Fast Airfoil Selection Methodology for Small Unmanned Aerial Vehicles

Featured Application

Provided results are intended to be used along with the airfoil selection procedure described in the author M. H. Sadraey’s textbook Design of Unmanned Aerial Systems. For more detailed information regarding the procedure, please refer to textbook Aircraft Design: A Systems Engineering Approach of the same author.

Abstract

The purpose of this study is to fill the gap that exists when applying the airfoil selection methodology according to the textbooks that appear in the above featured application section, in the low Reynolds number segment, by providing useful data. Data acquisition software was XFLR5. The major result is the construction of a prototype maximum lift coefficient versus ideal lift coefficient diagram, or $\left(C_{l_{max}}-C_{l_i}\right)$ diagram, composed exclusively of low Reynolds number airfoils. In addition, the necessary supplementary airfoil characteristics’ tables are provided, for conducting fast airfoil selection for Small Unmanned Aerial Vehicles (SUAVs). As a conclusion by implementing the proposed methodology, the SUAV designer is disengaged from the time-consuming process of the construction of similar $C_{l_{max}}-C_{l_i}$ diagrams and supplementary characteristic tables and the airfoil selection-processing time can be greatly shortened, because the main work of the process is reflected by the current findings. To express the time gain in a percentage manner, authors estimate that 85% of engineering time will be economized in the overall airfoil selection procedure if the current findings are used, due to the fact that no new airfoil simulations are required. Finally, candidate SUAV designers are encouraged to expand the airfoil database, according to the proposed methodology.

1. Introduction

Unmanned Aerial Systems (UAS), are being used increasingly over the years, compared to manned air vehicles, in order to accomplish certain aerial missions. The main advantage of the unmanned type of flight is the reduced cost of usage [1]. Specifically, the Small Unmanned Aerial Vehicles (SUAV) category is of special interest, because it can be used in a plethora of short-range aerial missions, such as in meteorological applications [2], forestry applications [3], agricultural applications [4], or in general purpose security surveillance and reconnaissance applications. The current airfoil selection methodology is a result of the «Euclid» SUAV development, which has a primary role of executing security surveillance and reconnaissance missions.

The UAV’s classification can be completed considering various criteria, such as (i) the presence of a main wing or not, (ii) the mass of the vehicle, (iii) the vehicle’s maximum altitude, (iv) the vehicle’s range and endurance, and (v) the nature of the mission that the vehicle is designed to execute [5]. Qualitative and quantitative widths, and also the naming of the UAV’s categories, are not strictly defined bibliographically, resulting in a mixed classification between various authors and organizations worldwide [6]. For example, the «Small» prefix in front of the UAV acronym, used in the title of the present article, is interpreted as a UAV of mass between 0.1–150 kg according to Australia’s Civil Aviation Safety Authority (CASA), and a UAV of mass ≤ 20 kg according to the Civil Aviation Authority (CAA) of Great Britain [7].

In order to be more precise in the current article, the «Small» prefix relates to the Reynolds numbers that the main wing of the vehicle faces. These numbers, of course, are, respectively, in analogy with the physical dimensions and overall performance characteristics of the UAV.

The airfoil, or the different type of airfoils, that will be placed in the main wing of an aircraft, can be either selected among a plethora of well-known geometries, or they can be designed from scratch. Usually, for the purpose of the design of a small aircraft such as a small UAV, the airfoil selection procedure is preferred, in order to preserve resources, as well as to reduce the complexity and development times [8]. For general information about the airfoil design procedure, the reader can refer to the textbook [9]. For the recent advances in the field, the reader can refer to scientific journal articles [10,11,12].

This study focuses on the airfoil selection means of obtaining an airfoil, which is an absolutely critical procedure for the final performance of the final product [13,14]. Different airfoil selection procedures are available when selecting an airfoil for other purposes, such as wind turbines [15,16,17], various propellers [18], special purpose airfoils such as supersonic airfoils [19], unique flying machines such as flapping wings [20], etc.

Figure 1 depicts the contribution of the current study within the broadest context, following the path with the green marking. Before the discussion of the details of the novelty of the current study, all of the possible internal processes of Figure 1 are discussed in detail, along with the necessary recent literature review.

When following the airfoil selection route, the designers have to decide if they are willing to apply a strict airfoil selection methodology which can be obtained from the international aviation literature textbooks, or to attempt applying a custom method. Various well known authors in the aviation design field, describe analytical methodologies in their textbooks [21,22,23].

In the following paragraphs, a literature review is undertaken among recent scientific journal articles where an airfoil selection procedure is taking place. The purpose of this literature review is to collect all of the common attributes from the examined studies, in order to express some useful conclusions for the current study’s significance. It should be noted that not under any circumstances are the authors of this study disputing the methodologies used or the results provided in these studies.

In study [24], an airfoil selection procedure for a “Flying Wing Micro Aerial Vehicle” was conducted, where 10 low Reynolds number airfoils were examined. A series of airfoil’s aerodynamic measured values, were presented in the tables. In study [25], the airfoil selection for a “Morphing and growing micro Unmanned Air Vehicle” was conducted, without providing enough information for the airfoil measurements or the process itself that could be reused by others. Study [26] discusses a “mini Unmanned Aerial Vehicle” design where three airfoils were subject to selection. Little reusable information is given. Reference [27] examines six NACA airfoils for a “UAV with m_tow = 200 kg”. No reusable information is given regarding the airfoils. In study [28], six airfoils participated in the selection for a “long-range Vertical Take-Off and Landing (VTOL)” aircraft. An interesting point in this study was the proposal of the “bucket width” characteristic to participate as a variable in the airfoil selection. Our study also gives a great importance to this specific attribute and also displays it in a graphical manner in the $\left(C_{l_{max}}-C_{l_i}\right)$ diagram. The importance of the “bucked width” attribute, is discussed later in our study.

Reference [29] provided a satisfactory amount of reusable information for 15 under selection airfoils, for a “Solar-Powered UAV”. It also provided a diagram which can be useful for any designer willing to replicate the study’s airfoil selection procedure, in other similar projects. This diagram displays $C_{l_{cruise}}$ in the x axis and $\raisebox{1ex}{$C_l{}^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$}\!\left/ \!\raisebox{-1ex}{$C_d$}\right.$ in the y axis. This diagram, unfortunately, was not useful for someone applying the base methodology of [8,21]. Finally, there were some published articles such as [30,31], where no useful information was given at all regarding the airfoil selection procedure. These studies are written in a manner of an overall vehicle design demonstration, where such details were skipped for practical publishing purposes.

All of the above studies surely accomplished their main target, which was to select the best airfoil for the given circumstances. Some common attributes of the examined studies are the following:

• For the majority of the studies, the simulation software used was either Xfoil or XFLR5;
• There are studies where useful information cannot be obtained for reuse, due to the small amount of the participating airfoils;
• In most cases, studies are not offering well organized and sufficient information regarding airfoil aerodynamic parameters which can be reused in similar new applications. As a result, there are a lot of overlapping simulations for the same airfoils;
• None of the above reviewed, indicative studies, but also none in a more extensive literature review that took place before taking the decision of conducting the current study, offers a $\left(C_{l_{max}}-C_{l_i}\right)$ diagram along with the necessary supplementary tables for conducting a low Reynolds number airfoil selection, that strictly follows the rules in the literature [8,21].

Continuing with the literature review of the various processes within Figure 1, it can be noticed that after an airfoil is selected or designed, using any of the possible methods, then this airfoil may be a subject of optimization in order to better suit the original requirements. In [32], the authors propose the use of a Genetic Algorithm for the purpose of optimizing UAV airfoils. An application of similar Genetic Algorithms is carried out in [33], where the authors are optimizing the airfoil of an agricultural aircraft. Optimizing processes can also be applied for airfoils of any type, such as wind turbine airfoils [34].

As long as all of the internal details of Figure 1 are now discussed, it is comprehensible that the aircraft’s design will result in an airfoil, more or less efficient for the given needs, whatever possible route is followed by the designers.

This study focuses on a certain path, which is marked in green color within Figure 1. Specifically, it concerns selecting an airfoil with the strict application of the methodology described in Dr. Mohammad H. Sadraey’s textbook Design of Unmanned Aerial Systems [21]. For the readers willing to acquire more information regarding this method, the same author’s textbook Aircraft Design: A Systems Engineering Approach [8], is the appropriate source.

This study offers the solution to the following problem:

Any high Reynolds number-operating aircraft designer will not face any difficulty applying the aforementioned airfoil selection method, due to the fact that the literature already offers all of the required data to do so.

In reverse, a low Reynolds number aircraft designer, who is willing to select an airfoil for a small UAV, will discover that the data available in the literature are not sufficient. This is one of the reasons that the overlapping simulations of the same airfoils are present in the indicative literature review previously conducted. The designer will eventually be forced to execute a new cycle of airfoil simulations, which will cost in terms of development time.

The novelty of this study consists in the following facts:

• It fills the gap that exists in the low Reynolds section when applying the airfoil selection methodology according to [8,21], as it provides the only bibliographically available $\left(C_{l_{max}}-C_{l_i}\right)$ diagram until now that presents the following unique characteristics in comparison with the similar diagrams that exists, of course, only for the high Reynolds section.
  • The diagram additionally displays the “bucket width” each studied airfoil has in its $\left(C_{l_{max}}-C_{l_i}\right)$ plot. The usefulness of this characteristic is discussed later in this study.
  • The diagram’s x and y axes are expressing different Reynolds numbers comparing to each other for increased accuracy, while the x axis corresponds to the cruise phase and the y axis corresponds to the take-off phase, where the vehicle’s velocities are different by nature;
• It provides supplementary airfoil tables containing the full set of the necessary variables that procedure [8,21] needs, for later use on airfoil comparisons.

The numerical performance gain that a small UAV designer will obtain by using the current study’s findings is not related to the performance of the produced UAV, however it is exclusively related to the reduction in the development times because:

• If the designer is satisfied with current study’s participating airfoils, no additional time-consuming simulations are needed.
• If the designer is willing to expand the airfoil database or include other Reynolds numbers, reduced times will also be needed due to the fact that the current study offers its own expansion, step by step, methodology.

To express the time gain in a percentage manner, the authors, after implementing the overall procedures into Euclid Small UAV, estimate that 85% of engineering time will be economized in the above circumstance outlined in 1. The time gain for the above circumstance 2 varies, as it is related to the expansion depth that the designer is willing to apply.

2. The Euclid Small UAV

«Euclid» SUAV, in which the proposed airfoil selection methodology was implemented for the first time, is the aerial subsystem of the homonymous Unmanned Aerial System (UAS) Euclid. It is a rapid deployment, fixed wing vehicle, for security surveillance and reconnaissance applications, which is being developed by the General (Core) Department of the National and Kapodistrian University of Athens.

Until now, the conceptual design phase and preliminary design phase of the system are completed, and research is entering into the detail design phase of the aerial vehicle.

After stability and control simulations are implemented to the vehicle, valuable stability and control derivatives, along with a plethora of other useful parameters, are imported to the Flight Dynamics Model (FDM) of a flight simulator, in order for the vehicle to be evaluated regarding its handling qualities according to the Cooper and Harper scale. The evaluation results indicated that all of the scores fluctuated in the 1–3 score region. This score region is translated as satisfactory handling qualities, without improvement needed to the system, according to [35]. The authors have the ambition to announce the detailed results of this research in the near future and to move on to the construction phase of the vehicle.

Table 1. Euclid SUAV characteristics.

UAV Characteristic	Description
Wingspan	2 m
Main wing geometry	Straight Trailing Edge, geometrically twisted, with winglets and flaps
Main wing area	0.35 m2
Fuselage length	1.15 m
Maximum Take Off Mass (MTOM)	2 kg
Aircraft structure materials	Low density 3D Printed PolyLactic Acid (PLA) and carbon fiber
Payload mass	150 g (camera)
Propulsion	Electric
Range	10 km
Stall Velocity (Vs)	9 m/s
Cruise Velocity (Vc)	15 m/s
Max Velocity (Vmax)	30 m/s
Launch type	Hand launched
Landing type	Belly landing

presents some useful information regarding Euclid Small UAV. In Figure 2, a 3-view of Euclid SUAV is demonstrated.

3. Main Airfoil Selection Procedure Description

The author, Sadraey, describes in his book entitled Design of Unmanned Aerial Systems [21], the steps that the UAV designer has to execute, in order to select the optimum airfoil for each case. Detailed information on the procedure can be found at reference [8] of the same author.

In this session, the internal procedures of the main airfoil selection procedure are discussed. The internal steps of the author Sadraey’s main selection procedure can be divided into three main groups, as Figure 3 depicts.

3.1. Lift Coefficients Calculation

The two main computational parameters the designer has to know at this point are the average weight $(W_{avg})$, of the aircraft and the main wing’s area $\left(S\right)$. These values are assumed to be already computed during preliminary design. The average weight can be determined using the simple Equation (1):

$$W_{avg}=\frac{1}{2} \left(W_i+W_f\right)$$

(1)

where $W_i$ represents the initial weight of the aircraft before cruise and $W_f$ represents the final weight of the aircraft after the cruise. If the UAV is electric powered, which is the most possible situation depending on the Reynolds numbers the article refers to, then $W_{avg}=W_i=W_f$.

All of the required parameters regarding the various lift coefficients, which are used in the procedure, can be calculated by applying the equations of the following

Table 2. Aircraft, wing and airfoil lift coefficients.

	Computational Parameters	Variable’s Name	Equations
Aircraft	Aircraft ideal lift coefficient during cruise	$C_{L_C}$	$\frac{2 W_{avg}}{\rho V_C{}^2 S}$
	Aircraft maximum lift coefficient during take off	$C_{L_{max}}$	$\frac{2 W_{TO}}{\rho V_s{}^2 S}$
Wing	Wing required lift coefficient during cruise	$C_{L_{C_{wing}}}$	$\frac{C_{L_C}}{0.95}$
	Wing maximum lift coefficient during take off	$C_{L_{ma{x}_{wing}}}$	$\frac{C_{L_{max}}}{0.95}$
Airfoil	Airfoil ideal lift coefficient during cruise	$C_{l_i}$	$\frac{C_{L_{C_{wing}}}}{0.9}$
	Airfoil gross maximum lift coefficient during take off	$C_{l_{ma{x}_{gross}}}$	$\frac{C_{L_{ma{x}_{wing}}}}{0.9}$
	Airfoil net maximum lift coefficient during take off	$C_{l_{max}}$	$$\begin{gathered} C_{l_{ma{x}_{gross}}}-\mathsf{\Delta }{C}_{l_{HLD}} \\ \left(\mathsf{\Delta }{C}_{l_{HLD}}\approx 0.35\right) \end{gathered}$$

.

3.2. Use of Airfoil $C_{l_{max}}-C_{l_i}$ Diagrams and Supplementary Tables

The next step, after the designer finishes the lift coefficients’ calculations, is to use corresponding airfoil diagrams in order to focus on a certain region of the airfoils that satisfy these values. These diagrams are referred to as the maximum lift coefficient versus ideal lift coefficient diagrams or $C_{l_{max}}-C_{l_i}$ diagrams. Such diagrams and relative information regarding the high Reynolds number airfoil section are given in [8,21], but no such organized information are available for the low Reynolds number section, either in [8,21], or in the broadest aircraft design literature. In the Materials and Methods section, we discuss the steps that were taken to collect this information. In the Results section, we present these reusable findings.

3.3. Airfoil Comparison

Having the valuable C_lmax − C_li diagram in hand, the designer can focus on an area of interest, according to the calculated C_lmax and C_li values. If there are a lot of airfoils found to be suitable, then the designer has to organize a «weight table», a type of comparison table, for further airfoil processing based on supplementary airfoil characteristics.

The airfoil characteristics to be evaluated, and also the weight of each characteristic, are subject to the discretion of the designer. An indicative/suggestive characteristics’ weight composition for the low Reynolds number section is presented in the following

Table 3. Indicative/suggestive weights for airfoils comparison.

Characteristic	Preference	Re	Weight (%)
Clmax	High values are preferred, within area of interest	100,000 using flaps	5
Cli	Preferred are those airfoils whose Cli is nearest to the calculated Cli.	200,000	5
Cdmin	Airfoil with minimum drag coefficient is preferred	50%: 200,000 50%: 350,000	10
(Cl/Cd)max	Airfoil with maximum lift to drag ratio is preferred (Re = 200,000).	200,000	5
Cm	Airfoil with minimum (negative or positive) pitching moment coefficient is preferred (33.3% for each re Red)	33.3%: 100,000 33.3%: 200,000 33.3%: 350,000	10
Stall quality	Manipulatable stall airfoils are preferred.	15%: 100,000 10%: 200,000 5%: 350,000 70%: 100,000 with flaps	20
Stall angle of attack	High values are preferred.	15%: 100,000 10%: 200,000 5%: 350,000 70%: 100,000 with flaps	30
Bucket width	Airfoils with large bucket width are preferred.	200,000	15
Total:			100

. The explanation of each characteristic variable can be found in Section 5.1.

In the case of large aircraft design, other airfoil characteristics may contribute to the selection process, such as manufacturability, room adequacy for the fuel tanks, etc. In this case, such characteristics are not participating because all of the twenty examined airfoils are easily manufacturable and there is no need for a large space inside the wing of a small UAV. The airfoil to be finally chosen is the one which will concentrate the best overall score.

4. Materials and Methods

In this section we discuss the steps that were taken in order to collect all of the critical values for the variables needed and for the construction of the C_lmax − C_li diagram for the low Reynolds number airfoils. Figure 4 visualizes these steps.

A SUAV designer who is not satisfied with the airfoils participating in this study, or a designer who wants to contribute and expand the current airfoil database, has to repeat Figure 4 steps 1–6 for each new airfoil.

Data acquisition for the proposed methodology is based on XFLR5 v6.48 software. XFLR5 is a free wing and aircraft computational software operating at low Reynolds numbers. Design and analysis are based on Lifting Line Theory, Vortex Lattice Method, and 3D Panel Method [36]. XFLR5 is based on Xfoil, a software inspired by Prof. Mark Drela. The validity in the XFLR5 results is scientifically documented since the Xfoil era [37], and continues to be verified by the scientific community until today, by comparing the software results to those acquired by computational fluid dynamics (CFD) simulations and wind tunnel tests [24,38].

The starting point of an airfoil selection is the Reynolds number determination. This number can be determined using the following Equation (2):

$$Re=\frac{Vl}{\nu }$$

(2)

$V$ describes the fluid velocity, $l$ the characteristic length of the studied arrangement which in this case is the length of the airfoil’s chord, and $\nu$ is the kinematic viscosity of the fluid. In this article, a typical chord length of $l=0.2 \mathrm{m}$ is considered, along with the three typical SUAV speeds appearing in

Table 4. Reynolds number calculation.

Velocities	Typical Values for SUAV (m/s)	Reynolds Number for the Simulation
Stall velocity Vs ≈ VTO	9	100,000
Cruise velocity Vc	15	200,000
Maximum velocity Vmax	30	350,000

. The kinematic viscosity of the fluid (air), is set at $1.511 \cdot {10}^{-5} \raisebox{1ex}{${\mathrm{m}}^2$}\!\left/ \!\raisebox{-1ex}{$\mathrm{s}$}\right.$, which corresponds to an ambient temperature of 20 °C.

Setting the precise calculated Reynolds number in the simulation software is not critical due to the fact that this number can change slightly between different missions. This is because, for example, the UAV operator may choose to fly at a slightly different speed from the recommended, or because of a different mass payload is attached. For these reasons, Table 4 contains the Reynolds numbers in increments of 50,000.

4.1. Literature Review in Low Reynolds Number Airfoils for Small UAV’s

An extensive literature review took place, aiming to locate airfoil families or discrete airfoils, whose effectiveness is proven in the SUAV field. From the literature review, twelve references qualified for the next step.

4.2. Selection of Adequate Number of Airfoils for Later Processing

Based on the qualified literature, twenty discrete airfoils were chosen to participate.

Table 5. The twenty airfoils analyzed.

ID	Airfoil Name	Designer(s)	Reference	Special Attributes	Plot
1	SG6043	Selig/Giguere	[39]	High L/D
2	SD7032	Selig/Donovan	[40]	Low Reynolds
3	FX63-137	F.X. Wortman	[40,41,42]	Human power aircraft airfoil
4	CAL2263M	Cristopher Lyon	[43,44]	CLARK-Y Derivative
5	CAL1215j	Cristopher Lyon	[44]	CLARK-Y Derivative
6	S8064	Michael Selig	[44]	Fast RC Aircraft
7	S9000	Michael Selig	[44]	RC sailplane
8	S1223	Michael Selig	[42,44,45]	High Lift
9	SD7037	Selig/Donovan	[43,45]	RC Glider airfoil
10	CLARK Y	Virginius E. Clark	[46]	Legacy GA Airfoil used in RC Applications
11	E201	Richard Eppler	[47]	Low Reynolds
12	E205	Richard Eppler	[33]	Low Reynolds
13	MH114	Martin Hepperle	[41]	Ultralight Airfoil
14	SA7038	Selig/Ashok Gopalarathnam	[48]	RC Sailplane Airfoil
15	E387	Richard Eppler	[38]	Low Reynolds
16	CR-001	Cody Robertson	[45]	Hand Launch RC Airfoil
17	MH32	Martin Hepperle	[45]	RC Sailplane Airfoil
18	S4083	Michael Selig	[45]	Hand Launch RC Airfoil
19	S7075	Michael Selig	[45]	RC Airfoil
20	E214	Richard Eppler	[42]	Low Reynolds number airfoil

presents those airfoils.

4.3. .dat File Construction with the Polars of Each Airfoil

Certain airfoil families, such as NACA, have the advantage that some of their properties are known only by reading the numbers of their name. XFLR5 can also take advantage of this convention and display an airfoil’s coordinates only by entering their name. For the special purpose airfoils studied in this article, such an automation is not present because there is not a correlation between the names and physical properties of the airfoils. In order to display them correctly in the software, the user must create a .dat file containing the numerical polars of each one. Some popular airfoil’s .dat files can be found on the Internet. In the case of absence, the .dat files can be created manually using the values of the polar tables in the corresponding source reference (all twenty participating airfoil’s .dat files can be found in .dat format under Supplementary Materials File S1, for methodology repeatability and verification purposes).

4.4. Construction of a Clone File of Each Airfoil and Integration of Trailing Edge Flap

Wishing to study the effect of the deflection of a trailing edge flap for each airfoil, a clone of each airfoil was created and a trailing edge flap was integrated at 80% of the cord, with a 30° down deflection angle.

4.5. Defining XFLR5 Simulation Parameters and Creation of .xfl Files

Multithreaded Batch Analysis was the selected type of simulation throughout the process. Three discrete Reynolds numbers were used (100,000, 200,000, 350,000) for the airfoils without flap deflection. The airfoils with a deflected flap were simulated at Re = 100,000. The angle of attack was studied within −6° + 25° range, with a 0.5° step.

4.6. XFLR5 Simulations

Twenty simulations were carried out, examining a corresponding number of airfoil pairs (with and without flaps). Generated diagrams were C_d-C_l, C_l-α, C_m-α and (C_d/C_l)-α (all twenty participating airfoil’s XFLR5 simulation files can be found in .xfl format under Supplementary Materials File S2, for methodology repeatability and verification purposes).

5. Results

Figure 5 contains the three steps that were taken for the results to be prepared for presentation. As stated at the beginning of this work, these steps represent the main results from the current study. These findings are sufficient to fast conduct an airfoil selection among the participating airfoils.

5.1. Results Export from XFLR5 and Import to Spreadsheet Software

Unfortunately, XFLR5 does not provide any automated routine for user-defined result exporting. Despite this fact, the user can acquire the precise numerical pairs of any given point on a plot curve. Given this, all of the measurements of interest were transferred manually to spreadsheets. The following

Table 6. Measurements of interest at Re = 100,000 and no flap usage.

Re = 100,000 (No Flaps)
ID	Airfoil	Cdmin	Clbucket_width	Cli	αi	Cm	(Cl/Cd)max	αs	Clmaxg	Stall Quality Scale: 1–5 5: Excellent
1	SG6043	0.019	0.94 (0.46–1.4)	0.84	3.1	−0.14	66	14	1.61	1.67
2	SD7032	0.016	0.84 (0.16–1)	0.64	2	−0.09	55	11	1.38	2.33
3	FX63-137	0.025	0.9 (0.3–1.2)	0.7	0	−0.17	63	11	1.66	4.33
4	CAL2263M	0.019	1.1 (0–1.1)	0.6	2	−0.07	53	14	1.34	1
5	CAL1215j	0.016	0.75 (0–0.75)	0.45	1.3	−0.07	51	13	1.21	1.67
6	S8064	0.025	0.5 (0.15–0.65)	0.4	3.3	−0.028	47	10	0.98	1.67
7	S9000	0.013	0.22 (0.48–0.7)	0.58	2.4	−0.058	53	11	1.27	2
8	S1223	0.022	0 (1.09–1.09)	1.09	−0.5	−0.26	52	8	1.9	1.33
9	SD7037	0.015	0.24 (0.59–0.83)	0.7	3.1	−0.073	55	10	1.26	3
10	CLARK Y	0.017	0.21 (0.68–0.89)	0.78	3.6	−0.089	53	12.5	1.36	2.33
11	E201	0.016	0.15 (0.2–0.35)	0.27	−0.8	−0.091	57	11.5	1.15	2
12	E205	0.013	0.03 (0.17–0.2)	0.18	−2	−0.071	55	9	1.1	2
13	MH114	0.03	0.85 (0.5–1.35)	0.56	0	−0.15	49	13	1.72	3.33
14	SA7038	0.015	0.17 (0.65–0.82)	0.73	3.2	−0.082	56	10	1.3	3
15	E387	0.015	0.04 (0.34–0.38)	0.36	−0.5	−0.093	60	8	1.24	1.67
16	CR-001	0.017	0.65 (0.35–1)	0.6	1.7	−0.092	64	10.5	1.34	2
17	MH32	0.015	0.8 (0–0.8)	0.36	1	−0.051	53	9.5	1.08	2
18	S4083	0.011	0.08 (0.36–0.44)	0.4	0	−0.086	56	10	1.23	2
19	S7075	0.018	0.6 (0.1–0.7)	0.42	1.3	−0.067	60	10.5	1.31	1.33
20	E214	0.02	0.96 (0.14–1.1)	0.68	2	−0.098	62	9.5	1.32	3.67

All variables’ units are dimensionless, except C_m units which are 1/rad and α_i and α_s which are degrees.

,

Table 7. Measurements of interest at Re = 200,000 and no flap usage.

Re = 200,000 (No Flaps)
ID	Airfoil	Cdmin	Clbucket_width	Clbucket_min	Clbucket_max	Cli	αi	Cm	(Cl/Cd)max	αs	Clmaxg	Stall Quality Scale: 1–5 5: Excellent
1	SG6043	0.013	1.1	0.28	1.38	0.87	1.66	−0.16	98	18	1.62	3.33
2	SD7032	0.009	0.56	0.31	0.87	0.54	0.85	−0.09	78	11	1.4	2.67
3	FX63-137	0.01	0.7	0.5	1.2	0.76	−1	−0.2	89	14	1.66	4.67
4	CAL2263M	0.01	0.55	0.2	0.75	0.49	0	−0.1	76	15	1.34	1.67
5	CAL1215j	0.01	0.52	0.12	0.64	0.41	0.87	−0.068	69	12	1.25	2.67
6	S8064	0.014	0.45	0.1	0.55	0.5	2.9	−0.018	64	10	1	1.67
7	S9000	0.0086	0.3	0.22	0.52	0.4	0.6	−0.071	71	11.5	1.3	3
8	S1223	0.018	0.11	1.12	1.23	1.18	1	−0.27	71	13	2.22	3
9	SD7037	0.009	0.2	0.4	0.6	0.51	1.23	−0.083	75	12	1.28	3
10	CLARK Y	0.01	0.24	0.32	0.56	0.45	0	−0.094	73	12	1.4	3
11	E201	0.01	0.12	0.21	0.33	0.27	−0.6	−0.076	78	11.5	1.18	2
12	E205	0.009	0.07	0.15	0.22	0.18	−1	−0.064	73	11	1.13	2
13	MH114	0.013	0.15	0.85	1	0.91	0.95	−0.18	88	13	1.74	4.67
14	SA7038	0.092	0.14	0.44	0.58	0.51	1.04	−0.087	77	11	1.31	2.67
15	E387	0.0097	0.05	0.35	0.4	0.35	−0.5	−0.083	82	10	1.25	1.67
16	CR-001	0.0065	0.1	0.5	0.6	0.55	0.5	−0.11	89	11	1.36	2
17	MH32	0.0091	0.2	0.39	0.59	0.49	1.7	−0.072	71	9	1.07	2
18	S4083	0.0079	0.04	0.35	0.39	0.37	−0.5	−0.089	70	9	1.22	2
19	S7075	0.0095	0.1	0.66	0.76	0.71	2.8	−0.091	81	13	1.38	1.67
20	E214	0.01	0.17	0.64	0.81	0.7	1.47	−0.13	88	10	1.33	3.67

All variables’ units are dimensionless, except C_m units which are 1/rad and α_i and α_s which are degrees.

,

Table 8. Measurements of interest at Re = 350,000 and no flap usage.

Re = 350,000 (No Flaps)
ID	Airfoil	Cdmin	Clbucket_width	Cli	αi	Cm	(Cl/Cd)max	αs	Clmaxg	Stall Quality Scale: 1–5 5: Excellent
1	SG6043	0.0084	0.89 (0.28–1.17)	0.8	−0.24	−0.17	126	16	1.65	5
2	SD7032	0.0067	0.54 (0.28–0.82)	0.44	0	−0.092	96	12	1.45	2.67
3	FX63-137	0.01	0.7 (0.5–1.2)	0.96	0.4	−0.2	103	14	1.69	4.67
4	CAL2263M	0.0074	0.47 (0.23–0.7)	0.48	0	−0.097	94	15	1.38	4
5	CAL1215j	0.0075	0.54 (0.16–0.7)	0.44	1.18	−0.05	82	13	1.35	3.33
6	S8064	0.009	0.3 (0.3–0.6)	0.5	3.5	−0.03	72	12	1.05	2
7	S9000	0.0066	0.35 (0.15–0.5)	0.33	0.2	−0.066	85	11.5	1.37	3
8	S1223	0.015	0.18 (1.07–1.25)	1.16	0	−0.26	87	13	2.28	2
9	SD7037	0.0064	0.12 (0.37–0.49)	0.42	0.4	−0.08	91	11	1.29	3
10	CLARK Y	0.0075	0.1 (0.37–0.47)	0.42	0	−0.082	89	13	1.41	3.33
11	E201	0.008	0.18 (0.3–0.48)	0.38	0.3	−0.076	92	11	1.18	2
12	E205	0.0078	0.12 (0.28–0.4)	0.34	0	−0.06	86	11	1.14	2
13	MH114	0.096	0.25 (0.85–1.1)	0.98	1.2	−0.19	116	14	1.77	5
14	SA7038	0.064	0.05 (0.38–0.43)	0.4	0	−0.083	93	11	1.34	3.33
15	E387	0.007	0 (0.34–0.34)	0.34	−0.5	−0.08	98	9.5	1.23	2
16	CR-001	0.065	0.09 (0.51–0.6)	0.55	0.25	−0.11	108	11.5	1.39	2.33
17	MH32	0.0064	0.11 (0.32–0.43)	0.37	0.5	−0.058	87	8	1.04	2
18	S4083	0.0066	0.02 (0.37–0.39)	0.38	−0.5	−0.088	79	8	1.17	2
19	S7075	0.0068	0.06 (0.56–0.62)	0.59	1.6	−0.091	99	13	1.47	2
20	E214	0.008	0.23 (0.41–0.64)	0.51	−0.7	−0.14	109	10	1.37	3.33

All variables’ units are dimensionless, except C_m units which are 1/rad and α_i and α_s which are degrees.

and

Table 9. Measurements of interest at Re = 100,000 and 30° flap deflection at 80% of chord.

Re = 100,000 (Flap @ 80% Chord, 30°)
ID	Airfoil	Clmaxg	ΔCLf	Clmax	αs	Stall Quality Scale: 1–5 5: Excellent
1	SG6043	1.89	0.28	1.33	11	1.67
2	SD7032	1.73	0.35	1.03	7	2
3	FX63-137	1.76	0.1	1.56	7	4
4	CAL2263M	1.72	0.38	0.96	10	1.67
5	CAL1215j	1.58	0.37	0.84	9.7	2.33
6	S8064	1.45	0.47	0.51	6	1
7	S9000	1.66	0.39	0.88	6.5	2.33
8	S1223	1.89	−0.01	1.91	4	1
9	SD7037	1.65	0.39	0.87	7.5	2.33
10	CLARK Y	1.7	0.34	1.02	10	3.67
11	E201	1.57	0.42	0.73	8	1.67
12	E205	1.57	0.47	0.63	6	1.67
13	MH114	2	0.28	1.44	10	3.67
14	SA7038	1.64	0.34	0.96	6	3
15	E387	1.67	0.43	0.81	6	1.67
16	CR-001	1.72	0.38	0.96	6	2
17	MH32	1.55	0.47	0.61	4.5	1.33
18	S4083	1.64	0.41	0.82	6	1.67
19	S7075	1.72	0.41	0.9	6.5	1.33
20	E214	1.6	0.28	1.04	5.7	3

All variables’ units are dimensionless, except α_s which are degrees.

, were constructed in order to be used by the SUAV designer at the airfoil comparison procedure, if needed (all twenty participating airfoil’s aerodynamic measurements can be found in .xlsx format under Supplementary Materials Table S2, for methodology repeatability and verification purposes).

The measured attributes of the above Table 6, Table 7, Table 8 and Table 9 are explained in detail in the following numbered paragraphs, according to [8,21]:

• Minimum drag coefficient C_dmin: Is the minimum C_d value in the C_d-C_l diagram (Units: dimensionless);
• «bucket width» C_{lbucket_width}: the authors thought that it could be useful to conduct a series of measurements under the C_{lbucket_width} name. It is observed that regarding the classic airfoils, such as the NACA series, the bucket always has a smaller width compared to the low Reynolds number airfoils, where the bucket is more spread out in the x axis. An example is demonstrated in Figure 6, where the SG6043 low Reynolds number airfoil is simulated at Re = 350,000, contrary to a classic NACA 66₂-415 at Re = 3,000,000. The low Reynolds number-widened bucket, is an excellent advantage both for the designer and the operator of the SUAV, as the possible suitable airfoils are increased for the designer and the deviation margin in the flight envelope is also bigger for the operator, without a big penalty in the range and the endurance of the vehicle. (Units: dimensionless);
• Ideal lift coefficient C_li: It corresponds to the minimum drag coefficient. When studying an ideal airfoil with a symmetric bucket, C_li should be in the middle of the bucket. In the real world, C_li can be anywhere close to the curve that we consider as the bucket. (Units: dimensionless);
• Ideal angle of attack α_i: Is the angle of attack that corresponds to C_li. (Units: degrees);
• Pitching moment coefficient C_m: The Variations of Pitching Moment Coefficient versus Angle of Attack. The design objective is to have C_m close to zero as far as possible. (Units: 1/rad);
• (C_l/C_d)_max: Is the maximum value of the C_d/C_l-α diagram. Large values are desirable. (Units: dimensionless);
• Stall angle α_s: Is the critical angle of attack beyond which the airfoil will suffer a decrease in lift force. Large values are desirable, especially at lower Reynolds numbers and when using flaps. (Units: degrees);
• Airfoil gross maximum lift coefficient C_lmaxg: It corresponds to the maximum C_l value on a C_l-α diagram. (Units: dimensionless);
• Stall quality: It is a prediction of what is going to happen in the uncomfortable situation where the airfoil will enter the stall region. More details on the stall quality judgment procedure can be found in the next Section 5.2. (Units: Likert 1–5 scale, where: 1 corresponds to the worst stall quality, while score 5 corresponds to excellent stall quality behavior);
• Flap deflection lift coefficient difference ΔC_Lf: It exclusively relates to the flap deflection data (Table 9). It is synonymous with ΔC_lHLD. It measures the difference in lift coefficients between the flap and absence of flap deflection. (Units: dimensionless);
• C_lmax: Is the maximum lift coefficient, calculated by C_lmax = (C_lmaxg − Δ_Lf). (Units: dimensionless).

5.2. Airfoil Stall Quality Judgement

All of the above variables are quantitative except for the stall quality variable. Quantitative values can be inserted with absolute accuracy to Table 6, Table 7, Table 8 and Table 9. A way to quantify the stall quality is described in Figure 7.

Figure 7 represents an ideal C_l-α diagram. Left part contains α_s and C_lmax points. Further to the right than the critical a_s point, three hypothetical stall curves are displayed. Obviously, the preference is green > orange > red. We consider a vertical line at distance Δx from the α_s point that intersects with the three stall curves. Afterwards, in the magnified right part of the diagram, we record Δ_y1, Δ_y2, Δ_y3 points. The curve which records the smallest Δy is the one to receive the best score to contribute to its selection process.

Unfortunately, things are not quite so easy, because with the aforementioned method we are studying ideal curves that are unlikely to exist in real simulation results because:

• Real under study points are close to each other so inaccuracy will appear in the measurements;
• Real simulation curves sometimes exhibit secondary or/and tertiary fluctuations (for example, while a curve seems to fade steeply, then it is being regularized, or vice versa.

For these reasons, a completely different method was chosen for the stall quality judgement. The proposed method faces the stall curves in a holistic way and is based on the blind judgement of three individual reviewers. A simple Likert scale was formed, where score 1 corresponded to the worst stall quality, while score 5 corresponded to excellent stall quality behavior. For each Reynolds number, an average value was calculated from the three reviewers’ opinion. Eventually, a final stall quality score was calculated for each airfoil, using

Table 10. Weights of each Re, towards final airfoil stall quality calculation.

	Re = 100,000 No Flaps	Re = 200,000 No Flaps	Re = 350,000 No Flaps	Re = 100,000 30% Flaps
Weight	15%	10%	5%	70%

weights.

The final stall quality scores that each airfoil received are presented in

Table 11. Table S1 (in Supplementary Materials). Airfoil stall quality score.

Ranking	Airfoil ID	Airfoil Name	Stall Quality Score	Ranking	Airfoil ID	Airfoil Name	Stall Quality Score
1	3	FX63-137	4.15	11	1	SG6043	2.0025
2	13	MH114	3.7855	12	11	E201	1.769
3	10	CLARK Y	3.385	13	12	E205	1.769
4	20	E214	3.184	14	18	S4083	1.769
5	14	SA7038	2.9835	15	15	E387	1.6865
6	9	SD7037	2.531	16	4	CAL2263M	1.686
7	7	S9000	2.381	17	17	MH32	1.531
8	5	CAL1215j	2.315	18	19	S7075	1.3975
9	2	SD7032	2.15	19	8	S1223	1.2995
10	16	CR-001	2.0165	20	6	S8064	1.2175

. The detailed judgement of each reviewer along with the stall curves diagrams, can be found in .xlsx format in Table S1. The average score value is 2.25.

5.3. Construction of the Airfoil «Map-Diagram»

The necessary visual aid to help the designer in the airfoil selection process is the maximum lift coefficient versus ideal lift coefficient diagram or C_lmax − C_li diagram. This diagram is a form of an airfoil map. C_li values lies at x axis and C_lmax values at y axis. Within the diagram, points exist, each one representing a certain airfoil. The designer can focus on a certain region of the diagram to further analyze the airfoils by comparison.

The main differentiation that the proposed C_lmax − C_li diagram (Figure 8; Table S2 in .xlsx format) introduces over against the corresponding high Reynolds number diagrams that can be found in the literature, consists of the following statements:

• It introduces two different Reynolds numbers across the two axes, instead of one. C_lmax is calculated at Re = 100,000, while C_li at Re = 200,000;
• Aside of the points that represent each airfoil, a faded line appears to the left and/or right of each point. This line represents the bucket width variable that we discussed earlier.

Remarks regarding Figure 8.

• The big bucket widths are now visually verified;
• The C_li points’ position is not mandatory to be in the middle of the bucket. The exact position has to do with the physical shape that the bucket has each time;
• The four airfoils (S1123, FX63-137, MH114 and SG6043) that appear at the upper part of the diagram (those with high C_lmax), are indeed characterized by their designers as High Lift, Human power aircraft airfoil, Ultralight Airfoil, and High L/D, respectively (see Table 5). All of these airfoils are of high camber. In combination with Table 9, ΔC_Lf measurement, it can be stated that flap deflection does not have a great effect on the lift coefficient improvement of those high camber airfoils. The S8064 airfoil which has the lowest C_lmax is a counterexample, as it is characterized by its designer as a fast RC aircraft;
• C_li dispersion is located around the 0.5–0.6 region and C_lmax dispersion is located around the 0.9–1 region.

6. Conclusions

This article’s findings disengage the SUAV designer from the time-consuming process of the construction of $C_{l_{max}}-C_{l_i}$ diagrams and supplementary characteristic tables when applying the main airfoil selection procedure [8,21] regarding a low Reynolds number aerial vehicle. To express the time gain in a percentage manner, the authors, after implementing the overall procedures into Euclid Small UAV, estimate that 85% of engineering time will be economized using the proposed $C_{l_{max}}-C_{l_i}$ diagram and the proposed supplementary characteristic tables. The work left for the SUAV designer is to focus on a certain region of the map and to compose an airfoil characteristics’ comparison table, in order to select the best airfoil for the given application.

The validity of the proposed methodology is reinforced with the successful use of it in the Euclid SUAV project. Finally, candidate SUAV designers are encouraged to expand the airfoil database, according to the proposed expansion methodology discussed in Section 4.