Vee-Tail Preliminary Design Methodology for Class I mini- UAV

Unmanned Air Vehicles (UAVs) are becoming increasingly popular and widely used in a variety of industries. They can be used for tasks such as agriculture, construction, delivery, surveillance, rescue operations, mapping, wildlife tracking and many more. With the advancements in technology, UAVs are becoming more autonomous and able to perform tasks with minimal human intervention, so are widely used for military and law enforcement purposes. V-tail configurations are commonly used on UAVs due to their advantages in control and stability performance, as well as their ability to reduce drag and improve overall efficiency. However, research on V-tail design and sizing is limited, particularly for Class I mini-UAVs. The objective of this paper is to identify a methodology for a V-tail sizing of a Class I Mini UAV (NATO classification), which refers to the Conceptual and Preliminary Design of the UAV. The methodology will follow the design of a V-tail from the characteristics of the conventional tail of the UAV. Once the characteristics of the conventional tail were extracted, V-tail geometric characteristics (reference area, aspect ratio, mean aerodynamic chord, tail span, dihedral angle), were computed. Therefore, the aerodynamic characteristics of the V-tail have to be extracted, first as an isolated tail, and then as an installed tail. The stability derivatives of the V-tail are then calculated. The methodology for the analytical aerodynamic characteristics and stability derivatives, is a combination of NACA Report No.823 and Marcello R. Napolitano methodologies. Paul E. Purser and John P. Campbell provide design methods for V-tail on a NACA report, which include some of the desired stability derivatives. The rest of them will be calculated with Napolitano’s method. Marcello R. Napolitano gives a methodology for conventional tail sizing; thus, the equations of its methodology have to convert for a V-tail configuration. Furthermore, the aerodynamic characteristics and stability derivatives of the designed V-tail will be verified by Low Fidelity Aerodynamics simulation (XFLR5 software), and then by High Fidelity Aerodynamics by means of CFD. The results between low fidelity analytical values and High-Fidelity Aerodynamics values indicate a relative error lower than 20%.


Introduction
V-tail is an unconventional aircraft tail configuration that combines the functions of both elevators and rudder into two surfaces that are combined in a V-shape [1].A V-tail configuration offers several advantages since it reduces the number of surfaces and intersections, which could lower the weight and drag of the aircraft, it avoids placing the vertical stabilizer in the line of the engine, which could improve the engine performance and it reduces the number of right angles on an aircraft, which could improve its stealth characteristics.Moreover, V-tail configuration has an improved aerodynamics and maneuverability compared to conventional tail configuration.In parallel introduces some disadvantages such as it requires larger tail surfaces than conventional tails to provide adequate stability and control, it may have reduced effectiveness at high angles of attack or sideslip due to flow separation, it has increased complexity of the control system due to the use of ruddervators and it may have increased susceptibility to flutter and buffeting due to the coupling of pitch and yaw modes.However, the literature about V-tail design and sizing are limited, especially for Class I mini-UAVs.Some of NASA reports are published on research about V-tails.Purser, P. E., and Campbell, J. P., studied a simplified theoretical model of V-tail behaviour from analysing data from previous studies on complete V-tail models [4].Polhamus, E. C., and Moss, R. J., published a paper for a wind tunnel study of the stability and control characteristics of a complete V-tail model [5].Schade, R.O. studied the effect of the geometric dihedral on the aerodynamic characteristics of two isolated V-tail surfaces in a wind tunnel [7].More recently research on V-tail configurations is presented in [8]- [14].These studies are investigating the performance of a V-tail configuration on a sideslip angles, and the flight control characteristics of the V-tail according to wind tunnel experimental investigation and flight tests.The purpose of this study is to identify a methodology for a V-tail sizing which is referred on the Conceptual and Preliminary Design of an Aircraft.For this methodology an aircraft (UAV) which is under design from Applied Mechanics Laboratory of University of Patras, is chosen for the evaluation.

Aircraft characteristics
First, the characteristics of the aircraft to be studied must be formulated.As mentioned in the Introduction, the characteristics will be obtained from an under-design aircraft of Applied Mechanics Laboratory of University of Patras.This aircraft is classified as Class I Mini UAS, according to NATO classification for UAVs.The overall parameters of the UAV are listed in Table 1

Vee-Tail Design and Sizing Methodologies
Our work was based on Purser's and Campbell's theoretical model from analysing data from previous studies on complete V-tail models and can be found in NACA Report No. 823 [4].According to this theoretical model and the methodology of Marcello R. Napolitano [3] for a conventional tail design and sizing, a new V-tail design and sizing methodology was created in order to verify the extracted values of the Purser's and Campbell's methodology and compare them with the results of Low-and High-Fidelity Aerodynamics.The two methodologies are described in more detail in the below subsections.3.1.Paul E. Purser and John P. Campbell methodology Purser and Campbell give eight equations for the V-tail stability and control derivatives, which are the major stability and control coefficients, four of them for an isolated V-tail, and the other four for the installed V-tail.These equations were converted for this unique configuration according to the vectors and angles of Figure 1 and are listed below.It's important to note that Purser's and Campbell's methodology follows the preliminary or the detailed design of an aircraft where the required stability and control derivatives are known.
Once the derivatives of the installed V-tail are known, you can calculate the parameters for the desired V-tail design (dihedral angle, v-tail surface, and control surface effectiveness).Their theoretical procedure for the V-tail design is described by the following eight steps of Figure 2. ).

Proposed methodology
The proposed methodology can be applied directly into the Conceptual Design of the aircraft, and procced instantly with the Preliminary Design with a V-tail empennage.Following the conventional methodology for aircraft design and sizing (Conceptual Design), as described from D.P. Raymer [2], the aircraft was fully sized, as well as the empennage with conventional tail.Marcello R Napolitano [3] provide a methodology for the stability and control derivatives estimation of a conventional tail aircraft.This part of the aircraft design is a part of the Preliminary Design.According to this methodology and the Purser's and Campbell's methodology and their assumptions, the proposed methodology for the V-tail sizing and design was created.
Therefore, the characteristics of the V-tail for this aircraft was calculated based on the Equation ( 14) and Equation (15), which are provided from the NACA Report No.823 [4], and values for the aspect ratio (ARt), the taper ratio (λt), and the control surface effectiveness (τRV) were assumed from existing aircrafts of this size.So, by this procedure the Conceptual design of the UAV was completed.In order to proceed with the Preliminary Design of the UAV, the calculations of the stability and control derivatives of the V-tail were taking place.The equations used to calculate them, are the converted equations of Marcello R. Napolitano methodology, and are listed below.
The methodology for the aircraft and V-tail sizing are provided on the following flowchart, where the aircraft sizing methodology is not appeared in detail.

Low-and High-Fidelity aerodynamic analyses
The aircraft was analysed with Low-Fidelity aerodynamics and then with High-Fidelity aerodynamics, as well as the isolated V-tail, for the evaluation of the analytical methods results (Purser's and Campbell's methodology, and the proposed methodology).
For Low-Fidelity aerodynamics, the XFLR5 aerodynamic software was used, and the isolated V-tail was analysed with 3D panel and VL methods.The results of these two analyses were almost the same, thus, the whole aircraft was analysed only with VLM method.Moreover, the aircraft and the isolated Vtail were analysed with High-Fidelity aerodynamics, using the Ansys Fluent software.The results of the analyses are listed in Table 2, along with the results of the analytical methodologies.

Conclusions
As it can be seen in the last column of Table 3, the relative error between the proposed analytical method and the High-Fidelity aerodynamics results are for most of the derivatives less than 10%, except two of them which are 14% and 17%, and one of them that has big relative error equal to 42%.Moreover, the relative error of the proposed analytical method results is less than the relative error of the Low-Fidelity aerodynamics analysis and the Purser's and Campbel's method, for most of the derivatives.Also, the one derivative which has big relative error (   ), appears to apply in all three cases, and it has to be investigated.Therefore, an efficient and robust analytical methodology for Preliminary Design and Sizing of a V-tail aircraft configuration was achieved, which is faster turnaround times than Low-and High-Fidelity aerodynamics, has a reasonable accuracy, and it cost much less than the abovementioned.Subsequently, the above-mentioned derivatives have to be checked that are satisfy stability of the aircraft, and the following four requirements: take-of rotation, crosswind recovery, spin recovery and, adverse yaw recovery, in order to be acceptable the design of the V-tail.

Figure 1 .
Figure1.Relations of angles and force coefficients for V-tail in pitch and sideslip[4]

Figure 3 .
Figure3.Value of K for computing slope of lift curve of V-tail in yaw[4]

Figure 4 .Figure 5 .
Figure 4. Variation of slope of the normal-forcecurve with aspect ratio[16] Figure5.Variation of section flap effectiveness with flap chord ratio for small Mach numbers and a small range of trailing-edge angle[17]

Figure 6 .
Figure 6.Flowchart of Proposed Method

Table 1 .
. Geometrical Characteristics of UAV Substitute the larger of the values of τ obtained from step 6 in equations 7 and 8 to determine final values for    , and    .8. Use the value of τ from step 7 with Figure 5 to determine the required value of or (11):

Table 2 :
Stability and Control Derivatives

Table 3 :
Relative error from High-Fidelity aerodynamics results