METU, Ankara A DESIGN OPTIMIZATION

4. ANKARA INTERNATIONAL AEROSPACE CONFERENCE 10-12 September, 2007 - METU, Ankara

AIAC-2007-073

A DESIGN OPTIMIZATION APPROACH FOR AN UNMANNED AIRCRAFT WITH A CONSTRAINED PROPULSION SYSTEM, WING SPAN AND TAKE-OFF DISTANCE Miraç K. AKSUGÜR *, B. Gürdal TUGAY †, Mehmet Ş.KAVSAOĞLU‡ and Melike NİKBAY§ Istanbul Technical University Faculty of Aeronautics and Astronautics

Istanbul, Turkey

ABSTRACT For a given propulsion system, pre-defined wingspan and take-off distance, an unmanned air vehicle is designed for the Air Cargo Challenge Design/Build/Fly Contest, which is organized by A.P.A.E. (Portuguese Association of Aeronautics and Space). Achieving the lightest aircraft and carrying largest amount of payload is the key for the success under the given constraints. In this paper, the design approach and the optimization problems that occur during the conceptual design are investigated to get the optimum empty and take-off weights while being capable to do the pre-defined mission profile. The design methodology started with the determination of the thrust with the given propulsion system. After the determination of thrust, the satisfaction of the pre-defined take-off distance and level flight requirements drive the design. As a result of this optimization process, we found a W o and S pair that satisfies the predefined take-off distance and level flight requirements. Later design studies show us that minimizing the aircraft’s drag and maximizing the lift is the way for the goals. To minimize the aircraft’s drag two components are selected to be optimized; one of them is the fuselage length and the other one is the tail geometry. These parameters build up the optimization problem. For a given wing span, take off distance and thrust, finding the optimum fuselage length which minimizes the drag is the main goal of the optimization problem. Equations for determining the parameters put into a spreadsheet file and several sequence of design variables are tabulated and evaluated in the spreadsheet file with the help of multi objective optimization software. A detailed explanation, derived equations and optimization algorithm are included. NOMENCLATURE Symbol AR

Definition Aspect Ratio of Wing

Symbol

AReff ARht

Effective Aspect Ratio for Biplanes Horizontal Tail Aspect Ratio

k2-k1 KA

α

Angle Of Attack

KT

at

l

b

Lift Curve Slope of Horizontal Tail with 3-D effects Lift Curve Slope of Wing with 3-D effects Span of Wing

bht Symbol

Span of Horizontal Tail Definition

aw

*

ηt

M µ µ Symbol

Definition Dynamic Pressure Ratio at the Horizontal Tail Apparent Mass Coefficient A coefficient contains aerodynamic terms A coefficient contains thrust terms Length of component Mach Number Ground Friction Dynamic Viscosity of the Air Definition

Undergraduate Student research assistant, ITU Control and Avionics Laboratory, Email: [email protected] Graduate Student, Email: [email protected] ‡ Professor and Chair person in Aeronautical Engineering Department, Email: [email protected] § Assistant Professor in Astronautical Engineering Department, Email: [email protected]

†

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Cmean.wing or Cw

AKSUGÜR,TUGAY,KAVSAOĞLU,NİKBAY

Cht

Wing Mean Aerodynamic Chord Length Horizontal Tail Mean Aerodynamic Chord Length Horizontal Tail Root Chord Length Zero Lift Drag Coefficient Miscellaneous Drag Coefficient(such as Landing Gear and Strut Zero Lift Drag Coefficient) Flat plate Skin Friction Coefficient(for each component) Horizontal Tail Volume Coefficient

CL CLcruise

Lift Coefficient of Aircraft Lift Coefficient of Aircraft at cruise

T tarm

CLmax.

Maximum Lift Coefficient of Aircraft

t/c

Cm

Moment Coefficient of the Fuselage Frontal Diameter of Component Total Drag of the Aircraft

Qc

Cmean.ht Croot,h.t. CD0 CDmisc.

Cfc

d D D0

N0 R

Reynolds Number

r S or Sw Sht

Shorterwinglift / longerliftwinglift Wing Area Horizontal Tail Area

Swetc

Wetted Area of the component

Sref

Reference Area (2 Times of Wing area for bi-plane) Thrust Length of the Fuselage between the mean wing’s quarter of mean aerodynamic chord up to the horizontal tail’s quarter of mean aerodynamic chord Maximum thickness of the airfoil with respect to mean aerodynamic chord of the component Interference Factor of the component Cruise Velocity Final Velocity of Aircraft at the end of Ground Roll Initial Velocity of Aircraft at the beginning of Ground Roll Maximum Take-Off Weight Interference Factor Air Density Dynamic Pressure Chord wise Location of the Airfoil maximum thickness point Aerodynamic center of the wing with respect to mean aerodynamic chord length Center of Gravity Location of the Aircraft

V or Vcruise Vf

f FFc

Zero Lift (Parasite) Drag of the Aricraft Induced Drag of the Aircraft Oswald Efficiency Factor Downwash Angle Fineness Ratio of Component Form Factor of Component

g

Gravitational Acceleration

xac

h

Height of endplates

xc.g.

Di e

ε

Neutral Point of the Aircraft

Vi W,W 0 ξ ρ q (x/c)m

INTRODUCTION Students from Istanbul Technical University are participating in AIAA Design/Build/Fly Competition for five years. This competition aims design, manufacture and radio controlled fly of a different aerial vehicle in each year that all stages are made by the aeronautical and astronautical engineering students. From design phase up to final representation of the aerial vehicle, students gain knowledge, experience and spirit of the teamwork. As a result, these projects prepare experienced engineers for companies, who know the requirement of a project, stages of the project, developing solution techniques for the problems between designed and manufactured vehicles, etc. On the other hand, these projects show the trend of the aerial vehicle in the unmanned vehicle’s market, because the rules are determined by the well known and companies and the competition administration. th In 2006, Istanbul Technical University took 5 place in the competition of AIAA Design/Build/Fly, the best place for a Turkish team has ever taken. This and similar achievements are improved the capabilities of the university and students by passing the know-how from experienced students to the freshmen students. In Portugal, APAE has announced an European Design/Build/Fly competition called “Air Cargo Challenge” (ACC) on December 2006, after the realization of the popularity of the AIAA’s Design/Build/Fly Competition. Looking at the restrictions of the rules [1] of APAE’s Air Cargo Challenge competition; 2 Ankara International Aerospace Conference

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•

Maximum wingspan is 1.6 meters.

•

Maximum take-off ground roll is 60 meters.

•

Propulsion system must be electric and the electric motor must be AXI brand’s 2820/20 model brushless motor.

•

Batteries must be Lithium Polymer based and have minimum capacity of 3 Ampere-hour with the discharge rate of 15 times of its capacity; i.e. a 3 Ampere-hour battery must be discharged safely under 45Ampers load.

•

Electronic brushless motor speed control unit must be capable of 45 Ampere of load continuously.

The aim of the competition is to design and manufacture an airplane being capable of heaviest payload that can be carried. DESIGN APPROACH To make an approach and find a way to design optimum airplane within the constraints of the rules, the constraints, the variables to be selected and the values to be calculated must be determined. These three main information boxes can be seen in Figure 1. CONSTRAINTS

VARIABLES TO BE SELECTED

VALUES TO BE CALCULATED

Maximum Wingspan

CLmax

Wo

Static and Dynamic Thrust

CLcruise S

Maximum Ground Roll Distance

CLtake-off

Air Density Based on Lisbon

Desired Ground Roll Distance

Propulsion System Weight (Wpropusion)

Initial CDo Value

lfuselage

AR

Real CDo

VHT

VVT

We/Wo

Figure 1 Information boxes of the design After being thought on constraints and the variables to be selected, a design approach for design was decided. According to the design approach, airplane design methodology would be conducted in two phase. In the first phase, by using the given maximum take-off ground roll into the ground roll formula, the W o and S values are determined. After determination of W o and S values, they are placed into the drag formula during cruise flight condition if they could beat dynamic thrust value or not. Thus, a W o and S value is selected that satisfies both take-off and cruise conditions. By this elimination, optimum W/S value would be determined. In addition to this, coefficients of both monoplane and biplane are used in the calculations conducted in the first phase. Please note that, biplane formulations are taken from “The Design of the airplane“[7] book. After that, W o and S values were calculated for both configuration and compared. After W o and S values found in the first phase, it is aimed to find the optimum fuselage length in the second phase of the calculations. In the second phase, firstly the effects of fuselage length on the other components or forces are investigated and with the help of this information, fuselage length of the aircraft is calculated by the optimization algorithm that maximizes the payload weight, with MODE-FRONTIER software. The design approach flowchart can be summarized in Figure2; 3 Ankara International Aerospace Conference

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Figure 2: Flowchart of the design process

As seen in Figure 2, Design constraints and some selected variables are used as inputs in the first algorithm; outputs of first algorithm and some selected variables are used as inputs in the second algorithm. The final configuration can be obtained after the calculations made in Second algorithm.

OPTIMIZATION PROBLEM 1 4 Ankara International Aerospace Conference

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After the development of the design approach, two concepts are considered during the optimization problem 1. In this problem, maximization of the maximum takeoff weight and minimizing the wing area are the objectives. These two objectives have to be achieved to overcome thrust and take off distance constraints. At the end of the optimization problem, the concept that gives the maximum takeoff weight with the same wing area is selected for the final configuration of the aircraft. Assumptions Before starting the calculations, we had to restrict the aircraft configurations and determine some sensible values for some variables, such as design CLcruise, CLmax, CD0. With respect to the previous experiences from DBF contests, we removed canard and tandem concepts that are called under unconventional configurations. As conventional concepts, we had monoplane, biplane and tri-plane configurations that can be used for ACC competition. After making building feasibility, monoplane and biplane configurations are decided to be used in our optimization algorithms. In addition, as we indicated before, we had to determine some design parameters in order to be the initial values for the optimization algorithm. Fort the first algorithm, the values assumed can be seen in Table-1 and Table-2 respectively. Note that, CLcruise value is taken by dividing CLmax value by 1,44. So, it means that we assume the airplane’s design cruise speed is equal to 1,2 times of airplane’s stall speed. In addition to this, the wing span is taken as 1,6 meters, which are set as maximum limits by the regulations of ACC competition. More, in order to reduce the induced drag, we set endplates for both design. Variable CLmax CD0 ρ

Value 1,5 0,03 1,18

Dim. kg/m3

µ

0,05

-

b

1,6

m

Table 1 Constant variables; variables to be selected Variable

Value

Dim.

Variable

Value

Dim.

h

0,2

m

h

0,2

m

ξ

0,5

-

r

1

-

Table 2 Assumptions for monoplane configuration

Table 3 Assumptions for biplane configuration

Formulation

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Table 3: Design approach flowchart The first algorithm is the most important phase of the whole design approach. To sum the technique, as first phase, we find the wing area (S) and take off weight (W 0) combinations that are based on certain thrust values and restricted as to be took-off from 60 meters. In the second phase, we test each S and W 0 combinations found in the first phase under cruise condition, if the motor can provide enough thrust to beat the drag force. If the S and W 0 values of each first and second phases can match, we find the possible combinations and take the combination having highest take-off gross weight. To say more, in the first algorithm phase, variables and aerodynamic coefficients are taken from the previous step that can be seen in Table-3. In the algorithm, the first calculation is take-off distance that is named as Equation (1.1)[5]; To describe the Algorithm #1; 2 K +K  V  T A 1 f  [5] ln SG= (1.1) 2  2 gK A  K + K V  A i   T

KT contains the thrust terms and KA contains the aerodynamic terms, the containing of each term is shown in equation (1.2)[5] and equation (1.3)[5] respectively. Please note that in Equation 1.1, Vi term, that is about initial velocity of the vehicle or wind speed, is zero.

T  [5]  − µ (1.2) W 

KT=  KA= ρ

1 µC L − C D0 − KC L (1.3) [5] W  2  S

(

)


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AKSUGÜR,TUGAY,KAVSAOĞLU,NİKBAY 2  T  1  K  W  − µ + ( ρ  W  µ CL − CD0 − KCL )V f      2  1 S     (1.4) SG= ln  2 gK A  T  K −µ   W     

(

)

In equation (1.1)[5], Vi is taken as zero because the airplane accelerates from rest and we made the calculations under zero head wind conditions. Placing the design constraints and the selected variables to Equation(1.1); Several W o and S pairs can be found. Do not forget that and lets proceed to the Equation(1.5). Please note that the thrust term (T) in Equation(1.4) is the mean thrust during take off phase, because thrust decreases when the aircraft gains speed on the runway. After finding W o and S pairs, these combinations are tested to see if they match with cruise condition or not. To find the cruise condition equation, we simply equate thrust and drag. Recall that design cruise speed is taken as 1.2 times of stall speed. T(v) is the thrust function which depends on the airspeed of the airplane. For cruise condition; Thrust = Drag Thrust =

1 ρVcruise 2 SC D 2

Drag coefficient consists of two components; parasite drag and induced drag;

CD = CD0 + CDi To write the drag coefficients more clearly;

CD = CD0 +

1 CL 2 π ⋅ AR ⋅ e

We can write the aspect ratio in terms of wingspan and wing area. Thus, the equation becomes;

CD = CD0 +

S C2 π ⋅ b2 ⋅ e L

As selected before, we know the relation between CLmax and CLcruise

CD = CD0 +

S C ( L max )2 2 π ⋅ b ⋅ e 1, 44

So, the finally the equation becomes;

CD = CD0 +

S ⋅ CLmax 2 (1, 442 ) ⋅ π ⋅ b 2 ⋅ e

To place the CD value to the thrust and drag equation during cruise flight;

  S ⋅ CLmax 2 1 2 Thrust = ρVcruise S CD0 +  2 (1, 442 ) ⋅ π ⋅ b 2 ⋅ e   For Cruise condition, if we write the lift equation;

Wo =

1 ρVcruise 2 SC L 2

We know that, as selected value; CLmax = 1,44 CLcruise (comes from Vcruise = 1.2 Vstall) Wo =

1 C  ρVcruise 2 S  L max  2  1,44  7

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If we write the “


1 ρVcruise 2 S ” value in terms of W o and C L max ; 2 W 1 ρVcruise 2 S = 1,44 o C Lmax 2

Thus, all the necessary equations are found. We place all the equations to the Thrust and drag formula;

 S ⋅ CLmax 2 Wo  Thrust = (1,44) CD0 +  C Lmax  (1, 442 ) ⋅ π ⋅ b 2 ⋅ e  In the formula above, on the left side of the equation, thrust value is not constant; it changes with the velocity of the aircraft. Thus, to find some values from the equation above, we had to determine the dynamic thrust characteristics of the electric motor with different propellers; 2  SC Lmax W  T(ν)= (1,44) C D0 +  (1.5) C Lmax  (2,0736)πb 2 e 

After determining Equation (1.4) and Equation(1.5), we can show the algorithm flowchart in Figure 3.

Figure 3: Algorithm Flowchart Optimization Technique for Optimization Problem 1 For the optimization problem a MATLAB m file is used.[9] In the file, all the variables, constraints are given to evaluate the objective functions. Later, 3-D graphs are obtained for both monoplane and bi-plane configurations. These graphs can be represented as;

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Graph 1 Take-off Distance vs. W-S pairs

Graph 2 Drag of the Aircraft vs. W-S pairs Bi-plane

Graph 3 Take-off Distance vs. W-S pairs

Graph 4 Drag of the Aircraft vs. W-S pairs

Results of Optimization Problem 1 From Graph 1,2,3, and 4, 2-D projections are considered and the junction are determined, after these studies, it is seen that achieving the takeoff distance with the given thrust values can be done with the biplane configuration. As a result, bi-plane configuration has been selected. Moreover, objective functions’ values are determined from graphical method, that is given in Table 4. Parameter Wo S (for one wing) AReff.

Value 58,6 0,477625 6,633

N m2 -

Table 4 Optimization Problem 1 Result Table Note that Aspect ratio (AR) , that is found as a result of Optimization Problem 1, is called effective AR because of the endplates we used for our design.


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OPTIMIZATION PROBLEM 2 After the determination of the aircraft’s concept, maximum take off weight, and wing area another optimization problem has to be solved to answer the question; “What will be the optimum fuselage length?” This question brings the investigation of two disciplines. One of them is the aerodynamic and the other is the stability. In aerodynamic consideration, fuselage has to be designed in optimum length to optimize the zero lift drag, and for stability discipline, fuselages’ tail length, which is the length of fuselage between the wings’ quarter chord and tail’s. It has to be long enough to satisfy the adequate stability of the aircraft. On the other hand, to achieve the stability of the aircraft, another component has to be discussed in the problem. Horizontal tail is the component that is effective in the stability of the aircraft. In flight, it turns the aircraft to its initial position when a disturbance is occurred. When the pilot gives an elevator deflection, it creates a force and if this force is adequate then it is multiplied by the moment arm and it overcomes the total moment produced by other parts of the aircraft. As a result, in the second optimization problem, these two conditions are going to be considered. The calculations are made for the level flight of the aircraft and the stick-fixed condition.

Problem Statement In level flight conditions, thrust is assumed as equal to the drag of the aircraft. Drag of the aircraft has two components, one of them is induced drag and the other one is the zero lift drag. It can be written as;

D = Di + D0 (1.6)[5] Zero lift drag (Parasite Drag) of the aircraft can be calculated with the geometrical properties of the aircraft and the dynamic pressure in the level flight.

D0 = qS wCD ,0 = In the design phase, the value

1 ρV 2 S wCD ,0 (1.7)[5] 2

CD ,0 is selected from the historical data. However, for small-scale U.A.Vs, these

historical data could not be reached easily, because of the industrial considerations. Another method to estimate

CD ,0 is the component build-up method, that is the method where CD ,0 of the

components of the aircraft are calculated separately .Total zero lift drag coefficient of the aircraft is the sum of these CD ,0 separately. A general expression can be seen in(1.8).

(CD0 ) = In this equation

∑ (C

fc

* FFc * Qc * S wetc ) S ref

+ CDmisc . (1.8)[5]

C f of the component can be calculated in (1.9) Cf =

(log10 R)

2.58

0.455 (1.9)[5] *(1 + 0.144* M 2 )0.65

And Form Factor is given in(1.10). 4

0.6 t t FF = (1 + *( ) + 100*   ) *(1.34* M 0.18 ) (1.10)[5] ( x / c )m c c (1.10) is used to determine the form factors of wing, horizontal and vertical tail and such components. Form factor of the fuselage is expressed in(1.11).

 60 f  [5] FF =  1 + 3 +  (1.11) f 400   10 Ankara International Aerospace Conference

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And for endplates FF is given in(1.12);

FF = 1 + (

0.35 ) (1.12)[5] f

In the equations, f is the fineness ratio of the component. The calculation of this value is given in(1.13).

f =

l [5] (1.13) d

Where d is the maximum diameter of the components’ frontal area and l is the length of the component. In this study, calculation of the C D ,0 , rather than a selection from historical data is important because of the specific thrust value, as mentioned before. As a result, achieving a smaller value of

CD ,0 will improve the performance of the

aircraft. Characteristic lengths of the components play a significant role in the calculation of the CD ,0 .As a result this makes the lengths to be the variables of the optimization problem. After the design considerations, minimizing the fuselage length and the horizontal tail’s geometry is determined as the optimization problem, to minimize both the zero lift drag coefficient and the weight of the aircraft as aerodynamic consideration. In the aerodynamic consideration, another effective factor is the fineness ratio of the aircraft. This value can not be small from 5 because the fuselage’s drag increased exponentially while this value is getting smaller.[3] Besides, a greater value from 16 will cause an increase in the fuselage friction drag.[3] As a result, this condition limits the fuselage length. For another consideration, it can be assumed as; if the fuselage length reduces, weight will decrease. Moreover, another subject has to be considered in the optimization problem. Minimizing the fuselage length and the horizontal tail’s geometry affects the static stability of the aircraft. Static stability is the response of the aircraft when it is disturbed. Mostly; in the design phase, longitudinal static stability is examined. Longitudinal static stability is the ability of the aircraft to turn its initial position when a disturbance by gust, or elevator deflection, etc. is occurred. Static margin is the indicator of the longitudinal stability. The distance between the center of gravity and the neutral point of the aircraft is mentioned as the static margin. Neutral point is the point where the moment of the aircraft does not change with the angle of attack of the aircraft. It [2] can be calculated as in (1.14) .

 dC dα  at ( ARh.t . ) dε N 0 = xac −  m (1 − )Ch.t .ηt (1.14)[2]  − α α d dC a d  L f w Positioning the center of gravity in front of the neutral point makes the aircraft stable. The margin between these two points is called Static Margin as mentioned before. In most of the aircraft, this margin is between 15% and 25% .However, for U.A.V.s or small scale aircrafts this margin can be reduced. Design team determines these values as 5%-10%. In summary, minimizing the zero lift drag coefficient, the length of the fuselage and the horizontal tail’s geometry are the aims of this study. These objectives are constrained by the limitation of static margin and fineness ratio. To establish the optimization problem, following variables are used to determine the optimum results of the objectives; Lnose: it is the length of the fuselage between the nose of the aircraft and the leading edge of the mean wing. Varies between 0.25m to 0.3m, these values are determined by the design team considering payload and battery placement.


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tarm: it is the length of the fuselage between the mean wing’s quarter of mean aerodynamic chord up to the horizontal tail’s quarter of mean aerodynamic chord. The boundaries are estimated as 0.5m to 2m. ARh.t.: is the aspect ratio of the horizontal tail, which indicates two geometrical expression of the horizontal tail, they are the span and the area of the horizontal tail. This value varies between 3 and 7. Ch.t.: is the volume coefficient of the horizontal tail. Volume coefficient’s formula is given in(1.15).

Ch.t =

tarm Sh.t . (1.15)[5] Cw S w

From(1.15), it can be seen that variable Ch.t. is not an independent variable. It can be assumed as a constraint for the multiplication of variables

tarm

bh.t 2 ARh.t .

by giving a range between 0.4 and 1.

Formulation With these variables, objective functions and constraints can be written as; Minimize

(CD0 ) = (CD0 ) fuselage + (CD0 ) h.t . + (CD0 )other _ components

Where;

 π (400d fus. (l fus.3 + 60d fus.3 ) + l fus. )  Q fus.   ρVl fus. 2.58 400l fus.2  (log10 ) *(1 + 0.144* M 2 )0.65  0.455

(CD0 ) fuselage =

µ

S ref 0.455

(CD0 ) h.t . =

ρVcmean ,h.t . 2.58 (log10 ) *(1 + 0.144* M 2 ) 0.65 µ

FFh.t .Qh.t . (

Ch.t .cmean ,wing S ref − (croot ,h.t .d fus. )) tarm

S ref

l fus. = lnose + tarm +

Minimize

Minimize

cmean , wing

bh.t . = ARh.t . S h.t . =

4

+

3cmean ,h.t . 4

ARh.t .Ch.t Cw S w tarm

Subject to;

FinenessRatio =

l fus. d fus.

;

l fus. d fus.

− 16 ≤ 0 ,

5−

l fus. d fus.

≤ 0;

StaticM arg in( S .M .) = xc. g . − N 0 ; S .M . − 0.10 ≤ 0 , 0.05 − S .M . ≤ 0

Where N0;

 π (k2 − k1 )(l fus. ) l fus . dα  at ( ARh.t . ) dε 2 N 0 = xac −  ( d dx ) (1 − )Ch.t .ηt  − fus . ∫  2 S ref cmean, wing 0  dC a d α L  w  f


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k2-k1 (apparent mass coefficient) is a function of the fuselage length[2] and at is a function of the horizontal tail’s aspect ratio.[4] Optimization Technique for Optimization Problem 2 With these variables, optimization problem is modeled with a software package, ModeFRONTIER[4].A spreadsheet that is making the detailed calculations is prepared, some screenshots from spreadsheet is given in Figure 5,6,7. As a result, calculation of aerodynamic and stability are gathered. In the spreadsheet variables Ch.t., horizontal tail’s Aspect Ratio, tarm, Lnose can be changeable with the help of the software. Software put these variables’ combination to the spreadsheet and uses an optimization method called NBI-NLPQLP, This multi-objective scheduler is based on the [6] Normal-Boundary Intersection (NBI) method, developed by I. Das and J. E. Dennis. The NBI method applies to any generic smooth multi-objective problem, and it reduces the problem to many singleobjective constrained sub problems (the so called "NBI sub problems"). So the NBI method has to be coupled with a single-objective solver in order to get the solutions of these sub problems. This NBI-NLPQLP scheduler uses the [8] NLPQLP algorithm as the single-objective solver. Later, software gets the calculation results from the spreadsheet for fuselage length, zero lift drag coefficient, static margin, fineness ratio and horizontal tail span length. Software tries to minimize both fuselage length and zero lift drag coefficient and also horizontal tail span length with the given constraints. Software compares the values that come from spreadsheet with the given constraint limits for static margin, and fineness ratio. If the calculated values exceed the constraint limits, then software marks those combinations as unfeasible. Whole chain can be seen in Figure 4;

Figure 4 ModeFRONTIER Interface and the Optimization Problem 2

Figure 5 CD,0 Calculation sheet 13 Ankara International Aerospace Conference

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Figure 6 Horizontal Tail's Geometrical Calculation Sheet

Figure 7 Static Margin Calculation Sheet Results of Optimization Problem 2 To see the effects of variables on the objectives some graphs are plotted. tarm and ARh.t. are selected for the minimization objectives in the Graph 5,6,7;

Graph 5 CD0 vs. (ARh.t. and tarm) 14 Ankara International Aerospace Conference

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Graph 6 Fuselage Length vs. (ARh.t. and tarm) Design Pareto Id Optimal 600 333 692 602 282 236

TRUE TRUE TRUE FALSE TRUE TRUE

Tarm

Lnose

Graph 7 bh.t. vs. (ARh.t. and tarm)

ARh.t.

Ch.t.

Lfus.

CD0

S.M.

f

1,01806 0,250357143 3,000081582 0,400611868 1,34304 0,024900 8,755% 13,4304 0,82460 0,25 3 0,4 1,14923 0,024941 9,301% 11,4923 0,92482 0,3 3 0,4 1,29945 0,024960 8,626% 12,9945 0,95741 0,3 3 0,406618525 1,33203 0,024980 9,025% 13,3203 1,22121 0,25 3 0,4 1,54584 0,025017 10,000% 15,4584 0,65012 0,3 3 0,4 1,02475 0,025288 10,000% 10,2475

bh.t. 0,5802 0,6442 0,6083 0,6028 0,5293 0,7255

Table 5 Design Table and Results From Table 5, design id 600 is selected with the considerations of the placement of payloads, structural and other design and manufacturing processes. In design id 600, the zero lift drag coefficient is calculated as 0.02490. In the first optimization problem for bi-plane configuration, this value is taken as 0.04 before. With the help of solution of the optimization problem, a 37.75% treatment is obtained. This treatment can be used in the first optimization problem and it could be effective to treat the takeoff weight and wing area of the bi-plane configuration.

CONCLUSION & FURTHER STUDIES After the placement of the zero lift drag coefficient in the first optimization problem, final W-S combination for bi-plane configuration is determined after several iterations as seen in Figure 8. The graphic slice is taken from 3 dimensional graphic of W, S and take-off ground roll. Note that the W and S values in Figure 8 are taken when take-off ground roll value is 60 meters. In the further studies, graphical optimization method of the first optimization problem can be embedded inside the second optimization problem, and it can be done automatically with the software. In the second optimization problem assumed as; a decrement in the fuselage length will cause a weight reduction. However putting structural considerations and calculations, investigating the similar aerial vehicle’s weight and fuselage length and the data which is obtained from the manufacturing process will give a formula for weight as a function of fuselage length. Minimization of this function will be more efficient to determine fuselage length.


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Figure 8 2-dimensional graphic of W and S 3D DRAWING OF THE DESIGN After calculations made by now, a conceptual sketch has been drawn. Two different views are seen in Figure 9 and Figure 10.

Figure 9 3-D model of the airplane, an isometric view


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Figure 10 3-D model of the airplane, a view from tail side

References [1] A.P.A.E Air Cargo Challenge Regulations, Retrieved June 5, 2007, from http://aircargochallenge.net/port al/downloads/Regulations.pdf. [2] Pamadi, B.N., Performance, Stability, Dynamics, And Control Of Airplanes, AIAA Education Series, 2nd edition, p:168-174, p:201-204, 2004 [3] Lan, C.E., and Roskam, J., Airplane Aerodynamics and Performance, DARCorporation, 3rd Printing, p.160, 2003 rd [4] Anderson, Jr.J.D., Fundamentals of Aerodynamics, McGraw-Hill, 3 edition, p.397, 2001 rd [5] Raymer, D.P., Aircraft Design: A Conceptual Approach, AIAA Education Series, 3 edition, p: 340-351 and p.565, 1999. [6] Das, I., and Dennis, J. E. 1998, Normal-Boundary Intersection: A New Method for Generating the Pareto Surface in Nonlinear Multi criteria Optimization Problems, SIAM Journal on Optimization, 8(3), 631 th [7] Stinton D., The Design of the Aeroplane, BSF Professional Books, 6 Printing, p.154-168, 1993 [8] ModeFRONTIER, multi objective optimization and design environment software package, www.esteco.com. [9] MATLAB, The Mathworks Inc., www.mathworks.com
