MAE 586 Project Work in Mechanical Engineering:

Tricopter Design

NC State University

Fall 2012

By

Paul J. Coco, PE

Advisor

Dr. Ashok Gopalarathnam

Tables of Contents

1.0 Introduction 1

2.0 Dynamics and Flight Control 4

3.0 Componet Selection 9

4.0 Tricopter Design 19

5.0 Flight Performance 28

6.0 Flight Control and System Modeling 38

7.0 Conclusion 44

Appendix A 45

Appendix B 46

Appendix C 48

References 55

Cover Page picture is of the project tricopter in an autonomous hover.

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1.0 Introduction 1.1 Project Proposal

For this project I will design, build, and fly a tricopter considered for use in military or commercial applications. These applications will development the appropriate operating envelope required to be incorporated into the design. These characteristics may include, but not limited to, size, payload, lift, and agility.

The design will involve the use of commercially available off the shelf components and material. I will investigating a frame design and stability control tuning for a micro UAV tricopter. This will include measuring the vibration and dampening of candidate material ie(wood, AL, and Carbon Fiber) produced by a running motor and propeller, in which I will develop a frequency response spectra. With this data I will also analyze the cyclic fatigue and fracture characteristics of the candidate material to further justify my selection. Once the frame is constructed I will do another vibration test analysis to evaluate the vibrations at the control board location and establishing a baseline signal for the board with all components and power systems installed.

As a part of the development for the code to fly the tricopter I will also investigate the aerodynamic forces which will have to be balanced to properly maintain controlled flight and determine the proper motor orientation. I will use the UIUC UAV propeller database for propeller selection and performance analysis. I will also you programs such as MATLAB and Xfoil to verify the UIUC database results and determine if there are any significant advantages for drag reduction in using symmetric airfoil shape motor fairing arm verses a circular or square fairing arm.

For the design of the control board I will use a small processor which can execute a code which will take into account structural vibrations from the motors and evaluate orientation on a x,y,z axis. The code will use this information drive for an error of zero in a closed feedback loop to maintain level flight. This will be done by the use of a combination of multi axis gyros and accelerometers. In all other flight conditions the process will take into account the requested signal input, along with structural vibrations and orientation, to achieve forward, side-to-side, and backwards flight. The closed loop all be tested on Matlab’s simulink to determine proper values for damping, overshoots, and system frequencies at about 400-600 iterations per second.

Once the code is functional and tuned it will be converted to the proper format for the board and installed into the frame for flight testing. Once the evaluation for the key elements of the flight test are completed the code will be upgraded if needed and the adapted to fly waypoints GPS around a track.

The deliverable for this project will be the creation and successful flight of a tricopter drone and the paper documenting the design, testing, theory, calculations, and conclusion. The major milestones for this project will be to:

- Establish the mission requirements - Complete vibration testing and endurance calculations of the of the candidate

material - Select components and build the frame - Vibrational testing of the frame - Develop the Code for operation/Aerodynamics - Upload code and test hardware.

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- Flight test - Autonomous Flight test

1.2 Background

With advancements in computer processing and reductions in hardware cost it has been possible for the average radio controlled (RC) enthusiast to create their own flying drone. A drone refers to aircraft that have the capability of autonomous flight or autopilot, which means that it can follow a mission from point to point, typically guided by GPS or maintain its orientation without human control. This differentiates it, on the one hand, from RC aircraft, which needs to be manually piloted, and on the other from uncontrolled vehicles like balloons or ballistic rockets. Usually drones are also known as unmanned aerial vehicles (UAV) or unmanned aerial systems (UAS), to include the ground-station components and also carry some sort of payload, which at a bare minimum includes cameras or other sensors as well as some method to transmit data wirelessly back to a base.

The U.S. military began experimenting with UAVs as early as World War I. Autopilot technology was first used in the 1930s to keep the aircraft level and allowed pilots to set a heading and altitude, knowing that the aircraft would continue to fly straight ahead until told otherwise. By World War II, unmanned craft could be controlled by radio signals, usually from another aircraft. Vehicles that could return from a mission and be recovered appeared in the late 1950s. Beginning in the Mid-1990s the US Military invested in the development of UAVs due to their ability to operate in dangerous locations while keeping their human operators at a safe distance. By the year 2000 the US Military had established operational UAV squadrons. The larger UAVs provide a reliable long duration, cost effective, platform for reconnaissance as well as weapons, becoming an indispensable tool for the military.

Most of the large military UAVs are fixed wing aircraft. Reducing the size of the UAV will give it greater maneuverability and versatility. The reduction in size comes at the penalty of less payload and endurance time. A rotary aircraft becomes the best alternative to a fixed wing aircraft for minimizing size while maintaining lifting capability. With its ability to hover and perform vertical takeoff and landings (VTOL), a rotary aircraft can maneuver in confined spaces giving it a broader range of applications when compared to a larger or fixed wing aircraft.

Traditional rotary aircraft seen today are helicopters, with a main and tail rotor. On a smaller scale, helicopters are harder to control and may not be as stable of a platform for most applications. Complex mechanical control linkages for rotor actuation, increases the possibility of failure and large main rotors can cause damage or injury. A multicopter can alleviate all the problems inherent to a small scaled helicopter design, while maintaining all its benefits.

A multicopter is a rotary aircraft with more than two rotors which often use fixed-pitch blades. Control of multicopter motion is achieved by varying the relative speed of each rotor to change the thrust and torque produced by each. In cases when an odd number of rotors are used, a servo thrust vectoring system must be employed to compensate for unbalanced torque. The use of multiple rotors ensures that individual rotors are smaller in diameter relative to the frame size which could create a larger equivalent rotor producing more lift when compared to a traditional helicopter of the same size.

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Multicopters that are piloted on the ground or are utilized as drones are currently being used in commercial applications. The film industry is already full of remotely piloted multicopters serving as camera platforms, with a longer reach than booms as well as cheaper and safer operations than manned helicopters. Some farmers now use drone multicopters for crop management, creating aerial maps to optimize water and fertilizer distribution. There are countless scientific uses for drone multicopters, from watching algal blooms in the ocean to low-altitude measurement of the solar reflectivity of the Amazon rain forest. Others are using the craft for wildlife management, tracking endangered species and quietly mapping out nesting areas that are in need of protection. Law Enforcement agencies employ these for surveillance and tracking.

For this project a tricopter (three rotor rotary aircraft) was selected for design and analysis due to its increased performance and versatility over other popular multicopters, such as quadcopters. Also with one less rotor, motor reliability of the system increases while design cost decreases, and finally there are few academics papers which research this design.

1.3 Safety and Regulations

By the legal definition, the tricopter for this project will operate in a manner which will no longer classify it as purely a RC recreational aircraft. While completing task in which the operator does not input control commands into a remote transmitter, the tricopter is considered a Micro Unmanned Aerial Vehicle (MUAV) or drone.

Inorder to meet federal regulations and safety guide lines for this project, the operator will be able to operate the tricopter at any time overriding all autonomous controls. If the operator signal is lost by the tricopter receiver at anytime, the tricopter will hover in place for one minute then gradually reduce power to each of the rotors until it lands. If the tricopter cannot maintain its initial positions for more than 5 seconds, during its hover, the tricopter will then cease all power to the rotors and deploy a recovery parachute for a controlled decent. If at any time all power is lost the recovery parachute will deploy. The recovery parachute will be spring loaded and held latched by an energized electromagnetic coil. When denergized the latch opens by spring force and deploys the recovery parachute.

During autonomous flight the tricopter will operate within .3 miles of the operator and the operator or a spotter will maintain a positive visual of the tricopter at all times.

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2.0 Dynamics and Flight Control

Understanding the dynamic characteristics of the tricopter is important in the development of the appropriate code for the flight controller. The flight controller is essential for the proper operation of the tricopter, in which it can react faster and with more precision than any human pilot. The flight controller completes this by manipulation of the motors and the servo to achieve the desired orientation based on the sensor indications (ie gyros and accelerometers). The flight controller processes the sensor inputs into an algorithm or code based on kinematic and dynamic equations using the principles of angular momentum to control the tricopter in stabile flight. The flight controller and code are further described in sections 3 and 6 respectively.

2.1 Rigid Body Equations of Motion

The rigid body equations of motion are obtained from Newton’s second law, which states that the summation of all external forces acting on a body is equal to the time rate of change of the momentum of the body; and the summation of external moments acting on the body is equal to the time rate of change of the moment of momentum (angular momentum). The time rates of change of linear and angular momentum are referred to an absolute or inertial reference frame.

The orientation of the tricopter can be described by Euler angles. The orientation of the body frame with respect to the fixed frame can derive the pitch(θ), roll(φ), and yaw(ψ) angles of the tricopter upon rotation along the y, x, and z axis respectively. Upon further derivation Figure 1 defines the forces, moments, and velocity components experience by an aircraft.

Figure 1. Dynamic representation of an aircraft

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The tricopter will also experience these same forces, moments, and velocity components which can be developed into a 6-degree of freedom nonlinear equations of motion. Due to its size and construction the tricopter can be assumed to be a rigid body object in which the rigid body equations of motion are expressed as the differential equations describing the translational motion, rotational motion, and kinematics in Figure 2.

Figure 2. Summary of kinematic and dynamic equations

Note that the terms S, C, and T refer to the Sin, Cos, and Tan of the subscripted Euler angle.

2.2 Flight Control

The tricopters motion in flight is similar to any other aircraft, in which the orientation and flight control is a product of roll, pitch, and yaw. The control strategy is the same as any tradition helicopter. Control strategies of tricopter are shown in Figure 3.

Figure 3(a) shows the roll control; varying the rotor speeds of the forward two rotors will generate a roll. By decreasing rotor speed 1 the tricopter will roll to the left and rotor speed 2 roll to the right. Figure 3(b) shows the pitch control; varying the rotor speeds from front and aft rotors will generate a pitch. By decreasing rotor speed 1 and 2 and increasing rotor speed 3 the tricopter will pitch down and sustain forward flight. By increasing rotor speed 1 and 2 and decreasing rotor speed 3 the tricopter will pitch up and fly backwards.

Figure 3(c) shows the yaw control; the yaw is controlled by varying the angle of rotor 3 to vector the thrust to product a torque moment which will yaw the tricopter left or right. Inorder to maintain lift the rotor speed increases while the thrust angle changes. Figure 3(c) shows the tricopter yawing right.

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Figure 3(a) Roll Control

Figure 3(b) Pitch Control

Figure 3(c) Yaw Control

In order to change altitude the tricopter synchronously increases or decreases the speed of all three rotors.

The rotational speed of each of the rotors translates to thrust and torque. The thrust and torque the tricopter can produce is dependent of the propeller’s performance parameters, ie thrust and torque coefficients. The thrust and torque is proportional to the thrust coefficient (CT) times the square of the rotational speed (ω) and torque coefficient (CQ) times the square of the rotational speed(ω). Values for the thrust and torque

1

1

1

1

1

2

3

2

2

2

3

2

3

3

3

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coefficients can be obtained from testing and found on various sites such as the University of Illinois at Urbana-Champaign (UIUC) Propeller Database.

In a tricopter configuration the forward rotors, 1 and 2, turn in opposite directions of each other causing the resultant effect or torque to cancel out or be so small it is negligible. Rotor 3, the aft rotor, is tilted at an angle α, as shown in Figure 4, in order to compensate the resultant force produced by torque, Fq, with the resultant force produced by thrust, Fr, in y axis. In the z axis Fq provides a small contribution for lift. Assuming there is no flapping in the propeller angles α and θ are equal.

Figure 4. Tail rotor force balance

As the rotational speed increases so do the resultant forces and therefore a change in the angle α. The yaw gyro working in a closed feedback loop will vary the angle of thrust in order to maintain yaw stability. Equations 1 and 2 derived from the free body diagram in Figure 5 show the balance of equations required to achieve equilibrium.

α

Fr=Rotor Thrust

Fz

Fy = Fq*cos(θ)-Fr*sin(α)

= Fr*cos(α)+Fq*sin(θ)-mg/3

θ

Fq=Torque Force

Fq and Fr are a Function of ω, as ω increase so does Fq and Fr.

(1)

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Figure 5. Tricopter Free Body Diagram

Based on the design of the frame all rotor arm lengths are equal, as are the angles between the rotor arms. Rotor arm lengths are 0.45 meters and the angle is 120ᴏ

l1 l2

l3

ϑ

ϑ

ϑ

1

3

1 2

(2)

(2)

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3.0 Component Selection

The components selected for the tricopter were based on project mission goals. The required mission goals for this project are for the tricopter be designed to be agile in flight while maintaining stabile handling characters, reduced vibrations, operate autonomously, and have the ability to carry a payload. To meet the mission goals the design attributes are dependent on the frame construction, material selection, and the components used. The combination of the selected power train, to include the motor, propeller, electronic speed controller (ESC), and power supply, will determine the tricopters agility and payload carrying ability. The onboard flight controller and sensors will aid in the tricopters handling characteristic and the ability of operate autonomously. The frame construction and material selection will alleviate excess vibrations in the tricopter.

Since a majority of the components used are from the radio controller industry, it is not enough that components are selected alone based on manufacture specifications. Testing individual components was completed and research was done on various academic, hobby databases, and forums to asset the selected components past performance and reliability.

3.1 Propulsion and Power System

The proper selection of a propulsion and power system, constituting the power train, for any UAV is based on the synchronization of the propeller not over loading the motor, and the combination of the two not exceeding the capability of the battery and the electronic speed controller. Component specifications, manufacture test data, and user field test are used to determine the proper combination for the power train. The flight profile and operational requirements will determine the need for a power system whether it is designed for speed, lift, or a combination of both.

Under-propping(too small of a propeller) or over-propping(too small of a propeller) can do irreversible damage to electric motors and ESCs, because an incorrect propeller will force the motor to work harder than it was designed to. Placing an oversize propeller on an electric motor will not cause the motor stall. It will just keep on trying to turn the propeller causing motor to draw higher current. Eventually it will exceed the maximum amperage rating of the motor or ESC and will burn it out. With too small a propeller, the motor can exceed its RPM rating and damage can result from the motor spinning too fast.

Since rotary aircraft need to use their rotors to produce thrust and lift, the required thrust to weight ratio is higher. This means that the combined thrust of the three rotors needs to exceed the weight of the tricopter by a certain factor. In RC model airplanes a thrust to weight ratio of 1 is considered aerobatic, but for a tricopter is will only hover an inch off the ground in ground effect. Through prototype testing a ratio of 2 was required to properly fly with light wind, and a ratio of 3 was observed to be ideal for speed and sufficient to carry a payload while operating at higher wind speeds.

Based on the objectives of this project the tricopter is designed for taking both lift and speed into its design consideration in achieving a thrust to weight ratio of 3. Modifications to the frame as described in section 5 will enable the tricopter to achieve greater speeds from its contemporary design.

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Based on static motor testing, the selected motor and propeller combination produced 2.38 lbs of static thrust at 100% throttle. With the tricopter weighting in at 2.5 lbs, the thrust to weight ratio is 2.85. To ensure the proper power train combination was selected a watt meter was used to determine the loads the motor and propeller combination placed on the ESC and power supply. At 100% throttle there was 21 amps drawn. This required an ESC rated for 25 amps. Since all the ESCs are wired in parallel this requires a power supply which can deliver a total of 63 amps.

3.1.1 Motor

The motor is the first component to select based off of the requirements and size of the tricopter. The tricopter will be comprised of 3 Brushless DC Motor attached to a propeller at the end of each arm.

The Brushless motor differs from the conventional Brushed DC Motors in that the commutation of the input voltage applied to the armature's circuit is done electronically, whereas in the latter, by a mechanical brush. In spite of the extra complexity in its electronic switching circuit, the brushless design offers several advantages over its counterpart, to name a few: higher torque/weight ratio, less operational noise, longer lifetime, less generation of electromagnetic interference, low heat generation when properly loaded, and less vibrations.

The main of advantage of using a brushless DC motor for applications in a tricopter, or in any multicopter design, is that since it is an electronically commutated motor, which are synchronous motors, it is easy to calibrate all 3 motors to synchronously operator at the same RPMs for a given throttle through an electronic speed controller. Field testing with an optical tachometer (device used to measure RPMs) shown that once the three motors were calibrated and synchronized there was less than a 25 RPM variation in each of the motors through the throttle range without excessive correction from the flight controller board. This is further corrected by trimming through the flight controller board to achieve a negligible RPM difference in each of the motors.

Brushless motors are normally evaluated by their size, technical performance specifications, and motor constants. Motor size is typically based on industry standards for the required radio controlled aircraft size it is to be used for. Technical performance specifications are the manufactures published analysis of voltage loads, power outputs, max amperages, and recommended propeller sizes. The motor constant, kv, is the rating of the motor in RPMs/Volts inorder to give users an indication of the motor speeds for a desired power supply.

For tricopter applications the kv constant is chosen based on the arm length, which is determined in section 4. A high kv motor is required for shorter arms and lower kv for longer arms. The reason this is the case has to do with the moment response for each of the arms and the thrust to weight ratio of your design. The shorter the arms of the tricopter give a smaller moment of inertia, making the tricopter more susceptible to changes in its orientation thus making it less stable. The higher kv over the throttle range also gives a greater step increase in RPMs of the motor, which is faster in responding to changes in orientation to maintain stability. As a consequence of high kv motors, the motor also produces less torque therefore only having the capability of turning smaller propellers. Smaller propellers require higher RPMs in high kv motors to generate the required thrust.

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For the tricopter design, the main considerations were to lift its required payload, achieve a desired speed, and maintain stability. This was achieved by using a larger propeller; generating more thrust, with larger arms on the frame; higher moments of inertia therefore more stability, and a lower kv motor; higher torque to spin the larger propeller.

3.1.2 Propeller The purpose of any aircraft propeller is to convert rotational motion into thrust. A pressure difference is produced between the forward and rear surfaces of the airfoil-shaped blade, and a fluid is accelerated behind the blade. Propeller dynamics can be modeled by both Bernoulli's principle and Newton's third law. The thrust produced depends on the density of the air, the propeller's RPM, diameter, the shape and area of the blades, and pitch. RC propellers are designated by their manufacture, diameter and pitch. There are multiple sites such as the UIUC Propeller Database which provide performance data for commercial RC propellers. From these databases, performance coefficients can be obtained to determine the utility of the selected propeller for the desired application.

The diameter is based on the length of propeller from tip to tip measured in inches. The pitch is the distance the propeller should advance in one revolution measured in inches. The pitch speed is the mean geometric pitch times RPM, which is the theoretical speed of the aircraft if there was no slip. The propeller's output power is equal to the thrust times the pitch speed. With a given power, the more thrust you have, the less top speed achieved. Assuming the same power the following thumb rules are made for propeller selection:

Larger diameter & less pitch = more thrust, less top speed. Smaller diameter & more pitch = less thrust, more top speed.

The recommended prop P/D (Pitch/Diameter) ratio for sport RC airplanes is 1:2 to 1:1. With a too large pitch, the prop becomes inefficient at low forward speed and high rpm, as when during the take-off and/or climb. Whereas a propeller designed for greatest efficiency at take-off and climb (with fine pitch & large diameter) will accelerate the plane very quickly from standstill but will give less top speed.

In most multicopter designs the desire is typically to have a pitch of around 3 to 5 and maintain a larger diameter propeller. This will naturally achieve the thrust requirement at the cost of speed. The tricopter design for this project does a combination of both. Based on the size and weight of the tricopter it would be typically recommended to be equipped with a 9 X 4.7 (D X P) propeller. Motor test show that this propeller can generate 1100 grams of thrust at 10220 RPMs with a pitch speed of 41 mph. The selected propeller, a 10 X 8, can generate 1100 grams of thrust at 8050 RPMs with a pitch speed of 45.8 mph for the same voltage and slightly higher amps.

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Figure 6 below shows Thrust & Drag vs Speed for 3 props with different P/D ratios. An aircraft reaches maximum level flight speed when the Thrust becomes equal to Drag.

Figure 6. Thrust & Drag vs Speed for 3 props with different P/D ratios

3.1.3 Electronic Speed Controller (ESC)

An electronic speed control or ESC is a circuit with the purpose to control an electric brushless motor's speed, its direction and possibly also to act as a dynamic brake in some cases. ESCs are often used on electrically powered brushless motors essentially providing an electronically-generated three phase electric power, with a low voltage source and are normally rated according to maximum current.

An ESC interprets control information in a way that varies the switching rate of a network of field effect transistors (FETs), not as mechanical motion as would be the case of a servo. The quick switching of the transistors is what causes the motor itself to emanate its characteristic high-pitched whine, which is especially noticeable at lower speeds. It also allows much smoother and more precise variation of motor speeds in a far more efficient manner than the mechanical type with a resistive coil and moving arm once in common use.

The ESC generally accepts a nominal 100 Hz Pulse Width Modulation (PWM) servo input signal whose pulse width varies from 1ms to 2ms. When supplied with a 1ms width pulse at 100 Hz, the ESC responds by turning off the DC motor attached to its output. A 1.5ms pulse-width input signal results in a 50% duty cycle output signal that drives the motor at approximately 50% speed. When presented with 2.0ms input signal, the motor runs at full speed due to the 100% duty cycle (on constantly) output.

Regardless of the pulse width of the signal, the frequency is a limiting factor in the stability of the tricopter. Most of the sensors which aid in controlling stability and the flight control board has processing speeds are well over 500 Hz. Various open source codes are available to modify off the shelf ESCs to achieve a signal frequency speed of 400 Hz. 3.1.4 Servo The servo on the tricopter is located on the aft rotor and is responsible for thrust vectoring the aft rotor as described in section 2.2 for yaw control and unbalance

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torque stabilization. The servo uses for the tricopter project is a metal gear digital servo. A servo receives a signal from the receiver through PWM exactly as the ESC. A traditional analog servo operates at a frequency of 50 Hz, while a digital servo operates about 300 Hz. A small microprocessor inside the digital servo analyzes the receiver signals and processes it into very high frequency voltage pulses to the servo motor. The pulses are shorter in length, but with many voltage pulses occurring, the servo motor will speed up much quicker and provide constant torque and increased yaw stability. 3.1.5 Power Supply

The power supply that the tricopter will use is a 3 cell lithium polymer battery. Lithium polymer batteries or LiPos are popular in the RC community due to their light weight, power density, and availability in different rating and capacities.

LiPos are typically designated by voltage, capacity, and C rating. The voltage of the LiPo is dependent on the amount of cells. Each individual cell maintains a nominal voltage of 3.7 volts and of normally attached with other cells in series or in parallel to achieve their desired rating. The capacity of the LiPo is measure in mAH. This is corresponds to the amount of current, in mAmp, the battery can discharge in one hour. The C rating is the discharge rate of the battery. It is a multiplication factor of how many times the capacity the battery can safety discharge. For example a 2200mAH 1C can provide a constant 2.2 amps for one hr, while if the same capacity battery was used but as a 40C, then the battery would provide a constant 88 amps for 1.5 minutes. When selecting the proper battery the product of the capacity times the C rating must equal the maximum amp draw.

Based on the power requirements of the three motors, it was originally stated that since all the ESCs are wired in parallel this requires a power supply which can deliver a total of 63 amps inorder to achieve 100% throttle. If the battery from the example above was used, 2200mAH capacity, it would be able to support about 2 minutes of 100% throttle for 63 amps. Since the tricopter will normally operate conservatively around an average 30% throttle, as its efficient power setting, the flight time increases closer to 7 minutes. A 3 cell (11.1 Volts) 40C 3000Mah battery was used for the project tricopter with an estimated flight time of 10 minutes.

With a nominal voltage of 3.7 volts per cell a full charge places cell voltage at 4.2 volts. In a discharge cycle at a given C rating the LiPo maintains a small change in voltage up to about 80% of its capacity. This point is normally when a rapid drop in cell voltage occurs as shown in the graph in Figure 7. Normal minimum voltage to maintain the cell without damage or decreased capacity due to over discharge is approximately 3 volts. A typical operating rule is to operate the battery to 80% of its capacity or until a minimum voltage of 3 volts is reached in each cell.

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Figure 7. LiPo discharge voltage vs % capacity

3.2 Stability Orientation and Position Sensors

Various sensors are used to help maintain the desired operating requirements of the tricopter. To insure proper operation the tricopter, at a minimum, needs to achieve stability. Stability is needed to ensure that the tricopter acts and behaves in a manner in which the operator can control it with a sufficient reaction time in response to changes in its orientation. Orientation will generally be attributed to the tricopters pitch, roll, and yaw, while position is generally attributed to translations in the x, y, and z axis by controlling the pitch, roll, and yaw.

3.2.1 Gyroscope

The tricopter is equipped with a 3 axis gyroscope (gyro). A gyro measures rate of rotation around a particular axis. When a gyro is used to measure the rate of rotation around the tricopter roll axis, it will measure a non-zero value as long as the tricopter is rolling, but measure zero if the roll stops. Based on the Kinematic and dynamic equations using the principles of angular momentum from section 2.1, the rate of rotation about the axis’s for pitch, roll, and yaw are derived from the rotational velocities, (p, q, r), and rotational angles, (φ, θ, ψ), for the tricopter orientation.

The angular velocity is the time derivative of the angle. Summing the signal of the gyro numerically, forming the integral derives the angle. By integrating the rate of rotation the tricopter achieves stability. The most basic flight controller requires only a 3 axis gyro to achieve stable and controllable flight. Unfortunately, the problem with this integration is that it will result in a drift in the estimation of the orientation of the tricopter. This is due to the bias error in the gyroscope and by integrating the constant error, it will result in a linear function and the estimation of the rotation will drift. The drift in most cases does not occur drastically, but when the operator is relaying on orientation and position, for example a stationary hover or straight and level forward flight, it is very noticeable. Drift rate is often measured in degrees per hour. Most high end gyros have a drift of 0.01 degrees drift per hour. Due to the size and cost value of high end gyros, other senors can be used to counter drift. Also, wind and vibrations can further complicate draft.

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3.2.2 Accelerometer

The 3 axis accelerometer has the ability to gauge the orientation of a tricopter relative to the earth’s surface. If the tricopter is in free fall, the acceleration will be shown to be zero. If it is only accelerating in a particular direction the acceleration will be indistinguishable from the acceleration being provided by the earth’s gravitational pull. An accelerometer accomplishes this by measuring linear accelerations.

An accelerometer alone cannot be used in a tricopter to achieve stability. In conjunction with a gyro it can eliminate any draft resulting from calculated error. This will ensure proper orientation in helping achieve level flight and dampening small perturbations which result from vibrations transmitted through the frame and excessive correction over shots from gyro corrections. From an operator perspective, a center stick position (Hands off), will place the tricopter in a level hover when utilizing a gyro and accelerometer. The accelerometer does provide an angle, but only in a stationary hover. If the tricopter is inclined, acceleration in the direction of the slope will occur, making the measured angle calculation invalid. A movement of constant velocity (zero acceleration) will measure the angle accurately.

The consistent velocity conditions are achieved during a hover or in short durations in forward flight. This is also when the tricopter is maintaining a constant angle making it most susceptible to drift. The signal of the accelerometer, under this condition, provides a reference to match the integrated gyro signal thus eliminating draft.

Under perfect flight conditions (ie. no wind), an accelerometer can be also used to maintain tricopter position. In real world conditions wind can cause the tricopter to drift from its desired position in an x,y,z plane.

3.2.3 Magnetometer

A 3 axis magnetometer is used to measure the strength and direction of the magnetic field of the Earth. This can be used to compute in which direction, along the Earth’s surface, in which the tricopter is pointing at. The magnetometer is also used to help counter the drift associated with the gyro error in the Yaw axis. Since the magnetometer is a compass, it will also provide navigational information to the operator display.

3.2.4 GPS

The GPS, Global Positioning System, sensor measures the position of the tricopter presented in geographical coordinates of longitude and latitude, and altitude. The GPS also measures the absolute velocity of the tricopter and provides navigational information to the operator display. Unfortunately lower cost GPS sensors are not as accurate for calculating height position for the z axis. For an altitude hold function, sonar and a barometer will by the primary sensor depending on height, with GPS as the backup.

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3.2.5 Sonar

The sonar sensor is an ultrasonic sensor that can measure distances by sending a high frequency sound wave and then receive the echo of the signal. By calculating the time interval between sending the signal and receiving the signal the distance to the nearest object can be determined. Unfortunately most sonar sensors operate at a limited height range of about 15ft from the ground. Below 15ft it will be the primary sensor used to determined position in the z axis, backed up by the barometer and then GPS.

3.2.6 Barometer

The barometer is a sensor that can measure the atmospheric pressure. Since the atmospheric pressure is decreasing with increasing altitude, this sensor can be used to calculate the altitude of the tricopter in relation to the sea level. This is type of sensor has been traditionally used for altimeters in most civil aircraft. The problem with this sensor is that it is not very accurate. The published accuracy it is about + or – 3 ft. This will be the primary senor to be used in conjunction with the optical flow sensor to determine position in the z axis, backed up by GPS over a height of 15 ft.

Figure 8 shows a manufacture graphic representation of the correlation between barometric pressure and altitude which is used in the barometer’s software.

Figure 8. Barometer and Altitude Relationship

3.2.7 Optical Flow Sensor

The Optical Flow Sensor (OFS) functions of the basis of the apparent visual motion seen by a tricopter when moving relative to a textured surface. This motion can used to determine the orientation and position of the tricopter relative to the surface. In the z axis, as the tricopter descends the objects viewed by the OFS appear to increase their distance from each other, while in an ascent the

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opposite occurs. In the x and y axis, it can control pitch and roll based on the perceived motion of stationary grounds objects.

Based on the complexity, this project will only utilize the z axis code to improve the altitude hold function.

The combination of all these sensors in harmonious operation will give the tricopter unparallel ability and versatility to complete its prescribed tasking. Figure 9 is a table which summarizes the functions of each the sensors selected.

Onboard Sensors

Gyroscope Accelerometer Magnetometer GPS Sonor Barometer Optical Flow

Primary Sensor

Function

Stability Orientation Orientation Position Position (Z axis <15ft)

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Figure 9. onboard sensor task

3.3 Mission Payload Package

Beside the sensor load out as described in the previous section, the basic mission of the tricopter for use by commercial or military applications will be of surveillance. To achieve this goal the minimum load out will include a high definition video camera to record the flight from the vantage point of the tricopter. A full load out would include a wireless real-time video uplink which will transmit video to the operator inorder control the tricopter through a First Person View (FPV) system and a command uplink to receive telemetry and re-task mission profiles from a ground station during autonomous flight.

3.3.1 HD Camera

The tricopter will use the 1080p HD HERO camera using a 170º wide angle recording 720p video at 60 frames per second. The camera was selected for its relatively low cost and extensive use and versatility for applications such as this.

3.3.2 Wireless Video System

The tricopter is equipped with a small 5.8Ghz 8CH transmitter power at 200mW. With high gain antenna, it has an advertised unobstructed range of to 2km. It will transit a signal from an onboard forward facing camera with video interlaced with onboard navigational data to a ground display for use of the operator to control the tricopter. This system was selected for its operating frequency which reduces interference to other onboard wireless frequencies and commercial bands. Unfortunate the signal can be blocked if the tricopter travels behind an object. This will not be an issue since, inorder to operate the tricopter federal regulations require it to be in direct line of sight of the operator.

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3.3.3 Wireless Telemetry Uplink

The tricopter will have 3DR Radio telemetry system, by 3DRobotics, serve as a command uplink to receive telemetry and re-task mission profiles from a ground station during autonomous flight. The 3DR operates at 915 mhz with an advertised air data rates up to 250kbps for a range of 1 mile. Note that during autonomous flight range will be no greater than .3 miles.

3.3.4 Recovery Parachute

Inorder to add a level of assurance in the safe operation of the tricopter, a recovery parachute was added and operated as described in section 1.3. The design restrains of the parachute are that it would have to be large enough to carry a load of 3 lbs down at a velocity of 5mph to reduce damage to the tricopter or persons upon impact. The following equations were used for the drag calculations to determine the diameter of the parachute:

FG = FD

m g = ½ Cd A v2

A = D2 / 4

The drag coefficient for a flat sheet (parasheet) is 0.75, or 1.5 for a parachute (true dome-shaped chute). The parachute was constructed from a flat sheet of light weight nylon rip stop and the rigging was made from tulle. The calculated diameter of the parachute is 56.35 inches. Figure 10 is a picture of the parachute deployment drop test with a test load of 3 lbs from a height of 150ft.

Figure 10. Recovery Parachute Drop Test

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4.0 Tricopter Design

One of the most integral parts of tricopter is its frame. The frame supports the motors and other electronics and prevents vibrations. Even the geometry of the frame can affect the flight characteristics and performance of the tricopter. To ensure the tricopter is well balanced and able to vector equally 360 degrees, the geometry of the motors must equate to an equilateral triangle with the center of gravity in the middle of the triangle. The two main frame designs, shown in Figure 11, are a Y and T configurations. The Y configuration was chosen do to its symmetry and less complex design for construction, testing, and modeling.

Figure 11. Tricopter frame configuration

The basics parts of the frame include the rotor arms, which hold motors, and a center plate, which holds the main electronics and the supports the rotor arms. The rotor arms need to be able to be strong enough to withstand the loads while in flight and dissipate vibrations. The center plate must also be strong and rigid inorder to provide a stabile anchor point of the rotor arms to attach into it and also be able to mount the electronics. Both need to be constructed from light weight material. The length of the rotor arms will also be dependent on several design factors:

Propeller Size: For a given propeller diameter the boom needs to be of a length

so that the propeller down wash is not blocked by the center of the frame and

adversely affect the other propellers to ensure maximum lifting potential.

Vibration Transmissibility: Vibration dampening is not only function of material

properties but also of dimensions to include length. Normally as the material

length increases more vibrations become dissipated through the structure, unless

a resonance condition is achieved.

Lifting capability and drag reduction: For the design of the tricopter in this project

an airfoil will be adapted over the rotor arms to help generate lift and reduce drag

in forward flight. The booms need to be of sufficient length so that the length of

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the airfoil is can provide an appreciable lifting and drag reduction force in forward

flight as explain in section 5.3

4.1 Material Selection

The frame of the tricopter is composed of a combination of materials chosen for their strength, weight, and flexibility. In any design of a machine capable of flight, weight must be greatly considered. The materials considered for this project were aluminum, wood, and carbon fiber. The first aircrafts were constructed of wood, which then evolved to aluminum and aluminum alloys, and today aircrafts are beginning to replace aluminum components with carbon fiber. Since tricopters are exposed to cyclic stresses and vibrations, a cyclic fatigue analysis and a vibration test analysis was completed on the candidate material to determine which will performance the best.

4.1.2 Strength and Fatigue Analysis

Fatigue occurs when a material is subjected to repeat loading and unloading. If the loads are above a certain threshold, microscopic cracks will begin to form at the surface. Eventually a crack will reach a critical size, and the structure will suddenly fracture. The cyclic fatigue can be analyzed from material properties and a given flaw size in the structure. The cyclic loads that would be experience on the tricopter are the vibrations due to the motor and the loads that occur in flight from the force and torque generated by the propellers. Due to the magnitude of each cyclic stress, failure due to fracture would most likely occur from flight loads on the frame.

In order to attach the rotor arms to the center plate and to the motors, small round holes were drilled to bolt the components in place. The anchor holes drilled into the material constituted the given flaw size for the fatigue calculations. An adhesive would have been a better option to eliminate the flaw size, but if a rotor arm would have to have been replaced, due to damage from a test flight, then further damage could be done to the frame in the attempts to complete the repair.

The fatigue analysis was completed based of the ultimate tensile strength of each material. The ultimate tensile strength corresponds to the maximum load placed on the material to cause failure prior to any cyclic loading. The analysis is based on a crack growth or damage tolerance analysis, which is concerned with the number of cycles until fracture. This analysis creates a plot that shows the decrease of the ultimate tensile strength of the material with a given flaw size over a number of cycles. Carbon Fiber had the largest initial ultimate tensile strength of the candidate materials and wood the least. Based on the analysis plotted in Figure 12, Carbon Fiber had the best fatigue life.

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Figure 12. Material fatigue analysis

Although carbon fiber had the best fatigue life, Figure 12 also shows that it had the greatest crack growth propagation. This is concerning since the analysis for the crack growth in the fatigue cycle does not take into account the 3 dimensional structural geometry of the rotor arms, which is not a material property, along with the various forces or torques which may apply. To accurately model this, a full computational model must be constructed, but it would be beyond of the scope of this project since the tensile strength and crack growth is only needed to make the appropriate selection. The anchor points, flaw areas, obtain the highest loading in normal operations and especially in a hard landings or a crash which could further accelerate crack growth and reduce the tensile strength of the material.

It was also observed from the plots and is a known material advantage that wood had the most resistant crack growth initially but was surpassed by the carbon fiber in later cycles. Inorder to achieve the best attributes of the strongest material and the smallest crack growth propagation, a composite of wood and carbon was selected. The carbon fiber beams are 10.5 x 10.5 mm square with an 8mm circular hollowed out cross section. An 8mm wooden dowel was glued inside of the carbon fiber beam. This was done with the intent of the wood reinforcing the crack growth of the carbon fiber from the anchor points. A cross section of this composite is illustrated on Figure 13, and used as the rotor arm of the tricopter.

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Figure 13. Composite beam cross section

4.1.3 Vibration Test and Analysis

One of the key design principles of a tricopter frame is to prevent the flight controller board from being exposed to motor and propeller vibrations that are traveling from the motors, through the rotor arms, and to the flight controller.

The whole tricopter can be model as a spring mass dampener systems, as described in section 6, in which a single rotor arm can be analyzed to determine the appropriate candidate material for construction of the frame based on material vibration characteristics. The main source of all vibrations is assumed to come from the motors operating at various throttle ranges. Assuming that the propellers are dynamically balanced, the propellers will only amplify the forces due vibrational accelerations created by the motors. A test frame was constructed to dynamically isolate a motor. A vibration measuring device measured installed at the base of the motor measured vibrations through the whole throttle range. The vibration measuring device was made for an analog 3 channel data logger and a 3 axis accelerometer, both powered by a mini LiPo. Information was uploaded from the data logger to a computer for data analysis. The data provided was in “G’s,” which corresponds to one acceleration of gravity or 32.2 ft/s^2. By multiplying the mass of the motor by the accelerations, force is obtained. Since the mass of the logger was equal to the mass of the motors propeller adapter, the test was conducted without the propeller adapter without a need for correction of the mass of the measuring device in the analysis. To ensure the motor was properly dynamically isolate in the test frame, a second vibration measuring device was used to observe that no vibrations from the motor was dissipated through the frame. The second vibration measuring device was an iphone 4 which contains a three axis gyro and accelerometer and with a vibration application that can measure, display, and log vibrations the phone experiences. A second data logger was used in the ESC to record voltage, RPM’s, and throttle as the motor was run without a propeller through a range of throttle positions. Figure 14 shows the test frame used and the data logger.

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Figure 14. Vibration motor test frame and data logger

Four motors were tested as described in the above method. The resultant accelerations from the X, Y, and Z axis of were combined and plotted against the % throttle which produced the graph in Figure 15.

Figure 15. Dynamically isolated motor operational profile

The graph in Figure 15 shows the results plotted with a moving average trend line. The graph shows that the highest vibration spikes occurred at the 57% and 80-100% throttle positions. This information is useful to determine the proper throttle ranges to operating in a hover condition which may require minimized vibrations and to ensure that the RPM’s related to the throttle position do not coincide with the natural frequency of the candidate materials to be used for the rotor arms.

Since the test was conducted with no propeller, ie a no load condition, the RPMs were used to correctly identify the occurrence of the vibration spikes. Different propellers on the motor will increase the loading while decreasing the RPMs. For example the no load max RPMs were approximately 12000 RPMs, while loaded the max was 8350 RPMs both corresponding to 100% throttle. Since the propellers are dynamically balanced, it is assumed little to no vibrations were caused by the propellers, the vibration spikes observed in the no load condition would occur at the same RPMs when loaded.

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The relationship between motor voltage and RPMs is linear. With the operator transmitter having the ability to use programmable curves, the throttle programming normally used in RC helicopter applications was used as shown in Figure 16.

Figure 16. Programmed Throttle Curves

From Figures 15 and 16 it is determined that motor vibration spikes occur at 11200 RPMs and 12000 RPMs and above. These values of RPMs are outside the operating range or flight envelope of the loaded motor profile. Any vibration spikes observed on the frame will be a factor of the natural frequency and the length of the rotor arms for each of the candidate materials. The natural frequency is a function of the rotor arm length and material properties of each of the candidate materials. To model the rotor arm analytically a vibration beam analysis was completed. The dimensions of the rotor arm were best modeled as a cantilever beam fixed on one end and the other free, as seen in Figure 17. The mass of the motor was neglected since it provides an upward force from the propellers. Torque was also neglected since it is considered to be small when compared to the thrust.

Figure 17. Cantilever beam

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The analysis of a cantilever beam was subjected to free vibration, and considered as continuous system in which the beam mass as distributed along with the stiffness of the shaft. The differential equation of motion that describe the transverse vibration of a beam is given as:

Using separations of variables the term becomes:

For the setup of the beam the following boundary conditions apply:

A full derivation of this the natural frequency calculation is found in Appendix C. From the derivation the natural frequency equation is described in equations 9 and 10:

There a multiple number of modes which this derivation yields. The first mode corresponds to the natural mode which can occur in the operation range of the motors. The other modes occur at higher frequencies, well above the motors operating range and are therefore neglected.

By using the material properties of each of the candidate material, an approximation for the moment of inertia based on the beam dimensions, and equations 8 and 9, the graph in Figure 18 was produced to provide an indication of what the best rotor arm length would be for the given material.

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Figure 18. Beam analysis

Figure 18 shows the area of constraint of the flight envelope, which is the operating RPM range of the loaded motor turning a 10 X 8 propeller. In this box it is undesirable to have the natural frequency of the material selected for the rotor arm to occur, which will cause excessive vibrations in flight. The rotor arm length was limited to 1 meter based on the availability of the material. The graph indicates that the favorable length and material for the rotor arm was 0.45 meters and carbon fiber. Aluminum was also acceptable for a length of .38 meters and wood .26 meters. At the lower end of the flight envelope the values were ignored since the corresponding lengths required would make the rotor arms easier to break.

The results of the analysis was tested by taking vibration measurements of a 0.45 meter length beam on its fixed end while running the motor, loaded with a propeller, at various throttle positions on the free end. The data from this experiment was used on conjunction with the data in Figure 15 to develop a vibration transmissibility profile for each of the candidate materials. A ratio was taken of the accelerations observed on the clamp end over the accelerations from the motor. A ratio less than one indicated that the material was absorbing the vibrations from the motor, where as a ratio greater than one indicated that the vibrations from the motor were being amplified by the material. The results of this test are on the graph in Figure 19. With the propeller being dynamically balance and beam properly clamped down, no extra vibrations appeared to come from the propeller except when running near 100% throttle and when excess vibrations were detected in the beam, in which the propeller seemed to amplify the effect. This was due to propeller blade flections from maximum loading on the blades while being hold stationary. A moving average curve was placed on the carbon fiber profile to better highlight the results.

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Figure 19. Loaded rotor arm transmissibility testing

As predicted from the beam analysis of the given length of 0.45 meters, the carbon fiber rotor arm was the best material. At a throttle range greater then 85% the carbon fiber began vibrating more to possible flections in the propeller blade as more thrust was produced. The vibrations can also correspond to the upper limits set in the beam analysis. The wood and aluminum rotor arms appeared to excessive vibrations through the throttle range greater than 60%.

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5.0 Flight Performance

5.1 Hover

The advantage of increasing the number of blades on a propeller of the tricopter will give it the ability to carry more loads. Too many blades will cause the tricopter to be inefficient in a hover and limit its forward flight speed. Since the major draw of the tricopter or any multicopter over tradition fixed wing mUAVs is its ability to hover, it is critical that it does this efficiently.

Inorder to verify the extent of these losses lab testing was completed in a wind tunnel with three different propellers, varying the number of blades and maintaining a constant the diameter and pitch. At varying speeds data was collected to determine the each propellers power and thrust coefficients, solidity, correction factor, and figure of merit.

These calculations a similar those done in calculating helicopter aerodynamics performances in hover conditions using moment theory. This approach is valid since the propellers on the tricopter are spaced far enough on the rotor arm not adversely affect each other. The momentum theory stems from Newton’s second law of motion, F=ma, and is developed on the basis that the axial velocity u of the fluid through the rotor disk is generally higher than the speed V with which the rotor is advancing through the air. The increase in velocity of the air from its initial value V to its value at the rotor disk, which arises from production of thrust, is called the induced or downwash velocity, and is denoted by v. The thrust developed by the rotor is then equal to the mass of the air passing through the disk in unit time, multiplied by the total increase in velocity caused by the action of the rotor.

In hovering or vertical climb, the action of the air influencing by a rotor is a shown in Figure 20

Figure 20. Airflow through a rotor in a hover

Because of the increase in velocity of the air mass by the rotor, there is a gradual contraction of the slipstream as it approaches the rotor, the maximum contraction or speedup of the air being accomplished within on rotor-diameter behind the disk.

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In using a simplified momentum theory the following assumptions were made:

1. The rotor is composed of an infinite number of blades and many therefore be considered as an actuator disk, uniformly accelerating the air through the disk with no loss of thrust at the blade tips.

2. The power required to produce the thrust is represented only by axial kinetic

energy imparted to the air composing the slipstream. A frictionless fluid is assumed so that there are no blade friction or profile-drag losses. Rotational energy imparted to the slipstream is ignored.

3. The disk is infinitely thin so that no discontinuities in velocity occur in the two

sides of the disk.

From further development of the moment theory equations 11, 12, and 13 are derived using nondimensional coefficients. These non dimensional coefficients of thrust, torque, and power are used to define rotor characteristics in a form that is independent of rotor size.

Another relationship used in calculating the torque and power coefficients is the relationship shown in equation 14. By substituting equation 14 in the power coefficient, equation 13, the torque and power coefficient values are determined to be numerically equal as shown in equation 15:

Reference area for each of these rotor coefficients is based on the rotor disc area, A. It is often desirable to use coefficients based on blade area, rather than on disc area. In order to do this, the rotor solidity ratio, σ, is defined as shown in equation 16:

In further investigation of the moment theory, an approximation can be made in determining the power coefficient. This is known as the modified momentum theory. The differential power coefficient can be reduced as seen in equation 17:

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Where dCpi is the differential power coefficient associated with induced flow and dCpo is that associated with blade section profile drag. The first term can be rewritten as:

Through substitution in the equation 17 the equation 19 is:

In a hover:

Assuming uniform inflow and a constant profile drag coefficient Cdo (taken from the published data of the propeller airfoil assume about 0.01), the following approximation, equation 20, known as the modified moment theory:

The total induced power in a hover or climbing flight is generally two or three times as large as the profile power. The deficiency of equation 20 is the assumption of uniform inflow. For a linear variation of inflow the induced power is increased by approximately 13%. This and other small correction factors such as tip loss are commonly allowed for by applying an empirical factor k to the first term in equation 10.

The term k is a direct correlation of the losses on the rotor which is generally suggested to be 1.15 in most rotor aircraft design books. An increased value of k yields to higher losses and less efficiency. The order of magnitude of the rotor power losses not considered by the simple momentum theory, expressed as a percentage of the total pwer required, are as follows:

Even with all these losses, rotors have an average efficiency of 83%. This efficiency is related specifically for operating military and civil helicopters. Since a tricopter is equipped with a standard radio controlled aircraft propeller, the efficiencies are significantly less. From experimental data published in the UIUC Propeller Databases,

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the best efficiency for the propeller chosen for the tricopter is approximately 60%. This is common for most radio controlled aircraft propellers.

The test for this experiment was completed at the United States Naval Academy Aerospace Engineering Laboratories using their Eiffle wind tunnel. The lab provided the motor and propellers, to avoid damage to the wind tunnel and balance sensors. The motor was installed on a sting which was attached to a balance hooked up to a data acquisition system that recorded drag and roll measurements at a rate of 100 iterations per minute and displayed the outputs on a computer screen. A voltage gage was used to apply voltage to the motor in one volt increments up to 22 volts. Since the relationship of motor RPMs and voltage is linear that voltage can directly correlate to the motor RPMs. Also a tachometer was used as a backup to prove this. A 2, 3, and 4-bladed propellers with the same diameter and pitch were tested. Each test consisted of varying voltage in one volt increments and at each increment, once equilibrium was reached, record voltage, RPM, drag, and roll. A picture of the test setup is seen in Figure 21 and the test data and calculations in Figure 22

Figure 21. Wind Tunnel Propeller Efficiency Test Setup

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Figure 22. Propeller efficiency test data

The data in Figure 22 concludes that the 2-bladed propeller has the lowest value of k of the three propellers making it the most efficient. The increase efficiency means less losses and more time the tricopter can remain on station increasing its endurance time. The 4-bladed propellers k value is almost double that on the 2-bladed propeller, but produces almost double the thrust at the same RPMs. If the propeller diameter size is restricted by the frame and a large payload was required, then the 4-bladed propeller would be ideal. In this case it would come at the cost of sacrificing performance for lift in which a 4-bladed propeller of the same diameter would place higher electrical loading on the train power of the motor, ESC, and battery. Inorder to compensate for this a motor, ESC, and battery of increased electrical specifications must be used to avoid damage to the power train. These upgraded components would also add extra weight and what may appear as a 100% increase in payload weight will only be around 30% after the power train has be upgraded to facilitate the new loads.

5.2 Forward Flight 5.2.1 Maximum Airspeed

There are a number of factors that govern the maximum speed of any aircraft. The obvious maybe the limitations of the power train or drag on a fixed wing aircraft. For a rotary aircraft in forward flight, the blades see a variety of airspeeds depending on its azimuth.

A rotor blade that is moving in the same direction as the aircraft is called the advancing blade and the blade moving in the opposite direction is called the retreating blade. The resultant velocity on the advancing blade is higher than the retreating blade. Forward flight speed is limited by the fact that eventually the advancing blade encounters compressibility effects, which cause increased drag and a nose down pitching moment resulting in increased vibrations. Forward

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speed is also limited by the retreating blade which encounters a decreasing resultant velocity with increasing forward speed until the blade stalls. Portions of the retreating blade encounters a region of reversed flow, where the resultant velocity is impinging on the trailing edge of the blade. Modern helicopter can have as much as 45% of the retreating blade in reversed flow before a retreating blade tip stall occurs. In most cases fixed pitch rotors will be limited by the retreating blade.

Balancing lift across the rotor disc is important to a rotary aircraft's stability. The amount of lift generated by an airfoil is proportional to the square of its airspeed. In a zero airspeed hover the rotor blades, regardless of their position in rotation, have equal airspeeds and therefore equal lift. In forward flight the advancing blade has a higher airspeed than the retreating blade, creating unequal lift across the rotor disc. Unless countered, dissymmetry causes the rotary aircraft to roll to the retreating side and pitch up, due to gyroscopic precession. This is shown in Figure 23.

Figure 23. Helicopter in Retracting Blade Tip Stall

Retreating blade stall is more likely to occur when the following conditions exist either alone or in combination:

High gross weight High airspeed

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Low rotor RPM High density altitude Steep or abrupt turns Turbulent ambient air

Forward flight in a tricopter is accomplished by the rear rotor generating a resultant force greater than the two forward rotors as explain in section 2 and shown in Figure 3. To generate that greater resultant force the rear rotor must spin at higher RPMs. The conditions for retreating blade tip stall are most likely to occur in the rear rotor. Stalling the rear rotor will result in a reduction of the greater resultant force, dropping the aft end of the tricopter. With the forward two rotors maintaining their resultant force, the tricopter will violently pitch nose up and fly in the reverse direction until the rear rotor recovers. If the forces are great enough the tricopter could execute a back flip.

To demonstrate this, a scale tricopter (50% scale to the project size) was made and tested. The rotor diameter, frame dimensions, and weight were scaled while the motors produced 150% scale power compared to the project tricopter. From this prototype the top speed could be measured as indicated by the onset of retreating blade tip stall. A small GPS data record was installed to measure the top speed and a data recorder in the ESC measured the rear rotor RPMs and throttle position. This data was then used to determine how much the retreating blade reversed flow or velocity unbalance occurred before a retreating blade tip stall occurred.

An analytical model in MATLAB provided a graphic representation the Resultant Blade Velocity. The MATLAB code is shown in Appendix B. From the experimental results, the scaled tricopter achieved a top speed of 28 mph, at 100% throttle for 15300 RPMs. The graph in Figure 24 shows the resultant blade velocity of the tricopter in a hover condition and forward flight at the velocity that retreating blade tip stall occurred. The analytical model neglected drag. The smaller scale size model was chosen because it was easier to overcome the effects of drag to reach its top speed. The full scale tricopter will not be as overpowered, and drag will be a factor for reaching its top speed.

Figure 24. Scale tricopter rotor velocity profile

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The data from the code and the graphs in Figure 24 show that a velocity imbalance occurred and a small reverse flow region developed large enough to create a tip stall condition corresponding to the maximum velocity of the scaled tricopter. Making scaling assumptions based off of the data from the test flight of the scaled tricopter, the maximum forward flight velocity was calculated for the project tricopter. The maximum velocity of the project tricopter was calculated to be 54 mph, assuming that the velocity imbalance and the reverse flow region in the project tricopter will occur proportionally to the scale tricopter. The graph in Figure 25 shows the resultant blade velocity of the tricopter in a hover condition and forward flight at the velocity which the retreating blade tip stall is expected to occur in the project tricopter.

Figure 25. Projected full scale tricopter rotor velocity profile

5.2.2 Drag

Upon the completion of the project tricopter, a test flight was conducted and determined that maximum forward flight velocity was 46 mph. During the flight there was no occurrence of a retreating blade tip stall. With the retreating blade tip stall calculated to occur around 54 mph, the tricopter can be designed to achieve a top speed of 50 mph without modifications to the power train. By minimizing the drag of the tricopters frame, extra speed can be obtained. The rotor arms have a square cross section and in forward flight the square translates 45 degrees into a diamond shape. A non-aerodynamic body in flight can cause significant drag. Figure 26 shown drags coefficients of various shapes. These shaped would have been tested on Xfoil, but the program would converge at varying angles of attack to find a solution. The originally intension of adapting airfoils to over the rotor arms was to generate lift and reduce drag. Since the airfoil would have been fixed on the rotor arm perpendicular to the surface, the pitch of forward flight would have generated lift and reduce power consumption. From flight testing with the project frame it was observed that the airfoil in forward flight was at too high of an angle of attack to generate appreciable lift and it also produced significant drag.

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rotor radius (ft)

roto

r ra

diu

s (

ft)

Tricopter Resultant Blade Velocity in Forward Flight Velocity =0kts =868.7333rad/sec

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0

50

100

10

0

200

200

20

0

300

300

300

30

0

400400

400

400

40

0

500500

50

0

500500

50

0

60

0

600600

60

0

600

600

600

70

0

700

700

700

70

0700

800

rotor radius (ft)

roto

r ra

diu

s (

ft)

Tricopter Resultant Blade Velocity in Forward Flight Velocity =46.9251kts =868.7333rad/sec

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

37

To benefit from an airfoil shaped rotor arm, research was done on a symmetric airfoil free vary its angle of attack. It was assumed that the free moving symmetric airfoil would act as a weather vane and point into the direction of flow. Although a symmetric airfoil at a zero angle of attack would not generate lift, it would reduce drag. Xfoil was used to do analyze the best airfoil.

Figure 26. Drag Coefficients for non-aerodynamic shapes

XFOIL is an interactive program for the design and analysis of subsonic isolated airfoils. Given the coordinates specifying the shape of a 2D airfoil, Reynolds and Mach numbers, XFOIL can calculate the pressure distribution on the airfoil and hence lift and drag characteristics. The program also allows inverse design, allowing varying an airfoil shape to achieve the desired parameters. A symmetrical airfoil was chosen from the UIUC airfoil database and analyzed in XFOIL. In XFOIL the percent camber thickness was manipulated and the airfoil was tested with a Reynolds number corresponding 50mph and the dimensions required to encapsulate the rotor arm. The airfoil which achieved the minimum drag observed under the test conditions was with a symmetric airfoil manipulated to have a 14% camber thickness. At a zero degree angle of attack the airfoil had a drag coefficient of 0.0163, producing 0.6 N of drag. The existing rotor arm pitched at 45 degrees under the same conditions had a drag coefficient of 0.8, producing 7.82 N of drag. The selected airfoil is plotted in Figure 27.

38

Figure 27. Rotor Arm Airfoil

6.0 Flight Control and System Modeling

6.1 Flight Controller and Autopilot

The flight controller and autopilot system selected for the tricopter project is the APM

(ArduPiloMega1) 1.0 Arducopter sold by DIY Drones. The board offers a unique platform for hardware integration of an autopilot system with a flight controller, updating with custom software, and expansion capabilities with various sensors and components. The board functions of a software code called Arduino. Arduino is an open-source code, similar to C++, used in most academic and hobby electronics in multidisciplinary projects. The code for the APM 1.0 Arducopter was modified for this project by updating the flight controller coding with the control feedback system. The board includes a 3 axis gyro and accelerometer, a barometer, and magnetometer. A sonar, wireless command uplink, GPS, and optical flow sensor were added to expand the board’s capability. Figure 28 shows the block diagram of the tricopter’s electrical components.

-0.008 -0.006 -0.004 -0.002

0 0.002 0.004 0.006 0.008

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

y(M

ETER

S)

Chord (METERS) Chord= 0.07851 meters, Cd@0AOA=0.0163, D'=0.4922N/m

Airfoil Scaled Geometry Optimized for 50 mph

11mm

39

Figure 28. Tricopter Block Diagram

The APM 1’s ArduPilot receives commands from the RC controller and ground station and uses the information from the IMU flight controller board to stabilize the tricopter while performing the commands. It's also responsible for the autonomous flight modes. Its output signals are control signals for the rotors and flight information to the ground station.

Uploading the modified code and the mission waypoints for autonomous flight used the APM graphical user interface (GUI) program developed for the board. From a computer the GUI over lays Google maps and allows the user to select points on the maps which then translate to GPS coordinates. Other information such as speed and altitude are also required. Figure 29 depicts an on screen shot of the APM GUI program while mapping waypoints.

Figure 29. GPS mapping GUI

40

6.2 Code Development and Control System The portion of the existing open source code that was modified for this project was the functions of the flight controller. Originally the code processes the information from the gyros and accelerometers using 3D vector generated angles. Although this worked sufficiently enough in flight, it lacked for stabilization in auto level control conditions using the inputs from the accelerometers. This deficiency was corrected by using other sensors. For example the GPS, in a position hold command, would keep the tricopter level as a function of maintaining its position. Without the GPS, auto level would initially hold but deteriorate rapidly due to the exponential increase of an error in the closed feedback loop. This would be problematic if an operator wished to take manual control of the tricopter. The auto leveling feature would provide an increased level of stability in manual operation while maneuvering the tricopter to different locations. Although the tricopter can be controlled manually without this feature, it limits excessive stick input from the operator. To correct this deficiency the code was modified to process the information from the gyros and accelerometers using the Euler angles described in section 2. Using the Euler angles and properly coding them for the gyro and accelerometers sensor inputs, eliminated the error and the tricopter was able to maintain it auto level feature without the aid of other sensors. Inorder to efficiently use the modified code, a control system with the addition of an inner rate feedback loop was used as shown in Figure 30. The inner-loop represents the angular rate feedback, and the outer-loop represents attitude feedback allowing integration of the gyro and accelerometers signals

Figure 30. Tricopter Control System

K1 and K2 are the gain values of Euler angle attitudes and angular rates. These gain values provide an input into the controller to offset the error. The magnitude of the gains is critical for the control and stability of the tricopter. Too small of a gain would cause the controller longer time to achieve its desired response, as too large of a gain may cause violent oscillations as the controller zeros into the desired response. No gain what so ever would cause the controller not to achieve its desired response as seen in Figure 31. The proper amount of gain will achieve the response with a slight overshoot to settle to the desired position in the required amount of time as seen in Figure 31. The Matlab codes for these graphs are in Appendix B

41

Figure 31. The first graph is of a controller with no gain given a step response input of 0.95. The second graph is of a controller properly tuned given a step response input of 0.95.

The most efficient controller used to achieve the appropriate stability through gains is a PID controller. The PID controller calculation involves three separate constant parameters: the proportional, the integral and derivative values, denoted P, I, and D. The controller calculates an "error" value as the difference between a measured process variable and a desired setpoint. The controller attempts to minimize the error by adjusting the process control inputs to achieve the desired outputs.

The proportional component (Kp) of the controller creates an output which is proportional to the error signal. The main advantage of this is its simplicity, but has the disadvantage of a steady state error. The steady state error is eliminated by using an integral controller. The advantage of this is that integral controller (Ki) is proportional to the steady state error, but since the integral term responds to accumulated errors from the past, it can cause the present value to overshoot the setpoint value. Inorder to minimize any error before it becomes too large, a derivative controller (Kd) is used. The disadvantage this controller is that it will not produce a response with a constant error and it is susceptibility to noise.

6.3 PID Tuning

Since every control system is unique in which the speed of the system response is affected by the mass and dimensions of the tricopter, lag time of the components, and operator preference. There is no exact value that can be used without properly tuning the board once it is installed into the tricopter to determine the proper PID gains. Tuning a tricopters gains is equivalent to deriving good flight handling characteristics in aircraft design. Methods of tuning PID controllers include manually tuning, software programs, and proven methods.

Manually tuning a PID control is the low cost approach but is subjective. It is done while the tricopter is operational. To fine tune the PID controller once stability is reached may vary on the personal prefers of the operator. Manual tuning a PID controller involves

42

setting the Ki and Kd values to zero. Increase the Kp value until the output of the loop oscillates quickly, then slightly back down. This corresponds to half of that value for a "quarter amplitude decay" type response. Next, increase Ki until any offset is corrected in sufficient time for the process. However, too much Ki will cause instability which will notice a slow oscillation. Finally, increase Kd, if required, until the loop is acceptably quick to reach its reference after a load disturbance. However, too much Kd will cause excessive response and overshoot. A fast PID correctly tuned will usually overshoots slightly to reach the setpoint more quickly; however, some systems cannot accept overshoot, in which case an over-damped closed-loop system is required, which will require a Kp setting significantly less than half that of the Kp setting causing oscillation. The effect each gain term has on the controller is shown in Figure 32. The smallest over shoot and the fastest response involves utilization of all three gain terms

Figure 32. PID contributive response

Standard and proven methods are also another way to tune a PID Controller. The Zielger-Nichols method is one of the most widely used with PID controllers. This method is based on a simple characterization of the frequency response of the process dynamics. In summary the Zielger-Nichols method establishes a value for an ultimate gain (Ku), which is twice the value of Kp as obtained through manual tuning. Ki is then a proportional term of Kp over the oscillation period (Tu), and Kd is a constant times the product of Kp and Tu. The Ziegler-Nichols method was based on extensive simulations. The design criterion was a quarter amplitude decay ratio, which means that the amplitude of an oscillation should be reduced by a factor of four over a whole period. This corresponds to closed loop poles with a relative damping of about ξ= 0.2, which is too small. For tricopter applications, the low damping would make it unstable in flight. For applications like marine ship autopilots this was sufficient. By changing the quarter amplitude decay ratio to gain a higher relative damping other method have sprung from Ziegler-Nichols.

A tricopter can be modeled as a mass-spring-dampener system described by the equation of motion in equation 22. M is the mass of the tricopter, b relates to

43

dampening, k is the spring constant, and u is the input. The mass of the tricopter can be measured and the spring constant can be approximated as a function of the material properties and dimensions of the frame.

From equation 22 and Figure 30, a transfer function can model the tricopter and in a closed loop model the PID gains can also be added as shown in Figure 33.

Figure 33. Tricopter dynamic system block diagram

The open loop of the block diagram reduces to equation 23. Equation 24 is the equation for the closed loop.

If the values for b and k were known, then a program like Simulink or Matlab can be used and selected values of Kp, Ki, and Kd to generate the proper response through a plot. Since they are unknowns they must be solved for first. The tail rotor was removed from the project tricopter and it was mounted on a rod with ball bears which allow the frame free to roll along the x axis. The ends of the rod were clamped in place preventing the tricopter from lifting. The tricopter was secure in place with the exception that it was allowed to roll freely and nearly frictionless about the x axis. With a known value of Kp, Ki, and Kd a step response was input to the tricopter. A high speed camera captured the control input and the tricopters response. Since the symmetric Y shape design was selected for the frame, the Kp, Ki, and Kd values for pitch and roll are assumed to be the same. The high speed camera captured the tricopters motion response at 300 frames per second. Each frame was analyzed to obtain the time stamp and roll angle the tricopter achieves while responding to the input until equilibrium was reached. The motion was plotted; the values of k and b were iteratively solved by fitting the best curve from equation 24 to the plot generated from the high speed camera. With the known values of b and k the tricopter dynamic system block diagram from Figure 33, can be used to plot the desired response by selecting Kp, Ki, and Kd.

(22)

(23)

(24)

44

7.0 Conclusion

Overall the design of the tricopter was a success. The tricopter flew very smoothly and was extremely stabile. It had sufficient power to perform its required tasks having a top speed of 51mph after the modification of the airfoils on the rotor arms. In the autonomous flight the tricopter was programmed to fly 5 ft off the ground using sonar, at 5 mph down the straight portion of a running track. It successfully completed 3 laps until midway through the fourth lap it stopped and then landed. The landing was due to a loss of transmitter signal due to the transmitter battery running low. This was an inadvertent test of its safety protocols. The tricopter was equipment with its full payload and transmitted data and a video signal back to the group station. All structure components such as the rotor arms, center plate, and motor fairings were bolted in place. At every intersection site that each component met a rubber washer was used to help further dampening the transmission of the vibration throughout the frame. In flight vibrations detected on the flight controller were no greater than 1.02 g’s.

The goal of increasing the maximum speed was achieved while the time in flight was only marginally increased. The airfoil free to rotate as a weather vane worked at low speeds but began to flutter at high speeds causing unexpected longitudinal oscillations of momentary positive and negative deflections due to possible turbulent flow over the airfoil. By incorporating a design which also levitates lift for the motors, the endurance time will increase. Future suggested designs might include a servo which will change the angle of attack of the airfoil based off of the tricopters pitch indications. This would require a code modification taking an offset angle from the pitch gyro to keep the angle of attack at a constant optimum angle, regardless of pitch. This would also correct the flutter observed in the test flight of the existing design.

The tuning of the PID controller is subjective and a trial and error effort. More research would be needed to identify ideal flight characteristics based on the tricopters ability and operators preference.

With the advancements in LiPo technology high power density cells in the near future would an enable longer endurance times in flight, expanding the possibilities of its capabilities and applications. The potential of these expanded applications and capabilities has caused controversy in the ethical used of UAVs and possible government regulation. Designs of tricopters, or any multicopter, based on sound engineering principles and proper use will ensure the safe evolution and application of this new and expanding field.

45

Appendix A: Measuring Devices and Equipment Used for Testing

50% scale tricopter used to determine retreating tip blade stall

GPS Logger used in flight to determine top speed

Tachometer used to measure blade RPMs

Data Logger ESC recorded: Voltage, Current, Temperature, Motor RPM, and Throttle travel

Vibration Logger

46

Appendix B: Matlab code

(Forward Flight Velocity Rotor Profile)

>> clear

Vmph=28

rpm=15000

omega=rpm*2*3.14/60;

Vkt=Vmph/1.15077;

Radius=4/12;

V=Vkt/0.5925;

psi1=0:0.01:2*pi;

rx=Radius*cos(psi1);

ry=Radius*sin(psi1);

m=-Radius*.45;

y=0;

psi=0;

n=-25:1:25;

for i=1:1:100

y=y+Radius/100;

for j=1:1:100

psi=psi+2*pi/100;

U(i,j)=omega*y+V*sin(psi);

crx(i,j)=y*cos(psi);

cry(i,j)=y*sin(psi);

end

end

v=[-100 -50 0 50 100 200 300 400 500 600 700 800 900 1000 1100];

[C,h]=contour(crx,cry,U,v);

colormap cool

clabel(C,h)

hold

plot(rx,ry,'r')

plot(n,m)

axis square

xlabel('rotor radius (ft)')

ylabel('rotor radius (ft)')

title(['Tricopter Resultant Blade Velocity in Forward Flight',' Velocity ='

,num2str(Vkt),'kts',' \Omega =' ,num2str(omega), 'rad/sec'])

(PID Tuning Transfer Function)

clear

47

s=tf('s'); M=3; b=13; k=11;

Kd=0;

Kp=0; Ki=0; sys=(Kd*s^2+Kp*s+Ki)/(M*s^3+s^2*(b+Kd)+s*(k+Kp)+Ki); t=[0:0.01:2]; step(sys,t);

Kd=15; Kp=5; Ki=2; sys=(Kd*s^2+Kp*s+Ki)/(M*s^3+s^2*(b+Kd)+s*(k+Kp)+Ki); t=[0:0.01:2]; step(sys,t);

48

Appendix C: Beam Analysis Derivation

49

50

51

52

53

54

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