pacelab APD Repository (component library). These user-created components can

then be called upon and used when an aircraft is being designed and analysed in the Pacelab Engineering

Workbench (Figure 17).

The Engineering Workbench is in short the program interface which utilizes the underlying code from

the Knowledge Designer to make a visual representation of the aircraft design tool. User created

components and implementations can be anything from a geometrical shape to a new weight estimation

calculation. These are as previously mentioned loaded from the Knowledge Designer via the Repository

and used in the aircraft preliminary design evaluations [4]. This gives the Pacelab APD users a way of

customizing their analyses to suit their own needs. The creation of additional components allows the

core code of Pacelab APD to remain unaltered which gives the users a possibility to always fall back to

the default aircraft preliminary design methods implemented by Pace. The components that can be

created in the Pacelab Knowledge Designer are primarily of two types: Engineering Objects and

Functional Objects. An Engineering Object, or EO, is an object which contains parameters with

integrated algorithms. EO:s can be used to outline the structure of a future product. They can have both

2D and 3D geometrical representations that describes the physical body of a product [17]. The

Functional Objects, or FO:s, describe the algorithms that are used as building blocks in the Engineering

Objects. The FO:s can be used to define relations and connections between different EO:s [17]. Most

weight estimation techniques require some geometrical and performance related parameters from the

aircraft intended for analysis. Such parameters need to be located in the Knowledge Designer for

implementation of new weight estimation methods. Parameters are of the EO-type and can e.g. describe

Figure 17. The Pacelab APD Portfolio.

25

different aircraft entities such as a specific length, engine diameter or a material density. Parameters that

are required but not existing in the Knowledge Designer needs to be defined by the user for some weight

estimations to work. Parameters that are not existing in Pacelab APD can be of various kinds but are

most often method specific parameters. They are for an example different fudge factors and values

derived from regression studies of aircraft statistics. Required parameters could also be geometrical data

that are not calculated in the standard APD configuration. This could be the wing sweep for an example

where different weight estimation techniques uses the sweep angle at different wing chord positions.

Pacelab APD and the Knowledge Designer are based on and implemented in the C# coding language.

Consequently, all added user-defined contents to the Knowledge Designer needs to be of the C#

language. Basic knowledge of software implementation and code writing is therefore beneficial when

designing own components in Pacelab APD.

27

4 Project Results The acquired project results are presented in this chapter. The outline of the project methodology is

partially followed in the coming sections.

4.1 Literature review and Statistics gathering

Several weight estimation techniques were found during the project’s literature review. Most of the

found weight estimations were however collections of formulas from already used techniques like the

ones presented in Torenbeek [1] or Nicolai and Carichner [7]. These weight estimations were mainly of

class I and II estimates. The most promising weight estimation technique that was tested was the NASA

wing weight build-up methodology (class II). The work of investigating new weight estimations were

in the end narrowed down to only this method. Consequently, the statistics gathering of aircraft weights

were focused on aircraft wing weights.

4.2 The NASA wing weight build-up

This methodology from York and Labell [15] was implemented in both Excel and Matlab, several

aircraft were tested with the calculation to estimate each aircraft’s wing weight. The weight of each wing

was then compared to the existing Berry wing weight estimation and actual wing weights to give a

verdict on if the methodology approximated the wing weight accurately. The following section describes

modifications as well as interpretations of the implemented methodology from [15].

4.2.1 Validation and interpretation

Many chapters in York and Labell [15] gave little or no information about the definition of different

parameters. This was true for both area and length definitions. One task was therefore to clarify how the

used parameters were specified. To achieve this, an F-16A fighter aircraft was used as a test for the wing

weight methodology. The F-16A was included in the original report presented by York and Labell [15],

and the implemented methodology was therefore likely to give the same results if the definitions of

lengths, areas and other parameters were interpreted correctly. The test results of the F-16A wing weight

can be seen in Table 1.

Table 1. The comparison between the estimated weight of the F-16A fighter aircraft wing and the actual wing

weight.

The following section describes how some of the different geometric parameters were interpreted

according to the authors. All parameter interpretations for the wing build-up are shown in Appendix C.

The presented parameters in this section and Appendix C are in accordance with Figure 14 from the

theory section.

The wing reference area, or SWing, can be defined in several different ways and are often standardized

within companies. The different methods are often publicly available and are sometimes described with

detailed pictures. Figure 18 shows the interpretation of the wing area definition on the Gripen fighter

aircraft. The wing area was measured and compared with publicly available data for the Gripen aircraft

and gave accurate results.

28

Figure 18. The wing reference area definition with included results. Original image by Kaboldy, used under CC

BY-SA / Edited from original

Areas that do not exist on the intended aircraft should be specified as zero. The Gripen C for example

has its main landing gears within the fuselage and the main landing gear doors are located there as well.

The main landing gear door area for the wing should therefore be specified as zero. The proposed

methodology by York and Labell [15] also utilizes several geometrical aircraft lengths and angles. The

interpretations of the top view definitions are illustrated in Figure 19 to the left. The wing span (b) is

defined as the distance from wing tip to wing tip, while the exposed wing span (bexp) is interpreted as

the wing span without a mean width of the fuselage-covered distance. The exposed root chord (Croot,exp)

and the tip chord (Ctip) are defined as the wing width at the wing-fuselage connection respectively the

width at the wing tip. The 40% sweep angle (Λ40%) is defined as the sweep between 40% of the root

chord and tip chord length. There is also a geometric parameter for a folded wing span (bfolded) that

defines the wing span for aircraft with foldable or sweepable wings (usually carrier-based aircraft). This

parameter is simply interpreted as the new wing span measured from tip to tip on sweepable wings or as

the span between the hinges on an aircraft with foldable wings. Figure 19 also shows the final

geometrical definitions on a front view of the aircraft. The wing tip thickness (ttip) is interpreted as the

thickness of the wing at a position before any wingtip weapon storages. The exposed root thickness is

interpreted as the wing thickness at the fuselage-wing connection.

https://commons.wikimedia.org/wiki/File:JAS39_Gripen.svg



29

Figure 19. The definition of different geometrical lengths and angles. Original image by Kaboldy, used under


Other parameters without geometry, were different weight definitions as shown in Figure 14. The

Maximum Zero Wing Fuel Weight (MZWFW) was interpreted as the Maximum Take-off Weight

(MTOW) without any fuel in the wing fuel tanks. The landing design gross weight (LDGW) was

interpreted as the publicly specified LDGW value for the intended aircraft. If not specified, it could be

calculated with its given formula from [15]. The same interpretation was made for the Take-Off Gross

Weight (TOGW). The weight of wing storages (WWstores) was defined according to York and Labell [15]

as “the summation of the heaviest stores weight on all wing stations including drop tanks”.

The ultimate load factor for manoeuvres (n) and ultimate load factor at landing design gross weight

(nLDG) were also needed as parameters for the wing build-up methodology. The ultimate-load factor was

defined as the limit load factor times 1.5, while the load factor for landing was interpreted as the nLDG

specified by the intended aircraft manufacturer (only used if the aircraft had landing gears on the wings).

The required velocities were the maximum flying speed and the aircraft stall speed. These were

interpreted as the respective velocities specified by an intended aircraft manufacturer. Finally, the total

thrust of wing mounted engines (Ttot) were, as the name implies, defined as the sum of all wing mounted

engine thrusts. The previously mentioned K-factors that determined the aircraft configuration were also

subject for some interpretation. An example was the K-factor for variable sweep and folded wings (KWS)

which was poorly specified in [15]. The conclusion drawn in this case was that a value of KWS = 0 should

be used if the aircraft had no variable or folded wings. KWS = 1 was to be used on aircraft with foldable

wings and KWS = 0.556 for aircraft with variable sweep wings. A general conclusion for the configuration

K-factors was that a value of zero should be used if the aircraft did not utilize the configuration type that

the K-value described. All K-factors used in the formulas can be seen in Appendix B.

Furthermore, the proposed method from York and Labell [15] contained tables with material data for

the wing box structure and wing box temperature dependence derived from the aircraft involved in the

study. These tables supplied the reader with other K-factors to multiply the wing box weight calculation

with. A mean value of the different factors for the wing box composition had to be used, as shown in

chapter 3.5.1. The problem with these factor tables were that the limit load factors for which the tables

were made only reached a value of 7.5. One of the requirements from Saab was that the limiting load

factor should reach a value of at least 9, which is a common load factor for modern manned fighter jets

[18]. These tables were therefore somewhat incomplete in terms of modern aircraft materials and load

factors. Weight and temperature factors for load cases above 7.5 was therefore needed.



30

4.2.2 Extrapolation of material data

The idea was to use the available values from York and Labell [15] and extrapolate additional values

for load factors up to 9 with the help of trend lines. The tool of choice for this task was Microsoft Excel

were the table values from [15] were plotted and a polynomial trend line fitted to the plotted points. The

equation for the trend line was then obtained which in turn gave an approximate for load factors above

the original report. These values did however deviate strongly with the order of approximation. The

problem with a polynomial trend line is that lower order estimations will give a curved line which

eventually will turn and give non-logical predictions. One should however be careful when predicting

values since it is impossible to actually know how values below and above the know range will behave.

A higher order polynomial trend line can also give non-logical predictions since the line is closely

connected to the existing values used for fitting the trend line. Estimations made with the higher order

polynomial line may consequently deviate strongly.

Another approach was therefor tried to obtain more reliable results. There are several trend line options

available in Microsoft Excel, each of them applicable in different areas and scenarios [19]. A structured

approach to the trend line fitting was conceived, which consisted of some general assumptions which

were used alongside the method for fitting a trend line to the existing data. It was assumed that the

behaviour of the K-factor would be same for a type of stiffener and material, i.e. Aluminium Y 12 should

not be linear at the same time as Aluminium Y 16 is logarithmic (see Figure 20). The type of equation

did not have to be the same for the upper or lower cover, as the trends did not necessarily exhibit the

same behaviour. If more than one type of equation for the trend line gave good R²-value, the type which

gave the overall best fit for that type of stiffener and material was chosen. The R2 value describes the

trend lines fitting and should be as close to 1 as possible for the best curve fit. A value of 1 is however

only the best fit against the existing values and do not necessarily give the best approximation for

extrapolated values. A threshold R2 value was specified as 0.9 for the trend lines as the limit for a good

fit. Trend lines with lower R2-value were considered somewhat unsure and should be used with care.

Figure 20. The extrapolations made for a multi-rib wing with aluminium cover with Y-stiffeners and integral

stiffeners.

The material data from the NASA wing weight build-up is quite vast and only a portion of the acquired

results are shown in this section. All used data tables, graphs with approximated trendlines and

31

extrapolations can be found in Appendix E and F. The achieved R²-value for the majority of the

trendlines were above 0.9, and often above 0.95 indicating a good fit. However, when the R²-value was

below 0.9 it was often well below. The worst fit achieved was for Aluminium Y-stiffener, 16 inch rib

spacing, lower cover with R²=0.0369 indicating a very poor fit.

An increase in rib or spar spacing gives a noticeable increase in the K-factor in all cases except when

increasing rib spacing for titanium Y-stiffeners. For the lower cover all the data points are identical. For

the upper cover the data points are very similar, with load factors between 2.5 and 5 having identical

values (12 and 16 in. spacing). Comparing the upper and lower cover of the same material and stiffener,

gives in many cases an indication of a connection, though some differences are visible. The difference

in K-factor between different 12 in. and 20 in. spacing for the lower cover is smaller than for the upper

cover, see Figure 21. The trendline with the best fitting is not always of the same mathematical type.

The temperature K-factor was extrapolated in a similar manner as the construction K-factor. For the

majority of the data, logarithmic trendlines gave the best fit (see Figure 22) and the overall fit achieved

was better compared to the construction factors. A general trend can be observed from the temperature

graphs: as the temperature increases the gradient of the trendline increases as well. The lower cover’s

temperature factor is also more sensitive to the applied load, as the increase is bigger from 2.5G to 7.5G

for the lower cover than the upper cover.

Notable is the data for advanced composite (see Figure 22), which did not indicate a discernible

correlation between different temperatures. The data points are scattered and have large variations, e.g.

300°F indicate that the value for 2.5 load factor is 1.022 while the data point for 7.5 load factor is 1.024,

Figure 21. Comparison between upper and lower cover for Aluminium and Titanium Z and Hat stiffeners. The

Titanium comparison show that the trendline equation type with the best fit differs between upper and lower

cover.

32

and the points in between have values ranging from 1.012 to 1.042. Additionally, the trendline fitting

only achieves R²-value ranging from 0.0007 to 0.2737, indicating a poor fit.

The data table, graphs and trendline equations for the temperature factor can be found in Appendix F.

Figure 22. Trendline fitting and extrapolation of temperature K factor for an upper cover made from titanium

(top) and composite (bottom).

4.3 Comparison between the Berry and NASA wing weight estimations

This section presents the results from the comparison between the Berry and NASA wing weight

predictions. The comparisons are done with the actual wing weight as the central value (0% weight

difference). The results of four aircraft wing weights estimated with the different techniques can be seen

in Figure 23 together with an estimate with just the NASA Wing Weight Build-Up.

33

Figure 23. The weight comparison between the Berry, NASA and actual wing weights are shown for the F-16A,

F-18A, SK-60 and the Hawk Mk.1 Aircraft. The F-22A wing weight is only estimated with the NASA Wing

Weight Build-Up.

The wing weight of the F-22A fighter aircraft is only estimated with the NASA Wing Weight Build-Up

technique since no corresponding prediction was done for this aircraft with the Berry Weight Estimation.

4.4 Result of Implemented Berry Weight Estimation code structure

The subject of this section is the finished structure of the implemented Berry Weight Estimation code.

The overall code structure is shown with reflections to the original structure of the calculation proposed

by Berry and Jouannet [6]. Pacelab APD’s local engineering- and functional object blocks are included

for a greater understanding of the Knowledge Designer implementation logic. The implemented

formulas of the Berry Weight Estimation are not shown in this overview of the code structure.

The first “building block” of the Knowledge Designer is the workspace for which the Aircraft Data

Model is located in (Figure 24). The standard workspace contains an EO Concept Project with default

APD aircrafts. An additional EO Concept Project (Saab Aircraft Project) was added for the

implementation of the Berry Weight Estimation and other Saab related implementations. The Saab

Aircraft Project was created by copying the Default APD Project, a reason for this was to be able to

change the original APD code and still have the default available as a backup. The standard parameters

defined in the default ADP Projects are also included in the Saab Aircraft, they are extended as needed

by custom made parameters. A custom fuselage and wing exists under the Saab Aircraft Project as EO

Concepts with connected geometries. The Berry Weight Estimation are added as two separate methods

under the custom fuselage and wing EO concepts. This was done to simplify the implemented structure

since the Berry Weight Estimation could be divided in two main parts, fuselage and wing. As Figure 24

shows, a Berry Fuselage Estimation exists under the Custom Fuselage EO concept as well as other

weight calculations included in the standard APD Projects. The same applies to the Custom Wing EO.

The dashed lines between the EO Concepts with geometries in Figure 24 represents the exchange of

information. This information can include specific parameters like mass, area and centre of gravity for

the stabilizer as an example, which are used in the Berry Weight Estimation.

34

Figure 24. The overall view of the Knowledge Designer with the implemented Berry Weight Estimation. Dashed

lines represent exchanges of information between blocks. A legend for the different blocks are shown in the

lower right corner.

4.4.1 Structure of the Berry Fuselage Estimation

The Berry Fuselage Estimation method contains all the calculations that are connected to the fuselage

weight estimation approach in [6]. The Berry Weight Estimation for the fuselage consists of two major

parts as described in the theoretical framework, the fuselage gross shell weight and the fuselage weight

penalties. The structure of the implemented fuselage calculations has been made to resemble these major

blocks of the Berry Weight Estimation. The Calculate SAWE141 Fuselage Stations Table in Figure 25

contains most of the fuselage gross shell weight calculations. The Multidimensional Data Table,

Fuselage Stations is used to define the number of stations that the fuselage is divided into. A

Multidimensional Data Table (MDT), can contain columns of either inputs or outputs. A MDT input is

something that can be specified and then used in calculations connected to the MDT, while a MDT

output is used as a “result output” for calculations. The Fuselage Stations MDT has an input for the

number of fuselage stations and several outputs for each intermediate result of the fuselage gross shell

weight calculations. The number of stations can be user specified and the number of output rows will

consequently increase.

35

The User Input Parameters contains values that the user needs to specify for the calculations. The

number of such user inputs has been kept to a minimum so that the majority of the parameters are

retrieved automatically. The fuselage length is for an example extracted and used from the Fuselage EO

instead of unnecessarily specified twice by the user. Some formulas in the Berry Weight Estimation do

however require parameters not defined in Pacelab APD. These parameters are consequently defined as

user inputs for the time being. The connection between the Custom Wing EO and the Calculate

SAWE141 Fuselage Stations Table Method comes from the theoretical framework of the Berry Weight

Estimation, where the results from the wing weight calculations are used in an iterative manor. The

acquired results from the Fuselage Stations MDT and the Calculate SAWE141 Fuselage Stations Table

Method are extracted and used in the Calculate Fuselage Mass Method. The final calculations of the

Berry Fuselage Weight are calculated here and includes the finalization of the fuselage gross shell weight

and the addition of all fuselage penalties. Apart from being connected to the Fuselage Stations MDT,

the Calculate Fuselage Mass Method is also connected to two additional MDT:s. The Fuselage Cut-

outs MDT has been created to calculate all weight penalties connected to cut-outs in the fuselage

structure. The benefit of isolating the cut-out penalties in a MDT is that the user can specify any number

of cut-outs as inputs in the table. The Cut-outs MDT has been designed so that the user can choose the

type, size and position of a cut-out. Figure 26 below shows an example of the cut-outs MDT with a short

explanation about the required inputs.

Figure 25. The structure of the implemented Berry Fuselage Estimation

36

A few examples of cut-outs are shown in Figure 26 with corresponding type, position and geometries.

The IsMirrored check-box specifies if the cut-out should be mirrored or not. This is useful if symmetrical

cut-outs such as windows or emergency exit-doors exists. The final MDT defined in the custom fuselage

EO is the ProductionJoints MDT. This MDT was created so that the user can specify any number of

production joints within the fuselage (Figure 27). The MDT requires the position of all production joints,

these inputs are then collected by the Calculate Fuselage Mass Method and used in the corresponding

weight penalty calculation connected to the fuselage production joints.

The combined results from the fuselage gross shell weight, Cut-outs MDT, ProductionJoints MDT and

other non-cut-out related penalties are finally merged in the Calculate Fuselage Mass Method and

returned as the newly calculated total fuselage mass. The total fuselage mass is then used as the starting

value for the next calculation loop in accordance with the Berry Weight Estimation.

4.4.2 Structure of the Berry Wing Estimation

The code structure of the Berry Wing Estimation is very similar to the structure of the fuselage

calculation (Figure 28). It contains the two major parts from the weight calculations presented by Berry

and Jouannet [6], the wing gross shell weight and the wing weight penalties. The majority of the wing

gross shell weight is calculated in the Calculate SAWE141 Wing Station Table which utilizes the Wing

Stations MDT. Similar to the Fuselage Stations MDT, the Wing Stations MDT has an input for the

number of stations and a number of outputs for the intermediate results of the wing gross shell weight

calculation. User Input Parameters are used with the same approach as in the Fuselage calculation. The

final calculations for the wing weight are done in the Calculate Wing Mass Method, the results from the

Figure 26. The Multidimensional Data Table for Cut-outs. The available types of defined cut-outs are shown

in the upper right corner.

Figure 27. The ProductionJoints MDT with example of input values.

37

Wing Stations MDT and Calculate SAWE141 Wing Station Table are collected and added with the wing

weight penalties. The wing weight penalties suggested by Berry and Jouannet [6] does not contain the

cut-out approach from the fuselage calculation and a corresponding cut-out MDT for the wing does not

exist. The same goes for the production joints MDT as the wing joints are calculated differently. All

wing weight penalties, including the calculation for the wing stiffness criteria, are for this reason located

within the Calculate Wing Mass Method. The combined result calculated in the Calculate Wing Mass

Method is finally returned as a new total wing mass and used for the next iteration of the Berry Weight

Estimation.

The implemented code structure allows the users to choose whether they like to use the combined Berry

Fuselage- and Wing Weight Estimation or use them as separate calculations with other fuselage/wing

weight estimations. It is therefore possible to add additional wing weight estimations, like the NASA

Wing Weight Build-Up Calculation, under the Custom Wing EO and use them with the Berry Fuselage

Estimation if desired.

4.5 Additional results for the Pacelab APD implementation

As previously mentioned, the implemented code uses aircraft parameters predefined by Pace. This will

result in deviating weight results as Bex has other predefined parameter values for a common aircraft. It

is however a demand to have the calculations connected to the overall structure of Pacelab APD and this

section therefore show the difference in the results that can be expected due to this.

4.5.1 Comparison of weight estimations between software

The acquired weight results of the wing and fuselage mass of the new implementation are here compared

with a former implementation of the Berry Weight Estimation in Bex. The weight estimations from both

software have been done on a common predefined aircraft. The difference in weight together with a

percentage of the difference can be seen in Table 2.

Figure 28. The structure of the implemented Berry Wing Weight Estimation.

38

Table 2. A comparison between the Pacelab APD implementation of the Berry Weight Estimation and Bex. Pace

calculations have been done with 1000 stations for both fuselage and wing. Bex had around 20 wing- and

fuselage stations.

4.5.2 Sensitivity- and trade studies of the implemented Berry Weight Estimation

One of the project’s research questions was to investigate how sensitive the Berry Weight Estimation

was to changing parameters. The implementation of the Berry Weight Estimation in Pacelab APD

allowed for the usage of the built-in trade-study tool. Trade-studies for both wing and fuselage are shown

in this section.

The most wanted sensitivity studies were to see the impact on the weight results for the number of

stations. This was wanted for both the wing and fuselage as no proposed number of stations were given

in [6]. Figure 29 shows the total wing weight difference with a varying number of wing stations.

Figure 29. A sensitivity study of total wing weight difference against the number of wing stations.

The sensitivity study in Figure 29 was done for the total wing weight, which is the wing gross shell

weight with added weight penalties. Figure 30 shows the weight difference for the fuselage gross shell

weight with different numbers of fuselage stations. The fuselage gross shell weight was used instead of

the total fuselage weight with penalties. This was done in order to simplify the comparison with Bex

39

Both Figure 29 and Figure 30 indicate that the estimation results have converged within 1% above 200

stations. The fuselage station sensitivity shows oscillation tendencies compared with the wing at fewer

stations than 200.

Figure 30. A sensitivity study for the fuselage gross shell weight difference against the number of fuselage

stations.

Additional sensitivity studies were conducted on a few chosen wing and fuselage parameters. The

investigated parameters were deemed as the most interesting by Saab, and values were varied ±10%

from the original. For the wing, the chosen parameters were: leading edge sweep, aspect ratio (AR),

taper ratio (TR), number of stations and thickness-to-chord ratio (T/C). T/C was set to be the same for

the entire wing span, and then varied for three given ratios (8 %, 12 % and 15 %). Some interesting

results from the sensitivity study can be seen in Figure 31, Figure 32 and Figure 33. All extracted graphs

from the study can be found in Appendix G. The AR has a significant effect on the wing mass, an

increase of AR with 23 % give a weight increase of roughly 26 % if T/C is 8 %. If the T/C is raised to

12 %, the same AR increase results in a weight increase of around 15 %. A T/C=15% results in 13%

weight increase. An overall observation that can be made when comparing the results is that a low T/C

results in a high wing mass for the aspect ratios analysed.

Figure 31. The aspect ratio and number of wing stations effect on wing mass at T/C=8%. 300 stations is chosen

as maximum limit for visualisation purposes, minimal variation to results above this value.

40





It was noticed that the behaviour of the calculations exhibited some form of correlation against the

number of wing stations when varying the different parameters. The results from the sensitivity analysis

were analysed further by plotting 3 different aspect ratios in the same graph, for a given set of parameters

(TR=0.2058, T/C=12% Sweep=26.94°). Figure 34 give an indication that different AR-values produces

a shift in the result, and not altering the general shape of the trend. To ascertain whether this was actually

true, the results were normalised against the end values and then plotted in the same manner (see Figure

35). It indicates that when the number of stations are 200 or more, the data points are essentially on top

of each other.

41

Figure 34. Wing mass sensitivity to number of wing stations and aspect ratio.

Figure 35. Wing mass sensitivity to number of station and aspect ratio. Normalised against end value (1000

station) to visualise difference between estimations.

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For the fuselage sensitivity study, the parameters chosen were: wing chord at the centreline as this would

affect the inter-spar distance, number of fuselage stations to visualise convergence of the calculation

similar to the wing, and fuselage length to see what effect this would have on the fuselage mass. A cut-

out of type 3 was added to the fuselage and its lengthwise (X) position varied to see how the position of

a cut-out would affect the fuselage mass. Part of the result from the trade-study can be seen in Figure

36. All produced graphs from the sensitivity study can be seen in Appendix G. The results indicate that

the closer the cut-out is to the spars, (originally located at X=14.07 m and X=17.69 m) or if they are

located at the spars, the weight increase will be bigger than if they are located far aft or far to the front.

An increased inter-spar distance have weight-reducing effect on the fuselage mass.

Figure 36. How the chord length (i.e. inter-spar distance) at the fuselage centreline affects the fuselage mass

(1000 stations). The different series represent different location (x, lengthwise) of a Type 3 cut-out with

dimensions 2x0.5x0.5 m (LxWxH).

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5 Discussion The used project methodology and acquired results during the project are subject for discussion in this

chapter. A summary of the answers for the aims and research questions are presented at the end together

with recommendations for future work.

5.1 Project Methodology

The outlined methodology in the beginning of the project was followed to the end with the exception of

the further delimited aims. Some reprioritizing was done according to these delimitations, see chapter

1.5.1. This section follows the project methodology and shed some light on how the project was carried

out and how it could have been done differently.

5.1.1 Literature review, Statistics gathering and Weight estimation testing

Many weight estimation techniques were found during the literature reviewing as mentioned in the

projects results chapter. Many of the found techniques were of little interest as they were based on, or

simply were a collection of formulas already used at Saab. A large part of the found techniques were

also based on aircraft statistics from 1950-1970. These were also deemed as less interesting as many

advancements in both materials and constructions has happened since then. The NASA wing weight

build-up technique presented by York and Labell [15] involved statistics of early versions of “modern”

fighter aircraft. It also featured detailed breakdowns of wing components weight as described in the

theoretical framework chapter. It was quickly deemed as one of the most encouraging estimation

techniques found during the literature review. The statistics gathering of military aircraft weights proved

to be very difficult. Publicly available aircraft specifications were almost entirely made up of different

take-off- and specified empty weights. Furthermore, the found empty weights had little or no explanation

about what weights that were included. Such take-off- and empty weight were of less interest as the

usage was very limited. The empty weight includes all aircraft components and it is impossible to

accurately guess the weight percentage of each component from only one value. Only a few aircraft

statistics sources, like Nicolai and Carichner [7], had individual component weights well specified and

broken down. A reason for the scarcely available weight statistics of fighter aircraft is that they are

military. Military aircraft statistics are guarded manufacturer secrets and are most commonly not

publicly available which makes an extensive statistic gathering complicated. Weight data for Saab

aircraft were collected but unfortunately never used. The original planning was to use the acquired

weight data from the statistics gathering to establish different fudge factors for involved weight

estimation formulas. The purpose of the fudge factors was to alter the weight formulas to better coincide

with mainly Saab aircraft statistics. As the project was further delimited, the objective changed to instead

identify were possible fudge factors would be most needed in the weight estimation formulas.

A few of the found weight estimation techniques were implemented in Matlab or Excel for evaluation

and testing. Estimation techniques that simply gave bad or unrealistic results for fighter aircraft weights

were excluded for further testing. The NASA wing weight build-up technique showed very promising

results already after the first implementation and was seen as interesting by Saab. The decision was

therefore made to focus on improving and adapt the proposed technique instead of searching for

additional aircraft weight estimations. More of the project time should have been spent on investigations

of other weight estimation techniques. However, the implementation of the Berry Weight Estimation in

Pacelab APD was top prioritized by Saab. The NASA wing weight build-up was consequently the only

weight estimation chosen for further work in order to keep the project time frame.

5.2 The NASA wing weight build-up

The results in Table 1 shows that the authors’ interpretation of the NASA wing weight parameters was

reasonable. The slight difference in the result against the stated weight can come from many areas in the

estimation and is most likely a result of the inaccuracy in measuring aircraft 3-view drawings. The F-

16A was as previously mentioned chosen as the aircraft for the parameter interpretations. This was done

since the F-16A had a very triangular shape without curved areas (as seen from the aircraft top view).

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The F-16A was also included in the aircraft collection used to derive the NASA wing weight build-up.

It therefore seemed like an obvious choice to use the F-16A as a reference aircraft for the parameter

interpretation. An improvement that could have been done to further establish the parameter

interpretation was to do the same evaluation for another aircraft involved in the used collection. It was

unfortunately never done and the F-16A was the only aircraft used for the interpretations. The results

are however very encouraging and shows that the wing weight can be measured quite accurately with

the proposed parameter definitions in Appendix C.

The interpretation of the K-factors in the NASA wing weight build-up methodology gave some ideas on

how the estimations could be further improved. The K-factors are basically used as fudge factors, they

scale estimations based on statistics of similar aircraft. The suggested K-factors in the original report

from York and Labell [15] could perhaps in the future be updated with statistics from various Saab

aircraft to point the weight estimations in the “right” direction. This is true for all K-factors describing

the aircraft configurations (see Appendix B). The K-factors for materials and temperature are currently

used as “penalties” to the calculated weight from the other parts of the method. The way the factors are

calculated are as an average of the constituents of the wing. This make validating the method against

aircraft from other manufacturers a bit cumbersome. Information is generally not available regarding

the material of the wing spars or other structural parts of the wing. However, sometimes an overall

percentage of composites or a certain metal in the wing could be available, this raises an issue of how

to calculate the factors in these cases. Possibly, a weighted way of calculating the factors could improve

the estimations, particularly in the overall percentage case.

A sensitivity study could have been done to identify what parameters had the greatest impact on the

NASA wing weight results. This was unfortunately never done due to limited time. Possible areas of

improvement for the NASA wing weight could in the future be identified by such a study. It would also

give some insight in what parameters the user needs to be extra careful with when specifying. An

example of this is the exposed wing area which can vary with aircraft and be hard to interpret.

Consequently, the result will differ a lot depending on the specification of the area if the weight

estimation is very sensitive to the exposed wing area parameter. The future sensitivity study could be

done for all involved parameters of the NASA wing weight build-up as it would act as a guideline for

the specification of sensitive parameters.

5.2.1 Extrapolation of material data

There are aspects of the extrapolation that could be improved, the approach to choosing trendline was

based on the R2-value and no method was found that had a scientific approach and guidelines on how to

select the best trendline. No research has been made on how Excel actually fits a trendline, or if the best

equation type is another than the ones built into the program. It is possible that the result would have

been different if another mathematical tool such as MiniTab or Matlab were used for the extrapolation

instead. Though, as the NASA wing weight method was not top prioritized by Saab no additional effort

was made to use available resources to increase the validity of the extrapolations. As an example,

material experts could have been consulted along with mathematicians to extract a logic behind the

material data and be suggested a scientific method for the extrapolations. There is also the possibility

that an increased accuracy could be gained if the trendlines were weighted to be more accurate for the

higher load factor data points than the lower ones. It was nevertheless decided that the current

extrapolation would be sufficient to evaluate the method, and should the results be promising more work

could be made on the extrapolations. Furthermore, the concept of having factors instead of actual

material data is making the impact of the material or construction choice harder to gauge. If the factors

were visibly dependent on regular material properties such as yield strength or Young’s modulus, other

materials could also easily be added to the method.

Regardless if the extrapolation is correct, some trends are visible in the aspect of where the data points

are located in reference to their corresponding trendline. In several graphs the data points for e.g. load

factor 2.5 are all located somewhat above the trendline. Similarly for load factor 3 data points which are

mostly positioned below the trendline, indicating that there are some correlation working in the

background. The decision to not limit the type of equation for the trendline could also have introduced

45

uncertainty to the results. It could be argued that the same type of stiffeners should have the same

equation type for the trendline for the upper and lower cover, this is not necessarily the case in the current

results. As an example, the graph for Aluminium Y-stiffeners lower cover indicate that the trendlines

are of type linear, whereas for the upper cover the corresponding equation type is of logarithmic type.

Regarding the temperature factors the confidence in them are higher, but there are still doubts. The fact

that the best trendline type for all variants except the “advanced composite” is the same is regarded as

logical since they are all metallic materials that should exhibit somewhat similar behaviour when

exposed to heat. The “advanced composite” is interpreted as the same carbon fibre/graphite epoxy as

specified in the materials data tables although this is not clearly stated in the original paper. While the

trendline fitting for the composite is poor, the indication that the factor does not increase notably with

higher temperatures is logical as composites are not affected by temperature the same way as metals.

Depending on the choice of resin/matrix for the composite the temperatures specified in the table could

have very low effect on the mechanical properties. The variation seen could be due to inherent nature of

composite where mechanical properties are not identical between two serial produced pieces of the same

composite. Due to the fact that the properties are heavily dependent on manufacturing procedure, fibre

volume fraction, possible voids in the material and more, the variation seen could be a side effect of this.

Another possible reason is that different manufacturing choices were made on the different aircraft in

the study [14]. A suggested approach when estimating extrapolated values for “advanced composites”

could perhaps be as simple as using a mean value of all available data for the same temperature in the

tables from [15].

5.3 Comparison between the Berry and NASA wing weight predictions

The comparison between the Berry and NASA wing weight estimations showed that both techniques

predicted the wing weight of the F-16A, F-18A, SK-60 and Hawk Mk.1 within 10% difference from the

actual wing weights. The NASA estimation had the overall lowest difference compared with the actual

wing weight. The results are encouraging and show that the NASA wing weight is more accurate at

predicting the wing weight in most of the cases. However, more aircraft wings predicted with the Berry

Weight Estimation should be compared with the NASA wing weights to make a final verdict on which

estimation that gives the overall best results. No comparison was done between the NASA and Berry

Weight Estimation for the F-22A wing weight due to limited time and available data.

The differences between the actual and estimated weights can come from many areas. One of the main

reasons can be the wing material and its corresponding K-factors. It was hard to find exact data of the

different wings composition, structure and material and this could very well have generated some

difference in the weight estimations. Other things that could have affected the weight estimations were

the interpretations of the different geometrical parameters involved in the calculations. A future

sensitivity study could perhaps give more clarity in why differences exists and point out the most

sensitive parameters of the NASA wing weight build-up. It would also give an indication of how much

the wing material affects the results. The extrapolation of the material data could as a consequence be

further improved if the sensitivity study shows that the calculation is very sensitive to the material related

parameters. More aircraft wing weights were run with the NASA estimation but these were excluded

since no publicly available weights were found for the corresponding aircraft. It would be interesting to

compare the estimated weights with actual ones in the future since some investigated aircraft featured

unconventional wings like forward swept. However, the NASA wing weight build-up has so far shown

good results compared with the Berry Wing Weight Estimation and can perhaps after further evaluation

act as a replacement for it. Another benefit with the NASA Wing Weight Build-Up is that it is non-

iterative and consequently much faster than the Berry Weight Estimation. This could give a part of the

answer for Research Question 1 of the project. The Berry Weight Estimation could perhaps, as stated

above, be improved by simply exchanging the wing estimation with the NASA wing weight build-up.

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5.4 Implementation in Pacelab APD

The Scrum software development methodology was used during the implementation in Pacelab APD.

This methodology was as previously mentioned suggested by Pace and no other software development

technique was further investigated for this reason. Scrum worked well for this project and only minor

changes had to be done between the specified intervals. The Scrum roles were not strictly followed due

to the number of developers. It is very possible that there are other methodologies better suited for

smaller groups. No problem was however encountered due to this and another methodology would most

likely have generated the same results. The finished implementation included results for both the

structure of the code, result comparisons against Bex and parameters individual impact on the end-result.

The aim of implementing the Berry Weight Estimation in Pacelab APD with an object oriented

programming approach was easily achieved since the software already utilized this methodology. The

implementation was therefore made so that the new code merged well with the already object oriented

programming structure of the Pacelab APD software. Furthermore, the implementation of the Berry

Weight Estimation in Pacelab APD was done in a way so that Saab easily could expand the

implementation in the future. Pacelab APD is at the moment mainly focused on civil aircraft and further

implementations and alterations to the software from Saab is needed to fully utilize the Berry Weight

Estimation in an efficient way. Many of the parameters that were implemented to be user specified could

be automated with further development in Pacelab APD. One example of this is the fuselage mounted

speed brake area which for the moment needs to be user specified in an input parameter. A future state

of the Pacelab APD implementation could include a geometrical definition with connected parameters

for a fuselage speed brake component. This would allow the Berry Weight Estimation to simply fetch

the corresponding speed brake parameters needed for the calculation. This is true for many other of the

user specified parameters defined at the moment. Some of the user specified parameters may however

be needed even in future versions. Those are most likely the material densities that needs to be specified

for the Berry Weight Estimation.

5.4.1 Implementation Structure

For the implementation, the Berry Weight Estimation was divided in to a fuselage- and a wing part. This

was done so that the users could choose whether they wanted to use the Berry wing- or fuselage

estimation. This also allows other estimation techniques of wing or fuselage to be used in combination

with the Berry Weight Estimation. The implemented structure of the Berry Weight Estimation resembles

the structure proposed in Berry and Jouannet [6] with the fuselage gross shell weight, fuselage penalties,

wing gross shell weight and wing penalties. The implementations of each part are quite extensive and

covers several hundred rows of code. A suggested restructuring of the code, closer to a finished version

for military aircraft, would be to divide each of the four major parts of the Berry Weight Estimation in

to a number of sub-functions. These could for an example be sub-functions for each weight penalty in

the wing and fuselage estimations. Eventual repeating patterns within the weight estimations would also

be subject for own functions in order to structure the code in a more appealing way. The usage of

functions would also include more FO:s which can give a better Knowledge Designer logic.

The fuselage cut-outs MDT was created so that the user could specify any number and type of cut-out.

The added mirror option to the MDT allowed the cut-out to be mirrored. This was mainly intended for

the type 1 and 2 cut-outs since they most often come in mirrored pairs. The option to mirror type 3 was

kept if a configuration like that was wanted. An alternative to the MDT would have been to have the

cut-outs automatically specified for cut-out required components. The nose landing gear could for an

example have an option to include a cut-out for it in Pacelab APD. This was however never done in the

implementation since many of the required components from Saab did not exist in the current software.

Time was also a limiting factor and a decision was made to create an MDT for all cut-outs instead. The

cut-out MDT can over time be used to a lesser extent as the implementation by Saab proceeds. The MDT

for production joints will probably remain even in future changes of the Berry Weight Estimation in

Pacelab APD. The position and number of production joints varies with aircraft type and the MDT

allows for an easy declaration of production joints.

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5.4.2 Result comparison, Sensitivity- and Trade studies

The acquired results from the comparison between the implemented Berry Weight Estimation and Bex

showed overall differences below 10%. The wing and fuselage gross shell weights had the lowest

inequalities. This difference can very well be due to the used number of stations. Bex uses around 20

stations for both fuselage and wing, and are implemented so that the number is very complicated to

increase. The performed sensitivity studies show that the number of stations have a great influence on

the results until it converges at around 200 stations. This is one of the explanations to why a difference

between the Pacelab implemented Berry Weight Estimation gives different results compared to Bex.

Additional differences between the implementations could be due to the different definitions of various

aircraft specific parameters. The predefined wing span of a common default implemented aircraft for

both software differs with approximately 1.5%. The reason for this is probably that different data sources

have been used in the definition of the predefined aircraft in Pacelab APD and Bex. The wing span

difference contributes to the difference in the final weight as it propagates throughout all formulas where

the wing span is used. The above is true for more parameters where the standard values of the same

aircraft differs slightly between the software. The combined contribution for the differences between

stations and software parameters could be the reason for the noticed inequality between the final weight

estimations of the two software. Defining all values similar for both software is possible but would

require extensive and time consuming work. It could however remove some of the differences seen.

The number of stations had, as previously mentioned, a big impact on the results of the Berry Weight

Estimation. The results shown in Figure 29 and Figure 30 show that the weight difference converges at

around 200 stations for both wing and fuselage. Bex had a more or less fixed number of stations and no

documented sensitivity study had been performed. The implementation of the Berry Weight Estimation

in Pacelab APD was done so that the number of stations could be user-specified for both the wing and

fuselage. The stations sensitivity study that could be performed due to this has shown that it is a clear

improvement against Bex as non-converged weights can be seen at 20 wing or fuselage stations. This

gives an answer to the second Research Question of the project. The Berry Weight Estimation is

sensitive to the used number of stations for both wing and fuselage. The results show that the fuselage

is most sensitive to the number of stations. The study also shows that the 20 stations used in the Bex

fuselage weight estimation is far from enough. A recommended new number of stations would be around

200 based on the acquired results from Figure 30. The wing is somewhat less sensitive to the number of

stations but still show a weight difference of around 4.5% at 20 stations. The recommended number of

stations for the wing is also around 200 according to Figure 29. This partly answers Research Question

1 as well since the estimations can be improved with the number of fuselage and wing stations.

The aspect ratio was a parameter that gave a large variation in wing mass during the sensitivity study. It

is logical that an increased aspect ratio will increase the wing mass as the wing span increases or chord

length decreases, this results in a more “sail-plane” type wing. However, a lower thickness-to-chord

ratio also gave significant increase in wing mass and this is logical as the wing need more material in

order to resist the bending loads. In a beam bending case the height of the beam is often a dimensioning

factor. It was noted from Figure 31, Figure 32 and Figure 33 that the general shape of the results was

similar. The converging behaviour of the number of wing stations can be seen in all of the results. The

wing stations are currently the only known parameter that show this behaviour. The results shown in

Figure 34 indicates that the AR parameter shifts estimate along the wing mass axis. This is further

supported by Figure 35, which show that it is in fact the case. From this it can be implied that the method

can handle varying AR better than low number of wing stations. The same could be true for other

parameters, but further analysis are needed before such a conclusion can be made.

5.4.3 Miscellaneous

The implementation of the Berry Weight Estimation should perhaps have been done very differently if

the authors would have had any previous knowledge of the C# language. This lack of knowledge in the

coding language was another indirect reason for the further delimitations of the project after start. The

structure and overall logic of the implemented code would most likely look very different if the

implementation of the Berry Weight Estimation would have been done again with the knowledge

48

acquired during the project. It is however worth to mention that the functionality of the implemented

calculation would be the same even if a restructuring would have been done. The reason for a restructure

would simply be a contribution to the appeal of the code.

5.5 Research Questions and Project Aims

The research questions that were established in the beginning of the project have been partly answered

throughout the conducted work. The purpose of this section is to collect the acquired results and answer

each of the proposed research questions.

5.5.1 RQ1. How can the Berry Weight Estimation be improved to get more accurate estimates?

The recommended main improvements of the Berry Weight Estimation is to increase the number of

wing and fuselage stations. Another possible improvement could be to exchange the wing estimation

with the NASA Wing Weight Build-up. Further evaluation is however needed before such a replacement

can take place.

5.5.2 RQ2. How sensitive is the Berry Weight Estimation to the number of fuselage- and wing stations used?

The study has shown that the Berry Weight Estimation is very sensitive to low number of stations (below

100 stations). The performed sensitivity study showed that the weight differences for both fuselage and

wing stabilised out at 200 stations or above.

5.5.3 Project Aims

The project aims that have been achieved (with the inclusion of certain delimitations) throughout the

project timeline are shown in the list below. The order of the proposed aims in chapter 1.3 is followed.

1. The implementation of the Berry Weight Estimation in Pacelab APD showed good results and

a glimpse of the benefits of using the software. The object oriented programming approach was

only used to some extent due to the missing components and parameters required for the Berry

Weight Estimation. These were however defined as user-inputs for the time being and the aim

is seen as achieved considering the scope of the project.

2. The aim of updating the Berry Weight Estimation with newer statistics was changed during the

project to instead identify where updates were most needed. This was mainly a consequence of

the reprioritization and difficulty of finding relevant statistical data. The areas in the calculation

where an update was of most importance were identified with the help of the sensitivity studies

tied to the research questions. These acquired results can in the future be used as a solid

foundation for the update of the Berry Weight Estimation with newer aircraft statistics.

3. The search for other relevant aircraft weight estimation techniques generated the NASA wing

weight build-up method. The test and evaluation of the methodology showed encouraging

results and a potential for future implementation in Pacelab APD.

4. The found wing weights from the statistics gathering were added to the Saab’s aircraft weight

database in accordance with the aims. The weight estimation functions that were found were

only the NASA wing weight build-up and it was not implemented in the Pacelab APD software.

This was mainly due to prioritizing and limited project time.

5. The NASA wing weight build-up with extrapolated material data was compared against known

wing weights. The results showed that the modified NASA estimation could predict wing

weights with sufficient accuracy for conceptual design. The estimation from the Pacelab

implemented Berry Weight Estimation was compared to Bex weight prediction. The results

showed some differences but were still less than 10%.

49

5.6 Recommendations for Future Work

During the project, some insight was given into what should be done in the future to improve the

accuracy of the weight estimations and capability of the Pace software. In this chapter, some

recommendations are given along with a short explanation of why it is suggested.

5.6.1 Berry Weight Estimation

The Berry Weight Estimation exhibited some areas for analysis or improvement which could be

suggested as future work packages of different magnitude. The different suggestions are separated into

programming or analysis/investigative focus to give an indication of the kind of work that is mostly

needed for the suggestion.

Analysis focused:

• Add Saab-specific data to existing graphs of component weights (i.e. aileron weight per area,

which depends on the surface loading of the wing), and make a new separate trendline. The

method is based on old American aircraft and design choices for components could differ, newer

materials could have an impact on the penalty. The results of the changed penalty could also

easily be verified against old, new estimates and actual weight.

• Add new materials to the wing calculations, since it currently only has Aluminium 755-T6, 245-

T81 and “Titanium”. New material data for materials used at Saab should improve the accuracy

of the results.

• Detailing of fuselage material density. It is currently an average density of the fuselage

materials. This would mainly increase the usability of the calculations as it currently could be

difficult to approximate an average fuselage material density. However, a too detailed

breakdown would increase complexity of the calculation. A choice to calculate the density from

a given formula could be a reasonable extension.

• Evaluate if the current Torenbeek wing stiffness criteria should be replaced with the wing

stiffness criteria proposed in SAWE#632 [20], which was never completed and used in the Berry

Weight Estimation. The impact on military aircraft could also be investigated for both proposals.

• Evaluate if the Berry Wing Weight Estimation could be used for horizontal stabiliser and

possibly vertical stabiliser to improve their corresponding weight estimations. It is possible that

the estimations could be improved since stabilisers and fins have similar structure to wings.

• Analyse all acquired trade-study data since more conclusions about the parameter sensitivities

can be drawn from it.

Programming focused:

• Detailing of now distributed loads into several point loads calculated individually (systems in

fuselage, engines on wing etc.). This is mainly a future implementation task as more components

are added to the Saab Pacelab APD.

• Possibly add data from penalty graphs in Hammit [5] to MDTs and let Pacelab handle

interpolation as a function exist for this. Though it needs to be evaluated from a performance

perspective as the drag polar currently is an interpolation and seem to be the slowest part of the

calculations.

• Add purely civil penalty functions from Bex, such as fillings and surrounds for windows, doors,

flooring etc.

• Refactoring of the implemented Berry Weight Estimation. Some aspects of the code are

repeating, and could be moved to a FO and called upon when needed. This would make the

calculations more transparent and easier to maintain, and could also possibly speed up the

calculations.

• Future proof the current implementation for more Saab-specific add-ons. While some efforts

have been made in this matter already, compatibility needs to be ensured.

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5.6.2 NASA Wing Weight Implementation

It is suggested that the NASA wing weight method is implemented into Pacelab and analysed to evaluate

its use as a replacement for the wing part of the Berry Weight Estimation. The mixing of the two methods

could provide an equally or more accurate and faster weight estimation. The extrapolation of material

and temperature factors could be further explored, and investigated in regards to what drives the factors.

If they can be decomposed into common characteristics, new materials or new data points can be added

to increase accuracy of the method. Furthermore, the different K-factors for different type of

configurations can be adjusted using Saab-specific data.

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6 Conclusions This project has been about the evaluation of new weight estimation techniques and an implementation

of the Berry Weight Estimation in Pacelab APD. The evaluation of new weight predictions generated a

wing weight estimation technique proposed by NASA. The found technique was tested and evaluated

against aircraft with known wing weights. Extrapolations of involved material data tables were

performed to adapt the weight estimation technique to Saab’s needs. The results of the NASA wing

weight build-up showed resemblance within 8 % to the actual wing weight of tested aircraft. Further

testing and future sensitivity studies of the NASA wing weight build-up could be done to evaluate if it

could replace the wing estimation part of the Berry Weight Estimation. Research Question 1 is partly

answered by the evaluation of the NASA wing weight build-up. The Berry Weight Estimation could

possibly be improved by exchanging its wing estimation part with the NASA wing weight build-up.

The implementation of the Berry Weight Estimation in Pacelab APD was done and several studies were

performed on the finished results. Performed sensitivity studies gave a good insight in areas where

improvement was needed. A found main improvement of the Berry Weight Estimation is to increase the

number of wing and fuselage stations. This answers the project’s Research Question 2: The Berry

Weight Estimation is quite sensitive to the number of stations. A recommended number for converged

weight results have been determined to around 200 stations for both fuselage and wing.

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7 References

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subsonic civil airplanes, Chichester: John Wiley & Sons Ltd, 2013.

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[Online]. Available: https://www.sawe.org/about. [Accessed 30 January 2018].

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Design (SAWE #141),” in Fifteenth National Conference of the Society of Aeronautical Weight

Engineers, San Diego, 1956.

[6] P. Berry and C. Jouannet, “Recycling Old Weight Assessment Methods and Giving Them New

Life In Aircraft Conceptual Design,” in 28th Congress of the International Council of the

Aeronautical Sciences (ICAS), Brisbane, 2012.

[7] L. M. Nicolai and G. Carichner, Fundamentals of Aircraft and Airship Design, Reston, Virginia:

American Institute of Aeronautics and Astronautics, 2010.

[8] R. Turner, Handbook of Project-Based Management: Leading Strategic Change in

Organizations, 4th Ed., New York: McGraw-Hill Education, 2014.

[9] D. P. Raymer, Aircraft Design: A Conceptual Approach, Washington, DC: Amarican Institute of

Aeronautics and Astronautics, Inc., 1992.

[10] K. Schwaber and J. Sutherland, “Download the official Scrum Guide,” July 2016. [Online].

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Swedish.pdf. [Accessed 27 March 2018].

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https://www.scrum.org/. [Accessed 27 March 2018].

[12] J. Roskam, Airplane Design: Part V - Component Weight Estimation, Lawrence, Kansas:

Roskam Aviation and Engineering Corporation, 1989.

[13] Saab Aeronautics AB, Saab internal documents.

[14] Gurit, “Composite Materials - Gurit Guide to Composites,” 2018. [Online]. Available:

http://www.gurit.com/Our-Business/Composite-Materials. [Accessed 14 March 2018].

[15] P. York and R. W. Labell, “Aircraft Wing Weight Build-up Methodology with Modifications for

Material and Construction Techniques, CR-166173,” NASA (Grumman Aerospace Corp.),

Moffet Field, California, 1980.

[16] C. Castro, PACE software solutions for preliminary design, Berlin: PACE, 2017.

[17] PACE, Pacelab Knowledge Designer Tutorial, Berlin: PACE Aerospace Engineering and

Information Technology GmbH, 2008.

[18] A. Venosa, “Medical Daily,” Newsweek Media Group, 14 January 2016. [Online]. Available:

https://www.medicaldaily.com/breaking-point-whats-strongest-g-force-humans-can-tolerate-

369246. [Accessed 4 April 2018].

[19] Microsoft, “Choosing the best trendline for your data,” Microsoft, [Online]. Available:

https://support.office.com/en-us/article/choosing-the-best-trendline-for-your-data-1bb3c9e7-

0280-45b5-9ab0-d0c93161daa8. [Accessed 20 March 2018].

[20] K. L. Sanders, “A Review and Summary of Wing Torsional Stiffness Criteria for Predesign and

Weight Estimations (SAWE#632),” The Society of Aeronautical Weight Engineers, Inc.,

Boston, 1967.

54

[21] PACE, “Pacelab APD 6.2 User's Guide,” PACE Aerospace Engineering and Information

Technology GmbH, Berlin, 2017.

55

8 Appendix

A. Wing Stiffness Criteria The wing stiffness criteria is an add-on weight penalty to the wing weight that is used to fulfil certain

stiffness requirements. These requirements describe the additional weight that is added to the wing to

avoid unwanted aeroelastic effects like flutter. The method is presented in Sanders [20] and describes a

number of semi-empirical formulas and procedures that can be used in preliminary aircraft design. The

actual weight penalty itself comes from an increased wing skin thickness. The extra thickness is

determined by the wing’s requirement to resist excessive torsion.

There are three aeroelastic phenomena that typically should be avoided in aircraft design according to

[20]. The first one is the previously mentioned wing flutter, a dynamic effect which is likely to occur on

non-swept wings and wings with high aspect ratios. Flutter can occur if the wing torsional stiffness is

too low, the wings then begin to oscillate and suffer from vibrations. The vibrations are undesirable due

to fatigue and possible harmonic motions that can lead to catastrophic failures. The second aeroelastic

effect that can occur is aileron reversal. This is a static effect that reverse the roll control input from the

pilot. The reversal is caused by simple roll movements, once the ailerons are deflected the difference in

lift on each wing side will cause a rolling moment. This results in an opposite torsional moment that

twist the wing. Both moments are dependent on the roll velocity of the aircraft. If the torsional stiffness

is too low, there is a velocity where the moments are equal or opposed. If this roll velocity is exceeded,

the aircraft roll control is reversed. Finally, the third aeroelastic effect is the torsional divergence. This

is as the aileron reversal, a static effect that causes the wing to twist resulting in higher local angles of

attack than the overall wing’s. It is caused by aerodynamically induced torque during high speed

manoeuvres which are strong enough to equal the elastic torque that acts restoring on the wing structure.

The method for determining the additional structural weight to avoid the above mentioned effects

resembles the gross shell calculations presented in the theory chapter and [5]. The result of the method

is the wing skin thickness necessary to withstand the possible torsion moments that can occur during

aircraft operation. The wing is divided into a number of aerofoil sections. Each section’s local wing box

area is then determined together with its perimeter. These are then used with the compression skin

thickness derived in the wing gross shell weight method to calculate the moment of inertia of each wing

section. The moment of inertia is later used to determine the minimum required wing skin thickness to

resist the torsion for each section. This together with fulfilled requirements to avoid the aeroelastic

effects generates a new additional weight to be summed up and added to the total wing weight. Detailed

information about the wing stiffness criteria method are found in Sanders [20] together with a

nomenclature with required aircraft parameters.

56

B. NASA Wing Weight Build Up Equations This appendix shows the formulas from York and Labell [15] which are summed up to form the total

wing weight estimation. The proposed selections of k-factors from York and Labell are also shown for

each component.

BASIC WING BOX COVER

0.039041 ∗ [𝑏∗ ∗ (𝐶𝑅 + 2𝐶𝑇) ∗ 𝐵∗ ∗ 𝑁𝐵𝑂𝑋 ∗ 𝑆𝑊

∗

𝐶𝑜𝑠2𝛬 ∗ (𝐶𝑅∗ + 𝐶𝑇) ∗ (2𝑇𝑅

∗ + 𝑇𝑇) ∗ (2𝐶𝑅∗ + 𝐶𝑇)

]

0.5074

∗ [𝑆𝐵𝑂𝑋∗ ]0.5279 ∗ [𝑉𝐿]0.1634

∗ 𝐾𝐹𝑆𝐶𝑉𝑅 ∗ 𝐾𝑀𝑇𝐿𝐶𝑉𝑅 ∗ 𝐾𝑇𝐸𝑀𝑃𝐶𝑉𝑅

Where KFSCVR can be 1.0 if the wing cover does not have a fail-safe or 1.261 if it has.

KMTLCVR and KTEMPCVR are the factors which are determined by the material, construction, temperature

and load driven factor tables.

BASIC WING BOX SUBSTRUCTURE

0.00636 ∗ [𝑆𝑊∗ ∗ 𝑁𝐵𝑂𝑋 ∗ 𝐵∗]0.5598 ∗ [𝑆𝐵𝑂𝑋

∗ ∗ (𝑇𝑅∗ + 𝑇𝑇)]0.1877 ∗ 𝐾𝐶𝑇

0.518 ∗ 𝐾𝑀𝑇𝐿𝑆𝑈𝐵

Where the KMTLSUB can be either 1.0 for an aluminium substructure or 0.787 for a titanium.

KCT is used for the wing carry through. 1.0 corresponds to a wing with continuous spars through the

fuselage and 2.0 is for a wing that is attached to the fuselage “skin”.

STORES PENALTY TO WING BOX

0.01 ∗ 𝑊𝑊𝑆𝑇𝑂𝑅𝐸𝑆

0.014 ∗ 𝑊𝑊𝑆𝑇𝑂𝑅𝐸𝑆 (for sweeping store stations. i.e, F-111A

MAIN LANDING GEAR PENALTY TO WING BOX (NO DOORS)

0.001416 ∗ 𝑁𝐿𝐺𝐷𝑊 ∗ 𝐿𝐷𝐺𝑊 ∗ 𝐾𝑀𝐺

Where KMG can be 0.0 for no landing gears on wing, 1.0 if landing gears on wing or 0.5938 if the

landing gears are located in engine nacelles on wing.

WING FUEL PENALTY TO WING BOX

0.9191 ∗ [𝑊𝑊𝐹𝑈𝐸𝐿]0.5436

ENGINE PENALTY TO WING BOX

0.004 ∗ 𝐹𝑊 or

0.03 ∗ [𝐻𝑃𝑊]

WING FOLD OR WING SWEEP PENALTY

0.03386 ∗ [𝐵 ∗ 𝑛]0.2477 ∗ [𝑆𝑊]1.244 ∗ [1 −𝑏′

𝑏]

1.307

∗ 𝐾𝑊𝑆

Where KWS is equal to 0.0 if the wing is of a normal type without folding or variable sweep. 1.0

corresponds to folding wings, 0.556 to variable sweep.

LEADING EDGE, TRAILING EDGE & MISCELLANEOUS

0.07235 ∗ [𝑆𝑊∗ − 𝑆𝐵𝑂𝑋

∗ ]0.2595 ∗ [𝑇𝑂𝐺𝑊∗]0.5281 ∗ [𝑆𝑊∗ ]0.3192 ∗ 𝐾𝐿𝐸𝐷

Where KLED is 1.0 for a wing without leading edge devices. If leading edge devices exists, KLED is

0.847.

LANDING GEAR DOORS & MECHANISM

0.8991 ∗ [𝑆𝑀𝐺𝐷𝑅]1.067 ∗ [𝑉𝐿]0.2252

57

AILERONS, ELEVONS, FLAPERONS & DECELERONS

0.06564 ∗ [𝑆𝑅𝑂𝐿𝐿]0.8697 ∗ [𝑇𝑂𝐺𝑊

𝑆𝑊]

1.049

∗ 𝐾𝑅𝑂𝐿𝐿 ∗ 𝐾𝐵𝑊

Where KROLL can be 0.0 for no control surfaces, 1.0 for ailerons, 1.732 for elevons, 1.023 for flaperons

and 1.609 for decelerons.

KBW is 1.0 if the control surfaces are unbalanced by balance weights and 1.541 if they are balanced.

TRAILING EDGE FLAPS

0.0008759 ∗ [𝑆𝐹𝐿𝐴𝑃] ∗ [𝑉𝐿]0.3565 ∗ [𝑛]0.1576 ∗ [𝐶𝐿𝑀𝐴𝑋∗ 𝐿𝐷𝐺𝑊]

0.3210∗ [𝑉𝑆]0.5 ∗ 𝐾𝑇𝑆

Where KTS is 0.0 if no trailing edge flaps, 1.0 if there are flaps and 1.976 if triple slotted flaps.

SLATS

0.2727 ∗ [𝑆𝑆𝐿𝐴𝑇] ∗ [𝑉𝐿]0.4703

LEADING EDGE FLAPS

0.3100 ∗ [𝑆𝐿𝐸𝐹] ∗ [𝑉𝐿]0.4703

SPOILER

0.2697 ∗ [𝑆𝑆𝑃𝑂𝐼𝐿]0.8699 ∗ [𝑉𝐿]0.3461 ∗ [𝑆𝑊]0.8445 ∗ [𝑏]−1.117

WING SPEED BRAKES WINGLETS

0.01053 ∗ [𝑆𝑊𝑆𝐵] ∗ [𝑇𝑂𝐺𝑊]0.5909 0.0386 ∗ [𝑊𝑊𝐼𝑁𝐺]

58

C. Interpretations of the NASA Wing Weight Build-Up parameters The results for the interpretation of the NASA wing weight build-up parameters are shown in this

appendix. Some parts of the interpretation of parameters from the result chapter are repeated.

The wing reference area, or SWing, can be defined in several different ways and are often standardized

within companies. The different methods are often publically available and are sometimes described

with detailed pictures. Figure 37 shows the interpretation of the wing area definition on the Gripen

fighter aircraft. The wing area described was measured and compared with publically available data for

the Gripen aircraft and gave accurate results.

The exposed wing area (SWing,exp) was interpreted as the wing area without the area occupied by the

aircraft fuselage. The fuselage-wing connection can be more sophisticated than just a straight line as

shown in Figure 38, and the interpretation is that the weight prediction will be more accurate if the area

is measured as thorough as possible. The area definition for the wing box (SWbox) is also shown in Figure

38 and is defined as the wing area seen from above without the leading- and trailing edge. It is simply

interpreted as the area between the front and rear spar of the aircraft wing. The exposed wing box area

(SWbox,exp) was interpreted in the same way as the exposed wing area and can be seen to the right in

Figure 38.

Figure 37. The wing reference area definition. Original image by

Kaboldy, used under CC BY-SA / Edited from original.



59

The size of components on the wing, such as control surfaces and high-lift devices, were also needed

for the method. Figure 39 shows the interpretation of the roll control surface areas (ailerons, Sailerons),

trailing edge high-lift devices (TE-flaps, STEFlaps) and leading edge high-lift devices (LE-flaps, SLEFlaps).

The area used for each component was interpreted as the total area occupied by a control surface as seen

from the top view of the aircraft.

Figure 39. The definition of control surfaces and high lift devices. From the left, the aileron surfaces, trailing

edge flaps and leading edge flaps. Original image by Kaboldy, used under CC BY-SA / Edited from original.

The illustrations of additional devices such as the leading edge slat areas (SSlats) and the wing spoiler

areas (SSpoilers) are shown on a Boeing 747-700 which can be seen in Figure 40. The areas are interpreted

as the total surface occupied by each device as seen from the aircraft top view.

Figure 38. From the left, the definition of the exposed wing area, wing box area and the exposed wing box

area. Original image by Kaboldy, used under CC BY-SA / Edited from original.





60

Figure 40. The definition of the slat surface areas (left) and the wing spoiler areas (right). Original image by

Julien Scavini, used under CC BY-SA / Edited from original.

The final area definitions are the wing speed brake areas (SSpeedbrakes) and wing main landing gear door

areas (SMLGD). Their respective interpretations are illustrated below in Figure 41 for the A-10C

Thunderbolt (left) and J-35 Draken aircraft (right). The areas are as before interpreted as the total device

area as seen from the aircraft top view or bottom view.

Figure 41. Left: The definition of the wing speed brake area. Original image by Kaboldy used under CC BY-SA /

Edited from original. Right: The definition of the main landing gear door area. Original image by Marcin

Zieliński used under CC BY-SA / Edited from original.

Areas that do not exist on the intended aircraft should be specified as zero. The Gripen C for example

has its main landing gears within the fuselage and the main landing gear doors are located there as

well. The main landing gear door area for the wing should therefore be specified as zero.



https://commons.wikimedia.org/wiki/File:Fairchild_A-10_Thunderbolt.svg


https://commons.wikimedia.org/wiki/File:SAAB_J-35F_Draken_0012.jpg


61

The proposed method by York and Labell [15] also utilizes a number of geometrical aircraft lengths and

angles. The interpretations of the top view definitions are illustrated in Figure 42. The wing span (b) is

defined as the distance from wing tip to wing tip, while the exposed wing span (bexp) is interpreted as

the wing span without a mean width of the fuselage-covered distance. The exposed root chord (Croot,exp)

and the tip chord (Ctip) are defined as the wing width at the wing-fuselage connection respective the

width at the wing tip. The 40% sweep angle (Λ40%) is defined as the sweep between 40% of the root

chord and tip chord length. There is also a geometric parameter for a folded wing span (bfolded) that

defines the wing span for aircraft with foldable or sweepable wings (usually carrier-based aircraft). This

parameter is simply interpreted as the new wing span measured from tip to tip on sweepable wings or as

the span between the hinges on an aircraft with foldable wings.

Figure 42. The definition of different geometrical lengths and angles. Original image by Kaboldy, used under


Figure 43 below shows the final geometrical definitions on a front view of the aircraft. The wing tip

thickness (ttip) is interpreted as the thickness of the wing at a position before any wingtip weapon

storages. The exposed root thickness is interpreted as the wing thickness at the fuselage-wing

connection.

Figure 43. The definition of the geometrical lengths seen from the front view of the aircraft. Original image by

Kaboldy, used under CC BY-SA / Edited from original.





62

Other parameters without geometry, were different weight definitions as shown in Figure 14.

The Maximum Zero Wing Fuel Weight (MZWFW) was interpreted as the Maximum Take-off Weight

(MTOW) without any fuel in the wing fuel tanks. The landing design gross weight (LDGW) was

interpreted as the publicly specified LDGW value for the intended aircraft. If not specified, it could be

calculated with a given formula from [15]. The same interpretation was made for the Take-Off Gross

Weight (TOGW). The weight of wing storages (WWstores) was defined according to York and Labell [15]

as “the summation of the heaviest stores weight on all wing stations including drop tanks”.

The ultimate load factor for manoeuvres (n) and ultimate load factor at landing design gross weight

(nLDG) were also needed as parameters for the wing build-up method. The ultimate-load factor was

defined as the limit load factor times 1.5, while the load factor for landing was interpreted as the nLDG

specified by the intended aircraft manufacturer (only used if the aircraft had landing gears on the wings).

The required velocities were the maximum flying speed and the aircraft stall speed. These were

interpreted as the respective velocities specified by an intended aircraft manufacturer. Finally, the total

thrust of wing mounted engines (Ttot) were, as the name implies, defined as the sum of all wing mounted

engine thrusts.

63

D. NASA Wing Weight Build-up, Material/Construction Data Tables

Note: Reproduced from [15]. Empty fields indicate data not provided in the original report.

Material/Construction Factors - Upper cover

Material: Aluminum 7075-T6 (R.T.) - Baseline Material: Titanium 6AL-6V-2SN Ann. (R.T.)

Limit Construction: "Z" stiff Construction: Hat stiff Limit Construction: "Z" stiff Construction: Hat stiff

load Rib spacing, inches Rib spacing, inches load Rib spacing, inches Rib spacing, inches

factor 12 16 20 12 16 20 factor 12 16 20 12 16 20

2,5 1 1,02 1,053 0,926 0,948 0,994 2,5 1,185 1,197 1,239 1,149 1,170 1,208

3,0 1 1,017 1,05 0,918 0,947 0,990 3,0 1,156 1,175 1,213 1,108 1,128 1,164

4,0 1 1,021 1,061 0,916 0,950 0,997 4,0 1,103 1,155 1,194 1,056 1,074 1,114

5,0 1 1,025 1,071 0,923 0,958 1,004 5,0 1,068 1,143 1,179 1,019 1,033 1,080

6,5 1 1,033 1,088 0,940 0,981 1,030 6,5 1,037 1,111 1,169 0,970 0,985 1,031

7,0 1 1,036 1,093 0,944 0,996 1,039 7,0 1,027 1,099 1,164 0,958 0,976 1,016

7,5 1 1,035 1,091 0,953 1,002 1,044 7,5 1,014 1,080 1,157 0,943 0,963 1,005

Limit Construction: "Y" stiff Construction: Integ. stiff Limit Construction: "Y" stiff Construction: Integ. stiff


factor 12 16 20 12 16 20 factor 12 16 20 12 16 20

2,5 0,982 0,985 0,990 0,903 0,943 1,004 2,5 1,308 1,308 1,309 0,909 0,974 1,097

3,0 0,962 0,966 0,977 0,918 0,956 1,014 3,0 1,246 1,246 1,247 0,894 0,941 1,061

4,0 0,943 0,946 0,971 0,953 0,994 1,048 4,0 1,166 1,166 1,168 0,888 0,925 1,022

5,0 0,934 0,947 0,974 0,976 1,025 1,082 5,0 1,110 1,110 1,113 0,893 0,931 1,005

6,5 0,934 0,953 0,994 0,997 1,054 1,116 6,5 1,047 1,048 1,054 0,916 0,939 0,992

7,0 0,934 0,959 1,002 1,002 1,065 1,127 7,0 1,030 1,031 1,038 0,918 0,943 0,994

7,5 0,936 0,960 1,006 1,007 1,067 1,131 7,5 1,014 1,014 1,021 0,918 0,945 0,991

Limit Construction: Flat sheet Limit Construction: Flat sheet

load Spar spacing, inches load Spar spacing, inches

factor 6 9 12 factor 6 9 12

2,5 1,410 1,737 2,086 2,5 1,971 2,394 2,859

3,0 1,350 1,666 2,004 3,0 1,882 2,293 2,742

4,0 1,274 1,563 1,884 4,0 1,751 2,144 2,570

5,0 1,215 1,480 1,786 5,0 1,645 2,023 2,430

6,5 1,143 1,378 1,663 6,5 1,541 1,867 2,249

7,0 1,122 1,349 1,625 7,0 1,492 1,820 2,195

7,5 1,099 1,317 1,586 7,5 1,431 1,772 2,137

Material: Stainless Steel PH15-7M0 (R.T.) Material: Graphite/Epoxy with Holes (R.T.)



factor 12 16 20 12 16 20 factor 12 16 20 12 16 20

2,5 1,645 1,655 1,693 2,5

3,0 1,595 1,600 1,646 3,0

4,0 1,525 1,535 1,599 4,0

5,0 1,494 1,504 1,570 5,0

6,5 1,453 1,470 1,525 6,5

7,0 1,444 1,462 1,512 7,0

7,5 1,430 1,448 1,498 7,5



factor 12 16 20 12 16 20 factor 12 16 20 12 16 20

2,5 1,413 1,485 1,619 2,5

3,0 1,357 1,440 1,552 3,0

4,0 1,311 1,388 1,497 4,0

5,0 1,282 1,365 1,473 5,0

6,5 1,272 1,350 1,453 6,5

7,0 1,270 1,352 1,450 7,0

7,5 1,270 1,343 1,444 7,5




2,5 2,900 3,478 4,122 2,5 0,873 1,032 1,225

3,0 2,764 3,330 3,950 3,0 0,852 1,000 1,189

4,0 2,567 3,110 3,703 4,0 0,805 0,958 1,135

5,0 2,411 2,929 3,500 5,0 0,789 0,933 1,093

6,5 2,213 2,699 3,233 6,5 0,782 0,890 1,037

7,0 2,154 2,630 3,152 7,0 0,790 0,882 1,008

7,5 2,091 2,559 3,069 7,5 0,796 0,866 1,006

64

Materials/Construction Data Table, cont.

Note: Reproduced from [15]. Empty fields indicate data not provided in the original report.

Material/Construction Factors - Lower cover

Material: Aluminum 7075-T6 (R.T.) - Baseline Material: Titanium 6AL-6V-2SN Ann. (R.T.)



factor 12 16 20 12 16 20 factor 12 16 20 12 16 20

2,5 1,000 1,004 1,015 1,022 1,044 1,055 2,5 1,203 1,214 1,241 1,238 1,254 1,302

3,0 1,000 0,998 1,009 1,019 1,042 1,054 3,0 1,137 1,147 1,175 1,158 1,179 1,220

4,0 1,000 1,004 1,010 1,033 1,064 1,083 4,0 1,039 1,047 1,080 1,041 1,062 1,096

5,0 1,000 1,002 1,022 1,058 1,094 1,105 5,0 0,965 0,971 1,001 0,979 0,993 1,014

6,5 1,000 1,010 1,035 1,071 1,114 1,137 6,5 0,912 0,918 0,929 0,930 0,942 0,961

7,0 1,000 1,007 1,036 1,065 1,125 1,141 7,0 0,898 0,904 0,913 0,921 0,927 0,951

7,5 1,000 1,006 1,036 1,072 1,129 1,143 7,5 0,884 0,889 0,899 0,905 0,915 0,941



factor 12 16 20 12 16 20 factor 12 16 20 12 16 20

2,5 1,098 1,098 1,100 1,025 1,045 1,064 2,5 1,495 1,495 1,495 1,037 1,089 1,192

3,0 1,086 1,087 1,091 1,054 1,064 1,087 3,0 1,382 1,382 1,382 0,988 1,029 1,116

4,0 1,080 1,085 1,092 1,107 1,114 1,130 4,0 1,213 1,213 1,213 0,946 0,973 1,016

5,0 1,084 1,089 1,096 1,133 1,158 1,172 5,0 1,094 1,094 1,094 0,931 0,952 0,987

6,5 1,083 1,080 1,131 1,142 1,171 1,185 6,5 0,997 0,997 0,997 0,935 0,946 0,977

7,0 1,077 1,090 1,135 1,144 1,178 1,196 7,0 0,977 0,977 0,977 0,934 0,973 0,977

7,5 1,075 1,094 1,141 1,148 1,171 1,185 7,5 0,957 0,957 0,957 0,931 0,948 0,972




2,5 1,532 1,851 2,213 2,5 2,153 2,566 3,036

3,0 1,434 1,741 2,083 3,0 2,013 2,408 2,854

4,0 1,292 1,563 1,872 4,0 1,789 2,153 2,558

5,0 1,211 1,418 1,702 5,0 1,610 1,946 2,319

6,5 1,137 1,249 1,496 6,5 1,393 1,694 2,026

7,0 1,121 1,207 1,438 7,0 1,334 1,625 1,946

7,5 1,100 1,165 1,383 7,5 1,275 1,556 1,864

Material: Stainless Steel PH15-7M0 (R.T.) Material: Graphite/Epoxy with Holes (R.T.)



factor 12 16 20 12 16 20 factor 12 16 20 12 16 20

2,5 1,716 1,738 1,757 2,5

3,0 1,614 1,635 1,656 3,0

4,0 1,460 1,475 1,501 4,0

5,0 1,346 1,358 1,382 5,0

6,5 1,252 1,258 1,270 6,5

7,0 1,233 1,238 1,248 7,0

7,5 1,209 1,213 1,230 7,5



factor 12 16 20 12 16 20 factor 12 16 20 12 16 20

2,5 1,613 1,717 1,824 2,5

3,0 1,501 1,576 1,695 3,0

4,0 1,368 1,401 1,494 4,0

5,0 1,307 1,331 1,382 5,0

6,5 1,259 1,272 1,303 6,5

7,0 1,246 1,258 1,293 7,0

7,5 1,229 1,260 1,203 7,5




2,5 3,197 3,737 4,393 2,5 0,944 1,116 1,316

3,0 2,984 3,503 4,130 3,0 0,906 1,068 1,252

4,0 2,644 3,128 3,699 4,0 0,877 0,975 1,136

5,0 2,374 2,828 3,347 5,0 0,875 0,928 1,059

6,5 2,048 2,451 2,915 6,5 0,854 0,875 0,962

7,0 1,959 2,358 2,797 7,0 0,853 0,875 0,943

7,5 1,870 2,256 2,679 7,5 0,853 0,862 0,913

65

E. NASA Wing Weight Build-up, Extrapolation of Material Factors Material/Construction Factor, Upper Cover

66

Material/Construction Factor, Upper Cover, cont.

67

Material/Construction Factor, Upper Cover, cont.

68

Material/Construction Factor, Lower Cover

69

Material/Construction Factor, Lower Cover, cont.

70

Material/Construction Factor, Lower Cover, cont.

71

F. NASA Wing Weight Build-up, Temperature Factor Data Table

Aluminium Titanium

Maximum Structural Temperature

200°F 300°F 200°F 300°F 400°F 500°F

1,086 1,259 1,013 1,033 1,067 1,107

1,102 1,285 1,021 1,063 1,112 1,159

1,108 1,300 1,057 1,124 1,185 1,239

1,111 1,307 1,083 1,152 1,221 1,280

1,110 1,317 1,092 1,168 1,259 1,322

1,113 1,324 1,099 1,179 1,268 1,334

1,113 1,331 1,106 1,197 1,275 1,343

Advanced Composit Steel

Maximum Structural Temperature

100°F 200°F 300°F 400°F 600°F 800°F 1000°F

1,008 1,022 1,035 1,005 1,010 1,021 1,250

1,014 1,032 1,038 1,006 1,013 1,039 1,328

1,005 1,019 1,029 1,013 1,036 1,108 1,488

1,004 1,011 1,019 1,034 1,080 1,177 1,625

1,008 1,022 1,037 1,059 1,116 1,240 1,780

1,008 1,019 1,037 1,065 1,118 1,252 1,810

1,008 1,014 1,031 1,070 1,130 1,267 1,848

Temperature Effects Factors - Lower cover

Limit Aluminium Titanium

load Maximum Structural Temperature

factor 200°F 300°F 200°F 300°F 400°F 500°F

2,5 1,037 1,093 1,022 1,052 1,084 1,119

3,0 1,039 1,097 1,026 1,063 1,104 1,144

4,0 1,039 1,104 1,047 1,095 1,142 1,188

5,0 1,039 1,121 1,060 1,119 1,167 1,214

6,5 1,048 1,152 1,068 1,127 1,188 1,239

7,0 1,053 1,163 1,070 1,131 1,193 1,248

7,5 1,054 1,169 1,070 1,132 1,199 1,257

Limit Advanced Composit Steel

load Maximum Structural Temperature

factor 100°F 200°F 300°F 400°F 600°F 800°F 1000°F

2,5 1,014 1,020 1,022 1,010 1,014 1,035 1,147

3,0 1,004 1,008 1,012 1,008 1,022 1,049 1,189

4,0 1,012 1,030 1,039 1,016 1,037 1,085 1,278

5,0 1,014 1,020 1,034 1,023 1,051 1,105 1,328

6,5 1,011 1,025 1,042 1,033 1,062 1,127 1,389

7,0 1,009 1,019 1,029 1,035 1,067 1,127 1,408

7,5 1,005 1,013 1,024 1,035 1,063 1,131 1,422

Temperature Effects Factors - Upper cover

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Temperature Factor, cont.

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G. Sensitivity Results

Weight Penalty Methods for Conceptual Aircraft Design

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Transcript of Weight Penalty Methods for Conceptual Aircraft Design