Parameterization of the Geometry of a Blended-Wing-Body ...

SYSTEMS REALIZATION LABORATORY 

Parameterization of the 

Geometry of a Blended- 

Wing-Body Morphing Wing 

ME 6104: Fundamentals of Computer-Aided 

Design 

Patrick Chang, Aditya Shah, Mukul Singhee 

4/28/2009 

Instructor: Dr. David Rosen

Acknowledgements 

We thank Dr. David Rosen for having provided us with the opportunity, the knowledge and the 

motivation to have realized this project. Dr. Rosen is Patrick’s advisor and as such the key sponsor for 

this project. 

We would also like to thank Dr. Fei Ding, Amit S. Jariwala and the RPMI for offering us the facility to 

create a rapid prototype model of the BWB morphing wing aircraft 

We express our gratitude to Jane Chu for the assistantship she has offered throughout the semester in this 

course and for solving many of our issues throughout the semester 

We would also like to thank the Systems Realization Laboratory faculty and students for providing us 

with the resources we needed to complete our project and creating a positive and supportive learning 

environment

Table of Contents 


Acknowledgements ............................................................................................................................... 2 

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

List of Figures ....................................................................................................................................... 3 

List of Tables ........................................................................................................................................ 5 

Abstract ................................................................................................................................................. 1 

1 Introduction and Background........................................................................................................ 2 

1.1 The Conventional, ―Tube,‖ Aircraft...................................................................................... 2 

1.2 Blended-Wing-Body Aircraft ............................................................................................... 3 

1.3 Morphing Wings ................................................................................................................... 4 

1.4 The NACA Airfoil ................................................................................................................ 5 

2 Problem Statement ........................................................................................................................ 7 

2.1 Problem Overview ................................................................................................................ 7 

2.2 Motivation ............................................................................................................................. 7 

2.3 Project Proposal .................................................................................................................... 8 

3 Goals and Objectives .................................................................................................................... 9 

3.1 Overarching objective ........................................................................................................... 9 

3.2 Project objectives .................................................................................................................. 9 

3.3 Learning objectives ............................................................................................................... 9 

3.4 Additional Objectives - Rapid Prototyping ........................................................................... 9 

4 Report Organization .................................................................................................................... 10 

5 Parameterization of Geometry of BWB ...................................................................................... 11 

5.1 Requirements ...................................................................................................................... 11 

5.2 Parameterization Method .................................................................................................... 12 

6 Parameterized Model in Pro/Engineer ........................................................................................ 14 

6.1 Top-Down Assembly of BWB Model ................................................................................ 14 

6.2 NACA Airfoil Profile.......................................................................................................... 14 

6.3 Skeleton Model ................................................................................................................... 17 

6.4 Individual Part Models ........................................................................................................ 19 

6.4.1 Left Wing ........................................................................................................................ 19 

6.4.2 Right Wing ...................................................................................................................... 20 

6.4.3 Fuselage .......................................................................................................................... 20 

6.5 Top Down Assembly .......................................................................................................... 21 

Parameterization of the Geometry of a Blended-Wing-Body Morphing Wing i


6.6 Top-Down Assembly with Motion ..................................................................................... 22 

6.7 Design Variations ................................................................................................................ 24 

6.7.1 Change management process .......................................................................................... 24 

6.7.2 Test Cases ....................................................................................................................... 25 

7 Rapid Prototype of CAD Model ................................................................................................. 37 

7.1 The Viper si2 SLA .............................................................................................................. 37 

7.2 RPT Model .......................................................................................................................... 37 

8 Conclusions and Remarks ........................................................................................................... 40 

8.1 Intellectual Questions Addressed ........................................................................................ 40 

8.1.1 Why components are shaped the way they are? .............................................................. 40 

8.1.2 How can a top-down product-wide approach for CAD modeling work? ....................... 40 

8.2 Future Work ........................................................................................................................ 41 

9 Critical Evaluations ..................................................................................................................... 42 

9.1 Patrick Chang ...................................................................................................................... 42 

9.2 Aditya Shah ......................................................................................................................... 43 

9.3 Mukul Singhee .................................................................................................................... 45 

10 References ................................................................................................................................... 48 

Appendix ............................................................................................................................................. 49 

Parameterization of the Geometry of a Blended-Wing-Body Morphing Wing ii

List of Figures 


Figure 1. The Airbus A340 (left) and the Boeing 747 (right) ............................................................... 2 

Figure 2. Boeing B-47 ........................................................................................................................... 2 

Figure 3. Basic design of the BWB fuselage ........................................................................................ 3 

Figure 4. The BWB aircraft .................................................................................................................. 4 

Figure 5. NACA 4-digit airfoil parameterization [5] ............................................................................ 5 

Figure 6. The BWB wing and its control surfaces ................................................................................ 7 

Figure 7. AAI Shadow UAV ................................................................................................................. 8 

Figure 8. Morphing of the airfoil of the AAI Shadow from NACA23015 to FX60-126 ...................... 8 

Figure 9. Flowchart for Modeling the Geometry of the Morphing BWB aircraft .............................. 13 

Figure 10. Parameters for the NACA 4-digit airfoil ........................................................................... 15 

Figure 11. NACA airfoil implement in Pro/E ..................................................................................... 15 

Figure 12. Family table of NACA airfoils for the BWB morphing wing ........................................... 16 

Figure 13. Airfoil instances used in the BWB morphing wing ........................................................... 17 

Figure 14. BWB dimension relations .................................................................................................. 18 

Figure 15. BWB aircraft skeleton ....................................................................................................... 19 

Figure 16. Viewing convention for the BWB aircraft ......................................................................... 19 

Figure 17. Left wing ............................................................................................................................ 20 

Figure 18. Right Wing......................................................................................................................... 20 

Figure 19. Fuselage ............................................................................................................................. 21 

Figure 20. Completed top-down assembly .......................................................................................... 21 

Figure 21. Three orthographic views of the assembly ........................................................................ 22 

Figure 22. Implemented pin joints for the inboard and outboard sections of the wing ....................... 23 

Figure 23. Utilization of the pin joints to create pitch motion in the inboard and outboard airfoils ... 24 

Figure 24. Change Management Process Flowchart ........................................................................... 25 

Figure 25: No morphing ...................................................................................................................... 26 

Figure 26: Inboard twist – Left:-15 0 ; Right: +15 0 ............................................................................... 27 

Figure 27: Outboard twist – Left wing: +25 0 ; Right Wing: -25 0 ......................................................... 27 

Figure 28: Winglet twist – Left wing: -20 0 ; Right wing: +20 0 ............................................................ 28 


Figure 30: Fuselage to root span = 9 ................................................................................................... 30 

Figure 31: Root to inboard = 12 .......................................................................................................... 31 

Figure 32: Inboard to outboard = 8 ..................................................................................................... 31 

Figure 33: Outboard to tip = 4 ............................................................................................................. 32 

Parameterization of the Geometry of a Blended-Wing-Body Morphing Wing iii


Figure 34: Winglet span = 8 ................................................................................................................ 32 


Figure 36: Inboard sweep = 45 0 .......................................................................................................... 34 

Figure 37: Outboard sweep = 60 0 ........................................................................................................ 34 

Figure 38: Tip sweep = 45 0 ................................................................................................................. 35 


Figure 40: Dihedral angle = 10 0 .......................................................................................................... 36 

Figure 41: Airfoil profiles for Root: 0015, Inboard: 0030, Outboard: 0012, Tip: 0015, Winglet 

airfoils: 0015 ............................................................................................................................................... 36 

Figure 42. The Viper si2 SLA system [11] ......................................................................................... 37 

Figure 45. Scaled dimensions for rapid prototyping ........................................................................... 38 

Figure 46. Inner cut of the BWB wing ................................................................................................ 38 

Figure 43: Rapid Prototype Model of the BWB Morphing Wing aircraft in default shape (No 

Morphing) ................................................................................................................................................... 39 

Figure 44: Rapid Prototype Model of the BWB Morphing Wing aircraft in default shape (No 

Morphing) – Isometric View....................................................................................................................... 39 

Parameterization of the Geometry of a Blended-Wing-Body Morphing Wing iv

List of Tables 

List of Tables 

Table 1. Parameters in the 4-digit NACA airfoil .................................................................................. 5 

Table 2. Initial BWB aircraft dimensions ........................................................................................... 12 

Table 3. Test Cases 1-4 for the morphing BWB wing ........................................................................ 26 

Table 4. Test Cases 5-10 for the morphing BWB wing ...................................................................... 28 

Table 5. Test Cases 11-14 for the morphing BWB wing .................................................................... 33 

Parameterization of the Geometry of a Blended-Wing-Body Morphing Wing v

Abstract 

Abstract 

Not long ago, the idea of building and aircraft wing that could change its entire shape to adjust for 

various flight conditions seemed impossible. However, with the advent of new design realization 

technologies, tools, and processes, new levels of morphing will soon be achievable through the advanced 

manufacturing of compliant, integral control surfaces that will allow a wing to achieve degrees of 

morphing seen only in nature. By applying this technology to a new, high-performance subsonic transport 

design, the Blended-Wing-Body (BWB) aircraft, a truly revolutionary breed of aircraft can be born. 

In our project, our group aimed to explore the possibility of using integral control surfaces to create a 

single, continuous BWB wing that can change its shape based on its current flight conditions and flight 

objectives. In order to study perform this study, our group parameterized the BWB wing in a CAD 

system. 

Using the CAD software package, PTC Pro/Engineer Wildfire 4.0, we were able to successfully 

parameterize the entire BWB wing using 33 parameters. 

Parameterization of the Geometry of a Blended-Wing-Body Morphing Wing 1

1 Introduction and Background 

Introduction and Background 

There are several important driving concepts, goals, and problems driving this project. These 

ideas are outlined in the following sections. 

1.1 The Conventional, “Tube,” Aircraft 

The conventional subsonic transport design is the most pervasive aircraft design in history. 

Aircraft such as the Airbus A340 and Boeing 747 (Figure 1) demand the vast majority of market share in 

Figure 1. The Airbus A340 (left) and the Boeing 747 (right) 

long-distance subsonic transport [1]. As can be seen from Figure 1, these aircraft rely on the same, 

widely accepted and time-tested design concept: a cylindrical, or ―tube,‖ fuselage with wings attached on 

either side of the aircraft. In this configuration, the fuselage and wing serve mutually independent roles. 

Simply put, the fuselage carries the payload and the wing generates lift; there is very little overlap in 

function between the two bodies. This design concept has existed since the Wright Flyer was invented in 

1903. In 1947, 44 years after the creation of the Wright Flyer, the Boeing-B47 took flight (Figure 2). This 

aircraft embodied the revolutionary concepts that exist even today: swept wings, rudders, and podded 

engines hung underneath the wing. Since then, very few critical changes have been made to the core 

design of the subsonic transport; the aircraft in Figure 1 embody the same basic spirit as the B-47, a plane 

created over five decades ago. 

Figure 2. Boeing B-47 



Although this design concept has improved with time and is highly effective for it purpose, its core 

design has not changed; there has not been a revolution in its design for over half a century [2]. 

1.2 Blended-Wing-Body Aircraft 

The Blended-Wing-Body aircraft (BWB), 

represents a completely new concept in the design of the 

subsonic transport. This design concept arose from 

designing the fuselage by using basic shapes that contained 

minimal surface area and were streamlined for flight [2]. As 

Figure 3 shows, two basic shapes, the cylinder and the disc, 

became the two major shapes driving the design of the 

fuselage. The cylinder fuselage tended toward the 

conventional design of aircraft whereas the disk became the 

basis for the design of the BWB aircraft. 

Since the initial design of the BWB wing in 1988, it 

has been refined to its current state (Figure 4). The principal 

concept behind the current iteration of the BWB is the 

blending of various components of the plane, including the 

fuselage, wings, and the engines, into a single lifting 

surface. As a result, the BWB fuselage is harder to 

distinguish from the wing (i.e. it is harder to tell where the 

wing ends and the fuselage begins). There are some key 

concepts to note about the design of the BWB: 

1. The BWB is a tailless aircraft: Because of the discshaped 

nature of the fuselage, the BWB does not 

have a tail. As a result, the BWB does not have a 

Figure 3. Basic design of the BWB fuselage 

rudder. 

2. The engine location of the BWB: Another important characteristic of the BWB design is position 

of the engines, are located at the aft sections of the plane. Because of the weight and balance 

considerations of the plane, the engines needed to be place at the rear of the plane [2]. 

Additionally, with the engines at the rear of the plane, the fuselage can serve as an inlet for the 

intake of air. 

3. Control surfaces: The control surfaces of the wing are located along the leading and trailing edges 

of the wing and on the winglets. The number of control surfaces can vary from 14 to 20 

depending on the BWB design. 


Figure 4. The BWB aircraft 


The BWB has several distinct advantages over the conventional tube aircraft. Some of these 

advantages are outlined below: 

1. Higher fuel efficiency: Initial testing of the BWB aircraft has indicated that it can have up to 

a 27% reduction in fuel burn during flight [2]. 

2. Higher payload capacity: Due to the blended nature of the fuselage, the fuselage is no longer 

distributed along the centerline of the aircraft. As a result, the fuselage is more ―spread out,‖ 

allowing for greater volume and a larger payload capacity [2]. 

3. Lower takeoff weight: Early design concepts have determined that the BWB can have up to a 

15% reduction of take-off weight when compared to the conventional baseline [2]. 

4. Lower wetted surface area: The compact design results in a total wetted difference of 14,300 

ft 2 , a 33% reduction in wetted surface area. This difference implies a substantial improvement 

in aerodynamic efficiency [2]. 

5. Commonality: One of the greatest advantages of the BWB is commonality of size and of 

application [3]. Firstly, the commonality of the components of the airplane will allow it the 

payload of the airplane to be varied at little cost. For the 250, 350, and 450 – passenger 

capacity of the BWB, many components are interchangeable. This interchangeability serves 

to drive down the cost of the aircraft. Secondly, commonality of function allows the BWB to 

be used in many applications, both military and civilian. The BWB can be modified to be 

used as a freighter, troop transport, tanker, and stand-off bomber in addition to its function as 

a commercial airliner. 

1.3 Morphing Wings 

A morphological wing is a wing that can change its configuration to maximize its performance 

for different flight conditions. The morphological wing is not a new concept; nearly all aircraft wings 

have components, such as ailerons, that allow the wing to change its shape. Although current aircraft each 

have their own methods for changing configuration—folding, telescoping, sweeping etc.—these methods 

all rely on a similar principle: individual control surfaces that have discrete, mechanical, and rigid 

structures that move relative to each other [4]. 


2 Problem Statement 

2.1 Problem Overview 

Problem Statement 

One of the BWB’s greatest disadvantages is the control of its motion. As a type of tailless 

aircraft, it lacks the control surfaces that are commonly found on the tail. Consequently, it suffers from 

important technical control issues, such as yaw control power, multi-axis instabilities, multiple control 

effectors for each control axis, and nonlinear effector control that can greatly diminish the control of the 

aircraft [9]. These problems must be addressed by the morphing wing of the aircraft. However, these 

morphing wings have issues satisfying the needs of the BWB aircraft. 

Figure 6. The BWB wing and its control surfaces 

The current morphing wing of the BWB aircraft utilizes between 14 and 20 control surfaces to 

control the motion of the aircraft. These control surfaces, although sufficient in direction motion of the 

aircraft, have many drawbacks. For instance, these morphing wings will often lack the optimal shape for 

their application because the wing shape is not continuous for the control surfaces [4]. Additionally, these 

wings have issues such as weaker structural integrity, large size, and an overabundant number of control 

surfaces [4]. Another important issue is the ambiguous function allocation of the control surfaces. The 

outboard split elevons, for instance, can provide both pitch, roll, and yaw movements [3]. These multiplefunction 

elevons can result in the saturation of a particular effector, or worse—conflicts between control 

surfaces. 

One other drawback of the BWB wing and its rigid control surfaces is function. Currently, only 

the control surfaces of the wing can change their shape and orientation. The body of the wing remains 

relatively rigid in relation to these control surfaces. This shape orientation limits the BWB to a maximum 

speed of Mach 0.85, or 289 m/s. However, different sweep and length configurations of the wing will 

allow it to reach speeds of up to Mach 0.95 [2]. The rigid BWB body does not allow the wing to achieve 

these sweeps, lengths, or orientations. 

2.2 Motivation 

In order to improve the control issues of the BWB wing and conventional aircraft wings in 

general, a fully morphing wing design has been proposed. This concept does not use external control 


Problem Statement 

surfaces to control each individual motion of the aircraft, but, instead, utilizes integral control surfaces to 

change the shape of the wing. Rather than use separate moving parts to change the shape of the leading 

and trailing edges of the wing, this wing design will allow the aircraft wing to remain as one continuous 

part with the ability to change all portions of its shape. An example of this type of morphing wing is the 

morphing of the shown below for the AAI Shadow Unmanned Aerial Vehicle (UAV) [10]. During flight, 

the AAI Shadow is able to change the shape of its airfoil from the NACA23015 shape to the FX60-126 

shape is fuel is consumed. This change allows the Shadow to achieve 22% greater endurance. 

Figure 7. AAI Shadow UAV 

Figure 8. Morphing of the airfoil of the AAI Shadow from NACA23015 to FX60-126 

The proposed morphing of the BWB will follow the same fundamental concept as the morphing of 

the AAI Shadow. However, the degree of shape change proposed is much larger in scale. Rather than 

change just the airfoil type of the wing, the BWB wing will be able to adjust all aspects of its shape, 

including length, taper, sweep, angle of attack, and dihedral angle. 

2.3 Project Proposal 

Until recently the technological means to achieve this degree of morphing was noticable absent. 

However, the onset of new design realization technology, such as additive manufacturing, has allowed for 

morphing wings to attain a new level of shape change to increase flight efficiency. In the world of 2030 

and beyond, we envision that this technology will enable the realization of morphing wings that can 

change their entire shape, thus resulting in a more versatile and efficient aircraft wing. To better 

understand how this technology will improve the performance of the BWB aircraft, we will model and 

parameterize the wing of a BWB aircraft so that it will be able to change its entire shape under different 

flight conditions. Specifically, we will analyze and characterize the shape of the BWB wing under 

different flight conditions (i.e. take-off, climb, cruise, loiter, land, etc.). 

In the context of CAD, our goal will be to design and parameterize a CAD model of a BWB 

aircraft wing so that it can change various components of its shape (i.e. camber, chord length, sweep, 

taper, etc.) for different flight conditions. In order to accomplish this goal, a top-down product-wide 

design approach will be implemented in a CAD system. This approach will allow the parameterization 

scheme to be implemented in a robust fashion. 


3 Goals and Objectives 

Goals and Objectives 

The objectives of this project can be divided into three main types of objectives: the main, 

overarching objective, project objectives, learning objectives, and additional objectives. These objectives 

are laid out as follows: 

3.1 Overarching objective 

The primary objective of this project is to explore the extent through which morphing can be 

achieved in the BWB aircraft wing through parameterization of the wing in a CAD system. 

3.2 Project objectives 

The specific project objectives can be subdivided into the objectives below: 

Explore the different types of morphing that can be achieved in a BWB aircraft 

Find and model the dimensions of the BWB wing and aircraft 

Develop a parameterization scheme for the airfoil of the BWB wing 

Develop a parameterization scheme for the extrusion of the airfoil across the wing 

Implement this parameterization scheme in a CAD system 

Study the relationship between parameters to each other and to the morphing of the BWB wing 

3.3 Learning objectives 

In addition to the project objectives outlined, we have also defined learning objectives in order to 

outline our learning considerations for the project. They are as follows: 

To understand how a parameterization scheme can be utilized in the design of components 

To understand how to implement design in a CAD system 

To understand how a top-down, product wide, design process can be utilized to improve the 

design of an assembly 

3.4 Additional Objectives - Rapid Prototyping 

In addition to the parameterization of the wing, we will attempt to rapid-prototype the BWB 

aircraft in an SLA machine. This will allow physical comparison between different BWB morphing 

scenarios. 


4 Report Organization 

Report Organization 

In order to fully convey the information of the project, the report will be laid out as follows: 

Chapter 1 provides background information regarding the project. 

Chapter 2 explains the main problems and motivations driving the project. 

Chapter 3 outlines the goals and objectives of the project. 

Chapter 4 outlines the report organization. 

Chapter 5 explains the parameterization requirements and method. 

Chapter 6 implements the parameterization scheme in a top-down product wide approach in a 

CAD package. It also presents several test cases exploring the capabilities of the parameterized 

BWB scheme. 

Chapter 7 explores the rapid-prototyping process used to create the physical, scale models of the 

parameterized BWB aircraft. 

Chapter 8 summarizes and evaluates the project. It then addresses and answers the intellectual 

questions posed by the project. Finally, it presents possible future work for the project. 

Chapter 9 presents self-evaluations for each group member. 

Chapter 10 shows the references of the project. 


5 Parameterization of Geometry of BWB 

5.1 Requirements 

Parameterization of Geometry of BWB 

Based on the defined scope of the project, we have focused on the geometrical aspects of morphing in 

a BWB wing morphing aircraft. Thereby, the requirements that we have listed are made off the geometry 

of the CAD model. The three categories that we have used are justified below: 

1. Airfoil Section: These requirements are imposed on the airfoil section in order to generate 

parameterized description of the airfoils that are used to define the wing 

2. Airfoil Location and Orientation: These requirements are imposed on the parameterization 

scheme and the modeling approach used in the CAD software in order to maintain flexibility for 

each airfoil section in the wing to relocate or rotate itself, thereby morphing the entire wing 

3. Overall Wing Orientation and Shape: These are the overall requirements from the morphing 

wing. These requirements are responsible for the visual impact of the morphing of the BWB 

aircraft wing. 

Requirements List for the CAD Model of a BWB Morphing Wing 

Aircraft 

# DW Requirements 

1 W 

Airfoil Section 

Should be defined in such a way that it is mutable 

Issued on: 

4/01/2009 

2 D The change in form must depend on a set of parameters 

3 D Must be readily re-usable for all sections in the wing 

4 D 

5 D 

6 D 

Airfoil 

Location 

and 

Orientation 

Overall Wing 

Orientation and Shape 

Each airfoil section’s orientation must be controllable 

independently 

The CAD Model must allow flexibility in relative location of 

airfoil sections 

The wing must be able to change its sweep angle 

7 D The wing must be able to change its dihedral angle 

8 D 

9 D 

Morphing of the wing must include localized twist, as well as 

change in span length 

The CAD model must be able to approximate the actual 

dimensions of a BWB wing 


5.2 Parameterization Method 


In order to parameterize the BWB wing, approximate dimensions of the fuselage and wings needed 

to be obtained. Unfortunately, the dimensions of the wing are highly proprietary and were difficult to 

find. The majority of the dimensions were found from [2, 3, 8]. Any other dimension that needed to be 

found were measured from scale drawings of the BWB as found from [2]. Table 2 below summarizes 

some of the initial dimensions of the BWB aircraft. 

Table 2. Initial BWB aircraft dimensions 

Airfoil Type NACA0015 

Wing Span (m) 24 

Root Chord Length (m) 22.14 

Inboard Chord Length (m) 15.12 

Outboard Chord Length (m) 4.84 

Tip Chord Length (m) 2.77 

Dihedral Angle 3° 

Sweep Angle 37° 

Fuselage Span (m) 12 

Span Distance from Root Chord to Inboard Chord (m) 6 

Span Distance from Inboard Chord to Outboard Chord (m) 8 

Span Distance from Outboard Chord to Tip Chord (m) 10 

Winglet Height (m) 3 

With the initial dimensions specified, a rough BWB dimension could be modeled and leveraged for 

parameterization. 


Locate fuselage origin 

Locate origin for root section 

relative to fuselage 

Locate origins for the various wing sections 

at specified sweep angle, span length, and 

dihedral elevation relative to root section 

Use the standardized airfoil profiles for 

both wing and fuselage sections 

Specify twist angle to represent 

morphing of the BWB 

Join the leading and trailing edges 

while maintaining G1 continuity 

Create the BWB surface that passes 

through the both wings (left and 

right) and the fuselage 


Figure 9. Flowchart for Modeling the Geometry of the Morphing BWB aircraft 

Description of the Steps and the Parameterization involved 

Create standardized airfoil 

profile based on NACA standards 

Location of the fuselage: This step is carried out to create the reference coordinate system for the 

CAD model and is basically the position of the fuselage. It is fixed and doesn’t have to be changed or 

shifted around. 

Locate origin for root section relative to fuselage: The root sections are roughly where the wings will 

start on a Blended Wing Body aircraft. These sections will remain fixed and are not parameterized to 

morph. The airfoil description itself can of course be changed. 


Parameterized Model in Pro/Engineer 

Locate origins for the various wing sections at specified sweep angle, span length and dihedral 

elevation relative to root section: These origins are located on both sides of the fuselage for the two 

wings. Their location will be parameterized. Thus, the relative span between different sections of the wing 

can be changed using a set of parameters. In addition their locations will depend on the sweep angle and 

the dihedral angle of the aircraft. 

Create standardized airfoil profile based on NACA standard: The standard airfoil descriptions used 

in this project are the NACA airfoil equations. (Reference). These equations are analytical equations 

which are controlled by four parameters, viz. the chord length, maximum thickness, location of maximum 

camber and maximum camber. All the airfoil sections in the CAD model will be defined by the 

standardized airfoil profile described here. 

Use the standard airfoil profiles for both the wing and fuselage sections: As pointed out in the last 

step, the airfoil sections will be described using a standardized NACA equation. These are implemented 

for the fuselage and the root sections in this step. 

Specify twist angles at the other wing sections to enable morphing by twist: The other wing sections 

for both wings need to possess the ability to morph by twisting about the leading edge. In order to satisfy 

this requirement, parameters are introduced in the way of the twist angles for each of these sections. 

These sections are also defined by the NACA standard equation. 

Join the leading and trailing edges while maintaining G1 continuity: After all the sections are 

defined, the leading and trailing edges are joined together using G1 continuous curves. 

Create the BWB surface that passes through all the sections in both the wings and the fuselage: The 

surface is now created and requires no additional parameterization, since it is based on the airfoil sections 

which are fully parameterized. 

6 Parameterized Model in Pro/Engineer 

6.1 Top-Down Assembly of BWB Model 

The parameterization method discussed in the previous section is implemented in Pro/Engineer 

Wildfire 3 to create an assembly model of the geometry of the BWB. Since the complete aircraft is one 

smooth surface, a bottom-up approach to modeling is not feasible since the surface characteristics of the 

individual components are interlinked. For instance, a change in sweep angle and span for the inboard 

section affects both the fuselage and the wing surface. Consequently, a top-down approach is needed in 

which all of the geometry is controlled by a single model. However, there are two main aspects of the 

aircraft that need to be parameterized: the locations of the different sections and the airfoil profile used at 

each section. Therefore, the geometry is controlled by two models – the skeleton references the airfoil 

profiles while the components reference the skeleton model. These aspects are discussed in more detail in 

the following sections. 

6.2 NACA Airfoil Profile 

The four-digit NACA airfoil series is used to model the different sections of the BWB aircraft. The 

model is parameterized through the use of Datum curves that are driven by equations and parameters. At 

the top-level, four parameters: maximum camber, position of maximum camber, maximum thickness, and 

chord length control the airfoil profile. The four digits correspond to the three parameters, as shown in 

Figure 10. 


* For cartesian coordinate system, enter parametric equation 

/* in terms of t (which will vary from 0 to 1) for x, y and z 

/* For example: for a circle in x-y plane, centered at origin 

/* and radius = 4, the parametric equations will be: 

/* x = 4 * cos ( t * 360 ) 

/* y = 4 * sin ( t * 360 ) 

/* z = 0 

/*------------------------------------------------------------------- 

c = chord_length 

m = 0.01 * camber_max 

p = 0.1 * camber_max_pos 

t_max = 0.01*thickness_max 

x_c = p*t 

y_c = m/(p+1e-9)^2*(2*p*x_c - x_c^2) 


y_t = t_max/0.2 * (0.2969*x_c^.5 - 0.1260*x_c - 0.3516*x_c^2 + 0.2843*x_c^3 - 0.1015*x_c^4) 

dyc_dxc = m/(p+1e-9)^2*(2*p - 2*x_c) 

theta = atan(dyc_dxc) 

x_u = x_c - y_t*sin(theta) 

y_u = y_c + y_t*cos(theta) 

x = x_u * c 

y = y_u * c 

Plot points 

Use parameters to 

define variables 

Define camber points 

Define airfoil points 

Since all the sections of the aircraft utilize NACA airfoils, duplicate models are not created for each 

section. Instead, multiple instances are created of the same NACA airfoil model, with different parameter 

values for each instance. In this way, the same model is used for each section and managing changes in 

the model becomes easier. A family table is used to create the multiple instances, as shown in Figure 12. 

Figure 12. Family table of NACA airfoils for the BWB morphing wing 

As a final step, the publish geometry feature is used to make the airfoil profile available to external 

models (Figure 11). Thus, with the airfoil profile paramterized, it is possible to create the skeleton model, 

which will serve as the driver for the top-down assembly. 


6.3 Skeleton Model 


The skeleton model contains all of the defining characteristics for the wings and the fuselage. Both 

wings of the BWB consist of six controlling sections: Root, inboard, outboard, tip, winglet1 and winglet2 

sections. Since the BWB’s fuselage generates lift, the section is also modeled as a NACA airfoil profile. 

Winglet2 

Winglet1 

Tip 

Outboard 

Inboard 

Root 

Fuselage 

Figure 13. Airfoil instances used in the BWB morphing wing 

Each section is controlled through parameters. For instance, the inboard section is controlled through 

four parameters and relations, as shown in Figure 14. Similarly, parameters and relations are used to 

define the locations for all of the remaining sections. The complete listing of relations and parameters is 

provided in the appendix. 


$D74 = INBOARD_PITCH_ANGLE_LEFT 

Twist angle (for morphing) 

$D1=INBOARD_SPAN_LENGTH 

Span length 

$D69 = D1 * tan(INBOARD_SWEEP_ANGLE) 

Sweep distance 

Figure 14. BWB dimension relations 


$D67 = D1 * tan(DIHEDRAL_ANGLE) 

Dihedral elevation of wing 

Once the coordinate systems for the different sections are located, the NACA profiles are referenced 

from the model described in the previous section using the copy geometry feature. After the sections are 

positioned and defined, trajectories connecting the sections are required to control proper surfacing across 

the aircraft. 

The sections can rotate about the local Z-axis and therefore sketches cannot be used since the 

trajectory points are not coplanar. Therefore, datum curves are created to pass through the end points of 

the NACA profiles. To establish G1 continuity, datum axes are created to establish direction vectors for 

the sections. The curves are created tangent to the axes at the end points and this establishes the tangency 

between the adjoining surfaces. The complete skeleton is shown in Figure 15. Refer to the appendix for 

views of the skeleton with all datum features visible. 

Finally, the combination of curves, datum references, and sketches are published so that they can be 

used to create the individual part models. 


6.4 Individual Part Models 

Figure 15. BWB aircraft skeleton 

The following convention for identifying the two wings is shown below: 

6.4.1 Left Wing 

Viewing direction 

Left Wing Right Wing 

Figure 16. Viewing convention for the BWB aircraft 


Using the copied geometry from the skeleton, surfaces are created through the boundary blend 

feature. The surfaces are constrained to pass through the airfoil profiles in one direction and the 

trajectories in the other direction. Since the trajectories are tangent to one another, the adjoining surfaces 

that are created have G1 continuity between them. After the surfaces are created, the ends of the wing are 



filled and the surfaces are merged pair-wise. Finally, the merged surface is solidified to create a solid part, 

which is shown in Figure 17. 

6.4.2 Right Wing 

Figure 17. Left wing 

The right wing is created in the same way as the left wing and is shown in Figure 18. 

6.4.3 Fuselage 

Figure 18. Right Wing 

The fuselage is also created in the same manner as the wings. The only addition is the hollow portion 

that is created to conserve material during the rapid prototyping process. The shell will be discussed in 

more detail in the next chapter. 


6.5 Top Down Assembly 

Figure 19. Fuselage 


The skeleton model simplifies the assembly of the individual components. Since the components and 

the assembly both are reference to the skeleton’s global coordinate system, the creation of the parts from 

the skeleton automatically assembles the components in the proper orientation and position. The complete 

top-down assembly is shown in Figure 20. Three orthographic views – front, top and left – are shown in 

Figure 21. 

Figure 20. Completed top-down assembly 


6.6 Top-Down Assembly with Motion 

Figure 21. Three orthographic views of the assembly 


To model the morphing of the wings of the BWB, a mechanism-based assembly was attempted, but 

with mixed results. 

Mechanisms are recommended for applications in which individual parts move relative to one 

another, i.e. the components are flexible. The four-bar mechanism is a good application for a mechanismbased 

assembly, in which the links are connected to each other via pin joints. In addition, top-down 

assemblies have traditionally been limited to rigid assemblies. Mechanisms could be created by reusing 

the top-down components to create a new bottom-up assembly with motion joints. However, a new 

feature of Pro/Engineer, namely the top-down assembly with mechanism, is utilized to create a top-down 

based assembly with mechanism support. The desired result is for dynamic control over the morphing of 

the wing instead of static control through parameters. 

However, the morphing BWB requires sections of the same part to have different motion joints 

assigned. For instance, the wing section requires four joints – one each for inboard, outboard, tip and 

winglet1 sections. This is shown in Figure 22, in which pin joints are defined for the inboard and 

outboard sections in the skeleton itself. This is an issue, since the joints are defined as separate parts in the 

skeleton model in spite of belonging to the same component. Moreover, to create dynamic surfaces, the 

trajectories to control the surfaces need to be created as assembly features and not in the skeleton. This is 

counter-productive from a modeling view point, since the skeleton should be a self-contained model 

containing all necessary controlling geometries. 



Pin Joints for 

Inboard and Outboard 

Figure 22. Implemented pin joints for the inboard and outboard sections of the wing 

The result is that it is possible to dynamically morph the wing, although the surfaces do not get 

updated. The surfaces can be updated manually, as shown in Figure 23. 



Figure 23. Utilization of the pin joints to create pitch motion in the inboard and outboard airfoils 

6.7 Design Variations 

Twist outboard 

section dynamically 

6.7.1 Change management process 

Pin Joints for 

Inboard and Outboard 

Regenerate 

Once the CAD model was finalized in ProEngineer, we proceeded to test the morphing capability. 

This is where the top-down approach to parameterization revealed its utility. In order to fully test the 

capability of the wing to morph, we describe the procedure to change all parameters and then regenerate 

the model. This process has been illustrated with screenshots taken from ProEngineer’s family table and 

parameter table. 


Adjust the NACA profile by changing 

the parameters in the family table 

(e.g. 0015 4315, chord length) 

Adjust parameter values 

(sweep, dihedral angle, span, twist) 

in the skeleton model 

Regenerate the assembly 

model to update individual 

parts and assembly 

6.7.2 Test Cases 

Figure 24. Change Management Process Flowchart 


Regenerate 

For the BWB wing, a total of 33 parameters were used to parameterize the entire BWB wing. 

Twenty of these parameters resulted from the parameterization of the five bounding airfoils (5 airfoils x 4 

parameters). The remaining 13 parameterized the wing itself (sweep angle, span length, dihedral angle, 

etc.). Using these parameters, a number of test cases have been tabulated in Table 3-Table 5 in order to 

demonstrate the full range of morphing capabilities of the BWB aircraft that we have modeled. Table 3 

lists cases with morphing capabilities in the twist angle of the airfoil sections. Table 4 lists the morphing 

capabilities with respect to the span of the different portions of the wing. Table 5 lists the morphing 

capabilities with respect to the sweep angle of different portions of the wing. Lastly in Figure 39 and 

Figure 40, we show the morphing capability with respect to change in the dihedral angle of the wings. 


Test Case No. Feature Being Morphed 

(Twist) 

Table 3. Test Cases 1-4 for the morphing BWB wing 


Morphing Specifications(Twist) Figure(s) 

Number 

1 None All twist angles = 0 Figure 25 

2 Inboard Twist Twist angle – 

Left wing =-15 0 ; 

Right wing =+15 0 

3 Outboard Twist Twist angle – 

Left wing =+25 0 ; 

Right wing =-25 0 

4 Winglet Twist Twist angle – 

Left wing = -20 0 ; 

Right wing = +20 0 

Figure 25: No morphing 

Figure 26 

Figure 27 

Figure 28 


Figure 26: Inboard twist – Left:-15 0 ; Right: +15 0 

Figure 27: Outboard twist – Left wing: +25 0 ; Right Wing: -25 0 



Test Case No. Feature Being 

Morphed (Span) 

Figure 28: Winglet twist – Left wing: -20 0 ; Right wing: +20 0 


Morphing Specifications(Span) 

in meters 

5 None Fuselage to Root = 6 

Root to Inboard = 8 

Inboard to Outboard = 4 

Outboard to Tip = 8 

Winglet Span = 5 

6 Fuselage to Root Fuselage to Root = 9 





7 Root to Inboard Fuselage to Root = 6 



Figure(s) 

Number 

Figure 29 

Figure 30 

Figure 31 


8 Inboard to 

Outboard 




Fuselage to Root = 6 





9 Outboard to Tip Fuselage to Root = 6 





10 Winglet Span Fuselage to Root = 6 






Figure 32 

Figure 33 

Figure 34 



Figure 30: Fuselage to root span = 9m 



Figure 31: Root to inboard = 12m 

Figure 32: Inboard to outboard = 8m 



Figure 33: Outboard to tip = 4m 

Figure 34: Winglet span = 8m 



Test Case No. Feature Being 

Morphed 


(Sweep) 

Morphing Specifications 

(Sweep) 

11 None Inboard Sweep = 40 0 

Outboard Sweep = 50 0 

Tip Sweep = 50 0 

12 Inboard Sweep Inboard Sweep = 45 0 



13 Outboard Sweep Inboard Sweep = 40 0 



14 Winglet Sweep Inboard Sweep = 40 0 





Figure(s) Number 

Figure 35 

Figure 36 

Figure 37 

Figure 38 


Figure 36: Inboard sweep = 45 0 

Figure 37: Outboard sweep = 60 0 



Figure 38: Tip sweep = 45 0 




Figure 40: Dihedral angle = 10 0 


Figure 41: Airfoil profiles for Root: 0015, Inboard: 0030, Outboard: 0012, Tip: 0015, Winglet airfoils: 0015 


7 Rapid Prototype of CAD Model 

7.1 The Viper si2 SLA 

Rapid Prototype of CAD Model 

After the CAD model of the BWB wing was completed, it was rapid prototyped using the Viper 

si2 Stereolithography Apparatus (SLA) system, manufactured by 3D Systems. The Viper SLA machine 

utilizes Stereolithography, an additive fabrication process that creates its parts in a vat of liquid UVcurable 

"resin." In SLA, parts are created on a platform one layer at a time. For each layer, a UV laser 

beam traces the cross-section of the part on the surface of the liquid resin, causing the traced resin to 

solidify. Once this process is completed, the platform submerges an incremental amount and the liquid is 

allowed to settle. Then, the next later is drawn. This process is continued until the part is completed. The 

SLA Viper uses a solid state Nd:YVO4, 100 mW, UV laser to cure layers of photopolymer resin [11]. The 

Viper is shown below: 

7.2 RPT Model 

Figure 42. The Viper si2 SLA system [11] 

The aircraft model was made hollow to reduce material requirements in the prototyping phase. CAD 

packages provide shell tools to automatically thicken parts and make them hollow. But due to the 

complex nature of the curves as well as the size considerations, conventional shell proved inadequate. As 

shown in Figure 43, the model was scaled as per the SLA bed size. Therefore, the wing-to-wing span of 

60 m was scaled to approximately 200 mm to fit in the SLA bed. As a result, the maximum thickness (at 

fuselage) is approximately 15 mm while the minimum thickness (at trailing edge of winglet2 section) is 

less than 0.5 mm. 


Minimum thickness < 0.5 mm (for SLA) 

4.5 m (Max thickness) ≈ 15 mm (for SLA) 

60 m (Span) ≈ 200 mm (Span for SLA) 

Figure 43. Scaled dimensions for rapid prototyping 


Due to the thickness variation across the wing and multiple surfaces (12), it was not possible to 

perform conventional shelling even for a small section for the wing. In addition, due to the morphing 

possibilities, dynamic cavity generation would entail a repetition of the steps used to create the wing 

itself. Also, a shell thickness of 3 mm in the RP component proved too thick when shelling of the wing 

was attempted. Thus, due to limited material savings, the additional model complexity and time was not 

considered and the wing was kept a solid. 

The fuselage, on the other hand, was made hollow since there are only two main surfaces (top and 

bottom) to be considered. Here also, conventional shelling failed due to the complex three dimensional 

shape of the surface. Therefore, an indirect method using surface offsetting was employed, as shown in 

Figure 44. The advantage of this method is that when the parameters are changed, the fuselage’s shape 

also changes and so the shell also gets updated. The resultant material savings is approximately 

7193 mm 3 , or a cube with sides of length 19 mm. 

Surface Offset 

Intersection of two 

solidified surfaces 

Figure 44. Inner cut of the BWB wing 



Figure 45 and Figure 46 below show the resulting BWB model in its default configuration. 

Figure 45: Rapid Prototype Model of the BWB Morphing Wing aircraft in default shape (No Morphing) 

Figure 46: Rapid Prototype Model of the BWB Morphing Wing aircraft in default shape (No Morphing) – 

Isometric View 

Unfortunately, the rapid prototype of the morphed BWB aircraft was unavailable at the time this 

report was submitted. 


8 Conclusions and Remarks 

Conclusions and Remarks 

Through this report we have expressed the motivation, background and scope which we have 

focused on during the course of this project. Further, we have outlined the requirements that we set out to 

fulfill with our CAD model of the BWB morphing wing aircraft. Based on these requirements, we 

identified a parameterization scheme which has been detailed both in an algorithmic format and 

subsequently in the actual implementation which was carried out in Pro/Engineer. Throughout this project 

in particular and the course in general we have gained a huge amount of learning with respect to modeling 

and the fundamental concepts of CAD. In this section we will now draw our conclusions, and enunciate 

the learning that each of us have individually taken from this course. 

8.1 Intellectual Questions Addressed 

8.1.1 Why components are shaped the way they are? 

At the commencement of this project, we were focused on the prime driver of the shape of a 

component, viz. the primary function that the component must serve. For an aircraft in particular the 

primary function is to increase lift and decrease drag. However, having gone through the process of 

actually modeling our CAD model of a BWB morphing wing aircraft, we realized that there are other 

aspects which affect the shape of a component. 

The primary function itself is satisfied by the shapes adopted in conventional aircraft which have a 

tubular fuselage and wings with limited morphing capability which are basically implemented with a 

modular trailing edge with several components which slide upon each other. However, we impose the 

requirement of the aircraft to perform in changing environments with varying mission objectives. The 

other categories which define the shape of components can be abstracted from our deliberations and 

subsequent implementation of parameterization in the CAD model. These are: 

Increased Efficiency: In order to achieve the best fuel efficiency, lift/drag ratio might even have 

to be reduced, for instance, during the landing phase. Correspondingly, the shape of the morphing 

wing will have to change shape to suit this requirement. 

Mutability: The fact that we want the flight to perform in different environments and achieve 

different mission objectives lends to the requirement of the wing to be mutable. Thereby, 

mutability drives the shape of the aircraft as well. 

Manufacturability: We realized the importance of Design for Manufacture with respect to the 

shape of a component when we were modeling lines and corners in our parts. It is important to 

fillet or round corners in a model in order to account for manufacturability. 

8.1.2 How can a top-down product-wide approach for CAD modeling work? 

Based on the systems perspective, we defined our geometry requirements for the CAD model. We 

realize that it is essential to have the geometry requirements set out in order to facilitate a top-down 

product wide CAD modeling approach. Thereafter, we look for the solution principle which satisfies these 

requirements in the form of functionality that is offered by the CAD software that we use. 

In context of our project, we defined the requirements in Section 5.1. Thereafter, we define the 

conceptual parameterization scheme which would fulfill these requirements (Section 5.2). In Chapter 6, 


Conclusions and Remarks 

we implemented the embodiment of our parameterization scheme in ProEngineer. In order to maintain a 

top-down approach in the CAD model, we defined a couple of models which control the geometry of the 

entire aircraft. The corresponding models are the airfoil profile and the skeleton. The skeleton references 

the airfoil profile and the components reference the skeleton. The inherent advantage of this approach is 

that the result of any changes that are made in one component are automatically applied to other 

components. 

Some aspects which are key to implementing the top-down approach are 

Surfaces must be created with a parameterized skeleton as the reference 

The skeleton must be created with parameterized sketches as the reference 

8.2 Future Work 

The work conducted during this project has laid a strong groundwork for the eventual use of 

fluidly morphing wings in BWB aircraft. However, there is much that can still be accomplished in this 

area. 

The current parameterization scheme for the BWB aircraft, although capable of performing some 

degree of morphing, does not represent the full capability of morphing in the BWB wing. Currently, the 

morphing of the wing is bounded by four NACA 4-digit airfoils and a trajectory sweep between these 

airfoils. Therefore, in order to morph the wing, only the airfoils or trajectories can be changed directly. If, 

for instance, a local change of the wing was desired in an area between the airfoils, and therefore, not 

directly influenced by changing the airfoils, then this change could not be achieved directly. In order to 

incur change in these areas, parameters would need to be specified for the areas not directly influenced by 

the airfoils. For instance, rather than having four airfoils specifying the root, inboard, outboard, and tip 

portions of the wing, more airfoils can be used. Using more airfoils to bound the aircraft will result in a 

greater degree of parameterization. 

Another important limitation of the current wing design is the airfoil type. Currently, only NACA 

4-digit series airfoils can be used. However, this type of airfoil represents a small fraction of the total 

airfoil designs available. Future work for this aircraft can be to adapt the airfoils to be able to account for 

5-digit, 6-digit, and so forth NACA airfoils. Also, unlike the NACA series airfoils, many airfoil designs 

cannot be parameterized because they cannot be represented using mathematical equations. Instead, they 

have been created empirically. Therefore, the current wing design can be modified to include tables of set 

airfoil types. 

One final extension of this project could be to explore how to implement this morphing wing 

design concept in the BWB aircraft. No current technology exists to engineer a wing capable of the 

morphing described in this project. However, new design realization tools such as additive manufacturing 

have allowed for this wing to be realizable in the near future. One particular method of interest relies on 

cellular structures as compliant mechanisms. Cellular structures are man-made materials, such as foams, 

honeycombs, and lattices, composed of unit cells. The key advantage of these structures is their high 

strength and their relatively low mass. A compliant mechanism is a type of cellular structure that is 

designed to transform its shape under the influences of force, motion, or energy [12]. Technologies such 

as compliant mechanisms can be explored to implement the morphing concepts outlined in this project. 


9 Critical Evaluations 

9.1 Patrick Chang 

Critical Evaluations 

When I first took the ME6104: Computer Aided Design, my goal was simply to understand the 

concepts and mathematical models driving the function of common CAD programs, such as Pro/Engineer 

and Solidworks. This class satisfied that goal easily. In the class, I learned the following: 

I was first given a basic introduction to the CAD. This included primitive instancing, such as how 

to create basic shapes (or primitives), and how to create complex shapes through simple Boolean 

operations between primitives. Then, I learned how to mathematically compute rigid-body 

transformations, including 2-D and 3-D translations and rotations, scaling, relative positioning, and 

rotation about an arbitrary axis. Finally, I was given an introduction into assembly modeling. 

Then, the course shifted to a new topic: parametric and variational modeling. Here, I learned why 

parametric modeling was so powerful; parametric models could be more flexible, robust, and adaptive 

than other, rigid models. I then applied this knowledge of parametric modeling to parametric curves. I 

learned about their advantages over non-parametric curves, such as their shape invariance under rigid 

body transformations. I learned how to implement these parametric curves and distinguish between 

different parametric curves, such as hermite, Bezier, B-spline, and NURBS curves. I then extended my 

learning to how to implement composite curves and enforce continuity between these curves. I was then 

taught how these types of curves could be applied to parametric surfaces. Through this tactic, I as able to 

create hermite, bezier, and composite surfaces. Finally, I learned about the concepts driving solid 

modeling. This included understanding how to quantify mathematically if solids can be realizable in 3-D 

space (such as the Klein bottle), learning the necessary and sufficient conditions for realizability and 

orientabilitby, and calculating the Euler characteristic to identify the general boundary properties of 

realizable objects. I also learned how to implement representation schemes to for solid models, such as 

CSG tress, boundary representation and winged-edge models. Finally, I learned about neutral CAD files, 

such as .SAT and .STEP files, and how to read and implement these files. 

Although the class satisfied my goals of understanding and implementing the mathematics behind 

CAD, it taught me much more. For instance, I was the given a brief overview of CAD systems and 

MATLAB, a powerful computational tool that can be used for technical computation. Throughout various 

lectures in the course, I learned about limitations of current CAD systems, including issues with 

tolerances, communication between CAD programs and CAM programs, and computational inefficiencies 

and limitations. I learned that due to these issues, not all designs could be realized in a CAD system. I 

was also presented with cutting-edge research being conducted in not only 3-D model representations 

(such as Coon’s patches, pseudo-edge surfaces), but also in user-interface modes and devices (haptic 

inputs, the sheet metal stamping system, etc.). I was even given an introduction to using CAD programs 

with CAM and manufacturing technology (injection molding, virtual prototyping, and rapid prototyping). 

As I learned about CAD and its role in design, my goals began to change because I was 

challenged to think critically about where CAD is today and how it will change to accommodate the 

needs of futures design engineers. With the knowledge I gained about the current mathematical models of 

CAD, my goals began to change from answering the question, ―how is CAD implemented and used 

today?‖ to answering the question, ―how can I leverage my knowledge of CAD to improve design in the 

future?‖ During the in-class exercise for developing new user-interfaces for machining processes, I began 

to understand how much potential there is for growth in CAD and CAM in general. I also realized where 

in the design process the CAD process can be used to facilitate work for design engineers. In terms of the 

Pahl and Beitz design process, CAD can be used effectively in all phases of the design process 

(conceptual design, embodiment, and detail design phases) except the first (planning and task 



clarification). For instance, CAD can be used as a visualization tool in the conceptual design phase. Also, 

a robust CAD system can allow for easy and efficient implementation and modification of designs in the 

conceptual and embodiment phases. A CAD system is also the primary tool in the detail design phase for 

finalizing dimensions and specifications. Therefore, an improvement in CAD systems can have a 

profound effect on the design process in general. In addition, the programs often associated with CAD, 

such as prototyping technologies, will also have a great influence on the design process. With new 

computer-related technologies beginning to appear more and more rapidly in the context of design 

realization, several questions to ponder could be ―how can new design tools incorporated into the design 

process?‖ and ―how can new design realization tools be made more robust and intuitive for designers?‖ 

As my goals in CAD have changed, so has my perception of how design tools that are currently used in 

the design process and how they can be potentially used in the design process. My original goal has been 

fulfilled—I have gained a basic understanding of CAD. However, my new goal is much more ambitious: I 

hope to take the knowledge I have gained and apply it in new and exciting ways. 

When I took the class, the only skill I expected to gain was a simple knowledge of a CAD system. 

However, although I have gained firsthand knowledge of how to use Pro/Engineer during the project and 

homework assignments, I also gained much more. From the homework, the most obvious skill I gained 

was a mastery of MATLAB. Although I had used MATLAB before, I had never used it to this advanced 

degree. From the use of MATLAB, I gained another skill: to apply parameterization to CAD models. In 

this class, I learned the true power of parameterization in models. I learned how parameterization can 

make a model more robust, adaptable, and easy to use. Viewing all models as functions of parameters will 

allow me to understand design at a different level. Another skill I have gained through CAD that will be 

useful as a designer is the concept of Top-Down design. Up until this class, I viewed CAD from a 

―bottom-up‖ sense. When I used CAD to create assemblies, I designed each part individually and then 

manufactured them in an assembly. However, in the project I learned how top-down design could be used 

much more effectively for assembly purposes; updating each component will not damage the integrity of 

the overall assembly. The greatest skill I have gained, however, is a solid understanding of the 

mathematics behind CAD. For instance, during our CAD project, we ran into problems defining surface 

boundaries and blends. Through the knowledge that we gained in class, we were able to solve this issue 

and understand that some limitations of our model were not due to the way it was defined, but due to the 

nature of the CAD system itself. 

In this class, I have truly learned about the ―fundamentals‖ of CAD. I learned not only about the 

mathematics behind 2-D (rigid body transformations, parametric curves) and 3-D modeling (parametric 

surfaces and solid modeling), but I have learned how to implement these concepts in CAD programs and 

MATLAB. I have even learned about the limitations of CAD and its application in various design 

processes. In this regard, I believe that I have gained a solid understanding of the ―fundamentals‖ of 

CAD. The knowledge I gain now will be essential for my future as a design engineer, whether it be in 

industry or academia. I now look to future—to apply what I have learned to advance design to new, 

unexplored heights. 

9.2 Aditya Shah 

My goals for the semester were to gain a deeper understanding of the concepts used in CAD, such as 

the mathematical foundation for constructing geometric entities. Along with this goal, I was also able to 

gain a better understanding of the benefits of CAD in the design process. Through the course and the 

project, I have come to appreciate the importance of surfaces in geometry creation. Surface modeling is 

becoming more important due to the advances in non-conventional manufacturing processes such as rapid 

manufacturing. Therefore, using the knowledge gained during the semester and in the project, one of my 

goals for the future is to increase my competency in surface modeling as well as implement the concepts 

that I learnt in the course. 



To aid in the fulfillment of my semester learning goals and more importantly, my future personal 

goals, I improved on existing skills and learnt new ones. The skills that I learnt during this course can be 

classified in three categories: conceptual learning, use MATLAB to solve problems, and 3D modeling in 

a CAD package. Another course that I took this semester, Linear Algebra, complemented the concepts 

that I learnt in the first half of the semester. My understanding of rigid body transformations, parametric 

curves and surfaces improved due to the theory covered in Linear Algebra. In addition, concepts such as 

transformations were useful as an application domain for the concepts covered in Linear Algebra. In 

addition to strengthening the concepts in class, the homework exercises improved my ability to use 

MATLAB for solving problems. 

Prior to this course, I had some exposure to the solid modeling environment of Pro/Engineer, but 

virtually no experience in surface modeling and top-down assemblies. Working on the project, and the 

exercises to a lesser extent, highlighted the necessity (and usefulness) of top-down assemblies and 

parameterized models. I also improved my surface modeling skills due to the requirements of the BWB 

aircraft. 

After taking this course, my approach to organizing models has changed and I have internalized the 

need for parameterization. Earlier, my approach to solid modeling was ad-hoc in the sense that I used the 

capabilities of CAD packages without concentrating on formal organization. Homework 2 was where I 

internalized the advantages of model organization and parameterization. The ability to manage multiple 

components and assemble them in MATLAB changed my preferences for model organization, as evident 

in this project and the subsequent homework exercises. 

Concepts such as G1 continuity, used in Homework 4 (Surface modeling), aided us during the 

modeling of the trajectories to ensure tangency across the different sections. It increased my awareness 

and knowledge of issues that arise during surface design of objects, where the shape of the object is 

crucial, such as in automobiles and aircrafts. 

The solid body representations such as winged-edge representations as well as the standard formats 

for storing geometric data (.sat files, ACIS, STEP formats) was a good learning opportunity from an 

information modeling point of view. The standardization found in these formats can be used as a 

reference when creating new frameworks for capturing design knowledge formally, such as through 

SysML. 

The fundamentals of CAD lie in the mathematical representation of physical objects. The 

mathematical representation involves creation of points, curves, surfaces and solids, manipulation through 

transformations, and storage in a standard format. Not only is the three-dimensional visualization of 

geometries an effective documentation tool, it also facilitates engineering design. For instance, CAD 

geometries are used to drive simulations such as structural, dynamic, flow behavior through FEA, CFD, 

etc. Moreover, proper selection of parameters driving the geometry is essential for satisfying design 

requirements. The car body design of automobiles and aircrafts undergo extensive surface design and 

analysis to ensure proper performance. 

Through this course, I have learnt different geometry construction techniques for curves and surfaces 

as well as their manipulation through rigid body transformations. CAD also plays an important role in 

human-computer interaction, allowing for greater immersion when creating complex designs. For 

instance, the Virtual Reality Applications Center creates an interface in which humans can intuitively 

interact with the CAD models, just as they would do in real life. Due to increasing demands placed on 

products in terms of performance, features, aesthetics and cost, more human-machine interaction will 

allow for more simulation and thereby reduce costs of prototype development. This will ultimately make 

possible more complex products possible. Thus, CAD helps in engineering design but I believe that the 

role of geometric modeling will change in the near future. 



Geometric modeling involves the creation of geometric representations of the product or system 

being designed. According to me, geometric models and geometric modeling are a part of the detailed 

design and refinement phase in the design process. It comes after the important parameters and design 

topologies are selected. This can be shown through an example. In an application that requires couplings 

between two shafts, the type of coupling needs to be selected before the important dimensions can be 

found. Consequently, geometric modeling can only begin after the topology is selected and the parameter 

values are calculated. At present, geometric modeling is a tool to express the designer’s intent of the final 

product in a model-based way. However, I believe that this will change, since the concept of CAD is now 

more focused on complete product lifecycle management and not just on detailed design and 

manufacturing. Therefore, CAD will play a more significant role during the design process, not only at 

the detailed design phase but at the conceptual design phase as well. 

Our project of modeling the geometry of a morphing BWB aircraft fits into the existing framework 

of where CAD is used in the product development cycle today. The geometry is created only after 

selecting the topology and the parameters that define the BWB wing. The parameters such as sweep, 

span, pitch angle, dihedral elevation and the decision for four wing sections (root, inboard, outboard, and 

tip) were decided before starting the CAD modeling phase. However, the parameterized CAD model is 

useful for design refinement, since the model can be updated easily by only changing the parameters. The 

CAD model can also be used in external simulation tools to perform flow and structural simulations, 

which can then be used to select optimal parameter values. The three dimensional geometry can also be 

used to conduct surface curvature analysis, an important criteria when dealing with multiple adjacent 

surfaces. 

At present, the role of CAD in engineering development is mainly in geometry creation and 

documentation. The functional specifications and design is carried out externally, usually on paper or 

spreadsheets, and the CAD models are constructed using the driving dimensions obtained from the 

design. CAD models can then be used to refine the detailed designs and then prepare drawings for 

manufacturing as well as NC code for automated manufacturing. 

I believe that CAD cannot replace human designers, but can augment the abilities of a designer to 

reduce overall time and effort spent on the design. Moreover, CAD provides a model-based environment 

for documentation of geometry and, to some extent, design through parametric and relation based models. 

The product development process should be completely integrated from cradle to grave through the use of 

models. This is possible if computer aided design is integrated throughout the PLM framework. This 

involves the use of models for requirements, design specifications, design calculations and simulations, as 

well as geometry calculation. In addition, CAD can be used to integrate different departments such as 

automatic integration with inventory management tools and other departments. The use of CAD/CAE in 

conjunction with modeling languages such as SysML promises to transform the engineering product 

development process. 

9.3 Mukul Singhee 

There are two distinct aspects of the learning that I have acquired in this course. These are 

classified under the fundamental technologies underlying the CAD, and the application of these 

technologies for engineering design. Subsequently, I evaluate the goals that I set out with at the beginning 

of the course and propose ways in which I can make use of my learning in this course for the near future. 

Fundamental Technologies 

I learned that CAD as a name encompasses those technologies that enable the definition of 

geometry, realization of a product in terms of its configuration and the space that it occupies and allows 

for the analysis and optimization of this configuration. CAD systems are based on the instancing of 

primitives or the realization of simple shapes, and subsequent combination of these instances. I learned 



that these combinations of primitives can be adequately described by construction trees which document 

the sequence of operations carried out on these primitives used to obtain the final product. A large set of 

skills that I developed in this course are due to the assignments which primarily used MATLAB 

programming. In these assignments, I learned how the instancing of primitives and subsequent operations 

can be realized. This process involved mathematical concepts of rigid body transformations which were 

implemented using homogeneous coordinates and matrix algebra. I realized that the reason for this was 

the ease of combining transformations in using matrices. One of the most difficult to understand 

fundamental aspects of the concept of rigid body transformations was the difference between global and 

local coordinate systems as references and the corresponding change in the order of multiplication of 

matrices in order to combine transformations. I realized that treating transformation matrices as a change 

of coordinates matrices solved the confusion, as I was able to relate a visual picture to the mathematical 

description of the transformation matrices and their combinations. 

The most important technical implementation that I learned about (the fundamental basis of our 

project), was the use of parametric modeling both in MATLAB and ProEngineer (or any CAD software 

for that matter). With regard to MATLAB, I learned how parametric curves and surfaces can be used to 

model shapes with the use of modular functions which connect through a set of parameters. I gained a lot 

of skill in MATLAB programming to this effect through assignments 1 through 4. Through the project, 

I learned how to make effective use of datum points, axes, coordinate systems and planes in order to 

parameterize a model. I realized that the parameterization that we achieved through MATLAB is 

implicitly already in use in CAD software, in the way the software creates curves, surfaces and 

extrusions. In particular, I became proficient in modeling Hermite, Bezier, B-Spline and NURBS 

representations of curves. An important aspect of implementing control of shapes and objects is 

continuity. I learned the theory behind G and C continuities, and was able to implement them as well 

through our homework and the mid-term examination. 

With respect to solid modeling, I realized that a solid model should be sufficiently capable of 

describing points that are inside a solid and points that are outside. The explanation for this concept can 

be best explained with solids that we can imagine in our minds but not algorithmically, or in CAD 

software. This became apparent through the first problem in HW5 where we were not able to build solid 

models out of cross-sections which had intersecting edges. This was further elucidated when we ran into 

issues in modeling the thin trailing edge of our wing for the project. The CAD software’s limitation crept 

in when we tried to create a shell of finite but negligible thickness (as compared to the airfoil’s thickness) 

I realize that the problem arises because of declared tolerances. Any geometry which has a dimension 

smaller than the tolerance defined in the CAD software is not realizable in 3-D space as a model. 

Application to Engineering Design 

In context of the design process CAD tools can be used in the conceptual design, embodiment 

design and the detail design phases. CAD models serve as the computational representation of an object 

which can be easily understood by people in different phases of product realization, such as the designers, 

the manufacturers, the assembly team, the suppliers etc. From the lectures, I learned that the primary role 

of CAD in engineering design is to model the geometrical features and constraints of a product. This 

is carried out by the geometrical modeling capabilities of CAD software. Geometric modeling plays a 

huge role in engineering design and the realization of a product. It describes the features of a product, the 

assembly involved in the product, and has the capability to provide flexibility in the geometry of its 

features and primitives. 

Assembly modeling can be done in two ways depending on the product development system 

being adopted. If distributed multi-disciplinary designers work on their own parts which later need to 

come together to form a complete product, assembly of completed part models is implemented. However, 

if a more product level approach is to be followed, the top-down approach is adopted in CAD modeling. 



I learned about the top-down approach in CAD modeling in particular from the project. We 

implemented the parameterization for the BWB morphing wing aircraft in a geometrically top-down 

approach. In tandem with the lectures, we decomposed the product into modules and defined the relevant 

interfaces between them even before we began sketching in the software. Thereafter, we defined the 

spatial layout and the datums and coordinate systems, after which we fleshed out the geometry 

progressively. I realized that approaching the design in a top-down approach helps us to build a modular 

CAD model which greatly reduces work later on in the design timeline as an changes to be made, or 

analyses to be carried out require only the change of a few parameters. The model thereby automatically 

adapts and adjusts all its parts to keep continuity. 

Goals 

The goals that I had at the beginning of the semester were to learn about the basics of CAD modeling 

and how CAD software are programmed so that they are able to realize such a wide range of 30d objects. 

With the help of the lectures and the project, I was able to achieve these goals. An additional goal that I 

had was to leverage my project in this course for my thesis work. This goal has not been realized yet, but 

I have developed some ideas with regard to the same. This has to do with our specific project, wherein I 

vision the involvement of sensors on the BWB morphing wing aircraft in order to design a system with 

interactive information flow in it. 

With the knowledge that I gained from the course, I have set a goal to develop CAD models for all 

the example problems that I use in my thesis. Having developed skills in CAD modeling, with the 

additional knowledge of its limitations, I feel that I am in a good position to accomplish this task. 


10 References 

References 

1. Irwin, D.A. and N. Pavcnik, Airbus versus Boeing revisited: international competition in the aircraft 

market. Journal of International Economics, 2004. 64(2): p. 223-245. 

2. Liebeck, R.H., Design of the blended wing body subsonic transport. Journal of Aircraft, 2004. 41(1): 

p. 10-25. 

3. Liebeck, R.H., Blended Wing Body Design Challenges, in AIAA/ICAS International Air and Space 

Symposium and Exposition: The Next 100 Years. 2003, American Institute of Aeronautics and 

Astronautics: Dayton, Ohio. p. 1-12. 

4. Jha, A.K. and J.N. Kudva. Morphing Aircraft Concepts, Classifications, and Challenges. in SPIE. 

2004. 

5. NACA Airfoil Series. 4/24/2009]; Available from: 

http://www.aerospaceweb.org/question/airfoils/q0041.shtml. 

6. Jacobs, E.N., K.E. Ward, and R.M. Pinkerton, The Characteristics of 78 Related Airfoil Sections 

from Tests in the Variable-Density Wind Tunnel 1933. 

7. The National Advisory Committee for Aeronautics (NACA). 4/24/2009]; Available from: 

http://www.centennialofflight.gov/essay/Evolution_of_Technology/NACA/Tech1.htm. 

8. Ikeda, T., Aerodynamic Analysis of a Blended-Wing Body Aircraft Configuration, in School of 

Aerospace, Mechanical and Manufacturing Engineering Science. 2006, RMIT University: 

Melbourne. p. 141. 

9. Bowlus, J.A., D. Multhopp, and S.S. Banda, Challenges and Opportunities in Tailless Aircraft 

Stability and Control. 1997, Wright Laboratory. 

10. Gano, S. and J. Renaud, Optimized Unmanned Aerial Vehicle With Wing Morphing For Extended 

Range And Endurance. 9th AIAA/ISSMO Symposium and Exhibit on Multidisciplinary Analysis 

and Optimization, Atlanta. 2002, GAAIAA-2002-5668. 

11. Viper SLA® system. 4/24/2009]; Available from: 

http://www.3dsystems.com/products/sla/viper/index.asp. 

12. Johnston, S., et al. Analysis of Mesostructure Unit Cells Comprised of Octet-truss Structures. in 

Solid Freeform Fabrication Symposium. 2006. 


Appendix 

/*****************/ 

/* for root section*/ 

/*****************/ 

Appendix 


* left 

$d113 = F2R_SPAN 

/*right 

$d135= -F2R_SPAN 

/*********************/ 

/* for inboard section*/ 

/*********************/ 

/* left 

$D1=INBOARD_SPAN_LENGTH 

/* for axis definition (to allow rotation) 

$D67 = D1 * tan(DIHEDRAL_ANGLE) 

$D69 = D1 * tan(INBOARD_SWEEP_ANGLE) 

/*right 

$D141=-INBOARD_SPAN_LENGTH 

$D142 = D141 * TAN(DIHEDRAL_ANGLE) 

$D143 = D141 * TAN(INBOARD_SWEEP_ANGLE) 

/**********************/ 

/* for outboard section*/ 

/**********************/ 

/* left 

$D34 = OUTBOARD_SPAN_LENGTH + D1 


$D77 = D34*tan(DIHEDRAL_ANGLE) 

$D76 = OUTBOARD_SPAN_LENGTH*tan(OUTBOARD_SWEEP_ANGLE) + D69 

/*right 

$D146 = -OUTBOARD_SPAN_LENGTH - D141 

/* FOR AXIS DEFINITION (TO ALLOW ROTATION) 

$D148 = D146*TAN(DIHEDRAL_ANGLE) 

$D147 = OUTBOARD_SPAN_LENGTH*TAN(OUTBOARD_SWEEP_ANGLE) + D143 

/****************/ 

/* for tip section*/ 

/****************/ 

/* left 

$D30 = tip_span_length + D34 


$D82 = D30*tan(DIHEDRAL_ANGLE) 

$D81 = TIP_SPAN_LENGTH*tan(TIP_SWEEP_ANGLE) + D76 

/*right 

$D151 = -TIP_SPAN_LENGTH - D146 


$D153 = D151*TAN(DIHEDRAL_ANGLE) 

$D152 = TIP_SPAN_LENGTH*tan(TIP_SWEEP_ANGLE) + D147 

/*****************************/ 

/* for rotations of the sections*/ 

/*****************************/ 

Appendix 


* left 

$D74 = INBOARD_PITCH_ANGLE_LEFT 

$D79 = OUTBOARD_PITCH_ANGLE_LEFT 

$D84 = TIP_PITCH_ANGLE_LEFT 

/*right 

$D144 = INBOARD_PITCH_ANGLE_RIGHT 

$D149 = OUTBOARD_PITCH_ANGLE_RIGHT 

$D154 = TIP_PITCH_ANGLE_RIGHT 

/**********************/ 

/* for winglet1 section*/ 

/**********************/ 

/* left 

$D87 = 0.6 

$D88 = 0.7 

$D94 = 0.8 

$D176 = WINGLET1_PITCH_ANGLE_LEFT 

/*right 

$D157 = -0.6 

$D156 = 0.7 

$D162 = 0.8 

$D160 = WINGLET1_PITCH_ANGLE_RIGHT 

/**********************/ 

/* for winglet2 section*/ 

/**********************/ 

/* left 

$D99 = 0 

$D96 = WINGLET2_SPAN 

$D98 = WINGLET2_SWEEP 

/*right 

$D163 = 0 

$D164 = WINGLET2_SPAN 

$D165 = WINGLET2_SWEEP 

Appendix 


Appendix 


Appendix 


Appendix 


Appendix

Parameterization of the Geometry of a Blended-Wing-Body ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?