Final Report Fixed Wing 2

1 FIGURE I-2 THE HOUSE OF QUALITY TRANSLATES THE VOICE OF THE CUSTOMER, INPUT AS CRS IN ROOM 1, INTO TARGET VALUES FOR ECS IN ROOM 8 .... The House of Quality translates customer require

REPORT AIRCRAFT DESIGN II

FIXED-WING

NO.2

CLASS GT10HK

6/2014

The main goals of subject

The project Aircraft Design 2 is the following step of Aircraft Design 1 which is carried on

by the resulting data of Aircraft Design 1 In this project, the QFD as well as the pugh matrix of the project is precisely determined Those are the foundation of the project, based on the need of the customers, the design must be the perfect product where the customer’s need meet the engineer’s requirements Besides, the project illustrates the specific calculating steps and resulting data for Stability and Performance In addition to Aircraft Design 1, those results guild the engineers to the next phase of the design

sequence, which is Detail Design.

Contents

PART I - ENGINEERING DESIGN 1

1 QUALITY FUNCTION DEPLOYMENT 1

1.1 Concept 1

1.2 The House of Quality Configurations (HOQ) 1

1.3 Steps for Building a House of Quality 3

1.4 Quality Function Development was applied to our project “Fixed Wing 2 seats” 5

2 Evaluation Method 9

2.1 Pugh concept selector method 9

2.2 Analytic Hierarchy Process (AHP) method 13

PART II - STABILITY 17

1 A brief of stability 17

2 Introduction 17

2.1 Geometry parameters 17

2.2 Layout 17

3 Static stability and control 19

3.1 Static stability and control 19

3.2 Longitudinal control 23

3.3 Sensitivity Analyses 24

3.4 Directional control 26

3.5 Aileron control 29

3.6 Table of comparison between the same class aircrafts 29

4 Equations of motion 30

4.1 Estimation of 𝐶 𝐷𝑝 30

4.2 Longitudinal stability derivative coefficients 35

4.3 Lateral stability derivative coefficients 36

4.4 Prediction of inertia moments 37

4.5 Longitudinal derivatives 37

4.6 Lateral directional derivatives 38

5 Dynamic stability 39

5.1 Longitudinal dynamic stability 39

5.2 Directional dynamic stability 41

5.3 Lateral dynamic stability 42

6 Transfer Functions 44

6.1 Short-Period Dynamics 44

6.2 Long-period Dynamics 47

6.3 Roll Dynamic 50

6.4 Dutch-roll Approximation 52

PART III - PERFORMANCE 59

1 Steady Flight 59

1.1 Thrust required (Drag) 59

1.2 The fundamental parameters: Thrust-To-Weight Ratio, Wing Loading, Drag Polar, and Lift-To-Drag Ratio 60

1.3 Power required and Power available 61

1.4 Calculation of Stalling Velocity: Role of (C L )max 62

1.5 Rate of climb 64

1.6 Gliding (Unpowered) Flight 65

1.7 Service and Absolute ceilings 66

1.8 Time to climb 67

1.9 Range 68

1.10 Endurance 69

2 Accelerated Flight 69

2.1 LEVEL TURN 69

2.2 THE V-n DIAGRAM 70

2.3 ENERGY CONCEPTS: ACCELERATED RATE OF CLIMB 73

3 TAKEOFF PERFORMANCE 76

3.1 Calculation of Ground Roll 78

3.2 Calculation of Distance While Airborne to Clear an Obstacle 79

4 LANDING PERFORMANCE 80

REFERENCES 83

APPENDIX 83

List of Figures

FIGURE I-1 DIAGRAM SHOWING THE FOUR HOUSES OF THE COMPLETE QFD PROCESS 1

FIGURE I-2 THE HOUSE OF QUALITY TRANSLATES THE VOICE OF THE CUSTOMER, INPUT AS CRS IN ROOM 1, INTO TARGET VALUES FOR ECS IN ROOM 8 2

FIGURE I-3 THE MINIMAL HOQ TEMPLATE INCLUDES ROOMS 1, 2, 4, AND 5 3

F IGURE I-4 R OOF OF HOQ 4

FIGURE I-5 CUSTOMER REQUIREMENTS OF HOQ LEVEL 1 6

F IGURE I-6 E NGINEERING C HARACTERISTICS OF HOQ LEVEL 1 7

FIGURE I-7 SHOWS DIRECT DECOMPOSITION OF A AEROBATIC TWO-SEAT LIGHTPLANE INTO SUBASSEMBLIES 10

FIGURE I-8 HIERARCHICAL STRUCTURE OF THE SCOOTER 14

F IGURE II-1 W ING CONTRIBUTION TO THE PITCHING MOMENT 19

FIGURE II-2 THE LIFT CURVE OF NACA 4415 AIRFOIL 19

F IGURE II-3 A FT TAIL CONTRIBUTION TO THE PITCHING MOMENT 20

FIGURE II-4 THE LIFT CURVE OF NACA 0012 AIRFOIL 20

F IGURE II-5 F USELAGE CONTRIBUTION – E STIMATE 𝐶𝑚0𝑓 21

FIGURE II-6 FUSELAGE CONTRIBUTION – ESTIMATE 𝐶𝑚𝛼𝑓 22

FIGURE II-7 WING BODY INTERFERENCE FACTOR 27

FIGURE II-8 CUTOFF REYNOLDS NUMBER 31

FIGURE II-9 TURBULENT MEAN SKIN-FRICTION COEFFICIENT ON AN INSULATED FLAT PLATE – ESTIMATE 𝐶 𝑓𝑤 32

FIGURE II-10 WING-BODY INTERFERENCE CORRELATION FACTOR 33

FIGURE II-11 TURBULENT MEAN SKIN-FRICTION COEFFICIENT ON AN INSULATED PLAT PLATE – ESTIMATE 𝐶 𝑓𝐻 AND 𝐶 𝑓𝑉 34

FIGURE III-1 THRUST REQUIRE CURVE AT 3000M 60

FIGURE III-2 THE POWER REQUIRE CURVE AND THE POWER AVAILABLE AT 3000M 62

FIGURE III-3 THE 𝑉 − 𝑛 DIAGRAM FOR A TYPICAL JET TRAINER AIRCRAFT FREE-STREAM VELOCITY 𝑉∞ IS GIVEN IN KNOTS 72

F IGURE III-4 T HE 𝑉 − 𝑛 D IAGRAM 73

FIGURE III-5 OVERLAY OF 𝑃 𝑠 CONTOURS AND SPECIFIC ENERGY STATES ON AN ALTITUDE-MACH NUMBER MAP THE 𝑃 𝑠 VALUES SHOWN HERE APPROXIMATELY CORRESPOND TO A LOCKHEED F-104G SUPERSONIC FIGHTER LOAD FACTOR 𝑛 = 1 AND 𝑊 = 18,000 𝑙𝑏 AIRPLANE IS AT MAXIMUM THRUST THE PATH GIVEN BY POINTS A THROUGH I IS THE FLIGHT PATH FOR MINIMUM TIME TO CLIMB 76

F IGURE III-6 I LLUSTRATION OF GROUND ROLL 𝑠𝑔, AIRBORNE DISTANCE 𝑠𝑜, AND TOTAL TAKEOFF DISTANCE 77

FIGURE III-7 SKETCH FOR THE CALCULATION OF DISTANCE WHILE AIRBORNE 79

FIGURE III-8 THE LANDING PATH AND LANDING DISTANCE 81

List of Tables T ABLE I-1 R ELATIVE WEIGHTING OF HOQ LEVEL 1 8

TABLE I-2 RELATIVE WEIGHTING OF HOQ LEVEL 2 8

TABLE I-3 RELATIVE WEIGHTING OF HOQ LEVEL 3 9

TABLE I-4 PUGH MATRIX OF WING 10

TABLE I-5 PUGH MATRIX OF TAIL 11

T ABLE I-6 D ECISION MATRIX OF ENGINES 11

TABLE I-7 PUGH MATRIX OF LANDING GEAR 12

TABLE I-8 PUGH MATRIX FOR EACH CONCEPT 13

TABLE I-9 MATRIX C 14

TABLE I-10 MATRIX CONSISTENCY AND CR VALUE 14

T ABLE I-11 D ECISION MATRIX 15

TABLE I-12 EXPLAINING TABLE FOR DECISION MATRIX 15

T ABLE II-1 C OMPARISON BETWEEN THE SAME CLASS AIRCRAFTS 29

TABLE II-2 SHORT-PERIOD TRANSFER FUNCTION APPROXIMATIONS 44

TABLE II-3 LONG-PERIOD TRANSFER FUNCTION APPROXIMATIONS 48

T ABLE II-4 D UTCH - ROLL TRANSFER FUNCTION APPROXIMATIONS 52

Part I - ENGINEERING DESIGN

1 QUALITY FUNCTION DEPLOYMENT

1.1 Concept

Quality function deployment (QFD) is a planning and team problem-solving tool that has been adopted by a wide variety of companies as the tool of choice for focusing a design team’s attention on satisfying customer needs throughout the product development process

The QFD process is known as a methodology for infusing the voice of the customer into every aspect of the design process The House of Quality translates customer requirements into quantifiable design variables, called engineering characteristics This mapping of customer wants to engineering characteristics enables the remainder of the design process More information can be interpreted from the House of Quality It can also be used to determine which engineering characteristics should be treated as constraints for the design process and which should become decision criteria for selecting the best design concept

Figure I-1 Diagram showing the four houses of the complete QFD process

1.2 The House of Quality Configurations (HOQ)

The HOQ takes information developed by the design team and translates it into a format that is more useful for new product generation This text uses an eight-room version of the House of Quality as shown in Fig 2

 Room 1: Customer Requirements “WHAT” from users and customer (CRs)

 Room 2: Engineering Characteristics “HOW” from engineering (Ecs)

 Room 3: Correlation Matrix means relationship of engineering characteristics

 Room 4: Relationship Matrix “Whats related to Hows”

 Room 5: Importance Ranking for decision what is the most important in WHATs

 Room 6: Customer Assessment Of Competing Products

 Room 7: Technical Assessment

 Room 8: Target Values

Figure I-2 The House of Quality translates the voice of the customer, input as CRs in Room 1,

into target values for ECs in Room 8

The end result of the HOQ is the set of target values for ECs that flow through the HOQ and exit at the bottom of the house in Room 8 This set of target values guides the selection and evaluation of potential design concepts Note that the overall purpose of the HOQ process is broader than establishing target values

The HOQ will become one of the most important reference documents created during the design process Like most design documents, the QFD should be updated as more information is developed about the design

1.3 Steps for Building a House of Quality

Figure I-3 The Minimal HOQ Template includes Rooms 1, 2, 4, and 5

Room 1: Customer Requirements

Customer requirements are listed by rows in Room 1 The CRs and their importance ratings are gathered by the team in design process Also included in this room is a column with an importance rating for each CR The ratings range from 1 to 5, importance ratings

of 4 and 5

Room 2: Engineering Characteristics

Engineering characteristics are listed by columns in Room 2 ECs are product performance measures and features that have been identified as the means to satisfy the

CRs One basic way is to look at a particular CR and answer the question, “What can I control that allows me to meet my customer’s needs?”

ECs are measurable values (unlike the CRs) and their units that are placed near the top of Room 2 Symbols indicating the preferred improvement direction of each EC are placed at the top of Room 2 Thus a  symbol indicates that a higher value of this EC is better, and a  symbol indicates that a lower value is better It is also possible that an EC will not have an improvement direction

Room 4: Relationship Matrix

The relationship matrices at the center of an HOQ Each cell in the matrix is marked with

a symbol that indicates the strength of the causal association between the EC of its column and the CR of its row Rules include significantly (9), moderately (3), or slightly (1) The cell is left blank if the EC had no impact on the CR

Rules:

Significantly 

Room 5 Importance Ranking of Ecs

Absolute importance is calculated in two steps First multiply the numerical value in each

of the cells of the Relationship Matrix by the associated CR’s importance rating Then, sum the results for each column, placing the total in Room 5a Relative importance (Room 5b) is the absolute importance of each EC, normalized on a scale from 1 to 0 and expressed as a percentage of 100 Rank order of ECs (Room 5c) is a row that ranks the ECs’ Relative Importance from 1 (highest % in Room 5b) to 10 This ranking allows viewers of the HOQ to quickly focus on ECs in order from most to least relevant to satisfying the customer requirements

The Correlation Matrix or Roof of the House of Quality

The correlation matrix shows the degree of interdependence among the engineering characteristics in the “roof of the house.”

Figure I-4 Roof of HOQ

Assessment of Competitor’s Products in House of Quality

In Room 6, Competitive Assessment, a table displays how the top competitive products rank This information comes from direct customer surveys, industry consultants, and marketing departments

Room 7 in the lower levels of the House of Quality provides another area for the comparison to competing products Room 7, Technical Assessment, is located under the Relationship Matrix Technical Assessment data can be located above or below the Importance Ranking sections of Room 5

Setting Target Values for Engineering Characteristics

Room 8, Setting Target Values, is the final step in constructing the HOQ By knowing which are the most important ECs (Room 5), understanding the technical competition (Room 7), and having a feel for the technical difficulty (Room 7), the team is in a good position to set the targets for each engineering characteristic

1.4 Quality Function Development was applied to our project “Fixed Wing 2 seats”

1.4.1 House of Quality level 1

Customer Requirement

Nowadays, the aviation industry have developed more than ever The first and crucial step in building an aircraft is to determine the requirements of customers through surveys There are several requirements come from the customers in designing a 2-seat aerobatic aircraft

 Endurance: Since aircraft is a high-speed transportation, this is the first quality of

the aircraft that the customers concern about High-speed saves time hence endurance is one of the most vital specifications of one airplane

 Control: In a light-weight aircraft, the customers are mostly the pilots In other to

approach a wide range of customer, the supplier have to make their product as controllable as possible

 Price: This is a classical criterion in every single industry, aviation is not an

exception

 Economics: The word “Economics” here is used to mention about the cost of

operating, repair and the ability to make profit of the airplane

 Aesthetics: One of the most important factors of an aircraft

 Safe: Moving too fast at such a high attitude makes aircraft have to be absolutely

safe, one small error can lead to catastrophic consequences

 Comfort: This is the factor contributes considerably to the competitiveness of the

product

 Range: Long range is one of the advantages of aircraft, one of the vital factors that

will be considered when customer want to buy some kind of aircraft

 Reliability

Figure I-5 Customer Requirements of HOQ level 1

After obtaining the customers requirements through several surveys, the design engineer have to draw out a set of technical specifications in other to meet with those requirements Every single specification in The House of Quality Level 1 will become the Requirements in The House of Quality level 2

Engineering Characteristics of House of Quality level 1

In other to carry out the mission in operation of an aircraft, some specifications have to

be draw out :

 Cruise Speed : the ability to move fast in a short period of time for the user

 Fuel Consumption : The amount of fuel used to maintain the mission, an aircraft

with a small SFC is definitely financially beneficial and competitive on the market

 Engine : significantly effects the operation of an aircraft

 Operating Cost : Economical Aspects are concerned with care when the project is

conducted

 Ceiling : the maximum attitude one aircraft is able to reach

 Payload : Crucial factor, depends on the purpose of the product

Engineering features bring the benefit to manufacture such like

 Maintenance: affects economical efficiency of the aircraft

 Manufacturing: give benefit to manufacture

Some of the specifications that effect directly to the customers usage

 Stability – Maneuverability: The compensation between these two values has to be

adjusted to the purpose of the airplanes, mission specifications of the project make

a big influence to this trade

Some social and environmental factors:

 Pollutant: Environmental criteria must be satisfied in order to bring the aircraft to

the commercial market

 Noise: this is included in the concept of “Environmental criteria”

Figure I-6 Engineering Characteristics of HOQ level 1

Through the QFD level 1 expressed in the attached Excel file, we can figure out the Relative Weights

Table I-1 Relative weighting of HOQ level 1

Cruise Speed Payload Empty Weight Fuel

1.4.2 House of Quality level 2

The design will become more specific as we conduct the HOQ 2 Specifications in HOQ1 will become Requirements in HOQ2

In this stage, the role of geometric parameters of the aircraft is very important These parameters effects considerably to aerodynamic aspects such as lift, drag and control The preliminary parameters is the basis of the design optimization process

 Wing’s Aspect Ratio

 Wing's Taper Ratio

 Wing's area

 Tail's Aspect Ratio

 Tail's Taper Ratio

 Tail's Area

 Vertical stability's area

 Vertical stability's Aspect Ratio

 𝑆𝑎/𝑆𝑤 Aileron

 𝑆𝑟/𝑆_𝑣 Rudder

 𝑆𝑒/𝑆ℎ Elevator

 𝑉ℎ và 𝑉𝑣

Otherwise, some feature affect to design process later

 Take off weight

 Coefficient of 𝐿𝑖𝑓𝑡/𝐷𝑟𝑎𝑔

 Coefficient of initial drag CD0

In the end of level 2, we will find out the factors that influence the parameters in level 1

Table I-2 Relative Weighting of HOQ level 2

Wing’s Aspect Ratio

Tail’s aspect ratio

Tail’s Taper Ration

Lift/Drag

1.4.3 House of Quality level 3

Because this is the preliminary design process, the QFD will end with some basic set of geometric parameters of the aircraft:

 Wing's Chord

 Wing's Span

 Tail's Chord

 Tail's Span

 Vertical stability's Chord

 Vertical stability's Span

 Distance from wing's CG to tail's

Table I-3 Relative Weighting of HOQ level 3

Wing’s Span Tail’s Chord Tail’s Span Thrust-Power

In brief, by QFD Process, we have important characteristics needing in the design

In fact, tail, wing and power are indispensable characteristics making the safe and stability for the aircraft

2.1.2 Steps of building the pugh matrix

Step 1: Choose the criteria by which the concepts will be evaluated

The QFD is the starting place from which to develop the criteria, the criteria will

be based on the engineering characteristics listed in the columns of the House of Quality

Step 2: Formulate the decision matrix

The criteria are entered into the matrix as the row headings The concepts are the column headings of the matrix

Step 3: Clarify the design concepts

The goal of this step is to bring all members of the team to a common level of understanding about each concept If done well, this will also develop team “ownership”

in each concept

Step 4: Choose the datum concept

One concept is selected by the team as a datum for the first round This is the reference concept with which all other concepts are compared The column chosen as datum is marked accordingly, DATUM

Step 5: Run the matrix

It is now time to do the comparative evaluation Each concept is compared with the datum for each criterion A three-level scale is used At each comparison we ask the

question, is this concept better (=), worse (-), or about the same (=) as the datum Same (=) means that the concept is not clearly better or worse than the datum

Step 6: Evaluate the ratings

Once the comparison matrix is completed, the sum of the +, -, and =ratings is determined for each concept While it is appropriate to take a difference between the+ score and the - scores, be careful about rejecting a concept with a high negative score without further examination

Step 7: Establish a new datum and rerun the matrix

The next step is to establish a new datum, usually the concept that received the highest rating in the first round, and run the matrix again

Step 8: Examine the selected concept for improvement opportunities

2.1.3 Decomposition in the Physical Domain

Figure I-7 Shows Direct decomposition of a Aerobatic two-seat lightplane into subassemblies

2.1.4 Pugh matrix of main components

Trapezoi d- Unswept- NonDiher

al Wing

Trapezoi d-Swept- Diheral Wing

Trapezoi d-Swept- NonDiher

al Wing

Rectangul ar- Unswept- Diheral Wing

Rectangul ar- Unswept- NonDihera

l Wing

Rectangul ar-Swept- Diheral Wing

Rectangul ar-Swept- NonDihera

Sum of "-" 3 3 2 3 2 2 3

The trapezoid wing is definitely a better design than the conventional one due to the decreasing of twisting force occurring on the wing during operation Despite the structural advantage, there are some drawbacks with this design, such as difficulties in manufacturing, higher cost makes it less competitive on the market

The swept wing design gives us higher lift/drag ratio since the swept angel decreases the perpendicular velocity of the airspeed Even though swept wing gives lower drag and lift coefficients but higher L/D ratio But like the trapezoid wing, the difficulties in manufacturing, operating and maintenance are significant

The dihedral design is applied when the designer require a more stable aircraft In civil aircraft designs, stability is one of the most crucial factors due to passenger’s comfort, dihedral design is mostly used

In this evaluation process, it is plain to see that the trapezoid-unswept-dihedral Wing is the best design It is not only fits the engineering criteria but also meets the customer requirements, it is available both technically and financially

- Tail

Table I-5 Pugh matrix of tail

Pugh matrix of concept Fuselage mounted Cruciform T-tail

The fuselage mounted design for tailwing of aircraft has a considerable advantage

is that it is cheap to manufacture , repair or replace, but still maintain the basic requirements concern with stability, aerodynamic aspects ( such as L/D ratio) and operating criteria (such as speed) Hence, the fuselage mounted design for tailwing is chosen to be the most ideal design in our design project

- Engine

Table I-6 Decision matrix of engines

Pugh matrix of concept Piston Engines Turboprop Engine

Base on the customer requirements and the mission specifications of the aircraft,

a piston driven propeller aircraft is adequate for the project

- Landing Gear

Table I-7 Pugh matrix of landing gear

Pugh matrix of concept Retractable Unretractable

Table I-8 Pugh matrix for each concept

Result: It is obviously that the concept 2 may be considered to the best solution because

it has the most pluses

Concept 2: rectangle, unswept, dihedral wing + fuselage mounted tail+ retractable landing gear + piston engine

2.2 Analytic Hierarchy Process (AHP) method

2.2.1 Concepts

AHP is a decision analysis tool that is used throughout a number of fields in which the selection criteria used for evaluating competing solutions that do not have exact, calculable outcomes

2.2.2 AHP process

2.2.3 AHP Process for Determining Criteria Weights

 Complete criteria comparison matrix [C] using 1–9 ratings

 Normalize the matrix [C] to give [Norm C]

 Average row values This is the weight vector {W}

 Perform a consistency check on [C]

 Calculate weighted sum vector, {𝑊𝑠} = [𝐶] × {𝑊}

Figure I-8 Hierarchical structure of the scooter

2.2.4 AHP of “Aerobatic two-seat lightplane” design

Table I-9 Matrix C

The weighting factor of each parameter has a little bit difference with the original because we apply AHP analysis for this problem

Decision matrix for aerobatic two-seat lightplane design

Table I-11 Decision matrix

Design

criterion

Weigh factor

Result: The choosen design is concept 3 because the total value of this design

is the largest value (0.384) It is the same with Pugh matrix method for each concept

This below table is explanation for decision matrix

Table I-12 Explaining table for decision matrix

Part II - STABILITY

1 A BRIEF OF STABILITY

Necessary condition for an airplane to fly is that airplane must be able to achieve equilibrium flight and it must have the capatibility to maneuver for a wide range of flight velocities and altitudes

Stability is a property of equilibrium state It means that the airplane has tendency

to return to its equilibrium state after displacement from equilibrium point The disturbance can be generated by pilot’s actions or atmospheric phenonmena The atmospheric disturbances can be wind gusts, wind gradients, or turbulent air

However, stability and control are two conditions that is contradicted It means that the more stability aircraft has, the less control it gets, and vice versa Stability is identified at a trim condition, i.e the resultant force as well as resultant moment about CG must both be equal to zero On the other hand, if the forces and moments do not sum to zero, the airplane will be subjected to translational and rotational accelerations

Static Stability: the tendency that the airplane returns to trimed condition after

disturbance

Dynamic Stability: concerned with the time history of the motion of the airplane

after it is disturbed from its equilibrium point during flight

3 STATIC STABILITY AND CONTROL

3.1 Static stability and control

𝑖𝑤 = 2𝑜

Wing airfoil NACA 4415

Figure II-2 The lift curve of NACA 4415 Airfoil

𝑅𝑒 = 𝑉𝑐𝑟𝑢𝑖𝑠𝑒𝑐̅𝑤

55 × 1.25871.86 × 10−5 = 3.7 × 106

𝑥𝐴𝐶𝑐̅ )

𝐶𝑚

𝛼𝑤 = 𝐶𝐿

𝛼𝑤(𝑥𝐶𝐺𝑐̅ −

𝑥𝐴𝐶𝑐̅ )

3.1.2 Aft tail contribution

Figure II-3 Aft tail contribution to the pitching moment

Tail airfoil NACA 0012

Figure II-4 The lift curve of NACA 0012 Airfoil

𝑅𝑒 = 𝑉𝑐𝑟𝑢𝑖𝑠𝑒𝑐̅𝑡

55 × 0.65091.86 × 10−5 = 1.92 × 106

𝑏𝑡 = 2.6 𝑚

y = 0.1133x - 0.0101 R² = 0.9988

0𝑡 = 𝜂𝑡 × 𝑉𝐻 × 𝐶𝐿

𝛼𝑡 × (𝜀0+ 𝑖𝑤 − 𝑖𝑡) = 0.1025 Aft tail contribution to 𝐶𝑚𝛼

𝑥=𝑙𝑓

𝑥=0

Figure II-5 Fuselage contribution – Estimate 𝑪𝒎𝟎𝒇

where 𝑙𝑓/𝑑𝑚𝑎𝑥 = 5.5/1.1713 = 4.7, from the figure, we have 𝑘2− 𝑘1 = 0.8

𝑥𝐴𝐶𝑐̅ ) → 𝐶𝑚0𝑤 = 𝐶𝑚

𝑎𝑐𝑤 = −0.09

𝐶𝑚

𝛼𝑤 = 𝐶𝐿

𝛼𝑤(𝑥𝐶𝐺𝑐̅ −

𝑥𝐴𝐶𝑐̅ ) → 𝐶𝑚

𝛼𝑤 = 0 Aft tail contribution

0𝑡 = 0.1025

𝐶𝑚𝛼𝑡 = −0.9776 𝑟𝑎𝑑−1Fuselage contribution

𝛼𝑡𝑟𝑖𝑚𝑝𝑖𝑡𝑐ℎ = −𝐶𝑚0

𝐶𝑚𝛼 = 1.37 Comment: 𝐶𝑚0 and 𝐶𝑚𝛼 satisfy the requirements of static stability Because the alpha trim pitch angle is 1.37 degree that is close to i_w = 2 degree Therefore, CG = 25%𝑐𝑤 is the design point

3.1.5 Stick fixed neutral point

Rear limit – ignore the influence CG movement on VH and set 𝐶𝑚𝛼 = 0

From the figure, we have 𝜏𝑒 = 0.4

𝐶𝑚

0𝑡 = 0.1025

Wing Aspect Ratio

Comment: If we increase AR, trim angle of attack (𝛼𝑡𝑟𝑖𝑚𝑝𝑖𝑡𝑐ℎ) and elevator angle to trim (𝛿𝑒𝑡𝑟𝑖𝑚) decrease rapidly whereas alpha trim angle (𝛼𝑡𝑟𝑖𝑚) remains constant

Comment: If we increase wing area, trim angle of attack (𝛼𝑡𝑟𝑖𝑚𝑝𝑖𝑡𝑐ℎ) and alpha trim angle (𝛼𝑡𝑟𝑖𝑚) remain constant whereas elevator angle to trim (𝛿𝑒𝑡𝑟𝑖𝑚) increase

Comment: If we increase 𝑙𝑡, trim angle of attack (𝛼𝑡𝑟𝑖𝑚𝑝𝑖𝑡𝑐ℎ) and elevator angle to trim (𝛿𝑒𝑡𝑟𝑖𝑚) increase whereas alpha trim angle (𝛼𝑡𝑟𝑖𝑚) remain constant

Comment: If we increase tail area as well as tail aspect ratio, both trim angle of attack (𝛼𝑡𝑟𝑖𝑚𝑝𝑖𝑡𝑐ℎ) and elevator angle to trim (𝛿𝑒𝑡𝑟𝑖𝑚) increase whereas alpha trim angle (𝛼𝑡𝑟𝑖𝑚) remains constant This means that alpha_trim is independent of tail area and tail aspect ratio

Tail Aspect Ratio

- 𝑘𝑛 an empirical wing-body interference factor that is a function of the fuselage geometry

𝑥𝑚 = 1.9456 𝑚; 𝑙𝑓𝑠 = 5.5 𝑚; 𝑥𝑚

𝑙𝑓𝑠 = 0.3537; 𝑆𝑓𝑠 = 3.3035 𝑚

2; 𝑙𝑓𝑠2

Figure II-7 Wing body interference factor

- 𝑘𝑅𝑙 an empirical correction factor that is a function of the fuselage Reynolds number

𝜈 = 1.86 × 10−5 𝑚2𝑠−1; 𝑙𝑓𝑠 = 5.5 𝑚; 𝑉𝑐𝑟𝑢𝑖𝑠𝑒 = 55 𝑚/𝑠

𝑅𝑒 = 𝑉𝑐𝑟𝑢𝑖𝑠𝑒𝑙𝑓𝑠

55 × 5.51.86 × 10−5 = 16.2 × 106From the graph, we infer 𝑘𝑅𝑙 = 1.56

= −0.48 × 10−3 deg−1 = −0.0275 Comment: Cnβwf ≈ 0 và < 0, so the contribution of wing and fuselage to directional stability is insignificant and they make aircraft become instable

- 𝑉𝜐 is the vertical tail volume ratio

𝑉𝜐 = 𝑙𝜐𝑆𝜐

𝑆𝑤𝑏𝑤 =

2.9554 × 0.73179.67 × 7.62 = 0.0293

- 𝜂𝜐(1 + 𝑑𝜎/𝑑𝛽) is the combined sidewash and tail efficiency factor

𝑧𝑤 = 0.2761 𝑚 The distance, parallel to the z axis, from wing root

quarter chord point to fuselage centerline

𝜂𝜐(1 +𝑑𝜎

𝑑𝛽) = 0.724 + 3.06 ×

0.73179.67

1 + cos 0𝑜 +0.4 × 0.2761

0.9614 + 0.009 × 6 = 1.0086

𝑅𝑒 = 𝑉𝑐𝑟𝑢𝑖𝑠𝑒𝑐̅𝑓

55 × 0.78921.86 × 10−5 = 2.33 × 106

𝐶𝑛𝛽 > 0 The aircraft has directional stability

3.5 Aileron control

𝑆𝑎

𝑆𝑤 =

0.56449.67 = 0.0583

From the graph, we infer 𝜏𝑎 = 0.19

3.6 Table of comparison between the same class aircrafts

Table II-1 Comparison between the same class aircrafts

Our Aircraft Cessna 172S Cessna 150 Brezzer

𝑊𝐵 = zero-lift drag coefficient due to contribution of wing and fuselage

- 𝐶𝑓𝑊 = drag coefficient of flow over wing airfoil

𝑐̅𝑤 = 1.2587 𝑚 = 49.555 𝑖𝑛𝑐ℎ𝑒𝑠 Choose 𝑘 = 0.16 × 10−3𝑖𝑛𝑐ℎ𝑒𝑠

Figure II-8 Cutoff Reynolds Number

From the graph, we infer 𝑅𝑙 = 2.9 × 10−7

Figure II-9 Turbulent Mean Skin-Friction Coefficient on an Insulated Flat Plate – Estimate 𝑪𝒇𝒘

From the graph, we infer 𝐶𝑓𝑊 = 0.0025

𝑙𝐵 = 5.5 𝑚 = 216.54 Choose 𝑘 = 0.16 × 10−3𝑖𝑛𝑐ℎ𝑒𝑠

- (𝑆𝑆)𝑒/𝑆𝑅𝐸𝐹 = (2 × 3.3035 + 2 × 3.54)/9.67 = 1.415

𝑑 = √1.2696

0.02542/0.7854 = 50.0558 𝑖𝑛𝑐ℎ𝑒𝑠 = 1.2714 𝑚

- 𝑅𝑊𝐵 = 0.93 with 𝑅𝑒𝑙𝑓𝑢𝑠 = 1.1 × 108 according to the following graph

Figure II-10 Wing-body Interference Correlation Factor

-

𝐶𝐷𝑏 =0.029 (

𝑑𝑏

𝑑 )3

√(𝐶𝐷𝑓)

𝑏where 𝑑𝑏/𝑑 = 0.3768/1.2714 = 0.2987

𝑏 = 𝐶𝑓𝐵

(

1 + 60(𝑙𝑑𝐵)

3+ 0.0025 (𝑙𝐵

𝑑))

𝐶𝑓𝐻 = 0.00395; 𝐶𝑓𝑉 = 0.0038 Airfoil of vertical tail and aft tail are NACA 0012 → 𝑡 = 0.12𝑐̅ tại 0.4𝑐̅ → 𝐿 = 1.2

Vertical tail and aft tail are non-swept, we obtain

𝑆𝑅𝐸𝐹

= 0.00395(1 + 1.07 × 0.12 + 100 × 0.124) × 1.07 ×2 × 1.02 × 1.6924

9.67

= 0.0017 (𝐶𝐷0)

𝑉 = 𝐶𝑓𝑉(1 + 𝐿 (𝑡

𝑐) + 100 (𝑡

𝑐)

4) (𝑅𝐿𝑆)𝑉×(𝑆𝑤𝑒𝑡)𝑉