Project Proposal & Feasibility Study
Team 2: 3-D Delivery
Jeff DeMaagd, Kemal Talen, Ross Tenney
ENGR 339/340 Senior Design Project
Calvin College
December 8, 2014
© 2014, Team2: 3-D Delivery and Calvin College
Executive Summary
The 2014-2015 Calvin College senior design team 3-D Delivery (team two), consists of members Jeff
DeMaagd, Kemal Talen, and Ross Tenney. All three team members are senior mechanical engineering
students. In this report, 3-D Delivery is proposing a project to design a multi-copter that can pick up, carry,
and drop off a 3 pound payload. The following pages outline the project’s feasibility and presents design
solutions to key design areas of the project such as frame design, electrical equipment selection, motor
thrust requirements, lifting mechanism design and landing gear design. The team also proposes that a
majority of the parts be made from 3-D printed materials, which allow for customizable geometries and
easily replaceable parts. The proposed design is being presented with stewardship, cultural appropriateness
and integrity in mind.
Table of Contents
1. Introduction
1.1 Senior Design and Project Introduction
1.2 Biographies
2. Problem Definition
2.1 Problem Statement
2.2 Objective
3. Project Management
3.1 Team Organization
3.2 Team Meetings
3.3 Schedule
3.4 Budget
3.5 Method of Approach
4. System Architecture
5. Design Norms
5.1 Cultural Appropriateness
5.2 Stewardship/Sustainability
5.3 Integrity
6. 3-D Printing
6.1 Reasons/Requirements
6.2 Material Comparisons
6.3 3-D Printer Capabilities/Options
7. Propeller Thrust & Motor Selection
7.1 Design Criteria
7.2 Design Alternatives
7.3 Selected Design
8. Electronic Interface
8.1 Design Criteria
8.2 Roll, Pitch, and Yaw
8.3 Micro-Controller
8.4 Electronic Speed Control
8.5 Materials
8.6 Design Alternatives
8.7 Selected Design
9. Frame Design
9.1 Design Criteria
9.2 Design Alternatives
9.3 Selected Design
10. Landing Legs Design
10.1 Design Criteria
10.2 Stress Analysis
10.3 Materials
10.4 Design Alternatives
10.5 Selected Design
11. Finite Element Analysis
12. Vibration Analysis
12.1 Theoretical Analysis
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12.2 Results
13. Package Attachment Mechanism (PAM)
13.1 Design Criteria
13.2 Design Alternatives
13.3 Selected Design
14. Cost
15. Test Plan
15.1 Impact Testing
15.2 Hover Stability Testing
15.3 Hover Time Testing
15.4 Flight Time Testing
15.5 PAM Safety Testing
15.6 Wind Simulation Testing
16. Safety
16.1 Public Safety
16.2 FAA
16.3 Safety Precautions
17. Conclusion
18. Acknowledgments
19. References/Bibliography
20. Appendices
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Table of Figures
Figure 3.1 Team organization chart
Figure 4.1 UAV System Architecture
Figure 6.1. ABS and PLA Tensile Test Dog bone Dimensions
Figure 6.2 ABS and PLA Tensile Test Stress vs. Strain
Figure 6.3 ABS and PLA Tensile Test Young’s Modulus
Figure 6.4 ABS and PLA Tensile Test Yield Strength
Figure 6.5 ABS and PLA Tensile Test Specific Strength
Figure 6.6 ProJet 3500 Series 3-D Printer
Figure 6.7 MakerBot Replicator 2X 3-D Printer
Figure 6.8 Cube 3-D Printer
Figure 7.1 Propeller Thrust
Figure 7.2. Total Lift Force of UAV in Relation to the Power per Motor
Figure 7.3. Selected 14 Inch Diameter and 4.7 Inch Pitch Propellers
Figure 7.4 Selected Tarot 4114/320 kV Motor
Figure 7.5 Selected LiPo 4000mAh -20/30c 7S battery
Figure 7.6 eCalc Final Configuration Model Data
Figure 7.7 eCalc Final Model Motor Characteristics
Figure 8.1 UAV Pitch, Roll, and Yaw
Figure 8.2 Electronic Interface for Basic Quad-Motor Configuration
Figure 9.1 Early Wooden Prototype
Figure 9.2 CAD Model of Motor Mount
Figure 9.3 CAD Model of UAV Body
Figure 9.4 CAD Model of Carbon Fiber Tube
Figure 9.5 UAV in its 4 arm configuration
Figure 9.6 UAV in its 8 arm configuration
Figure 9.7 CAD Model of Cover
Figure 9.8 Basic Dimensions of UAV
Figure 10.1 CAD Model of Landing Leg
Figure 11.1 FEA of 3 Foot drop on one arm assembly
Figure 11.2 FEA Analysis on leg
Figure 11.3 FEA Analysis on body
Figure 13.1 PAM design
Figure 13.2 Prototype Concept Design
Figure 13.3 Free body diagrams of peg-sphere and clamping lever arm(s).
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Table of Tables
Table 6.1 ABS and PLA Material Characteristic Comparison
Table 6.2. VisiJet Material Properties
Table 7.1. Performance for a Tarot 4114/320kV Motor with 15 Inch Propellers
Table 7.2. UAV Configuration and Setup Design Criteria Values
Table 8.1 Controller Board Functionalities and Cost
Table 10.1 Curved beam properties for PLA for 0.25” x 0.75” cross section and 20” radius of
curvature
Table 14.1 Propulsion Costs
Table 15.1 Impact Testing Results Rubric
Table 15.2 Hover Testing Results Rubric
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1.
Introduction
1.1.
Senior Design and Project Introduction
This year for the Calvin College Engineering department, Team 2, 3-D Delivery, will be working on an
Unmanned Aerial Vehicle (UAV) designed for small package delivery. The project will be supervised by
Professor Nielsen (M.E.) and various cross-disciplinary engineering faculty members. The main goal of
this project is to build and design a UAV that is safe, functional, and capable of performing the task of
remotely picking up and delivering a package.
The senior design course ENGR 339/340 is aimed to develop undergraduate senior engineering students in
areas of team building, project design and implementation, and oral/written communication. During the
duration of the course, the team will develop a Project Proposal & Feasibility Study, a team website and
poster, a final report/presentation, and display the final design at the Engineering Senior Design Fair in May
2015. The engineering department at Calvin College hosts the fair which exhibits all of the senior design
projects.
1.2.
Biographies
1.2.1. Jeff DeMaagd
Jeff DeMaagd is a senior engineering student in the mechanical concentration. He lives in Grand Rapids,
Michigan with his wife and two daughters. His engineering interests lie in rapid prototyping and new
product design and development, especially in industries where form and function meet. He is interested in
learning more about the emerging technologies of 3-D printing and commercial UAVs.
1.2.2. Kemal Talen
Kemal Talen is an engineering student in the mechanical concentration with a math minor and is pursuing
an honors designation. His hometown is Bethesda, Maryland. He is interested in learning about the
utilization of mechatronic systems in engineering, specifically 3-D printing. Some of his engineering skills
include stress and deflection analysis of beams, control systems design and optimization, and
thermodynamic analysis of power cycles.
1.2.3. Ross Tenney
Ross Tenney is an engineering student in the mechanical concentration with a math minor and international
designation. His hometown is Shoreview, Minnesota. After graduating from Calvin College, he desires to
enter the career field of the automotive, aerospace, defense, or biomedical industry. His interests correlating
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to the senior design project are 3-D printing, propeller thrust, machinery dynamics, plastics properties, and
stress and deflection analysis.
2.
Problem Definition
2.1.
Problem Statement
The Federal Aviation Administration (FAA) is scheduling to integrate UAVs into U.S. airspace by
September 2015.1 Currently, drones are a technology that has been limited to governments and hobbyists;
however, with the upcoming opening of U.S airspace to commercial UAVS, UAV technology will likely
become very popular. One of the reasons companies want to utilize UAV technology is that they are able
to go places where it is not necessarily safe or economical for people or large machines to go. UAVS have
many commercial applications because of their relatively small size and ability to fly without an on-board
pilot.1
There are many future possibilities for UAV’s commercial applications. One of the main applications is the
delivery of small packages. UAVs would allow businesses to ship and send packages of their products
directly to their customers without the need of human interference. Another application would be internet
service provided by solar-powered drones. The solar-powered UAVs would provide wireless internet all
around the world acting as movable wireless access points. UAVS can also be used for covering news
stories. The UAV’s could cover news events that normally would be a high-risk situation for news reporters.
Also, commercial UAVs have a large application in photography and video documentation. UAVs would
be able to acquire photos and video footage that normally would be impossible to gain. Agriculture would
also benefit from the capability of UAVs to monitor large areas of land remotely. Finally, UAVs would be
very beneficial for the public services domain of search and rescue missions that are normally very
dangerous for law enforcement.
Currently the design for drones is very one-dimensional and does not meet the variability associated with
commercial applications. For example, for commercial photography and video documentation, different
UAVs are needed for varying camera sizes and weights such as 4 arm/propeller drones for lighter cameras
and 8 arm/propeller drones for heavier camera setups. As a result, customers would need to invest in
different drones for different lifting capabilities. Furthermore, the current designs of drones are not fully
optimized in areas of material science, manufacturing/production, assembly, customization, ease of use,
impact strength, and modularity. In addition, the production of UAVs does not fully utilize the capabilities
of 3D printing in producing the structural parts. 3D printing is a growing field that currently is used in
industry for rapid prototyping, but some manufacturing facilities are using 3-D printing because of its
efficiency, customization tailoring capabilities, and sustainability. In conclusion, there is increasing demand
for UAVs in commercial industries to which drone engineering can be tailored for certain applications.
2.2.
Objective
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In order to meet the requirements of the customer and respond to the up-and-coming field of commercial
drone use in the United States, our design team plans to design and produce a 3-D printed drone multicopter. Creating a revolutionary design drone involves technical hurdles that can be overcome by engineers.
The main design function of the drone would be to have a modular design. This entails that the UAV will
have the ability to easily transform into multiple different rotor configurations to meet the lift needs of the
consumer based on previously stated commercial applications. The drone would be able to transform from
having 4 arms/rotors to 8 arms/rotors.
The drone would also have the function of package delivery for commercial use. The UAV will be able to
lift, deliver, and drop off a package of goods directly to the customer. The drone will be able to release the
package from the control device without human physical assistance. As a result, a package attachment
mechanism (PAM) will need to be designed.
For producing the drone, the team believes that the use of a 3-D printer would be very beneficial. The
structural parts will be designed and produced using a 3-D printer. The parts can easily be reproduced if
broken or worn out. Also, parts can be updated and further optimized without expensive tooling changes
allowing for easy design iteration. The use of a 3D printer allows for iterative design and complex
geometries that are not easily achieved through traditional manufacturing methods. Finally, the structural
drone parts would be compiled in an online library for commercial use.
3.
Project Management
3.1.
Team Organization
The 3-D Delivery team consists of three senior level mechanical engineering students. The team broke up
the tasks based on the interests and experiences of each team member as shown in Figure 3.1.
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Team 2
Jeff
DeMaagd
Kemal
Talen
Ross
Tenney
Frame
Design
Electronics
3D-Printing
PAM
PAM
Thrust and
Setup
Figure 3.1 Team organization chart
3.2.
Team Meetings
Team meetings were held each Monday to review the project schedule and go through the meeting agenda.
The previous week’s meeting minutes were used as the agenda and all of the action items assigned the
previous week were reviewed and documented. New action items were then added to the minutes. These
action items were assigned to one or more of the team members and the agreed upon due date was noted.
The project schedule was used to inform what new items needed to be added to the meeting minutes.
Completed action items that were complete the previous week were removed. These meeting minutes are
kept in the team’s Google Drive folder.
3.3.
Schedule
Microsoft Project was used to schedule the required activities and was managed by Jeff. The project was
broken into major topics and each topic was broken into sub-topics when appropriate. The required duration
of the work was then estimated and the critical path was mapped out using the “Predecessor” function. The
team reviewed the project schedule each week at the team meetings and upcoming items were noted in the
meeting minutes with action items assigned to team members. Contingency days were added to each major
section of the project for unforeseen circumstances. Schedule issues were addressed in team meetings and
schedule adjustments were made by the team during the meeting. The schedule from Microsoft Project is
shown in Appendix A.
3.4.
Budget
A budget was determined by the team based on the research that was done and was maintained by Ross.
The team reviewed the budget during the Monday team meetings, and any budget problems were addressed
at those meetings. The budget was kept in a Microsoft Excel spreadsheet. Both predicted and actual
numbers were kept on that sheet, and the actual cost of items informed changes to the predicted cost of
items.
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3.5.
Method of Approach
The team decided to use a method of collaboration to inform all individuals of each other’s activities. The
team met before any major research or design work was done and agreed upon the direction. Individual
team members were then assigned work; they did this work while keeping in mind the direction agreed
upon by the team.
The project was broken into sections, including materials, rotor and electronic configurations, safety and
sustainability. The individual team members were tasked to do the research for their respective sections.
Each team member would then present their findings to the team, and the team would decide which design
direction to go. A team member was then tasked to pursue that design.
An atmosphere of openness and respect was important to the team. The team did not want to stifle ideas by
being overly critical. All ideas, no matter how “out there” they were, were received by the team with respect
and were discussed. This was done to ensure no team member felt like they had to keep their ideas to
themselves for fear of being ridiculed.
4.
System Architecture
The UAV system breakdown is shown in the block diagram of Figure 4.1. The UAV system is broken down
into three main sections, the electronics, frame, and PAM. The electronics involve aspects that give the
UAV the power to fly, control attitude, and receive user control inputs. The electronic interface is broken
down into further design sections of flight control configuration, wiring and soldering, and tuning and
calibration. The frame design is heavily dependent on the weight-to-thrust ratio of the UAV. The frame
also incorporates the use of 3-D printed plastic materials for the sections of the body, motor mounts, and
landing legs. The PAM involves the main function of the UAV for picking up, carrying, and releasing
packages. The PAM design breaks down further into areas of the package, spring clamping mechanism,
and the accepter cone.
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UAV
Electronics
Frame
Package
Attachment
Mechanism
Flight Controller
Configuration
Body
Package
Wiring and
Soldering
Landing Legs
Spring clamping
mechanism
Tuning and
Calibration
Motor Arms
Accepter Cone
Figure 4.1 UAV System Architecture
5. Design Norms
There are three main design norms that apply to the scope of this project: cultural appropriateness,
sustainability, and integrity.
5.1.
Cultural Appropriateness
In the last couple of years, the general public has been exposed to news about military drone attacks and
more significantly, the covert operation of these drones. Therefore, there is a certain negative predisposition
towards the use of drones for delivery. The design decisions made incorporated the importance of cultural
appropriateness into the design. For example, when delivering packages, the UAV must not fly directly
over people’s houses as this raises concerns of privacy and even safety. Furthermore, the UAV must have
an extremely safe PAM that ensures the package does not detach from the UAV during flight. The UAV
must also be quiet enough so as not to disturb others.
5.2.
Stewardship/Sustainability
The design of the UAV incorporates sustainable features, such as PLA material and modular arm
attachments. PLA material is an industrially recyclable material that is made from corn, potatoes, or sugar
beets. The material is also very strong and is a great material for small-scale hobby projects.
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The design of the frame of the UAV will incorporate a modular arm attachment mechanism that will allow
for arm configurations of four or eight arms. For all users who want to lift a 3 pound package, the four arm
configuration will work. The eight arm configuration will be an optional configuration that the customer
will have to purchase new motors and/or batteries for.
Furthermore, having most of the parts 3-D printed will mean that customers who own 3-D printers will not
have to drive to the store to purchase parts or order parts online. As a consequence, customers will usually
be able to enjoy their UAV without having to wait 3-5 days for parts.
5.2.
Integrity
Finally, having a design that is robust and resistant to impact collisions is the last design norm that
influenced the design decisions for this project. The UAV must also be stable during flight and be extremely
stable when attempting to pick up packages on the ground. The throttle must feel intuitive and natural to
the customer when flying with or without a package attached. The design must be full-proof and error-free.
Furthermore, the design calculations must be double-checked against other reliable sources to ensure
accuracy and trust in the design.
6.
3-D Printing
6.1.
Reasons/Requirements
A critical component of the team’s desired outcomes for the drone design is that it incorporates 3-D printing
for a significant portion of the drone.
3-D printing facilitates an iterative design approach. Parts can be designed on the computer and printed
over the course of a few hours. The part can then be reviewed and tested in its final form. Any changes can
then be made, and the part can be printed and reviewed again. This also allows for replacement parts to be
quickly made when parts fail or break. This means that the replacement parts do not need to be kept in stock
and only parts that need to be replaced are made.
A second reason for using 3-D printing is its ability to make complicated parts without needing expensive
tooling, or without needing to spend a lot of time and money having a machinist make it. This works really
well for parts that are low volume or highly customizable.
According to many 3-D printing proprietary resources, including Proto Paradigm’s research, “For a material
to prove viable for 3-D Printing, it has to pass three different tests: initial extrusion into Plastic Filament,
second extrusion and trace-binding during the 3-D Printing process, and finally end use application.” 1 In
order to pass the first test, each plastic’s material properties must allow the plastic to form properly into the
3-D Printer feedstock called the plastic filament. Once inside the plastic filament, in order to pass the second
test, the plastic must process well during 3-D printing to produce accurate parts. Finally, passing the third
1
“The Difference Between ABS and PLA for 3D Printing.” ProtoParadigm. N.p., n.d. Web. 07 Nov. 2014
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test requires that the completed 3-D printed plastic piece matches the requirements of its desired application,
which in our design includes elements such as strength, durability, temperature-resistance, modularity,
sustainability, and aesthetics. 2
6.2.
Material Comparisons
There are three main 3-D printable plastics to consider when implementing into the UAV design: ABS,
PLA, and acrylic. Each type of printed plastic has certain advantages and disadvantages.
Acrylonitrile butadiene styrene (ABS) is a thermoplastic made from petroleum-based products. As a
thermoplastic, the plastic can become soft and moldable when heated while returning to a solid when
cooled. ABS can produce very accurate parts, however, there can be some part warping characterized by
the surface of the part curling upwards. This occurs when the part is in direct contact with the print bed and
the print bed is not heated and/or smooth. ABS can also have warping at surface edges if there is not
sufficient air cooling on the part. ABS has characteristics of high strength, flexibility, machinability, and
higher temperature resistance when compared to PLA.3
Polylactic Acid (PLA) is a thermoplastic made of corn-starch and sugar cane. It is also a thermoplastic that
reacts similar to heating and cooling like ABS. There are a few differences between ABS and PLA in terms
of part accuracy. PLA generates much less part warping when compared to ABS because it melts at a lower
temperature. A lower melting temperature provides sharper details when cooled as well as stronger layer
binding during the printing process. PLA has characteristics of high strength, rigidity, fast printing speed,
sharper printed corners, and pleasing aesthetics. A summary characteristic comparison table for ABS and
PLA is shown in Table 6.1.
2
3
“The Difference Between ABS and PLA for 3D Printing.”
"3D Printer Filament Buyer's Guide." ProtoParadigm. N.p., n.d. Web. 09 Nov. 2014.
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Table 6.1 ABS and PLA Material Characteristic Comparison3
There is also a significant difference between using a line pattern and honeycomb pattern printing geometry
for ABS and PLA 3-D printed plastics. In “Fabrication of FDM 3D objects with ABS and PLA and
Determination of their Mechanical Properties,” Enno Ebbel and Thorsten Sinemmann created a dog bone
tensile test for determining the material properties of 3D-Printed ABS and PLA with both line and
honeycomb patterns. The tests were for various common 3D-Printers such as Felix 1.0e, CB-printer, and
uPrint Plus. The dog bone dimensions are shown in Figure 6.1. Diagrams for Stress-Strain, Young’s
Modulus, and Yield Strength and Specific Strength are shown below in Figures 6.2, 6.3, 6.4, and 6.5,
respectively.
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Figure 6.1. ABS and PLA Tensile Test Dog bone Dimensions4
Figure 6.2 ABS and PLA Tensile Test Stress vs. Strain7
4
Ebbel, Enno, and Thorsten Sinemman. "RTejournal - Forum Für Rapid Technologie." Fabrication of FDM 3D
Objects with ABS and PLA and Determination of Their Mechanical Properties —. RTejournal, 2014. Web. 09 Nov.
2014.
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Figure 6.3 ABS and PLA Tensile Test Young’s Modulus7
Figure 6.4 ABS and PLA Tensile Test Yield Strength7
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Figure 6.5 ABS and PLA Tensile Test Specific Strength7
Based on the data in the foregoing diagrams, PLA Lines from the Felix Printer has the highest Young’s
modulus, yield strength and specific strength. PLA lines has a high yield strength, but is more brittle than
other thermoplastics. Therefore, PLA components in the design will fracture very close to the yielding
value, which will influence the design decisions made in the stress analysis.
Another alternative option for 3-D printable plastics is the less-used Acrylic, specifically the VisiJet line of
acrylic based plastics. VisiJet plastics are known for strength, part accuracy and high-definition, toughness,
high temperature resistance, durability, stability, water tightness, biocompatibility, and machinability. A
chart of the material properties for the VisiJet line of plastic materials is shown in Table 6.2. A full
comparison of the three main options can be seen in Appendix B. It should be noted that the VisiJet M3-X
black thermoplastic (available at Calvin College) has a slightly lower tensile strength (35.2 MPa) than PLA
lines (40 MPa – Figure 6.2).
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Table 6.2. VisiJet Material Properties5
6.3.
3-D Printer Capabilities/Options
In order to produce 3-D printed plastic parts, the team needs to utilize the best 3-D Printer available. There
are three 3-D printers that are accessible to the team: Calvin College’s ProJet 3510, and GR Makers Cube
and MakerBot Printers. Each 3-D printer has advantages and disadvantages regarding plastic material use,
printing methods, printing time, cost, platform size, and part resolution.
Calvin College currently owns a ProJet 3500 in the Engineering Building shown in Figure 6.6. The ProJet
3500 only uses its own VisiJet line of plastic materials as previously mentioned. According to Calvin
College Engineering Department Metal and Wood Shop Supervisor, Phil Jasperse, the printing method of
the ProJet involves multi-jet printing (MJP) in which the printer head prints layers of UV curable liquid
plastic onto the platform, which has wax support material jetted into fill voids of the part structure.
Afterwards, the UV lamp flashes to solidify material creating a fully cured plastic part. The support wax is
then melted away leaving the finished printed part. As a result of the need of support wax, there has to be
two holes within the part material design in order to drain the wax and have an air hole. These holes could
possibly be stress risk areas for the plastic part design. The ProJet Printer costs $170 per pound of VisiJet
plastic material and takes seven hours per inch in the vertical axis to complete. In summary, the ProJet is
very expensive and time-consuming. The platform size for the ProJet 3500 is 11.75 x 7.3 x 8 inches which
is relatively small, but this is a constraint the team will have to work within when producing certain 3-D
printed plastic parts. For part accuracy, the ProJet 3500 is recognized for producing very precise and highresolution parts with a resolution of 375x 375 x 790 DPI; 32 micro layers.
5
Precision Productivity. N.p.: 3DSystems, n.d. Projet 3500 SD. 3DSystems Corporation. Web.
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Figure 6.6 ProJet 3500 Series 3-D Printer
The next option of available 3-D Printers is GR Makers’ MakerBot Replicator 2X shown in Figure 6.7. The
MakerBot Replicator 2X is capable of printing PLA and ABS thermoplastics. The printing method involves
Fused Deposition Modeling (FDM) which produces parts by extruding beads of material through a nozzle
which hardens immediately to form layers.6 The printing time would be significantly less than the ProJet.
Through GR Makers, the cost of printing would only be dependent on a $30 per person per month
membership fee and is independent of material use. The platform size of the MakerBot Replicator 2X is
9.7 x 6.0 x 6.1 inches, which is somewhat smaller than the ProJet 5300. Although the part accuracy is
excellent, based on the printing method and printing time, the part layers are not fused together as well as
the ProJet 3-D Printer and only has a layer resolution of 100 microns (about 3 times the resolution of the
ProJet 3-D).
6
“FDM Technology.” About Fused Deposition Modeling. N.p, n.d. Web. 09 Nov. 2014
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Figure 6.7 MakerBot Replicator 2X 3-D Printer7
The final option for 3-D Printers is GR Makers’ Cube Printer shown in Figure 6.8. The Cube 3-D Printer
has the same material capabilities, FDM printing method, printing time, and printing cost as the MakerBot
Replicator 2X. The platform size for the Cube 3-D Printer is 6 x 6 x 6 inches, which is significantly smaller
than the other alternatives. The part resolution is similar to the MakerBot Replicator 2X.
Figure 6.8 Cube 3-D Printer8
7
"MakerBot Replicator 2 Desktop 3D Printer." MakerBot. N.p., n.d. Web. 09 Nov. 2014.
"Cube 3d Printer Technical Specs -www.cubify.com." Cube 3d Printer Technical Specs -www.cubify.com. N.p.,
n.d. Web. 09 Nov. 2014
8
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The 3-D printer and material selection will be determined by all these factors, specifically on the applicable
material to be used and the platform size constraint. Each individual design component of the UAV will
have varying uses of plastic based on these same constraints relative to the application. These will be
described in later design sections.
7.
Propeller Thrust & Motor Selection
7.1.
Design Criteria
In order for the UAV to achieve flight, it needs to have enough thrust to lift off of the ground, hover, and
maneuver in the air. For multi-rotor aerial vehicles, the rotor disk is generally oriented such that the force
is called lift instead of thrust. As shown in the Figure 7.1 below, the source of thrust is from the propeller
propulsion system. The thrust is caused by a change of pressure across the propeller disk which can be
rewritten in terms of a velocity change using Bernoulli’s equation. The general correlation is that the larger
the propeller disk area, also called the propeller sweep area, the larger the lift/thrust force.
Figure 7.1 Propeller Thrust9
Equation 7.1 shows the general thrust force equation used for the UAV system. The velocity portion of the
equation is just the change in velocity across the propeller disk. The exit velocity can be approximated to
be the pitch speed of the propeller.
𝟏
𝑭𝒍𝒊𝒇𝒕 = 𝟐 𝝆
𝝅𝒅𝟐
(𝒗𝟐𝒆
𝟒
− 𝒗𝟐𝒐 )
(7.1)
In order for the UAV to have enough thrust to hover, the total force weight of the UAV has to equal the
thrust force. However, the UAV needs to also have enough thrust force to lift off and maneuver; thus, the
thrust force equaling the UAV system weight will not be sufficient. The general consensus is that to have
9
“Propeller Thrust.” Propeller Thrust. N.p., n.d. Web. 09 Nov. 2014
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enough throttle space for lift and maneuverability, the throttle force needs to be around twice the all-up
weight (weight including electronics) of the UAV and attached package.
The design criteria for propeller thrust is to select a propeller diameter and motor in order to have enough
thrust force to lift the UAV and package with reasonable maneuverability. In addition, the motor needs to
be working towards the highest efficiency possible at maximum power usage and also at hover. Next, the
linear throttle needs to be less than 80 percent in order to have enough space for maneuverability, which
involves tilting therefore decreasing the thrust force of the UAV. Preferably, the throttle will be around 50
percent at hover without the package and less than 80 percent with the attached package.
Another main portion of the design criteria of the propeller motor configuration is to have around 10
minutes of flight time when the UAV is carrying the package. This designed time will be enough time to
attach, carry, and release packages to desired locations within a local range of a campus. Other design
considerations are to choose a configuration that has a maximum power that does not exceed the limit of
the motor and the critical temperature for overheating. The design of the motor mounts, which will be
printed using 3-D printable thermo-plastics, must also account for the risk of plastic distortion during high
power maneuvers.
In addition, there are also design criteria for the propeller size and number of motors/arms in terms of the
frame and material selection. The larger the propeller size, the longer the arms that hold the motors need to
be away from the main body of the UAV since there needs to be clearance between adjacent propeller
blades. For a larger amount of motors/arms, there also needs to be longer arms as there is less space between
adjacent arms. As a result, there are design obstacles for the length of possible plastic arms needed. The
length of arm is constrained by the 3-D Printer platform size and the maximum stresses and impact forces
due to external forces. There also is an additional cost for more motors, propellers and arm material if an
eight arm multi-copter is to be built. Therefore, if the desired criteria are for lifting the additional package
with a low cost, then an additional design goal would be to limit the size of the propellers and number of
motors/propellers.
7.2.
Design Alternatives
7.2.1. Approach
The process for finding the proper motor and propeller configuration first involves the determination the
amount of power needed by each arm motor in order to lift the entire all-up weight of the UAV. The all up
weight is the total weight of the UAV, including the extra weight of the package. Based on methods by
Professor of Aeronautical Engineering, Dr. Barnes W. McCormick10, and the equations shown below by
helicopter flight emulator production company, Heli-Chair11, the theoretical thrust generated by a propeller
or rotor can be calculated.
10
McCormick, Barnes Warnock. Aerodynamics of V/STOL Flight. Mineola, NY: Dover Publications, 1999. Print
"Helicopter Aerodynamics, Calculating Thrust Loading, Disk Loading, Power Loading." Heli-Chair. N.p., n.d.
Web. 06 Dec. 2014.
11
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Equation 7.2 shows the lift per individual motor by assuming the maximum lift needs to be twice the weight
of the drone with variable N equaling the number of arms.
𝑳𝒊𝒇𝒕𝒎𝒐𝒕𝒐𝒓 =
𝟐𝑾
𝑵
(7.2)
The next step is to determine a parameter called power loading in units of horsepower per square foot. The
power loading is defined as the mechanical power delivered to the propeller per unit area of propeller.
Power loading is calculated using Equation 7.3.
𝑷𝑳𝒐𝒂𝒅𝒊𝒏𝒈 =
𝑷
𝑨
(7.3)
After finding the power loading parameter, McCormick’s empirically defined formula is used to calculate
thrust loading, which is in units of pound-force per horsepower, and is a function of power loading. Thrust
loading is calculated using Equation 7.4.
𝑻𝑳𝒐𝒂𝒅𝒊𝒏𝒈 = 𝟖. 𝟔𝟖𝟓𝟗 ∗ 𝑷𝑳𝒐𝒂𝒅𝒊𝒏𝒈 −𝟎.𝟑𝟏𝟎𝟕
(7.4)
The next equation involves finding the thrust loading and lift per individual motor and relating it to the
power needed for each motor while including an estimate for the efficiency, η, of the motor. The electrical
power needed for each motor is calculated in Equation 7.5.
𝑳𝒊𝒇𝒕𝒎𝒐𝒕𝒐𝒓
𝑳𝒐𝒂𝒅𝒊𝒏𝒈 𝜼
𝑷=𝑻
(7.5)
These equations were then solved in EES with varying all-up weights of the UAV, number of arms from
four to eight arms, and propeller sizes in a range of eight to sixteen inch diameters to determine the power
needed per motor. The EES calculations are in Appendix C.
The following graph, Figure 7.2, shows the total lift force produced per watt of electrical power delivered
to each motor. The total lift is produced from four equal power motors of 85% efficiency. This curve was
used to determine a suitable power per motor requirement when evaluating a motor’s peak power rating
(20% greater than the continuous power rating). The estimated weight of the UAV with a 3 pound package
and four motors was determined to be 11 pounds. The markers on the graph are used to indicate the
necessary power required to produce double the weight in thrust.
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Figure7.2. Total Lift Force of UAV in Relation to the Power per Motor
7.2.2. Thrust Calculations Synthesis Method
The different combinations of estimated weight, number of rotors, propeller diameter, and motor power
needed were entered into the Multicopter Calculator “eCalc” to determine the best possible outcome based
on the propeller thrust and motor configuration desired criteria.12 The calculations done by eCalc were later
confirmed afterwards by the team using methods of McCormick and common power-thrust and battery
calculations. The calculations for confirmation of results are also shown in Appendix C.
Within the eCalc multi-rotor calculator, there were general trends determined for alternative solutions: 1.)
Increasing the diameter of propellers causes an increase in motor power. 2.) Increasing the number of arms
with propeller diameter constant, the smaller the motor power becomes. 3.) An increase in propeller
diameter will increase the flight time. 4.) The flight time is also dependent on the motor power and will be
the highest at a certain range of optimal efficiencies.
With a higher kV motor selection, the larger the current and smaller the voltage, usually causing a larger
power outcome. With too high of a power, the maximum power used by the motor can be over the limit of
the motor. If too small a power, there will not be enough available power sufficient to hover. With too large
a current, the maximum current will go over the limit of the speed controller and battery selected.
Muller, Markus. “ECalc-the Most Reliable RC Calculator on the Web.” ECalc-the Most Reliable RC Calculator
on the Web. N.p., n.d. Web. 09 Nov. 2014.
12
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7.3.
Selected Design
Based on the calculations for motor thrust, the determined optimal design selection to carry the three pound
package was determined to be a quad-coptor UAV with a propeller size of 14 inches and pitch of 4.7 inches
shown in Figure 7.3. The pitch is described as the distance a propeller would move in one revolution if it
were moving through a soft solid, like a screw through wood. A higher pitch reaches a higher maximum
speed, but at a slower acceleration. The selected motor was a Tarot 4114/320 kV shown in Figure 7.4. In
addition, a chart for the Tarot motor with a 15 inch propeller blade was provided in Table 7.1. The chart
shows various performance data for the 15 inch propellers. Knowing that the RPM will increase for a
smaller propeller diameter, the team determined an average performance value of around 7000 rpm for the
selected 14 inch propeller when doing the calculations, which therefore correlated nicely with the eCalc
values. The optimal battery was a LiPo 4000mAh -20/30c 7S-2P battery shown in Figure 7.5. The full
specifications and theoretical outcomes are shown in Figure 7.6, and a graph of the motor property data is
shown in Figure 7.7.
Figure 7.3. Selected 14 Inch Diameter and 4.7 Inch Pitch Propellers13
13
HobbyKing, n.d. Web. <
http://www.hobbyking.com/hobbyking/store/__39776__14x4_7_SF_Carbon_Fiber_Propellers_CW_and_CCW_Rot
ation_1_pair_.htmll>.
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Figure 7.4 Selected Tarot 4114/320 kV Motor14
Table 7.1. Performance for a Tarot 4114/320kV Motor with 15 Inch Propellers15
14
"Tarot 4114 High Power Brushless Motor (320kv Black)." Motors for Quadcopter / Hexacopter. Helipal, n.d.
Web. 07 Dec. 2014. <http://www.helipal.com/tarot-4114-high-power-brushless-motor-320kv.html>.
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Figure 7.5 Selected LiPo 4000mAh -20/30c 7S battery15
Figure 7.6 eCalc Final Configuration Model Data16
15
"ZIPPY Compact 4000mAh 7S 25C Lipo Pack." HobbyKing Store. N.p., n.d. Web. 07 Dec. 2014.
<http://www.hobbyking.com/hobbyking/store/__21364__ZIPPY_Compact_4000mAh_7S_25C_Lipo_Pack.html>.
16
Muller, Markus. “ECalc- the Most Reliable RC Calculator on the Web.” ECalc-the Most Reliable RC Calculator
of the Web. N.p., n.d. Web. 09 Nov. 2014.
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Figure 7.7 eCalc Final Model Motor Characteristics20
The selected setup of a quad-copter with 14 inch propeller blades provides a configuration that meets the
design criteria previously mentioned. The quad-copter is a very efficient system with an average efficiency
of around 85%, which is the maximum realistic efficiency for a UAV motor. In addition, the configuration
has a mixed flight time of about 9.4 minutes, which is very close to the goal of around 10 minutes of flight
time. Next, the hover throttle with the 3 pound package is at 67%, which is a good value since it meets the
requirement of being less than 80% throttle for minimum maneuverability. Finally, the quad-copter has a
maximum speed of 23.6 mile per hour, which is a respectable speed in order to deliver packages in a timely
manner.
The eCalc tabulated results for the UAV without the package is shown in Appendix D. The results show an
extended flight time of 13.1 minutes and a higher maximum flying velocity of 35.4 miles per hour for the
UAV without the carrying load of the three pound package. In addition, the hover throttle will be 46%
without the package, which is very close to the design criteria of being around 50% hover throttle for a
UAV during normal flight without an additional load.
The selected UAV design would have the ability to convert to a different configuration of 8 motors to carry
different weighted packages, but would have a different optimal efficiency for doing so. The octo-copter
would still have the same setup as the quad-copter including the same battery, controller, and motors, but
just having 4 additional motors. Important thrust and flight results for the octo-copter are shown in the
eCalc results table in A-5 involving specific additional loading cases: no-carrying load, a 3 pounds, a 6
pounds (twice the load of the quad-copter), 8 pounds (minimum maneuverability), and 14 pounds (max
throttle necessary just for lift). A summary of important results to meet design criteria of flight time, throttle,
and maximum speed for the octo-copter as well as the quad-copter is provided in Table 7.2 below. As
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shown in Table 7.2, both configurations provide the necessary setup in order to meet the design criteria and
prove the feasibility of the efficient flight and carrying a load.
Table 7.2. UAV Configuration and Setup Design Criteria Values
Configuration
4
8
Loading
[lbf]
No load
3
No load
6
8
14
Flight Time
[min]
13.1
9.4
10.7
6.9
4.4
3.1
Hover Throttle
[%]
46
67
31
53
79
99
Maximum Speed
[m/s]
35.4
23.6
38.5
30.4
6.2
?
In conclusion, the selected quad-copter configuration involving the selected propellers and motors meets
all of the design criteria previously mentioned in order to efficiently fly and carry 3 pound package. A
possible disadvantage of this configuration would be the estimated temperature of 140° F at maximum
motor use. This temperature would be higher than the distortion temperature of PLA. Another disadvantage
to this configuration is the large dimensions of the arms. By having 14 inch propeller blades, the UAV arms
carrying the motors will need to be long enough so that the propeller's sweep areas do not cross. Therefore,
this will be a factor involving the frame design and using a 3-D printer with a set platform size.
8.
Electronic Interface
8.1.
Design Criteria
The on-board IMU must be fully calibrated before being installed into the UAV and distributed to the
customer. The micro-controller must incorporate a fail-safe mechanism to ensure the UAV does not crash
when transmitter connection is lost during flight. The electrical wiring and components must be well
insulated and protected from the outside environment, and magnetic fields generated from the motors. The
PAM interface with the controller must limit motor current draw when tightening around the package in
order to save power.
8.2.
Pitch, Roll, and Yaw
A quad-copter uses two pairs of counter rotating propellers to maneuver. For a quad-copter in a “plus”
orientation shown in Figure 8.1, each pair of motors lie on the same axis. In order to yaw, which is rotating
about the z-axis (perpendicular to the ground), one pair of motors increase speed and the other pair of
motors decrease speed. The increase in torque from the pair of motors causes the frame to rotate. In order
to pitch or roll, one motor decreases speed while the opposite motor increases speed. This causes the quadcopter to tilt and move forward in the direction of the tilt.
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Figure 8.1 UAV Pitch, Roll, and Yaw17
8.3.
Micro-Controller
The most important electrical component of a UAV is the micro-controller. The purpose of a microcontroller is to stabilize the UAV during flight by using a continuous feedback control system. There are
two types of micro-controller boards used for aviation: inertial measurement unit (IMU) integrated, and
non-integrated IMU controller boards. The most common interface for programming micro-controllers is
through the Arduino IDE (integrated development environment). Some micro-controller interfaces include
software that allows the user to easily configure a micro-controller for a specific flight pattern. Other microcontrollers simply supply source code that the user must adjust via the Arduino IDE. The group researched
many different controller boards; Table 8.1 shows the best types of available controller boards. The group
evaluated the performance of each configuration against the different design criteria.
“UAV Society.” Quadcopter Mechanics. N.p, n.d. Web. 08 Dec. 2014. <http://uavsociety.blogspot.com/2014/06/quadcopter-mechanics.html>
17
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Table 8.1 Controller Board Functionalities and Cost
Controller Board
Integrated IMU
Yes
OpenPilot Revo
Yes
ArduPilot APM 2.6
Yes
Hobby King
MultiWii/MegaPirate
Arduino Mega
RCTimer Crius V2
No
Yes
Programming
Interface
OpenPilot GUI
Mission Planner GUI
Ardupilot Mission
Planner GUI /
MultiWii
Configuration GUI
Arduino IDE
Ardupilot Mission
Planner GUI /
MultiWii
Configuration GUI
Cost
$40
$180
$50
$30
$50
The best controller board that meets the design criteria, and has the lowest relative cost, is the RCTimer
Crius V2 controller board. This board features the 16 MHz Atmel ATMEGA250 micro-controller, which
is also used on the Ardupilot 2.6 controller board, but is $100 less. The Crius V2 features a 10 degree of
freedom integrated IMU, which allows for very accurate attitude positioning and proportion-integralderivative (PID) tuning. Furthermore, the Crius V2 is cross platform compatible with the MultiWii interface
and the Ardupilot Mission Planner interface. The IMU can be configured and calibrated using either
programming interface.
8.4.
Electronic Speed Control
The design requirements for the electronic speed control (ESC) are that it has a maximum current rating of
+20% of the maximum current draw from the motor. It should be noted that each motor will require an
individual ESC due to the high power draw from the 7S-2P (25V) 4000 maH battery.
8.5.
Materials
The electronic interface will consist of the following components:






Lithium Polymer battery – 4000 maH 7S 2P
Controller board with integrated IMU – RCTimer Crius V2
Transmitter and Receiver – Spektrum 2.4 GHz
ESC(s) – Turnigy 30A
Brushless DC motors – Tarot 4114 320 (kV)
Servo motor – Futaba High Torque
The following schematic, Figure 8.2, shows the layout of the electronic interface. The schematic is for a
quad-copter configuration. The Crius V2 controller can support up to 8 motors, plus 2 more servo outputs.
It also features an I2C communication port for an additional sensor. In Figure 8.2, PPM stands for pulse-
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position modulation and is the communication protocol between the controller, receiver, servos, and the
ESCs.
Figure 8.2 Electronic Interface for Basic Quad-Copter Configuration
Looking at Figure 8.2, the additional servo motor (*) will be used for the spring-latch system of the PAM.
The additional ESC may or may not be necessary depending on the required torque of the servo motor.
8.6.
Design Alternatives
There are two open source platforms that the team found are most popular for aviation control: MultiWii
and Ardupilot. Both of these control programs are developed for Arduino Mega based flight control boards.
The MultiWii platform has less sophisticated control algorithms than the Ardupilot control program, but
offers a wide range of supported controller boards, including the Arduino Uno. The Ardupilot platform has
limited controller board options due to its support of only Arduino Mega based flight controllers, but it has
a more successful control algorithm, which has won it awards in the 2012 and 2014 UAV Outback
Challenge. The Ardupilot platform is supported by the DIYDrones online community, and like MultiWii,
is also built and compiled using the Arduino IDE.
8.7.
Selected Design
The final design interface will incorporate an RCTimer Crius V2 controller board. The controller board will
be configured using the Ardupilot open source platform. The IMU and electronic speed controls will be
calibrated using the Mission Planner graphical user interface (GUI). Additional hardware (servos) will also
be configured using the Mission Planner software. If additional customization is necessary, an auxiliary
Python script will be added to the controller RAM through the Mission Planner interface.
Two 4000 maH 7S (25V) batteries will be used to power the UAV. These batteries will be connected in
parallel. Each motor will be connected to an ESC, which will be connected to the PPM output pin of the
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controller board. The channel wires from the receiver will connect to the PPM input pins of the controller
board. The power from one ESC will be used to power the controller board (not shown in Figure 8.2). The
additional servo motor used for the PAM will be connected to the servo output pin of the controller board.
9.
Frame Design
9.1.
Design Criteria
The frame of the UAV will be configured to have mounts for up to eight arms. There will be two different
configurations: quad and octo-copter. The user should be able to switch between these with a reasonable
effort so the arms will not be permanently affixed to the frame but instead be removable with readily
available tools.
The frame will have a place to mount the PAM. This mounting point will need to be strong enough to carry
the PAM along with its payload. The PAM mount will also be designed such that the PAM can be easily
removed and other devices, such as camera gimbals, can be mounted to it.
The natural frequency of the frame must be engineered to be higher than the frequency of the blades during
maximum rotational velocity in order to eliminate resonant stresses. The frame will also be designed for
infinite fatigue life due to the high frequency vibrational forces induced during each flight.
The arms will be able to lift the body of the UAV, along with its payload, with limited deflection as
deflection in the arms can cause the UAV to be unstable.
9.2.
Design Alternatives
One option for a UAV frame is to simply purchase one that is available on the market. There are many
companies and people who make and sell these frames at a variety of price points, and they are readily
available to purchase. These frames are made specifically for a fixed number of motors, so a new frame
would need to be purchased if a different number of motors is required. Many of these frames are injection
molded into a single part so if part of the frame fails, the whole frame needs to be replaced.
A second option is to make the frame out of aluminum. Aluminum is readily available in extruded tubes of
varying sizes and shapes, is relatively inexpensive and has a good strength to weight ratio. An aluminum
frame would be made by welding the extruded tubes together, or by connecting them with fasteners.
Welding aluminum is difficult to do and requires specific equipment that is not readily accessible to the
general customer. Also, connecting parts of the frame with fasteners make for more areas for stress risers.
Fasteners are also more likely to fail in the presence of vibrations.
9.3.
Selected Design
To help visualize the required dimensions of the frame, a wooden model of the UAV was created as shown
in Figure 9.1. This also allowed the team to easily adjust the dimensions based on the thrust calculations
and translate the dimensions into a CAD model.
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Figure 9.1 Early Wooden Prototype
The design that was selected uses 3-D printed parts with carbon fiber arms.
The motor mounts, body, and cover will be made from 3-D printed PLA plastic and are shown in Figures
9.2, 9.3, and 9.7, respectively (material properties can be found in Appendix B). The geometries were
designed in Solid Works and will be printed on a MakerBot Replicator 2X at GR Makers. This will make
it much easier to produce the necessary complex geometries.
Figure 9.2 CAD Model of Motor Mount
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Figure 9.3 CAD Model of UAV Body
The arm shaft will be made from 25 millimeter diameter carbon fiber tubes with a 1 millimeter wall
thickness shown in Figure 9.4. Carbon fiber works well because it is very stiff so it is not affected as much
by vibrations from the motor and propellers. It also has a high strength to weight ratio. Carbon fiber was
selected mainly because the length required for the arms exceeds the printer platform size of the MakerBot
Replicator 2X.
Figure 9.4 CAD Model of Carbon Fiber Tube
Each arm will consist of two parts assembled together. The first part of the arm is the carbon fiber shaft.
This is the portion that connects the body to the motors. In the 4 arm configuration, the length of each will
be 9 inches. The second part of the arm is the motor mount. This will include a 2 inches diameter flat portion
for the motor to sit. There will be 4 holes at the bottom of the mount for attaching the motor as well as holes
to allow the motor to dissipate heat. The shaft will be inserted into the motor mount and attached with 2
bolts.
The body will be designed to allow for four or eight arms to attach to it. The quad-copter setup is shown in
Figure 9.5, the octo-copter is shown in Figure 9.6, and the basic UAV dimensions are shown in Figure 9.8.
The arms will be inserted into the side slots, which will be integrated into the main body. The inside edge
of the side slots will be left open to allow room for the ESCs and wiring for the motors. There will be a
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platform in the center of the body for the electronics to be attached. On the bottom of the frame will be
reinforced holes for the PAM and landing arms to securely attach.
Figure 9.5 UAV in its 4 arm configuration
Figure 9.6 UAV in its 8 arm configuration
The cover of the frame will be designed to fit tightly over the frame of the UAV. It will secure to the frame
with 4-6 nuts and bolts and will be mainly for aesthetics but will also protect the electronics of the UAV in
case of flipping over.
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Figure 9.7 CAD Model of Cover
Since the motors and propellers are not perfectly balanced, they create vibrations. These vibrations are
especially hard on areas at which two components join. Efforts are going to be made to help reduce the
effects of these vibrations. A key component of this will be to place dampening materials in these joints.
Rubbers and some plastics do a good job of reducing the transfer of these vibrations.
Figure 9.8 Basic Dimensions of UAV (inches)
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10.
Landing Legs Design
10.1. Design Criteria
The landing legs must be able to safely absorb impact energy from vertical drops of up to 3 feet. The landing
legs must also be light-weight due to the very sensitive weight requirements of the scope of this project.
The safety factor against yielding must be at least 2.0.
10.2. Stress Analysis
A curved beam stress analysis for a 0.25 x 0.75 inch rectangular cross section with 20 inch radius of
curvature and arc length of 10 inches was performed in order to determine the maximum static stress. Then,
Castigliano’s method was used to determine the static deflection of the curved beam. Finally, the static
deflection was used to determine the impact force from the vertical drop, and then the impact force was
inserted back into the static stress equation to determine the impact stress. For more information on these
calculations please refer to Appendix E.
10.3. Materials
Four 3-D printed materials were researched for building the landing legs. These include: PLA honeycomb,
PLA lines, ABS honeycomb, and ABS lines. It should be noted that the honeycomb distinction means that
the printer saves material when printing solid cross sections by printing a honeycomb pattern. See Appendix
B for yield strength, specific strength, and Young’s Modulus values for these materials printed using
common printers. Based on the safety factors determined from the maximum stress calculations, PLA lines
is the best option for constructing the landing arms. Table 10.1 summarizes the stress and safety factors
from the calculations.
Table 10.1 Curved beam properties for PLA beam with 0.25 x 0.75 inch cross section and 20 inch
radius of curvature
Yield Stress (psi)
5800
Maximum Impact Stress
(psi)
2300
Yielding Safety Factor
2.5
10.4. Design Alternatives
Other material options include ABS honeycomb, ABS lines, and PLA honeycomb. Based on the maximum
stress calculations, the landing leg design was significantly weaker and more prone to yielding when using
ABS and PLA honeycomb.
The major design alternative is to use a u-shaped rectangular landing leg geometry. This could save cost on
material because it will only require two legs, instead of four curved legs. However, the stress seen by the
curved portion of the u-leg will significantly increase due to the smaller radius of curvature.
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The major material alternative is to use a honeycomb cross-section to minimize the printed material while
still maintaining the required safety factor of 2.0. However, based on research18 from Enno Ebbel and
Thorsten Sinemann, PLA lines has the highest specific strength of almost 40 J/g, versus PLA honeycomb
which has a specific strength of 30 J/g.
10.5. Selected Design
The final design will be a curved beam landing leg shown in Figure 10.1 that is constructed using PLA
lines. The cross-sectional area of the landing leg will be 0.25 x 0.75 inch with a radius of curvature of 20
inches. The MakerBot Replicator 2X will be the printer of choice for printing the landing arms. The four
landing legs will be attached to the frame of the UAV by using screws fasteners.
Figure 10.1 CAD Model of Landing Leg
18
Ebbel, Enno, and Thorsten Sinemman. RTeJournal, 2014
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11.
Finite Element Analysis
Finite Element Analysis (FEA) was run on the key components of the frame to get a sense of the stresses
the geometries would face in a rough landing. The simulation that was run was one at which the UAV falls
freely from a height of 3 feet and lands evenly on each leg. The top of the body was made to be rigid and a
force of 11 pounds was applied to the bottom of the leg, which is the equivalent impact force. The FEA
results for the one arm assembly, the individual leg, and the body are presented in Figure 11.1, 11.2, and
11.3, respectively.
Figure 11.1 FEA of 3 foot drop on one arm assembly
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Figure 11.2 FEA Analysis on Leg
The results from the FEA were promising. The stresses found in the FEA did not exceed the yield stress of
the PLA printed plastic used in the legs and body, or exceed the yield stress of the carbon fiber used in the
arms. This means the UAV has a good chance of surviving a rough landing or being dropped as long as it
lands on its legs.
One thing that needs to be noted is that the stresses in the body were not entirely accurate. For the sake of
making the FEA analysis easier, the arm and body were meshed together. The stress at the bottom of the
hole where the arm is inserted has really high stresses. In reality, this will not be the case because the arm
and body will not be rigidly fixed.
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Figure 11.3 FEA Analysis on body
12.
Vibration Analysis
12.1
Theoretical Analysis
A vibrational analysis was performed on the carbon fiber arms to assess the risk of reaching resonant
frequency during flight. First, the resonant frequency of the carbon fiber rods had to be theoretically
determined by assuming the arms resemble a rigidly fixed cantilever arm. The following equation is the
stiffness of a cantilever beam.
𝒌=
𝟑𝑬𝑰
𝒍𝟑
(12.1)
The Modulus of Elasticity (E), second moment of area (I), and the length (l) where given based on the
dimensions of the arm and the material properties of carbon fiber. Then, using the following theoretical
equation for natural (resonant) frequency, the natural frequency was determined.
𝒌
𝝎𝒏 = √
𝒎
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(12.2)
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Finally, the maximum frequency of oscillation had to be determined if the natural frequency would be
reached during flight. The maximum frequency of oscillation was determined using the following generic
equation.
𝝎𝒎𝒂𝒙 = 𝟐𝝅𝒏𝒎𝒂𝒙 𝑩
(12.3)
Where nmax is the maximum rpm of the motor, and B is the number of blades per propeller.
12.2 Results
The dimensions of each carbon fiber rod are: length (9in – 228.6mm), diameter (25mm), and thickness
(1mm). Based on these dimensions, the natural frequency of each arm was determined to be 2562 radians
per second. The maximum frequency of oscillation, based on max revolutions per minute of 7000 and two
blades per propeller, was determined to be 1466 radians per second. This yielded a safety factor of about
1.7 against resonant frequency. Calculations for vibration analysis are located in Appendix G.
13.
Package Attachment Mechanism (PAM)
13.1. Design Criteria
The Package Attachment Mechanism or PAM will be used to center the UAV over the package and attach
the package to the UAV. The package should be aligned with and connected to the UAV using only
electrical controls (without it being manually manipulated). The PAM design will be low weight to keep
the weight of the UAV low and keep the flight time high. The package will be securely attached to the PAM
to prevent it from being released while in flight and potentially injure someone or damage personal property.
The PAM will hold the package in such a way that it does not make the UAV difficult and dangerous to
pilot.
13.2. Design Alternative
One design alternative is to have the PAM fixed to the UAV and have a person manually place and remove
the payload to/from the UAV. This procedure is how the DHL UAV is designed. The issue with this is that
a person has to manually load and unload the payload.
A second design alternative is to connect the package to the UAV manually and have the PAM release the
package from the UAV. This is how the Google and Amazon UAVs work. The issue with this is that the
UAV cannot pick up the package without the use of an auxiliary mechanism.
A third design alternative is to have a mechanism that can pick up any shaped box. This would be flexible
enough to accommodate many different sizes and shapes and would carry the package is such a way that
keeps the package intact and the cargo inside safe. This design would increase the weight and power
consumption, which would make the design not worth pursuing.
A fourth design alternative is to have a mechanism that connects to the outside of a fixed dimension box.
The mechanism would grab the box by its outside edge by coming from a larger footprint and moving the
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lifting arms towards the center until the package is secure. An issue with this mechanism is aligning the
mechanism with the top of the box. Either the UAV needs to be perfectly aligned with the package when
picking it up or the lifting arms need to extend well past the outside parameter of the package. This would
require an unrealistically stable UAV or a large and heavy mechanism.
13.3. Selected Design
The design that was chosen is one that can lift, carry, and drop off a package without a person physically
interacting with it. The UAV will be flown over the package and lowered onto the package where the PAM
will capture and secure it. The PAM will be secured to the bottom of the UAV with a series of 4 bolts.
The package will have a pole extending out of its top with a ball at the end of it. This ball will enter the
bottom of the PAM where it will be secured. The ball will be secured with two clamping levers with a
reduced diameter hole that will prevent the larger ball from sliding through. The clamping levers will be
held closed by an extension spring and will be opened with a small high-torque servo, which will be
controlled from the flight control transmitter. The PAM design and concept prototype are presented in
Figures 13.1 and 13.2, respectively.
Figure 13.1 PAM design
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Figure 13.2 Prototype Concept Design
The UAV will be guided onto the package peg with the help from a cone that is affixed to the bottom of the
PAM. This cone, which will be made from a lightweight plastic such as Lexan, will allow the pilot to lower
the UAV over the peg while the peg slides on the cone, thus guiding the UAV to its center. The servo will
then be activated to open the clamping levers and capture the package.
Once the PAM has secured the package, the UAV will be ready to lift it and carry it to its destination. In
flight, the ball will be allowed to articulate freely. This will allow the package to remain under the UAV’s
center of gravity as it is accelerated and turned.
One final parameter for the selected PAM design is the spring stiffness necessary to keep the ball from
sliding out of the grip of the clamping levers. Using an extension spring with a natural length of 0.3 inches,
the spring stiffness must be 15 pounds per inch to ensure a safety factor of 1.5 against the weight of a 3
pound package. See Appendix F for these calculations. Figure 13.3 shows the free body diagrams for the
peg-sphere and the clamping lever(s). In reference to Figure 13.3, “P_weight” is the package weight acting
at the center of gravity of the peg-sphere, “F_f” is the frictional force, “F_N” is the normal force, and
“F_Spring” is the spring force.
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Figure 13.3 Free body diagrams of peg-sphere and clamping lever arm(s).
14.
Cost
For the design being proposed above, the total cost for parts is just under $1000. This cost can be broken
down into two major components, the cost of the propulsion system and the cost of the frame.
The cost of the propulsion system is outlined in Table 14.1 below. This includes the electronics and motors
required to fly the UAV. The main costs come from the batteries and motors. Expensive batteries and
motors were required due to the requirement to lift the 3 pound payload.
Table 14.1 Propulsion Costs
Item
Qt. Price Total
320 kV Motors
4
$40
$160
30A ESCs
4
$20
$80
14" Carbon fiber props
6
$6
$36
Batteries
2
$55
$110
Wiring
1
$25
$25
Flight controller
1
$50
$50
Servo
1
$20
$20
Transmitter and receiver
1
$60
$60
ESC programming card
1
$10
$10
GPS
1
$20
$20
Grand Total
$571
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The cost of the frame is dependent on where and how the parts are 3-D printed. It was decided that the
frame parts will be printed at GR Makers using their MakerBot Replicator 2X printer. The materials for
this printer are free, as they were donated to GR Makers, but the use of the printer requires a membership
to their club. This membership costs $30 a month for students. The total cost of the membership will be
$420. This would give Jeff and Kemal access from January through May, and Ross access from February
through May.
15.
Test Plan
15.1. Impact Testing
A testing mechanism will be created to do impact testing on the arms and landing gear. A pendulum set up
will be created that holds the part to be tested and a weight will be attached to the pendulum arm. The part
will then be attached to a rigid plate; the pendulum arm will be pulled back a fixed amount, and will be
released. The weight will impact the arm to simulate an impact it may face in flight. The part will then be
inspected for failure. The impact testing rubric is outlined in Table 15.1 below.
Table 15.1 Impact Testing Results Rubric
Inspection Result
Part intact (no cracking)
Part intact (non-structural cracking)
Part intact (major structural damage)
Complete fracture of part
Test Result
Pass
Pass
Fail
Fail
15.2. Hover Stability Testing
To test hovering stability, the UAV will be attached to the ground with 4 cables at each corner. The cables
will be long enough for the UAV to rise off the ground 2-3 feet. The other end of the ropes will be anchored
to the ground with one anchor for each arm. When the UAV takes the slack from the cable, the test fixture
will be such that the UAV will be flying level to the ground and the ropes will make an angle to the ground
between 25 and 45 degrees. There should be enough rope to allow the UAV to hover in a radius of 2 feet
from its starting point when hovering at the determined flight.
The UAV will then be turned on and the throttle will slowly be increased until the UAV is hovering above
the test platform. The UAV will be observed and its flight will be documented. The hover testing rubric is
shown in Table 15.2 below.
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Table 15.2 Hover Testing Results Rubric
Observed Behavior
Hovering stable above starting point
Hovering within 2 foot radius
Hovering outside 2 foot radius
Not Hovering
Test Result
Pass
Pass
Fail
Fail
15.3. Hover Time Testing
To test flight time, the throttle will be increased until the UAV is hovering 2-3 feet off the ground. A timer
will be started when the UAV leaves the ground. The UAV will be allowed to hover until the batteries are
depleted and it returns to the ground. The timer will be stopped and the hover time will be documented.
15.4. Flight Time Testing
To test the flight time, the UAV will be flown back and forth on a 100 yard path. An open area away from
people will be used such as a football or soccer field. Starting on one side of the field, the UAV will be
lifted to a height of around 10 feet, with the timer starting when the UAV leaves the ground. The UAV will
then be flown to the other end of the field and hover over the other end for 20 seconds. The UAV will then
be flown to the other end of the field and hover over the other end for 20 seconds. This will be repeated
until the battery runs low and flight cannot be sustained. The timer will stop when the UAV returns to the
ground and the elapse time will be documented.
15.5. PAM Safety Testing
The PAM will be attached to the center of a 2 x 2 foot piece of 1 inch plywood. An I-bolt will be connected
at each corner. A 4-foot long piece of cable will be connected to each I-bolt and the other side will be
attached to an anchor above it. The PAM package will then be loaded with its maximum carrying weight
of 3 pounds and attached to the PAM. The whole assembly will be lifted to the anchor point of the rope and
will be dropped. The PAM will pass the test if the package is still securely attached.
15.6. Wind Simulation Testing
The wind simulation testing will use the same testing fixture as the hover stability testing. The UAV will
be attached to the test fixture and made to hover 2-3 feet of the ground. A stick will then be used to sharply
tip up one side of the UAV arms a couple inches and the UAV should recover and re-stabilize. If it does
not, it will be a failure.
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16.
Safety
16.1. Public Safety
While the use of UAVs by the general public is becoming much more common place than even 2 years ago,
it is important to remember that these machines are not toys and can cause harm with those who come in
contact with them. The rotors are thin and spin at high rotational velocity. If they come in contact with a
person, the rotors can lacerate the skin.
The UAV being explored in this PPFS also poses a risk to people as it will be heavy. The whole setup will
be over 8 pounds and will be able to travel at a high velocity. This means that the UAV has a lot of kinetic
energy at a high speed and can cause harm to anyone it runs into.
16.2. FAA
The FAA is the governmental body tasked with the US airspace. They ensure that air traffic is run in a safe
manner. As of now, the FAA has not introduced regulation for the inclusion of UAVs in US airspace. They
have a blanket ban on UAV use for commercial purposes but do allow UAV use for non-commercial
purposes and are classified as model aircraft.
Model aircraft can be used, but must be used within certain guidelines. First, a UAV may not be flown at
any altitude within 2 miles from an airport. Second, a UAV may not fly higher than 400 feet from the
ground. Third, a UAV must be tested to ensure it can fly safely before it can be flown near spectators.
Fourth, a UAV may only be flown in an area “a sufficient distance” from populated areas. Last, the UAV
must always be flown within “line-of-sight” of its operator.
16.3. Safety Precautions
To prevent accidents that harm people or damage property, a series of precautions will be taken. Before
flying in public areas, the UAV will be tested to ensure it flies in a safe and predictable manner. Before
each flight, the UAV will be visually inspected to make sure all the parts are in good working order. After
any crash or hard landing, they UAV will be inspected to ensure it is not damaged. If the UAV is inspected
and found not to be in good working order, the issues will be corrected before it is flown. Before each flight,
the weather conditions will be assessed and the UAV will only be flown in conditions in which it can be
predictably controlled.
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17.
Conclusion
In conclusion, this project is feasible. The next step will be to order parts, get a membership to GR Makers,
print parts, and eventually build testable UAV models. Building the design will be an iterative process as it
is expected that much will be learned in the process. The goal will be to fail early and quickly adjust the
design based on the learnings from those failures. The issues that are expected to be the most difficult to
overcome are making the UAV stable enough to land on the package, finding ways to fasten parts together
in a way that is not adversely affected by the vibrations, and printing parts in such a way that ensures the
parts are of high quality.
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18.
Acknowledgments
The team would like to acknowledge the assistance provided by the Senior Design Professors, with special
regard to our team advisor, Professor Nielsen, who gave the team guidance throughout the duration of the
course and design process. In addition, the team expresses appreciation to other engineering faculty
members for their help. Professor Emeritus DeJong was very helpful in providing insight to the vibration
section of our design. Finally, Phil Jaspers provided assistance and knowledge pertaining to 3-D printing,
materials, and metal shop.
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19.
References/Bibliography
"Cube 3d Printer Technical Specs -www.cubify.com." Cube 3d Printer Technical Specs www.cubify.com. N.p., n.d. Web. 09 Nov. 2014. <http://cubify.com/en/Cube/TechSpecs>
Ebbel, Enno, and Thorsten Sinemman. "RTejournal - Forum Für Rapid Technologie."Fabrication of FDM
3D Objects with ABS and PLA and Determination of Their Mechanical Properties —.
RTejournal, 2014. Web. 09 Nov. 2014.
"FDM Technology.” About Fused Deposition Modeling. N.p., n.d. Web. 09 Nov. 2014. <
http://www.stratasys.com/3d-printers/technologies/fdm-technology>
"Helicopter Aerodynamics, Calculating Thrust Loading, Disk Loading, Power Loading." Heli-Chair.
N.p., n.d. Web. 06 Dec. 2014. < http://www.heli-chair.com/aerodynamics_101.html>
HobbyKing, n.d. Web. <
http://www.hobbyking.com/hobbyking/store/__39776__14x4_7_SF_Carbon_Fiber_Propellers_C
W_and_CCW_Rotation_1_pair_.htmll>.
"MakerBot Replicator 2 Desktop 3D Printer." MakerBot. N.p., n.d. Web. 09 Nov. 2014. <
https://store.makerbot.com/replicator2>
McCormick, Barnes Warnock. Aerodynamics of V/STOL Flight. Mineola, NY: Dover Publications, 1999.
Print.
Muller, Markus. “ECalc- the Most Reliable RC Calculator on the Web.” ECalc-the Most Reliable RC
Calculator of the Web. N.p., n.d. Web. 09 Nov. 2014.
“Precision Productivity.” ProJet. N.p., n.d. Web. 09 Nov. 2014. <
http://www.3dsystems.com/sites/www.3dsystems.com/files/projet-3500-plastic-1213-usweb.pdf>
"Propeller Thrust." Propeller Thrust. N.p., n.d. Web. 09 Nov. 2014. Nasa.gov
< http://www.grc.nasa.gov/WWW/k-12/airplane/propth.html>
"Tarot 4114 High Power Brushless Motor (320kv Black)." Motors for Quadcopter / Hexacopter. Helipal,
n.d. Web. 07 Dec. 2014. <http://www.helipal.com/tarot-4114-high-power-brushless-motor320kv.html>.
"The Difference Between ABS and PLA for 3D Printing." ProtoParadigm. N.p., n.d. Web. 07Nov. 2014.
< http://www.protoparadigm.com/news-updates/the-difference-between-abs-and-pla-for-3dprinting/>
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“UAV Society.”: Quadcopter Mechanics. N.p, n.d. Web. 08 Dec. 2014. <http://uavsociety.blogspot.com/2014/06/quadcopter-mechanics.html>
"ZIPPY Compact 4000mAh 7S 25C Lipo Pack." HobbyKing Store. N.p., n.d. Web. 07 Dec. 2014.
<http://www.hobbyking.com/hobbyking/store/__21364__ZIPPY_Compact_4000mAh_7S_25C_
Lipo_Pack.html>.
"3D Printer Filament Buyer's Guide." ProtoParadigm. N.p., n.d. Web. 09 Nov. 2014. <
http://www.protoparadigm.com/news-updates/3d-printer-filament-buyers-guide/>
"7 Commercial Uses for Drones - Boston.com." Boston.com. The New York Times, n.d. Web. 09 Nov.
2014. <http://www.boston.com/business/2014/03/14/commercial-uses-fordrones/dscS47PsQdPneIB2UQeY0M/singlepage.html>
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20.
Appendices
Appendix: Table of Contents
A. Microsoft Project Schedule
B. 3-D Printable Plastic Material Comparison
C. Power-Thrust Calculations
D. eCalc UAV Configurations with Varying Loads
E. Landing Arm Calculations
F. PAM Calculations
G. Vibration Calculations
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51
52
55
58
61
62
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Appendix A. Microsoft Project Schedule
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Appendix B. 3-D Printable Plastic Material Comparison
Material
Properties
Table B.1 3-D Printable Plastic Material Comparison
ABS Lines
ABS
PLA Lines
PLA
Honeycomb
Honeycomb
20 MPa (u
printer)
1300 MPa
15 MPa (cb
printer)
1000 MPa
40 MPa (felix)
2500 MPa
17 MPa
(felix)
1200 MPa
22.5 Nm/g
22 Nm/g
39 Nm/g
31.5 Nm/g
some part
warping
same as
ABS Lines
Flexibility
mild flexibility
Modifications
easily sanded,
machined
same as
ABS Lines
same as
ABS Lines
Recyclability
very high
Earth-friendly
petroleumbased
208.4 degrees F
same as
ABS Lines
same as
ABS Lines
same as
ABS Lines
liquefies, sharper same as PLA
details, stronger lines
layer binding
more rigid
same as PLA
lines
with more work, same as PLA
sanded and
lines
machined
medium
same as PLA
lines
plant-products
same as PLA
lines
110 degrees F
same as PLA
lines
same as
ABS Lines
translucent/gloss
y
Yield Strength
Young’s
Modulus
Specific
Strength
General
Characteristics
Part Accuracy
Heat Distortion
Temperature @
0.46 MPa
Aesthetics
soft milky
beige
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VisiJet M3
Black
(Acrylic-base)
35.2 MPa
1594 MPa
34.5 Nm/g
sharp and highresolution details
some flexibility
easily sanded,
machined
low
organic material
134 degrees F
same as PLA black/glossy
lines
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Appendix C. Power-Thrust Calculations
"Power-Thrust Calculations"
"SETUP"
W= 11.38908[lb_f]
N_motor=4
n=0.85
RPM =7000
"All-up weight of UAV"
"Number of motors/propellers"
"Average efficiency of motors"
"Estimated setup RPM"
"BATTERY"
V=25
N_Batt=2
C=8000
"Selected motor voltage in volts"
"Number of batteries in parallel"
"Battery cell capacity in mAh"
"PROPELLER"
D=14 [in]
Pitch=4.7 [in]
A=0.25*pi*D^2
A_ft=A*convert(in^2, ft^2)
"Propeller diameter in inches"
"Propeller pitch in inches"
"Propeller sweep area in square inches"
"Propeller sweep area in square feet"
"FULL THROTTLE"
PL=(P_in*n)/A_ft
TL=8.6859*PL^(-0.3107)*1[lbf/hp]
Lift=TL*(P_in*n)
Lift_Total=Lift*N_motor
P_inWatt=P_in*convert(hp,W)
Lift_Total=2*W
"Power loading equation"
"Thrust loading equation"
"Lift per Motor"
"Total lift of the UAV"
"Power input to motor in Watts"
"Common Thrust-to-Weight Ratio
to generate needed lift"
I_tot=I_motor*N_motor
I_motor=P_inWatt/V
P_inWatt=P_outWatt/n
KV_req=RPM/V
NomKV_req=KV_req/n
"Total UAV current "
"Current of motor"
"Power relation involving motor efficiency"
"Required KV of motor"
"Nominal KV (labeled) of motor
which accounts for efficiency"
ESC_req=I_motor*1.2
"Required ESC current for motor"
"HOVER"
PL_H=(P_Hin*n)/A_ft
TL_H=8.6859*PL_H^(-0.3107)*1[lbf/hp]
Lift_H=TL_H*(P_Hin*n)
Lift_HTotal=Lift_H*N_motor
P_HinWatt=P_Hin*convert(hp,W)
Lift_HTotal=1*W
"Power loading equation for hover"
"Thrust loading equation for hover"
"Lift per motor at hover"
"Total lift of the UAV at hover"
"Power input to motor at hover in Watts"
I_Htot=I_Hmotor*N_motor
I_Hmotor=P_HinWatt/V
P_HinWatt=P_HoutWatt/n
"Total hover UAV current "
"Current of motor at hover"
"Power relation involving motor efficiency"
"ENDURANCE"
t_hover=(60*(C/1000)*(60/100)*N_Batt)/I_Htot
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"Hover endurance time based on the battery
capacity and motor current with margin of
error"
t_fullthrottle=(60*(C/1000)*(60/100)*N_Batt)/I_tot
"Full throttle endurance time based on
the
battery capacity and motor current
with margin of
error"
t_average=(t_hover+t_fullthrottle)/2
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"Average endurance time"
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Table C-1. Various Combinati ons to Produce 22 lbf Lift
Number of
Motors
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
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Propeller
Power to
Diameter [in] Motor [W]
8
764.1
8.5
723.5
9
687.2
9.5
654.5
10
624.9
10.5
598
11
573.5
11.5
550.9
12
530.2
12.5
511
13
493.3
13.5
476.8
14
461.4
14.5
447
15
433.6
15.5
420.9
16
409.1
16.5
397.9
8
279.5
8.5
264.7
9
251.4
9.5
239.4
10
228.6
10.5
218.8
11
209.8
11.5
201.5
12
194
12.5
187
13
180.5
13.5
174.4
14
168.8
14.5
163.5
15
158.6
15.5
154
16
149.7
16.5
145.6
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Appendix D. eCalc UAV Configurations with Varying Loads
Figure D-1. Quad-Copter with No Additional Load
Figure D-2. Octo-Copter with No Additional Load
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Figure D-3. Octo-Copter with 3 Pound Load
Figure D-4. Octo-Copter with 6 Pound Load
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Figure D-5. Octo-Copter with 8 Pound Load (Minimum Maneuverability)
Figure D-6 Octo-Copter with 14 Pound Load (Maximum Throttle Necessary just for Lift)
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Appendix E. Landing Legs Stress Analysis
"Landing Leg Calculations"
"UAV"
Weight = 11.22 [lbf] / 4
"Geometry"
r_c = 20 [in]
t = 0.75 [in]
d = 0.25 [in]
arc_length = 10 [in]
platform_x = r_c - cos(theta)*r_c
platform_y = r_c*sin(theta)
"Radius of Curvature of the Landing Leg"
"Thickness of leg"
"Depth of leg"
"Arc Lengh of Landing Leg"
"Printing platform dimension"
"Printing platform dimension"
"Derived Geometry"
theta = (arc_length/r_c)*(180[deg]/3.14159)
chord = (sin(theta/2)*r_c)*2
"Angle of Curvature"
"Chord Length"
"Moment Leg"
arm = abs(chord*cos((180[deg] - theta)/2))
"Moment Leg"
"Moment Force at Fixed End"
M = Weight * arm
"Moment force at fixed end"
"Curved Beam Parameters"
r_o = r_c + (t/2)
r_i = r_c - (t/2)
e = r_c - ((r_o - r_i)/(ln(r_o/r_i)))
c_i = (t/2) - e
c_o = (t/2) + e
"Static Stresses"
sigma_i = (M*c_i)/(e*t*d*r_i)-(Weight/(t*d))
sigma_o = -(M*c_o)/(e*t*d*r_o)-(Weight/(t*d))
"Yield Stresses - Source: https://www.rtejournal.de/ausgabe11/3872"
Yield_Stress[1] = 20 * convert(MPa,psi)
"ABS - Lines - uPrint"
Yield_Stress[2] = 15 * convert(MPa,psi)
"ABS - Honeycomb - CB"
Yield_Stress[3] = 40 * convert(MPa,psi)
"PLA - Lines - Felix"
Yield_Stress[4] = 17 * convert(MPa,psi)
"PLA - Honeycomb - Felix"
"Deflection for Curved Beam - Castigliano"
Youngs_Mod[1] = 1300 * convert(MPa,psi)
Youngs_Mod[2] = 1000 * convert(MPa,psi)
Youngs_Mod[3] = 2500 * convert(MPa,psi)
Youngs_Mod[4] = 1200 * convert(MPa,psi)
"ABS - Lines - uPrint"
"ABS - Honeycomb - CB"
"PLA - Lines - Felix"
"PLA - Honeycomb - Felix"
"Second moment of area"
I = (d*(t^3))/12
"Polar integration angles"
angle_1 = 180 [deg]
angle_2 = 180[deg] + theta
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"Static Deflection Analysis"
y_bending[1] = (2*Weight*(0.5*((3.14159[rad]+sin(angle_1)*cos(angle_1))(3.14159[rad]+sin(angle_2)*cos(angle_2))))*r_c^3)/(4*Youngs_Mod[1]*I)
y_bending[2] = (2*Weight*(0.5*((3.14159[rad]+sin(angle_1)*cos(angle_1))(3.14159[rad]+sin(angle_2)*cos(angle_2))))*r_c^3)/(4*Youngs_Mod[2]*I)
y_bending[3] = (2*Weight*(0.5*((3.14159[rad]+sin(angle_1)*cos(angle_1))(3.14159[rad]+sin(angle_2)*cos(angle_2))))*r_c^3)/(4*Youngs_Mod[3]*I)
y_bending[4] = (2*Weight*(0.5*((3.14159[rad]+sin(angle_1)*cos(angle_1))(3.14159[rad]+sin(angle_2)*cos(angle_2))))*r_c^3)/(4*Youngs_Mod[4]*I)
y_axial[1] = (Weight*r_c*0.5*((3.14159[rad]-sin(angle_1)*cos(angle_1))-(3.14159[rad]sin(angle_2)*cos(angle_2))))/(Youngs_Mod[1]*t*d)
y_axial[2] = (Weight*r_c*0.5*((3.14159[rad]-sin(angle_1)*cos(angle_1))-(3.14159[rad]sin(angle_2)*cos(angle_2))))/(Youngs_Mod[2]*t*d)
y_axial[3] = (Weight*r_c*0.5*((3.14159[rad]-sin(angle_1)*cos(angle_1))-(3.14159[rad]sin(angle_2)*cos(angle_2))))/(Youngs_Mod[3]*t*d)
y_axial[4] = (Weight*r_c*0.5*((3.14159[rad]-sin(angle_1)*cos(angle_1))-(3.14159[rad]sin(angle_2)*cos(angle_2))))/(Youngs_Mod[4]*t*d)
y_total[1] = y_bending[1] + y_axial[1]
y_total[2] = y_bending[2] + y_axial[2]
y_total[3] = y_bending[3] + y_axial[3]
y_total[4] = y_bending[4] + y_axial[4]
"Impact Force - assume n = 1 which is assuming mass of stationary object is greatly larger than UAV"
h = 36 [in]
"height of drop"
"Impact Factors"
IF[1] = 1 + sqrt(1+((2*h)/abs(y_total[1])))
IF[2] = 1 + sqrt(1+((2*h)/abs(y_total[2])))
IF[3] = 1 + sqrt(1+((2*h)/abs(y_total[3])))
IF[4] = 1 + sqrt(1+((2*h)/abs(y_total[4])))
"Impact Forces"
F_i[1] = Weight*IF[1]
F_i[2] = Weight*IF[2]
F_i[3] = Weight*IF[3]
F_i[4] = Weight*IF[4]
"Impact Moments"
M_i[1] = F_i[1] * arm
M_i[2] = F_i[2] * arm
M_i[3] = F_i[3] * arm
M_i[4] = F_i[4] * arm
"Inner Stresses"
sigma_i_i[1] = (M_i[1]*c_i)/(e*t*d*r_i)-(F_i[1]/(t*d))
sigma_i_i[2] = (M_i[1]*c_i)/(e*t*d*r_i)-(F_i[2]/(t*d))
sigma_i_i[3] = (M_i[1]*c_i)/(e*t*d*r_i)-(F_i[3]/(t*d))
sigma_i_i[4] = (M_i[1]*c_i)/(e*t*d*r_i)-(F_i[4]/(t*d))
"Outer Stresses"
sigma_o_i[1] = -(M_i[1]*c_o)/(e*t*d*r_o)-(F_i[1]/(t*d))
sigma_o_i[2] = -(M_i[2]*c_o)/(e*t*d*r_o)-(F_i[2]/(t*d))
sigma_o_i[3] = -(M_i[3]*c_o)/(e*t*d*r_o)-(F_i[3]/(t*d))
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sigma_o_i[4] = -(M_i[4]*c_o)/(e*t*d*r_o)-(F_i[4]/(t*d))
"Safety Factors"
N_f[1] = Yield_Stress[1]/sigma_i_i[1]
N_f[2] = Yield_Stress[2]/sigma_i_i[2]
N_f[3] = Yield_Stress[3]/sigma_i_i[3]
N_f[4] = Yield_Stress[4]/sigma_i_i[4]
Table E-1. Landing Leg Stress Analysis (Dimensions: radius of curvature - 20 in, arc length - 10 in,
thickness - 0.75 in, depth - 0.25 in)
Material
Impact
Force
(lbf)
Impact
Factor
Impact
Safety
Bending Factor
Moment Against
Yielding
Maximum
Inner
Stress
(psi)
Maximum
Outer
Stress
(psi)
ABS-Lines
ABSHoneycomb
21.33
19.05
8.649
7.726
52.22
46.65
1.354
1.01
2143
2155
-2314
-2067
PLA-Lines
PLAHoneycomb
28.52
20.6
11.56
8.354
69.82
50.44
2.757
1.149
2104
2147
-3094
-2236
Material
Yield
Stress
(psi)
Youngs
Axial
Bending
Total
Modulus Deflection Deflection Vertical
(psi)
(in)
(in)
Deflection
(in)
ABS-Lines
ABSHoneycomb
2901
2176
188549
145038
0.000294
0.000382
-1.252
-1.628
-1.252
-1.628
PLA-Lines
PLAHoneycomb
5802
2466
362594
174045
0.000153
0.000318
-0.6512
-1.357
-0.651
-1.356
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Appendix F: PAM Calculations
"PAM Spring Stiffness Calculations"
Package_Weight = 3
"Package Weight - lbf"
Sphere_rad = 0.5
Lever_contact = 0.2
"Peg-Sphere Radius - in"
"Clamping Lever Contact Distance - in"
theta = arccos((Sphere_rad - Lever_contact) / Sphere_rad) "Arc Angle - degrees"
normal_contact_angle = theta/2
"Normal Angle Contact - degrees"
F_n*sin(normal_contact_angle) = Package_Weight/2
"Normal Force - lbf"
F_t = F_n * cos(normal_contact_angle)
"Spring-Tension Force - lbf"
Safety_Factor = 1.5
"Safety Factor"
F_t_actual = F_t * Safety_Factor
"Actual Spring-Tension Force - lbf"
Table F-1. Solutions
Normal Force
3.354 lbf
Spring Tensile
3 lbf
Force
Actual Spring
4.5 lbf
Tensile Force
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Appendix G: Vibration Analysis
"Carbon Rod Stress and Vibration Calculations"
"Knowns"
density = 1830 [kg/m^3]
E = 150*10^9
t = 0.001 [m]
l = 0.228 [m]
D_o = 0.025 [m]
D_i = D_o - 2*t
I = (pi/64)*(D_o^4 - D_i^4)
k = (3*E*I)/(l^3)
m = 0.25*pi*(D_o^2 - D_i^2)*l*density
freq = (7000/60)*2*pi
max_freq = 2*freq
"density of carbon fiber"
"Young's Modulus"
"thickness of wall"
"length of rod - 9 in"
"outer diameter of rod"
"inner diameter"
"Second moment of area"
"Rod stiffness"
"Mass of carbon fiber rod"
"Maximum frequency of motors"
"Frequency of 2 rotor propellers"
"Calculated Values"
omega_n = sqrt(k/m)
safety_factor = omega_n/max_freq
"Natural Frequency - rad/s"
"Derived Safety Factor"
"Maximum Stress Analysis"
landing_arm_distance = 0.1 [m]
attachment - 4 in"
F_impact = 11.04 * convert(lbf,N)
calculations"
Moment = F_impact * (l - landing_arm_distance)
center hub"
sigma_max = (Moment*D_o)/I
"Distance from rod attachment to landing arm
"Impact force from PLA lines landing arm
"Moment arm applied at rod attachement to
"Maximum Stress"
Table G-1. Solutions
Moment
6.286 N-m
28.9 Mpa
max (maximum
bending stress from
impact)
206469 N/m
k (stiffness)
2562 rad/s
n (natural
frequency)
1466 rad/s
Maximum
Frequency
1.747
Safety Factor
Against Resonance
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