Weight Penalty Methods for Conceptual Aircraft Design

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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

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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

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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

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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.

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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 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

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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]

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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

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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.

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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

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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.

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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.

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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.

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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.

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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

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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.

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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]

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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

Figure 5. Schematic illustration of three common types of fuselage structures. Left: Semi-monocoque structure with stringers. Middle: Semi-Semi-monocoque structure with longerons. Right:

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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

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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]

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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

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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.

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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

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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

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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.

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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

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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.

Weight Penalty Methods for Conceptual Aircraft Design