Control surface design for radio-controlled aircraft. Case: SAE aero design micro-class prototype

: This research article presents a design methodology for primary control surfaces (Ailerons, Rudder and Elevator) for experimental unmanned radio-controlled aircraft. The methodology is based on the proposal and standardization of the required mechanical and aerodynamic analysis for each control surface sizing, considering the SAE Aero Design competition objectives within Micro Class. It is used on empirical results previously described in references about aeronautical design, computerized fluids dynamics (CFD) software


Introduction
The SAE Aero Design competition is intended to provide engineering students with real-life challenges, posing the kind of problems that engineers must address in the work environment [1]. Thus, the participation in the Micro category of the competition is aimed at the design of a micro-UAV (unmanned aerial vehicle) of low weight, which can be assembled in the shortest time possible and deployed manually, carrying the greatest amount of cargo in relation to its unladen weight [2]. The design and construction of unmanned aircraft evolve depending on the needs of users and their expectations: universities, government agencies, technology companies, public and private research and development centers, mostly, carry out research according to their interests [3]. Moreover, other report shows that UAVs are used in other applications such as precision agriculture and mapping [4]. Therefore, the design of the competition's Micro category aircraft must consider proper control and ease of maneuvering, so as to avoid forced landings or partial or total loss of the aircraft. A poor design of the aircraft control surfaces means that the aircraft does not meet the requirements of the competition.
The aircraft design is a collaborative and multidisciplinary process.
It involves several experts with different disciplinary competences that often belong to different departments or organizations, such as developing a new generation of multidisciplinary design analysis and optimization (MDAO) frameworks for aircraft design [5]. The design of an aircraft goes through an initial phase of conceptual design in which the requirements requested by customers are considered: technological level, size of the aircraft, appropriate engines, airworthiness; comprehensive solutions in the form of schemes where aspects such as practical knowledge, production methods, and commercial scope have great relevance [6,7]. The design of an aircraft is a complex process that considers different disciplines holistically: safety requirements, reliability goals, performance specifications required by the mission to be fulfilled, among others [8]. For example, after establishing the preliminary design of the aircraft, stability is analyzed, and control surfaces are designed [9]. In the design of control surfaces, two aspects are particularly relevant, their dimensioning and the associated control laws. These aspects can be approached through optimization strategies. Regarding the design of control surfaces, through the application of an optimization process in the airfoils of a BWB, blended wing body configuration, an improvement in aerodynamic performance is obtained in a transonic regime [10]. Regarding optimization techniques, plant-controller optimization problems can be solved by sequential, iterative and simultaneous strategies, the latter being the one that guarantees optimal results due to the coupling of the fields [11]. Consequently, the dimensioning of control surfaces and the design of the corresponding control laws constitute a coupling problem, whose resolution can be approximated by techniques such as multidisciplinary optimization (MDO) or linear matrix inequalities (LMI), among others [12]. In obtaining the control variables and calculating the dynamic stability a CFD modeling by means of the panel method is proposed highlighting the importance of computer modeling to complement the results of experimental tests, such as wind tunnel testing [13]. The use of wind tunnels occurs in the last phases of the design. For example, the evaluation of the different aerodynamic behavior of a low aspect ratio wing at high angles of deflection by means of an experimental wind tunnel test campaign on a generic regional turboprop aircraft model with a modular vertical tail with a rudder [14]. However, sometimes, the quality of the air flow may affect the aerodynamic performance [15,16]. With the increase of the computer's calculation capacity, in terms of memory, and speed, the programs have evolved in complexity, efficiency and precision of their results. Although programs based on numerical methodologies can be time-consuming in the development of simulations, they provide increasingly accurate results. For instance, the dynamic response data of modal analyses in aircraft's structures can be identified through numerical methodologies as in [17].
Flow analysis by means of CFD is an alternative to carrying out expensive experimental tests performed, for example, with fully developed flows with high Reynolds numbers [18]. In this regard, a numerical model, based on the methods of the panels and images is proposed to analyze the influence of the dynamic ground effect on the aerodynamic characteristics of a rectangular wing [19]. On the other hand, the finite element method (FEM) allows, for example, designing a landing gear during the conceptual stage to analyze the impact loads during take-off and landing of an unmanned aircraft [20]. However, throughout the process of the conceptual design stage, problems may arise in the adaptation of mesh generation tools with other design programs. In this regard, a description list of programs used in the conceptual phase of aircraft design is displayed and highlights the increasing time designers spend on repetitive tasks such as mesh generation and refinement or iterative calculation for post-process analysis. To this end, a modeling methodology consisting of the parametrization of geometric variables of the external surfaces of an aircraft is proposed in order to increase the efficiency of the design process. In this way, the next new step for design and optimization consists of the fully automated framework of aircraft components [21]. A fully automated framework dedicated to the high-fidelity multidisciplinary design optimization of the passenger aircraft wing is developed, integrating a set of popular commercial software using their scripting capabilities [22].
Following this trend, this work focuses on the development of a methodology for the design of control surfaces in radio-controlled and unmanned aircraft that allows the improvement of efficiency in the design phase and provides the designer with more time for analyses in other design areas. The control surfaces considered are the elevator, the ailerons and the rudder.
For the modeling, the proposed methodology considers the use of the open-source CFD program XFLR5 [23]. The work is structured as follows; Section 2 describes the guidelines for the development of the design methodology for each of the control surfaces involved. Section 3 details the numerical and analytical approach to the methodology applied to control surfaces in radio-controlled experimental airplanes. Section 4 presents the results of applying the methodology to the latest aircraft design: the aileron's design sensitivity analysis and the optimization of the control surfaces weight in relation to the aircraft's takeoff weight.

Methodology
The first step to develop the design methodology is to classify the aircraft according to its Class, Phases of Flight, and Levels of Acceptability. This classification is made following FAA (Federal Aviation Administration) Part 23 airworthiness regulations for GA utility aircraft [24] and Mil-F8785C military standards for aircraft design used by the USAF (The United States Air Force) [25]. This allows us to set a working envelope for design as stated by aeronautical regulators regarding control requirements. The prototype is considered as a utility aircraft with a maximum takeoff weight (MTW) less to 6000 Kg. After the prototype is tossed, it must climb up to a determined height, then must complete turns, descent and land. During this mission, it is essential that the aircraft responds effectively to the control orders. Therefore, the prototype is defined as a "Class I" aircraft that must accomplish "Phase C" flight operations and from which is expected a "Level 1" of Acceptability.

Considered design variables
Design variables are categorized according to each control characteristics and requirements. The variables are classified in: environmental variables, geometrical variables, aerodynamic variables, and inertial variables.   The methodology evaluates geometrical relations from the minimum recommended value. If the minimum value does not satisfy the design requirements for that specific design stage, designers evaluate the next higher value until the requirement is met. Inertial variables are related to the airplane's moments of inertia with respect to the CG. These variables depend on the punctual masses of each structural element, electronic components, and the payload of the airplane, see Table 3.

General considerations for control surface design
Once the variables are presented, some general design considerations must be established. The CG position is fixed during the flight mission because it is a UAV and does not burn fuel. The maximum control surface deflection must be less than the control deflection that causes the stall of the respective lifting surface [28].

Elevator design
The elevator is the longitudinal control surface about the lateral axis of the airplane. When the elevator is deflected upwards, the tail's lift coefficient decreases, producing a nose-up pitching moment and causing the aircraft to climb. Operation is reverted when the elevator is deflected downwards. This surface helps to maintain longitudinal stability and is generally mounted in the horizontal stabilizer covering a portion of its chord. For elevator design must be established that: a) deflections (δ E ) will be positive (+) downwards, b) a positive deflection (+) increases the horizontal stabilizer's lift, generating an upward movement of the tail and a (-) pitching moment that causes the aircraft to descent. Table 4 indicates the parameters to obtain using the methodology:

Aileron design
Ailerons provide lateral control about the plane's longitudinal axis. For the ailerons, it must be taken into count that: a) every deflection (δ A ) will be positive (+) if produces a clockwise roll and b) every (+) deflection decreases the lift in the right wing and increases the lift in the left wing. This situation induces a clockwise roll and a subsequent turn to the right. The parameters to determine in the aileron methodology are shown in Table  5. Table 5 Parameters to obtain as a result of the ailerons design

Parameters of the ailerons Expression
Maximum deflection

Rudder design
The Rudder provides directional control with respect to the vertical axis of the plane. The guidelines for the development of the methodology consider that: a) rudder deflection (δ R ) will be positive (+) to the left and b) positive deflection of the rudder produces a lateral force on the vertical stabilizer in the right direction, generating a negative yaw moment that turns the aircraft nose towards the left. The parameters to determine in the methodology are appreciated in Table 6. Landing and takeoff in crosswind conditions are the most critical condition for the rudder operation.

Methodology development
The control surface design process is presented by posing the design methodology for ailerons, elevator, and rudder.

Elevator design methodology
The goal is to calculate the elevator's efficiency (τ E ) in order to determine the chord relation between the elevator and the horizontal stabilizer ( C E C h ) and, ultimately, the elevator chord (C E ). Figure 1 shows the chord ratio as a function of the elevator efficiency.

Figure 1
Elevator efficiency versus chord ratio graph [27] If separation of the boundary layer of the airflow on the top of the airfoil is likely to occur, and stall could be induced [29].

Phase num. 1 Identification of longitudinal control requirements and determination of the elevator chord C E :
The elevator efficiency is calculated from Equation 1 and .  . is the planform surface of the horizontal stabilizer.
During takeoff, the control mission of the elevator is critical because it has to overcome the inertia and elevate the aircraft off the ground. Figure 2 represents the forces present in an aircraft at the moment of takeoff and Table  7 shows a summary of them. In the case of the micro category aircraft's, the fuselage has minimum influence regarding the generation of lift.
Therefore, it is assumed that L wf ≈ L w , see Equation 8 and is the distance to the wing-fuselage aerodynamic center which is located at ±5% of the MAC, mean aerodynamic chord, and the aerodynamic center of the wing at ±25% of the MAC [31].
is the aerodynamic variable that indicates the aircraft's linear speed during takeoff rotation. In order to increase the safety, the margin is considered equal to the stall speed (V S ), and (C L T O ) is the coefficient of lift of the aircraft at takeoff. (checked in phase 2) and, in turn in, Equation

Phase num. 2 comparison of results (C L h ) with XFLR5
It is checked that the horizontal stabilizer lift coefficient value (C L h ) is approximate to the one calculated using numeric methods, to the one obtained by the CFD modelling. In this case, with XFLR5 program under the same flow conditions and the same angle of attack. Given some previous experiences of the design team with aero models, a difference of less to 25% between both results is considered acceptable.    Thus, maximum (+) deflection in cruise flight is, Equation 14.
(C m0 ) is the aircraft's pitching moment coefficient obtained by XFLR5 when AOA = 0°, (C mα ) is aircraft's pitching moment curve slope as a function of the change in the AOA, which is determined by analysis in XFLR5 and Finally, if the Equation 10 criterion is accomplished, then the phase culminates. If it is not accomplished, designers must return to phase num. 1. Ultimately, from ( C E C h ) a (C E ) value is calculated.

Phase num. 4 stall at takeoff avoidance
It must be verified that the elevator deflection at takeoff does not induce a stall over the horizontal stabilizer during takeoff. According to the recommendation in Table 2, if the downward or upward elevator's deflection does not exceed 25°, then stall should not occur. Thus, designers recommend a maximum upwards and downwards deflection of 25°in order to avoid a stall.

Aileron design methodology
In this section, the parameters related to the aileron design are calculated; some of them are the steady-state roll rate (P SS ), the moment of roll (L A ), the aerodynamic coefficient of the aileron during roll (C la ), and its control derivative (C l δ A ).

Phase num. 1 identification of lateral control requirements and determination of preliminary geometrical relations
Some preliminary geometrical relations are to be determined, specifically the inner (b Ai ) and outer (b Ao ) aileron tips coordinate along the aircraft's lateral axis, see Table 5. By recommendations of the military standards, the outer tip of the aileron is located between an 85% and 90% of the half-wing span (b/2) and that the span ratio ( is in the range of 0.6-0.8 [27]. A preliminary aileron-to-wing chord ( C A C ) was also selected, as shown in Table 2. From this relation, the aileron's efficiency (τ A ) was determined to be used in later stages of the design. Based on the geometry relations, the designer calculates the Steady State Roll Rate (P SS). This condition occurs when the Roll moment is balanced with the Restoring moment caused by the airplane's lateral stability. If the ailerons do not return to their neutral position, the airplane will continue to roll until the wings reach an angle where no further lift can be generated. (P SS) can be calculated by Equation 16.
is the coordinate of mean drag of the three lifting surfaces (wing, horizontal and vertical stabilizers) located at 40% of the aircraft's half-wing span measured from the wing root. (L A ) is the moment of roll due to the maximum aileron deflection, given by Equation 17. (18) where (b) is the aircraft's wingspan and (C la ) is the aerodynamic coefficient of the aileron during roll, Equation 18. From that Equation, (δ Amax ) is the maximum aileron deflection in radians whose selection is recommended in Table 2 and (C l δ A ) is the lateral control derivative of the aileron aerodynamic coefficient during roll, obtained from Equation 19. When integrating within the inner (b Ai ) and outer (b Ao ) coordinates of the aileron and considering a tapered wing (λ), Equation 20 is obtained.
If ϕ 1 > ϕ req then calculate t (ϕreq) by Equation 22. t (ϕreq) is the time that the aircraft needs to reach the required bank angle (ϕ req ). For that, the rate of roll (Ṗ ) is determined in Equation 23. If ϕ 1 < ϕ req , then calculate (t 2 ), which is the time that the aircraft needs in order to reach the required bank angle (ϕ req ). This time is the sum of the time that the aircraft takes to reach the steady-state roll rate (t ss ) and the time difference (∆t R ) for reaching the required bank angle; this is calculated as indicated in Equations 24, 25 and 26.
A maximum difference between t (ϕreq) and (t 2 ) must not exceed 10%. If this condition is fulfilled, this phase is finished. On the contrary, return to phase num. 1, selecting the coordinates of the aileron tips. If the aircraft is under the requirement for its roll performance, then the initial span relations were correctly selected, and it is now a process of optimization whereby the number approaches that of the requirement.

Phase num.3 stall in operation avoidance
According to the recommendation in Table 2, if the downward or upward aileron's deflection does not exceed 25°, then stall should not occur. Generally, the airplane is designed for a stall to occur from the root of the wing in direction to the tip, allowing lateral control for the longest possible time. Nevertheless, aerodynamic studies on stall conditions are outside this research scope.

Rudder design methodology
The rudder should be capable of keeping aircraft's directional control in every; still, a specific control mission is determined, for example, aerobatic maneuvers or adverse weather operations. For Micro class aeromodels, it has been determined that the critical control mission of the rudder is to keep directional control in flight with a crosswind [33].

Phase num. 1 identification of directional control requirements and selection of critical flight control mission
According to the Federal Aviation Regulations (FAR) in their section N°23, utility aircraft must keep directional control while in a crosswind blowing perpendicular to their flight trajectory [24]. In a similar sense, the military standard establishes that the maximum wind component which is applicable for design must be 20 knots for these types of model´s classification [25]. However, considering the small size of the model aircraft, it is convenient to design for a maximum wind component between 8 and 10 knots. Furthermore, it is worth mentioning that this crosswind operation is more critical during takeoff and landing phases, when the flight speed approaches the stall speed of the aircraft (V S ). The relative wind (V T ) corresponds to the combined components of the wind coming from in front of the aircraft and the crosswind, as observed in Equation 27.
Wind loads are applied in a point denominated aerodynamic center (X AC ) this point is located in the airplane's profile over the side surface exposed to the wind (S S ). For calculating that area's centroid, the model profile is subdivided into areas of recognizable geometry, and the "x" coordinate of the centroid of the surface is calculated as in Equation 28.  according to Table 2. Utilizing this ratio, the rudder effectiveness (τ R ) is obtained from Figure 1, performing a mechanical analysis of the forces present during crosswind operations as seen in Figure 5. This mechanical analysis results in a system of nonlinear equations which is constituted by aerodynamic, environmental and geometric variables. The system of equations must be solved to obtain the rudder deflection (δ R ) and the crab angle (σ), Equations 29 and 30.
where (δ R ) is the maximum rudder deflection recommended by Table 2, (F W ) is referred to the wind force calculated as a function of the side area (S S ) and of the crosswind component (V w ), Equation 31. In the same equation, (C D Y ) is the coefficient of side drag that has a value between 0.5 and 0.8 [27]. β is the sideslip, obtained from Equation 32. is the dynamic pressures ratio in the zone of the vertical stabilizer [32]; this has a recommended value between 85% and 95%. (l v ) measures the vertical stabilizer arm, (S v ) is the vertical stabilizer planform surface, (K f1 ) is a correction factor for the fuselage contribution to the control derivative (C n β ) and is between (0.65 < K f1 < 0.85) [27]. (K f2 ) is a correction factor the fuselage contribution to the control derivative (C y β ) and is between (0.75 < K f2 < 1) [35]. Because the model's fuselage aerodynamic contribution is considerably small (K f1 ) and (K f2 )are considered to be less than the recommended values. To calculate directional control derivatives, (C y δ R ) and (C n δ R ), are developed in Equations 35 and 36.
(V V ) and (b V ) are the coefficient of volume of the vertical stabilizer and its span determined in previous aircraft design stages, respectively. Once the elements for the equations system are obtained, the system is solved to obtain the crab angle (σ) and the rudder's deflection (δ R ).

Phase num. 3 stall in operation avoidance
If (δ R ) obtained from the system of equations is less than the maximum required to avoid a stall in the vertical stabilizer, the ( C R C V ) relation must be modified, and the designers must return to phase 2. On the contrary, the design is finished. .

Workflow diagrams
What is described previously is summarized in workflow diagrams which are intended to help with the corresponding programming of these methodologies in a C++ program. From Figure 6 to Figure 8 the workflows are shown.

Result
The use of the proposed methodology allows standardizing the design of the control surfaces in Micro Class prototypes of UNIMET SAE Aero Design. Reduction in time use regarding this design stage is considerable, allowing a more efficient use of resources available to finish the project within the deadlines.

Aileron's design sensitivity analysis
In the case of the latest aircraft design, the aileron's needed to assure a 30°bank angle in 1.3s. For this requirement, a sensitivity analysis was performed by setting the aileron-to-wing chord ratio ( C A C ) at 20% and the aileron's outboard position at 90% of the wing semi-span. Then, the aileron-to-wing span ratio was iterated until the requirements were met. Figure 9 shows the sensitivity analysis' optimal result within the operative boundaries suggested by designers. Figure 10 shows the sensitivity analysis' optimal result for an aileron-to-wing chord ratio ( C A C ) at 15%, and the aileron's outboard position at 80% of the wing semi-span. The analyses aim to provide a visual tool to determine the design boundaries when varying the aileron's outboard position, the aileron-to-wing chord ratio and the aileron-to-wing span.

Weight analysis of the control systems
Micro Class in SAE Aero Design demands, among other challenges, that the aeromodels have the least empty weight (E w ) possible. Thereby, control systems' weight directly affects the design objectives. The application of the methodology allows reducing the size of the control surfaces dimensions and reduce the (E w ) without sacrificing the control mission requirements. As a comparison, the relation between the total weight of control systems (W control ) and (E w ) of prototypes from 2018, 2019, and 2020 competitions is shown in Table 8.
(W control ) is the sum of the weights of structure and coating of Elevator, Rudder and Ailerons, as well as the servo motors that move each of these surfaces. The servo motors selection depends on the required torque to move the control surfaces [36]. Table 8 Control systems to aircraft's empty weight fraction [33], [36,37]  In 2018, the team designed control surfaces following recommended sizing from literature examples [36]. This approach led to oversizing the control surfaces. The following year, designers established control mission requirements for each surface and approached a preliminary version of the design methodology [37]. This helped reduce control surface size but did not satisfy adequate handling characteristics for the flight mission.
In 2020, the proposed methodology helped reduce the W control Ew (g) in 1.1% compared to the 2019 prototype. Therefore, designers are now able to distribute the spared weight in the selection of a more potent power plant and to manufacture a more robust structure to absorb landing stresses.

Conclusions
The proposed methodology has enabled the development of a sequence of stages in the process of design and optimization of control surfaces in prototypes of the Micro Class of Aero Design. Its application has allowed the reduction of the relation between control systems to aircraft's empty weight in circumstances with higher empty weight requirements. In addition, the methodology facilitates the performance of sensitivity analysis with design parameters until optimal results are obtained. It is recommended to adapt the methodology to model aircraft whose characteristics and mission are different from those required for the Micro category of the SAE Aero design competition. In the same sense, it is proposed to evaluate the methodology for the design of the rudder under critical conditions different from the landing and takeoff to crosswind, such as coordinated turn, adverse yaw and spin of the aircraft.

Declaration of competing interest
We declare that we have no significant competing interests, including financial or non-financial, professional, or personal interests interfering with the full and objective presentation of the work described in this manuscript.