AIAA_VALASARAPTOR

8/3/2019 AIAA_VALASARAPTOR

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1American Institute of Aeronautics and Astronautics

Design and Testing of a Quadrotor Aircraft

Nathan Calvert

University of Colorado at Boulder, Boulder, CO 80310

Kevin Basore, Cody Burkhart, Aaron Cabrera, Mikhail Kosyan,

Scott Potter, Chris Saro, Joseph Sweeney and Chris van Poollen

University of Colorado at Boulder, Boulder, CO 80310

The purpose of this paper is to introduce the overall concept of a quadrotor aircraft

and a methodology for the design, theoretical analysis, verification and validation of each

primary subsystem. The similarities and differences between a quadrotor and other vertical

takeoff and landing vehicles such as a single rotor helicopter are enumerated with an

emphasis on the inherent advantages of a quadrotor system in terms of relative feasibility,

efficiency and robustness. Details of the design phase for each subsystem is then discussed in

conjunction with associated theoretical analysis and expected performance parameters. In

addition, the results of relevant subsystem tests are presented and compared to analytical

models as a means of verifying project requirements and ensuring an optimal design given

appropriate constraints. Integration of a National Oceanic and Atmospheric Administration

(NOAA) microbarom sensor probe serves as demonstration of a practical implementation of

the aircraft. A measurement of project success is based not only on the ability of the aircraft

to physically transport the probe, but also on determining the sources and magnitudes of

potential payload interference. Lastly, this paper suggests ways in which the design and

analysis of a quadrotor vehicle can be improved.

Nomenclature

A = area of single rotor disk

CP = coefficient of power

CT = coefficient of thrust

FM = figure of merit

P = power consumed by a single rotor

T = thrust produced by a single rotor

vc = climb velocity of rotor

vh = hover velocity of rotor

vi = induced velocity of rotor

= air density

= angular velocity of rotor

I. IntroductionIRCRAFT capable of vertical takeoff and landing maneuvers have historically presented a significant

engineering challenge. Although many design concepts and configurations have been investigated, each seemsA


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to introduce a variegated array of limitations to the aircrafts operation and efficiency. Moreover, analysis of critical

design parameters has proved quite difficult due to the relatively complex and uncertain nature of the aerodynamic

and control subsystems.1

The quadrotor concept was established primarily in an effort to decouple and simplify many of the issues

that currently plague traditional vertical takeoff and landing aircraft. The basic quadrotor design consists of four

complete rotor assemblies attached at equal distances from each other and a central hub. All the rotors are located

within the same plane and oriented such that the thrust generated by each rotor is perpendicular to the vehicle as

shown in Figure 3. If the rotors are comprised of parts with the same specifications and expected performance, each

will produce the same amount of thrust given a specific power input. The angular momentum of any of the four

rotors generates a torque about the inertial center of mass of the vehicle which can be effectively counterbalanced by

the torque created from the opposing rotor.1 This configuration requires that opposite rotors spin in the same

direction while adjacent rotors spin in opposite directions. An immediate advantage to the quadrotor design is that it

is not necessary to implement additional equipment such as control moment gyroscopes with the sole purpose of

negating extraneous torques on the vehicle.1

The quadrotor offers many different advantages over other vertical takeoff and landing vehicles. The single

rotor helicopter is notoriously difficult to control and requires blades that are usually much larger than the vehicle

itself.2 The main hub is extremely complex with multiple actuating motors and a series of gears to pivot the rotor.

Tri-axis control moment gyroscopes are traditionally implemented to counteract the significant torque produced bythe main rotor in addition to tail blades and ailerons. 2 A quadrotor is able to perform all of the same functions

exclusively with fixed rotors thereby reducing the weight of the aircraft while increasing overall reliability.

Another popular option for vertical takeoff and landing is the coaxial dual rotor aircraft which relies on the

difference in angular momentum between the rotors to maneuver.1 Although the counter-rotating blades produce

virtually opposing torques, a significant amount of aerodynamic interference is incurred between the rotors resulting

in an inherently less efficient design.1 Also, it is still necessary to provide a geared or segmented shaft for the fixed

rotors thereby adding some complexity to the structure. As will be demonstrated later in this report, the quadrotor is

not only optimal in terms of aerodynamic efficiency and structural simplicity but the control algorithms are much

more straight-forward, robust and responsive than the design alternatives.

II. Aerodynamics and Rotor PerformanceThe aerodynamic performance of each rotor in a quadrotor aircraft may be analyzed with a combination of

traditional momentum theory and vortex ring state approximation.3 Momentum theory essentially assesses the

exchange of momentum between the rotating blade disk and column of air that is being accelerated through the

rotor. Several assumptions must be made to generate an analytical model of rotor performance. First and foremost,

non-dimensional coefficients were chosen based on historical data for symmetrical airfoils fixed at an angle of

attack which produces maximum lift. In Equations 1 and 2 for thrust and power consumption, CT and CP are set to

values of 0.009 and 0.008, respectively, in order to achieve an assumed figure of merit (Equation 3) of

approximately 0.75.3

=

(

)2

= ()3 = 3/22

= 3/22

(1)

(2)

(3)


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Analysis of vertical climb and descent is depicted in terms of induced-to-hover velocity and power ratios.

Momentum theory is once again applicable except in the region of induced-to-hover velocity ratio between -2 and 0

due to the dominance of vortex ring interactions.3 In this case a fourth-order polynomial is utilized to relate the

induced-velocity-to-climb-velocity ratio.3 Equations 4- 6 provide the induced-to-hover velocity ratio for vertical

climb, rapid descent and the vortex ring state, respectively. Figure 1 graphically depicts the entire spectrum of non-

dimensionalized rotor vertical motion.

= 2+ 2 + 1

= 2 2 1 = + 1

+ 2

2

+ 3 3

+ 4 4

1 = 1.125 2 = 1.372 3 = 1.718 4 = 0.655

Figure 1. Induced Velocity Ratio Profile3

In an effort to further simplify the design and increase reliability and safety of the vehicle, it was decided to

use pusher and tractor propellers that attach directly to the shaft of a gearbox which in turn interfaces with the motor.Ideal aerodynamic performance is not expected to change since the thrust calculation depends only on the area and

angular velocity of the rotor disk. Based on a total estimated vehicle mass of 10 kg, each rotor must have a diameter

of at least 34 cm (13.4 in). However, considering all possible deviations from ideal conditions it is advisable to

select a larger propeller blade.

Motor selection is a pivotal step in the design process since the decision ultimately affects nearly every

other vehicle subsystem. Although electric motors may limit the payload capacity and continuous flight duration of

the vehicle, they are necessary for model quadrotor aircraft because they provide consistent and easily regulated

(4)

(5)

(6)


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performance. The quadrotor

which was designed and

fabricated at the University

of Colorado known as

VALASARAPTOR

(Vertical Ascent and

Landing Aircraft for the

Study of Atmospherics in

Recording Acoustic

Propagation of Terrestrial

and Oceanic Radiation)

employs a NeuMotors

1115/1.5D custom-built in-

runner motor with a

maximum angular speed of

60,000 rpm at 60 A current

draw. The mass of a single

motor and gearbox withwires and connections is

only 250 g resulting in one

of the highest performance-

to-weight ratios of electric motors currently on the market. NeuMotors assembles and rigorously tests each motor

individually to verify that it performs within a very narrow margin of the expected specifications. Motor consistency

is particularly important for a quadrotor since stability of the aircraft depends solely on the difference between

rotational speeds of the four rotors.

Several independent thrust tests were performed to verify the theoretical thrust prediction for various rotor

configurations. Both 15 and 16 inch diameter APC plastic propellers with a twist of 10 inches were tested then

compared to analysis as a means of verifying rotor performance. The test stand consists of a spring-loaded motor

mount free to move horizontally on rails secured to a heavy aluminum plate. A 20 lb load cell was placed between

the motor mount and the stand base to directly measure the force generated by the rotor. The voltage output of the

sensor was recorded then processed to obtain plots of thrust as a function of current drawn by the motor as

demonstrated in Figure 2 after passing the data through a low-pass filter to remove apparatus vibration noise. A

further analysis of vehicle vibration is included in Section VI of this report.

III. Quadrotor ControlDynamic control of a quadrotor is achieved by simultaneously changing the angular velocity of opposing

rotors. For example, forward motion is accomplished by decreasing the angular speed of rotor 1 while increasing the

angular speed of rotor 3 thereby causing a torque imbalance that pitches the vehicle downward.1 Positive pitch is

achieved by accelerating rotor 1 and decelerating rotor 3 and results in backward translational motion. Due to

symmetry, a roll maneuver can be performed in the same way as pitch except by employing rotors 2 and 4 instead.In order to remain consistent with the sign convention of traditional aircraft, positive roll is defined as clockwise

rotation about the horizontal thrust axis.1

A yaw maneuver is performed by increasing the angular speed of two opposing rotors while simultaneously

decreasing the angular speed of the other two rotors.1 If rotors 1 and 3 accelerate and rotors 2 and 4 decelerate, the

vehicle will undergo yaw in a counterclockwise direction. Vertical translation is achieved by simultaneously

increasing the angular speed of all four rotors to the point where the total thrust generated exceeds the weight of the

vehicle. As expected, the quadrotor will hover if the total thrust generated is exactly equal to the weight of the

0 10 20 30 40 50 60 700

1

2

3

4

5

6

7Average thrust vs current

Thrust(lbf)

Current (amps)

Average Thrust data

Fitted line

95% Confidence level of each average point

Figure 2. Thrust of a Single Rotor vs. Motor Current Draw


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vehicle. It has been demonstrated that a vertical takeoff and landing vehicle should be able to create at least 25%

more thrust at maximum power than the weight of the vehicle in order to safely and efficiently maneuver.3

Figure 3 demonstrates the layout of a basic quadrotor aircraft along with control algorithm differential

power gains where rotor 1 is defined at the front of the vehicle and each subsequent rotor is numbered clockwise.

Figure 3. Quadrotor Layout and Control Diagram

VALASARAPTOR is piloted with the Spektrum DX7 R/C controller which has 8 programmable channels

for signal mixing and processing. Remote pilot input is transmitted to a receiver onboard the aircraft which is wired

to a separate speed controlled unit for each of the four rotors. In general, a speed controller functions by accepting

an electrical signal from the receiver to regulate the voltage delivered from the battery to the motor. The Castle

Creations Phoenix 80 speed controller contains a battery eliminating circuit (BEC) and multiple programmable

modes to protect the motor from variable battery discharge and current surge.

The nature of a

quadrotor vehicle results

in substantial moment-

arms about the x- and y-

axes, thereby

automatically stabilizing

the pitch and roll modes.1

In contrast, yaw is more

challenging to control

exclusively with pilot

input due to the lowmoment of inertia about

the vertical axis.

VALASARAPTOR will

eventually adopt a yaw

stability augmentation scheme such that yaw occurring without direct pilot input would be counteracted. The

algorithm requires detection of incidental motion from a tri-axis rate gyroscope and commands to the appropriate

motors are processed and sent by a central microcontroller.

Figure 4. Yaw Stability Augmentation Algorithm Block Diagram


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Aluminum was selected as the main structural

material due to its excellent strength-to-weight ratio,

desirable thermal characteristics and ease in precise

machining. Several bend and failure tests were performed

on the aluminum sheet and rods and it was determined that

the expected maximum forces and stresses that the vehicle

will experience are far less than those required to plastically

deform the material. The simulation in ANSYS shown in

Figure 6 revealed a maximum displacement of less than

0.47 inches per rotor arm, well within operating

requirements. Thermal analysis showed that the maximum

operational temperature reached by the speed controllers is

approximately 34 C which is far less than the melting

temperature of the plastic zip ties used to secure the

component to the central hub. Exact vehicle symmetry is

essential in the quadrotor design for stability and is most

readily achieved with a combination of precise machining

and balance of parts.Several landing gear options have been

investigated in an effort to avoid the possibility of

aerodynamic interference and accidental tipover. At first it was assumed that vertical posts connected with flat skis

would suffice, but ultimately the design was abandoned because the required probe clearance rendered the landing

gear highly susceptible to extreme entry angles and speeds. The final version consists of four aluminum rods at 45

angles with respect to the central hub attached to a plastic tube hoop approximately 1.5 m in diameter. The landing

gear acts in a similar fashion to an outrigger thereby permitting more precarious landing scenarios without posing a

risk to the vehicle.

The total mass of VALASARAPTOR without the sensor probe is approximately 6.5 kg. The mass of the

entire payload system is 2.2 kg resulting in an integrated mass of 8.7 kg (1.3 kg less than the initial estimate of 10

kg). Electrical components and wires are secured to the vehicle structure with Velcro and plastic zip ties, each of

which adds negligible mass but allows for easy integration. The overall vehicle structure was designed such that it

could be completely assembled, transported and disassembled by a single person with minimal tool requirements.

Figure 6. ANSYS Rotor Arm Bending Model

Figure 5. Assembled Quadrotor Aircraft


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VI. Payload IntegrationOne of the primary goals in designing VALASARAPTOR was the ability to transport payloads of various

dimensions and weight to extreme environments. The vehicle is currently in a configuration to carry a mock-up of a

microbarom acoustic sensor probe built and tested at the NOAA facility in Boulder, Colorado. The probeconsists of

a PVC pipe approximately 3 inches in diameter and 36 inches long. While the front half of the tube is hollow, a

majority of the second half is filled with a copper mesh that acts like an acoustic low-pass filter to eliminate high-

frequency noise entering the device. An acoustic pressure sensor is mounted near the back end of the probe which is

tuned to detect and record the propagation of pressure waves centered at a frequency of about 0.2 Hz known as

microbaroms. Wind tunnels tests of the probe assembly have shown that -17 is the optimal angle of attack when

mounted to a hovering aircraft in wind traveling at 20 m/s.

NOAA scientists are attempting to address the correlation between the characteristics of microbarom

signals and changes in hurricane intensity and the direction of travel. The objective is to create a microbaromic

database for hurricanes which have occurred throughout the Pacific Ocean over the past six years. Microbarom data

werecollected from the 157US signal array and two buoys located off of the coast of California during Category 5

Hurricane Elida in 2002. Analysis of the data demonstrated that infrasound signals are generated by a nonlinear

interaction of standing ocean waves. The theoretical microbarom frequency was calculated to be twice the frequency

of simultaneous ocean waves.NOAA has also performed infrasound studies on tornados and earthquakes. There isevidence that infrasound may provide improved warnings of tornados and act as a precursor to substantial seismicactivity. The eventual goal is to improve natural disaster diagnostic tools in an effort to protect human life and

property.

The acoustic output spectrum of VALASARAPTOR was recorded during an initial flight test to ensure that

the vehicle would not produce pressure wave frequencies that would interfere with payload operations. It was

determined that the lowest dominant frequency produced in flight is approximately 220 Hz with a peak at 74 dB

from a 100 ft range. The data from this test were taken by Dr. Alfred Bedard, leader of the NOAA infrasonics group,

and are presented in Figure 7 where the horizontal axis is time and the vertical axis represents frequency. Dr. Bedard

is convinced that the vehicle acoustic output will not corrupt the microbarom data taken by the probe.

Figure 7. Acoustic Output Spectrum of VALASARAPTOR Flight Test

Excessive vibration of the vehicle may also prohibit the probe from obtaining valid data. The thrust test

stand was designed such that vibrations originating from the rotor would be captured with the force data taken by theload cell. Obviously the sensor itself produces a certain amount of noise but at a frequency that is centered near 0

Hz. The raw data from the thrust test were processed using a Fast Fourier Transform to reveal two dominant

vibration frequencies at approximately 51 and 143 Hz as shown in Figure 8. Once again, the vibrational modes of

the vehicle in flight are not expected to inhibit the probe from taking valid infrasound data. Figure 9 demonstrates a

histogram of the thrust data after they have been filtered to eliminate vibration of the test stand. The thrust of one

rotor assembly produces an average of 6.76 lb of thrust at a standard deviation of 0.164 lb.


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Figure 8. FFT of Single Rotor Vibration

Figure 9. Histogram of Single Rotor Thrust

VII. ConclusionThe VALASARAPTOR quadrotor aircraft was successful in accomplishing each of the initial project

goals. First and foremost, the system achieved vertical takeoff and landing and is capable of a full range of

translational motion as described within the control section of this report. Secondly, VALASARAPTOR is able to

0 20 40 60 80 100 120 140 160 1800

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Frequency (Hz)

|Y(f)|

FFT of unfiltered data

6.2 6.4 6.6 6.8 7 7.2 7.4 7.6 7.8 80

50

100

150

200

250

#

ofbins

Thrust (lbf)

Filtered Data


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transport an acoustic probe to gather pertinent data without interference. Preliminary data suggest that the actual

acoustic output of the vehicle is considerablyabove the minimum requirement set by the project customer while

vibrations produced by the rotors are not a concern for structural stability and payload integration.

Future work on the vehicle would most likely entail closed-loop control, whether in the form of yaw

stability augmentation or active control for all six degrees-of-freedom. Although VALASARAPTOR is controlled

exclusively from remote pilot input, adding closed-loop stability control would permit operation by less experienced

pilots or in more extreme environments such as the perimeter of a hurricane or tornado. Also, a larger capacity

power supply could be placed within the system to provide longer endurance than is currently possible.

Lastly, it could be feasible to streamline the manufacturing and assembly process to make the vehicle

available on a commercial scale. The entire cost of the project including spare parts, integration and testing totaled

less than the $4,000.00 initial budget. The cost of a second identical system would be further reduced by reusing test

apparatusand eliminating non-essential spare parts while relying on experience gained from the prototype. Current

off-the-shelf multiple-rotor model aircraft can cost in excess of $15,000; therefore, the VALASARAPTOR system

would be a very competitive addition to the market.

Acknowledgments

The authors of this report would like to acknowledge their faculty advisors at the University of Colorado at

Boulder, Dr. Donna Gerren and Dr. Eric Frew. They would also like to thank Dr. Al Bedard, Trudy Schwartz and

Matt Rhode for providing guidance and support in the project.

References

1Castillo, Lozano & Dzul, Modelling and Control of Mini-Flying Machines, 2005 Springer

2Done & Balmford, Bramwells Helicopter Dynamics, 2

nd Edition, 2001 AIAA

3J. Gordon Leishman, Principles of Helicopter Aerodynamics, 2000 Cambridge University Press

4John Seddon, Basic Helicopter Aerodynamics, 2nd Edition, 2001 AIAA

5Analog Devices, ADIS16350 Data Sheet, Revision A, 02/2008

6Parallax Industries, BASIC Stamp 2e Data Sheet, Revision E, 08/2007

7Parallax Industries, Memory Stick Datalogger, Revision 1.1, 2008

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