Introduction

The idea of this project was to...

The initial data provided for the development of the aircraft were arranged in the following table for better organization:

Table 1: Input data for calculations.

Firstly, for better understanding and analysis, existing UAV models were researched as a basis for calculations and comparison. The model used as an example for sizing, which presents characteristics such as engine power and rough load close to the data provided, was the Elbit Hermes 450 (RQ 450), which has the following specifications: [1]

Initial Analyses

Considering the UAV model described above, the development of the aircraft began. Firstly, for the sizing project, based on the engine's load capacity and its power, the maximum weight that the aircraft can have been found, that is:

Once the maximum weight was obtained, the first approximation of the wing area, based on the wing loading, is:

⟹ Therefore,

Since a reference value of the aspect ratio equivalent to 18 was defined, the wingspan can be approximated as:

⟹ Therefore, 𝑏 = 9.3819 𝑚

To determine the aircraft's fuselage, the total volume occupied by the engine, payload, and fuel was first defined, as follows:

• Engine: As a first approximation, we consider the engine as a box with dimensions that were provided by its technical drawing. With this, its respective volume is:

• Payload: Knowing that the payload has a mass of 100 kg and a density equal to that of water, then:

• Fuel tank: For the basis, we use avgas fuel whose density is ρ_avgas=690 kg/m³. In this way:

Therefore, the total volume to be loaded inside the fuselage is equivalent to:

For the development of the structural design, the Elbit Hermes 900 UAV (Figure 1) was used as a model format, considering that all the calculated volume must be contained inside the UAV. Figure 2 shows the model related to the projected UAV, developed with the help of OpenVSP software, which will be detailed throughout the report.

Figure 1: Side view of the Elbit Hermes 900.

Figure 2: Side view of the UAV developed in OpenVSP.

Development

To find the most effective values for the UAV under study, some variables had to be analyzed. For this investigation, it was necessary to carry out a brief iterative process to reach the best values, which will be described and presented. This process was necessary to find the height that optimized the range and flight duration and the other flight parameters of the aircraft.

The first step in sizing the aircraft was to calculate the exact weight of its parts using Raymer's and Gudmundsson's formulas, as weight is essential for verifying the other characteristics of the UAV.

To implement the formulas, it was necessary to calculate the estimated weight of the aircraft first. Thus, through the total volume of the UAV provided by OpenVSP, 𝜗_𝑡 = 3.054 𝑚³, and by the average density, we have:

Therefore, evaluating the weight of each part separately:

Wing

Table 2: Variables of Raymer's and Gudmundsson's formulas. Source: Author's own

Horizontal Stabilizer

Table 3: Variables of Raymer's and Gudmundsson's formulas. Source: Author's own

Vertical Stabilizer

Table 4: Variables of Raymer's and Gudmundsson's formulas. Source: Author's own

Fuselage

Table 5: Variables of Raymer's and Gudmundsson's formulas. Source: Author's own

With that, the values collected from OpenVSP, presented in tables 2, 3, 4, and 5, and with the implementation of the formulas in Python, the following values were obtained:

• Wing mass: WW = 58.9692 kg
• Mass of the horizontal stabilizer: WHT = 5.8901 kg
• Mass of the vertical stabilizer: WVT = 2.0573 kg
• Fuselage mass: WFUS = 82.0558 kg
• Total mass: W= WW+WHT +WVT+WFUS+WM+WCP= 304.0282 kg

After having calculated all the weights and checked the values, the other speeds of the aircraft were studied and analyzed at an altitude of 2300m, as it is a relatively good height for a border surveillance UAV.

Aerodynamic Coefficients

Having designed the aircraft, where the EPPLER 420 airfoil was used with the help of OpenVSP itself, the value of parasitic drag was found. Given that CDo depends directly on the flight speed and air density, which is a function of altitude, the cruise speed was fixed at 36m/s, and the height varied from 0 to 4500 m, and the drag was calculated for each altitude.

Table 6: Variation of parasitic drag and air density with altitude. Source: Author's own

Analyzing the table above, it is possible to notice that the drag presents a very small variation, on the order of 10-4, since the variation of air density is minute when evaluated in this interval. Therefore, for the continuation of the project, the following values were fixed:

• Cruise speed: 36 m/s
• Altitude: 2300m
• Temperature: 0.1ºC
• CDo = 0.01934

The next step was to determine the lift coefficient in cruise. For this, as in level flight, lift and weight are equivalent - 𝐿 = 𝑊 = 2982.66 𝑁 -, so

Substituting the values, the lift coefficient equals CL=0.5892. Subsequently, from the CL, the value of induced drag - CDi=0.00682 - was found by the following relationship

In sequence, the value of the drag coefficient was found, where

And, consequently, the total drag acting on the aircraft, in cruise, equals

Required Power

The power consumed by the aircraft is of utmost importance for discovering efficiency and also the maximum flight speed. It is known that this power is intimately related to the aerodynamic coefficients and the flight speed, that is.

Thus, to visualize the operation of the motor, the three-dimensional graph present in figure 3 was plotted, relating the Required Power as a function of the Flight Speed and Altitude, since the drag and lift coefficients are height-dependent.

Figure 3: Graph of required power as a function of speed and altitude.

Characteristic Speeds

Maximum Flight Speed

The maximum speed of the UAV is essential for understanding the operational limits of the aircraft. To find this value, the graph in Figure 3 was plotted in 2D for better visibility and then superimposed on the graph of the motor's Available Power as a function of speed.

Figure 4: Graph of required and available power as a function of speed and altitude.

To superimpose the graphs, it was necessary to approximately extend the available power since the provided graph did not have corresponding values above 60 m/s. Thus, evaluating the intersection of the curves, it can be seen that the maximum flight speed is related to the curve corresponding to the altitude of 4500 m and equals Vmax=67 m/s.

Stall Speed

The stall speed - Vstall - is the minimum speed at which an aircraft must fly to stay level, that is, at values below this the aircraft stalls and loses altitude. This speed is given by the following equation

Since this speed depends on the maximum lift coefficient and the same is linked to the airfoil model used, then, first, the characteristics of the EPPLER 420 airfoil that was used in the design of the UAV will be analyzed and, thus, the speed for the aircraft itself will be concluded.

The EPPLER 420 airfoil presents a maximum thickness of 14.3% at 22.8% of the chord, maximum curvature of 10.6% at 40.5% of the chord and the following shape:

Figure 5: EPPLER 420 Airfoil.

With the help of Airfoil Tools[5], the CL x α graph was plotted for different Reynolds numbers in order to find the CLmax for the airfoil.

Figure 6: CL x α graph of the EPPLER 420 airfoil.

Observing the graph, it is noticed that CLα=0=1.2 and that the maximum value for the lift coefficient for the EPPLER 420 is approximately CLmax=2.3, corresponding to Reynolds 1E6.

Having found these values, we can reflect them to the entire wing. Thus, for such value, it is assumed that the CLα=0 and CLmax of the wing are equivalent to 80% of the airfoil's value, so for the continuation of the project the used values are CLα=0=0.96 and CLmax=1.84.

Because of the value found above, substituting the numbers into the equation, it is found that Vstall=20.37 m/s.

Range Speed (Minimum Thrust)

The minimum thrust speed is the necessary condition for a given weight and maximum L/D ratio to maintain level of flight. The maximum L/D ratio is directly related to the aircraft's maximum range, as well as its speed, until the total fuel consumption. The speed for the best range is determined by the following formula:

Substituting the respective values into the formula, the aircraft has an ideal speed for the best range of VR=27.74 m/s.

Endurance Speed (Minimum Power)

The minimum power speed is the necessary condition for the aircraft to continue flying at minimum power. This condition is directly related to an aircraft's endurance, which is the maximum flight time it can have. This speed, for the longest flight time, is given by:

So, we have that VE = 21.08 m/s. And as mentioned earlier, due to wing modifications, it is verified that V_stall $< VE and, then, the aircraft is capable of maintaining level flight at a height of 2300m.

Propulsive Efficiency

Once the Range and Endurance speeds have been obtained, with the help of the graph in figure 7, which relates propulsive efficiency with flight speed, it was possible to find the values for each speed, which are E=0.58 and R=0.68.

Figure 7: Propulsive efficiency versus flight speed graph.

It is known that efficiency is determined by the ratio between available power - Pa - and shaft power - Pb, i.e.:

However, the available power is the power required during flight, so it is related to drag by the following formula: Pa=TV=DV

Thus, by manipulating the equation and evaluating the drag values and endurance and range speeds, one can find the respective shaft powers (propulsion power) for each case, i.e., Pb,E=6.54 hp and Pb,R=6.36 hp. And by analyzing these calculated values, we can see the convergence of the shaft powers for both range and endurance cases at a height of 2300m.

Motor Rotation and Fuel Consumption

With the shaft powers calculated in the previous item, the final values can be found that will allow the calculation of topics 4, 5, and 6. That is, considering the graph of shaft power by altitude at different rotations, in Figure 8, it can be noted that for the previously calculated powers of 6.45±0.1 hp, there is no line corresponding to the different rotations that intercepts the shaft power line, which shows an oversizing of the motor for the UAV.

Figure 8: Graph of shaft power versus flight altitude evaluated at different motor rotations.

Now, analyzing the graph relating fuel consumption to flight altitude, shown in Figure 9, it is noted that the best consumption, CC=7 l/h, refers to a rotation of 3000 rpm. Thus, returning to Figure 8, as there is no interception, the rotation equivalent to 3000rpm was chosen for a lower demand on the motor.

Figure 9: Graph of fuel consumption versus motor rotation.

Takeoff

• Takeoff is one of the most demanding phases of flight, as the engines are typically operating at maximum power. The aircraft's takeoff can be divided into the following parts: • Ground roll distance • Rotation distance • Transition distance • Climb-out phase

Figure 10: Parts of the takeoff run.

The definition of the takeoff run is based on the distance traveled by the aircraft - SG - until it reaches the takeoff speed - V_G = V_LOF (Lift-off velocity) -. Usually, the takeoff speed is defined based on the stall speed, that is, V_LOF = 1.1 · V_stall. Thus, for the UAV under study, V_G = V_LOF = 22.407 m/s.

Assuming that the aircraft has an average acceleration during the takeoff run, the run distance can be calculated by

Where the negative sign is used for a headwind component and the positive sign, for a tailwind component. The average acceleration is calculated by:

Where the average drag and lift values are defined by

The average speed and optimal lift coefficient are defined as follows

The average thrust - T_avg - is determined as a function of the average speed by analyzing the graph in Figure 11, thus, as shown, for V_avg, it is found that T_avg = 650 N.

Figure 11: Graph of thrust versus speed.

Substituting the respective values into the formulas, and knowing that the friction between the asphalt and the UAV wheel is μr = 0.025, that the angle between the aircraft and the runway - φ - is zero, and that CD = CDo + K · C α=0 (at sea level), the takeoff distance is equivalent to SG = 136.6898 m.

Endurance

As defined earlier, endurance is the maximum flight time that an aircraft can have until all fuel is exhausted. This duration in the air is defined by

Where: ▪ C: specific fuel consumption ▪ Wi: weight of the aircraft without fuel ▪ Wo: weight of the aircraft with fuel ▪ CL,E: lift coefficient at endurance speed ▪ CD,E: drag coefficient at endurance speed

For C, it is then given by:

Thus, substituting the values, and applying in the written code, the maximum flight time is E=10.31 h.

Range

The range determines the maximum distance that an aircraft can fly until the total consumption of its fuel. This distance is defined by

Where: ▪ CL,R: lift coefficient at range speed ▪ CD,R: drag coefficient at range speed

In this case, the specific consumption is given by:

With this, substituting the values and implementing the code, the maximum distance that can be traveled is R=1029.79 km.

Static Stability

Stability can be understood as the aircraft's tendency to develop aerodynamic forces or moments in order to return to equilibrium condition after a disturbance in uniform flight. With this in mind, an aircraft can be statically stable and dynamically unstable, but a dynamically stable aircraft is automatically statically stable.

As a method of studying and analyzing the static stability of the UAV in question, the procedures were performed, as in step 1, with the help of the Open VSP software, which allows structural modifications, and with VSPAero, which allows running the diagnostics related to aircraft stability.

Firstly, the primordial point to start the procedure was to calculate the center of gravity - CG - of the aircraft and to ensure that it is in front of the aerodynamic center—AC. For this, the bodies inside the structure, which represented the fuel tank, the payload and the engine, were replaced by point masses with their respective weights and positioned and kept in each position, and then slightly moved to meet the requirements that will be better described in the following topics.

In figure 12, you can see the point masses, after all the modifications, referring to the payload, the fuel tank and the engine positioned at the nose of the aircraft, the wing and the tail of the aircraft, respectively.

Figure 12: Top, side and isometric views, respectively, of the UAV.

In figure 13, after the analysis in section cuts, it can be noticed that the CG, represented by the red point, is in front of the AC, that is, the aircraft wing.

Figure 13: Top, side and isometric views, respectively, of the sections analysis.

a. Longitudinal Stability

Longitudinal stability is related to the pitch moment, where it can cause instability by rotating the aircraft's nose in a way that increases the angle of attack until stall occurs, or it can restore the disturbance suffered, causing the plane's nose to return to equilibrium position. For the aircraft to be longitudinally stable, the following criteria had to be respected, since the orientation of the y-plane in the software is the same adopted in the classroom:

• Negative pitch moment coefficient: Cmα $< 0 • Positive pitch moment coefficient at α=0: Cm0 $> 0

With the help of VSPAero, the following CMy x Alpha graph was generated.

Figure 14: Graph of the pitch moment coefficient as a function of α.

b. Lateral Stability

Lateral stability is directly related to the roll moment, that is, if there is a disturbance in relation to the longitudinal axis of the aircraft, causing it to roll, it will return to the equilibrium position. To achieve stability in this regard, the following criterion must be met:

• Negative roll moment coefficient: Clβ $< 0

When plotting the graph in the software, it can be seen that the CMx X Beta line has a positive orientation (figure 15), however, since the reference axis (x-axis) in Open VSP is in the opposite direction to the axis studied in class, it means that the coefficient has a negative sign in the standard orientation plane.

Figure 15: Graph of the roll moment coefficient as a function of β.

c. Directional Stability

Directional stability is associated with the yaw moment, that is, if there is a disturbance in relation to the vertical axis, causing the UAV to rotate, this moment must be able to return the aircraft to the initial position. Thus, with this objective in mind, the following parameter must be met:

• Positive yaw moment coefficient: Cnβ $> 0

Plotting the graph shown in figure 16, it can be seen that the line's orientation is negative, different from the requirement that must be followed, however, just as it happened to the x-axis, the z-axis in the software also has the opposite orientation to the standard, thus, in the orientation plane, the yaw moment coefficient is negative as expected.

Figure 16: Graph of the yaw moment coefficient as a function of β.

Dynamic Stability

An airplane can be considered dynamically stable if, after being disturbed from its equilibrium position, the resulting movement gradually decreases over time. The degree of dynamic stability is of utmost interest, which is usually related to the time it takes for the movement to be dampened to half its initial amplitude or, in the case of unstable movement, the time it takes for the initial amplitude or disturbance to double. Such performance verification is done by frequency or period of oscillation.

The aircraft's stability derivatives are extremely important for the ensuing calculations, which will be better shown in the relations present in the next topics. For this, values of certain coefficients related to the stability derivatives referring to the UAV under study were collected from the OpenVSP software and then implemented in Python for ease of calculations.

a. Longitudinal

This is related to the pure pitch moment, where the airplane's center of gravity is forced to move in a straight line and at constant speed, but the pitch movement is free to occur around the center of gravity. For this situation, the following longitudinal derivatives are related as in the table below, where for ease of calculation and analysis were written in a Python language code.

Figure 17: Table referring to the summary of longitudinal derivatives.

After the longitudinal simplifications, the vibration frequency and damping factor of the phugoid (long period) and the short period are defined by the following formulas:

Figure 18: Table with the formulas of the frequency and damping factor of the phugoid and short period.

Each stability derivative plays a role in the aircraft's sizing, to better understand how they affect the long and short period motion, the table below relates each derivative to the affected mode and how it is affected.

Figure 19: Table of relations between the longitudinal derivatives and the mode and how it affects.

With this in mind, using the values from table 7 and applying them to the formulas related to the long period and short period modes, the following values were obtained:

• Phugoid: 𝜔𝑝 = 0.6765 𝑟𝑎𝑑/𝑠 and 𝜁𝑝 = 0.1188
• Short Period: 𝜔𝑠𝑝 = 18.7919 𝑟𝑎𝑑/𝑠 and 𝜁𝑠𝑝 = 0.623

As the UAV project falls into small and light aircraft, it falls into Class I and, with non-terminal flight phases that are executed with gradual maneuvers and without precise follow-up, but with precise trajectory control, it is in Category B. By flight quality criteria, the phugoid and short period parameters need to be within a certain range, referring to the flight category, for the flight to be stable and efficient. For better qualities, the aircraft should be within level 1 or 2 at most.

Figure 20: Quality criteria table for phugoid mode and short period.

Analyzing the values obtained after implementing the code and simulations and comparing them with the values in the table above, it can be seen that they meet the flight quality requirements of level 1.

b. Lateral-directional

This stability case relates to pure roll, where the aircraft only has the freedom to rotate around its x-axis, and pure yaw, where the UAV is free to rotate around the z-axis. The lateral-directional derivatives, which are necessary in the analysis, are presented in the table below. They were written in Python, like the longitudinal derivatives, for ease of calculation and analysis.

Figure 21: Summary table of lateral-directional derivatives.

These assessments of pure yaw and roll can be approximated and evaluated in the following modes:

• Spiral
• Roll
• Dutch Roll (Rolling Holland)

With the possible analysis modes in view, they will be treated separately next.

b.i. Spiral

For the UAV to meet the spiral approximation criterion, it must satisfy the following relationships based on the lateral-directional derivatives.

b.ii. Roll

For the roll-related mode, the relationship that will determine the flight quality is.

b.iii. Dutch Roll

The aircraft meets the Dutch roll criterion by meeting the parameters related to a frequency and damping factor which are determined by the following formulas.

So, after preparing a writing in Python based on the aircraft's values, the following values related to each mode were obtained:

• Spiral: 𝐿𝛽𝑁𝑅 − 𝑁𝛽𝐿𝑅 = 8040.2993
• Roll: 𝜏 = 0.0004𝑠
• Dutch Roll: 𝜔𝐷𝑅 = 1.6478 𝑟𝑎𝑑/𝑠 and 𝜁𝐷𝑅 = 0.8244

Thus, for the UAV to have lateral-directional stability and allow a quality flight, such results found above must be within pre-established limits, just like in the longitudinal analysis. Therefore, such quality parameters can be seen in the tables below.

Figure 22: Flight quality criteria tables referring to the spiral mode and roll mode, respectively.

Figure 23: Quality criterion table for the Dutch roll mode.

Checking the values obtained for each criterion for the UAV under study and comparing with the tables in figures 22 and 23, it can be seen that it fits into the following levels of flight quality for each mode:

• Spiral: stable (level 1)
• Roll: level 1
• Dutch Roll: level 1

Note: The levels of flight quality in spiral mode are related to the case of instability and consider the time until the amplitude doubles in size, once our criterion was greater than zero, the aircraft is automatically stable in spiral mode.

Detailing of Modifications

Throughout the development and study until obtaining the aircraft that was previously presented, many parameters had to be altered. This will be described and compared, through images, the stages of the project until its completion.

The first modification was in relation to the wing, where the aspect ratio was increased from 11.11 to the maximum value of 18 in the final project. Initially, the aspect ratio was at this value to obtain a greater difference between the Endurance and Stall speeds, but after investigations and analyses, it was notified that keeping the difference as it is presented, which already meets the flight criterion, and using the maximum value, the performance of the aircraft is improved, which consequently changed the wingspan and the wing chord as well, as can be noticed in the figure below.

Figure 24: Top views of the first project and the final project, respectively.

Another change made was regarding the airfoil used, which instead of NACA 4412 was used the EPPLER 420 because it has a higher CLmax and consequently reduces the stall speed of the aircraft.

During the static stability analysis, the position was changed and slightly thrown forward of the aircraft, and such modification was maintained in the final project, as well as the incidence angle of -3° in the horizontal stabilizer. However, the horizontal stabilizer had its area reduced, compared to the previous model, in order to reduce the roll moment.

Similarly, the vertical stabilizer was decreased for reduction of directional stability. But also, such modifications, as seen in figures 24 and 25, were made with the intention of ensuring dynamic stability in the spiral and Dutch roll modes.

Figure 25: Side views of the first project and the final project, respectively.

The last and crucial, changes made to obtain the stable aircraft were to slightly lower the position of the wing on the fuselage, as can be noticed in figure 25, and the increase of the wing tilt angle (dihedral), in order to increase the dihedral effect and meet the presented spiral criterion, as can be seen in the figure below.

Figure 26: Front views of the initial project and the final project, respectively.

Conclusion

After conducting numerous simulations and structural modifications to the aircraft, the final values, for better visualization, are presented in table 7.

By evaluating the obtained values, especially those related to dynamic stability, it can be observed that the values are within the level 1 flight quality criteria, as required for optimal performance of the UAV. Thus, it is concluded that, as the main objective of the work, the aircraft has been successfully developed to be stable, both statically and dynamically, and efficient, while exhibiting a high level of flight quality.

Table 7: Table of final values for the UAV. Source: Authorial.

With this in mind, figure 27 displays images of the finalized project based on the values presented in table 7.

Figure 27: Top, isometric, side, and front views of the final project.

Team

• Pieter van Tilburg Bernardes
• Yuri Winche Achermann