An Efficient Preliminary Design and Optimization ...

An Efficient Preliminary Design and Optimization Methodology for Light Aircraft Stabilizer and Control Surface Geometry 저자

Daniel Neufeld, Nguyen Nhu Van, Jae-Woo Lee, Sangho Kim

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한국항공우주학회 학술발표회 논문집 , 2011.11, 56-59 (4 pages)

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한국항공우주학회 The Korean Society For Aeronautical And Space Sciences

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http://www.dbpia.co.kr/Article/NODE01839451

APA Style

Daniel Neufeld, Nguyen Nhu Van, Jae-Woo Lee, Sangho Kim (2011). An Efficient Preliminary Design and Optimization Methodology for Light Aircraft Stabilizer and Control Surface Geometry. 한국항공우주학회 학술발표회 논문집, 56-59.

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An Efficient Preliminary Design and Optimization Methodology for Light Aircraft Stabilizer and Control Surface Geometry Daniel Neufeld1*, Nguyen Nhu Van, Jae-Woo Lee, Sangho Kim Konkuk University1

ABSTRACT This paper describes a methodology for preliminary design of the stabilizers and control surfaces for a general aviation class light aircraft. The approach implements Multi-Disciplinary Design Optimization, integrating aerodynamics and weight analysis modules. The optimal stabilizer and control sizing is determined such that the drag in the cruise phase of flight is minimized the aircraft is stable and has desirable handling qualities during all phases of flight for all allowable loading situations. The approach has been implemented in the conceptual and early preliminary design phases of a new light aircraft, the KLA-100, currently under development. The results show a good agreement between optimized stabilizer configurations and that of currently available aircraft designs. Key Words: Design Optimization, stability and control

1.Introduction

2. Design Goals

The development of the stabilizer and control surface geometry of light aircraft is typically performed in the conceptual and preliminary design stages by implementing statistics-based equations and charts to roughly establish a design with positive static stability and adequate controllability. The initial designs may be revised using high fidelity analysis and other more reliable tools later in the design process for the case of sophisticated commercial or military aircraft [1]. However, for light aircraft design, such methods are rarely implemented. Additionally, light aircraft designers rarely perform flight dynamics analysis during the design process. Weaknesses in the stabilizer and control design might only be exposed once flight testing begins, and many design iterations may be necessary in the late stages of the aircraft design process to satisfy design goals relating to stability and handling qualities. If a better design can be established early in the design process, it may be possible to avoid these costly revisions. In this research, we present a stabilizer preliminary design tool that implements a modern Multi-Disciplinary Design Optimization (MDO) approach that integrates weight analysis, aerodynamics, and flight dynamics to establish stabilizer and control surface configurations that are more likely to satisfy design goals, avoiding costly revisions, than those designed using traditional approaches. The approach enables designers to establish goals for static and dynamic stability as well as flight handling qualities to establish the best possible initial design for the stabilizer and control surface geometry of light aircraft.

It is important in the field of optimization to establish meaningful design goals. A poorly thought-out set of design goals will lead to poor results regardless of the sophistication of the optimization process itself. The design goals for the KLA-100 were established based on both certification guidelines and handling quality guidelines based on other well-known sources. These sources include the MIL-S8785C document which includes a set of guidelines that relates subjective handling qualities based on pilot surveys to specific numerical targets for dynamic stability coefficients [2]. The document defines Level 1, 2, and 3 flight qualities for small, low speed aircraft to large, high speed commercial and military aircraft. All 3 levels are defined as airworthy, with level 1 being the most desirable, level 2 being acceptable, and level 3 being undesirable. The design goals for the KLA-100 were established to enforce flight handling qualities that comply with the level 1 specifications outlined in the document. The specifications include targets for phugoid, spiral, short period, and dutch roll modes. In addition to these, constraints were established to ensure adequate elevator authority in the flared condition during landing, and for takeoff rotation with a front-most CG condition. A maximum rearward static margin was set to 5% for the aft-most CG condition. Longitudinal static stability was also considered, constraining the yaw moments due to sideslip and roll according to guidelines given in several publications [3], [4]. The constraints for the stability and handling characteristics are summarized

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in Table 1. Table 1 - KLA-100 Design Goals Design Constraints Symbol Unit Min Longitudinal Flying Qualities Phugoid Damping 0.040 Short Period Damping 0.30 Lateral Flying Qualities Dutch Roll Damping 0.08 Dutch Roll Frequency rad/s 0.4 Roll time constant s Spiral time to double s 20 Static Stability Requirements Static margin 5 Yaw moment/sideslip 1/rad +0.040 Yaw moment /roll 1/rad -0.030 Other Requirements Takeoff rotation 0 Flare elevator def. deg Full flap stall speed m/s Constraint

3.

Max 2.00 1.4 20 25 20.6

Analysis Module Integration

The stabilizer and control optimization implements two analysis codes – a statistical mass estimation algorithm and a Vortex Lattice Method (VLM) based aerodynamics solver. The solvers were integrated in a Multi-Discipline-Feasible (MDF) based MDO framework. The MDF method ensures a consistent set of variable states between the different analysis methods by performing a system analysis using fixed point iterations at every update of the design variable vector [5–7]. The MDF method is an early and classical MDO approach, but is more suitable than other approaches in this application, since the number of design variables is small and the quantity of information exchanged between disciplines is also not large. The mass estimation equations include a set of statistical equations for each of the major components of the aircraft configuration. The methodology is widely applied in the conceptual design phase of aircraft design [3], [8], [9]. The equations were developed by sophisticated statistical analysis of a database of general aviation equations. To ensure the predicted mass estimations from the weight analysis module were sufficiently accurate, calibration factors were added to the equations. These were developed by modeling and testing many currently available light aircraft and computing the average discrepancies in the total mass prediction. Since LSA

and VLA aircraft belong to a relatively new class of aircraft and since many are built with modern composite materials, the classical statistical analysis methods tend to over-predict the total empty and gross mass of the aircraft in the VLA/LSA aircraft database. Therefore, the equations were scaled such that the average error of the equations when compared to the database entries becomes zero. The approach allows mass predictions with a typical error rate relative to existing designs of around 5%. The mass estimation module loads a data file containing information on how the aircraft is typically loaded. Scenarios with empty and full fuel, one and two occupants, and full and empty baggage compartments were considered in order to cover all allowable CG locations that may be encountered in the practical use of the aircraft. The empty mass, the operating takeoff mass, and the moments of inertia are computed. In addition to the loading condition, the mass input files can overwrite the predicted mass values with values delivered from other departments in the design organization, allowing the predictions to be updated as the knowledge about the design increases with new progress. Additionally, a simple schematic of the aircraft geometry and mass locations along with the CG and aerodynamic neutral point is automatically generated. Figure 1 shows the mass breakdown schematic for the most recent iteration of the KLA-100 design.

vertical stab 6 kg

panel 17 kg CG

wing 2 32 kg

neutral point

fuselage + misc. masses payload 118 kg 75 kg

fuel tank 2 47.5 kg main gear 14 kg

Engine system 111 kg

nose gear 11 kg

fuel tank 1 47.5 kg

horizontal stab 1 and 2 12 kg

occupants 180 kg

wing 1 32 kg

Figure 1 - Statistical Mass Breakdown The aerodynamics module implements a parameterized VLM model representing the wing and stabilizer surfaces and simplified fuselage geometry was developed. The model may be altered, updated and analyzed automatically, enabling the use of design optimization algorithms to dynamically test alterations to the design.

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The VLM method is a computational approach for analyzing 3d aerodynamic effects on single or multiple finite wing surfaces. It is a much simpler and faster solving approach than Navier-Stokes based CFD solvers, but remains a fast and accurate method for low speed, pre-stall aerodynamics [10]. The well-known Athena Vortex Lattice (AVL) solver was implemented [11].

Figure 2 - VLM Aerodynamics Model The algorithm implements the MDF approach for integrating the aerodynamics discipline and the weight analysis discipline. The optimizer revises the aircraft geometry by updating the design variables for every new iteration. The geometry is assessed by the aerodynamics solver using estimated mass and CG values to determine the constraints and the flight conditions and loading conditions that are required as input for the statistical weight analysis. The weight analysis is then carried out, calculating the mass properties and CG location required as input to the aerodynamics solver. A fixed-pointiteration solver performs iterations until the variables are consistent between analyses. The performance predictions with respect to mass, CG, static, and dynamic stability are stored and assessed against the constraint targets. Figure 3 shows a simplified schematic of the algorithm.

Optimizer geometry

performance

VLM Aerodynamics

loads

Statistical Weight Estimation

CG

Figure 3 - Simplified Algorithm Outline

4.

Results

The optimizations were carried out to determine stabilizer and control surface geometry that yields an

aircraft capable of complying with all of the static and dynamic design goals while minimizing the total surface area of the stabilizers. This ensures a low-drag, lowmass design. Three flight conditions were considered – takeoff roll just prior to rotation, landing during the flare, and flight at the design cruise speed of 60 m/s. The takeoff condition is used to assess the horizontal stabilizer’s ability to rotate the aircraft well before liftoff. Full stability assessments are carried out at both the landing and cruise flight conditions for every user defined aircraft loading condition. The results shown indicate only the constraint value that lies closest to the boundary. In general, the low speed landing configuration drives the static and dynamic stability constraints. The design variables considered are given in Table 2. They include the geometry of the stabilizers and the chord ratio of the associated control surface as well as the location of the main wing. The objective function was to minimize the total combined surface area of the vertical and horizontal stabilizers. This constraint has the effect of driving the designs to lighter and lower drag solutions. Table 2 - Design Variables Design Variables Symbol Unit Horizontal Stab Span Horizontal Stab Area Vertical Stab Span Vertical Stab Area Elevator Chord Ratio Rudder Chord Ratio Flap Chord Ratio Flap Span Ratio Main Wing Apex

-

Min 1 1 1 0.5 0.1 0.1 0.1 0.5 1

Max 5 5 5 5 0.5 0.5 0.3 0.75 3

The optimization was carried out using the gradient based Sequential Quadratic Programming (SQP) solver provided in the MATLAB optimization toolbox [12]. Convergence occurs rapidly, with solution times ranging from 20 to 40 minutes on a modern desktop computer. The convergence history is shown in Figure 4. The optimized stabilizer and control configuration is shown in Figure 5 and the final design variables are shown in Table 3. The convergence history clearly indicates that all the constraints have been met or exceeded and the objective function has improved from the starting conditions, reducing the total stabilizer area from 10 to 4.2 square meters in total.

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Objective Function / Max Constraint Violation

28

Objective Constraints

23

values from a light aircraft database are 0.506 and 0.33 respectively, indicating that the results are in good agreement with currently available designs.

Acknowledgements

18

The authors would like to appreciate that this research was supported by a grant (1615001723) from the Light Aircraft Development Program funded by Ministry of Land, Transport and Maritime affairs of Korean government

13 8 3 -2 0

10

20

30

References

Function Evalutions

Figure 4 - Optimization Convergence History

Figure 5 - Optimized Configuration Table 3 - Final Design Variables Variable Horizontal Stab Span Horizontal Stab Area Vertical Stab Span Vertical Stab Area Elevator Chord Ratio Rudder Chord Ratio Flap Chord Ratio Flap Span Ratio Main Wing Apex

Value 3.00 1.88 1.30 1.05 0.35 0.45 0.25 0.57 1.40 m

5. Conclusions In this paper, we present a stabilizer and control surface sizing approach that considers both static stability and flight dynamics to determine optimal stabilizer configurations for the preliminary design phase of light aircraft design. The results can be produced very quickly using a SQP based solver. The resulting horizontal and vertical stabilizer volume ratios were 0.52 and 0.031. Average

[1]

R. Perez, H. Liu, and K. Behdinan, “Multidisciplinary optimization framework for control-configuration integration in aircraft conceptual design,” Journal of Aircraft, vol. 43, no. 6, pp. 1937-1948, Dec. 2006. [2] “Flying Qualities of Piloted Airplanes.” [Online]. Available: http://www.google.com/search?q=Flying+Qualities +of+Piloted+Airplanes&ie=utf-8&oe=utf8&aq=t&rls=org.mozilla:enUS:official&client=firefox-a. [Accessed: 23-Sep2011]. [3] D. Raymer, Aircraft design : a conceptual approach, 3rd ed. Reston VA: American Institute of Aeronautics and Astronautics, 1999. [4] J. Roskam, Airplane flight dynamics and automatic flight controls. DARcorporation, 2001. [5] S. Yi, J. Shin, and G. Park, “Comparison of MDO methods with mathematical examples,” Structural and Multidisciplinary Optimization, vol. 35, no. 5, pp. 391-402, May 2008. [6] N. Tedford, “Comparison of MDO Architectures within a Universal Framework,” University of Toronto, 2006. [7] N. M. Alexandrov and S. Kodiyalam, “Initial results of an MDO method evaluation study,” AIAA Paper, 1998. [8] J. Roskam, Airplane design. DARcorporation, 2000. [9] E. Torenbeek, “Quick estimation of wing structural weight for preliminary aircraft design,” Aircraft Engineering and Aerospace Technology: An International Journal, vol. 44, pp. 18-19, 1993. [10] P. Konstadinopoulos, D. F. Thrasher, A. H. Nayfeh, L. Watson, and D. T. Mook, “Vortex-Lattice Method for General, Unsteady Aerodynamics,” Journal of Aircraft, vol. 22, no. 1, pp. 43-49, 1985. [11] M. Drela and H. Youngren, “Athena Vortex Lattice,” Software Package, Ver. 3.27, 2008. [12] The Mathworks, MATLAB (R). Natick, MA: The Mathworks, 2010.

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