Proposal for a Very Light Jet Transient Trainer Aircraft by Sina Golshany

20077-2008 AIAA A Foundation n Individua I al Aircrafft Design n Compeetition -Prroposal-

“A Aquila” Sina Golshanny Univerrsity of Southern S n Califorrnia

Table of Content Page #

Nomenclature

Acknowledgement

Summery

Overview of approach and methods

1. Preliminary Design: Initial Sizing and Analyses 1.1 Statistical and mission based weight estimation

1.2 Sensitivity Analyses

1.3 Performance Sizing

1.4 Class I component weight estimation

1.5 Configuration trade-off

1.6 Airfoil Selection

1.7 Initial Fuselage Geometry

1.8 Center of Gravity

2. Detailed Design & Analyses: Aerodynamics, trim and inlet integration 2.1 Determination of wing incident angle

2.2 Wing Planform Design

2.3 Sizing of High Lift Device

2.4 Initial Drag Analyses & Wing Dihedral Determination

2.5 Determination of Wing Longitudinal Location

2.6 Horizontal Tail Surface Area Estimation

2.7 Vertical Tail Surface Area Estimation

2.8 Landing Gear Design

2.9 Inlet Design

3. Design Verification: Aerodynamics, Weight & Performance 3.1 Detailed Drag Verification

3.2 V-n Diagram

3.3 Detailed Structure Weight Estimation

3.4 Detailed Estimation of Power Plantâ&#x20AC;&#x2122;s Weight

3.5 Detailed Estimation of Fixed Equipments

3.6 Locating Center of Gravity Based on Detailed Weight

72 1

3.7 Detailed Performance Validation

4. Stability & Control Analyses: Trim, Static and Dynamic Stability 4.1 Sizing of the Elevator

4.2 Trim Satisfaction

4.3 Longitudinal & lateral-directional static stability

4.4 Longitudinal dynamic stability

4.5 Sizing of the ailerons

4.6 Lateral-directional dynamic stability

5. Interior detailed design Systems, structure and adoptable flying qualities 5.1 Cockpit Layout

5.2 Internal Arrangement and system positioning

5.3 Structural Configurations

5.4 Structural Analysis & Integrity Verification

5.5 Variable flying qualities

5.6 Automated design tools

Nomenclature a, b, c, d,A,B a ARW AC A∞ Athrust Bthrust , ,… a g

Coefficients in the speed versus thrust quadratic equation Average deceleration in ground run

1 πeAR Airplanes clean zero-lift drag coefficient Maximum lift coefficient for clean stall configuration

BDPClean

Induced drag coefficient,

C D 0Clean , M C L max

Regression coefficient for drag calculation Speed of sound Wing aspect ratio Inlet area Stream tube cross-section at infinity

S ( Clean )

C L opt , MaxR

Lift coefficient correspond to the optimum range performance

C lδ

Section-lift-coefficient-due-to-flap deflection derivative

C Lα

, C Lα

C l′ δ Clδ C l δTheory Cf

Clα

Contribution of wing-fuselage and horizontal tail to lift curve slope The rolling effectiveness of two full-chord ailerons The correction factor for aileron lifts effectiveness Inlet duct equivalent plate friction

The average airfoil lift curve slope of that part of the wing covered by the

Cla

aileron Airplane rolling-moment-coefficient due to ailerons deflection

C mα ,

Airplane pitching-moment-coefficient-due-to-AOA derivative

Cl β

Airplane rolling-moment-coefficient-due-to-yaw rate-derivative

Cnβ

Airplane yawing-moment-coefficient-due-to-side-slip-derivative

C N max , C N max ( − ) C yβ v

Maximum positive and negative normal fore coefficient Vertical tail contribution to the airplane sideforce-coefficient-due-to-

C l P , C l P ,V , . . .

sideslip derivative Contribution of different aerodynamic surfaces to the airplane rolling-

CGR

moment-coefficient-due-to-roll-rate derivative Climb gradient

Ratio of elevator chord to horizontal tail chord Distortion constant ( ΔP P )

ΔC Dws dm

Increment in airplane drag coefficient due to windshield Maximum cowl diameter for the inlet

dc ΔW Fusedi

Cowl diameter at the inlet position Fuel weight used in the i’th segment

Δc l δfTO , Δclδf L

Change of sections airfoil coefficient due to flaps deflection

ΔC LWδfTO , ΔC LWδfL

Change in wing lift coefficient due to flap deflection

ΔT Δc l max

Temperature increment for atmospheric properties calculation

Δc l

maximum lift coefficient at constant AOA due to deflection of flaps In context of performance: Correction factor due to pilot technique and handling qualities Aileron deflection angle

Δn

δa δe

Elevator deflection angle Flap surface deflection

δ f TO

∂WTO

∂WTO ∂WTO ∂WTO

∂WTO

Ratio of airfoils section maximum lift coefficient to change in airfoils

∂ WPL

Sensitivity of takeoff weight to payload weight

∂ WE

Sensitivity of takeoff weight to crew weight

∂c j

Sensitivity of takeoff weight to specific fuel consumption

∂R

Sensitivity of takeoff weight to range

∂L D

Sensitivity of takeoff weight to lift to drag ratio

∂E

Sensitivity of takeoff weight to lift to endurance

∂WTO

⎛ ∂n ⎞ ⎜ ⎟ ⎝ ∂V ⎠VC

Slope of gust line for design cruise speed

⎛ ∂n ⎞ ⎜ ⎟ ⎝ ∂V ⎠VD

Slope of gust line for design dive speed

dεh dα

Downwash gradient at the horizontal tail

e Clean ηi f

Clean Oswald’s coefficient Flap inboard station, in term of wing half span

ηO f

Flap outboard station, in term of wing half span

ηa i , ηa O

Aileron inboard and outboard station, in terms of wing half span

ηinl inc

Incompressible inlet pressure recovery

FWStructure , . . . f F1

Weight fractions Parasite surface area

FCr

Ratio of cruise thrust to takeoff thrust

FMax ,Cont

Ratio of maximum continues thrust to the thrust at takeoff sea level Inlet extra drag factor Bank angle

Finl ext φ φT

Thrust inclination angle Bank angle achieved for the required roll time by FAR-23

φactual

Facto correction for type of certification

Maximum bank angle to maximum side-slip ratio during Dutch roll D

γ hTO hS I Power I xx B , I yy B , I zz B ′, K L′ KTO

K BPR K trim K EngPerf M ff m& a m& gas m& cool M Cr Max μg μinl NP free

nlimit (+), nlimit (-)

n ult l mc Level φt LevelTR Level S Levelζ D Levelζ D , 23 Levelωn D

Glide angle Take-off altitude Stall altitude Power index Moment of inertia along the body axis Flap effectiveness for take-off and landing Bypass ratio factor Trim penalty incurred by use of flaps Engine performance factor Fuel Fraction Total air mass rate at engine inlet Air mass flow required for engine combustion Air mass flow rate required for engine cooling Maximum cruise Mach number Wing-ground rolling friction coefficient Inlet inverse flow ratio Free stick neutral point location in terms of wing aerodynamic chord Positive and negative load factor limits Design ultimate load factor Inlet duct length Level for the roll performance Level for roll-mode time constant Level for spiral stability Level for Dutch rolls damping Level for Dutch rolls damping based of FAR-23 requirements Level for Dutch rolls frequency

Levelωn D ζ D

Level for Dutch rolls X damping ration

Level P Level ζ SP Levelωn ,SP λw Λw ωnP ,long

Level for Phugoid stability Level for short period damping Level for short period frequency Wing taper ratio Wing sweep angle Longitudinal phugoid mode un-damped natural frequency

ωn ,S .P ωnD

Short period un-dapped natural frequency Dutch roll undamped natural frequency

Pm Π Ψ PSpExPwr Pextr

Static load per landing gear Engine setting Landing gears lateral tip over angle Specific excess power (for climb)

Q1 R x , R y , Rz ρF Rturn STOG SW S wet SW f SW SM SM free

TUnIns avail t c w TC long ( 1 ) ,… T1

( ) 2P

T2 P TS Tset

TR T2S U1

Power extracted from the engine by the accessories Steady-state Pitch-rate Radiuses of gyration Fuel density Turn radiuses Take-off ground run distance Wing surface area Wet surface area Ratio of flap area to wing area Average static margin Free stick static margin Density ratio Available engine uninstalled thrust Thickness to chord ratio of the wing Longitudinal time constant(s) Time to halve the amplitude in phugoid mode Time to double the amplitude in phugoid mode Spiral role mode time constant Steady-state thrust Roll mode time constant Time to double the amplitude in spiral mode Steady state speed

VSclean

Clean stall speed

VS( ) V Aeas VBeas

Stall speed for maximum negative normal force coefficient Design optimum maneuver speed (Equivalent airspeed)

VC eas (min)

(Equivalent airspeed) Design speed for maximum gust intensity Minimum design equivalent speed (Equivalent airspeed) Lift-off velocity

V LOF VM

Optimum maneuvering speed Trapped fuel weight

Wtfo

WPL W PL exp,i WE W TO

(W S ) (W T )

TO max TO max

X apex W x ac , x ac wf , x ac h X CG , YCG , ZCG x cg

Payload weight Expendable payload weight of the i’th segment Empty weight Take-off weight Maximum take-off wing loading Maximum take-off power loading X coordinate of the wing apex (i.e. distance b/w wing quarter chord station and the nose reference point) X coordinate of aerodynamic center in terms of mean aerodynamic chord

ζ SP ζ P ,long

Location of center of gravity X coordinate of center of gravity in terms of mean aerodynamic chord Short period mode damping ratio Longitudinal phugoid mode damping ratio

ζD

Dutch roll mode damping ratio

Acknowledgement: Having finished this project, I would like express my appreciation for the people who have supported me. First of all, I wish to thank the persons who have initiated this project: Dr. Ron Blackwelder, Mr. Blain Rawdon and Mr. Mark Page. With their experience in the field of Aerospace Engineering they have been very supportive in all of the phases of this project, when they were teaching in the aerospace department of University of Southern California. During this project I also received significant assistance and support from Dr. Seyed Mohammad Malaek (Sharif University of Technology, Tehran, Iran) with regard to aircraft design issues. I appreciate the discussions we had in our periodic conversations. Thanks goes to Daniel Ravanshenas in USCâ&#x20AC;&#x2122;s writing center for his contribution to the editing of this proposal. Several people have been instrumental in allowing this project to be completed, but above all I am obliged to my promoters, Professors Larry Redekopp, Daniel Erwin, Eva Kanso and Ossama Safadi, who supported me over the last year. Stimulating discussions and encouragements they provided helped me get through the arduous process of writing this proposal. And last but not least I wish to give thanks to all my friends and family, for being there and for their encouragement to finish this project, in one way or another.

May 2008, Los Angeles Sina Golshany

Summary:

ery Light Jet(VLJ) aircrafts have been argued to be capable of replacing a majority of small propeller powered fleet over the next three decades. Characteristics such as

high cruising speed combined with reasonable fuel efficiency and low maintenance costs, have also made VLJ’s a favorable choice for point to point air taxi services. While opinion may vary on how the market will respond to this new type of aircraft*, there is a general consensus that VLJs have been, and will continue to be, the focal point for the latest in aircraft advances, including highly integrated avionics and modern jet propulsion. Although they are thought to be simpler to fly than piston powered aircrafts, there seems to be a high demand for a suitable trainer jet that can provide pilots with proper training on the new technologies and the unique flying qualities of the VLJs. With the FAA projecting at least 4,500 VLJs entering service over the next ten years†, providing viable and realistic training to pilots may be a crucial factor in the commercial success of these aircrafts. This proposal is intended to present the design of Aquila ‡ , to demonstrate the possibilities in design of a commercial trainer utilizing the most recent technologies, similar to those used in VLJ aircrafts. The goal of the designer has been to create a safe and financially feasible transition trainer for commercial purposes, mainly training the certified turboprop and piston plane pilots to fly VLJ’s. The main element that distinguishes Aquila from current trainer jets is the adoptable flying quality system that would allow the instructor to select a certain aircraft for training: Aquila’s flight qualities can be adopted in a way to emulate the selected platform for instructional purposes.

Croft, John “Very Light Jets: Bloom or Blip”, Aerospace America, AIAA, May 2006 “Smaller, faster, cheaper new jets may transform flying.” USA Today 19 Jan. 2006 A7+ ‡ Classic Latin word for Eagle * †

In order to approach the process of the design, methods of management and in particular the method of design structure matrix are used. As a result, the number of feedback cycles is kept to a minimum and more alternative designs have been studied in detail. In order to achieve a reasonable cost for the product, mathematical models for aerodynamics and cost estimations have been used as a basis for derivation of a multidisciplinary optimization method, to make a balance between performance and cost of the final design. Correspondingly, Computer Aided Design (CAD) and Computer Aided Engineering (CAE) packages are used in order to aid the visualization and optimization for both performance and cost. Being a single engine trainer, extensive effort has been spent on improving the safety of the Aquila, particularly in the areas of propulsion integration and inlet design. Highly detailed 3 dimensional CAD models are used to define the geometry of the aircraft, which made precise 3 dimensional CFD analyses possible. Many of the aerodynamic issues, such as asymmetric flows and separated regions due to geometric irregularities were discovered as a result of these analyses in early stages of the Aquila design. Issues such as effects of high angle of attack on the performance of the inlet have received special attention, due to the significance of the stability of the inlet airflow and its crucial role on flight safety. This project also incorporates the use of numerous pieces of MATLAB code in order to assist the operations that the commercial software packages in the validation of the structural integrity of the design. Project Advisor: Dr. Ron Blackwelder ________________________

1460

________________________

283128

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281677

Faculty Advisor: Dr. Oussama Safadi Designer: Sina Golshany

Overview of approach and methods:

he general design philosophy of the Aquila has been substantially influenced by methods presented by Jan Roskam * , Edward Heinemann † and Daniel P. Raymer ‡ in

their widely published text books. It should be noted that these methods are often quite extensive and they cover technical aspects of the analyses in detail.

The majority of

calculations performed utilize published graphs and tables in order to determine the constants and parameters, and they often consist of many steps. The theoretical backgrounds of these methods are discussed in various parts of this proposal, but in order to be concise, many of the mathematical models and statistical data used in the design are not presented in their entirety. In order to allow the full engineering evaluation of this project, the calculations are presented in two separated volumes in digital format provided alongside with this proposal, and necessary references are made to them. The Design Structure Matrix (DSM) as a modern method of development has been applied in order to determine the optimum design process by combining feedback cycles and determining the possible parallel analyses.

This method which is

described by Eppinger et al. § in detail is used to organize interrelated tasks in the design process in a way to minimize the number of feedback cycles. In order to

ID 1 2 3 4 5 6

Task Preliminary Research Preliminary Sizing and Configuration Preparing Surface Models & Drawings Perform Aerodynamics Analysis+Loads Perform Initial Engine Integration Perform Detailed Aerodynamics, weight and performance analyses 7 Perform Detailed Weight & Inertias Analyses 8 Perform Stability & Control Analyses 9 Preparing Detailed Solid Models and Internal arrangement CAD Drawings 10 Preparing the FEA Models and Elements Table 1. Design Tasks Before application of DSM

Roskam J., Airplane Design ,part I trough VIII , DAR Corporation, Wichita 2003 Heinemann, E., Raussa, R. and Van Every, K., Aircraft Design, The Nautical and Aviation Publication Co., 1985. ‡ Raymer, Daniel P. , Aircraft Design – A Conceptual Aproach, AIAA Education Series, Veston, VA 1992. § Eppinger, Steven D. and Ulrich, Karl T., Product Design and Development, Second Edition, Irwin McGraw-Hill, Boston, 2000 * †

apply the method, the development process is broken down to 10 major tasks in its initial order as shown in table 1. The design matrix, which includes a representation of different tasks and their interactions in a matrix format has been defined as shown in Figure 1.

Fig. 1) Initial Design Structure Using PSM32 Code: Both rows and columns represent the same tasks. Zero elements on the intersection of a certain row and column represent the relation between the two tasks. For example the zero elements located on the intersection of the 7th row and the third column represents a one way relation between weight and inertia analysis (7) and the geometry of the aircraft (3). It should be noted that for instance, geometry of the aircraft does not use the result of weight and inertia analysis as an input and therefore the relation is one way.

By diagonalizing the design matrix using the PSM 32 algorithm, the parallel processes are identified. As an example CFD analysis could be done almost independently of the internal arrangement of the aircraft. Parallel processes are presented on figure 2 below.

Fig. 2) Parallel process in the design matrix. Green rows are tasks with minimum degree of dependency on the output of other operations.

Due to the high level of interdependencies among half of the 10 main tasks, initial ordering of the tasks was not change. Consequently, the method of approach to the design problem was only modified to â&#x20AC;&#x153;tear-offâ&#x20AC;? the parallel process in order to make the project more time 12

efficient. The final approach presented by Roskam * has been slightly modified in order to allow for additional parallel process: Mission Specification & Mission Profile

WTO

TTO

C L max

WPL

Preliminary Configuration Layout and Propulsion System Integration. Configuration Candidates Identified and One or More Selected for Further Study.

Sensitivity Studies: ● Definition of R and L/D ratio. ● Refinement of Preliminary Sizing

● Initial Layout of Wing and Fuselage ● Class I Analysis: Tail Sizing, Weight and Balance, Drag Polar. ● Initial Landing Gear Disposition

Sizing Iteration and Reconfiguration. Refinement of Preliminary Configuration: -Detailed Stability and Control

Preliminary Configuration Design Finished

● Layout of Wing Fuselage and Empennage. ● Class II: Weight and Balance, Drag Polar, Flap Effects, Stability and Control ● Performance Verification ● Landing Gear Disposition and Retraction ● Cost Estimation

Fig. 3) Preliminary Design Flowchart (from [Roskam, 1997])

It appeared that the performance of the final design have a high dependency on the method of inlet integration. As a result of application of DSM method, and also improved computing resources, it became possible for the designer to experiment with two different methods of inlet integration. Due to the crucial rule of the inlet development on performance and safety, this proposal presents a comparison between two successive designs. Both of these designs *

Roskam J., Airplane Design Part I; P-iv , DAR Corporation, 1997

are developed in high level of details in order to make a precise comparison possible and ensure the validity of the design assumptions. Different modules of ANSYS multiphysics package have been used for computational fluid dynamics and finite element analysis to ensure the calculation results achieved using usual methods of analysis. As the main computer aided engineering software, Advanced Aircraft Analysis (AAA) [DAR Corp]

is being used almost in all of the areas of the preliminary design and analysis*. Using this package as tested and widely accepted software for General Aviation design purposes (which also comply in terms of methodology of design with my choice), following compensations were achieved: -

Conserving efforts to write and verify codes necessary for performing the iterative and none â&#x20AC;&#x201C; iterative numerical design calculations.

Well designed and user-friendly interfaces.

Ability to provide data in terms of spreadsheet files & data tables

Possibility of having results in both metric and imperial units.

Other software packages are utilized in the process of design, making it possible for the designer to present the most accurate and detailed vision of the design of Aquila. These softwareâ&#x20AC;&#x2122;s and the process of their utilization is explained in different parts of this proposal.

The exceptions are including the determination of dynamic loads on landing gear and tire sizing which have been done manually.

Perliminary Design Initial Sizing and Analyses

1.1 Statistical and mission based weight estimation The lack of available statistical data on similar aircrafts presented a great challenge about the estimation of the aircraft weight. In the following equation, regression constants presented by Roskam * are used to estimate the empty and takeoff weight using AAA software: log 10 W E =

log 10 W TO − A B

Eqn. (1)

Where constants A and B are: A= 0.6632 (Single Engine Military Trainer) B=0.8640 (Single Engine Military Trainer) A more sophisticated algorithm is used to refine the above results based on the mission requirements. The initial values for the aircraft’s take-off and empty weight, combined with the statistical values of fuel fraction ( M ff ) for different segments of flight, are used to estimate the overall fuel fraction using equations 2 and 3: W E = [1 − (1 − M ff )(1 + M ff ) − M fto ]WTO − (W PL + Wcrew + W PLexp ) n

M ff = ∏ M ff i + i =1

1 WTO

n ⎧⎪ n −1 ⎡ ⎛ ⎜ W 1 − ⎨∑ ⎢ PLexpi ⎜ ∏ M ff i ⎪⎩ i =1 ⎣⎢ ⎝ j =i +1

⎞⎤ ⎫⎪ 1 ⎟⎥ ⎬ − ⎟ ⎠⎦⎥ ⎪⎭ WTO

n ⎧⎪ n −1 ⎡ ⎛ ⎜ W 1 − ⎨∑ ⎢ Frefuel ⎜ ∏ M ff j ⎪⎩ i =1 ⎣⎢ ⎝ j =i +1

Eqn. (2)

⎞⎤ ⎫⎪ ⎟⎥ ⎬ ⎟ ⎠⎦⎥ ⎪⎭

Eqn. (3)

Where:

M ff i =

Wi − ΔW Fusedi

Eqn. (4)

Wi n

W PL exp = ∑W PL expi i =1

Eqn. (5)

Roskam J., Airplain Design Part I; 1999 Section 2.7.1, P. 69

The airplane’s empty weights calculated from the two equations are compared.

If the

condition shown in equation 6 is satisfied, the hypothesized take-off weight will be accepted as the take-off weight for this particular airplane. If the condition is not satisfied, the AAA code would adjust the guessed take-off weight and repeat the calculation until the condition is satisfied: W E ( Eqn .2 ) − W E ( Eqn .1) < 0.05lbs

Eqn. (6)

Once the take-off weight is determined, the weight of the fuel used in the mission is estimated from:

W Fused = (1 − M ff )WTO

Eqn. (7)

and the total fuel weight is calculated using equation 8:

(

)

W F = 1 + M Fres W Fused

Eqn. (8)

Correspondingly, the airplane weight at the beginning of each mission segment is computed from equation 9: Wbegin i = Wbegini −1 − ΔW Fused i + W Frefuel i −1 − WPL expi −1

Eqn. (9)

Where the fuel weight at the beginning of each segment is computed from equation 10:

W Fbegini 1 = ΔW Fused i + W Frefuel i

Eqn. (10) 2

The required mission profile by the RFP is notable for the long and low-altitude loitersegment (45 minutes), which demands a high lift-to-drag ratio in low altitudes. Given the low altitude of the loiter-segment and since the majority of flight training schools are located in or near large metropolises, special attention should be paid to environmental parameters such as engine noise levels and pollution yield.

The mission profile for Aquila is demonstrated in figure 4, and a detailed list of parameters for each flight segment could be found in Data Unit Volume I I*.

Fig. 4) Mission profile: 1) Warm-up & taxi 2) Takeoff 3) Climb to 35K ft 4) Cruise 5) Decent 6) Loiter at 1000 ft 7) Approach land and taxi

The results of the initial weight and mission analysis are presented in tables 2 and 3. Mission segment Wbegin ( lb ) Warm-up Taxi Take off Climb Cruise Descent Loiter Land/Taxi

ΔW FUsed ( lb )

W Fbegin ( lb )

M ff

0.8039

24.1 11.9 11.9 27.9 297.9 20.3 62.8 15.6

543.3 519.2 507.3 495.4 467.5 169.6 149.3 86.5

WFused

472.4 lb

WF W Fmax

543.3 lb 543.3 lb

W Fres

70.9 lb

Wtfo

24.1 lb

WCrew Wuseful

440 lb 983.8 lb

WE WTO

1400.5lb 2408.5 lb

2408.5 2384.8 2372.5 2360.6 2332.7 2034.8 2014.5 1951.7

Table 2. Weight table for the mission ↑ Table 3. Initial weight breakdown →

From these analyses it is evident that the most significant portion of the aircraft takeoff weight (22 %) is consisted of fuel, with the most part being consumed during the cruise, loiter, and climb segments, respectively. This result also justifies the application of statistical weight *

“Aquila Project Technical Data Unit”, Vol. I” P. 3+

factors to the result of sensitivity analysis presented in section 1.2 for the aforementioned flight segments, in order to prioritize the design parameters.

1.2 Sensitivity Analyses The sensitivity analysis assesses the effects of different design specifications on the final product performance by means of evaluating proper partial derivatives of performance characteristic equations. The results of these studies affect the initial configuration of the aircraft through eliminating improper configurations in terms of range and endurance, as well as determining the parameters which drive the design. The theoretical background and the derivatives are presented in Data Unit Volume I*. All of these derivatives are defined as the summation of continued product of a sequence of fuel fractions. As an example, the sensitivity of take-off weight to expended payload weight at k'th segment is calculated from:

− BWTO ∂WTO = ∂WPL C .WTO (1 − B ) − D + B(1 + M Fres )ΔWF

Eqn. (11)

For which the variables C and D are calculated from:

C = 1 − (1 + M Fres )(1 − M ff ) − M tfo

Eqn. (12)

D = WCrew + WPL + W PLexp − W Frefuel

Eqn. (13)

The fuel weight correction for the expended payload and/or refueled fuel weight is given by:

(

n ⎧ ⎪ ΔWF = ∑ ⎨ WPL expi − WFrefuel i i =1 ⎪ ⎩

)⎛⎜⎜1 − ∏ M n

⎝

j = i +1

⎞⎫⎪ ⎟⎬ ⎟⎪ ⎠⎭

Eqn. (14)

In the case of this aircraft, since no air-refueling takes place, there is no

∂WTO

payload expansion during the flight, the parameter ΔW F is zero.

∂WTO

∂WPL ∂WE

10.74 1.49

Table 4. General sensitivity partials

“Aquila Project Technical Data Unit”, Vol. I” PP. 5-8

Mission Segment

∂WTO

Warm-up Taxi Take-off Climb Cruise Descent Loiter Descent Land, Taxi

------------509.7 6740.5 ----1361.1 ---------

∂c j (lb − hr )

∂WTO

----------------3.5 -----------------

∂R

(lb nm )

∂WTO -------------31.1 -354.6 -----57.5 ---------

∂L D

∂WTO

⎛ lb ⎞ ∂E ⎜⎝ hr ⎟⎠

------------1441.7 --------996.3 ---------

Table 5. Sensitivity partials

The result of the calculation is presented in tables 4 and 5. It appears that the specific fuel consumption and the takeoff weight is the most affected by the lift-to-drag ratio during the cruise segment. The partial derivate of takeoff weight due to change in specific fuel consumption ∂WTO ∂c j suggests that, aside from the maximum thrust and weight parameters of the engine, an engine with the smallest specific fuel consumption is possibly the best candidate for the project, given that the aircraft spends the longest portion of its operation while cruising. derivative of takeoff weight due to change in lift-to-drag ratio

∂WTO

∂L

The partial

suggests that a high

lift-to-drag ratio can cause significant reduction in the aircraft takeoff weight, almost 350 lbs per unit increase in lift-to-drag ratio. Given the relatively high estimated market price for a commercial jet trainer, options such as customized airfoil design, advanced tip fins and highly elastic composite wings are available to the designer as financially feasible solutions to improve the L D .

1.3 Performance Sizing* The optimum wing loading and power loading was determined through a series of studies Based on the technical requirement specified by the RFP. The importance of this analysis was to eliminate two of the most important preliminary design variables, which was thrust of the engine, and the surface area of the wing.

1.3.1 Sizing to stall speed Stall performance of the aircraft was sized based on the criteria defined by Chapter 49 of FAR. FAR 23.49 require aircrafts with less than 6000 lbs takeoff weight to have stall speed no greater than 61 knots. Considering this criterion and also considering the required clean stall speed by the RFP (70 kts.), the maximum allowable wing loading for stall could be determined using equation 15:

WTO ⎛ W ⎞ ⎛W ⎞ ⎜ ⎟ = ⎜ ⎟ ⎝ S ⎠TO WS ⎝ S ⎠ S

Eqn. (15)

1 ⎛W ⎞ 2 ⎜ ⎟ = ρVs C L maxS ⎝ S ⎠S 2

Eqn. (16)

2{Wcurrent − Tset sin (α current + ϕT )} ρSW C L max

Eqn. (17)

Where:

VS =

†

The assumptions made can be found in Data Unit Volume I I . The results are shown in table 6.

1.3.2 Sizing for takeoff distance

(W S ) (W S )

TO SC ln

TO S

23.57 lb 27.39 lb

ft 2 ft 2

Table 6. Sizing for stall speed

Based on FAR-23 requirements, the optimum wing loading and thrust-to-weight ratio was calculated using equation 18. Assumptions used for this calculation are presented in table 7. *

As Roskam suggest performance sizing should be done after the determination of configuration. Due to limited choices in terms of power plant and landing gear this method has been adapted as presented. † “Aquila Project Technical Data Unit”, Vol. I” PP. 15-16 Table 17

⎛T ⎞ ⎜ ⎟ ⎝ W ⎠TO

⎛W ⎞ ⎜ ⎟ ⎝ S ⎠TO = 0.0296STOσC L max FTO

Eqn. (18)

The required thrust-to-weight ratio is plotted on the matching plot with three different lift coefficients all close to the statistical data obtained from other light weight jet trainer aircrafts. The resulting matching plot is shown in figure 5 which contains the graphs of thrust-to-weight ratios versus wing loading to fulfill takeoff distance and stall speed requirements.

Fig. 5) Matching plot for stall speed and takeoff distance

1.3.3 Sizing for Maximum Cruise speed In order to achieve the required maximum cruise speed specified by the RFP, the drag polar of the aircraft was first determined by means of extrapolation of statistical data from similar aircrafts, and applying regression coefficient as suggested by Roskam

and Loftin

†

, also

reflected in the volume I of this project’s technical data unit ‡. Based on the estimated drag coefficient, equation 19 was used in order to determine the optimum wing loading and thrustto-weight ratio. *

Roskam J., Airplane Design Part I; Section 3.4.1, P. 118-127 , DAR Corporation, 1997 Loftin, Jr., L.K, Subsonic aircraft: Evaluation and the Matching of Size to Performance, NASA Reference Publication 1060. 1980 ‡ “Aquila Technical Data Unit, Vol. I” PP. 17-19, †

CD0 ,Clean ⎛ W ⎞ BDPclean ⎛ W ⎞ ⎛T ⎞ + ⎜⎜ Cr ⎟⎟ ⎜ ⎟ ⎜ ⎟ =q WTO ⎠ q FCr ⎝ S ⎠TO ⎛W ⎞ ⎝ W ⎠TO ⎝ FCr ⎜ ⎟ ⎝ S ⎠TO

Eqn. (19)

The results are plotted on top of the last matching plot and are shown in figure 6.

Fig. 6) Matching plot for maximum cruise speed

Assumptions made and the results of this calculation are presented in tables 7 and 8: S wet f

385.25 ft 2

Altitude Π cr

35000 0.245

VCrmax

350 kts 0.930

C D 0Clean

2.31 ft 2 0.0219

C D 0Clean , M

0.0239

WCr

B DPClean

0.0455

8.53 Assumed

M CrMax

0.642

ARW C D 0Clean , M

0.0239

eClean

0.82

Table 7. Aerodynamic parameters ↑ Table 8. Cruise performance parameters →

WTO

1.3.4 Sizing for landing distance

Using equation 20, the landing distance requirements for wing loading was plotted:

W ⎛W ⎞ ⎜ ⎟ = 0.5ρ h, L ( ISA) C Lmax L S L F1 TO WL ⎝ S ⎠L

Eqn. (20)

The factor F1 for FAR 23, JAR 23 & VLA certification is: F1 = 5.55

The matching plot is shown in figure 7.

Fig. 7) Matching plot for rate of climb per FAR-23.65a

1.3.5 Sizing for Climb Requirements The thrust-to-weight ratio to meet FAR 23.65.a Rate of Climb (RC) requirements was plotted using the following relationship: 0.5 ⎡ ⎤ ⎛ ⎞ ⎟ ⎢ ⎛ RC 23.65 ⎞ ⎜ ⎥ ⎜ ⎟ ⎥ 1 ⎢ ⎝ 60 ⎠ ⎜ 1 2 ρ ⎟ ⎛T ⎞ 0.5 ⎜ ⎟ + 2 C D0 ,TO −up BDPTO ⎜ ⎟ = ⎢ ⎥ ⎝ W ⎠TO FMax ,Cont ⎢ ⎛ W ⎞ ⎜ C D 0TO ⎟ ⎥ ⎟ ⎢ ⎜⎝ S ⎟⎠TO ⎜ B ⎥ DPTO ⎠ ⎝ ⎣⎢ ⎦⎥ The J1200 engine was selected for the power plant, although trade

(

)

studies were required to confirm this choice, considering the possible increase in manufacturing and maintenance costs.

Eqn. (21)

105.45 ft 2

L T

21 ft 1200 lbf 543.3 lb

The combined results are plotted in the following matching plot shown Table 9. Sizing parameters for climb sizing

In figure 8. The design point (represented by the black dot) is the configuration which minimizes the wing area and the minimum thrust required in order to satisfy the performance criteria set by the RFP.

Fig. 8) Final matching plot Fig. 8) Final matching plot

Based on the studies performed, it can be concluded that a wing loading approximately 24

, and a thrust-to-weight ratio about 0.51

lb f

lb can satisfy the design requirements for

performance. In term of Class I estimated takeoff weight, this combination of loading corresponds to an engine with approximately 1200 lb f of thrust and a wing with an area of 100 square feet. Detailed geometry of the wing has been determined based on optimization of the aircraft drag which is presented in section 2.2.

1.4 Class I Component Weight Estimation * The Class I weight estimation method allows a rapid estimation of airplane component weights. This method relies on the assumption that, within the jet trainer airplane category, it is possible to express the weight of major airplane components (or groups) as a simple fraction of the airplane flight design gross weight. In this project, the designer used available fractional

The Class I weight estimation method is also referred to as the Weight Fraction method

weight information for light weight aircrafts mentioned in Data Unit Volume I I*. Estimated weight fractions and Class I weight breakdown is presented in tables 10 & 11.

FWStructure

0.330

FWPP

0.198

FW fix

0.091

FWE

0.613

FWw

0.103

FWemp

0.025

FW f

0.130

FWn

0.013

FW gear

0.057

FW gross

1.0

Component

FW Fuselage 0.126 Wing 0.102 Empennage 0.022 Landing Gear 0.048 Nacelle 0.009 Structure 0.305 Power plant 0.137 Fixed Equipment 0.166 Empty Weight 0.632

Westimate (lb) 300.6 243.0 51.9 113.4 21.4 730.3 327.1 395.4 1452.8

ΔW (lb )

Weight (lb)

-10.8 -8.7 -1.9 -4.1 -0.8 -26.3 -11.8 -14.2 -52.3

289.8 234.2 50.1 109.3 20.7 704.0 315.3 381.2 1400.5

Table 11. Class I component weight breakdown

Table 10. Weight Fractions ↑

Fixed Equipment, 26%

Fuselage, 20%

Fig. 9) Empty weight breakdown → Wing, 16% Power plant, 22% Empennage, 7%

Nacelle, 1% Landing gear, 8%

1.5 Configuration trade-off † In order to proceed towards the final goal of the design, the optimum configuration for the airplane was determined. Given that the main purpose of the aircraft is training pilots to fly VLJ aircrafts, it is suggested that the cockpit might have a side-by-side arrangement to improve the communication between the student and the instructor. It is also notable that the aircraft is required to endure hard landings and therefore will necessitate a large travel length for shock absorbers. In order to keep the weight low and to preserve good handling qualities

“Aquila Project Technical Data Unit, Vol. I” P. 10, Table 8 As Roskam suggest this trade off should be done before the performance sizing. Due to limitations in term of choices for power plant type and many other limiting factors, this method have been adopted in order to reduce the number of variables before configuration studies.

†

on the ground, the landing gear length should be kept to a minimum in order to avoid a large weight penalty due to a complicated and large undercarriage system. Another important parameter of the initial configuration that can significantly affect the performance of the aircraft is the power plant installation and the subsequent issue of inlet integration. Two main scenarios for engine installation are considered in this project:

• Externally mounted engine • Buried installation (inside the fuselage) Due to the RFP’s requirement for the aircraft to use a single jet engine, the safety and reliability of the power plant installation is incredibly important. Also, in order to ensure financial success of the project, the cost of maintenance should be kept to a minimum. This can be achieved by means of providing good accessibility to the engine and therefore eliminating the need for complex and time consuming structural modifications for disassembling the engine from the aircraft. External engine installation provides exceptional quality in terms of accessibility to the engine components, and eliminates the heavy ramping system for the air inlet. On the other hand, this type of installation increases the frictional drag due to the addition of a pylon, and will require extra structural reinforcement at the engine hardpoint which increases the weight of the structure. Also, in the case of an external installation, the hot exhaust gasses should be directed away from the control surfaces and critical aircraft components, which limit the choices of the empennage configuration. Given the necessity of a short (therefore lightweight) undercarriage, and the single engine requirements by the RFP, the engine cannot be installed under the wings: it is the designers’ opinion that an asymmetric engine installation should be avoided in case of a trainer. Such a design fails to emulate the condition and flying qualities of common VLJs and business jets.

Also considering the ground clearance requirements and the relatively short landing gears, the engine cannot be installed under the fuselage. This leaves the option of external installation limited to mounting the engine on the top of the aircraft. Given the proximity of the engine to the empennage, a V-tail may be utilized in this design to allow the hot exhaust gasses to pass in between the tails. It is notable that a V-tail reduces the wetted surface area compare to other conventional empennage configurations and correspondingly reduces drag. Aside from aerodynamic efficiency, control capabilities of the V-tail are weak due to reduced control areas compared to conventional tail configurations, and irregular dynamic responses such as â&#x20AC;&#x153;adverse roll-yaw couplingâ&#x20AC;?* are expected to occur which make this configuration an unfit platform for a transition trainer. Also in case of structural failure in the empennage, the aircraft will experience a total loss of pitch and yaw control. Internal engine installation does not have the aerodynamic issues such as the increased drag and creation of turbulent regions behind the engine pod, but it introduces the issue of engine inlet design, which can affect the performance of the engine significantly. Also, designing a highly accessible internal installation system is a challenging task that will increase the development cost of the aircraft. Addressing the issue of inlet integration will require rigorous CFD simulations to ensure the pressure recovery of the inlet and proper functioning of the inlet system in a wide range of angle of attack and sideslip angles. In order to comply with ground clearance requirements and preventing foreign objects from getting in to the engine, the option of having the inlet under the fuselage is not considered in this project. Following four initial configurations are selected for further studies:

This phenomenon is due to production of a rolling moment in opposition to the desired direction of turn by the V-tail surfaces. It is notable that one of the most famous trainer aircrafts, Beachcraft Bonanza S-35, used this type of empennage. Empennage structural failures and dynamic behaviors of the aircraft ultimately caused the FAA to issue two Airworthiness Directive (AD) notes concerning the V-tail. Consequently the tail design was modified and a conventional empennage replaced the popular V-tail in further production of the aircraft.

•

Case 1: High wing installation, internal engine mounting with a bifurcated inlet, and a tricycle landing gear.

•

Case 2: Low wing installation, internal engine mounting with a bifurcated inlet, and a tricycle landing gear.

•

Case 3: High wing installation, internal engine mounting with an S-duct inlet, and a tricycle landing gear.

•

Case 4: Low wing installation, internal engine mounting with an S-duct inlet, and a tricycle landing gear.

Aside from the methods of inlet integration, the difference between these cases is the wing installation. Studies have shown that generally due to reductions in the down-wash flow over the horizontal tail, a 20 percent increase in horizontal tail area would be needed. In terms of maneuverability, high wing installation has an unfavorable effect on the aircraft performance due to positive moment created by the wing drag about the center of gravity (which is located lower than the wing). Although this type of wing installation will require a shorter landing distance, it will increase the take-off field length caused by lack of ground effects on lift*. In terms of structural design, this type of wing installation usually requires more reinforcement such as external structural members and therefore dictates a higher structural weight. One possibility is that the aircraft could have a low wing configuration in which would enable better take-off performance due to higher ground effects on lifting surfaces†. It should be noted that a low wing is easier to reinforce at the hard point connections than a high wing and therefore it does not have the extra weight penalty caused by the additional reinforcement

* †

“ Engineering Science Data Unit”, Series 2 Volumes on Aerodynamics, Vol. 2-c, 71007; ESDU Int. Ltd., 1987 “ Engineering Science Data Unit”, Series 2 Volumes on Aerodynamics, Vol. 2-c, 71007; ESDU Int. Ltd., 1987

usually required for a high wing installation:* the main spars in the left and right wing could be connected and therefore would not need to be reinforced by external members. This would reduce the amount of frictional drag produced by the wing particularly in high speeds common in jet flights. Low wing installation is superior in terms of maneuverability because of the destabilizing effects of wing drag by producing a negative moment about the center of gravity. In terms of disadvantages, it should be noted that this kind of wing installation would increase the landing distance due to a higher lift coefficient produced by lifting surfaces that are affected by the ground. Another disadvantage of this configuration is the increased stall speed as a key requirement for a trainer aircraft, because of the high aerodynamic interference drag produced by the wing and body. Given that both the S-duct and bifurcated inlets are utilized with success in VLJ aircrafts with similar performance capabilities, the decision was made to develop two successive designs in high detail, in order to make a comparison. Given the aerodynamic and structural superiority of the low-wing installation, the decision was to use this type of installation.

1.6 Airfoil Selection Considering the determined value for the maximum lift coefficient required during the cruise segment, the ideal lift coefficient for cruising was calculated from equation 22: Cli =

C LC 0.9

Eqn. (22)

This assumption implies an 11 percent margin of error for lift coefficient during the cruise. Where: C L C =

2 mg Ď VC2 S

Eqn. (23)

This is due to superior strength of the links under tension compare to those under buckling. Hypothetically reinforcement links between the fuselage and the wing in case of a low wing aircraft are more vulnerable than those in high-wing aircrafts; therefore they usually have a larger cross section and will cause tremendous drag in jet speeds.

As a result, any airfoil with the ideal lift coefficient C l i *greater than 0.2036 and a C l max greater than 1.5 will satisfy the criteria for the airfoil. Considering that the aircraft spends a large portion of its flight time in speeds greater than mach 0.4, a laminar airfoil is suggested by Risö National Laboratory’s report†. The following airfoils have been selected and studied closely to determine which airfoil suits the aerodynamic configuration of the airplane best. NACA Airfoils: 64(1)-112, 64(1)-A212, 64(2)-A215, 64(1)-212, 67(1)-1-215, 63-210, 65(2)-215, 63-415. Graphs representing sections lift coefficient and drag coefficient vs. angle of attack, and also pressure coefficient vs. chord wise stations have been studied and compared between different choices of airfoil. Among the mentioned airfoils, NACA-64(1)-212 and NACA 64(1)-112 satisfies the required maximum lift coefficient while producing the lowest amount of drag. These airfoils could be seen in figure 10.

Fig. 10) NACA 64(1)-212 & 64(1)-112

Considering that a trainer jet is always exposed to dangerous accidental deep stall, acceptable stall behavior is crucial in creating a safe design. In order to determine which of the selected airfoils will have a more benign post stall behavior; ANSYS software is used in order to determine which airfoil will have a more stable boundary layer in a high angle of attack. Due

This parameter corresponds to the value of the lift coefficient for the optimum lift-to-drag ratio of the airfoil Franck Bertagnolio, Niels Sorensen, Jeppe Johansen and Peter Fuglsang ; Wind Turbine Airfoil Catalog, Riso National Laboratory, Roskilde, Denmark - Risø-R-1280(EN) August 2001 P.9

†

to the complexity of the flow in high angle of attack, the virtual viscosity method is used to converge the analyses*. The result of these analyses is seen in the following series of figures.

Fig. 11) Velocity contour NACA 64(1)-212, (AOA=20ยบ)

Fig. 13) Velocity contour NACA 64(1)-112, (AOA=20ยบ)

Fig. 12) Velocity vector NACA 64(1)-212, (AOA=20ยบ)

Fig. 14) Velocity vector NACA 64(1)-112, (AOA=20ยบ)

Figure 11 and 12: NACA 64(1)-212 airfoil is modeled using 2-D Fluent elements in ANSYS. This transient analysis simulates airflow with ISA properties and 36 m/sec. (70 Knots) airspeed. Shear Stress Transport model is used to simulate the turbulences in high Reynolds number ( Re = 8.82 ร 10 6 , c = 2m ). The main separation could be observed occurring at 0.55 c in this analysis. Figure 13 and 14: two dimensional model of NACA 64(1)-112 is analyzed with identical conditions to the prior model. As it can be observed, the flow remains attached at 20 degrees, which is considered way above the linear regime of both airfoils.

It appears that the boundary layer for NACA 64(1)-112 in post-stalling regions of angle of attack is more stable than NACA 64(1)-212, and therefore this airfoil is selected for the further development of this project. *

ANSYS Release 11.0 documentation, key world: Artificial Viscosity Method

1.7 Initial Fuselage Geometry 1.7.1 Fuselage side and top profiles: In order to determine the fuselage approximate dimensions, the required useful volume of the fuselage is determined to be ~110 cubic feet. The fineness ratio of the fuselage (~ 6.7) is selected based on statistical data on similar aircrafts. These criteria, dictate fuselage geometry with approximate length of 21.5 ft. and an average width of 3.7 ft. Considering the sizes for standard pilot with height of 6’-2”*, the given dimensions for engine, approximate sizes of fixed equipments † , and the minimum visibility requirements, a 2-dimensional CAD drawing of internal configuration has been prepared. An initial side profile is presented in figure 15:

Fig. 15) Initial side profile and internal arrangement. The equipment presented in this sketch represents slightly modified components used in light business jets and military trainer aircrafts. An initial sketch of the s-duct is also added in order to demonstrate the effect of the inlet integration on the internal arrangement of the aircraft.

Roskam J., Airplane Design Part III; Fig. 2.8, P. 16 , DAR Corporation, 1987 First Edition This include the integrated avionics package, environmental unit, hydraulic and pneumatic accumulators, baggage and the furnishing. †

In this design, general rules for cockpit layout have been pursued, particularly the recommended seat arrangements for light airplanes by Roskam*. In order to minimize the

pressure loss of the inlet system, an attempt was made to reduce the vertical distance between the inlet and the engine centerline as much as possible. This design decision resulted in an asymmetric side profile which requires validation in terms of zero lift moment coefficients to satisfy stability standards. As it can be observed from the side profile drawing, enough room has been dedicated to seat installation.

Also a stowage

compartment (approximately 6.7 cubic feet) in front of the cockpit has been considered in order to carry the baggage and other necessary equipment. The top profile has been designed with respect to the side profile and a 52â&#x20AC;? wide cockpit arrangement (see figure 16) in order to fit all the required equipment. In order to ensure similarity in pilot-aircraft interference with current VLJ aircrafts, a sidearm controller is selected as the main control device for rolling and pitching.

Fig. 16) Initial top profile and internal arrangement. The engine and the mid-body fuel tank could be seen in this view. It should be noted that due to safety issues and conflicts with the main landing gear retraction process, the fuel tank was changed to an integral wing tank with the same capacity later on during the project.

Roskam J., Airplane Design Part III; Figure 2.8, P. 16 , DAR Corporation, 1987 First Edition

1.7.2 Fuselage Cross-sections: Based on the 2-dimensional profiles defined for the fuselage, and considering the possible interference with cockpit, wing, power plant and empennage, cross-sectional CAD drawings have been prepared by applying modified double elliptical geometries. Guidelines set by ESDU 77028* are used in order to fit modified double elliptical cross-sections to the side and top fuselage profiles.

These cross-sections have been used in order to create a three

dimensional model with goal of modeling the air flow around the fuselage, specifically concerning the asymmetry of the fuselages side profile. The cross-sections and the result of the lofting procedure for the asymmetric body is seen in figure 17 below.

Fig. 17) Initial fuselage cross sections and the result of the first rough lofting operation.

In order to study an alternative design, a symmetric side profile was developed by lowering the engine centerline nearly 5â&#x20AC;?. This symmetric side profile could be seen in figure 18. Fig. 18) Modified side profile with symmetric aft body.

Engineering Science Data Unit, Series 2 Volumes on Aerodynamics, Vol. 3-a, 77028 Geometrical characteristics of typical bodies, ESDU Int. Ltd., 1987

The changes to the cross section ns geometry were minim mal, and, overrall the area distribution d o of the fusselage was im mproved by the modifieed cross-secttions. It should be notticed that th his modificcation may make m the bifuurcated inlet system s a more appropriate choice forr the design as a a resultt of the lowered engine. The modifieed lofting surrface models can be seen in the figurees below. Also area distribution grraphs for botth symmetricc and asymm metric fuselagge longitudinal cross-seections are sh hown in figuures 21 and 22.

Fig. 19) Initial symmeetric side profille

Fig. 21) Arrea distribution n, asymmetric side profile

F 20) Cockppit mesh, cockppit cut-outs Fig.

Fig. 22) 2 Area distriibution, symmetric side profi file

Descrip ption of Fig. 211 through 24: Fig. 19)) Lofting has been b performed ed using AutoD Desk Mechaniical Desktop surface s editing g package. Fig. 20)) Mesh has beeen refined an nd ‘normal adj djustment’ hass been perform med, and the cockpit c cut-ou ut has been en created usin ng AutoDesk Mechanical M D Desktop surfacce editing pack kage. Followiing this proces ess the messh was refined d and ‘normal adjustment’ a ha been perforrmed again. has Fig. 21 & 22) Area distribution di graaphs, for the asymmetric a siide profile and d the symmetr tric side profille. These graphs g also deemonstrate th he relative smooothness of th he geometry of o the symmettric side profi file compare red to the asym mmetric design gn. Since Aqui uila is not inten nded for transsonic flights, the th wave drag is negligib ble and thereffore the Whitc tcomb area ru ule does not apply. ap Althou ugh, it appearrs that the areea distribu ution is direct ctly related too the curvatu ure of the sur urfaces of thee body: the better b the areea distribu ution, the smooother the curvvatures and theerefore less tur urbulence arou und the fuselag ge.

3 35

In order to validate the created topology, 3 dimensional CFD analyses are used to study

the vortices created adjacent to the fuselage. 1.7.3 CFD comparison of symmetric and asymmetric longitudinal profile: Using the defined group of surfaces in section 1.7.2, two 3 dimensional CFD models are constructed using ANSYS in order to compare the effects of the symmetry of fuselage side profile on the surrounding air flow during the cruise segment. The number of CFD elements exceeds 80,000, and therefore causing the analyses to require large processing power in order to achieve a convergence.

The exhaust velocity is estimated by applying the impulse

momentum theorem, and the result is used to determine the initial conditions on the CFD model, in order to simulate the effects of exhaust flow.

Fig. 23) Velocity contour Fig. 23) Velocity contour showing the model being exposed to air flow with static pressure of 21330 Pa, Ď =0.318,Ď&#x2026;=0.00005 which is identical the atmospheric properties of the cruising segment( 180 m/sec.)with 0.7 thrust setting. Boundary layer in the upper aft body is thicker than the lower body. ( Î =0.1 idle) Fig. 24) The highly turbulent region due to the asymmetric upper body causes large negative moments, threatening the stability of the aircraft. Fig. 25) CFD elements for this analysis. Note the region of refined elements surrounding the fuselage. The size of the block is 12x15x12 meters.

Fig. 24) Turbulent kinetic energy

Fig. 25) ANSYS/Fluent elements of the model

Plotting the turbulent kinetic energy over the longitudinal cross-sections of the non-symmetric model reveals that the airflow becomes exceedingly turbulent nearing the higher end of the fuselage, therefore causing a larger drag force acting on the upper parts of the fuselage compared to the bottom*. This unbalanced distribution of the drag force on the longitudinal fuselage cross-section is believed to induce an unfavorable negative pitching moment in the aircraft, which will require adjustment of control surfaces in order to preserve the dynamic equilibrium during the level flight. This hypothesis was validated by evaluating the summation of the sheer force moment acting on the fuselage surface about the origin defined at the aircraft nose. By dividing this value by the corresponding q.S wet , the non dimensional pitching moment for each fuselage was calculated. As a result of this calculation, it appeared that the symmetric fuselage (-0.00023) has a pitching moment less than half that of the asymmetric design (-0.00054). In order to reduce drag caused by high deflection of the elevator (trim drag) over the long cruise periods, the decision is made to use the symmetric aft body for the further development of the project. On the other hand it can be argued that the reduction of the efficiency of the inlets as a result of this modification may overcome the effect of the increased drag by the asymmetric profile.

This argument will be addressed through trade studies in order to

determine the effects of the geometric inlet parameters on the engine performance. Due to the complex nature of the relations, and also other critical issues such as distortion and swirl† in the inlet which are not yet well understood, a purely theoretical approach is extremely complicated. Therefore a more subtle comparison will require including the effects of the inlet integration in the design, and will be presented in section2.9 *

Turbulent flow causes a higher value of drag compare to the laminar flow of the same speed on the fuselage; therefore the more turbulent regions cause a larger drag force acting on the adjacent surfaces. † J. Seddon E. L. Goldsmith, “Intake Aerodynamics”, AIAA Education Series, Reston, VA, P. 266

1.8 Center of Gravity Based on the configuration and placement of major components, using information presented in the Data Unit Volume I*, and also suggested values for each component C.G.†, the center of gravity of the aircraft was estimated. Component

Weight

Fuselage Group Wing Group Empennage Group Landing gear group Nacelle Group Power plant group Fixed Equipment Group

289.3 234.2 50.5 109.3 20.7 315.3 381.2

X CG ( ft ) 11.16 11.31 19.10 9.07 21.27 19.25 5.19

YCG ( ft ) 0 0 0 0 0 0 0

Table 12. Empty weight components center of gravity ↑ Table 13. Empty CG locations →

Z CG ( ft ) 3.77 3.39 6.25 0.96 3.94 3.69 4.05

Wstructure

704.0 lb

WE X CGstructure

1400.5 lb 11.75 ft

X CGE

11.65 ft

YCGstructure

0 ft

YCGE

0 ft

Z CGStructure

3.39 ft

Z CGE

3.64 ft

As required by the RFP, the change in the location of the center of gravity, due to fuel consumption over different segments of flight is studied. These studies are used later on in order to determine the longitudinal location of the wing installation and study the possibility of maintaining the trim in all flight conditions. Results of these analyses are presented in table 14 below: Mission segment Warm-up and Taxi Take off Climb Cruise Descent Loiter Land/Taxi

W FBegin ( lb )

X CG ( ft )

543.3 507.3 495.4 467.5 169.6 149.3 86.5

10.93 10.91 10.90 10.88 10.70 10.69 10.63

Z CG ( ft ) 4.00 3.98 4.06 3.99 3.94 3.89 3.89

Table 14. CG travel during flight

* †

“Aquila Project Technical Data Unit, Vol. I” PP. 11-12

Advanced Aircraft Analysis documentation, component center of gravity, DAR. Corporation

It shouuld be noted that the incrrease in the z-componen z nt of the centter of gravityy between th he stages of take-off and a climb iss caused by the landing gear retracttion, which results in th he displaceement of thee CG of landiing gear grouup by 16 inch hes during th he landing gear retraction..

F 26) Comp Fig. ponent Locatioons (see table 14 1 for component names)

C Component

Weight(lb)

1-Fuselage Group G 2 2-Wing Grouup 3 3-Empennag ge Group 4 4-Landing geear group 5 5-Power plan nt group 6 6-Fixed Equuipment 7 7-Crew 8-Trapped Fuel F and Oil 9 9-Mission Fuuel Group 10-Baggage

289.3 234.2 50.5 109.3 315.3 381.2 440 24.1 507.3 50.0

X CG ( ft ) 11.16 11.31 19.1 9.07 19.25 5.19 7.73 12.13 12.13 2.81

YCG ( ft ) 0 0 0 0 0 0 0 0 0 0

Z CG ( ft ) 3.77 3.39 5.23 0.96 3.69 4.05 4.07 4.62 4.62 3.57

Table 14. Centter of gravity for f the takeofff weight

o the first class weigh ht The prresented estiimations forr the centerr of gravity are based on estimattions. A mo ore detailed and precise analyses is performed p fo ollowing thee second classs weight estimation, which w is sligghtly differen nt from the result r achieveed using firsst class weigh ht estimattions here.

3 39

Detailed Design & Analyses Aerodynamics, trim and Inlet Integration Because of the important contribution of fuselage-wing aerodynamics and geometry to

stability and flying qualities of the aircraft, many iterative design processes are performed in order to achieve the optimum aerodynamic and geometric configuration of wing, empennage, and other aerodynamic surfaces. Due to the crucial effect of the inlet system on the general safety of the aircraft, specific attention is paid to the inlet integration. In order to determine the optimum configuration for the inlet system, two main designs are developed in parallel and compared to each other in terms of weight, inlet performance, cost, and safety. As a part of the detailed design and analysis phase of the project, AAA was used as the main computer aided engineering software package to aid the trade studies. Particularly, weight, aerodynamics, propulsion, and stability module of this software is used in order to achieve the optimum configuration for the aircraft. Analyses which are mentioned in this chapter, have been repeated due to the fact that the input parameters were updated with higher accuracy and precision (i.e. second class weight estimations, second class drag analysis, and second class C.G analysis).

2.1 Determination of Wing Incident Angle Considering the significance of the cruise flight segment in the aircrafts mission, the wing incident angle is determined based on the ideal lift coefficient for the cruise phase ( C l i ,Cruise = 0.2036 ). This parameter, which is defined as approximately 10 percent higher than the required lift coefficient for the cruise segment * , represents the highest section lift coefficient for which the sectionâ&#x20AC;&#x2122;s drag coefficient is minimized (See figure 27).

See Eqn. 24

Using C l vs. α graphs for NACA 64(1)112 provided by Abbot and von Doenhoff*, the

corresponding

C l i ,Cruise = 0.204 is

angle determine

to to

the be

approximately 3 degrees. This angle is the angle in which the wing’s lift to drag is maximized during the cruise segment of the flight, and therefore is the most suitable angle for the wing installation given the relatively high value of the sensitivity derivative of the takeoff weight due to the lift-to-drag ratio. Fig. 28) C l vs. α for different Reynolds numbers, NACA 64(1)-112

Fig. 27) C l vs. C d for different Reynolds numbers, NACA 64(1)-112 [ESDU 97020] *

I.H. Abbott and A.E. von Doenhoff, Theory of Wing Sections, Dover Publications Inc., New York, 1959.

2.2 Wing Planform Design In order to determine the optimum wing geometry for the aircraft, an optimization was performed in order to minimize the weight of the wing structure and the related RDTE cost of the structural design, which is shown to be directly proportional to the structural weight*. Equation 24 and 25 represents two widely used relations between the optimum aspect ratio and the wing quarter chord sweep for subsonic and transonic aircrafts, based on the NACA

1039 report †: Subsonic regime:

Eqn. (24)

Transonic regime:

Eqn. (25)

Roskam cites the statistical method developed by General Dynamics Company‡ in order to estimate the structural weight of the wing:

Ww GD = (1+ Fcorr )

0.00428S 0w.48 AR w M 0H.43 (WTO n ult )0.84 λ0w.14

( )

33.11 t c

0.76

Eqn. (26)

1.54

(cos Λ c ) 2

Where Fcorr = 0.02 , M H = 0.55 , λ w = 0.45 and n ult = 6 .

Given that the aircraft’s flight envelope is limited to the subsonic regime, equation 25 was substituted into the equation 27 for AR. Partial derivative of this equation was calculated with respect to the wing sweepback angle using Maple symbolic manipulator.

The result of

derivation which is a tedious exponential/trigonometric function was set to zero. Solving this equation numerically, 4 different values of Λ c was calculated. Among these solutions the 2

only real solution between zero and 90˚ is 0.195 radians equal to 11.2˚, which implies an optimum aspect ratio of 8.53. *

Roskam J.; Airplane Design Part VIII; 1990. Section 3.9 P. 22-28 Shortal, J. and Bernard Maggin, NACA Technical Note 1093 ‡ Roskam J.; Airplane Design Part V; 1999. Section 5.1.2 P. 69-71 †

2.3 Sizing of High Lift Device Considering the flap as the only low cost solution for high lift devices, the flap sizing has been performed based on the assumptions made for the maximum lift coefficient in section 1.3.1. The method presented by Roskam and Torenbeek for sizing the flap is based on solving the equation 28 for the outboard station of the flap using numerical methods, in consideration of the expected values for the maximum lift coefficient and also airfoil geometric and aerodynamic properties: S wf Sw

ΔC Lwδf ΔC lmax Δc l

3 ⎛ Δclδ f ⎜ cos 4 Λ c 4 ⎝

⎞⎛ 2 ⎟⎜1.0 − 0.08 cos Λ c 4 w ⎠⎝

⎞ ⎟ w⎠

Eqn. (27)

The outboard station of the flap is solved using the following relation for the flapped wing area ratio:

S wf Sw

(η

− ηi f

1 + λw

) [2 − (1 − λ )(η w

)]

− ηi f .

Eqn. (28)

The ratio of the increment in the maximum sectional lift coefficient due to flaps to the increment in the sectional lift coefficient is found from figure 7.4 in Airplane Design Part II as a function of flap chord ratio and the flap type: Δclmax Δcl

⎛cf ⎞ = f ⎜⎜ , Type ⎟⎟ ⎝ cw ⎠

Eqn. (29)

Due to the reasonable compensation between the complication of the mechanism and good aerodynamic efficiency compared to plain or double slotted flap systems, the flap type is chosen to be single-slotted. Considering the maximum diameter of the fuselage in the wing region to be 3.6 ft., it was assumed that the wing fairing will occupy approximately 0.5 ft. of the wing span, moving the

inboard station of the flap surface to 17 percent of the half-span of the wing.

The

assumptions for this analysis and results of the numerical calculations are presented in tables 20 and 21. C Lmax

δf

35 deg.

C Lmax

δf

Δc lmax

1.500

1.750 35 deg.

C Lmax,Clean

1.2

20% Cw

Δc l

0.8252

c lδ f

3.6793 rad .−1

′ K TO K L′

0.6223

Δclδf

0.6223 1.3987 1.3987

17 %

ΔC LWδfTO

0.3150

K trim

1.050

ΔC LWδfL

0.3150

⎛t⎞ ⎜ ⎟ ⎝ c ⎠w ARw

12 %

SW f

0.299

8.53

105.45

λW

0.46

ηi

ηO

SW 43.0%

Table 21. Results of the analyses and intermediate parameters for flap sizing

Table 20. Assumed aerodynamic characteristics for flap sizing

Figure 29 shows the initial top view of the aircraft, with the wing placed in an arbitrary location in the mid fuselage region (which will be refined later on during the project). As illustrated in this figure, the flap occupies a small fraction of

Fig. 29) Initial wing installation and flap geometry. up dated top view

the exposed wing span in order to maximize the span possible to be dedicated to aileron surfaces. To verify the choice which was made for the flap chord to wing chord ratio, the effect of this parameter on wings’ maximum lift coefficient was studied by mean of plotting values of C L max versus flap deflection angle for different values of

C w . As it can be seen from the graph

presented in figure 30, in order to achieve C L max = 1.50 with flap deflection of 35º,

should be around 0.2.

Fig. 30) CL,max vs. flap deflection for different chord ratios

Fig. 31) Velocity countor, V= 70kts. 35˚ deflection

Fig. 30) The effect of the flap chord to wing chord ratio on the maximum expected lift coefficient achieved Fig. 31) In order to avoid the flutter effects on the flap surfaces, an ANSYS CFD analysis was performed. This figure shows the air speed profile around the wing with the flap deflected at 35º, in critical stall condition (Alt =0 ft, V= 70 kts., α=3 º). K-ω model is used to simulate the turbulence. Fig. 32) This figure shows the enlarged view of the air velocity vector plot on top of the deflected flap. It is evident that the flap structure is required to be reinforced against vibrations created by the vortices detached from the flap surface.

Fig. 32) Velocity vectors, vortex on flap surface

Fig. 33) The single-slotted flap designed for the NACA 64(1)112 is shown.

Fig. 33) Single-slotted flap

2.4 Initial Drag Analyses Based on the method outlined by Roskam * presented in Data Unit Volume I † , initial drag curves have been plotted in order to demonstrate the effects of various aerodynamic configurations in different flight segments on lift and drag (see fig. 34). This calculation of drag characteristics was refined after determining exact geometry and lift properties of the aircraft through performing detailed aerodynamics analyses.

Note: the increased drag during landing is due to the higher deflection of the flaps (45˚) compare to takeoff setting (30˚)

Fig. 34) Lift Coefficient vs. Drag Coefficient

Also, studies were performed in order to validate the choice of the airfoil and aerodynamic configuration by mean of plotting lift coefficient versus ratios of different powers of C L and C D simultaneously for cruise condition. These graphs could be seen in figure 35.

Note: The optimum L0.5/D also roughly matches the optimum CL-Cd of the airfoil at the setting angle of the wing. The small deviation is due to the assumption of a finite wing for this analysis.

Fig. 35) Lift Coefficient vs. Drag Coefficient & Ratios of different powers, in cruise condition * †

Roskam J., Airplane Design Part II; Section 3.4.1 PP 118-127; 1997 “AquilaProject Technical Data Unit, Vol. I” Pages.18and 19

2.5 Determination of Wing Longitudinal Location One of the goals of this design was to keep the static margin (S.M.) of the aircraft in between 30-40%. Studies were performed using the aerodynamic module and detailed static margin feature of AAA to determine the proper longitudinal location of the wing. After the first cycle of iterations, using the stability and control module of the same software, the required empennage surface areas were determined and implemented to optimize the longitudinal location of the wing. Thanks to the capabilities of AAA, each of the calculations has been done in sufficient theoretical detail presented in provided Data Units. 2.5.1) Lift curve slopes of wing and horizontal tail: The lift curve slopes of the wing, horizontal and vertical tail were calculated based on the relations presented in Data Unit Volume I*. It has been assumed that the horizontal tail will use cambered NACA 6-series (with t c = 12%) as a cross-section airfoil. Therefore, C l α was estimated based on the method provided in Data Unit Volume I † , and the airfoil data presented by Abbot and von Doenhoff ‡. The same process was repeated in order to determine the C Lα for the combination of the wing and fuselage. Results are presented in table 22 below: Segment: C Lα

C Lα

(rad -1 ) (rad -1 ) (rad -1 )

1 2 3 4 5 6 7 4.7489 4.7735 4.8410 5.5381 4.8488 4.9495 4.7735 0.671

0.6711 0.6710 0.6586 0.6710 0.6705 0.6711

5.4200 5.446

5.5120 6.1966 5.5198 5.6200 5.4446

Table 22. Components of the lift curve slope for different flight segments

“Aquila Technical Data Unit, Vol. I” PP. 30-32, Methods represented here is obtained from “Synthesis of subsonic aircraft design” by E. Torenbeek. † “Aquila Project Technical Data Unit, Vol. I” P. 36 Equation 7 ‡ I.H. Abbott and A.E. von Doenhoff, Theory of Wing Sections, Dover Publications Inc., New York, 1959.

2.5.2) Location of aerodynamic center: Based on the relations presented in Data Unit Volume I*, the location of the Aerodynamic Center [A.C.] of each aerodynamic component was determined. Using the quarter chord method presented by Roskam † , initial sizes for the empennage were estimated, and it was assumed that they are installed at the end of fuselage. 2.5.3) The airplane pitching-moment-coefficient-due-to-AOA derivative: Using the method presented in Data Unit Volume II ‡ , the airplane’s pitching-momentcoefficient-due-to-AOA derivative ( C m ) was calculated. α

The result of this analysis is

presented in table 23. Segment: 1 (N/A) 2 3 4 5 6 7 -1 Cmα , (rad ) -1.8645 -1.8954 -1.8688 -1.9578 -2.2150 -2.2402 -2.3107 Table 23. pitching-moment-coefficients-due-to-AOA derivative.

2.5.4) The downwash gradient at the horizontal tail (

dεh ) and final wing apex: dα

Using the method presented in Data Unit Volume I§, the downwash gradient at the horizontal tail was determined (see table 24). This estimation was refined during the process of design based on change in aerodynamics and geometry of the wing and empennage later on. Segment: 1 2 3 4 5 6 7 dεh 0.4070 0.4091 0.4149 0.4746 0.4155 0.4242 0.4091 dα Table 24. Downwash gradient at the horizontal tail

Using the class I weight and C.G. information, the wing’s apex and vertical location was changed by a minimal degree range in order to obtain the proper value of the Static Margin**.

“Aquila Project Technical Data Unit, Vol. I” PP. 33-35 Roskam J., Airplane Design Part II; Section 11.1 PP 259-263; 1997 ‡ “Aquila Project Technical Data Unit, Vol. II” P. 23 § “Aquila Project Technical Data Unit, Vol. I” PP. 40-41, Equations 32 to 35 ** Range of changes has been limited to mid body region: eight to ten feet from the nose reference point. †

Repeating this process for all seven flight conditions, the best value for

the wing apex was determined to be 9.47 ft. The results of final

ARW λw Λw X apex W

105 ft 2 8.53 1.0 11.2 Deg. 9.4 ft

X ac wf

11.09 ft

∂X CG ∂S h C Lh

0.001 ft

estimations for S.M. are presented in table 25. In addition, a review of the assumptions used in this section is presented in tables 26. Methods and relations applied for detailed calculations of Static Margin could be found in Data Unit Volume II*.

20.3 ft 0.4220

x cg

xac

0.3679 0.3666 0.3630 0.3262

0.3625

0.3572

0.3666

dεh dα

34.40

40.13

39.86

42.44

SM %

34.81

33.90

31.59

Table 25. Static Margin for different flight phases

4.2024 rad

Xach

1 2 3 4 5 6 7 0.0239 0.0185 0.0239 0.0103 -0.0387 -0.0415 -0.0578

-1

36.73 %

Table 26. Assumptions or SM

2.5.5) Wing dihedral angle: Since performing instructional missions is the major goal of this design, static stability characteristics, and specially spiral flight modes, play an important role in developing the design parameters. The airplane dihedral effect coefficient or rolling-moment-coefficient-dueto-sideslip-derivative ( C l β ) is heavily affected by the wing dihedral angle. This coefficient affects both spiral and Dutch roll modes of the aircraft, which should be considered in order to comply with guidelines provided in military and civil design codes†. The negative value for C l β should be maintained in all of the flight conditions in order to meet design codes. On the other hand, if C l β takes too large of a negative value it can result in lowering the damping ratio of the Dutch roll mode and lead to low flight handling qualities while performing Dutch roll maneuvers. Considering C l β being equal to -0.10, using AAA’s *

“Aquila Project Technical Data Unit, Vol. II” PP. 28-29 MIL-F-87830 Military Specification Flying Qualities of Piloted Airplanes; Nov. 5th, 1980: Air Force Flight Dynamics Laboratory, WP AFB, Dayton, Ohio Also : Codes of Federal Aviation Regulation, FAR-23 & FAR25 (CFR) Title 14, Parts 1-59 Jan. 1st 1990, US Government Printing Office.

†

stability derivatives module, an iteration was performed in order to calculate the corresponding value of the dihedral angle. This value was determined to be approximately 3 degrees. Phillips* presents a theoretical solution to this problem, and it could be considered for more accurate estimations of dihedral angle in further phases of the detailed design. C nβ

2.6 Horizontal Tail Surface Area Estimation

0.1039 rad −1

The main goal of this analysis was to rapidly size the horizontal tail surface area, in order to satisfy the minimum S.M. of 20 percent† as Roskam suggests‡ for initial sizing of light weight aircrafts. Results were

considered against the required surface area for the initiation of

X CG ,avr x cg ,avr

10.80 ft. 0.0077 0.6620

designed elevator for longitudinal trim. Based on the relations

x ac Sh

presented in Data Unit Vol. I §, the required area for the horizontal

x ac h Airfoil

take-off rotation later on, in order to validate the properties of the

31.32 ft 2 2.5028

NACA 64-209 tail was estimated. This process has been repeated for all of the Table 27. Horizontal tail flight conditions and different values of S.M. in order to determine the largest area required for the horizontal tail surface. The results of this analysis can be found in table 27. The incident angle of the horizontal tail was determined based on the trim characteristics of the aircraft, and will be mentioned in section 4.2.

2.7 Vertical Tail Surface Area Estimation In order to ensure the directional stability characteristics of the design, the method presented in Data Unit Volume I** was applied to determine the required surface area for the vertical tail.

W.F. Philips, “Analytical Solution for Wing Dihedral Effects” Journal of aircraft, Vol. 39 №3. 2002 The difference between this assumption and the assumption made in section 2.5 is because of application of different weight factors to the contribution of the horizontal tail to the static margin. ‡ Roskam J., Airplane Design Part II; Section 11.1 PP 259-263; 1997 § “Aquila Project Technical Data Unit, Vol. I” PP. 24-25 Equations 28-32 ** “Aquila Project Technical Data Unit, Vol. I” PP. 42-44 †

It is assumed that the yawing-moment-coefficient-due-to-side-slip-

C yv

derivative ( C n β ) should be between 0.0570 and 0.1000 per radians*.

X acv

19.83 ft

C nβ

-0.0817 rad −1

Based on the projected geometry for the fuselage, wing, and vertical tail, contributions of each component to this parameter were

3.3575 rad −1

18.67 ft 2

Airfoil NACA 0009

calculated during the cruise condition and the results are shown in table 28. Knowing the approximate location of the vertical tails aerodynamic center, (based on quarter chord rule) vertical tail surface area was determined to be 18.7 ft 2 .

Table 28. Assumptions made

The initial geometry of the vertical tail was modified based on aesthetic considerations† that can tremendously affect the market for such an aircraft. The final vertical tail is a tapered and swept back surface with a similar surface area. Parameter l v , or vertical tail arm, was increased as a result of this improvement, which increases the effect of the tail on directional stability of the aircraft. result performing

Based on the

acquired

by analyses

mentioned in sections 2.4 and 2.5, the 2-dimensional CAD drawing of the aircraft was updated (see figures 36). Fig. 36) Updated 3-view for wing placement, and empennage design

Suggested by: Roskam J., Airplane Design Part II; Section 11.2 P 265; 1997 J. Roskam, Roskam’s Airplane War Stories, DAR Corp. 2002 P. 82: Cessna 172’s sales have been increased by almost 30% as a result of similar changes effecting the look of the design. Such an improvement in sale can be crucial for the profitability of Aquila, given that the market for a transition trainer for commercial purposes is not well understood as of now. †

2.8 Landing Gear Design A tricycle landing gear is the optimal design for the following reasons: -

Good visibility in take-off operations

Low weight and cost properties due to simplicity of shock absorption system

Good takeoff rotation properties compared to other types of landing gear layouts

Good handling performance on the ground (i.e., load distribution)

Based on the light weight of the aircraft, and considering the properties of tires presented by Roskam in aircraft design part IV * , it was concluded that 3 tires could satisfy the load

consideration for hard landings. The method suggested by Roskam is used in order to determine the strut travel length capable of absorbing the kinetic energy during a very hard touchdown, which is a usual case for a trainer. Equation 30 expresses the stroke of the shock absorber during touchdown as a function of the landing weight ( WL ), rate of sink ( Wt ), maximum static load per strut ( Pm ), and the efficiency of the tire ( ηt ) and the shock absorber ( ηS ): ⎧ W S S = ⎨0.5 L (Wt )2 g ⎩

(n P N ) − η S ⎫⎬ S m

⎭

ηS

Eqn. (30)

FAR-23 suggests the landing gear load factor of 8 in the case of a trainer aircraft ( N g = 8 ), and based on the statistical data presented by Roskam, the critical rate of sink has been assumed to be 13 feet per second, similar to other jet trainers. A fluid Oleo is considered for the design because of its 0.8 efficiency 0.8 ( ηs = 0.8 ), given the high load factor and sink rate. Based on the suggestions made by Roskam†, one inch has been added to the result of this

Roskam J., Airplane Design Part IV ; Section 2.4.5 P 33; 2004 Heinemann also narrate the story of the additional one inch to the travel length of the oleo with regard to the design of the A-1 Skyraider in his biography, “Combat Aircraft Designer”. Apparently the same equation was... †

stroke calculation, requiring the length of the shock absorber to be almost 0.5 ft for 13 feet per second sink rate. Static loads are calculated by solving the static equilibrium equation for nose and main landing gear in order to transfer 80 percent of the static load to the main landing gear. This load distribution is necessary in order to create good on-ground handling qualities for the nose landing gear. Based on this load distribution, and also taking in to account the safety factor of 1.25, the main landing gear tire is determined to be a Goodrich type VII with dimensions of 4.4”×16” and the nose tire with the dimensions 4.0” × 12.5”. Considering the location of CG for landing and takeoff, the landing gear geometry was determined to be in compliance with requirements for tricycle layouts presented by Roskam*. As it can be seen in figure 37, a tail clearance of 16˚ is achieved. The lateral tip-over Ψ is found to be 61.3˚ and 62.4˚ respectively for takeoff and landing condition

Fig. 37) Landing gear disposition, tail clearance and longitudinal tip-over

using the method presented in data unit vol. II † . The average height of the landing gear in order to

satisfy

the

tail

clearance

requirements is determined to be Fig. 38) Landing gear disposition, front view

20.5” while the distance between the two main landing gears is measured to be 67” inches to satisfy the lateral directional tip-over requirement of 50 degrees.

causing the unfavorable shock absorptions in hard landings, which was resolved by adding approximately 1 inch to the length of the shock absorber as a fix while A-1 was still in active service. * Roskam J., Airplane Design Part IV ; Section 2.8.2 P 76; 2004 † “Aquila Project Technical Data Unit, Vol. II” P. 80, Equations 1-6

Based on the considered volume for the landing gear retraction during the initial interior configuration of the aircraft (see section 1.7.2), a hydraulically powered retraction system was designed. The nose landing gear retracts forward into the nose compartment using a multi-bar retraction system, while the main landing gear retracts sideways inside the fuselage, using a simple retractable column.

Fig. 39) Landing gear retraction schematic

2.9 Inlet Design As it was understood during the initial configuration trades studies, two arrangement of bifurcated and S-duct inlets are considered for the further development and analysis. Given the engine properties of the J1200, the method presented by Roskam* is used in order to design the optimum inlet for the aircraft with the goal of minimizing the pressure loss in the cruise segment. Based on Roskamâ&#x20AC; , the required inlet area for a subsonic jet engine is calculated from: m& a U1 Ď Were the total air mass flow rate at the engine inlet is calculated from:

* â&#x20AC;

AC =

Eqn. (31)

m& a = m& gas + m& cool

Eqn. (32)

Roskam J., Airplane Design Part VI ; Section 6.2 PP 147-182; 1990 Same place.

The air mass flow rate per engine required for engine cooling is found from: Eqn. (33)

m& cool = 0.06 m& gas

The air mass flow rate per engine required for the proper combustion is found from:

m& gas = K BPR

TTO N eng

The value suggested for the bypass ratio factor ( K BPR ) is 0.0003 slug for engines with the bypass ratio between 2 and 4. The result lb.s

of this calculation is presented in table 29. Based on the result of this calculation two inlet geometries are developed in conjunction with the fuselage layout determined in

Eqn. (34)

U1 M1 Ď 35, 000

m& gas m& cool m& a AC

350 kts. 0.587 0.00062 slug ft 3 1.08 slug s . 0.06 slug s . 1.14 slug s . 2.91 ft 2

Table 29. Inlet parameters

section 1.7. The cross-sections for the s-duct inlet were designed in order to achieve a reasonable rate of change in the area of the diffuser. Surface model for the s-duct inlet was prepared using the surface editing package of Autodesk Mechanical Desktop. The result of the lofting and normal adjustment can be seen in figure 40a below.

Fig. 40a) s-duct inlet cross sections and adjusted surface model. Note the inlet gap at station 7

A similar process was repeated in order to obtain the suitable geometry for the bifurcated diffuser. Using the result of the CFD analyses performed in the preliminary design stage to

% # $

" #

# !

" &'

! !

" # $ % "# & ' & %% ' % ' %# # & ( )' ,3& & & !+,-, . / & 0 $ ! % 2 % 2# )' * & & ,' 34' 35 & # ' # %# "' # % * %% ! # * % ' % * %% # ' & % ' # # & ' % # ' ' # * # 6 #& # % % ' % & # '# * #* ' & % * % " # & )' # # # # &% # & %1 $ # 1 % # & ' # &# & # )' * ' '# # & ' ' $ % ' * &# # & # # ' # & # # ' # # % * % " ! ' # % ' % " # &* ' & # & % ' % "& ' # # * & # & # # && ' # #

$ " # $ % "# & ' & %% ' % ' %# # & ( )' * % # & & & !+,-, . / & 0 $ ! 1 % )' * & & ,' 34' 35 & # ' # %# "' * %% ! # * % ' % * %% # ' & ' % # ' ' # * # 6 #& # % % ' % & #* ' & % * % "

# * #

# & ( )' % ' # 3'

# # #

% ' & &

&" '' ' # # * &# # &

&0 %

1 $ " ' ' # % ' & "# 7 & &

2 #

11 2# % % ' # # & # '# *

& '

' (

! '# "

)

, -./

Equation 36 shows the relation for the distortion coefficient: ΔP Pmax Pmin = P P

Eqn. (35)

For n number of computational sectors, the average distortion coefficient is calculated from:

ΔP n =1 P n i

∑

Eqn. (36)

The engine inlet surface has been decomposed to radial elements in polar coordinates, with the radial increments of 0.125” and polar increments of 10 degrees. This decomposition has created 2710 sectors for which the distortion coefficient is calculated and averaged. The results of these analyses for different conditions are given in table 30. Condition

ΔP

P avr Bifurcated Configuration, 200 kts. Alt = 35000 ft 0.1253 Bifurcated Configuration, 350 kts. Alt = 35000 ft 0.3849 S-duct Configuration, 200 kts. Alt = 35000 ft 0.0976 S-duct Configuration, 350 kts. Alt = 35000 ft 0.3725

ηinl 0.9745 0.9357 0.9912 0.9407

Table 30. Distortion performance of both inlet configurations

Based on these analyses it appears that the s-duct have slightly less pressure distortion than the bifurcated inlet. Given the importance of the inlet performance in high angles of attacks for a transient trainer, the CFD analyses are repeated assuming higher attack angles. These analyses are mainly concerned about the properties of the duct’s boundary layer and the swirl created as a result of the incident of the inlet during the flight. As a result, it appears that the S-duct inlet generates a strong swirl, and a very thick boundary layer at the engine inlet as the

Fig. 53) Isometric view of the swirl at engine inlet, S-duct inlet, α=10˚, V=100 kts., velocity vectors

angle of attack increases. Sedon et al. suggests placement of fixed grids or free spin turbines in order to correct this type of phenomena, by means of balancing the kinetic energy in the cross-section of the flow*, while compromising the efficiency of the inlet. It should also be noted that the S-duct installation is extremely vulnerable to high angles of attack due to its location on the upper part of the fuselage. This vulnerability is caused by the turbulent and low pressure wakes created by the fuselage nose on the upper parts of the fuselage in high angles of attack. In order to demonstrate the effects of high angles of attack on the local flow around the fuselage, a 3-dimensional CFD simulation of the fuselage is exposed to 80 knot airspeed in 1000 ft. altitude with an attack angle of 10 degrees and 45 %thrust setting ( Π = 0.45 ). The result of this simulation can be seen in figure 54.

Fig. 54) side cross section of velocity contour, V=41.15 m/sec., α=10˚, Thermal loads are applied on the engine exhaust

Given the importance of the stability of the inlet surge in high angles of attack for a trainer, the bifurcated engine presents a significant advantage over the s-duct configuration by mean of less sensitivity to the orientation of flight path. Therefore this configuration is selected for further development of the Aquila. As it can be seen from figures 45 and 47, there is a low speed region of fluid separating the internal flow of the right duct from the left duct of the bifurcated inlet. It has been suggested that such a disturbance in the airflow may cause the extreme vibration of the fan and compressors blades together with the engine shaft, ultimately reducing the mechanical reliability of the engine by increasing the chance of blade loss and

J. Seddon E. L. Goldsmith, “Intake Aerodynamics”, AIAA Education Series, Reston, VA, P. 277

deformation of the main shaft. The following modifications in the design of the inlets are considered in order to resolve this issue: •

Reducing the angle between the internal walls at the point where the ducts are intersecting in front of the engine inlet.

•

Addition of vortex generators to the interior walls of the inlet. This method of flow control is shown to be extremely effective in reducing the thickness of boundary layers and generally improving the pressure recovery of the inlets by Jiräsek*.

•

Reducing the thickness or, if possible, removing the boundary layer on the interior walls at the intersection of the inlet ducts by mean of creating suction on the surface of the inlet walls. This can be accomplished by mean of using the vacuum pump unit installed on the power plant. Figures 55 and 56 are demonstrating this idea.

Fig. 55) internal boundary layer bleeding system

Fig. 56) isometric view of the flow control system installation

Although one may argue the issue of weight as a disadvantage of the bleeding system, it should be noticed that the increase in weight of the inlet system is compensated by the improved reliability and durability of the engine and, as a result, the aircraft.

Jiräsek, A.,”Design of the Vortex Generator Flow Control in Inlets”, Journal of Aircraft, Vol. 43. № 6, Nov.Dec. 2006, AIAA

Design Verification Detailed Aerodynamics, Weight & performance analyses

The purpose of detailed analyses of aerodynamic, weight, and performance is to increase the precision of estimations made in the previous chapter and verify the assumptions and the results achieved in previous chapters. Due to the importance of the stability and control in case of this aircraft, a separate chapter of this proposal is dedicated to this subject. The analyses were also used to determine the flight envelope, and flight capabilities, while acquiring a more detailed view of the changes that may be necessary in order to increase the quality of the final reasonably priced product.

Given the length and complexity of the analytical

methods utilized, and also in order to be concise, these methods are not presented in this proposal. The necessary references are made to the supplementary Data Units with regard to the equations and the analytical assumptions used in these calculations.

3.1 Detailed Drag Verification Using the method and relations presented in Data Unit Volume I*, and based on the flight conditions defined by the RFP, a detailed drag analysis was performed using AAA. The result of this analysis was used in order to determine the flight envelope for the aircraft. 3.1.1 Drag produced by lifting surfaces: Relations presented in Data Unit Vol. I† are used in order to calculate the drag produced by wing, horizontal and vertical tails. Due to the slight changes in the aerodynamic properties of the wing, and other surfaces in different altitudes ( C l α and correspondingly C Lα ), the

* †

“Aquila Project Technical Data Unit, Vol. I” PP. 70-82 “Aquila Project Technical Data Unit, Vol. I” PP. 70-71

calculations were repeated for all seven flight conditions outlined in the introduction to drag analyses in Data Unit Vol. I*. 3.1.2 Drag produced by the fuselage: Using the relations presented by Covert † and Roskam ‡, which can also be found in Data Unit Volume I §, drag produced by the fuselage was calculated. Due to the different angles of attack required for the aircraft trim in different flight conditions, the fuselage drag coefficient was estimated in different flight phases, and detailed results are provided in data unit vol. I**. 3.1.3 Drag produced by the Flaps The method suggested by Roskam†† was used in order to estimate the drag produced by the deflected flaps. This estimation was repeated for different values of flap deflection, and the results are plotted (in the form of C L versus C D ) showing the corresponding values of C D flap for different flap deflections. This graph is shown in fig. 57. 3.1.4 Drag produced by the landing gears

Fig. 57) CL vs. CD for different flap deflections

Based on the method outlined by Torenbeek ‡‡, and presented in the Data Unit Vol. I§§, drag of the landing gears was estimated for takeoff and landing conditions. The values for the landing gear drag coefficient changes minimally around 0.018 during landing and takeoff***

“Aquila Project Technical Data Unit, Vol. I” PP. 70-82 Covert E.; “Thrust and Drag: It’s prediction and verification” Section V, 2.2.2 P 140, 1985 ‡ Roskam J., Airplane Design Part VI ; Section 1.1-4.13 P 44-116; 1990 § “Aquila Project Technical Data Unit, Vol. I” Pages 78 and 79 ** “Aquila Project Technical Data Unit, Vol. I” Page 80 †† Roskam J., Airplane Design Part VI ; Section 4.6 P 82-89; 1990 ‡‡ Torenbeek, E. , Synthesis of subsonic aircraft design, Appendix G, P 550, 1981 §§ “Aquila Project Technical Data Unit, Vol. I” Page 82 *** The landing gear drag is a function of lift coefficient based on Roskam, which varies b/w landing & takeoff †

3.1.5 Drag produced by deflected control surfaces This portion of detailed analysis of the drag was completed after first studies of static stability presented in section 4.4. Knowing the deflection angles (of elevator) required for maintaining the state of the equilibrium, the corresponding drag was calculated. The results of this analyses are presented in Data Unit Volume I*. 3.1.6 Inlet drag Method presented by Roskam† the inlet drag is calculated. For subsonic spillage drag calculations, the inlet extra drag is found from equation 37:

C Dinl , ext

⎛ ⎧d − d c ⎫ = C f ⎜⎜ 1 + 0.33⎨ m ⎬Finl ext ⎩ l mc ⎭ ⎝

⎞ ⎟ ⎟ ⎠

1.667

Ac Sw

Eqn. (37)

For which the inlet extra drag factor is found from:

Finl ext

⎛ ⎞ ⎜ ⎟ ⎜ μ inl − 1 ⎟ = 11.75⎜ ⎟ ⎜ μ ⎛⎜ A m − 1 ⎞⎟ ⎟ ⎟⎟ ⎜ inl ⎜ A ⎠⎠ ⎝ c ⎝

Eqn. (38)

Where the inverse inlet flow ratio is defined as: AC A∞ 3.1.7 Windshield drag

Eqn. (39)

μ inl =

The drag coefficient due to the windshield is determined from:

C Dws = ΔC Dws

‡

Eqn. (40)

“Aquila Project Technical Data Unit, Vol. I” Pages 80-82. Roskam J., Airplane Design Part VI ; Section 6.2 P 147-182; 1990 ‡ Roskam J., Airplane Design Part VI ; Section 4.8 P 98-102; 1990 †

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..... ..... .... & ' & '! '! &' &*( * !& '** ' &1 '* ! !( * ( * & '( ' (! ( ''*& ' ' ! "#

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3.2 V-n Diagram Since performing an instructional mission is one of the possible

nlimit

3.80 g

missions for this aircraft, possible maneuvering limits in terms of

n limit ( − )

-1.52 g

C N max ( − )

-0.715

66 keas

V S (− )

96.7 keas

V Aeas

129 keas

VBeas

127 keas

process of design, in order to make critical design decisions. (i.e.

VCeas (min)

156 keas

possible changes in aerodynamic configuration,

V Deas (max)

222 keas

⎛ ∂n ⎞ ⎜ ⎟ ⎝ ∂V ⎠VB

0.0211 keas −1

⎛ ∂n ⎞ ⎜ ⎟ ⎝ ∂V ⎠VC

0.0152 keas −1

⎛ ∂n ⎞ ⎜ ⎟ ⎝ ∂V ⎠VD

0.0076 keas −1

aerodynamic and flight regulations have a significant effect on the aircraft’s structural design. Therefore it was a goal of the designer to assess the aerodynamic limits of the aircraft as early as possible in the

alternative power

plants, preferences in terms of structural materials and design and therefore cost considerations & …) In order to achieve this goal, a maneuver flight envelope was determined for the aircraft using the relations and assumptions mentioned in Federal Aviation Regulation title 23*. Also, gust conditions suggested by this code were applied to determine dictated

Table 32. Flight envelope parameters

limitations by

the

atmospheric turbulences. Methods,

assumptions,

and detailed results are presented in Data Unit Volume I†. The final V-n diagram could be seen in figure 62. Fig. 62) V-n diagram (equivalent airspeed vs. n) * †

Code of Federal Regulation, FAR-23 & FAR-25 (CFR), Jan. 1st 1990, US Government Printing Office. “Aquila Technical Data Unit, Vol. I” PP. 45-48

3.3 Detailed Structural Weight Estimations Based on the methods presented in Data Unit Volume I*, the detailed weight of the aircraft was determined based on the geometry, and design requirements. Following goals were achieved by performing these analyses: -

Verifying the initial estimation of the take-off weight

Acquiring a more accurate estimation of the weight of the aircraft.

Study the effects of different possible choices of material for the aircraft structure on the empty weight (and corresponding effects on the final cost).

A more accurate estimation of mass distribution properties of the aircraft.

3.3.1 Wing:

Using the relations mentioned in Data Unit Volume I for 3 different methods,

the weight of the wing was estimated and the average weight was selected as the final result. Safety factors suggested by Young-Niu†have been applied in order to account for the accidental loadings. Detailed results of this estimation can be found in table 33.

3.3.2 Horizontal and Vertical tail: The weight of the vertical and horizontal tail was estimated using the methods presented in the project technical data unit ‡.

nult

6.60 g

W wCessna

214.0 lb.

nult

6.60 g

nult

6.60 g

W wUSAF

244.9 lb.

WvCessna

27.8 lb.

W hCessna

45.7 lb.

WTorenbeek

204.7 lb.

WVUSAF

20.7 lb.

W hUSAF

42.2 lb.

221.2 lb.

22.4 lb.

39.8 lb.

Table 33. Wing weight

Table 34. Vertical tail weight

Table 35. Horizontal tail weight

3.3.3 Fuselage: Using methods developed by Cessna and United State Air Force*, weight of the fuselage was estimated. Results are shown in the table 36. *

“Aquila Project Technical Data Unit, Vol. I” PP. 48-49 Chun-Yung Niu, Airframe Structural Design: Practical Design Information and Data on Aircraft Structures, Lockheed aeronautical systems company, Burbank, California ‡ “Aquila Technical Data Unit, Vol. I” Pages 50 and 51 †

3.3.4 Landing gear weight: Based on the relations that are presented in Data Unit Volume I†, a detailed estimation of the undercarriage weight was performed. Results are shown in table 37. W f Cessna

5.70 g 58.8 lb.

W fUSAF

117.2 lb.

102.9 lb.

n Ult

Table 36. Detailed fuselage weight ↑ Table 37. Detailed landing gear weight →

W ng Cessna

38.1 lb.

W ng Rorenb

33.5 lb.

Wng

35.8 lb.

W mg Cessna

105.5 lb.

W mg Torenbeek

107.4 lb.

Wmg

73.5 lb.

Based on the calculations mentioned in sections 3.3.1 through 3.3.4 the total weight of the aircraft structure was calculated and demonstrated in table 38 and figure 63 below.

221.2 lb.

39.8 lb.

22.4 lb.

281.7 lb.

W gear

99.1 lb.

Wing 15%

Horizontal Tail 33%

Vertical Tail Fuselage Landing gear

Total Structure 665.2 lb. Table 38. Detailed structural weight ↑ Fig. 63) Structural weight breakdown →

43%

6% 3%

3.4 Detailed Estimation of Power Plant’s Weight Since properties of the engine are available in a detailed manner, it is possible to estimate the weight of all of relevant power plant systems, such as engine control, fuel system, engine installation, and the nacelle. In the following sections, the process of estimating the power plant’s weight was described.

* †

Roskam J., Airplane Design Part V ; Section 5.3.1 Pages 75 and 76; 1999 “Aquila Project Technical Data Unit, Vol. I” PP. 54- 55

3.4.1 Engine weight: Using the technical data provided for the selected engine (J-1200), the weight of the engine, as a major part of power plant group, has been determined to be 300 lbs. This given value complies with the estimations performed using the methods suggested by Roskam*. 3.4.2 Engine installation and control system:

Weng

300 lb

Assuming that the engine installation is to be designed by the aircraft

m& f ,TO

0.1 lb./sec.

W Eng ,Ctrl

7.6 lb.

Wess

10.6 lb.

W PGD

18.2 lb.

W PTorenb

4.6 lb.

11.4 lb.

†

manufacturer, methods presented in Data Unit Volume I were used to estimate the weight of the engine installation and control systems. The results of this estimation are presented in table 39.

3.4.3 Fuel system:

Table 39. Detailed engine installation and control weight.

Given the dangers presented to the cockpit in case of an accidental fire, the decision was made to remove the main fuselage fuel tank and replace it with a wing integral tank. The wing tank is designed to extend from 12 % to 90 % of the half span and from 25 % to 60 % chord wise initially. Volume of the fuel tank was found using AutoDesk Mechanical Desktop to be slightly more than the anticipated 11.7 cubic feet, housing 595 lbs of jet-A fuel type. As a result the location of the center of gravity was changed slightly (see section 3.6). Required fuel system weight for the fuel weight of the aircraft

* †

Fig. 64) Integral fuel tank layout

Roskam J., Airplane Design Part V ; Section 6.1.1 P 84-85 “Aquila Project Technical Data Unit, Vol. I” PP. 57- 58

(584 lb.) has been estimated using the method provided in Data Unit Vol. I*. It has been assumed that the engine consumes aviation Jet fuel grade A. This estimation includes weight of the integral fuel tanks, required fuel tubing, and volume measurement and

W Fmax

583.8 lb.

ρF

6.74

lb. (Jet-A) gallon

N sft

K tiptank

0.4

FIntegral

1.0

W fsCessna

34.2 lb.

breakdown diagram of the power plant group’s weight is shown

W fsUSAF

57.9 lb.

in figure 65.

W fsTorenbeek

253.4 lb.

W fs

115.2 lb.

monitoring devices. Result of the estimation is presented in table 41 and the

Engine

19% Fuel System

Table 40. Fuel system weight

Engine control Nacelle weight

55%

21%

Fig. 65) Power plant weight breakdown

Weng

300 lb.

W fs

115.2 lb.

WP Wn

30.4 lb. 107.9 lb.

WPP

553.5 lb.

Table 41. Propulsion system weight

3.5 Detailed Weight Estimation of Fixed Equipments The weights of different subparts of fixed items were determined using methods presented in the first volume of data units for this project. In the following sections, the process of this estimation is described and results are presented.

3.5.1 Flight control systems: Methods introduced by General Dynamics Company and Torenbeek are applied in order to calculate the flight control systems weight†. The average value of these estimations

K fcs Power

1.0

W fcs Cessna

67.4 lb.

W fcs ,USAF

294.5 lb.

W fcs ,Torenb

86.0 lb.

W fc

136.3 lb.

Table 42. Flight control sys. * †

Aquila Technical Data Unit, Vol. I” Pages 56 and 57 Roskam J., Airplane Design Part V ; Section 7.1.2, Pages 99; 1999

is accepted as the flight control systems weight. Results of these calculations are presented in table 42.

3.5.2 Instrumentation, Avionics, and Electronics: The Method presented by Roskam *has been applied in order to estimate the weight of the instrumentation, avionics, and electronics for the aircraft based on the number of pilots. Weight of these components is estimated to be 186 pounds.

3.5.3 Air-conditioning and related subsystems: The weight of the required air conditioning/pressurization system is determined by applying methods presented in Data Unit Volume

I†.

The result

of this estimation is presented in table 44. Similar to many light weight designs this system is assumed to be a part of the power plant related items. Also, the weight of additional oxygen system is calculated using the method presented by Roskam‡ 3.5.4 Cockpit furnishing: This particular weight group is accounts for the following parts of the aircraft: Seats, insulation, trim panels, sound proofing, instrument panels, control stands, lighting and wiring, and luggage containers. Methods presented in Data Unit Volume I§ were applied in order to perform the estimation.

The results of this

estimation are presented in table 44.

VPax N Crew

48 ft 3 2

LCabin

5.0 ft.

W apiTorenbeek

53.0 lb.

Wapi GD

66.9 lb.

Wapi

60.0 lb.

Wox , GD

11.4 lb.

Wox ,Torenbeek

42.4 lb.

Woxygen

26.9 lb.

Table 43. Air conditioning

N Crew

N Pax

N Seat , Row

W furCessna

41.0 lb.

W furTorenbeek

56.0 lb.

W furnish

48.5 lb.

Table 44. Air conditioning

Roskam J., Airplane Design Part V ; Section 7.4.0 Pages 103; 1999 “Aquila Project Technical Data Unit, Vol. I” Page 55 ‡ Roskam J., Airplane Design Part V ; Section 7.6.2 Pages 106; 1999 § “Aquila Project Technical Data Unit, Vol. I” Page 62-63 †

3.5.5 Auxiliary Power Unit (APU): Given the importance of ensuring the flow of hydraulic and electric power and

Flight Control System Instrumentation 27%

considering the dependency of the critical function of flight control, it

10%

Airconditioning APU Furnishing

Oxygen System Other

is determined that a light weight 12%

APU can benefit the general reliability of the aircraft.

The

Figure 66) Fixed equipment

38%

weight of this unit is estimated using the available statistics of light business jets. This data presented in the appendix A of airplane design part V* reveals that on average the weight of the APU is 0.7 percent of the takeoff weight. As a result the APU for Aquila will weight approximately 17 lbs. The weight of the fixed items was presented in table 45 and the weight breakdown is shown in figure 66. The overall takeoff weight of the aircraft is calculated based on the estimates presented in sections 3.5.1 to 3.5.5, and the result can be seen in table 46 and the weight breakdown could be seen in figure 67. 20%

Fixed Equipment

21%

Structure Power Plant Payload and Crew Fuel

19% 26%

W fix

534.0 lb.

W Structure WPP WPL WCrew M ff

665.2 lb. 368.5 lb. 50.0 lb. 440 lb. 0.8039

Mtfo

0.2 %

W FUsed

503.3 lb.

WF Wtfo

503.3 lb. 5.1 lb.

WE WTO

1567.7 lb. 2566.2 lb.

14%

Fig. 67) Takeoff weight breakdown

Table 46. Detailed takeoff weight

Roskam J., Airplane Design Part V ; Section 7.7 Pages 107; 1999

3.6 CG Location Based on the Detailed Weight Based on the decisions made about internal configuration, and according to the data discovered by performing detailed weight analysis, location of the center of gravity was found for the aircraft. The applied methods for locating the center of gravity of each component are presented in the technical data unit volume I*. The defined locations of the empty weight components are shown in table 47, and are also located in the updated side profile for the aircraft in figure 67. Component

Weight (lb.)

1-Wing 2-Horizontal tail 3-Vertical tail 4-Fuselage 5-Nose Landing Gear 6-Main Landing Gear 7-Engine 8-Fuel System 9-Propulsion System 10-Flight Control System 11-Instrumentation, Avionics, Electronics 12-Electrical System 13-Air Conditioning/Press./Anti Icing 14-Oxygen System 15-Auxilary Power Unit 16-Furnishings 17-Other Items (i.e. Cargo Handling)

221.2 39.8 22.4 281.7 25.7 73.5 241.9 115.2 11.4 136.3 185.9 99.6 60.0 26.9 16.9 48.5 9.3

X CG ( ft .) 12.63 20.40 20.20 9.39 3.64 12.73 18.71 10.17 18.25 9.49 5.40 8.01 11.04 9.49 10.59 8.47 2.83

YCG ( ft .) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Z CG ( ft .) 3.17 3.93 6.31 4.15 1.19 1.28 3.93 3.18 3.24 5.05 4.84 4.79 5.50 4.19 2.18 3.54 3.57

Table 47. Detailed CG location

X CG

10.46 ft.

YCG

0 ft

Z CG

4.06 ft.

Table 48. Empty weight CG

Fig. 68) Location of empty weight items *

â&#x20AC;&#x153;Aquila Project Technical Data Unit, Vol. Iâ&#x20AC;? Page 65

Moments of Inertia of the aircraft have been calculated based on

I xx B

49.4

the placement of the interior components. Relations used in this

I yy B

1298.2 Slug − ft 2

I zz B

1248.8 Slug − ft 2

I xz B

-51.8 Slug − ft 2

calculation are given in data unit volume I .

3.7 Detailed Performance Validation†

Slug − ft 2

Table 49. Moments of inertia

Using the methods presented by Roskam ‡, the installed thrust characteristics of the engine has been determined. This method also accounts for power extractions by mechanical parts such as gear box, fluid power systems, and electrical generators in detail, therefore yielding a more accurate estimation of the available thrust. The available installed thrust for the engine is calculated based on the provided data for J1200 from:

[

)]

(

Tavail = TUnIns avail 1 − 0.35 K EngPerf M 1 1 − η inl inc − 550

Pextra M 1a

Eqn. (41)

for which the methods and assumptions used in order to calculate the extracted power ( Pextra )is described in Data Unit Volumes II§. Based on the result of this calculation, the regression constants were found using AAA propulsion module for all flight conditions in order to fit a quadratic curve to the available thrust data (see Eqn. 42). Results of the available installed thrust could be seen in table 50: Flight Segment 1 - Taxi 2 - Takeoff 3 - Climb 4 - Cruise 5 - Descent 6 - Loiter 7 - Landing

M1 0.015 0.117 0.224 0.587 0.233 0.324 0.117

ηinl inc

TUnIns avail [lbf]

1.00 1.00 0.96 0.97 0.67 1.00 1.00

1200 1200 556 480 720 800 400

Tavail [lbf] 769 1146 527 379 691 780 346

Pextr [hp] 13.23 13.23 13.23 13.23 13.23 13.23 13.23

Athrust N/A 0.001 0.001 0.000 -0.002 -0.002 N/A

Bthrust N/A 1.50 -1.45 -0.43 -0460 -1.924 N/A

C thrust N/A 1200 994.3 453.3 895.44 1117.26 N/A

Table 50. Propulsion performance during the mission *

“Aquila Project Technical Data Unit, Vol. I” Pages 13 and 14 Detailed information about the methodology of performance calculation is presented in the second volume of Data Unit pages 1 to 15 ‡ “Aquila Project Technical Data Unit, Vol. II” Pages 1 and 2 § “Aquila Project Technical Data Unit, Vol. II” Pages 1-3 †

3.8.1 Validation of Maximum Cruise Velocity: Using the acquired regression coefficients, equation 42 is used in order to model the available thrust for the aircraft: Tavail = (A Thrust V 2 + BThrust V + C Thrust )

Eqn. (42)

The required thrust is found using the following equation:

Treq =

C D 0Clean , M ρS wVCr2 max 2 cos(α + φ T )

2WCr2 BDPclean ρS wVCr2 max cos(α + φ T )

Eqn. (43)

Both of the relations are plotted versus velocity in order to determine the maximum cruising speed for the aircraft in 35000 ft. altitude.

It was

discovered that the maximum cruising speed exceeds the specified value by the RFP by approximately 25 kts. ( Vmax =374 kts.)

Figure 69) Available and required thrust versus velocity (cruise)

3.8.2 Maximum Rate of Climb: In order to calculate the maximum rate of climb for the aircraft, relations presented in data unit volume II* were used. The rate of climb (R/C) and climb path angle were plotted versus velocity, in order to determine the maximum rate of climb for the aircraft. This graph is shown in figure 70. Using the relationship for rate of climb, the corresponding time to climb

“Aquila Project Technical Data Unit, Vol. II” Pages 13 and 15

between the altitudes of 1000 ft. and 35000 ft. was calculated by integrating the equation 44 numerically using the corresponding values of RC for every altitude h: Eqn. (44)

Same calculation was repeated for different climb scenarios and results are presented in table 50. Based on the requirements

t (1000→35000) t (10000→35000) t (1000→10000) t (10000→20000)

9.02 min. 6.49 min. 2.25 min. 2.65 min.

defined by the RFP, the maximum climb rate at 36000 ft. isTable 50. time to climb for different scenarios calculated to be 112 ft./min. therefore verifying the service ceiling of approximately 36000 ft. The results of these calculations are presented in tables 51. Alt. α R/C CGR

PSpExPwr

36000ft. 7.53 deg. ft 112 min 0.03 3360.9

ft min

5000ft. -0.73 deg. ft 3587 min 0.22 ft 6.177 min

Table 51. Maximum ROC assumptions and result Fig. 70) ROC and γ vs. velocity for cruise altitude

3.8.3 Range and Endurance: One of the goals for this design is to create a vehicle having a range greater than 950 nautical miles exceeding the range requirement of the proposal both in constant altitude and constant speed cruise (800n.m.). To validate the fulfillment of this goal, the range and endurance calculations (in constant altitude or speed) based on the outlined method in Data Unit Volume II * were performed. For both analyses it is assumed that the aircraft uses a fuel tank with a capacity of 550 lbs. of fuel (Maximum fuel weight considered in detailed weight analysis), and will consume 460 lbs. of fuel during the cruise segment (84%). Fuel consumption properties were obtained from the released performance characteristics of the engine (J-1200) as a *

“Aquila Project Technical Data Unit, Vol. II” PP. 7-9

supplement to the RFP. Result of the range and endurance analysis is presented in tables 52 thought 54. C LAR

0.50

Tavail α U1 C Lopt , MaxR

360 lb 1.90 deg 226.0 kts. 0.4303

R Cr , h = CTS

937.4 nm

Altitude

35000 ft.

Table 52. Range at constant altitude

360 lb

WFl

460 lb

Tavail

380 lbf

R Cr ,V = CTS

-0.77 deg. 0.2093 816.9nm

Treq

173 lbf

350 kts.

α U1 C L E = Max .

1.90 deg 226 kts 0.7454

E Cr , h = CTS

248.9 min

Tavail α CL

Table 53. Range at constant speed

Table 54. Endurance for constant altitude

3.8.4 Maneuverability Analysis: The airplane’s instantaneous, and sustained pull-up/push-over performances are calculated based on the method presented in the data unit volume II*. The maneuver condition was applied in order to calculate the minimum turning radius, maximum pull-up load factor, and turn rate through plotting required and available power and maneuver load factor versus

VM Treq

226 kts. 173 lb

0.1174 rad sec. 461 lb.

velocity. It was assumed that the most advanced maneuver

Tavail φ

capabilities could be achieved when the maximum amount of

TurnRate

excess power is reachable. Results of the analysis for pull up

Rturn

0.183 rad sec. 2077.3 ft

nturn

2.39 g

maneuver and instantaneous turning in maneuver flight segment

65.26˚

Table 55. Maneuvering performance

are presented in tables 55.

3.8.5 Stall Speed: The stall speed is evaluated using the equation 45:

VS =

2{W − Tset sin (α current + φT )} ρS w C Lmax

Eqn. (45)

“Aquila Project Technical Data Unit, Vol. II” PP. 10-11

Where the angle of attack is found from:

α=

C Lmax − C L0

Eqn. (46)

C Lα

The airplane lift coefficient in zero angle of attack (CL0 ) was determined for all flight conditions based on the method presented in Data Unit Volume I*. It should be noted that since the fuel weight make a considerable portion og the weight of the aircraft, the stall speed while landing is significantly different from that of takeoff by almost 14

V S ,T .O

69.3 kts

percent†. The result satisfies the requirements of the request for proposal,

V S , Land

59.0 kts

in terms of lowest clean stall speed for both take-off and landing (70 kts.).

Table 56. Stall speed

3.8.6 Takeoff Field L Length: The required takeoff field length is determined through applying relations presented in the Data Unit Volume II‡, and considering the ground effect on generated lift and drag§. It is assumed that the aircraft uses the flaps during takeoff, and therefore the maximum lift coefficient ( C L

max

= 1.50 ) is reachable. Assumptions and information regarding takeoff, and

also the result of this analysis are presented in tables 57 and 58. C L max

C DO ,TO

L D

1.500 0.0369 9.00

VSTO

69.28 kts

VLOF

83.14 kts

μg

0.02

S TO

1430 ft

0.40

S TO ,G

869 ft

Table 57. Take-off condition

Table 58. Take-off performance

“Aquila Project Technical Data Unit, Vol. I” Pages 95 and 96 The weight of the consumed fuel makes 18 percent of the takeoff weight. The deviation is caused by the change in the neutral AOA due to CG travel, which affects the CL0 and therefore the stall speed aside from the change in weight. ‡ “Aquila Project Technical Data Unit, Vol. II” Pages 4 and 5 § “ Engineering Science Data Unit”, Series 2 Volumes on Aerodynamics, Vol. 2-c, item71007; ESDU Int. Ltd., 1987 †

3.8.7 Landing Distance: Based on the RFP, the aircraft should be able to land on an airfield with the same length as it took-off from. In order to validate this characteristic, landing distance is

VSL

0.200 0.04 59.05 kts

in table 59. As it can be seen from the results, the total length of the

VA S air

76.77 kts 1351 ft

S LG

642 ft

landing field (1993 ft.) satisfies the required maximum length of the landing

1993 ft

calculated considering the ground effects*. The method used is introduced †

in detailed in Data Unit Volume II . Results of this analysis are presented

distance by the RFP (2000 ft.).

Table 59. Landing performance

Stability & control analyses: Trim, static and dynamic stability

The main objective of performing stability and control analyses is to get a collection of data detailing the stability characteristics, and effectiveness of control surfaces of the designed aircraft, and compare it against suggested values by Roskam‡ (or resources such as ESDU§ and USAF Stability & control DATCOM**). Due to extensive abilities of AAA software package for

stability and control analyses, this software was the tool of choice for these analyses. Flying quality analyses were performed to determine the level of handling ability of the aircraft during different maneuvers and flight conditions. A collection of data is presented in the Data Unit Volume II, that describes the details of these calculations, and therefore detailed aspects of technical procedures are not given in this proposal, although necessary references are made both to resources and the Data Units.

Engineering Science Data Unit”, Series 2 Volumes on Aerodynamics, Vol. 2-c, item71007; ESDU Int. Ltd., 1987 “Aquila Project Technical Data Unit, Vol. II” Pages 11 -12 ‡ J. Roskam, Airplane Flight Dynamics and Automatic Flight Controls Part I, DAR Corp. 2003 § “ Engineering Science Data Unit”, Series 2 Volumes on Aerodynamics, items in Vol. 9 a to c, Stability and flight control; ESDU Int. Ltd., 1987 ** Hoak. D.E.,”USAF Stability and Control DATCOM, Write Paterson AFB, OH †

4.1 Sizing of the Elevator The following criteria are considered in order to size the suitable elevator: -

Satisfying the trim requirements in the most critical condition of flight

The ability to initiate takeoff rotation

Several steps were taken in order to determine the size of the elevator surface. 4.1.1) An initial configuration was selected in order to start the ce

design process which is shown in table 60.

4.1.2) The required pitching moment for initiating the takeoff rotation is calculated from equation 48:

M t = M 0WB + M CG - MWB

0.15-0.30

δe (+)

20 deg.

δe (-)

20 deg.

Eqn. (48)

Airfoil NACA 64-209

Relevant moment coefficients were calculated using relations Table 60. Elevator configuration

presented in Data Unit Volume I*.

4.1.3) Solving equation 49 the required tail lift coefficient in order to maintain the state of equilibrium, was determined for the most forward location of CG in the cruise condition: Mt - C LT = 1 ρV 2 S (X MG - X CG ) 2

Eqn. (49)

CLT = - 0.1374

In order to determine the elevator chord, the derivative C L e for different values of

c h has

been plotted versus the elevator deflection angle, using relations presented in Data Unit Volume II†. The generated graph can be seen in figure 71.

* †

“Aquila Project Technical Data Unit, Vol. I” PP. 96-100 “Aquila Project Technical Data Unit, Vol. II” P-49 (Particularly equations 1-5)

As it can be seen from this graph, as the deflection angle increases, the slope of the lift coefficient curve decreases.

This can be

(justified) by the creation of slow and turbulent flow regions on the elevator surfaces in angles more than ±12º. Based

the

calculations

performed for the lift coefficient

Fig. 71) Elevator lift coefficient ( C Le ) vs. elevator deflection ( δe ) for different c e c

of the horizontal tail (with no elevator effect), it is possible to determine the maximum increase necessary in the tail lift coefficient to maintain the trim: C LT

= C L H + C L e → -0.1374 = -0.0147 + C L e → C L e = -0.123

Eqn. (50)

Referring to the graph presented in figure 71, it can be seen that an elevator surface with ce

c h ≈ 0.25 can produce such a lift coefficient while having a deflection of 20º.

4.1.4) The horizontal tail and the elevator design were analyzed in order to determine whether or not they are capable of initiating the takeoff rotation. The method suggested by Roskam * was applied, which could be found in Data Unit Volume II†. Ground effects were considered in order to achieve a higher accuracy in calculations. The required horizontal tail surface area for initiating the takeoff rotation was determined to be 26.62 square fett and the value compared to the designed horizontal tail area for satisfying the trim requirements (31.32 ft2): *

J. Roskam, Airplane Flight Dynamics and Automatic Flight Controls Part 1, Section 4.9 PP 288-292 DAR Corp. 2003 † “Aquila Project Technical Data Unit, Vol. II” PP.76-77

S hreq = 26 .62( ft 2 ) < 31 .32( ft 2 ) √

Therefore the designed surface area is suitable for initiating the takeoff rotation.

4.2 Trim Satisfaction Satisfaction of the state of equilibrium for this configuration was studied using two methods: 1- Calculating the required elevator deflection for maintaining trim 2- Plotting trim diagrams for different flight conditions

4.2.1 Method 1: Based on the method presented in Data Unit Volume II*, the required deflection angle for the trimmed lift coefficient was found for all of the flight conditions. Since the center of gravity is located in different locations, ranging from most forward to most aft-ward station, these calculations demonstrate the fulfillment of trim requirements if all the elevator deflections are within the range of possible deflections (-20˚ to +20˚). Segment δ e trim (deg)

1 N/A

2 11.38

3 9.54

4 6.04

5 8.62

6 12.11

7 4.30

Table 61. Required elevator deflection for maintaining trim in different flight conditions

As it can be seen from this table, the required angles are in between the range of elevator deflection selected in section 4.1.1 and trim could be achieved during all flight conditions.

4.2.2 Method 2: A trim diagram † is a graphical solution for determination of trim possibility, based on the equations presented in Data Unit Volume II ‡ . The trim diagram is comprised of a lift coefficient vs. angle of attack graph and a lift coefficient vs. pitching moment coefficient graph. The "trim triangle" is defined as the triangular area bound between the forward and (aft)

“Aquila Project Technical Data Unit, Vol. II” PP.68-70 Trim diagram sometimes being called trim triangle. ‡ “Aquila Project Technical Data Unit, Vol. II” PP.70-72 †

center of gravity lines and by the maximum airplane angle of attack line. This method is useful in demonstrating the following: 1) Whether or not an airplane can be trimmed at any center of gravity location with reasonable surface deflections in different flight conditions. 2) Whether or not tail stall is a limiting factor in trim. 3) The elevator deflection and lift coefficient at different angles of attack and center of gravity locations. This method is offering a more detailed view of effective elements in trim of the aircraft. Trim diagrams are constructed for all of the flight conditions, and status of the aircraft is studied in comparison to boundaries of trim triangle. An example of generated trim diagrams can be found in figure 72*. All the diagrams have been studied in order determine whether the

Fig. 72) Trim diagram, cruise condition

aircraft could maintain the state of equilibrium in all flight conditions by using the elevator. No elevator tab was considered in these analyses, although, due to small elevator deflections, a proper light-weight elevator tab should be considered in further development of the project.

All of the trim diagrams could be found in data unit II PP. 71-75

4.3 Longitudinal & lateral-directional static stability 4.3.1) Static longitudinal stability: The static longitudinal stability of the aircraft was studied by two means: 1) Location of the aircraft’s neutral point (NP) compared to the location of CG 2) Calculating important longitudinal stability derivatives C mα , C mα& Based on MIL-F-8785 B*, every aircraft with a neutral point located behind the most aft center of gravity has static longitudinal stability in all flight conditions. The location of the aircraft’s neutral point was determined using the method presented in Data Unit Volume II†. Results are presented in table 62. As it can be seen from this table, the location of the free stick

x cg

neutral point, in terms of wing

chord,

NP free

0.3679 0.3666 0.3630 0.3262 0.3596 0.3422 0.3383 0.3031

0.3625 0.3382

0.3572 0.3322

0.3666 0.3477

SM free

.3356

.3769

.3737

.4055

x ac

always

behind the location of the

1 2 3 4 5 6 7 0.0239 0.0185 0.0239 0.0103 -0.0387 -0.0415 -0.0578

.3237

.3144

.2928

Table 62. free stick neutral point and static margin

center of gravity in all segments of the flight. In order for the aircraft to be statically stable, pitching moment coefficient due to the angle of attack ( C mα ), and pitching moment coefficient due to angle of attack rate derivatives ( C mα& ) both should be negative. These derivatives are calculated based on the methods provided in Data Unit Volume II‡ § and results are represented in tables 63. Segment: C mα rad −1

1 2 3 4 5 6 7 -1.8645 -1.8954 -1.8688 -1.9578 -2.2150 -2.2402 -2.3107

−1

-5.6624 -5.7372 -5.8491 -7.3922 -6.1652 -6.3958 -6.0949

C mα&

( ) (rad )

Table 63. C mα

and C m

α&

for different flight segments

Military Specification MIL-F-8785 B Flying Qualities of Piloted Airplanes; 1969: Air Force Flight Dynamics Laboratory, WP AFB, Dayton, Ohio † “Aquila Project Technical Data Unit, Vol. II” PP. 28-29 ‡ “Aquila Project Technical Data Unit, Vol. II” Page 23 § “Aquila Project Technical Data Unit, Vol. II” Page 25

Notice that these derivatives are negative in all of the flight conditions and therefore the initial static longitudinal stability requirement is satisfied. 4.3.2) Static lateral-directional stability: FAR-23 suggests that every eligible aircraft should be capable of maintaining directional stability, and does not include any specific lateral stability requirements. In order to verify the lateral and directional static stability of the aircraft, yawing-moment coefficient-due-to-sideslip derivative ( C n β ) should be positive, and rolling-moment-coefficientdue-to-sideslip derivative ( C l β ) should be negative. These derivatives were calculated based on the method presented in Data Unit Volume II* †, and results are presented in table 64. Flight Segment : 1 (N/A) 2 3 4 5 6 7 −1 -3.01489 -0.0920 -0.0852 -0.0905 -0.0827 -0.0803 -0.0936 Clβ rad

Cnβ Table 64.

( ) (rad ) −1

0.0932

C l and C n β

0.0729

0.0628

0.0765

0.0739

0.0644

0.0780

for different flight segments

As it can be seen from the data table, the mentioned requirements for static lateral-directional stability are satisfied in all flight conditions defined by the mission profile.

4.4 Longitudinal dynamic stability Longitudinal dynamic stability derivatives were evaluated along x, y and z axis, in order to determine the transfer functions and characteristic equations. The methods applied were obtained from USAF Stability and Control DATCOM ‡, and are presented in Data Unit Volume II§. Natural frequencies and damping ratios for short period oscillations, and phugoid mode,

“Aquila Project Technical Data Unit, Vol. II” Pages 35 and 36 “Aquila Project Technical Data Unit, Vol. II” PP. 32-35 ‡ Hoak. D.E.,”USAF Stability and Control DATCOM, Write Paterson AFB, OH § “Aquila Project Technical Data Unit, Vol. II” PP. 83-86 †

were calculated based on the methods presented by Roskam*. Values of short period and long period natural frequencies and damping ratios could be seen in table 65. Flight segment: ⎛ rad ⎞ ω n ,S . P ⎜ ⎟ ⎝ s ⎠

1 (N/A) ---------

2 3.5320

3 6.1129

4 8.0105

5 5.4859

6 10.6457

7 11.2989

ζ SP

--------2.7704

0.407 0.3096

0.382 0.1701

0.246 0.0893

0.323 0.1739

0.412 0.1164

0.761 0.2246

-0.238

0.026

0.062

0.55

0.066

0.129

-0.147

TC long ( 1 ) (s)

0.433

--------

TC long ( 2 ) (s)

0.815

--------

TC long( 3 ) (s)

---------

--------

TC long( 4 ) (s)

---------

--------

rad ⎞ ωnP ,long ⎛⎜ ⎟ ⎝ s ⎠ ζ P ,long

Table 65. Dynamic longitudinal stability characteristics in different flight conditions

Since FAR/VLA requirements do not set specific limits on the undamped natural frequency, military requirements (MIL F-8785C) were adopted for the purpose of verifying the longitudinal flight qualities, and dynamic stability characteristics.MIL-F-8785C requires the equivalent undamped natural frequency of the short period mode to be within the limits mentioned in table 66 for the three flight phase categories. Flight Phase

Category A and Category C

ζ SP

0.35 0.25 0.15

1.30 2.00 --

0.30 0.20 0.15

2.00 2.00 --

min

Level 1 Level 2 Level 3

Category B

max

min

max

Table 66. MIL F-8785C requirements about short period damping ratios for different flight quality levels

Based on MIL-F-8785 C, the long-period air-speed oscillations (phugoid) which occur when an airplane seeks a stabilized air-speed following a disturbance, must meet the requirements mentioned in table 67.

J. Roskam, Airplane Flight Dynamics and Automatic Flight Controls Part I, Section 5.2.4 & 5.2.5 PP 329-337 DAR Corp. 2003

Flight Phase

MIL-F-8785 C ζ Plong

FAR Requirements ζ Plong

Level 1 Level 2

≥ 0.04 ≥ 0.04 ln( 2 ) ≤ 55 ωnP ,Long

No requirements No requirements

Level 3

No requirements

Table 67. Requirements about long period phugoid damping ratios for different flight quality levels

Results of these analyses were plotted using defined boundaries for flight qualities in order to demonstrate the levels achieved for all flight conditions. An example of these plots could be found in figure 73. demonstrates

Table 68

the

achieved

Fig. 73) Longitudinal mode checking for flight

phase category B, Cruise Condition

longitudinal flying qualities by the proposed design. Flight segment: T2 sec. P

sec.

Level P Levelξ SP

2 -----

3 -----

4 -----

5 -----

6 -----

7 -----

85.001 65.791 50.030 60.247 10.624 83.529 II I

I I

II I

Table 68. Dynamic lateral-directional stability characteristics in different flight conditions

4.5 Sizing of the ailerons Due to the acceptability and availability of FAR-23 standards for GA, and light weight aircrafts, guidelines suggested by this code are used in order to estimate the size of the required ailerons for the aircraft.

To estimate the size of the aileron for this aircraft, a theoretical approach

presented in the Technical Data Unit Volume I (pages 83 to 88) has been used. In order to be concise, this method is not presented in this proposal. The goal of achieving “level I” rolling qualities in the takeoff flight condition was followed using the rolling time constant (TR) 86

suggested by FAR-23. Assuming the aileron to have a Ca/Cw equal to 15 percent starting at 44 percent of the half-span (following the flap), the outboard station of the aileron is calculated to be located at 79 percent of the half span. This aileron geometry was validated later during the analysis of the lateral directional flying qualities trough fulfilling the rolling requirements defined in FAR-23.

4.6 Lateral-directional dynamic stability Longitudinal dynamic stability derivatives were evaluated along x, y and z axis, in order to determine the transfer functions and characteristic equations. Applied methods are obtained from USAF Stability and Control DATCOM * , and are presented in Data Unit Volume II † . Dutch mode roll’s undamped natural frequency and damping ratio and also spiral mode time constant are calculated and are presented in table 69. Flight Segment: ⎛ rad ⎞ ωnD ⎜ ⎟ ⎝ s ⎠ ζD TS (s) TR (s)

1 --------

2 2.3230

3 3.3376

4 4.7042

5 3.1182

6 5.2178

7 2.3451

-------- 0.321 0.186 0.105 0.193 0.195 0.289 -------- -21.106 155.337 1055.368 -92.585 131.962 -25.230 -------- 0.013 0.008 0.010 0.011 0.005 0.013

Table 69. Dynamic lateral-directional stability characteristics in different flight conditions

In order to have enough damping during a Dutch roll, FAR-23 & 25 suggests following the criteria listed below, and does not specify any level for Dutch roll flying qualities: FAR 23 & VLA: ζ D > 0 .052 FAR 25: ζ D > 0 .0 In order to determine the lateral-directional flying qualities of the aircraft, military standards (MIL-F-8785C) were adopted. The requirements for rolling performance are obtained from FAR-23 in order to determine the rolling performances of the aircraft in different flight

* †

Hoak. D.E.,”USAF Stability and Control DATCOM, Write Paterson AFB, OH “Aquila Project Technical Data Unit, Vol. II” Pages 103-110

conditions. These requirements are presented in Data Unit Volume II*. There are no specific requirements for spiral stability in any airplane. However, the military requirements place limits on the allowable divergence of the spiral mode, and are presented in Data Unit Volume II page 109. The results of the analysis for the Dutch-roll mode were illustrated through locating the status of the aircraft on a lateral-directional stability diagram for all of the flight conditions. An example of this kind of diagram is presented in figure 74. Achieved flying qualities by the proposed design are presented in tables 70 and 71. 2 0.8672

3 0.9042

4 1.4278

5 0.9938

6 0.7705

7 0.8373

T2 S (s)

14.630

------

64.175

-------

17.488

T1 (s)

------

107.672

731.525

------

91.47

-------

LevelS

Stable

Levelζ D Level ζ D , 23

1 Met

Level ω n D

Level ω n D ζ D

Table 70. Dutch roll and short period flying qualities and characteristics in different flight phases

LevelT R23

2 Met

3 N/R

4 N/R

LevelTR Levelφ t

1 1

5 6 7 N/R N/R N/R 1 1

1 1

φ actual (deg) 59.9 158.8 527.4 120.9 94.0

1 1 79.0

Table 71. Rolling flying qualities for different flight phases Note that there is no criteria set by the FAR-23 for the majority of the flight phases, therefore military standards (MIL-F-8785 C) is utilized. (N/R) = No requirements exist

Fig. 74) Minimum Dutch-roll frequency and damping ratio requirements for cruise flight condition, flight category: B

“Aquila Project Technical Data Unit, Vol. II” Pages 104-109

Interior detailed design Systems, structure and adoptable flying qualities

In this chapter the interior design of the aircraft and its impacts with structural design, along with the concept of adoptable flying qualities are discussed. To be concise, descriptions of detailed load determination, structural sizing, and finite element analyses for structural validations were omitted and only some of the results are presented.

5.1 Cockpit layout Based on the RFP, the cockpit should accommodate two 6’-2” adults in the airplane. Therefore, using the standard dimensioned views of 6’-2” pilots with (no helmet) released by Boeing in Wichita*, the cockpit for the aircraft is designed. Lots of effort has been paid to pilot

visibility in order to comply with the suggested cockpit layout by Roskam † for light weight aircrafts. The scaled 3-view drawing of the cockpit showing passengers inside the cockpit can be seen in figure 75.

Fig. 75) Cockpit Layout

Visibility patterns for the right and left seats were plotted, and can be seen in figures 76 and 77.

* †

Roskam J., Airplane Design Part III; Figure 2.8, P. 16 , DAR Corporation, 1987 First Edition Roskam J., Airplane Design Part III; Figure 2.8, P. 16 , DAR Corporation, 1987 First Edition

Considering the extensive use of digital display screens and glass cockpit technology in nearly all VLJs, the decission is made for the aircraft to utilize the existing

Fig. 76) Right seat visibility pattern

fully integrated avionics suites such as Garmin 1000 for the purpose

instrumentation,

navigation, flight control, and comunication.

Fig. 77) Left seat visibility pattern

With one integrated system from one supplier, issues with component

compatibility and cross functionality are minimized. Avionics issues that may arise can be rectified more quickly and completely when dealing with just one vendor. Also the Garmin 1000 avionics system offers two additional functions: Garmin Traffic Information System (TIS) and Terrain Avoidance Warning System (TAWS), which are used onboard many modern VLJs. Fig. 78) Instrumentation panel considered for the test flights. Two 14â&#x20AC;? multifunctional displays are used as the main element of the human-interference for the aircraft, while two MIDIU keyboard displays are used by the evaluation pilot during the testing process. The cockpit also accommodates two side-arm controllers, and a back-up set of basic analogue instrumentation and circuit breakers to improve the failsafety of the design. A full size Multifunctional display could replace the front panel for further development of the aircraft, making the cockpit more flexible to emulate other aircraft decks.

5.2 Internal Arrangement and system positioning Using the decisions made in the preliminary design phase and also additional details, an interior arrangement consistent with the earlier assumptions about location of sub systems was prepared. Based on the information provided by the RFP regarding the geometric properties of the power plant and the related accessories, the design of engine installation was performed. Due to unavailability of the detailed geometric data regarding the recently developed or under development subsystems specifically designed for VLJ aircraft, data for similar sub-systems that are utilized in business jets, turboprop, and jet powered trainers (and, in some cases light piston powered aircrafts) was acquired, in order to create a more realistic internal arrangement of the Aquila. Based on the current trends in the design of light aircrafts, a satellite based weather system such as XMWX data link is considered as the first choice for monitoring the weather during the flight. Given the large number of airborne weather radars in service today, especially in commercial jetliners and many of the relatively older military cargo aircrafts, the decision was made in order to incorporate the choice of light-weight weather radar in the design. Honeywell Perimus-880 weather radar has been selected for this aircraft, as one of the lightest choices available to the designer. Technical details for this system has been acquired from Honeywell’s online product library and is used in order to modify the nose compartment to be capable of housing all 3 types of antenna units (8”, 10”, 12” diameter) designed for this device. In addition to the digital displays considered for the cockpit, a wide angle projection system is used in order to provide vital information (air speed, ILS indicators, AG and SL altitudes) on the lower part of the windshield. Recently Siemens has introduced a new singleunit projection system for general purposes that can display a digital image by illuminating the transparent florescent coating of the windshield. Such a system can provide a great advantage for the instructor and student in conditions such as approach or low level loiter, for which the

pilot should have a fair deal of awareness of the outside situation while simultaneously being able to acquire vital flight parameters via instrumentation. In such conditions, a windshield display system can provide a more convenient way for the pilot to acquire information without being distracted from the outside situation. Using all the assumptions mentioned and also the structural arrangement considered for the design, an initial inboard profile drawing is prepared which can be seen in figure 79.

Fig. 79) Inboard profile. Please note the large clearance around the power plant installation particularly on the top of the fuselage( 8â&#x20AC;?). This clearance makes the engine removal possible without the need for prior structural modification, as is the usual case for buried engines.

5.3 Structural Configurations 5.3.1 Materials: Two main choices of material were considered, Aluminum alloys (2000, 5000, and 7000 Series) and a wide series of composites (Carbon-fiber based composites and fiberreinforced metal laminates). The decision was made to use 5000 series aluminum alloys for framing of the fuselage, horizontal, and vertical tails. This choice is justified by the wide variety of alternatives in terms of welding methods and also the low cost of using 5000 series aluminum alloys. Given the intense loading of the wings due to the existence of the integral fuel tanks over a large percentage of the span, the maximum yield strength of untreated 5000 series would not be sufficient for the purpose of main structural elements of the wing; therefore 7075-T-6 alloy was used for the design of the wing spars and ribs (Yield strength=

72’000 PSI)*. 5056 H-18 alloy could be used for fuselage and empennage structural members, because of its great qualities for frictional welding and relative simplicity of the pre-forging process. It should be noticed that frictional welding can reduce the number of linking members and result in lower finished cost for the aircraft.

5.3.2 Fuselage: Based on guidelines suggested by Roskam† for light-weight aircraft structures, the initial structural layouts are prepared. A frame spacing of 20”, and a longeron spacing of 10”, has been selected, with the initial frame layout prepared according to the fuselage geometry developed in section 1.7.2. Framing consists of “Z” cross sections, which make the installation of external panels possible without the use of structural adapters. An example of the fuselage cross sections can be seen in figure 80 on the fold out. Since the total depth of the frames is no more than 2” in any single place, forging is suggested for the manufacturing of the frames, and therefore a reduction in cost is possible by avoiding large size hydroform deep drawing operations which requires more expensive tooling‡. After sizing for the cross sectional area of the longerons, a standard Z cross-section was selected. This decision is mainly made due to availability of automated longeron forming systems using computers. Figure 81 shows the cross section selected for the longerons. Based on the load determination, and sizing of the fuselage structural components, the fuselage structural layout is prepared. A section of this drawing is shown in figure 82. As it can be seen from this drawing, the frame spacing in the region of connection to the wing is affected by the placement of the wing spars. In addition, a compartment having the approximate volume of 6 cubic feet, has been dedicated to installation of instrumentations and electronics in front of the cockpit. *

Properties of aluminum alloys in this section are taken from Reynolds metal corporation handbook of aluminum alloys, Louisville, Ky. † Roskam J., Airplane Design Part III; P. 124, DAR Corporation, 1987 First Edition ‡ P. Schubert, Die Method: Design, Fabrication, Maintenance, and Applications, Industrial Press Inc. NY 1966

5.3.3 Wing: A wing-box structure is used in this design, due to the simplicity of analysis and manufacturing, ultimately lowering the cost of the development. Using the suggested values by Roskam * for wing structure of light weight aircrafts, a value of 20â&#x20AC;? has been considered for rib

spacing, and two main spars are selected for the design of the wing. Chord wise locations of the wing spars are demonstrated in table 72. The front and rear spars for this aircraft are consists of an integrated

x c Spar: Front spar 26.0 % Rear spar 63.3 % Table 72. wing spars

and simple spars, sized for the most critical determined loading (Gust considerations, and high pull-up acceleration of 6.6 gâ&#x20AC;&#x2122;s). With regard to the results of the sizing operations, a drawing is prepared showing the geometry of the wing structure.

This drawing together with the

completed three dimensional model of the wing structure can be seen in figure 83.

5.3.4 Empennage: Based on the suggested values of rib spacing and spar locations by Roskam, a rib spacing of 12 inches is used in order to design the structure of horizontal and vertical tails. The structure module of AAA is used in order to size the structure for the empennage, considering loads determined, using the load module of the same software. For the horizontal tail, three main spars are chosen and their chord-wise stations are noted in table 73.

x c Spar: Front spar 13.7 % Rear spar 56.8%

Table 73. Horizontal tail spars

In the case of the horizontal tail, for the purpose of reducing the cost of tooling, all of the connectors and root joint members are identical. The vertical tail is given a sweep angle of 35Âş, to improve the aesthetics of the aircraft (as mentioned in section 2.7). Initial drawings of the empennage can be seen in figures 84 and 85. Finite element stress analyses are performed using ANSYS in order to ensure the integrity of the structure and will be discussed in section 5.4.

Roskam J., Airplane Design Part III; P. 220, DAR Corporation, 1987 First Edition

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5.4 Structural Analyses & Integrity Verification Based on the designed structure for fuselage, wing, empennage, and undercarriage, a three dimensional model of the detailed structural arrangement is prepared. Having a tolerance of ±0.05 inches for the main structural components as suggested by Young-Niu*, this model is used in order to perform finite element analysis using ANSYS, to validate the fulfillment of failure criteria in important structural members such as the wing spars. Guidelines set by ESDU 84042 † are used in order to simplify the major structural assemblies for finite element

analysis. As an example, the finite element analysis of the wing based on the critical loading data is shown here in order to demonstrate the accuracy of the estimations for the spar and rib’s dimensions and the shelling thickness. Although an incredibly powerful tool in handling the complex coupled analysis, ANSYS lacks the simple interference required in order to apply and distribute very complex sets of loading manually. In order to assist applying the determined loads resulted from the Advance Aircraft Analysis load module, a MATLAB code was written in order to distribute the shear forces and moments. This code receives the number of the loaded nodes and the perimeter of the ribs as an input from the user and returns the values for the shear forces and moments along x,y, and z axis for each loaded node. Since in the generated FEA model (see figure 91), ribs share

nodes with the wing shelling and spar elements (as a result of numerical merge operation on the model with proper tolerance), the loads are applied equally along the cross section of the ribs. Results show that the wing skin is far less stressed than the spars and ribs, considering that the maximum von-Miser stress on the shelling of the wing is approximately 0.4×108 Pa., comparing to that of the spars ( 0.5×109 Pa.) * †

Chun-Yung Niu, Airframe Structural Design: Practical Design Information and Data on Aircraft Structures, “ Engineering Science Data Unit”, Series 3 Volumes on Aerostructure, items 84042 IHS Co., 2003

Fig. 88) Wing FEA model

Fig. 89) Front spar, von-Mises stress

Fig. 88) Shell elements used to analyze the structure of the wing, including spars, ribs and shelling. Total number of elements = 250,000. Fig. 89) von-Mises stress distribution in left wing front spar, yield stress for the Al-7075 T-6, is equal to 570 MPa., shown in red. Fig. 90) von-Mises stress distribution in the upper shell of the left wing. The maximum stress plotted is equal to 0.3×108Pa. Maximum deflection of the wing tip is equal to 12.3 millimeters equal to approximately 0.5 inches.

5.5 Variable flying qualities

Fig. 90) Left wing top shell, von- Mises stress

Given the uncertainties about the future of VLJ market, it is determined that in order to ensure the financial successes of the Aquila, secondary market opportunities should be considered during the design process. One of the possible secondary markets for the aircraft is a “broad-spectrum” transient trainer that can also be utilized in order to train pilots for both flying commercial jets and military cargo planes. In order to provide the most appropriate emulation of the behavior of the mentioned types of aircraft, a training platform with variable flying quality present a major advantage over the common jet trainers. Using an analog “flyby-wire” (FBW) system, that is, hydraulic power-actuated control surfaces commanded by electrical signals, a computer can control the positioning and the deflection of the aircraft control surfaces in a different and selective manner in order to initiate different dynamic behaviors in the aircraft, matching the desired aircrafts for the training. In order to achieve

the flexibility in the longitudinal behavior and flying qualities of Aquila, two main methods were considered by the designer: CG management and aerodynamic modifications such as a tail with variable incident angle or highly deflectable elevators.

Given that the CG

management method will require the fuel to be stored inside the fuselage over a large portion of the aircraftâ&#x20AC;&#x2122;s length and considering the safety issues raised by the presence of fuel inside the fuselage, the CG management method is not suggested for the further development of the design. Highly deflectable elevators and variable incident angle tail can both pose serious threats to the safety of the aircraft in case of failure, but due to the utilization of the FBW method, a critical failure mode could be easily avoided by creating a redundant flight control system, independent of the computer interruptions. Lack of viable data about the flying qualities and stability characteristics of the under development or newly operational VLJs prevented the design of the system in a more detailed manner, although based on the analysis performed in sections 4.5 and 4.6, Aquila possesses excellent flying qualities for the light aircraft category, making it possible to integrate the variable flying quality system with no major change in the configuration or geometry of control surfaces (elevators and ailerons). A general system diagram is prepared showing the concept of the variable flying quality in the stand point of system integration, and can be seen in figure 91.

Fig. 91) Variable flying quality system. Note that the diagram is a general sketch which is applicable to both longitudinal and lateral-directional control systems

5.6 Automated design tools 5.6.1 ANSYS Inc., ANSYS and CFX finite element analysis: First introduced in 1971, ANSYS is one of the most advanced developed software packages available for the purpose of finite element analysis. Containing more than 100â&#x20AC;&#x2122;000 lines of kernel code, this software is capable of performing a variety of finite element analysis including structural, computational fluid dynamics, vibrations and so on. Two different versions of this software have been utilized in this project, Release 10, which later on has been updated to the release 11.0 (released: mid 2007). Optimization features of this package have been used in order to enhance the geometry of few structural members, such as the wing and horizontal tail spars. The CFD module of the software was used in order to ensure the flow stability around the wing, fuselage and deflected control surfaces also in order to perform trade studies regarding the induced pitching moment by the fuselage, as described in section 1.7.3. Also this module was used to perform the validation of the inlet pressure recovery and distortion while using ANSYS CFX in order to post-process the results. 5.6.2 DAR Corp, AAA, Advanced Aircraft Analysis: Release 3.1(2007) of AAA software package have been used in almost all of the phases of the Aquilaâ&#x20AC;&#x2122;s design. The code consists of several modules which cover specific disciplines such as the weight, aerodynamics, performance, geometry propulsion, stability & control, flight dynamics, loads, structures and the costs. Each module requires a particular set of input data, and produces a predefined data set. The designer determines which module to be used and in what order, based on the selected strategy mentioned in the introduction to this proposal. The user-friendly interference of the software has allowed the designer to perform the analysis and

trade studies while having the opportunity to compare the result achieved from these calculations with those achieved in similar projects to ensure the correctness of the physical models defined. A great customer service provided by DAR Corporation has proven to be very efficient for debugging the code regarding structure and load modules. 5.6.3 Autodesk Inc. Mechanical Desktop: The Mechanical Desktop package is used for CAD modeling in this project. Capable of modeling and managing complex 3D geometric assemblies, and also having elite potential for modeling complicated three dimensional surfaces, this software made it possible to create the accurate illustrations presented in this proposal set. Having also a simple 2 dimensional and 3 dimensional finite element analysis module, this software has been used in order to rapidly analyze stresses in small members of the structure during the process of the design. Although most of the structure members have been modeled in this software package, they have also been converted to IGES format to be analyzed in ANSYS. Built-in features for design of metal sheet components helped to consider the die-ejection process of manufacturing. Mechanical Desktop suggests possible changes in the geometry of components (such as corner radiuses and regions with unfavorable curvature) in order to improve the production cycle. An extensive library of standard parts such as fasteners, beam sections, and hole profiles allow the designer to create very detailed drawings in a very short time.

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