3D Printed Quadcopters

Luke S. DaiLuke.S.Dai@gmail.com

Marc A. Hararythales2718@gmail.com

Carly T. Pompeictpompei@gmail.com

Steven L. Shansteven.shan99@gmail.com

Melissa J. Tumelissat729@gmail.com

New Jersey Governor’s School of Engineering and Technology 2016

Abstract

The principle objectives of the follow-ing project were twofold. First, it sought toinquire into the underlying physics of quad-copter drones and the fundamentals of 3Dprinting. Second, it attempted to deter-mine whether additive manufacturing is aviable option for constructing a quadcopter.To accomplish the former goal, a rudimen-tary model was assembled so as to be easilyreplicable by amateurs and hobbyists. Forinstance, it lacked any auxiliary sensors be-yond the most basic that are required forquadcopters to operate stably. During thedesign and assembly processes, it was con-firmed that additive manufacturing is op-timal for constructing quadcopter vehicles,as it enables versatile customization of thedesign, is relatively inexpensive, and incor-porates highly flexible and durable materi-als. Moreover, polylactic acid (abbreviatedPLA), one of the two most common plas-tic composites available was determined tobe more suitable than acrylonitrile butadi-ene styrene (abbreviated ABS) for 3D print-

ing quadcopters, given that it caused fewercomplications during the printing process.

1 3D Quadcopters

In recent years, drones have rapidlygrown more commonplace in almost everyfacet of daily life. Quadcopters, or aerialvehicles propelled by four rotors, in partic-ular have enjoyed enormous popularity overthe past decade in a wide range of fields,due to their user-friendliness and count-less other advantages. They serve as indis-pensable tools for hobbyists, military orga-nizations, realtors, law enforcement agen-cies, and countless other professionals thatbenefit from quadcopters’ seemingly unlim-ited potential. It is abundantly clear thatquadrotor aircraft, along with other drones,will only continue to grow ever more inte-gral to an increasingly automatized world.

Yet, despite their prevalence, quad-copters are highly complex vehicles that re-quire extensive knowledge to fully compre-hend. The following experiment attemptsto investigate their applications and the

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physics and flight mechanisms underlyingtheir operation. Furthermore, it attemptsto determine the obstacles involved in cre-ating quadcopters via additive manufactur-ing. Research inquires into propeller design,flight stability and efficiency, electronic sta-bility control to optimize the drone’s perfor-mance, and contrasts between quadcoptersand single-rotor helicopters. In order toaccomplish the latter goal, an experimen-tal approach is taken. A simple quad-copter is assembled from 3D-printed com-ponents and research into the printing pro-cess and computer-simulated stress tests isconducted, so as to develop a model easilyconstructible by any hobbyist or amateur.

During the design process, the quad-copter’s frame must be developed in compli-ance with a number of constraints. For one,the 3D printer available is unable to pro-duce items that exceed six inches in length,width, or height, such that it is necessary todesign a chassis that can be printed in andassembled from multiple parts. To maxi-mize the payload the vehicle is able to sup-port, its frame must be extremely light, as isgenerally the case for most aircraft. Finally,the model must be drafted as expeditiouslyas possible.

Although the main goal is to designa simple quadcopter for recreational pur-poses, the model can be easily adapted toother applications through constructionalmodifications. For instance, a photogra-pher filming aerial shots of a landmarkmight use a larger and stronger version ofour design that can stably support a cam-era. An educator might teach a lesson onwind currents using the quadcopter to showhow wind speed affects a moving object. Inthis case, a smaller, lighter model would bemost suitable. Quadcopters have many usesbeyond being simply recreational and theseuses can be discovered through extensive re-search.

2 3D Modeling and Quad-copters

Figure 1: The assembly of the quadcopter.

Quadcopters are multirotor helicopterspropelled by four rotors, each of which ishorizontally oriented to generate lift. Asseen in Figure 1, the propellers are alignedhorizontally to the ground. In most cases,they use two pairs of fixed propellers. Tworotate clockwise while their counterpartsrotate counterclockwise. By changing eachpropeller’s rotational speed, it is possibleto generate varying thrust, propelling thequadcopter along any trajectory desired. Atorque, or net force that induces the quad-copter to rotate about its central axis, canbe produced through similar means. Be-cause of this unique design, quadcopterspossess a far greater and more versatilerange of motion than conventional, single-rotor helicopters.

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2.1 3D Printing

Figure 2: The first quarter of thequadcopter is being printed.

3D printing, also known as additivemanufacturing, is the process of convert-ing a digital design into a tangible model.Thin layers of a material are formed one ontop of the other which creates the specifiedobject, all under computer control. Thiscan be seen in Figure 2. With the use of3D printing, virtually any imagined objectcan be produced in real life. 3D printablemodels can be created using a computeraided design package or 3D scanning tool.Among the many modeling softwares avail-able, the most prevalent are those in theAutodesk suites, such as Inventor, Auto-CAD, and SolidWorks. Since 3D printersrely on successive cross sections of the fi-nal part to ensure accurate results, the dig-ital mesh needs to be checked for hidden er-rors that may cause the print to fail. Oncethe file is run through an application andchecked for holes, a software will process themodel by “slicing” the model into a series ofthin layers. If the file is problem-free, thesoftware will produce a G-code file whichcontains instructions tailored to a specific3D printer. When the model is ready to beprinted, the data is sent to the 3D printerand through a computerized process, andthe object is created.

2.2 3D Printing Processes

The most common additive manufac-turing processes are fused deposition mod-eling, or FDM, selective laser sintering, orSLS, and stereolithography, or SLA.

Stereolithography is the process of usinga source of light, most commonly a preci-sion laser or DLP projector, to cure crosssections of a 3D model in a UV-sensitiveliquid polymer [1]. As the polymer curesand hardens, the print is displaced, and an-other layer of polymer is cured directly onthe previous layer. The primary advantageof SLA is that it can produce highly ac-curate and detailed parts. However, it re-quires a large amount of post processing. Inaddition, because the polymer is UV sensi-tive, parts created using SLA cannot be ex-posed to sunlight for large amounts of timeor else they will become brittle and thenbreak. This is undesirable because quad-copters will be constantly exposed to sun,which means that SLA is not ideal.

Selective laser sintering is the processof using a laser to trace and melt a layerof polymer or metal powder. Once a layeris completed, the entire build platform, in-cluding both the sintered and unused pow-der, is lowered and another layer is laid ontop. The process is then repeated. SLShas many advantages including the abilityto produce parts in a wide variety of mate-rials. This is desirable because one wouldbe able to produce a quadcopter in a mate-rial that balances strength and weight best.In addition, SLS does not require supportstructures, which means that more complexobjects can be created in a single print.However, SLS requires a very specializedenvironment and specific tools to produceprints. Unfortunately, a lab with these ca-pabilities was not available during the cre-ation of the quadcopter.

Fused deposition modeling is by far the

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most prevalent 3D printing process. FDMis the process of using an extruder to tracelayers of a 3D model while extruding amelted thermoplastic. The most commonthermoplastics used in FDM are acryloni-trile butadiene styrene (ABS) and polylac-tic acid (PLA). FDM is the most acces-sible 3D printing technology because un-like SLS, FDM does not require a special-ized environment. Because they can be cre-ated from relatively simple and inexpensiveparts, FDM printers are the most commontype of printers. Although FDM is limitedto thermoplastics, the final product’s qual-ities can be easily modified through differ-ent slicing settings such as layer height, wallwidth, and infill density. However, partscreated from FDM are generally not as di-mensionally accurate as those from othermethods and their strength is only limitedto the strength of thermoplastics.

2.3 ABS vs PLA

3D printing filaments vary greatly inchemical and physical properties. Twoplastics, ABS and PLA, are the most com-monly used plastics by hobbyists, educa-tors, and manufacturers. They share a fewsimilarities since they are both thermoplas-tics, which means they become soft andmalleable when heated and return to a rigidsolid state when cooled [2]. Furthermore,you can repeat the process without affect-ing the durability and integrity of the ma-terial. While both filaments are used in theprocess of 3D printing, specific variationsset them apart.

ABS, is generally a very durable andstrong plastic. Furthermore, it is flexible

and has a great heat resistance (Refer toFigure 3). The filament, depending on thebrand, ranges in tensile strength from 35to 45 MPa [3]. These specific propertiesare ideal for most projects. However, ABSmust be printed on a very hot print bed.If the printing surface does not reach theproper temperature, the filament will notstick to the plate properly or extrude prop-erly. This causes problems to arise: the3D print will come out deformed or theprinter could possibly be damaged. ABSis the cheapest plastic of the two filamenttypes and is widely used for various pur-poses. Due to the properties of this ma-terial, it can be sanded from jagged edgesto smooth curves. Additionally, printed orbroken parts can simply be pieced back to-gether with ABS glue. The filament, whenhardened, is soluble in acetone.

Nevertheless, there are still many draw-backs to ABS. It is extremely toxic, and thefumes it produces when printing are harm-ful to the environment and anyone nearby[4]. When exposed to moisture, spools ofABS swell, and air pockets form with the fil-ament. Upon printing, the plastic bubblesat the tip of the nozzle which reduces the vi-sual quality and strength of the 3D printedpart. ABS will curl upwards when in di-rect contact with the printing bed whichcauses corners to be rounded off. Mostimportantly, the filament shrinks signifi-cantly when cooling because it cools veryrapidly and contracts. The design musttake into account this shrinkage and bescaled. Guesswork is involved and requiresmultiple prints in order to ensure proper siz-ing of the model.

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Figure 3: This is a graph of different strengths of PLA vs. ABS. [5]

On the other hand, PLA is a biodegrad-able, non-toxic thermoplastic. This makesit more environmentally friendly than ABS.The filament typically has a tensile strengthof 60 MPa. PLA is tough, but tends tobe brittle when cooled. Unlike ABS, PLAis printed at relatively low temperatures,around 160 degrees Celsius - 220 degreesCelsius, and is very slow to cool. WhenPLA is exposed to moisture, physical prop-erties change, such as color, strength, anddensity. Compared to ABS, PLA warpsmuch less. Furthermore, PLA is known forits ability to print sharp, detailed prints athigh speeds.

While ABS filament produces a strongerquadcopter, issues arose while printing withthis particular plastic. As discussed ear-lier, without a hot enough plate, ABS willnot stick properly and pull off the surface.During printing, the model will deform and

fail. Instead of sticking to the plate prop-erly, the material would move, resulting inexcess strips of printed ABS attached to thedesign. Albeit possible alternatives couldhave been taken, the materials necessaryto make these changes were not availableat the time. As a result, PLA was chosenas the filament for the 3D printed quad-copter. Although it was not ideal, PLAhas many properties that aided the print-ing process. The filament heats up easily,making it easy to print detailed designs wellwith sharp corners. PLA shrinks less thanABS. Therefore, designing a model on acomputer is simpler than scaling a modelbecause one does not have to account asmuch for shrinkage. Additionally, PLA canbe printed at a faster pace with no compli-cations.

2.4 Benefits of 3D Printing

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Figure 4: The differences between traditional and additive manufacturing waste. [6]

3D printing requires a relatively low ex-pense budget for any quadcopter hobbyist.It allows the designer to personalize his/herown model through multiple methods. Forexample, one can directly edit the file dig-itally or adjust the printer’s settings, suchas speed, fill percentage, and resolution, toaffect the properties of the model. The fila-ments all have different properties that canadd strength or flexibility. Furthermore, itis a very productive and accurate manufac-turing method. The 3D printing machineitself is affordable and durable. Due to itsability to build a model from the bottomup, 3D printers can produce shapes thatcannot be fabricated any other way. Be-cause additive manufacturing only uses ma-terial that will be in the final product, littleto no waste is produced.

As seen in Figure 4, traditional formsof machinery often leave up to 90 percentof metal wasted. However additive man-ufacturing generates far less waste to be-gin with [7]. Additionally, 3D printing pro-vides a cheaper alternative to replacing bro-ken parts. Instead of having to wait for a

week or longer for a single piece of a store-bought quadcopter to come in the mail, a3D printed copter can have any broken partreprinted in a few hours for a fraction ofthe cost. The printed objects are mass pro-ducible because they can be made on vari-ous printers and the parts are easily replace-able. If a 3D part were to break, all onewould have to do to replace it is print anew one.

2.5 Benefits of Quadcopters

Quadcopters are easy to manufactureand are sold at an affordable price. Thesequadcopters utilize four propellers whichmeans that the product has a lot of power tobe able to lift off the ground [8]. The devicecan easily take on a small load. Further-more, only having four propellers meansthat the quadcopter has great maneuver-ability and thrust in comparison to othercopters.

For example, a tricopter is unbalancedand hard to maneuver due to its undis-tributed weight over three motors. On the

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other hand, a hexacopter which has six mo-tors and propellers has an increased speedand greater power than a quadcopter dueto its larger size. However, its dimensionsmake the copter harder to fly in tight spaceswhile its controls are much more complex.Meanwhile, the eight motor and propellercopter, the octocopter, is a fast, agile de-vice that can reach exceptionally high el-evations. Since it is so large in size, thebattery life is often far less than that of thequadcopter. Similar to the hexacopter, theoctocopter is very challenging to maneuver.Ultimately, quadcopters are far better thanother type of copters. Their size and mo-bility is just right, which means that thedevices can have more applications. Quad-copters, moreover, are inexpensive and thussuitable for novices and hobbyists, in con-sideration for whom this project’s modelwas designed.

3 Methods/Experimental De-sign

3.1 Physics

A quadcopter’s propellers generatelift, a force perpendicular to the groundthat counter-balances the vehicle’s weightto keep it aloft. Adjacent propellers mustrotate in opposite directions in order tocancel out lateral and vertical forces andthereby prevent the vehicle from unstablyspinning in place (Refer to Figure 5). Be-cause horizontally oriented propellers addsignificantly to a quadcopter’s weight, theyare highly inefficient and unfavorable. In-stead, to move in a horizontal direction, thevehicle must generate a net force parallelto the ground by creating an imbalance offorces between its four propellers [9].

One pair of adjacent propellers producesmore lift than the other, inducing a torque,or twisting force, along either the vehicle’s

roll or pitch axes [10].

Figure 5: This is a diagram that displaysthe direction of each spinning propeller on

the quadcopter.

Figure 6: The imbalance of forces from thepropellers drives the quadcopter laterally.

[11]

Now, with the quadcopter angled andthe propellers still creating a net force per-pendicular to the quadcopter, the net forcehas a slight horizontal component which

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can drive the quadcopter in a lateral direc-tion (Refer to Figure 6).

Quadcopters have physical limitations.The upward force created by the four pro-pellers must be stronger than the gravita-tional downward force caused by the weightof the whole structure itself. This then lim-its the equipment that can be added to thequadcopter. Stronger motors usually tendto be heavier motors, which cannot be sup-ported by a device designed for small mo-tors.

Even larger-scale quadcopters are un-able to support the load of a heavy motorand battery because the frame’s strengthand weight must increase to accommodatethe heavy additions as well. The thrustgained from the heavy duty motors is lessthan the weight gained from the new frameand battery. That is why using quadcoptersas a method of transportation is not possi-ble with today’s technology.

The number of propellers affects theamount of load the quadcopter can carry,as well as its stability and maneuverabil-ity. First, as previously stated, the up-ward force that counteracts the gravita-tional pull is only generated by the spinningpropellers. Therefore, the more propellersthere are, the more overall lift the quad-copter receives. Because there are morepoints around the quadcopter that can gen-erate a torque, the quadcopter becomes lessdependent on each single propeller, whichmeans it is more stable.

Also, more propellers can create morevariable directions to move in, makingthe quadcopter more maneuverable as well.Due to budget limitations, only four pro-pellers are used in this model to understandthe other aspects of quadcopters. Addingpropellers increases the amount of suppliesrequired to run the motors as well as thecomplexity of the whole quadcopter. Onewould require something to control the mo-

tor, as well as the battery power sufficientenough to run an additional motor. If adrone were to have more propellers, thepropellers would need to be at all times,which would convolute the movement com-mands. However, each motor would requireless power. The addition of more propellerswould also increase the cost of the project,which is limited.

3.2 Design Process: Foundation

Figure 7: These were the two potentialdesigns of the quadcopter.

The quadcopter’s design primarily con-sists of elements from two Thingiverse mod-els. The chassis of the first model (Model1 in Figure 7) consisted of several compart-ments along with four connections to attachthe motor arms. Each motor arm had ahollow cylinder with one open end and oneclosed end with several slits, which were de-signed to hold the screws that attached themotors. This model’s primary advantagewas its flexibility in motor mounting be-cause the slits allowed for different mount-ing orientations and dimensions. However,a major problem to this design was itsmulti-layered compartment design becauseeach compartment consisted of a ceiling andfloor with empty space between. This poseda major problem to the printing process be-

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cause we were using fused deposition mod-eling. FDM builds new layers of a printon top of previous printed layers, so it willnot print well when there is an empty space.In addition, the design’s compartments hadvery thin walls, which limited the group’scapabilities in modifying the strength ofthe resulting print through adjusting den-sity and wall thickness [12]

The second model (Model 2 in Figure7) consisted of a flat mesh with hexagonshaped cutouts. It was split into four sepa-rate parts to allow users to print it in sepa-rate prints so that no piece would be toolarge for the printer’s maximum volume.This model was the most apparent in thefinal design of the quadcopter. However,the motor mounting points were not sizedcorrectly for the motors. But, unlike thefirst model, this model was flat and did nothave any overhangs, which means it wouldbe very easy to print on a FDM printer.In addition, this model was easier to printand assemble because it was split into fourparts. Furthermore, the uneven edges al-lowed for each part to be securely fastenedto the other parts.

3.3 Design Process: Modeling

The final quadcopter included the mo-tor mounts from the first model and themesh chassis of the second model. The pro-gram chosen for cutting these parts fromeach model was Netfabb because of its meshcutting features and reliable boolean opera-tions. The cylinder of the motor mount wasfirst cut from the model of the entire arm toreduce the polygon count, thereby makingit easier to work with. Then, a basic pipewas created with the exact dimensions ofthe motors. The model of the motor mountwas stretched to fit the pipe and then thedifference was taken into account for the fi-nal motor mount. In addition, the second

model was re-scaled to fit the print bed ofour 3D printer. Finally, boolean additionwas performed on the modified version ofthe second model and the motor mount toproduce the final body of the quadcopter.Although the body was able to be modi-fied from the original files, the landing gearneeded to be designed from scratch to ac-commodate the smaller chassis. A digitalcaliper was used to measure the inner di-ameter of a hexagon on the quadcopter tothe nearest hundredth of a millimeter. Thishexagon shape was recreated using poly-lines in Autodesk 123D and extruded to 5.5mm (the thickness of the body of the quad-copter). A similar hexagon was then cre-ated and extruded to 40 mm, which was thedesired height of the landing gear. Thesetwo parts were combined and printed fourtimes.

3.4 Design Process: Printing

Being very large flat prints, each quar-ter of the quadcopter had to be printed verycarefully to prevent warping. When cool-ing, plastics will shrink, which will causeprinted parts to peel off of the build platewhile the printer is still printing. Thiswas countered by printing a brim aroundedges of the quadcopter to increase its sur-face area on the print bed and putting glueon the print bed to increase surface adhe-sion. In addition, the usage of each partwas considered when setting the slicing pa-rameters of each print. Overall, the quad-copter must be light in order to reduce un-necessary strain on the motor but maintainthe strength needed to sustain a crash orhard landing. Using the model of the stressgradient, the infill density was increased inmore stressed areas to increase the strengthand rigidity in those areas. In addition, toaccount for the shrinking of each print as awhole, each part was sliced at 102% scale.

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4 Results/Discussions

The quadcopter is based on designsfound on an online repository [13]. Thedesign process of modifying and combin-ing existing designs significantly expeditedthe project’s design phase because of theability to merge the most advantageous as-pects of each model. Many designs wereconsidered but ultimately, a combination ofseveral models was created. The resultingmodel was four sections of flat mesh withmany honeycomb cutouts across the body(Refer to Figure 8). This design maximizedits structural strength while minimizing itsweight and made it easier to print.

4.1 Stress Testing

Figure 8: This is the final 3D model of thequadcopter.

The designer must consider various fac-tors such as strength and deformation be-fore choosing a model. While beginninga print immediately after finding a quad-copter design is ideal, the factors must betaken into account. A stress test can bedone through various programs to see howthe model will perform with a load. For thechosen honeycomb design, a test was run to

examine possible deformation. One of thequarters of the quadcopter’s body was se-lected at random. From there, a load wasplaced on the motor’s mounting point andthe corner opposite - the point where all ofthe quarters meet in the center of the quad-copter - was set as a fixed point.

Figure 9: This is an example of thedeformation of the quarter.

Figure 10: This is the strain gradient on aquarter.

As pictured in the Figure 9, piece B isthe design without any applied stress, andpiece A is the design with the maximumamount of stress applied. The section be-gan to curl at the ends as more force wasapplied in the upward direction, simulat-ing the moving propeller’s pull on the piece.Figure 10 shows where the stress dispersesthroughout the model. The red displays thearea that absorbs most of the amount ofstress, while the blue reveals the area thatis barely affected by the load. Therefore,the motors will generate stress near their

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mount points but little to no stress on thecenter of the quadcopter where all of theelectronics lie.

4.2 Failures

Figure 11: Four different stages of thequadcopter design.

While constructing the quadcopter,there were many issues. The first issuethat appeared was the fact that ABS wouldnot stick to the plate. While the print-ing bed was hot enough, the ABS filamentwould not stick to the plate. Test pieces ofboth PLA and ABS were printed to com-pare which was stronger. However, the ABSmodel would not print well. Therefore, thematerial was switched to PLA. While PLAis a weaker material, the design was modi-fied to ensure that the quadcopter would bestrong enough. It was pertinent that thequadcopter could be assembled in a rela-tively easy manner and the printability ofthe parts is very important. This is dueto the goal of the project which is to cre-ate a simple quadcopter that a beginnercould assemble. The primary issue whenthis quadcopter was being sliced was ac-counting for the shrinkage during the print-ing process. The motor mount needed tobe tight enough to securely fasten the mo-tor while not being too small to restrictits movement. Another problem the groupran into was that the wires that protrudeperpendicularly from the motor were not

accounted for in the modeling process, sothere was no hole in the cylindrical motormount for the wires to pass through.

We fixed this through another iterationof the design by removing a rectangulararea from the wall of the motor mountto create an area for the wires to escape(shown in Figure 11 print 2). The last errorin the iterations before the final model wasthat the cylindrical motor mount was toohigh, which was problematic because themotors were outrunner motors and wouldscrape against the edges of the mount. Thiswas fixed by removing the top centimeter ofthe motor mount (shown in Figure 11 print3).

Figure 12: This is a picture of the weightsthat were needed to press down the

quadcopter as the four quarters were gluedtogether.

After a few more trials and errors in 3Dprinting, the final four pieces were printed.Since FDM printers are generally not verydimensionally accurate, it was hard to con-nect the pieces together. While the pieceswere supposed to snap together, they hadto be glued together instead (Refer to Fig-ure 12).

Not only were there problems in theprinting process, but multiple issues arosewhen constructing the actual quadcopter.The first main issue was that there were

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no manuals or specifications for the Ar-ducopter, the flight controller used in thisproject which commands the overall quad-copter. The proper connections were found,but they were scattered in various forumsand video tutorials. Because the equip-ment used were not exactly the same, multi-ple educated guesses were performed whileconnecting the wires. While using the twofirmwares installers recommended for Ar-ducopter, Mission Planner and APM Plan-ner, there was a bad barometer health errorwhich could not be troubleshooted. Therewas no adequate support or cases onlinewhere the barometer had bad health so nosolution was found. Eventually, a loanedPixhawk, another flight controller, was im-plemented. Additionally, one of the mo-tors for the propeller was defective whichdrained the budget for repurchasing an-other set.

5 Conclusion

Additive manufacturing is an ex-tremely effective tool for quadcopter en-thusiasts designing their own vehicles. 3Dprinting is ideal due to its affordability, thefreedom it grants designers to readily cus-tomize their unit, the flexibility and dura-bility of the materials used in the 3D print-ing process, and its environmental friendli-ness. Although ABS plastic is superior instrength and durability to PLA, the lat-ter was found to present fewer complica-tions during the printing process and there-fore to be preferable for inexperienced de-signers. Moreover, quadcopters were deter-mined to be a superior alternative in thiscase to other multi rotor helicopters, whichsuffer from issues in stability, maneuver-ability, and battery life. When designinga frame, stress tests are imperative to per-form in order to determine the location of

structural weak points where vibration andmechanical stress must be mitigated. Otherhobbyists might improve the design hereindeveloped by foregoing the purchase of aflight transmitter and instead operating itdirectly from a computer, further reducingthe device’s cost. A camera might also beadded, which, though raising the cost of thequadcopter, would allow it to be flown at agreater distance from its operator.

Figure 13: This is the final 3D quadcopter.

Acknowledgments

The authors of the foregoing papergratefully acknowledge invaluable guidancefrom their mentor, Kristian Wu; assistancefrom Alex Hobbes, research coordinator forthe New Jersey Governor’s School of Engi-neering and Technology; supervision fromJean Patrick Antoine, dean of the Gov-ernor’s School; support from Ilene Rosen,the Academic Integrity Facilitator for SOE;several pieces of equipment loaned by theInstitute of Electrical and Electronics En-gineering; and generous donations fromLockheed Martin, Rutgers University, Novo

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Nordisk, the Gannet Foundation, New Jer-sey Resources, Silverline, Morgan Stanley,and South Jersey Industries.

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