Development of an Unmanned Aerial Vehicle - A Tricopter

A Project Report On

Development of an Unmanned Aerial Vehicle - A Tricopter

by

RAMANN BHARADWAJ M (AM.EN.U4EEE09041)

Submitted to

AMRITA SCHOOL OF ENGINEERING

AMRITAPURI CAMPUS, CLAPPANA P.O., KOLLAM-690525, KERALA.

In partial fulfilment of the requirements for the award of the degree of B.Tech

Project work carried out at

Council of Scientific and Industrial Research

National Aerospace Laboratories,

Bangalore - 560017.

Under the guidance of

Internal Guides External Guide

Dr Balakrishnan Shankar, Mr S Santhosh Kumar,

Professor and HOD, Scientist C,

Mechanical Department. Propulsion Division,

Amrita School of Engineering, Kerala. NAL, Bangalore.

Mr. Joshua D Freeman,

Assistant Professor,

Electrical and Electronics Department,

Amrita School of Engineering, Kerala.

January-June 2013

AMRITA SCHOOL OF ENGINEERING

AMRITAPURI CAMPUS, CLAPPANA P.O., KOLLAM-690525, KERALA.

CERTIFICATE

This is to certify the project work entitled “Development of an Unmanned

Aerial Vehicle – a Tricopter” carried out by

Name REG No

RAMANN BHARADWAJ M AM.EN.U4EEE09041

Is a bonafide work carried out at Amrita School of Engineering, Kerala, in partial

fulfilment for the award of the degree of Bachelor of Technology in Electrical &

Electronics Engineering at Amrita University during the academic year 2012-

2013.The project report has been approved as it satisfies the academic

requirements in respect of project work prescribed for Bachelor of Technology

degree.

Signature of Guide Signature of Guide Signature of HOD

Dr.Balakrishnan Shankar, Mr. Joshua D Freeman Dr. Chandramohanan Nair,

Mechanical Department. Dept. of EEE Dept. of EEE,

Amrita School of Engg, Amrita School of Engg, Amrita School of Engg,

Kollam, Kerala. Kollam, Kerala. Kollam, Kerala.

External Viva

Name of the Examiners Signature & Date 1. 2.

DECLARATION

I, hereby declare that the entire work embodied in this dissertation has

been carried out by us and no part of it has been submitted for any

degree or diploma of any institution previously.

Place: Signature of the student

Date: (RAMANN BHARADWAJ M)

NATIONAL AEROSPACE LABORATORIES

National Aerospace Laboratories, Bangalore is a constituent institution under the Council

of Scientific and Industrial Research. NAL is a high technology oriented institution

concentrating on advanced topics in aerospace and related disciplines. Originally started as

National Aeronautical Laboratory, it was renamed National Aerospace Laboratories to reflect its

major involvement in the Indian space programme, its multidisciplinary activities and global

positioning. It is India's only civilian aerospace laboratory with a high level of competence and

the expertise of its scientists is globally acknowledged.

Additionally, NAL has sophisticated test facilities, which are the best in the country.

Composite Structure Facilities, 1.2m Trisonic Tunnel Complex, Full Scale Fatigue Facility,

Acoustic Test Facility, Engineer-in-Loop Facility, Advanced Turbo machinery, Combustion

Laboratories, Failure Analysis Laboratory and Electromagnetic Laboratory are among these. All

these are manned by specialized teams who operate the facilities, conduct experiments, analyze

the data and provide value added inputs to programs.

NAL over the years has made significant contributions to a large number of aerospace

programs like civil and military aircraft programs, space programs, engine development

programs, defense and strategic programs of the country and has also contributed vital industrial

and societal outputs. NAL is an acknowledged center for excellence in many fields including

Composite Structures, High Speed Wind Tunnel Testing, Aircraft Fatigue and Aerospace

Acoustics, Failure Analysis and Accident Investigation.

NAL is the harbinger of civil aviation design and development activities in India. NAL

designed HANSA trainer aircraft is flying in different flying clubs of India and is all set to reach

overseas market. The light transport aircraft SARAS is undergoing flight testing and is designed

to meet the critical need in the civil aviation segment.

Currently NAL is developing Fixed Wing Micro Air Vehicles that are capable of flying

for 30 minutes to a range of 2km with a span of 300mm and can give live video feed from that

distance. NAL has successfully given demonstration of this technology to varying agencies and

services. NAL is furthering this vehicle developing technology to smaller size of 150mm.

PROPULSION DIVISION

The Propulsion Division is involved in applied research pertaining to Turbo machinery,

Combustion and Heat Transfer, Mechanical Aspects of Turbo machinery as well as in the

Design/Development of Propulsion and Energy Systems. It gives R&D support to the country's

National Aerospace Programmes being carried out at the Gas Turbine Research Establishment

(GTRE), Defense Research and Development Laboratory (DRDL), Vikram Sarabhai Space

Centre (VSSC) and the Liquid Propulsion Systems Centre (LPSC) besides taking up grant-in-aid

projects from the Aeronautical Research and Development Board. International collaborative

programs with Pratt & Whitney, USA and Canada are also being carried out.

The Division has made significant contributions to the development of the Kaveri engine

for Tejas. These include development of the afterburner flame holder and igniter, main

combustion chamber, controlled diffusion aero foils for the fan and squeeze film dampers.

Advanced supersonic combustors for the High Mach Number Flight Demonstrator vehicles of

VSSC & DRDL have been developed. A versatile High-speed Combustor Test Facility has also

been setup. A National Test facility for Rolling Element Bearings with the dual purpose of

testing indigenously developed synthetic aviation lubricants and aerospace quality bearings has

been commissioned.

The current activities include the development of active magnetic bearings, micro-gas

turbines, and Wankel engines for UAVs, novel afterburners, advanced ramjet/scramjet

combustors, advanced compressors, ultra-light helicopters, micro-air vehicles and the testing of

synthetic aviation lubricants and rolling element bearings. The collaborations R&D programmes

with Pratt & Whitney Canada & USA on gas turbine technologies, specifically related to turbo

machinery aerodynamics, combustors and Heat transfer are being actively pursued.

Future activities will include development of technologies for advanced gas turbines and

ramjet/scramjet combustors pulse jet and foil/magnetic bearings. A small gas turbine test bed and

a versatile turbine test bed will be set up and the high speed combustor test facility will also be

augmented.

MAV DIVISION

Micro Air Vehicle (MAV) has attracted consider- able attention during recent years due

to their unique operational capabilities. Understanding of MAV aerodynamic characteristics is

significant for the improvement of their performance. Obtaining reliable and accurate

experimental data is challenging due to a number of factors such as the low Reynolds number

flight regime, small size with low aspect ratio, large propellers slipstream, gust environment,

light weight and flexible airframes etc. Wind tunnel testing has an important role to play in the

development of mission capable MAVs with high endurance. Micro air vehicle Aerodynamics

Research Tunnel (MART) at CSIR-NAL is being established to meet all the special requirements

for MAV studies. Some of the features of this low speed, suction type closed test section low

turbulence wind tunnel include open jet test section with a large Betz chamber and active gust

generation mechanism. The open test section has the advantage of having no boundary layer

effects and reflections due to wall during flapping/rotary wing studies. The Betz chamber helps

in maintaining the static pressure in the open jet test section. It also helps in recording the flight

trajectory of insects, butterflies, dragonflies etc. under varying gust conditions. The active gust

generation mechanism consists of oscillatory vanes to generate sinusoidal variation in the tunnel

flow velocity at different frequencies. For studies involving measurements of unsteady low

loads, 3D deformation on flexible/flapping wings and propulsive models, highly specialized

instrumentation is being developed; these include high precision low load balances, LDV, time

resolved stereo PIV, Digital Image Correlation (DIC) and NI based wireless data acquisition

systems. The facility and the advanced instrumentation is funded by AR&DB under the National

Program on Micro Air Vehicle (NPMICAV). This wind tunnel is the first of its kind in India and

is being made available to all the projects under NPMICAV and other research organizations,

academic institutions, industries to carry out research and development in MAVs.

ACKNOWLEDGEMENTS

On the successful completion of this project, I would like to acknowledge and extend my

heartfelt gratitude to the following people who have made the completion of this project

possible:

I have immense pleasure in expressing my deep sense of gratitude and indebtedness to

Mr. Santhosh Kumar S and Mr. Vinod Kumar N, Scientists, Propulsion Division, Mr.

Roshan Antony and Mr. Suraj C.S, Scientists, MAV Unit, National Aerospace Laboratories,

for their invaluable guidance and advice.

It is with utmost gratitude that I express my sincere thanks to Mr. Shyam Chetty,

Director, National Aerospace Laboratories and Dr. J.S. Mathur, Head KTMD for making me

part of their great research community and allowing me to pursue my work.

I extend my thanks to Mr. Jayaraman, Scientist „G‟, Head, Propulsion Division, for

extending me all research, computational and essential resources to carry out this work.

To extend my thanks to my beloved Principal Dr. Shankaran, for providing an ideal

atmosphere to pursue my objectives under his able administration.

I express my sincere thanks to Dr. Balakrishnan Shankar, H.O.D, Mechanical

Engineering department and Mr. Joshua D Freeman, Assistant Professor, Department of

Electrical and Electronics engineering for their encouragement, effective guidance and valuable

suggestions right from the beginning of the project till its completion, without which this project

work would not have accomplished.

I am also thankful to my H.O.D Prof. Dr. Chandramohanan Nair, Department of

Electrical & Electronics Engineering who has given valuable suggestions during the work and

his moral support and encouragement.

I would like to express my heart full thanks to all the lecturers, staff members and student

friends of the National Aerospace Laboratories and Amrita School of Engineering for

constructive suggestions and constant encouragement.

Not to forget the outstanding support and encouragement from my parents throughout the

course of this project. I am greatly indebted to them.

TABLE OF CONTENTS

1 INTRODUCTION .............................. Error! Bookmark not defined.

1.1 HISTORY OF VERTICAL FLIGHTError! Bookmark not defined.

1.2 DEFINITION ............................. Error! Bookmark not defined.

1.3 HISTORY OF UAV ................... Error! Bookmark not defined.

2 ELECTRIC PROPULSION SYSTEMError! Bookmark not defined.

2.1 MOTOR SELECTION ............... Error! Bookmark not defined.

2.2 ELECTRONIC SPEED CONTROLLER (ESC)Error! Bookmark not

defined.1

2.3 BATTERY ............................... Error! Bookmark not defined.2

2.4 SERVO MOTOR ..................... Error! Bookmark not defined.4

2.5 MICROCONTROLLER .......... Error! Bookmark not defined.5

2.6 FLIGHT CONTROL BOARD ................................................... 18

2.7 TRANSMITTER & RECEIVER CONTROLS ......................... 20

2.7.1 FUTABA TRANSMITTER SETTINGS ............................ 21

2.8 MECHANICAL FRAME .......................................................... 22

3 CALCULATION AND SIMULATION RESULTS ................... 24

3.1 MOTOR...................................................................................... 24

3.2 BATTERY ................................................................................. 24

3.3 ELECTRONIC SPEED CONTROLLER .................................. 25

3.4 SIMULINK MODEL – BATTERY .......................................... 26

3.5 SIMULINK MODEL – BLDC MOTOR ................................... 27

4 PROPULSION THEORY AND ANALYSIS .............................. 31

4.1 INTRODUCTION TO PROPELLERS ..................................... 31

4.2 PROPELLER THEORY ............................................................ 32

4.2.1 MOMENTUM THEORY: .................................................. 32

4.2.2 BLADE ELEMENT THEORY: ......................................... 33

file:///C:/Documents%20and%20Settings/bharat/My%20Documents/Downloads/Report%20-%20Final.docx%23_Toc356126201

























4.2.3 COMBINED BLADE ELEMENT MOMENTUM THEORY.....35

4.3 PROPELLER ANALYSIS: ....................................................... 38

4.3.1 BLADE ELEMENT THEORY(BET) ANALYSIS: .......... 44

4.3.2 STATIC THRUST BENCH ANALYSIS: .......................... 57

5 Conclusion ......................................... Error! Bookmark not defined.2

Appendix I ................................. Error! Bookmark not defined.4







LIST OF FIGURES

Figure 1-1Paul Cornu - 24hp Gasoline Flight VehicleError! Bookmark not

defined.

Figure 1-2N°2 quad rotor designed by OemichenError! Bookmark not defined.

Figure 1-3UAV Sector in the US (Autonomous Flying Robots)Error! Bookmark

not defined.

Figure 1-4BQM-34 Firebee UAV of the US Air ForceError! Bookmark not

defined.

Figure 1-5The Asctec Pelican ................. Error! Bookmark not defined.

Figure 1-6Draganflyer X6 ....................... Error! Bookmark not defined.

Figure 2-1Brushed DC motor ................. Error! Bookmark not defined.

Figure 2-2Design & Prototyping of Brushless Motor – MITError! Bookmark not

defined.

Figure 2-3Turnigy Aero Drive Motor ..... Error! Bookmark not defined.

Figure 2-4 APC Style Propeller (10X5) . Error! Bookmark not defined.

Figure 2-5Drive Calculator™ Results .... Error! Bookmark not defined.

Figure 2-6Propeller Calculator™ ResultsError! Bookmark not defined.

Figure 2-7Turnigy Plush 60/80A ESC .... Error! Bookmark not defined.

Figure 2-8Zippy Flightmax Li-Po batteryError! Bookmark not defined.

Figure 2-9Wiring Schematic ................... Error! Bookmark not defined.

Figure 2-10A mechanical Gyroscope ..... Error! Bookmark not defined.

Figure 2-11 A digital Head Lock gyro .... Error! Bookmark not defined.

Figure 2-12HK401B Gyro – A closer lookError! Bookmark not defined.

Figure 2-13ESC – Motor – Receiver Wiring, Castle Creations Inc.Error!

Bookmark not defined.

Figure 2-14HobbyKing KK 2.0 Flight Control BoardError! Bookmark not

defined.

Figure 2-15A typical transmitter outlook, Linkoping University.Error! Bookmark

not defined.

Figure 2-16 Futaba Transmitter .............. Error! Bookmark not defined.

Figure 2-17Talon Tricopter Frame ......... Error! Bookmark not defined.

Figure 2-18 Tail Servo Mount ................ Error! Bookmark not defined.

Figure 2-19Turnigy Digital Servo .......... Error! Bookmark not defined.

Figure 4-1 Propellers of various sizes ..... Error! Bookmark not defined.

Figure 4-2 Actuator Disk Model ............. Error! Bookmark not defined.

Figure 4-3 Geometry of propeller Blade ElementError! Bookmark not defined.

Figure 4-4 Blade Element Angle DefinitionError! Bookmark not defined.

Figure 4-5Sectioning of a propeller ........ Error! Bookmark not defined.

Figure 4-6Chord Distribution ................. Error! Bookmark not defined.

Figure 4-7Twist Distribution .................. Error! Bookmark not defined.

Figure 4-8Blade profile at 20mm section Error! Bookmark not defined.

Figure 4-9Blade profile at 40mm section Error! Bookmark not defined.

Figure 4-10Blade profile at 60mm sectionError! Bookmark not defined.




Figure 4-14 Lift Coefficient for various Angles of AttackError! Bookmark not

defined.

Figure 4-15 Drag Coefficient for various Angles of AttackError! Bookmark not

defined.

Figure 4-16 Thrust Coefficient Vs Advance Ratio at 4000 RPMError! Bookmark

not defined.

Figure 4-17 Torque Coefficient Vs Advance Ratio at 4000 RPMError! Bookmark

not defined.

Figure 4-18 Propeller Efficiency Vs Advance Ratio at 4000 RPM Error!



not defined.


not defined.

Figure 4-21 Propeller Efficiency Vs Advance Ratio at 5000 RPM Error!



not defined.


not defined.

Figure 4-24 Propeller Efficiency Vs Advance Ratio at 6000RPM . Error!



not defined.


not defined.




not defined.

Figure 4-29 Torque Coefficient Vs Advance Ratio at 8000 RPM . Error!





not defined.


not defined.

Figure 4-33 Propeller Efficiency Vs Advance Ratio at 9000RPM Error!


Figure 4-34 Load Cell of 1.5kg Capacity Error! Bookmark not defined.

Figure 4-35Thrust Bench Apparatus ....... Error! Bookmark not defined.

Figure 4-36Thrust for various RPM ....... Error! Bookmark not defined.

Figure 4-37Thrust for varying Current ... Error! Bookmark not defined.

Figure 4-38Power for various RPM ........ Error! Bookmark not defined.

Figure 4-39 Comparison between Thrust Bench and BET resultsError! Bookmark

not defined.

ABSTRACT

Aerial robotics is an emerging field combining both aerospace and robotics. Tricopter, an

aerial robot, is an unmanned aerial vehicle which can be controlled from a remote location using

complex dynamic automation systems. The present work highlights construction and testing

aspects of a Tricopter. Unlike a helicopter that rises on a single column of air, the Tricopter rises

on 3 columns of air making it more stable. It uses three standard brushless out runner motors

with standard aerodynamically designed propellers. The configuration of the Tricopter

constructed is three arms spaced at 120 degrees separation to maintain continued stability even

while hovering. Speed controllers are employed to control the speed of each motor. The three

propellers connected to three DC brushless motors produce enough thrust so that the UAV takes-

off to desired heights varying the throttle. The throttle is reduced in steps so as to safe land the

UAV. System is made stable by using gyroscopes, which measure the orientations of the UAV in

three directions such as roll, pitch, and yaw. As the system is equipped with the closed loop

mechanism, the feed-back controller provides a necessary feed-back to the gyros so as to bring

the system back to stability.

Estimation of weight of the Tricopter pertaining to a specific application lays the basis for

selection of most of the components. A preliminary weight of 1000 grams with a payload

capacity of 500 grams has been chosen. The motors, ESC, battery and propellers were precisely

selected based on this assumption. For the propeller selection and performance both Combined

Blade Element Theory Analysis and Static Thrust Bench Analysis have been performed. The

components were thus validated and their selection justified using MATLAB SIMULINK

models. Several software analyses have been performed to simulate real flight environment and

behavior of different components under these circumstances has been analyzed. An onboard

flight controller is used to stabilize the UAV against turbulent orientations on the three arms. A 6

channel transmitter receiver pair is used to control and maneuver the Tricopter in different

directions.

1

CHAPTER 01 – INTRODUCTION

1.1 HISTORY OF VERTICAL FLIGHT:

Manned flight takes its roots to the 1900‟s when Paul Cornu constructed a vertical flight

vehicle (Figure 1.1) reported to have carried a human off the ground for the first time ever.

Although, the sighting of such a machine over long distances has never been verified,

documentations suggest the vehicle made several tethered flights for a few seconds at low

altitudes. The machine was reportedly powered by a 24hp gasoline engine that could hardly

propel the vehicle to a hovered flight. In 1907, the Breguet brothers built the first helicopter N°1

– a quad rotor look-alike powered by a 40hp engine. This machine also suffered severe stability

problems and never flew freely.

Figure 1.1 Paul Cornu - 24hp Gasoline Flight Vehicle

In 1922, Peugeot engineer, Etienne Oemichen flew his indigenously designed 800kg

quad rotor - N°2 (Figure 1.2). In addition to its four main rotors, the N°2 featured five other

rotors – for lateral stability. A separate motor was specifically allotted for nose steering. On May

4th

, 1924, it became the first flight to complete the 1km closed circuit with an average speed of

2.2m/s. Vertical flight was in fact man‟s first experiments of the 20th

century. An insight into the

stability of these first vehicles led engineers to think of the modern highly stable, multi-purpose

Unmanned Aerial Systems (UAS). The term “robotic aircraft” picked up pace and thus laid the

2

Figure 1.2 N°2 quad rotor designed by Oemichen

foundation for a new era of aerial robotics. Today, the United States defense budget allotment for

the development of UAS sector is close to 2 billion dollars. Although the primordial idea of

UAV development was limited only to the military sector, recent trends have opened their use to

civil applications also. Majority of the US UAV market share is contributed by companies like

Boeing, Lockheed Martin, Sikorsky, Lew Aerospace, and General Atomics etc. (Figure 1.3)

Figure 1.3 UAV Sector in the US (Autonomous Flying Robots, F. Kendoul, K. Nonami)

3

1.2 DEFINITION:

The American Institute of Aeronautics and Astronautics (AIAA) defines an Unmanned

Aerial Vehicle as “An aircraft which is designed or modified, not to carry a human pilot and is

operated through electronic input initiated by the flight controller or by an onboard autonomous

flight management control system that does not require flight controller intervention.” Although

the AIAA doesn‟t differentiate between an Unmanned Aerial Vehicle (UAV) and a Micro Aerial

Vehicle (MAV), the Defense Advanced Research Projects Agency (DARPA) of the United

States Department of Defense (DOD) classifies an MAV as an aerial vehicle of dimensions of

15cm or less. A pilot is not carried by an Unmanned Aerial Vehicle and only the power source

that produces dynamic lift is controlled by pre-programmed flight operation center. Hence,

neither a rocket nor ballistic cruise missiles belong to this category. Unmanned airships powered

by lightweight gases are also not included in this category. (Autonomous Flying Robots, F.

Kendoul, K. Nonami)

1.3 HISTORY OF UAV:

The first UAV was developed by Americans Lawrence and Perry in 1916. An auto-pilot

with a gyroscope was developed to stabilize thevehicle. This came to be known as “attitude

control.” The device was named as “Aviation Torpedo” and it flew 30 miles before staging its

first halt. Development of UAV‟s began in full scale at the advent of the Vietnam War with the

defense community emphasizing on military scale applications. The BQM-34 Firebee UAV

(Figure 1.4) of the US Air Force played spoilsport creating devastating effects during the war.

Figure 1.4 BQM-34 Firebee UAV of the US Air Force

Currently, companies like Ascending Technologies (Asctec), Dragon Fly, DIY Drones

etc. manufacture multi copter vehicles (Figure 1.5 and Figure. 1.6) for civil applications.

4

Figure 1.5 The Asctec Pelican

Figure 1.6 Draganflyer X6

Applications range from aerial surveillance, first respond operations, environmental

research, crop optimization techniques, terrain inspection etc. UAV platforms are categorized as:

5

Fixed Wing UAV – Refer to airplanes that require a runway to take-off and land. Can

also be launched by catapulting. These generally have high endurance and can cruise at

great speeds.

Rotary Wing UAV – Also called rotorcraft UAV‟s or Vertical Take-off and Land

(VTOL) UAV‟s. Have great maneuvering capability and hovering capacity. Most multi-

copter vehicles with coaxial rotors come under this category.

Flapping Wing UAV – Most often treated to be MAV‟s with flexible and/or morphing

small wings generally inspired by insects and birds.

Blimps – Balloons and airships that have high endurance and fly at low speeds.

There are some hybrid conFigureurations that can take-off vertically and tilt their rotors.

These have been designed to account for one or more flying factors such as endurance and

cruising speeds. Typical examples include the High Altitude and Long Endurance (HALE –

Northrop Grumman‟s Global Hawk), Medium Altitude and Long Endurance (MALE – General

Atomics‟ Predator) etc.

Thus, aerial robotics is a fast emerging field that has revolutionized both the fields of

aeronautics and robotics. Its application in both the civilian world and the military sector has

been the sole inspiration for this project. The construction of the tricopter was intended for relief

and first respond operations.

6

CHAPTER 02 – ELECTRIC PROPULSION SYSTEM

2.1 MOTOR SELECTION:

Typically, most unmanned aerial vehicles (UAV‟s) are either propelled by electric motors

or internal combustion engines (IC Engines). Since IC engines are a lot heavier than electric

motors, their use is limited to specific applications. Direct Current (DC) motors are basically

categorized as brushed and brushless motors. Irrespective of the classification, electrical motors

consist of two main significant parts – a stationary part most often referred to as a stator and a

rotating part, a rotor. The stator can also be referred to as an armature and the rotor as field or

vice-versa, depending on the position and alignment of the magnets and windings on the stator

and rotor. When a voltage is applied across the terminals of the motor, current flows through the

winding and due to the presence of magnetic poles produces a turning effect. In order to facilitate

rotation of the motor shaft in the same direction, brushed DC motors use carbon brushes for

commutation in every half cycle. A typical brushed DC motor is shown in Figure. 1.1 below.

Though this serves the purpose to a great extent, the brushes wear out over a period of time and

hence require constant maintenance.

Moreover, when the rotor poles are aligned at an angle of 90 degrees to the stator poles,

the torque produced is zero. The motor cannot start in this position and hence poses a grave

threat when employed in aerial vehicles. Also, in such a position, the carbon brushes would come

in contact with each other and hence lead to sparking. This is highly undesirable and eliminates

the option of using brushed DC motors. The recent trend in aerial robotics is to employ brushless

DC motors or BLDC motors owing to their wide range of advantages over their brushed

counterparts. An insight into the working of these motors reveals their high torque to weight and

high torque to watt ratios that give them an extra edge over the conventional motors. Moreover,

the electronic commutation system in these motors proves less susceptible to mechanical wear

and tear, thereby reducing the cost of servicing and use of complex electronics. Although the

term “Brushless motors” encompasses a wide range of motors including the AC induction

motors, Permanent Magnet Synchronous motors and other motors that technically don‟t have

brushes; the term is largely limited and confined to Brushless DC motors. BLDC motors usually

have stators that contain the windings and rotors that carry the magnets. The position of the rotor

can either be “inside” or “outside” thus bringing up a classification as “inrunners” and

“outrunners”.

7

Figure 2.1 Brushed DC motor

Figure 2.2 Design & Prototyping of Brushless Motor and Motor Controls – Shane W. Colton, MIT

However, in both these cases (inrunners & outrunners), it is the rotor that rotates and the

stator remains stationary. Since this report is based on the underlying assumption that weight

8

forms the basis for the selection of all other components of the tricopter, motor selection plays a

pivotal role as the thrust produced by the motor is what is responsible for vertical take-off and

landing (VTOL). Most international competitions like the “International Aerial Robotics

Competitions (IARC)” conducted by Association for Unmanned Vehicle International (AUVSI)

specify a total weight limit of 1500 grams. To comply with international testing standards, the

weight of the tricopter was also set at 1500g. Standard aerodynamically designed propellers with

pre-determined pitch and diameter sizes were considered. As per the usual convention, the first

number in the propeller size denotes the diameter in inches and the second number signifies the

pitch (also in inches). A number of motor-propeller combinations were analyzed and the thrust

produced by each combination was tabulated as per the Abbott equation for propellers described

below:

Thrust (kg) = Pitch∗(Diameter)³∗(RPM)²∗10¯¹°∗0.02835

MOTOR

PROPELLER

THRUST

KD 36-22S

BRUSHLESS

OUTRUNNER

1440KV

APC STYLE (10X5)

1440g

GRAUPNER SLOWFLY (9X6)

1259.9g

APC STYLE ELECTRIC (10X4.5)

1296.2g

POLYMAX (8X5)

737.4g

KD 36-12M

BRUSHLESS

APC STYLE (10X5)

3278g


2867.6g

9

OUTRUNNER

1370KV


POLYMAX (8X5)

NTM PROP

DRIVE SERIES

1400KV

APC STYLE (10X5)

3420g


2994.5g


3080.8g

POLYMAX (8X5)

1752.6g

TURNIGY AERO

DRIVE SK3

1340KV

APC STYLE (10X5)

3136g


2743.3g


2822.4g

POLYMAX (8X5)

1605.6g

Motor – Propeller Combinations

As evident from the table, the Turnigy Aero drive SK3 motor (Figure 2.3) and the APC

Style propeller (Figure. 2.4) provide the highest thrust. Though the Abbott equation is not

precise, it gives an account of the static thrust produced by a given motor-propeller combination.

The actual thrust produced is determined by an experimental setup called “Thrust Bench

Analysis” discussed in the subsequent sections. However, the thrust produced by a given motor

and propeller combinations has also been verified by the Drive Calculator™ and Propeller

10

Calculator™ software. The results have been displayed below (Figure 2.5 and Figure 2.6). Thus,

the motor-propeller combination is now assumed to provide the required thrust, thereby paving

way for the selection of the battery and Electronic Speed Controller (ESC).

Figure 2.3 Turnigy Aero Drive Motor Figure 2.4 APC Style Propeller (10X5)

Figure 2.5 Drive Calculator™ Results

11

Figure 2.6 Propeller Calculator™ Results

2.2 ELECTRONIC SPEED CONTROLLER (ESC):

An electronic speed controller is a stand-alone unit employed to vary the speed of a

motor. Brushless ESC‟s consist of a 6 step inverter circuit used to drive a 3 phase motor. The

motor requires an analog signal for operation and the microcontroller‟s computation power

wouldn‟t be sufficient to control the motors. Thus the need for an external controller arises. The

ESC is powered by a battery and the DC signal from the battery is fed to the inverter circuit in

the ESC resulting in three output signals that are given to the motor. The direction of rotation of

the motor can be varied by interchanging any two output signals from the ESC. ESC‟s are often

classified based on the input current drawn from the motor and the programmable features,thus

enabling its use in various applications. A battery eliminator circuit (BEC) is a DC-DC voltage

regulator equipped in most ESC‟s to supply the receiver and other equipment from the main

battery pack. Absence of this circuit in the ESC necessitates the need for an additional power

source to power the receiver and servo motors. The Turnigy Aero drive SK3 motor draws a

maximum input current of 28A. Thus the ESC for this motor needs to be rated a little higher than

the input current rating of the motor to account for any unforeseen losses. To accommodate a

higher current rating and programmable features into the ESC, the TURNIGY Plush 60A ESC

(Figure 2.7) has been selected. The ESC is rated for 60A continuous current and 80A burst

current. Though the availability of a much smaller rating ESC of 40A cannot be denied, the

requirement of a BEC and programmable features demands the selection of the 60A rating. The

12

ESC receives input Pulse Width Modulated (PWM) signals ranging from 1000 – 2000

microseconds (µs). The pulse width 1000 corresponds to zero throttle and 2000 to full throttle.

Figure 2.7 Turnigy Plush 60/80A ESC

2.3 BATTERY:

The battery plays a very significant role in the construction of an unmanned aerial

vehicle. Flight endurance, agility, capability to hover and a host of other factors are determined

by the capacity of the battery. Conventional batteries include the Nickel metal hydride (Ni-Mh),

Lithium Ion and Lithium Polymer (Li-Po) configurations. Most batteries are rechargeable and

are usually composed of multi-cells. The energy density of Li-Po batteries is around 20% higher

than Li ion batteries and approximately 45% higher than Ni-Mh batteries. Moreover, Li-Po

batteries have a much slower discharge rate than Nickel hydride cells (Propulsion system

Optimization for an unmanned lightweight quad rotor – Eva Saade Latorre). Thus, Li-Po seems

to be the obvious choice. A cell measures a nominal voltage of 3.7V and when fully charged

should measure 4.2V. However, when fully discharged the voltage should not fall below 3V.

Multi-cell batteries have cells wrapped in a foil pouch called “pouch cell” and stacked together

thus avoiding the need for metal cans. This also ensures less weight, making them the obvious

choice in weight specific applications. Thus, a 3cell battery inadvertently implies a voltage of

3∗3.7V = 11.1V and hence most often expressed as “3 Cell” or “3 Li-Po” in case of Lithium

Polymer. Most battery capacities are either expressed as mAh (milliamp/hr.) or Ah (Amp/hr.) to

indicate the battery size. A higher capacity battery runs for a longer time than a lower capacity

battery. When speaking of batteries, discharge current is usually expressed as C-rate to normalize

the measure against battery capacity. 1C literally means that the discharge current discharges the

entire battery in one hour. Thus, when a battery is rated as 1000mAh and 20C, it implies that the

battery pushes 1∗20 = 20A of discharge current. When the same battery is rated for 1C, the

battery discharges 1A in one hour. Although in the former case, the battery discharges 20A, it

does so at the cost of endurance. The battery discharges quickly and hence results in reduced

13

flight time. To ensure longer flight time, higher batteries are chosen and thus the increase in

weight. Thus a compromise between battery capacity, weight and flight endurance is inevitable.

It is always better to run a higher C-rated battery at a lower C-rate than to run it the other way

round, the most plausible reason being improved battery performance.

Since, the Turnigy Aero drive SK3 motor draws 28A burst current, the three motors in

the tricopter collectively draw 84A. Now, the battery in consideration should be able to provide a

slightly higher value than that required and at the same time ensure long endurance. A number of

batteries were analyzed for this purpose and the results stated in the table below:

BATTERY

RATING

CURENT OUTPUT

Zippy Flightmax 3S1P

2200mAh, 25C

55A

Zippy Flightmax 3S1P

2650mAh, 40C

106A

Turnigy Nano Tech

2650mAh, 35~70C

185.5A at 70C

Battery Feasibility Check Table

The Zippy Flightmax 2650mAh, 40C battery (Figure 2.8) seems to be the most profitable

choice among the three. Although the 70C configuration provides a higher current output, its

weight being too large, eliminates it from the fray.

14

Figure 2.8 Zippy Flightmax Li-Po battery

Thus the flight time can be calculated as:

Flight time = (60 minutes)/(C rating)

= (60)/40

= 1.5 minutes.

Though this seems to be too low, the flight time is expected to be much more than this

value since the motor does not consume 28A at all times. The motor draws 28A during the initial

take-off but later settles down to a lower value when it climbs up to a certain height. Flight time

during experimental tests was found to be around 6-7 minutes.

2.4 SERVO MOTOR:

The tricopter configuration in this paper necessitates the rotation of all the three motors in

the same direction. This produces enough torque causing the entire body to rotate in the direction

of rotation of the motors. A tricopter exhibits 3 directional tendencies while in the air – roll, pitch

and yaw as explained below. In order to control the yaw motion, the tail motor mount is linked to

a servo gear. The bidirectional movement of the servo gear enables movement of the tail mount

in either direction thus controlling the yaw motion as and when desired. There are two types of

servo motors that can be used in such applications – Digital servos and Analog servos. The servo

motor under consideration should be able to produce enough torque to rotate the motor mount

quickly. The size and weight of the servo motor also play an important role and are largely

dependent on the tricopter servo frame allotments. More on this in the subsequent sections.

15

2.5 MICROCONTROLLER:

The microcontroller can be considered to be the “heart” of the electronic stability system.

The wiring schematic is shown below in Figure. 2.9. As per the Figure, the three motors are

connected to the three ESC‟s and are rested on three arms placed 120° apart. The three ESC‟s are

connected to the battery in parallel either through a printed circuit board (PCB) or by direct

connection.

Figure 2.9 Wiring Schematic

A Gyroscope is a device used to measure angular orientation (Figure 2.10). With stark

relevance to the tricopter, three gyros (as shown in Figure. 2.9) are placed on three arms to

measure the orientation in the respective axial directions. On an otherwise perfectly stable plane,

the gyros wouldn‟t initiate any action. When the vehicle tends to orient in a particular direction,

the gyro pertaining to the arm subjected to orientation, calculates the error (measured in degrees)

and sends the error signal in the form of a digital pulse width modulated signal to the ESC. The

ESC then either reduces or increases the speed of the concerning motor to match up with the

other motors. The magnitude of the error signal would be translated into an equivalent PWM

signal of appropriate pulse width and thus the change in speed would either be added or reduced

as per the requirement. The gyro again measures the error and continues to do so until the error is

zero which in other words would mean the tricopter to be stable.

16

Figure 2.10 A mechanical Gyroscope

However, choosing the right gyro for an application still poses various questions about

the different features available on different models. Four gyros are required for the current

application – three on three arms and one for the yaw rate control. The three gyros for the three

arms can include the basic features and not much thought is needed for their selection. The yaw

gyro demands careful introspection into its features and working principle. There are basically

two types of yaw control gyros – the yaw rate gyro and the heading hold gyro (Figure 2.11 and

Figure 2.12).

Figure 2.11 A digital Head Lock gyro Figure 2.12 HK401B Gyro – A closer look

17

A yaw rate gyro dampens the yaw motion to a certain extent by sending a command to

the tail servo. The servo then initiates necessary action by moving in the appropriate direction to

control the yaw motion. However, these gyros would only be able to dampen the yaw motion but

cannot eliminate it completely. The head lock gyros are a superior class in such scenarios. They

use complex software to accurately calculate the angular measurement required by the servo to

completely control the yaw motion. Once in action, the vehicle would be perfectly stable despite

strong winds and irregular change in rotor speeds. However, the gyro would suspend action

when the pilot wishes to create some sort of yaw. Most RC pilots refer to this function as

“heading hold” or “head locking”. Digital head lock simply implies more precision on the head

locking function.

Figure 2.13 ESC – Motor – Receiver Wiring, Castle Creations Inc.

The above Figure (Figure 2.13) depicts the connections pertaining to the ESC, motor and

the receiver. When an actions, say, as an increase in throttle is initiated in the transmitter, an

equivalent signal in binary form is sent to the receiver. The gyros which are connected to the

receiver receive the given signal and pass it to the ESC. The ESC translates the input signal into

an appropriate signal based on the pulse width and feeds it to the motor. The motor thus revolves

at the desired speed. But the use of the gyroscopes still remains unexplained at this point. As

discussed earlier, tricopters tend to orient in three different directions – roll, pitch and yaw. In

order to move forward, the speed of the two motors in the front is reduced allowing it to lean

forward. Thus the forward motion is made possible. The gyros on these two arms ensure the

forward lean to be within limits – just to produce forward motion. Excessive leaning leads to

excessive thrust exhibited by the tail rotor thus resulting in flipping. Similarly, during right

banking, the gyro on the right arm ensures the right motor‟s speed is within limits so as to

18

produce a change in direction, specifically towards right. Again, the absence of gyro eliminates

boundary limits and can cause the tricopter to flip to the right. Thus gyros play an important role

in stabilizing the vehicle while ensuring smooth flight. The microcontroller now hosts the

limitations for all the gyro orientations, the maximum and minimum speeds of the rotor and the

signal translations from the transmitter to the other components onboard. Moreover, transmitter

configurations can be effectively calibrated in the microcontroller to suit the flyers needs and

experience. For example, in the case of an amateur flyer, the transmitter can be configured to

control only the four basic movements of forward, backward, right and left motions. In the case

of experienced RC pilots, the transmitter can be configured accordingly to include extra set of

commands such as reverse flying, inverted flying, acrobatic stunts etc. The latter case is just

beyond the scope of this project as it is confined and limited to basic flying features. However,

advanced flying options would require more computing power and programming skills and thus

the need for higher microcontrollers. Most aerial vehicles in the RC world make use of flight

controllers such as the ArduPilot™ from DIY drones, KK flight control boards etc. The

ArduPilot is a hardware platform that requires an open source control program such as the

ArduCopter™. Most of these boards require a constant upgrade of 256kB flash memory and thus

an updated firmware for stabilization. Due to lack of superior programming skills, the idea of

manual programming was given up and the KK 2.0 flight control board has been employed as

the sole stabilizing unit.

2.6 FLIGHT CONTROL BOARD:

The KK 2.0 Multi-Rotor LCD Flight Control Board (Figure. 2.14) is the state of the art

stabilizing unit for aerial vehicles designed by Rolf R. Bakke, grandfather of KK revolution, for

HobbyKing™. The board houses up to 8 different configurations of aerial vehicles ranging from

single copter to octacopter. Of these wide varieties of aerial vehicles, multiple designs of quad

rotors and tricopters like the “+” and “X” configurations are also included.

19

Figure 2.14 HobbyKing KK 2.0 Flight Control Board

The circuit design of the board is similar to Figure 2.9 except that it also carries external

modules such as a 3 axis Analogue Devices™ accelerometer and a piezo buzzer. In contrast to

the four gyro system described above, the KK 2.0 consists of two InvenSense™ Gyros and an

Atmel™ Mega 324 microcontroller. It consists of 8 motor layout pins to the right and 5 receiver

outputs to the left. The transmitter - receiver channels and options will be explained later. The

LCD board displays outputs and allows calibration of ESC‟s, sensor modules such as the gyro‟s

and accelerometer and helps the user to choose from a variety of motor layouts. The Proportional

Integrator (PI) gain values can also be adjusted with the help of four buttons provided at the

bottom. The transmitter channels can be adjusted as per the convenience of the flyer and the

maximum and minimum values for each channel can also be set. The servo gain values can be

adjusted based on the type of servo chosen. Self-leveling option in the board allows the user to

stabilize the tricopter as desired. The board can be armed by moving any of the four channels on

the transmitter provided a suitable setting has been configured prior to arming it. The settings on

the board can be changed as long as the board is unarmed. This is indicated by a glow of a red

LED followed by a beep. The sensors on the board have to be calibrated by placing it on a flat

surface. After a few seconds, all the sensor values are calibrated to the initial measurement

values recorded while on the flat surface. The KK board settings with reference to the tricopter

will be explained in detail in the next chapter.

20

2.7 TRANSMITTER & RECEIVER CONTROLS:

The transmitter and receiver occupy a very significant role in the control of any

unmanned aerial vehicle. Typical receivers have 4 channels and the number varies depending on

the vehicle configuration and the flying style. The 4 basic channels of a receiver are Aileron,

Elevator, Throttle and Battery. While using an ESC equipped with a BEC, the receiver need not

be powered separately and any ESC connected to one of the channels powers the receiver. Thus

for ESC‟s with built-in BEC, the battery channel can be configured for any other purpose. In the

case of a tricopter, a 6 channel receiver is required to account for the rudder and AUX options.

Thus, a 6 channel receiver would inadvertently require a 6 channel transmitter at the least and

there is no higher limit to the number of channels on the transmitter.

Aileron accounts for the roll motion and can be controlled by moving the right stick to

cyclic left and right (Figure 2.15). Thus, when intending to move right, the right stick is moved

to cyclic right reducing the speed of the motor on that arm. The tricopter bends to its right and

banks in the desired direction. Similarly, moving the right stick on the transmitter to cyclic left

reduces the speed of the motor on the left arm and the tricopter banks left. When looking for

forward motion, the right stick on the transmitter is moved up, thus reducing the speed of the

front motors. The tricopter leans forward and produces forward motion. For backward motion,

the right stick on the transmitter is pushed back. The front two motors rotate at a greater speed

than the tail motor and hence the vehicle moves backward. This motion of moving forward and

backward is termed as pitching and is controlled by the Elevator channel on the transmitter.

Figure 2.15 A typical transmitter outlook. Fig 2.16 Tricopter Transmitter

Similarly, pushing the left stick up increases the throttle and all the three motors pick-up

speed. Pushing it down decreases the speed of the motors. Moving the left stick on the

transmitter to cyclic right controls the motion of the servo motor on the right. Thus, the tail rotor

mount is tilted to its right producing anti-torque to oppose the yaw motion. Similarly, the tail

21

rotor mount can be tilted to its left by moving the transmitter stick to its left. This is known as

rudder.

2.7.1 FUTABA TRANSMITTER SETTINGS:

REVR 1rev

2rev

3rev

4rev

5nor

6rev

DR1 up 50 down40

2 up 50 down40

4 up 100 down100

EP A1 30%

2 30%

3 100%

4 100%

5 35%

630%

NTH on 0 25 50 75 100

NPI on 0 25 50 75 100

ITH inh

IPI off

HOLD inh

REVO inh

GYRO -35%

SWT inh

22

SWSH a -40%

e +40 %

p +100%

FS channel 3 20%

In case of a flight control board, all the above settings are configured by default and any

PI gain values can be changed in the KK board itself. However, it is highly recommended that

novice RC pilots refrain from making any changes and fly using the default values.

2.8 MECHANICAL FRAME:

The mechanical frame has been purchased from HobbyKing™. The Talon Tricopter V1.0

Carbon fiber frame (Figure 2.16) is a cheap, well-fabricated structure equipped with a camera

mount and flexible arms. The frame weighs only 350g and is the ideal choice for amateur pilots.

The frame also provides provision for a servo motor on the tail arm. The tail rotor mount is

connected to the servo gear by two link rods which are held together by 4.8mm ball cups (Figure

2.17).

Figure 2.17 Talon Tricopter Frame

23

Figure 2.18 Tail Servo Mount Figure 2.19 Turnigy Digital Servo

The servo mount only allows enough space for a micro servo and hence a digital servo of

suitable dimensions has to be selected. The Turnigy MG90S metal gear servo (Figure 2.18) fits

in exactly in the mount and weighs only 13.4g. The output PWM rate for digital servos is quite

high, around 400Hz and hence a higher operating speed. Taking all the above factors into

consideration, the MG90S has been finalized to control the yaw motion.

The structure houses a two plate design for any external modules such as GPS, XBEE

etc. All in all, the frame is the most cheap and durable of all the ready-made frames available in

the market. Any unforeseen losses during flight tests can be reinforced by frame parts available

on the HobbyKing website.

24

CHAPTER 03 – CALCULATION AND SIMULATION

RESULTS

3.1 MOTOR:

TURNIGY AERODRIVE SK3-3530-1340KV BRUSHLESS OUTRUNNER

Turns – 24

Voltage – 2~3S LiPo

Operating Current = 20A

RPM/V – 1340KV

For 1V – 1340 rpm

For 11.1V, Speed = 14,874 rpm.

Power (in Watts) = 11.1V X 20A = 222W

For 3 motors, total power produced = 222X3 = 666W.

From Blade Element Momentum Theory:

Thrust (each motor) = 5000* 14,874 * 10 *0.02835

= 3.136kg/motor.

Total thrust produced by three motors = 9.4kg.

3.2 BATTERY:

ZIPPY FLIGHTMAX 2650mAh 3S1P 40C LiPo BATTERY

Continuous AMP Draw = (mAh)*0.001*(C Continuous Rating)

AMP Draw = 2650*0.001*40 = 106A Continuous.

25

Motor‟s Burst Amperage = 28A

Total Burst Current = 28*3 = 84A.

Verdict : Good to go !!!

Battery Discharge Time = (2.65*11.1)/(666)

= 0.04416 hours

= 2.65 min

3.3 ELECTRONIC SPEED CONTROLLER:

TURNIGY PLUSH 60A SPEED CONTROLLER

Continuous Current – 60A

Burst Current – 80A

BEC Mode – Switching

BEC – 5V/3A

26

3.4 SIMULINK MODEL – BATTERY:

The above figure depicts the MATLAB SIMULINK™ model of the LiPo battery. The

specifications of the battery used in this project have been imported into the model to observe

various changes encountered during the actual battery operation. The results thus obtained from

the simulation are attached below.

27

The above figure illustrates the plot of voltage, speed of the motor (DC machine depicted in the

model) and armature current versus time. SOC is the state of charge of the battery. It is initially

charged to 100% and decreases over time due to battery operation. The charge reduction of the

battery is limited to 40%, which implies that the SOC is set at a threshold decrease of 40, to

avoid rapid discharge and unwanted results.

3.5 SIMULINK MODEL – BLDC MOTOR:

The block diagram shown above represents the SIMULINK™ model of the DC motor. The

characteristics of the Turnigy SK3 3530-1340 kv have been imbibed into the model to replicate

actual DC motor operation. The maximum speed limit was set to 14000 rotations per minute and

its characteristics were observed.

The figures below depict the plot of line-line voltage, stator current, back EMF, rotor current and

torque versus time. Since the DC motor has been modeled using a permanent magnet

synchronous motor with trapezoidal input, the line-line voltage has been observed to trace a

trapezoidal waveform. Similarly, all the other waveforms have been observed to show

satisfactory results, if not accurate, to validate the selection of the motor.

28

Vab :

Stator Current:

29

Back EMF:

Rotor Speed:

30

Torque:

Thus the selection of the DC motor and battery has been justified using MATLAB

SIMULINK™ models.

31

CHAPTER 04 – PROPULSION THEORY & ANALYSIS

4.1 Introduction to Propellers

Aircraft propellers, also known as Airscrews are devices that convert rotary motion from

engines or electric motors (in this case) for providing propulsive force. All the propellers

available in the market will be similar in shape and design. They do vary in minor ways one from

the other. They all look similar with a taper from central hub to the outer tip. The width varies

slightly from hub to the outer tip and the blades are also twisted over the whole length. The

primary purpose of a propeller is to convert rotary motion of an electric motor to axial thrust via

torque transfer to the propeller. The rotating propeller produces thrust by capturing air and

expelling out at the back. The more air it expels over time, it consumes more power and generate

greater thrust. In order to push the air, the blades need to capture the air and hence they will be

twisted so that they can propel into the air. The main objective is to make every part of blade

along its length to advance axially the same distance in a revolution. This way each section of

blade produces maximum amount of thrust at same time. A propeller is generally defined by its

diameter and pitch. For example APC 10 x 5 propellers, it implies the propeller is 10inch in

diameter and has a pitch of 5inch. Diameter is one the crucial parameters in determining the

amount of power the propeller consumes to produce the thrust. The pitch is defined as the

forward distance travelled in one revolution. The angle of the blade increases from tip inward to

the hub. This angle is called blade angle. The hub region is thick as high stresses will be acting

near the hub. The Figure shows general COTS (commercial-off-the-shelf) propellers.

Figure 4.1 Propellers of various sizes

32

4.2 Propeller Theory

As there is no provision for experimental wind tunnel analysis for in-flight performance

test, the theoretical methods were opted instead to predict the performance of the propeller.

Various propeller theories are presented and discussed in this section.

Various propeller theories are:

1. Momentum theory

2. Simple Blade- element theory

3. Combined Blade-element momentum theory

4.2.1 Momentum theory:

Momentum theory is the simplest theory which explains the operation of a propeller. In

this theory, the propeller is assumed to be replaced by uniformly loaded actuator disk with

infinite number of blades (which implies the disk with infinitesimal thickness). The inflow and

outflow are assumed to be uniform. The Figure below illustrates the situation.

Figure 4.2 Actuator Disk Model

Far in front of the disc the static pressure and speed conditions are given by p and V. At

the disc, the velocity of air is assumed to be V+v. the pressure in front of the disc is assumed to

be p while the pressure behind the disc is assumed to be p p . The increase in pressure p is

caused by the propeller that adds energy to the flow. Now the Bernoulli equation is applied in

two stages: first to flow ahead of the propeller and then to the flow behind the propeller.

Ahead of the disc

2 20.5 0.5 ( )p V H p V v

Behind the disc

33

2 2

1 10.5 ( ) 0.5 ( )p V v H p p V v

Where H is total pressure ahead of the disc

1H is total pressure behind the disc

1v is induced velocity increase far downstream

Solving the above two equations for p ,

2 2 11 1 10.5 ( ) ( 0.5 )

2

vp H H p V v p V V v

If the propeller disc area is A then the thrust produced by the propeller is

11

2

vT A p A V v

Where T is thrust

A is the area of the actuator disc

p is the pressure jump

is density of the fluid

V is the free stream velocity

1v is the induced velocity

The serious drawback with this theory is that it does not consider the geometry of the

propeller in calculating its performance. It is not very useful in predicting the propeller

performance and hence momentum theory was not chosen as the main theoretical method to

predict the performance of the propeller.

4.2.2 Simple Blade Element Theory:

Another theoretical tool to predict the propeller performance is Simple Blade Element

theory developed by William Froude. It differs from the momentum theory by considering the

airfoil geometry and aerodynamic characteristics of propeller blades. In this theory, the whole

blade is divided into a large number of elements, each with its own width and chord.

Here the blade element at radius r is moving with a spin velocity of 2 rn , where n is the

propeller rotational velocity is revolutions per second. In addition, the propeller has forward

velocity V, or propeller advance velocity. The Lift and Drag forces on each element are dL and

dD respectively. The thrust and torque of a blade element are dT and dQ respectively. The angle

34

is called the geometric pitch angle. The rotational speed r is much less at the hub than at

the tip of the propeller. As advance velocity is same across the propeller blade, the local angle of

attack of a blade element at the hub is much less than that at the tip and could become even

negative, if the blades are not twisted. That is the reason to increase the geometric pitch angle at

the hub such ass to maintain efficient angle of attack. Hence, the propellers are twisted form

central hub to the outer tip.

Figure 4.3 Geometry of propeller Blade Element

The lift and drag components of the blade element can then be resolved to obtain the

respective thrust (T) and torque (Q) from the blade element, where

2cos sin 0.5* * * * *( cos sin )R l ddT dL dD V c dr C C

2( sin cos ) 0.5* * * * *( sin cos )R l ddQ dL dD r V c rdr C C

Where is the helix angle

c is the blade chord at radius r

35

The above equations are integrated over the entire propeller to determine the total thrust

T and total torque Q. But, for this calculation the sectional aerodynamic characteristics of each

blade must be known, which can be calculated accurately if we know the induced velocity due to

lift production on each blade element. But this theory doesn‟t account for induced velocity

distribution. Although such a method can give good results, a better theory will be combined

blade element momentum theory.

4.2.3 Combined Blade Element Momentum Theory:

This theory combines both Momentum theory and Simple Blade Element Theory in

predicting the propeller performance. The main problem of Blade Element theory is solved by

combining Momentum theory which calculates the induced velocity required for Blade element

theory.

If the number of blades of propeller is B , then the total elemental thrust from Blade

Element theory ( Neglecting the Drag term) is

00

0

cossin sin( ) sin cos i

R

V V

V

Where 0 and 0RV are shown in the Figure below.

Figure 4.4 Blade Element Angle Definition

The induce velocity component in the thrust direction is iV 0cos .

From momentum theory, the total elemental thrust may also be written as

0 0*(2 )*( cos )*(2 cos )i iBdT rdr V V V

From the above two equations

36

2

0

0

* * *( )

8 *( cos )

l Ri

i

B C c VV

r V V

Assuming the induced angle to be small,

00

0

cossin sin( ) sin cos i

R

V V

V 0

tan i

R

V

V

And replacing 0 *( )lC a

Where 0a is section lift curve slope of the blade airfoil.

Hence the above equation can be re-written as

0 *( )* *

8 (sin cos )

acB

r

Now we can replace 2

* * *

* *

B c R B c

R R , solidity ratio of propeller.

The solidity ratio of a propeller is defined as the ratio of total blade area to the area of the disc.

And the blade section is non-dimentionalized as r

xR

We can re-write the above equation as

2 0 0cos sin ( ) 08 8

a a

x x

For relatively low thrust conditions, the above equation can be solved by neglecting 2 -term.

0

( )

8 sin1

x

a

And 0

2cos cos

cosR R

nrV V

Finally from the Figure above, the elemental thrust and elemental torque of B-bladed propeller is

given by

2 2 22

0 02

2* * cos * *( cos sin )

cosl d

n rdT B cdr C C

37

2 2 32

0 02

2* * cos * *( sin cos )

cosl l

n rdQ B cdr C C

The above equations are integrated over the entire propeller to determine the total Thrust T and

total Torque Q.

The Thrust Co-efficient and Torque Co-efficient are defined as

2 4T

TC

n Dand

2 5Q

QC

n D

The Following step-by-step procedure is suggested to determine the magnitudes of TC andQC .

Step 1: 1tan2

V

nr

Step 2: Bc

r

Step 3: r

xR

Step 4:

0

( )

8 sin1

x

a

Step 5: ( )

Step 6: ,l dC C values are determined

Step 7: 0

Step 8: 2 2 2

2

0 02

2* * cos * *( cos sin )

cosl d

n rdT B cdr C C

2 2 3

2

0 02

2* * cos * *( sin cos )

cosl l

n rdQ B cdr C C

Step 9:

2

1

( )

r

r

dT f r dr and

2

1

( )

r

r

dQ f r rdr

38

Step 10: Using Trapezoidal Rule for integration ( ) ( )

( ) ( )2

b

a

f a f bf x dx b a

4.3 Propeller Analysis:

Selection of a propeller can be based on either Blade-Element theories explained earlier

or by performing propulsion tests. In this section, we briefly discuss the prediction of propeller

performance using BET and propulsion tests.

As mentioned in earlier section, the theoretical method of propeller analysis deals with

propeller‟s thrust generation and power consumption. And we need to know the propeller

geometry data and airfoil data. The commercial propeller manufacturers do not provide us with

any such data and therefore, the required data was measured by sectioning the propeller, which is

unpractical and inaccurate approach. But, we can get accurate results of thrust and power

consumption from static propulsion tests using Thrust-Bench.

The sectioning of the propeller can be illustrated with the help of the Figure below.

Figure 4.5 Sectioning of a propeller

In this project, APC 10*5 propeller has been selected. The geometry data of this propeller

was taken from CMM (co-ordinate measuring machine) available at metrology lab of NAL .As

illustrated in the above Figure, the propeller blade of 5inch i.e.,127mm has been sectioned

accordingly along the blade length in steps of every 20mm i.e., 20mm, 40mm, 60mm, 80mm,

100mm and 120mm.

39

The geometry data can be represented as below:

r(mm) Chord(c) Angle(β) Radius(mm) c/R r/R

20 17.89 39.17 127 0.140866 0.15748

40 25.01 28.43 127 0.196929 0.314961

60 25.7 20.49 127 0.202362 0.472441

80 21.83 15.08 127 0.17189 0.629921

100 15.92 11.37 127 0.125354 0.787402

120 10.98 5.48 127 0.086457 0.944882

The CMM machine provided us with the coordinates of each section of the propeller

blade. The coordinates obtained are inaccurate with sharp edges and lengthy chord lengths due to

slip of the measuring tool over the blade profile. These coordinates have been smoothened using

CAD Software packages available. The sharp edges have been removed providing a smooth

radius at both leading and trailing edges. The modification of the coordinates has been done very

accurately as they need to be imported into XFLR5 to obtain lift coefficient and drag coefficient

values over various angle of attacks. The operation of XFLR5 is discussed in detail in later part

of this section.

After modifying the obtained coordinates, the chord and blade twist of each section have

been measured using SOLIDWORKS software package and tabulated as shown above.

From this data, the chord distribution and twist distribution of the propeller is plotted.

From the chord distribution graph plotted, we can clearly understand how the chord length varies

along the blade i.e, gradually increasing and then decreasing, and the maximum chord

distribution occurs at r/R=0.5. And from the twist distribution graph plotted, we can infer that the

blade twist gradually decreases from the central hub to the outer tip of the propeller.

40

Figure 4.6 Chord Distribution

Figure 4.7 Twist Distribution

0

0.05

0.1

0.15

0.2

0.25

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

c/R

r/R

Chord Distribution

0

5

10

15

20

25

30

35

40

45

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

β

r/R

Twist Distribution

41

The modified coordinates are plotted as shown below. The coordinates for 20mm section of

propeller is attached in Appendix.

Figure 4.8 Blade profile at 20mm section


-14-13-12-11-10

-9-8-7-6-5-4-3-2-10123456789

1011121314

-14-13-12-11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

r=20mm

-14-13-12-11-10

-9-8-7-6-5-4-3-2-10123456789

1011121314

-14-13-12-11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

r=40mm

42



-14-13-12-11-10

-9-8-7-6-5-4-3-2-10123456789

1011121314

-14-13-12-11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

r=60mm

-14-13-12-11-10

-9-8-7-6-5-4-3-2-10123456789

1011121314

-14-13-12-11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

r=80mm

43



-14-13-12-11-10

-9-8-7-6-5-4-3-2-10123456789

1011121314

-14-13-12-11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

r=100mm

-14-13-12-11-10

-9-8-7-6-5-4-3-2-10123456789

1011121314

-14-13-12-11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

r=120mm

44

4.3.1 Blade Element Theory (BET) Analysis:

As explained in the previous chapter about the BET, it divides the whole propeller blade

into various elements. And at each element, elemental thrust and elemental torque will be

calculated. They are integrated over the entire element to get the component of thrust and torque

each element provides. After calculating the thrust and torque for each blade element, the total

thrust and total torque are obtained by summing up the components from all blade elements.

Even though Combined Blade Element Theory predicts the propeller performance

accurately, the calculations are quite tedious, esoteric and time consuming. Hence, Simple Blade

Element Theory has been used instead of CBEMT. The process is explained as follows.

Firstly, we have no idea about the flight forward velocity or RPM of the propeller. So, for

the calculation of BET, we have considered a velocity range of 2m/s to 14m/s and RPM varying

from 4000 to 9000. For each RPM selected, for every section, varying the velocity from 2m/s to

4m/s, the Reynolds number values have been calculated. These Reynolds number values vary

along the blade for each section for a particular RPM. Now, we need to know the coefficient of

lift and coefficient of drag of each section for various angles of attack for considered RPM and

forward velocity to input into BET calculations. For this, software named XFLR5 has been

used.XFLR5 is an analysis tool for airfoils, wings and planes operating at low Reynolds

Numbers. It gives the polar of the airfoils in 2D environment. This software imports propeller

section coordinates and then de-rotates and normalizes the profile. Then a batch analysis has

been run varying both Reynolds number and angle of attack. Then coefficient of lift vs angle of

attack and coefficient of drag vs angle of attack plots and values has been obtained from the

simulation results of XFLR5. These values are taken as an input for BET calculations. So, for a

particular section, with specified RPM and forward velocity, Reynolds number has been

calculated and for that Reynolds number coefficients of lift and drag are taken from XFLR5

results. Now, with all the inputs, thrust and torque of a propeller for given RPM and Velocity

are calculated by following the step-by-step procedure explained below.

A sample calculation of overall BET is done for 9000RPM.

Input Values

APC Propeller (10‟‟ x 5‟‟) Radius, R 0.127 m

Angular Speed , n 150 rev/s

Air density, ρ 1.225 kg/m3

45

Step 1: 1 1 2tan tan 0.105761

2 2 *150*0.02

V

nr

Step 2: 0.02

0.157480.127

rx

R

Step 3: ( ) 0.68329 0.105761 0.577529( ) 33.1(deg)rad

Step 4: ,l dC C values for this angle of attack are obtained from XFLR5 results

The curves obtained will be as shown below

Figure 4.14 Lift Coefficient for various Angles of Attack

-1-0.9-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.1

00.10.20.30.40.50.60.70.80.9

1

-24-22-20-18-16-14-12-10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36

Lift

Co

effi

cie

nt

Angle of Attack

Cl VS AOA

Re 10000

Re 20000

Re 30000

Re 40000

46

Figure 4.15 Drag Coefficient for various Angles of Attack

For Given Angle of Attack lC = 0.7884 dC =0.30826

Step 5:

21* *( ) * *( cos sin )

2R l ddT V cdr C C

21*1.225*(18.945) *0.0178* 0.7884cos(0.105761) 0.30826sin(0.105761)

2

2.9407dT dr

21* *( ) *( * ) *( sin cos )

2R l ddQ V c r dr C C

21*1.225*(18.945) *(0.0178*0.02) *(0.7884sin(0.105761) 0.30826cos(0.105761))

2dQ dr

00.020.040.060.08

0.10.120.140.160.18

0.20.220.240.260.28

0.30.320.34

-24-22-20-18-16-14-12-10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36

Dra

g C

oef

fici

en

t

Angle of Attack

Cd Vs AOA

Re 10000

Re 20000

Re 30000

Re 40000

47

0.030506dQ dr

Step 6:

2

1

( )

r

r

dT f r dr and

2

1

( )

r

r

dQ f r rdr

2 0.04

1 0.02

( ) ( )

r

r

dT f r dr T f r dr

Where f( r)= 2.9407 for r=0.02

Similarly we can calculate for r=0.04, f( r)=19.2476

2 0.04

1 0.02

( ) ( )

r

r

dQ f r dr Q f r dr

Where f( r)=0.030506 for r=0.02

Similarly we can calculate for r=0.04, f( r)=0.309168

Step 10: Using Trapezoidal Rule ( ) ( )

( ) ( )2

b

a

f a f bf x dx b a

For the Integration process, the trapezoidal rule has been taken. According to this formula,

2.9407 19.2476(0.04 0.02)* 0.221883

2T N

Similarly adding up the thrust components for all the elements, the total thrust is =5.011149N

1000(5.011149)* 510.82

9.81T g

And for torque, using the same formula,

0.030506 0.309168(0.04 0.02)* 0.003397

2Q Nm

48

Similarly adding up the torque components for all the elements, the total torque is =0.049055Nm

This whole process of BET has been done for various RPM and forward velocities.

The Propeller Performance characteristics i.e,

2 4T

TC

n Dand

2 5Q

QC

n D for Various Advance Ratios,

VJ

nD have been plotted.

The thrust coefficient and torque coefficient for various advance ratios.

i. For 4000RPM

Figure 4.16 Thrust Coefficient Vs Advance Ration at 4000 RPM

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Ct

J

Ct Vs J

49

Figure 4.17 Torque Coefficient Vs Advance Ration at 4000 RPM

Figure 4.18 Propeller Efficiency Vs Advance Ration at 4000 RPM

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Cp

J

Cp Vs J

0

0.1

0.2

0.3

0.4

0.5

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

ƞ

J

ƞ vs J

50

ii. For 5000RPM



0

0.005

0.01

0.015

0.02

0.025

0.03

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Ct

J

Ct Vs J

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Cp

J

Cp Vs J

51


iii. For 6000RPM


0

0.1

0.2

0.3

0.4

0.5

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

ƞ

J

ƞ Vs J

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Ct

J

Ct Vs J

52



0

0.005

0.01

0.015

0.02

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Cp

J

Cp Vs J

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

ƞ

J

ƞ Vs J

53

iv. For 7000RPM



0

0.01

0.02

0.03

0.04

0.05

0.06

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

Ct

J

Ct VS J

0

0.005

0.01

0.015

0.02

0.025

0.03

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Cp

J

Cp VS J

54


v. For 8000RPM


0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

ƞ

J

ƞ VS J

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

Ct

J

Ct VS J

55



0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

Cp

J

Cp Vs J

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

ƞ

J

ƞ Vs J

56

vi. For 9000RPM



0

0.02

0.04

0.06

0.08

0.1

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Ct

J

Ct Vs J

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Cp

J

Cp Vs J

57


4.3.2Static-Thrust Bench Analysis:

A thrust bench is a vertical retort stand to which a horizontal fixture is attached. A motor mount

is fixed to the horizontal fixture paving way for the motor to be mounted onto it. As shown in

Figure 2.13, the motor is connected to an ESC and the ESC is connected to a receiver. When

powered by the battery, the motor speed can be varied by using any user interface program such

as the EagleTree System‟s data logger or National Instrument‟s power analyzer. By varying the

voltage in the UI, the speed of the motor is varied and the thrust at each speed is tabulated in the

data logger. Apart from motor speed and thrust, input current, power delivered by the motor can

also be recorded. We have conducted a static analysis of propeller on Thrust bench at MAV

department of NAL. Here the thrust is measured using a pre-calibrated load cell of 1.5kg

capacity.

Figure 4.34 Load Cell of 1.5kg Capacity

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

ƞ

J

ƞ Vs J

58

Figure 4.35 Thrust Bench Apparatus

The results obtained are tabulated as below

Throttle

(%)

Voltage(v) Current(A) RPM Thrust(Kgf) Power Consumed

(w)

0 NA NA NA NA NA

10 NA NA NA NA NA

20 11.95 0.26 2150 0.032 3.107

30 11.86 2.2 5150 0.21 26.092

40 11.64 6.85 7675 0.495 79.734

50 11.3 15 9825 0.83 169.5

60 10.875 25.15 11275 1.108 273.50625

70 10.365 37.8 12150 1.315 391.797

80 10.1 39.5 14100 1.498 398.95

90 NA NA NA NA NA

100 NA NA NA NA NA

59

Figure 4.36 Thrust for various RPM

From the above graphs, as the speed of the motor increases, thrust increases gradually. And after

the 12000RPM, there was an aberration in the thrust value due to the motor damage.

Figure 4.37 Thrust for varying Current

In a similar fashion, current also increases with increasing thrust and reaches maximum at1.4kg.

However, the motor cannot rotate at a higher speed beyond this point as higher currents would

damage motor windings.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 2000 4000 6000 8000 10000 12000 14000 16000

Th

rust

(K

g)

RPM

Thrust Vs RPM

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 5 10 15 20 25 30 35 40 45

Th

rust

(Kg

)

Current(A)

Thrust Vs Current

60

Figure 4.38 Power for various RPM

Power also increases with speed and reaches maximum value at the highest speed. At

12000RPM it consumes a power of 400W.

Now we can compare Thrust Bench and BET results.

Figure 4.39 Comparison between Thrust Bench and BET results

0

50

100

150

200

250

300

350

400

450

0 2000 4000 6000 8000 10000 12000 14000 16000

Po

wer

Co

nsu

mp

tio

n (

W)

RPM

Power Vs RPM

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 5000 10000 15000

Th

rust

(k

g)

RPM

Thrust Vs RPM

Thrust Bench

BET

61

The BET results almost coincide with the experimental Thrust Bench analysis results. The

discrepancy in the results is due to various reasons such as

i. The airfoil coordinates obtained from CMM are not accurate.

ii. The XFLR5 results obtained are only for 2D flow whereas the Thrust Bench analysis

deals with the 3D flow over the propeller blade.

iii. The Static Thrust Bench Analysis is done on static propeller, but we are comparing these

results with BET results at 2m/s.

iv. We can obtain more accurate results if we predict the propeller performance using

Combined Blade Element Momentum Theory (CBEMT).

Finally, we can conclude from the above graph that, results predicted by BET are fairly good and

in accordance with experimental results. We can also infer that the theoretical methods are quite

good at low Reynolds number applications. Wind tunnel tests can be compared with BET

calculation with appropriate test setup in future.

62

CONCLUSION

An unmanned aerial vehicle, a tricopter, has been developed using dynamic automation and

control systems. The components used in the development of the UAV have been modeled and

validated using various software analyses. Despite meticulous and precise calculations, stabilized

flight could not be achieved due to a broken servo link rod (shown below).

63

The servo link rod is vital to control the yaw motion and its absence tends to rotate the tricopter

in the direction of rotation of the motors. The same has been experienced in this case also.

Various flight tests have been conducted and the main objective of developing a full-fledged

tricopter has been partially fulfilled.

The prospects of the project can be extended to mount a camera for real time video transmission

of affected areas. Digital image processing and wireless data transmission could be taken up as

another major project.

64

APPENDIX I

Coordinates at r = 20mm

4.214 -6.669

4.085 -6.253

3.956 -5.837

3.79012 -5.52313

3.62425 -5.20925

3.45838 -4.89537

3.2925 -4.5815

3.12662 -4.26763

2.96075 -3.95375

2.79488 -3.63987

2.629 -3.326

2.49925 -3.136

2.3695 -2.946

2.23975 -2.756

2.11 -2.566

1.97275 -2.3825

1.8355 -2.199

1.561 -1.832

1.418 -1.64925

1.275 -1.4665

0.989 -1.101

0.84 -0.92575

0.691 -0.7505

0.393 -0.4

0.23375 -0.21975

65

0.0745 -0.0395

-0.244 0.321

-0.5495 0.65

-0.855 0.979

-1.024 1.15125

-1.193 1.3235

-1.362 1.49575

-1.531 1.668

-1.699 1.837

-1.867 2.006

-2.203 2.344

-2.35 2.4785

-2.497 2.613

-2.644 2.7475

-2.791 2.882

-2.93625 2.9885

-3.0815 3.095

-3.372 3.308

-3.53125 3.404

-3.6905 3.5

-4.009 3.692

-4.17525 3.77025

-4.3415 3.8485

-4.674 4.005

-4.84875 4.064

-5.0235 4.123

-5.373 4.241

-5.73525 4.31825

66

-6.0975 4.3955

-6.45975 4.47275

-6.822 4.55

-7.0395 4.567

-7.257 4.584

-7.4745 4.601

-7.692 4.618

-7.906 4.6255

-8.12 4.633

-8.334 4.6405

-8.548 4.648

-8.758 4.633

-8.968 4.618

-9.139 4.5305

-9.31 4.443

-9.481 4.3555

-9.54988 4.04688

-9.44775 3.82575

-9.34563 3.60462

-9.2435 3.3835

-9.14138 3.16237

-9.03925 2.94125

-8.93713 2.72013

-8.835 2.499

-8.664 2.14

-8.493 1.781

-8.39075 1.602

-8.2885 1.423

67

-8.084 1.065

-7.8475 0.7

-7.611 0.335

-7.3965 0.058

-7.182 -0.219

-6.9285 -0.4735

-6.675 -0.728

-6.361 -1.0005

-6.047 -1.273

-5.7215 -1.512

-5.396 -1.751

-5.021 -1.985

-4.646 -2.219

-4.2345 -2.468

-3.823 -2.717

-3.421 -2.941

-3.019 -3.165

-2.6055 -3.382

-2.192 -3.599

-1.7385 -3.8335

-1.285 -4.068

-0.8675 -4.282

-0.45 -4.496

0.012 -4.725

0.474 -4.954

0.8815 -5.158

1.289 -5.362

1.7405 -5.562

68

2.192 -5.762

2.447 -5.88875

2.702 -6.0155

2.957 -6.14225

3.212 -6.269

3.4415 -6.381

3.671 -6.493

3.9425 -6.581

4.214 -6.669

Development of an Unmanned Aerial Vehicle - A Tricopter

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