Design and Performance of Modular 3-D Printed Solid-Propellant Rocket Airframes

aerospace

Article Design and Performance of Modular 3-D Printed Solid-Propellant Rocket Airframes

Rachel N. Hernandez 1, Harpreet Singh 1, Sherri L. Messimer 2 and Albert E. Patterson 2,*

1 Department of Mechanical and Aerospace Engineering, University of Alabama in Huntsville, OKT N274, 301 Sparkman Drive, Huntsville, AL 35899, USA; [email protected] (R.N.H.); [email protected] (H.S.) 2 Department of Industrial & Systems Engineering and Engineering Management, University of Alabama in Huntsville, OKT N143, 301 Sparkman Drive, Huntsville, AL 35899, USA; [email protected] * Correspondence: [email protected] or [email protected]

Academic Editor: Konstantinos Kontis Received: 23 February 2017; Accepted: 20 March 2017; Published: 23 March 2017

Abstract: Solid-propellant rockets are used for many applications, including military technology, scientific research, entertainment, and aerospace education. This study explores a novel method for design modularization of the rocket airframes, utilizing additive manufacturing (AM) technology. The new method replaces the use of standard part subsystems with complex multi-function parts to improve customization, design flexibility, performance, and reliability. To test the effectiveness of the process, two experiments were performed on several unique designs: (1) ANSYS CFX® simulation to measure the drag coefficients, the pressure fields, and the streamlines during representative flights and (2) fabrication and launch of the developed designs to test their flight performance and consistency. Altitude and 3-axis stability was measured during the eight flights via an onboard instrument package. Data from both experiments demonstrated that the designs were effective, but varied widely in their performance; the sources of the performance differences and errors were documented and analyzed. The modularization process reduced the number of parts dramatically, while retaining good performance and reliability. The specific benefits and caveats of using extrusion-based 3-D printing to produce airframe components are also demonstrated.

Keywords: modular design; aircraft design; solid-propellant rocket; design of experiments; additive manufacturing; fused deposition modeling

1. Introduction and Background The present study develops and tests a modular design method for small solid-propellant (SP) rockets utilizing the benefits of additive manufacturing (AM) technologies during design and fabrication. The design process thus developed will take advantage of the many benefits offered by AM to produce excellent rocket airframe designs while modularizing the system as much as possible. For the purposes of this study, a SP rocket will be defined as being an aircraft that uses a fast-burning solid propellant for motion, aerodynamic fins as control surfaces, and a strictly atmospheric range domain. The aircraft can fly either vertically or horizontally, may or may not have active control, and will always carry a small payload. Examples of such aircraft are legion; sounding rockets for carrying small scientific instruments [1,2], military hardware (particularly air-to-air missiles, ballistic missiles and missile defense [3–5], atmospheric booster stages on some orbital vehicles [6,7], model rockets for education, research, and entertainment [8,9], and controlled avalanche triggering devices [10]. Modularization is a product design technique in which the system is divided into subsystems or modules, which can be designed and manufactured independently and, ideally, used in several

Aerospace 2017, 4, 17; doi:10.3390/aerospace4020017 www.mdpi.com/journal/aerospace Aerospace 2017, 4, 17 2 of 25 Aerospace 2017, 4, 17 2 of 24 different systems. Examples of modular products ab abound,ound, from furniture furniture to construction construction equipment, equipment, production tooling, officeoffice cubicles,cubicles, and eveneven homes.homes. The The basic reason for the modularization of products is to overcome design and production issu issues,es, control control the the product product lifecycle lifecycle more more effectively, effectively, produce moremore flexibleflexible product product lines, lines, and and to to gain gain more more output output from from invested invested time time and and resources resources [11 –[11–13]. 13]. To best accomplish these goals, several specific objectives must be developed for the product in designTo [ 14best,15 accomplish]. In informal these terms, goals, these several are: specific objectives must be developed for the product in design [14,15]. In informal terms, these are: 1. Design tasks should be done by teams of specialists to facilitate efficient development; 1. Design tasks should be done by teams of specialists to facilitate efficient development; 2. Customize and improve the production and assembly process for the subsystems; 2. Customize and improve the production and assembly process for the subsystems; 3. Standardize every possible aspect of the system or subsystem; 3. Standardize every possible aspect of the system or subsystem; 4. ConsiderConsider testing, testing, maintenance, maintenance, and repair re requirementsquirements when designing the architecture; 5. DesignDesign products products such such that individual parts and subsystems can be easily upgraded; 6. DesignDesign products products to to be easily reconfigurable reconfigurable for different missions; 7. DesignDesign products products such such that disassembly an andd recycling at end-of-life is simplified;simplified; 8. DesignDesign products products that that have a specific specific core miss missionion but that are easily customized byby thethe user.user.

Traditionally, thesethese objectivesobjectives areare metmet by the designdesign and production of independent independent subsystems, subsystems, each containing various parts of the system (Figure(Figure1 1).).

Part 1 Part 2 Part 3 Part 4 Part 5 Part 6 Part 7 Part 8 Part 9 Part 10

Part 1 Part 8 Part 4 Part 6 Part 2 Part 9 Part 5 Part 7 Part 3 Part 10 Subassembly 1 Subassembly 2 Subassembly 3 Subassembly 4 Subassembly

Final Product

Figure 1. Part-Subsystem-System conﬁguration.configuration.

The main issue with this approach is the problems problems with integration and communication between the various subsystems once they are assembled. Each subsystem would traditionally be designed by a teamteam ofof specialists, specialists, each each team team using using a slightly a slightly different different architecture architecture and controland control technique technique [15]. Many [15]. systemsMany systems engineering engineering (SE) product (SE) product lifecycle lifecycle engines, engines, such as such the SE as Engine the SE usedEngine by theused US by National the US AeronauticsNational Aeronautics and Space and Administration Space Administration (NASA) [16 (NASA)] and the [16] Systems-of-Systems and the Systems-of-Systems approach used approach by the USused Missile by the Defense US Missile Agency Defense (MDA) Agency [17], (MDA) develop [1 sophisticated7], develop sophisticated and complex and techniques complex fortechniques dealing withfor dealing theseintegration with these problems.integration problems. A moremore effective,effective, if if yet yet not not fully fully proven, proven, technique technique for modularization for modularization is the integration-of-functions is the integration-of- method,functions inmethod, which in advanced which advanced manufacturing manufacturing techniques techniques such such as AM as AM can can be be used used to to produce multi-function parts [18,19]. [18,19]. This This reduces reduces or eliminates the need for using subsystems to gain the benefitsbenefits of modularization. This technique also remo removesves most or all the inherent inherent integration problems encountered with subsystems; it is well known that most systems failures happen at interfaces, so eliminating interfaces raises the reliability andand qualityquality ofof thethe entireentire systemsystem [[20,21].20,21]. Objections could be raised to this, as thethe technique removes standardization from the modularization process and and requires requires all all the the system system components components to to be be specialized. specialized. This This objection objection is iseliminated eliminated by by one one of of the the basic basic characteristics characteristics of of AM AM technologies, technologies, mass mass customization customization [[22,23].22,23]. Since AM does not require anyany specialspecial toolingtooling to produceproduce parts and thethe partsparts areare infinitelyinfinitely customizablecustomizable within the design software [24], a supply chain of readily available on-the-shelf parts is not necessary. Figure 2 shows graphically how the modularization concept is modified by the use of AM. Aerospace 2017, 4, 17 3 of 25 within the design software [24], a supply chain of readily available on-the-shelf parts is not necessary. FigureAerospace2 2017shows, 4, 17 graphically how the modularization concept is modified by the use of AM. 3 of 24

Function 3 Function 10

Function 5 Function 7 Function 2 Function 9

Function 1 Function 4 Function 6 Function 8

Part A Part B Part C Part D

Final Product

Figure 2. Functions-Part-Product conﬁguration.configuration.

While it is sometimes practical to print final products as single parts, this suppresses the other While it is sometimes practical to print ﬁnal products as single parts, this suppresses the other benefits of modularization, particularly those offered by Goals 4–8 (see above); systems fabricated in beneﬁts of modularization, particularly those offered by Goals 4–8 (see above); systems fabricated in this way usually will be throw-away products that are not meant to be repaired or upgraded. this way usually will be throw-away products that are not meant to be repaired or upgraded. Therefore, Therefore, it is assumed for most products that would be modularized that the subsystem level is the it is assumed for most products that would be modularized that the subsystem level is the highest highest level at which it is practical to combine functions into single parts. This has introduced the level at which it is practical to combine functions into single parts. This has introduced the concept of concept of feature cataloging [25], contrasted with the old method of part or subsystem cataloging. feature cataloging [25], contrasted with the old method of part or subsystem cataloging.

2. Materials and Methods I: Modular Additive Manufacturing (AM)-Based DesignDesign MethodologyMethodology This section expands expands on on the the previously previously discusse discussedd topic topic of ofproduct product modularity modularity and and develops develops the thebasic basic model model for a formodular a modular AM-based AM-based design designmethod methodology.ology. There is not There yet isa clear not yetand auniversally clear and universallyaccepted general accepted definition general of definition “product ofmodularizatio “product modularization”n” [26]; therefore, [26 ];in therefore, the context in of the the context present of thestudy present and previously study and discussed previously research, discussed the authors research, offer the the authors following offer definition the following for a traditional definition system: for a traditionalProduct system: modularization is the process of decomposing a complex system into standardized and moreProduct easily manageable modularization subsystems is the process with five of decomposingmajor characteristics: a complex system into standardized and more. The easily subsystems manageable are subsystemscomposed of with a high five percen majortage characteristics: of standard off-the-shelf components; . The subsystems are easily serviceable and recyclable; The subsystems are composed of a high percentage of standard off-the-shelf components; . The subsystem itself or any of its components can be replaced or upgraded by the user at will; . TheThe subsystemssystem has area core easily mission, serviceable but andthe recyclable;specific configuration of subsystems allows it to accomplishThe subsystem more itself than or one any mission; of its components can be replaced or upgraded by the user at will; . TheThe systemmodular has system a core mission,offers time but theor specificcost saving configurations or another of subsystems significant allows benefit it to to accomplish the user, comparedmore than with one mission;a non-modular system for the same task. The modular system offers time or cost savings or another significant benefit to the user, compared As described previously, AM technologies allow the integration of functions within a design. with a non-modular system for the same task. While traditional modularization mainly involved the collection of similar or complementary parts into Asgroups described [27], the previously, integration AM of technologies functions involves allow the the integration manufacturing of functions of more within complex a design. parts Whileinstead traditional of subsystems. modularization This would mainly seem counterintui involved thetive collection to the casual of similar observer, or complementary but the introduction parts intoof AM groups technologies [27], the integration and infinite of functionstool-less involvescustomization the manufacturing into the equation of more allows complex this parts idea instead to be ofeffective. subsystems. Lack Thisof customization would seem counterintuitive within modularizations to the casual is sometimes observer, but a thehard introduction price to pay of AMfor technologiesspecialized systems, and infinite as the tool-less use of customizationone-off parts is into highly the equationdiscouraged allows [27]. this idea to be effective. Lack of customizationAll AM parts within are, modularizationsby definition, one-off is sometimes parts; complex a hard price and to simple, pay for standardized specialized systems, parts are as theequally use ofdifficult one-off to parts produce. is highly However, discouraged it is [impo27]. rtant to maintain system flexibility as much as possible;All AM AM parts allows are, almost by definition, infinite one-offflexibility parts; during complex design and and simple, fabrication, standardized but none parts in are the equally field. difficultFrom this to knowledge, produce. However,it is clear that it is a important modularity to-based maintain design system process flexibility for additively as much manufactured as possible; AMproducts allows requires almost infinitea marriage flexibility of both during modularity design andprinciples fabrication, and traditional but none innon-modular the field. From design this knowledge,principles. Each it is clearof the that authors’ a modularity-based modularization design principles process discussed for additively above are manufactured affected by this: products . Standardization of components: An AM-based methodology eliminates standardization almost completely; all the components used are theoretically customized. In a non-AM system, this could give the optimal design for a particular application but would be prohibitively expensive. AM offers the optimization benefits without the high cost, but does not eliminate the standardization problem. Aerospace 2017, 4, 17 4 of 25 requires a marriage of both modularity principles and traditional non-modular design principles. Each of the authors’ modularization principles discussed above are affected by this:

Standardization of components: An AM-based methodology eliminates standardization almost completely; all the components used are theoretically customized. In a non-AM system, this could give the optimal design for a particular application but would be prohibitively expensive. AM offers the optimization beneﬁts without the high cost, but does not eliminate the standardization problem.

AerospaceServiceability 2017, 4, 17 and recyclability of the system components: Since subsystems are replaced4 of 24 by single complex parts, serviceability of the subsystems is nearly impossible. However, this may . notServiceability be a large problem and recyclability if the complex of the parts system are inexpensivecomponents: enoughSince subsystems such that are they replaced are easily by and cheaplysingle replaced. complex parts, The savingsserviceability in manufacturing of the subsystems and is assembly nearly impossible. cost from However, using complex this may parts insteadnot be of a subsystemslarge problem will if the likely complex offset parts the are non-serviceability inexpensive enough of thesuch components. that they are easily Recyclability and willcheaply most likely replaced. dramatically The savings improve in manufacturing with the use and of AM,assembly as the cost parts from will using likely complex be made parts from a instead of subsystems will likely offset the non-serviceability of the components. Recyclability single material. will most likely dramatically improve with the use of AM, as the parts will likely be made from Usera single customizability: material. Producing a modular system that the customer can modify at will is much . moreUser difficult customizability using AM,: Producing as fewer a parts modular means system less that on-the-go the customer customizability. can modify However, at will is much the user couldmore have difficult much using more AM, input as fewer into parts the designmeans less at theon-the-go beginning, customizability. reducing However, the desire the and user need to customize.could have much more input into the design at the beginning, reducing the desire and need to Corecustomize. mission: While most integrated AM-made products will likely be less flexible for the user, . theCore increased mission: user While input most during integrated design AM-made will provide products the bestwill possiblelikely be less benefit flexible to the for userthe user, and the lowerthe costincreased likely user means input that during the userdesign could will affordprovide a the wider best range possible of products,benefit to the reducing user and the the need forlower a do-all cost product. likely means that the user could afford a wider range of products, reducing the need for a do-all product. In lightIn light of thisof this knowledge, knowledge, the the authors authors proposepropose a definition definition of of AM-based AM-based design design modularization modularization (Figure(Figure3 shows 3 shows the the definition definition graphically, graphically, compared compared to to the the traditionaltraditional method): method):

Characteristic Traditional Modularization Method AM-Based Modularization Method

Configuration Individual part s grouped int o subsystems Part functions grouped into customized complex parts

Standardization All subsystems are easily serviceable Few to none of the parts are standardized and are manufactured on-demand; no parts kept on hand, because even standard parts can be made on demand

Serviceability All or most parts are standardized and off-the- Multi-functional parts are usually not shelf; spares of custom parts kept on hand serviceable but are easily fully replaced on- demand

Recyclability Subsyst ems must be disassembled before Customized parts easily recyclable with no recycling disassembly required

Customization Customization of subsystems is limited to Nearly infinite customization During Design available standard part configurations

Customization Customization of subsystems is limited to None - design of system components is fixed; During Use available standard part configurations however, they are easily replaced with new custom system components

Mission change is very difficult but t he M ission Flexibility Mission flexibility is easy but is determined by available standard part configurations customizability of the design and original fabrication provided less need for mission flexibility; if flexibility is needed, a new system designed for the new mission can be made on-demand

Figure 3. Traditional vs. additive manufacturing (AM)-based modularization method. Figure 3. Traditional vs. additive manufacturing (AM)-based modularization method. AM-based product modularization is the process of decomposing a complex system into several complex multi-function components that can be optimized for a particular mission. This design methodology has five major characteristics: . Few to none of the parts are standardized; . No parts are kept in stock and all parts are made on-demand and optimized for the system and mission at hand; Aerospace 2017, 4, 17 5 of 25

AM-based product modularization is the process of decomposing a complex system into several complex multi-function components that can be optimized for a particular mission. This design methodology has ﬁve major characteristics:

Few to none of the parts are standardized; AerospaceNo 2017 parts, 4, 17 are kept in stock and all parts are made on-demand and optimized for the system5 andof 24 mission at hand; . Aerospace 2017, 4, 17 5 of 24 TheThe multi-functional partsparts areare rarely rarely to to never never serviceable, serviceable, but but are are easily easily replaced replaced on demandon demand and andeasily easily recycled; recycled; . . TheThe multi-functional multi-functional parts parts are are not rarely customizable to never serviceable, in use, but but they are are easily easily replaced customizable on demand during The multi-functional parts are not customizable in use, but they are easily customizable during designand easily and fabrication; recycled; . design and fabrication; . TheThe system multi-functional has only partsone coreare not mission customizable per configuration, in use, but they but are the easily lower customizable cost and powerduring of Thedesign system and hasfabrication; only one core mission per configuration, but the lower cost and power of customizability during design and fabrication allows users to obtain more than one system to . customizabilityThe system has during only one design core and mission fabrication per configuration, allows users but to obtainthe lower more cost than and one power system of to serve their needs. servecustomizability their needs. during design and fabrication allows users to obtain more than one system to serve their needs. 3. Materials and Methods II: Rocket Design 3. MaterialsIn order to and demonstrate Methods II: the Rocket AM-based Design modular designdesign process, a case study was developed; the topic ofIn thethe order studystudy to demonstrate waswas thethe modularizationmodularization the AM-based ofmodularof smallsmall solid-propellantdessolid-propellantign process, a case rocketrocket study airframes.airframes. was developed; An excellentexcellent the modeltopic to of reference the study is was the USthe Navymodularization AIM-9X SidewinderSidewinde of small solid-propellantr missile [[28],28], a rocket rough airframes. sketch of which An excellent is shown in model Figure to4 4.. reference TheThe missilemissile is the isis steeredsteeredUS Navy toto AIM-9X itsits targettarget Sidewinde withwith thether aid aidmissile ofof aa [28], jetjet vane,vane, a rough soso allsketchall thethe controlofcontrol which surfacessurfaces is shown areare fixedfixedin Figure [[29],29], a 4. configurationconfiguration The missile is thatthat steered lendslends to itselfitselfits target wellwell with toto thethe the useuse aid of ofof AMAMa jet totovane, fabricatefabricate so all the thethe control airframe.airframe. surfaces are fixed [29], a configuration that lends itself well to the use of AM to fabricate the airframe.

Figure 4. Rough artistic representation of AIM-9X Sidewinder missile airframe. Figure 4. Rough artistic representation of AIM-9X Sidewinder missile airframe. Figure 5 shows an exploded view of the Sidewinder missile; clearly, there are many ways that FigureFigure5 shows 5 shows an an exploded exploded view view of of the the SidewinderSidewinder missile; clearly, clearly, there there are are many many ways ways that that this type of airframe could be optimized into subsystems or complex parts. Level 1 shows the major thisthis type type of of airframe airframe could could be be optimized optimized intointo subsystemssubsystems or or complex complex parts. parts. Level Level 1 shows 1 shows the the major major airframe pieces, while Level 2 shows potential subassemblies that could be created. Level 3 shows airframeairframe pieces, pieces, while while Level Level 2 shows2 shows potential potential subassemblies subassemblies that that could could be be created. created. Level Level 3 3 shows shows the ﬁnalthethe final stage final stage ofstage the of of the AM-based the AM-based AM-based design design design modularization. modularizati modularization. Three ThreeThree parts parts parts remain; remain; remain; the th nosethe enose nose cone cone cone (guidance), (guidance), (guidance), the upperthethe upper upper section section section (payload/warhead), (payload/warhead), (payload/warhead), and and and the thethe lower lower section sectionsection (propulsion). (propulsion). (propulsion). Many Many Many other other other conﬁgurations configurations configurations are possible;areare possible; possible; what what what is shown is is shown shown here here ishere a veryis is a a very very simple simplesimple example example to demonstrate toto demonstrate demonstrate the the concept.the concept. concept.

Figure 5. Cont. Figure 5. ContCont.. Aerospace 2017,, 4,, 1717 6 of 24 25 Aerospace 2017, 4, 17 6 of 24

Figure 5. Example modularization of AIM-9 Sidewinder missile. Figure 5. Example modularization of AIM-9 Sidewinder missile. In order to examine this design approach further and provide a detailed example of rocket In order to examine this design approach further and provide a detailed example of rocket design,In order a series to examine of new rocket this design designs approach must be further generated. and A provide configuration a detailed similar example to that of of rocket the AIM- design, design, a series of new rocket designs must be generated. A configuration similar to that of the AIM- a series9 missile, of new with rocket four wings designs at the must bow be section generated. of the A aircraft configuration and four similar at the stern, to that was of chosen; the AIM-9 the front missile, 9 missile, with four wings at the bow section of the aircraft and four at the stern, was chosen; the front withand four rear wings wings atwere the off-set bow section from each of the other aircraft at 45-degree and four angles. at the The stern, length was of chosen; the new the airframes front and was rear wingsandspecified rear were wings as off-set 40 were cm. from Theoff-seteach design from other variable each at 45-degree other between at 45-degree angles. the two The was angles. length decided The of tolength the be new the of shape airframesthe new of the airframes was wings, specified as was specifiedasshown 40 cm. inas The Figure40 design cm. 6;The the variable design shapes between variable chosen were thebetween two the wasdelta the decidedtwo, the wasclipped to decided be delta, the shapeto elliptical, be the of theshape and wings, rectangular. of the as wings, shown In as in shownFigureorder6 in ;to the Figure best shapes assess 6; the chosen the shapes effect were chosen of the the delta, werefin shapes the delta clipped on ,the the delta,airframe clipped elliptical, performance,delta, elliptical, and rectangular. they and were rectangular. Inallocated order toIn orderbestaccording assess to best the to assess effecta 2-level ofthe thefull-factorial effect fin shapes of the design onfin the shapes (Table airframe 1).on the performance, airframe performance, they were allocated they were according allocated to a according2-levelThe full-factorial to choice a 2-level of designfins full-factorial to analyze (Table1 ).wasdesign purely (Table a design 1). decision, as many different combinations are possibleThe choice beyond of thefins fins four to analyzechosen. The was purpose purely aof design this study decision, was to as explore many the differentdiff designerent combinationsmodularization are possiblemethod, beyond so several the four designs chosen. were The generated purpose purely of th this tois study explore was the to effectiveness explore the of design the method. modularization Future method,studies so should several be designs done to morewere rigorouslygenerated analyze purely theto explore effects of the the effectiveness various fin combinations, of the method. as veryFuture studieslittle literatureshould be exists done on to themore topic rigorously and most analyze previous the work effects was of done the various long ago fin fin and combinations, without the aid as veryof littlesophisticated literature exists design on and the analysis topic and tools. most previo previousus work was done long ago and without the aid of sophisticated design and analysis tools.

Figure 6. Selected fin shapes: (a) delta; (b) clipped delta; (c) elliptical; and (d) rectangular.

Figure 6. SelectedSelected fin ﬁn shapes: ( (aTablea)) delta; delta; 1. Experimental( (bb)) clipped clipped delta; delta; design. ( (cc)) elliptical; elliptical; and and ( (d)) rectangular. rectangular.

Design LowerTable 1.Fin Experimental Shape Upper design. Fin Shape A Clipped delta Rectangular Design Lower Fin Shape Upper Fin Shape DesignB LowerElliptical Fin Shape Rectangular Upper Fin Shape AC ClippedElliptical delta Rectangular Delta A Clipped delta Rectangular BBD ClippedElliptical Elliptical delta Rectangular Delta Rectangular CC Elliptical Elliptical Delta Delta DD Clipped Clipped delta delta Delta Delta Aerospace 2017, 4, 17 7 of 25 Aerospace 2017, 4, 17 7 of 24

While thisthis designdesign experiment experiment is is quite quite simple, simple, it demonstratesit demonstrates the the concept concept and and approach approach in a clearin a andclear effective and effective way, paving way, paving the way the for way more for complex more complex studies in studies the future. in the Figure future.7 shows Figure the 7 setshows of ﬁnal the designs,set of final created designs, according created toaccording the experimental to the expe design.rimental Similar design. to the Similar AIM-9 to missilethe AIM-9 case missile previously case discussed,previously thediscussed, airframes the wereairframes designed were todesigned be made to in be three made pieces: in three the pieces: booster the section, boosterthe section, payload the section,payload andsection, the noseand the cone, nose each cone, printed each printed as a single as a piece. single As piece. these As rockets these rockets will be will launched, be launched, it was necessaryit was necessary to include to include a set of alaunch set of launch rail lugs, rail clearly lugs, clearly seen in seen Figure in 7Figure. 7.

Figure 7. Selected rocket designs.

The rockets werewere manufacturedmanufactured from from polylactic polylactic acid acid (PLA), (PLA), which which is is biodegradable, biodegradable, in in case case any any of theof the specimens specimens or parts or parts were lostwere during lost launches;during laun it isches; slightly it is heavier slightly than heavier standard than ABS standard (acrylonitrile ABS butadiene(acrylonitrile styrene) butadiene plastic styrene) but more plastic environmentally but more environmentally responsible. The responsible. rockets were The printed rockets with were the fusedprinted deposition with the fused modeling deposition method, modeling using 0.8 method, mm walls using and 0.8 3% mm inﬁll, walls for and a total 3% emptyinfill, for weight a total of aroundempty weight 80 g for of a around 40 cm airframe. 80 g for a The 40 cm internal airframe. engine The cavity internal in theengine booster cavity section in the was booster designed section to accommodatewas designed to Estes accommodate C11-3 model Estes rocket C11-3 engines model during rocket launches. engines during launches.

4. Materials and Methods III: Fluid Dynamics Analysis Now that the designs have been established, performanceperformance analysis on the rocket designs can begin. In order to guide expectations from the laun launchch experiments and aid aid in in interpreting interpreting the the results, results, some preliminary performance performance knowledge knowledge is is vital. vital. To To estimate estimate these these performance performance characteristics, characteristics, a ® adigital digital windwind tunnel tunnel mo modeldel was was constructed constructed using using the the ANSYS CFX ® computationalcomputational fluid fluid dynamics (CFD) packagepackage (ANSYS(ANSYS Inc.,Inc., CecilCecil Township,Township, PA,PA, USA). USA). First, the drag coefficientscoefficients for each of the designsdesigns were calculated in order to provide input for a preliminary analyticalanalytical performanceperformance analysis. analysis. For For each each of of the the designs, designs, the the drag drag coefficient coefficient was was found found at variousat various speeds, speeds, from from 10 to 10 100 to m/s, 100 andm/s, plotted and plotte in Figured in8 .Figure The fluid 8. The tested flui wasd tested air at onewas atmosphere air at one ofatmosphere pressure, of 28 pressure, degrees Celsius,28 degrees and Celsius, with a and medium with a turbulence medium turbulence factor of 0.05. factor The of 0.05. cross-sectional The cross- areassectional for eachareas rocket for each design rocket were design identical; were identical; the differences the differences in drag were in drag due towere the due various to the geometry various combinationsgeometry combinations of fins. of fins. The basic CFD model was built and analyzed in five major steps:

1. The geometry of each rocket was created using commercial 3-D modeling software (Siemens SolidEdge® ST9®, Siemens AG, Munich, Germany) and imported into the ANSYS geometry environment. Within this environment, a fluid domain was modeled around the rocket; the domain was square in cross-section and provided approximately 0.5 m of fluid distance from each surface of the rocket. 2. Upon geometry and fluid domain definition, the model was meshed using the ANSYS mesh environment. The mesh was set to fine for the entire domain, generating around 1.8 million elements per rocket, 380,000 of which were in the domain very near the interface between the rocket and fluid. Aerospace 2017, 4, 17 8 of 25

3. The meshed model was then imported into ANSYS CFD Pre®, in which the analysis characteristics are set. The center of mass and center of pressure for the rocket were found automatically by the software. The airspeed was set, as well as the ANSYS CFX® properties within this domain. Convergence tolerance was specified to be 1 × 10−5 with no limit on the allowed number of model iterations. 4. The model was then analyzed in ANSYS CFX® to find the drag coefficients on the rocket bodies. The drag was measured by tracking the force on the rocket body, in the direction of fluid flow, until steady state was reached. The average number of iterations to convergence of 1 × 10−5 was about 650, requiring around 25 min to run for each case. Aerospace5. Finally, 2017, 4 the, 17 model was analyzed in ANSYS CFD Post®. 8 of 24

Figure 8. Drag Coefﬁcients from ANSYS CFX® Analysis; cross-section of aircraft shown. Figure 8. Drag Coefficients from ANSYS CFX® Analysis; cross-section of aircraft shown.

TheWithin basic the CFD ANSYS model CFD was Post built®, two and other analyzed pieces in of five information major steps: were gathered. In order to be able to make some predictions about the stability and performance of the airframes before launch, a contour 1. The geometry of each rocket was created using commercial 3-D modeling software (Siemens map of the pressure gradient after model convergence was collected, as well as the streamlines of the SolidEdge® ST9®, Siemens AG, Munich, Germany) and imported into the ANSYS geometry air flowing over the airframes. The results are shown in Figures9 and 10. In the cases shown, the environment. Within this environment, a fluid domain was modeled around the rocket; the traveling speed was 50 m/s. It was assumed that the angle of attack was constant during the CFD domain was square in cross-section and provided approximately 0.5 m of fluid distance from analysis, with no major deviation from perfectly vertical flight. each surface of the rocket. There are noticeable differences between the pressure gradients in Figure9, particularly between 2. Upon geometry and fluid domain definition, the model was meshed using the ANSYS mesh the upper fin shapes. The formation of the pressure wave ahead of the fins indicates that the rectangular environment. The mesh was set to fine for the entire domain, generating around 1.8 million fins will produce more drag, which was also found in Figure8 above. The results do not indicate any elements per rocket, 380,000 of which were in the domain very near the interface between the severe imbalances that will cause major instability during the flight. However, the streamline plots rocket and fluid. (Figure 10) tell a different story. The flow pattern over Design A indicates that there may be significant 3. The meshed model was then imported into ANSYS CFD Pre®, in which the analysis disturbance in the flow during launch. It is anticipated that Design A will be the most unstable of the characteristics are set. The center of mass and center of pressure for the rocket were found four designs during flight. The others appear to be stable, with Design D providing the most straight automatically by the software. The airspeed was set, as well as the ANSYS CFX® properties and stable flow pattern. within this domain. Convergence tolerance was specified to be 1 × 10−5 with no limit on the allowed number of model iterations. 4. The model was then analyzed in ANSYS CFX® to find the drag coefficients on the rocket bodies. The drag was measured by tracking the force on the rocket body, in the direction of fluid flow, until steady state was reached. The average number of iterations to convergence of 1 × 10−5 was about 650, requiring around 25 min to run for each case. 5. Finally, the model was analyzed in ANSYS CFD Post®.

Within the ANSYS CFD Post®, two other pieces of information were gathered. In order to be able to make some predictions about the stability and performance of the airframes before launch, a contour map of the pressure gradient after model convergence was collected, as well as the streamlines of the air flowing over the airframes. The results are shown in Figures 9 and 10. In the cases shown, the traveling speed was 50 m/s. It was assumed that the angle of attack was constant during the CFD analysis, with no major deviation from perfectly vertical flight. Aerospace 2017, 4, 17 9 of 24 Aerospace 2017,, 4,, 1717 9 of 24 25

Figure 9. 3-D pressure contour map from ANSYS CFX® ((v = 50 m/s) 50 m/s). Figure 9. 3-D pressure contour map from ANSYS CFX® ( = 50 m/s) .

FigureFigure 10.10. Streamline mapmap fromfrom ANSYSANSYS CFXCFX®® (v = 50 m/s)50 m/s).. Figure 10. Streamline map from ANSYS CFX® ( = 50 m/s). There are noticeable differences between the pressure gradients in Figure 9, particularly between ThereTo better are noticeable understand differences the results between from this the section,pressure a gradients brief extra in literatureFigure 9, particularly review was between done to the upper fin shapes. The formation of the pressure wave ahead of the fins indicates that the thefind upper similar fin results shapes. from The the formation published of literature. the pressu A similarre wave CFD ahead model of the to the fins one indicates presented that in the rectangular fins will produce more drag, which was also found in Figure 8 above. The results do not presentrectangular study fins was will completed produce more by Grover drag, which Aerospace was also [30], found which in used Figure rockets 8 above. with The only results four controldo not indicate any severe imbalances that will cause major instability during the flight. However, the indicatesurfaces andany asevere much higherimbalances velocity. that The will drag cause coefficients major instability found are during comparable the flight. to those However, found in thisthe streamline plots (Figure 10) tell a different story. The flow pattern over Design A indicates that there streamlinechapter, after plots taking (Figure onto 10) consideration tell a different the story. differences The flow in pattern velocity; over they Design are, on A average,indicates around that there 0.1 may be significant disturbance in the flow during launch. It is anticipated that Design A will be the maylower be than significant the ones disturbance found here, in but the this flow is during easily explainedlaunch. It byis anticipated the differences that inDesign velocity A will and be a fewthe most unstable of the four designs during flight. The others appear to be stable, with Design D mostcontrol unstable surfaces. of Inthe a secondfour designs interesting during study flight. that The was others performed, appear Niskanen to be stable, [31] foundwith Design that drag D providing the most straight and stable flow pattern. providingcoefficient the varied most from straight 0.30 toand 0.40 stable in simulation flow pattern. and from 0.25 to 0.40 in wind tunnel tests, both with Aerospace 2017, 4, 17 10 of 25 subsonic flight speed. The rocket design studied had three control surfaces and flew at a significantly faster speed than the rockets used in the present study. Accounting for these characteristics, the results were comparable to those found in this paper and in [30].

5. Materials and Methods IV: Analytical Calculations As the drag coefficients were calculated in the previous section, an analytical dynamic analysis can be performed on the rockets in order to predict the flight altitude (apogee). The flight analysis is subjected to the following assumptions:

1. The air is static (no significant wind); 2. The properties of the air remain constant throughout the flight; 3. At the end of a time delay following burnout, the rocket motor will stop free-flight motion by ejecting the payload, in this case an instrument package and recovery system.

The engine characteristics from the manufacturer are shown in Table2. The manufacturer stated that the delay time between burnout and payload ejection is subjected to a tolerance of 10%. The exact velocity profile of the rocket during flight is not known, so minimum and maximum apogees will be calculated based on the minimum and maximum drag coefficients calculated in the previous section. It will be assumed that all of the original propellant will be burned off during the powered launch time, and therefore the mass will change with time. Launch site characteristics are shown in Table3.

Table 2. Estes C11-3 model rocket engine performance speciﬁcations [32].

Maximum Lift Maximum Thrust Initial Propellant Time Impulse (N·s) Weight (g) Thrust (N) Duration (s) Weight (g) Weight (g) Delay (s) 170 22.1 0.8 10.00 32.2 11.00 3

Table 3. Launch site characteristics.

Launch Site Gravity Coefﬁcient g Air Temp Air Pressure Relative Air Density Altitude (m) 1 (m/s2) 2 (◦C) 1 (KPa) 1 Humidity (%) 1 (kg/m3) 3 274 9.79651 32.5 101.83 88 1.144 1 Site measurement; 2 Based on latitude and elevation; 3 Based on pressure, humidity, and temperature.

The flight calculations [33–35] for a dynamic flight path provide the total flight altitude that should be expected from launch. The flight is divided into four regions (Figure 11): (1) pre-flight, when the motor is providing thrust to accelerate the rocket, but no motion has occurred yet; (2) powered flight, when the motor is providing thrust to the airframe; (3) free flight, where the rocket continues to coast until the payload ejection time; and (4) recovery, where the recovery system has been deployed Aerospaceand the 2017 rocket, 4, 17 falls until it reaches the ground. 11 of 24

Thrust Duration Time Delay

Pre- Powered Free Flight Recovery Flight Flight Motion Start of of Start Payload Eje ction Burnout

Figure 11. Rocket flight regions. Figure 11. Rocket ﬂight regions.

Figure 12 shows the free body diagram for a rocket launch. The thrust force propels the vehicle forward, while weight and drag forces oppose it. In this study, the airframes weighed approximately 80 g, the motor weighed 32 g at lift off and 21 g at burnout, the recovery system (a plastic streamer) weighed approximately 10 g, and the instruments weighted approximately 10 g, for a total of about 132 g (1.2945 N) at launch and 121 g (1.1866 N) at burnout. The thrust-to-weight ratio therefore is 17.0722, where 13.2563 is the minimum allowable for the motor (see Table 2). The drag coefficient was found in Section 4; a summary of the extrema is shown in Table 4. Weight Drag

Thrust

Figure 12. Rocket free body diagram.

Table 4. Minimum and Maximum Drag Coefficients.

Design Minimum ( = /) Maximum ( = /) A 0.5012 0.5836 B 0.5127 0.5914 C 0.4965 0.5673 D 0.4908 0.5627

As shown in Figure 11, the flight time of the rocket until maximum altitude is the sum of the powered flight time and the free flight time. Equation (1) demonstrates the relationship.

= + (1) The altitude reached at the end of powered flight is given by Equation (2), where the is the rocket mass (kg), is the drag factor (dimensionless), is the motor thrust (N), g is the gravity coefficient (m/s2), and is the burnout velocity (m/s). −g− =− ln (2) 2 −g Aerospace 2017, 4, 17 11 of 24

Thrust Duration Time Delay

Pre- Powered Free Flight Recovery Flight Flight Motion Start of of Start Payload Eje ction Burnout

Aerospace 2017, 4, 17 11 of 25 Figure 11. Rocket flight regions.

Figure 12 shows the free body diagram for a rocketrocket launch. The thrust force propels the vehicle forward, while weight and drag forces oppose it. In In this this study, study, the airframes airframes weighed weighed approximately approximately 80 g, the motor weighed 32 g at lift off and 21 g at burnout, the recovery system (a plastic streamer) weighed approximately 10 g, and the instruments weighted approximately 10 g, for a total of about 132 g (1.2945(1.2945 N) atat launchlaunch andand 121121 gg (1.1866(1.1866 N)N) atat burnout.burnout. The thrust-to-weight ratio therefore is 17.0722, wherewhere 13.256313.2563 is is the the minimum minimum allowable allowable for for the the motor motor (see (see Table Table2). The 2). dragThe drag coefﬁcient coefficient was foundwas found in Section in Section4; a summary 4; a summary of the of extrema the extrema is shown is shown in Table in 4Table. 4. Weight Drag

Thrust Figure 12. Rocket free body diagram. Figure 12. Rocket free body diagram.

Table 4. Minimum and Maximum Drag Coefﬁcients. Table 4. Minimum and Maximum Drag Coefficients.

DesignDesign Minimum Minimum Cd ((v = 10 m//s) MaximumMaximum (Cd =(v = 100 / m) /s) AA 0.5012 0.5012 0.5836 0.5836 BB 0.5127 0.5127 0.5914 0.5914 CC 0.4965 0.4965 0.5673 0.5673 DD 0.4908 0.4908 0.5627 0.5627

As shown in Figure 11, the flight time of the rocket until maximum altitude is the sum of the As shown in Figure 11, the flight time of the rocket until maximum altitude is the sum of the powered flight time and the free flight time. Equation (1) demonstrates the relationship. powered flight time and the free flight time. Equation (1) demonstrates the relationship. = + (1) Alttotal = Altpow + Alt f ree (1) The altitude reached at the end of powered flight is given by Equation (2), where the is the rocketThe mass altitude (kg), reached is the at drag the endfactor of (dimensionless), powered flightis given is the by motor Equation thrust (2), (N), where g is thethe mgravityis the rocketcoefficient mass (m/s (kg),2), andD is the is the drag burnout factor (dimensionless),velocity (m/s). T is the motor thrust (N), g is the gravity coefficient (m/s2), and v is the burnout velocity (m/s).−g− =− ln (2) 2 −g m T − mg − Dv2 Alt = − ln (2) pow 2D T − mg

The altitude reached at the end of free ﬂight is shown in Equation (3), where the m is the rocket mass (kg), D is the drag factor (dimensionless), g is the gravity coefﬁcient (m/s2), and v is the burnout velocity (m/s). m mg + Dv2 Alt = ln (3) f ree 2D mg Aerospace 2017, 4, 17 12 of 25

Burnout velocity is calculated using Equations (4) and (5), where the m is the rocket mass (kg), D is the drag factor (dimensionless), T is the motor thrust (N), t is the motor burn time (s), and g is the gravity coefficient (m/s2). r T − mg 1 − e−x v = (4) D 1 + e−x where: p (T − mg)D x = 2t (5) m The burn time (distinct from the thrust time) is given by Equation (6). This is a function of the motor thrust T (N) and impulse I (N·s). I t = (6) T The manufacturer of the engine gives an impulse efficiency rating of 0.90. Considering this, Equation (6) becomes Equation (7). I t = 0.9 (7) T Finally, the drag factor is given by Equation (8). Area A is the cross-sectional area of the airframe 2 3 (m ), ρ is the air density (kg/m ), and Cd is the drag coefficient (see Table4).

1 D = ρC A (8) 2 d Given the information in Tables2–4, the drag factors for the four designs were calculated and are shown in Table5. The values of air density and cross-sectional area are constant and the drag coefﬁcient was varied. Table6 contains the results for this section.

Table 5. Minimum and maximum drag factors.

3 2 Design Air Density (kg/m ) Area A (m ) Min Cd Max Cd Min D Max D A 1.144 1.2 × 10−3 0.5012 0.5836 3.44024 × 10−4 4.00583 × 10−4 B 1.144 1.2 × 10−3 0.5127 0.5914 3.51917 × 10−4 4.05937 × 10−4 C 1.144 1.2 × 10−3 0.4965 0.5673 3.40798 × 10−4 3.89395 × 10−4 D 1.144 1.2 × 10−3 0.4908 0.5627 3.36885 × 10−4 3.86237 × 10−4

Table 6. Expected launch performance range.

Minimum Cd Maximum Cd Design Max v Powered Free Alt Total Alt Max v Powered Free Alt Total Alt (m/s) Alt (m) (m) (m) (m/s) Alt (m) (m) (m) A 65.54 13.51 157.84 144.64 65.28 11.51 123.28 134.78 B 65.50 13.50 156.72 143.74 65.26 11.62 123.51 135.13 C 65.55 13.51 158.30 145.02 65.33 11.74 126.13 137.87 D 65.57 13.51 158.87 145.47 65.35 11.70 126.18 137.88

6. Materials and Methods V: Experimental Launches To test the effectiveness of the designs, to collect experimental data to compare to the analytical solution, a series of launches were performed on the various rocket designs. The technical speciﬁcations were discussed in depth in the previous sections. Table7 shows the results from the launches. All the designs performed well except Design A, which was predicted by the streamline analysis in Section4. Both launches of Design A (two separate aircraft) failed to reach any signiﬁcant altitude and both were observed to tumble severely during the launches, crashing before the payload ejection in both cases. The instrument used was an AltimeterThree from Jolly Logic [36], one of the best compact instrument packages available for rockets, drones, and other small aircraft. Aerospace 2017, 4, 17 13 of 24

6. Materials and Methods V: Experimental Launches To test the effectiveness of the designs, to collect experimental data to compare to the analytical solution, a series of launches were performed on the various rocket designs. The technical specifications were discussed in depth in the previous sections. Table 7 shows the results from the launches. All the designs performed well except Design A, which was predicted by the streamline analysis in Section 4. Both launches of Design A (two separate aircraft) failed to reach any significant altitude and both were observed to tumble severely during the launches, crashing before the payload ejection in both cases. The instrument used was an AltimeterThree from Jolly Logic [36], one of the best compact Aerospaceinstrument2017, 4packages, 17 available for rockets, drones, and other small aircraft. 13 of 25

TableTable 7. 7.Launch Launchdata. data. Powered Free Powered Free Flight Total Burnout v Design Launch Powered Free Powered Free Flight Total Burnout v Design Launch Flight (s) Flight (s) Flight Alt (m) Alt (m) Altitude (m) (m/s) Flight (s) Flight (s) Flight Alt (m) Alt (m) Altitude (m) (m/s) 1 0.35 0.40 8.23 6.71 14.94 54.66 A 1 0.35 0.40 8.23 6.71 14.94 54.66 A 2 0.30 1.85 6.40 10.67 17.07 46.72 2 0.30 1.85 6.40 10.67 17.07 46.72 1 0.35 4.20 4.57 131.98 136.55 59.07 B 1 0.35 4.20 4.57 131.98 136.55 59.07 B 2 20.35 0.35 5.055.05 4.27 4.27 135.03 135.03 139.29139.29 55.2355.23 1 0.30 4.70 6.10 112.78 118.87 48.57 C 1 0.30 4.70 6.10 112.78 118.87 48.57 C 2 20.35 0.35 5.105.10 5.18 5.18 138.68 138.68 143.87143.87 54.0654.06 1 0.40 4.30 7.62 117.35 124.97 62.88 D 1 0.40 4.30 7.62 117.35 124.97 62.88 D 2 20.35 0.35 4.754.75 6.10 6.10 126.80 126.80 132.89132.89 56.8456.84

7.7. ResultsResults Figure 13 shows the altitude results for the experiment. The experiment was run twice in order Figure 13 shows the altitude results for the experiment. The experiment was run twice in order to to collect consistency data, as well as performance data. collect consistency data, as well as performance data.

FigureFigure 13.13. LaunchLaunch altitudealtitude data.data. (Detailed(Detailed datasetdataset cancan bebe accessedaccessed inin thethe supplementarysupplementary material.)material.)

In addition to collecting the altitude data, the instrument package was able to capture the 3-D acceleration of the rocket as well. Both longitudinal and latitudinal acceleration were captured (Figure 14). The longitudinal acceleration was the normal, expected launch acceleration. Latitudinal acceleration gives a good view of the stability of the aircraft during ﬂight. The results are shown in Figure 15; it is very clear from these plots that the different designs had noticeably different stabilities. The coefﬁcient of gravity (g) is 9.79651 m/s2. AerospaceAerospace 2017 2017, ,4 4, ,17 17 1414 of of 24 24

InIn additionaddition toto collectingcollecting thethe altitudealtitude data,data, thethe instrument instrument packagepackage waswas ableable toto capturecapture thethe 3-D3-D accelerationacceleration ofof thethe rocketrocket asas well.well. BothBoth longitudinallongitudinal andand latitudinallatitudinal accelerationacceleration werewere capturedcaptured (Figure(Figure 14). 14). The The longitudinal longitudinal acceleration acceleration was was the the normal, normal, expected expected launch launch acceleration. acceleration. Latitudinal Latitudinal accelerationacceleration gives gives a a good good view view of of the the stability stability of of the the aircraft aircraft during during flight. flight. The The results results are are shown shown in in FigureFigure 15; 15; it it is is very very clear clear from from these these plots plots that that the the different different designs designs had had noticeably noticeably different different stabilities. stabilities. Aerospace 2017, 4, 17 14 of 25 TheThe coefficient coefficient of of gravity gravity (g) (g) is is 9.79651 9.79651 m/s m/s2.2 .

LongitudinalLongitudinal Acceleration Acceleration

LatitudinalLatitudinal Acceleration Acceleration

FigureFigure 14. 14. Acceleration Acceleration directions. directions.

FigureFigure 15. 15. Acceleration Acceleration data. data. (Detailed (Detailed dataset dataset can can be be accessed accessed in in the the suppl supplementarysupplementaryementary material.) material.)

8. Analysis and Discussion: Experimental Results

8.1. ANOVAand Model Adequacy Figures 13 and 15 show the experimental results; the altitude data for each design are shown in Figure 13 and the stability performance is shown in Figure 15. It is clear in the plots that Design A Aerospace 2017, 4, 17 15 of 25 failed on both launches, but the other six launches performed well. The design with the best altitude performance and consistency was Design B, while the most stable design during flight was Design D. The spikes in acceleration from approximately 0 to 1 s and from 4 to 5 s are due to the powered flight time and the payload ejection. In order to explore the results more deeply and harvest additional conclusions, an analysis of variance (ANOVA) was performed on the experimental data to test the influence of the modular design on a variety of experimental responses, as shown in Table8. The basic ANOVA assumptions were tested for each response; residuals must be plotted from a general linear model and satisfy the standard Fisher assumptions of normality, equal variances between replications, and run-order independence [37]. Any datasets whose residuals do not follow a normal distribution must be transformed using a common statistical method known as the Box-Cox transformation [38]. The raw data model was adequate for an ANOVA for five of the seven responses, while the two additional responses required a transform; the details are shown in Table8. Model adequacy tests were performed using standard methods, with the normality tested using the Anderson-Darling Test [39] and variances tested using the well-known Levine’s Test. The independence was checked by scatter-plotting the data in run order; none of the plots showed signs of patterning or data dependence. A standard test for the independence of data is the Chi-Squared test, but that could not be applied here because it requires integer data [40]. The p-values for the model adequacy test are shown in Columns 5 and 6 of Table9. The level of significance used was α = 0.10, with a p-value above that indicating adequacy.

Table 8. Experimental ANOVA responses.

Response Description Box-Cox Transform 1 Maximum Altitude (m) None required 2 Mean Altitude (m) None required 3 Maximum Longitudinal Acceleration (m/s2) None required 4 Mean Longitudinal Acceleration (m/s2) y = x3 5 Maximum Latitudinal Acceleration (m/s2) y = ln(x) 6 Mean Latitudinal Acceleration (m/s2) None required 7 Standard Deviation of Latitudinal Acceleration (m/s2) None required

Table 9. Experimental ANOVA data and p-values.

p-Values: Experiment p-Values: Model Adequacy Response A: Lower B: Upper Normality A × B Variance Test Independence Test Fin Design Fin Design Test 1 0.001 0.001 0.001 0.678 0.932 Scatterplot 2 0.001 0.001 0.001 0.553 0.950 Scatterplot 3 0.469 0.871 0.279 0.913 0.375 Scatterplot 4 0.263 0.134 0.116 0.013 0.131 Scatterplot 4: Box-Cox 0.232 0.052 0.040 0.170 0.321 Scatterplot 5 0.076 0.177 0.347 0.060 0.118 Scatterplot 5: Box-Cox 0.022 0.092 0.624 0.945 0.215 Scatterplot 6 0.024 0.072 0.048 0.534 0.405 Scatterplot 7 0.057 0.059 0.297 0.532 0.287 Scatterplot

The full ANOVA results are shown in Table9. A 2-way ANOVA was performed, so the main effects (upper and lower fin design) as well as their interactions can be explored. As stated above, the level of significance used was α = 0.10. All data p-values (Columns 2–4 in Table9) below 0.10 indicated that the factor of interaction had a significant influence on the response in question. The conclusions were: Aerospace 2017, 4, 17 16 of 24

Aerospace 2017, 4, 17 16 of 25 indicated that the factor of interaction had a significant influence on the response in question. The conclusions were: . MaximumMaximum and and mean mean altitude altitude was was ve veryry significantly significantly influenced influenced by the fin fin combinations, as well asas their their interaction interaction during during flight; flight; . NeitherNeither of of the the sets sets of of fins fins nor their interaction had an influenceinfluence on maximum longitudinal accelerationacceleration and and only only had had some some influence influence on the on mean the meanof this ofacceleration this acceleration after the afterBox-Cox the transform;Box-Cox transform; . TheThe lower lower fin fin design design has has a a weak weak influence influence on on the the latitudinal latitudinal acceleration, acceleration, which which was much more pronouncedpronounced after after the the Box-Cox Box-Cox transform; transform; . TheThe fin fin designs designs and and their their interaction interaction had a had weak a but weak significant but significant influence influence on the mean on latitudinal the mean acceleration;latitudinal acceleration;

. TheThe fin fin designs, designs, but but not not their their interaction, interaction, had had a a weak but significant significant influence influence on the standard deviationdeviation of of the the latitudinal latitudinal acceleration. acceleration.

In terms ofof flightflight performance,performance, the the formal formal conclusions conclusions from from the the graphical graphical and and statistical statistical analysis analysis of ofthe the tested tested cases cases were were that thethat combination the combination of elliptical of elliptical lower finslower with fins rectangular with rectangular upper fins upper produced fins producedthe best and the most best consistent and most altitude consistent performance, altitude performance, while combining while clipped combining delta lowerclipped fins delta with lower delta finsuppers with produced delta uppers the most produced stable the flight. most The stable combination flight. The of clippedcombination delta of lower clipped fins delta and rectangular lower fins andupper rectangular fins produced upper a highlyfins produced unstable a andhighly unreliable unstable design. and unreliable design.

8.2. Experimental Error Analysis Clearly, there were discrepanciesdiscrepancies between the theoretical and experimental data. Figures 16–1816–18 show the one-on-one comparison of the theoretica theoreticall and experimental results for the altitude and burnout velocity. The The ranges ranges for for the the theoretica theoreticall results results were were those those based on the minimum and maximum drag coefficients, coefﬁcients, while those for the expe experimentalrimental results were fr fromom the two experimental iterations. The The discrepancies discrepancies were were thought thought to tobe be introduced introduced into into the the experiment experiment via viafour four modes: modes: (1) rocket(1) rocket skinskin fluid ﬂuid friction friction from from 3-D 3-D printing printing lines; lines; (2) potential (2) potential payload payload ejection ejection before before true true apogee; apogee; (3) launch(3) launch rail rail friction; friction; and and (4) (4) angle angle of ofattack attack variations. variations. Each Each of of these these possible possible sources sources of of error error were examined in detail. General random uncertainty within the experiment was considered to be trivial in magnitude compared compared with with the the ob obviousvious error error sources sources and and was was therefore not not considered considered in in detail in this analysis.

Figure 16. Theoretical vs. experimental experimental performance, powered flight. ﬂight. Aerospace 2017, 4, 17 17 of 25 Aerospace 2017,, 4,, 1717 17 of 24

Figure 17. TheoreticalTheoretical vs.vs. experimentalexperimental performance,performance, freefree flight. ﬂight.flight.

® Skin friction was tested using an ANSYSANSYS CFXCFX® model,model, comparingcomparing thethe dragdrag coefficientscoefficients coefficients forfor the the nose cone for smooth and realistically layered mode models.ls.ls. PayloadPayload ejectionejection timetime waswas comparedcompared with with the the true apogee to determinedetermine if thethe ejectionejection prematurelyprematurely disrupteddisrupted thethe flight.flight. Launch rail friction was analyzed to determine if it significantly significantly influencedinfluenced thethe poweredpowered flightflight altitude.altitude.

FigureFigure 18. TheoreticalTheoretical vs.vs. experimentalexperimental experimental performance, performance, burnout burnout velocity. velocity.

8.3. Error Error Analysis: Skin Skin Friction Friction Since the parts used in this experiment were 3- 3-DD printed, they have a slightly rougher surface finishfinish than parts made using injection molding or other common plastic fabrication fabrication techniques. techniques. Logically, this could could have have some some effect effect on on the the drag drag coefficient coefficient around around the the nose nose cones cones of the of the rockets, rockets, as theas the laminar laminar boundary boundary around around thethe surface surface is thinnest is thinnest atat thethe atthe beginningbeginning beginning ofof thethe ofthe flowflow flow [37].[37]. [37 However,However,]. However, inin manyin many cases, cases, a rougher a rougher surface surface at the at beginning the beginning of the of flow the flowmay actually may actually decrease decrease the drag, the as drag, it forces as it theforces flow the to flow become to become turbulent turbulent earlier earlier[41,42]. [ 41While,42]. it While is obvious it is obvious that this that caused this caused some kind some of kind effect, of whethereffect, whether that effect that is effect positive is positive or negative or negative was unknown, was unknown, requiring requiring a brief a briefexperiment experiment to answer to answer the question.the question. An ANSYS ANSYS CFX CFX®® simulationsimulationsimulation waswas was builtbuilt built toto totesttest test thethethe influeinflue influencence of the of surface the surface roughness roughness on the on nose the conenose conedrag, drag, comparing comparing the drag the drag coefficient coefficient between between the the smooth smooth and and a arealistically realistically rough rough surface (Figure 1919).). TheThe relativerelative roughnessroughness for for the the geometry geometry tested tested was was about about 1.97 1.97× ×10 10−−−33... OnlyOnly Only thethe the nosenose nose conecone was tested,tested, asas backgroundbackground research research [ 41[41,42],,42], and and the the flowline flowline analysis analysis (Figure (Figure 10 10)) indicated indicated that that most most or orall all of theof the of the of dragthe drag induced induced by surface by surface roughness roughness would would occur onoccur the cone.on the Computational cone. Computational expense expensewas a factor was in a thefactor decision in the as decision well and as required well and several required hours several to perform hours to the perform analysis the to aanalysis tolerance to ofa tolerance1 × 10−6 onof 1 the × 10 realistic−−66 onon thethe cone realisticrealistic alone. conecone alone.alone. The smooth cone model was created using a standard revolved axis protrusion, while the realistic cone was built as a series of 0.20 mm layer, with protruding ridges equal to the lateral Aerospace 2017, 4, 17 18 of 25

The smooth cone model was created using a standard revolved axis protrusion, while the realistic Aerospace 2017, 4, 17 18 of 24 cone was built as a series of 0.20 mm layer, with protruding ridges equal to the lateral uncertainty for theuncertainty printer that for wasthe printer used to that create was the used original to create parts. the The original ﬂow was parts. standard The flow dry airwas at standard one atmosphere dry air ofat one pressure, atmosphere ﬂowing of overpressure, the cone flowing surface over at the a normal cone surface speed at of a 50normal m/s. speed Both models of 50 m/s. were Both analyzed models twicewere usinganalyzed different twice computers using different and fresh computers formulations and fresh for each; formulations the results for were each; identical the results for the were two runsidentical of each for model,the two indicating runs of each that model, the setup indica wasting correct that the and setup consistent. was correct and consistent.

FigureFigure 19.19. Skin drag analysis models.models.

The analysis indicated strongly (Table 10) that the realistic roughness on the skin actually The analysis indicated strongly (Table 10) that the realistic roughness on the skin actually provided provided an advantage by reducing the drag coefficient. This result was interesting, but not an advantage by reducing the drag coefficient. This result was interesting, but not unexpected; unexpected; such results are fairly common [41,42] for blunt-type geometries such as cones in a such results are fairly common [41,42] for blunt-type geometries such as cones in a turbulent flow. turbulent flow. The roughness likely caused the flow to trip earlier, providing thicker laminar The roughness likely caused the flow to trip earlier, providing thicker laminar boundary layer coverage boundary layer coverage on the surface in the flow. This deserves further study in future work. on the surface in the flow. This deserves further study in future work.

Table 10. Drag coefficients for smooth and rough cones. Table 10. Drag coefficients Cd for smooth and rough cones. Surface Smooth Model Rough Model NoseSurface Cone Smooth 0.3994 Model Cd Rough 0.2358 Model Cd Nose Cone 0.3994 0.2358 8.4. Error Analysis: Payload Ejection 8.4. Error Analysis: Payload Ejection It was noted earlier in this paper that much of the discrepancy between the theoretical and experimentalIt was noted performance earlier in likely this paperwas due that to muchpayload of ejection the discrepancy before true between apogee thewas theoretical reached. Upon and experimentalfurther study performanceof the raw data, likely this was phenomenon due to payload is obvious; ejection Table before 11 true clearl apogeey shows was that reached. the payload Upon furtherejection studywas indeed of the rawa significant data, this limiting phenomenon factor ison obvious; the total Table altitude 11 clearly of the showsrockets that and the most payload likely ejectionexplains wasthe different indeed a between significant the limiting theoretical factor and on ex theperimental total altitude altitude of thevalues rockets, except and for most the likelyfailed explainsDesign A. the In differentthe six successful between thelaunches, theoretical the aircraft and experimental continued for altitude a significant values, amount except for of thetime failed after Designejection A. (see In Table the six 11 successful and Figure launches, 13), indicating the aircraft that continued the rockets for maintained a significant significant amount ofmomentum time after ejectionbefore ejection. (see Table This 11 limitingand Figure factor 13), should indicating be co thatnsidered the rockets strongly maintained in future significant experiments; momentum a motor beforewith a ejection.much longer This limitingdelay or factorno ejection should should be considered be utilized. strongly in future experiments; a motor with a much longer delay or no ejection should be utilized. Table 11. Experimental apogee vs. payload ejection. Table 11. Experimental apogee vs. payload ejection. Post-Burnout Design Launch Burnout Velocity (m/s) Payload Ejection Time (s) Experimental Apogee Time (s) Post-Burnout Design Launch1 Burnout54.66 Velocity (m/s) 4.25 0.40 A Payload Ejection Time (s) Experimental Apogee Time (s) 2 46.72 4.50 1.85 1 54.66 4.25 0.40 A 1 59.07 4.50 5.20 B 2 46.72 4.50 1.85 2 55.23 4.10 5.05 1 59.07 4.50 5.20 B 1 48.57 4.20 4.70 C 2 55.23 4.10 5.05 2 54.06 4.80 5.10 1 48.57 4.20 4.70 C 1 62.88 4.05 4.30 D 2 54.06 4.80 5.10 2 56.84 4.05 4.75 1 62.88 4.05 4.30 D 2 56.84 4.05 4.75 8.5. Error Analysis: Launch Rail Friction The friction between the rockets and the launch rail was the most likely culprit for the high error found in the powered flight time performance (Figure 16), as the error for the free flight (Figure 17) is much lower or not present. It could also explain the lower-than-expected burnout velocity (Figure Aerospace 2017, 4, 17 19 of 25

8.5. Error Analysis: Launch Rail Friction The friction between the rockets and the launch rail was the most likely culprit for the high error Aerospace 2017, 4, 17 19 of 24 found in the powered flight time performance (Figure 16), as the error for the free flight (Figure 17) is much18). To lower test the or influence not present. of this It could friction also source, explain a thesimple lower-than-expected analytical model was burnout constructed velocity to (Figure calculate 18). Tothe testpotential the influence friction offactor. this frictionThe free source, body diagram a simple is analytical shown in model Figure was 20. It constructed was assumed to calculate that the the potential friction factor. The free body diagram is shown in Figure 20. It was assumed that the dynamic friction coefficient =0.05 [43] for a plastic-steel interface. = dynamicThe launch friction mass coefficient of eachµk rocket0.05 was [43] 132 for g a plastic-steel(1.295 N), and interface. the engines used produced a thrust of 22.1 N.The Using launch basic mass static of eachmoment rocket analysis was 132 (Figure g (1.295 20), N), the and upper the thrust engines reaction used produced (1) was a thrustfound ofto 22.1be 1.653 N. Using N and basic the staticlower moment (2) was analysis 1.652 (FigureN, for a20 total), the of upper 3.305 thrust N. Thus, reaction the dynamic (RF1) was friction found force to be ) 1.653was: N and the lower (RF2 was 1.652 N, for a total of 3.305 N. Thus, the dynamic friction force was:

Ff rict ==µk((RF11 + +RF 22)) ==0.165 N N (9) (9) While this is not a large force, it is certainly significant in the problem at hand; it adds 12.7% to While this is not a large force, it is certainly signiﬁcant in the problem at hand; it adds 12.7% to the apparent weight of the aircraft at launch for a total weight of 1.4595 N (148.8 g); this is nearly the the apparent weight of the aircraft at launch for a total weight of 1.4595 N (148.8 g); this is nearly the weight of the recovery system and instrument package combined. The new thrust-to-weight ratio is weight of the recovery system and instrument package combined. The new thrust-to-weight ratio is 15.142, not far from the minimum allowable ratio of 13.256. This additional friction force certainly 15.142, not far from the minimum allowable ratio of 13.256. This additional friction force certainly contributed to the error found in this experiment, particularly the errors shown in Figure 16. contributed to the error found in this experiment, particularly the errors shown in Figure 16.

18 mm

Lug 1

Rocket Body Thrust Reaction Force 5mm 3.2 mm Dynamic Friction

Lug 2 Thrust Reaction Thrust Force 247 mm Reaction Body Rocket Force

Dynamic Friction

6.35 mm Not to scale

Thrust Force Figure 20. Launch rail friction. Figure 20. Launch rail friction.

8.6. Error Analysis: Angle of Attack Variation One of thethe basicbasic assumptionsassumptions mademade during during the the CFD CFD and and analytical analytical analyses analyses was was that that the the angle angle of attackof attack was was constant constant during during flight. flight. If this If assumptionthis assumption is invalid, is invalid, the wetted the wetted area of thearea airframe of the airframe changes, increasingchanges, increasing the drag area. the drag Since area. the rockets Since usedthe rocket in thiss studyused in had this a totalstudy of eighthad a control total of surfaces eight control at two locations,surfaces at the two roll locations, rotation anglethe roll is alsorotation influential angle inis this.also Ininfluential order to analyzein this. In the order potential to analyze effects thisthe maypotential have, effects a brief this sensitivity may have, analysis a brief was sensitivity performed. analysis Design was D,performed. the most stableDesign of D, the the four most designs, stable ® wasof the analyzed four designs, in ANSYS was analyzed CFX in in the ANSYS same CFX way® as in inthe Chapter same way 4 but as in with Chapter the angle 4 but of with attack the offset.angle ◦ ◦ ◦ Threeof attack offsets offset. were Three used: offsets 1 , 2were, and used: 5 . These1°, 2°, areand reasonable 5°. These are points reasonable of observation, points of as observation, the observed as rocketthe observed behavior rocket during behavior flight (on during the six flight successful (on th flights)e six successful did not show flights) significant did not deviation show significant from the constantdeviation flight from angle.the constant In order flight to test angle. the effectIn order of rollto test angle, the effect two orientations of roll angle, were two used; orientations one with were the used; one with the upper control surfaces set at 90° and the other with the lower control surfaces set the same way. Two different air velocities were used, 50 and 100 m/s. The model setup is shown in Figure 21, and the results of this study are shown in Figure 22. Aerospace 2017, 4, 17 20 of 25 upper control surfaces set at 90◦ and the other with the lower control surfaces set the same way. Two different air velocities were used, 50 and 100 m/s. The model setup is shown in Figure 21, and the Aerospace 2017, 4, 17 20 of 24 Aerospaceresults of2017 this, 4, study17 are shown in Figure 22. 20 of 24

Figure 21. Angle of attack sensitivity study configuration. Figure 21. AngleAngle of attack sensitivity study configuration. conﬁguration.

FigureFigure 22.22. AngleAngle ofof attackattack sensitivitysensitivity studystudy results.results. Figure 22. Angle of attack sensitivity study results. AsAs seenseen in in Figure Figure 22 ,22, the the impact impact of varying of varying the angle the ofangle attack of hadattack a trivial had impacta trivial on impact the measured on the As seen in Figure 22, the impact of varying the angle of attack had a trivial impact on the dragmeasured force ondrag the force body. on Whilethe body. all of While the orientations all of the orientations were subjected were subjected to a higher to drag a higher force drag than force the measured drag force on the body. While all of the orientations were subjected to a higher drag force originalthan the run original (from run Chapter (from 4), Chapter the largest 4), the variation largest at variation 50 m/s wasat 50 around m/s was 3.46% around (an increase3.46% (an of increase 0.03 N), than the original run (from Chapter 4), the largest variation at 50 m/s was around 3.46% (an increase whileof 0.03 it N), was while 3.81% it (increasewas 3.81% of (increase 0.14 N) at of 100 0.14 m/s. N) at While 100 m/s. not anWhile overwhelming not an overwhelming factor in this factor study, in of 0.03 N), while it was 3.81% (increase of 0.14 N) at 100 m/s. While not an overwhelming factor in itthis does study, add toit does the apparent add to the vehicle apparent mass; vehicle the results mass; imply the results that this imply would that be this a major would consideration be a major this study, it does add to the apparent vehicle mass; the results imply that this would be a major atconsideration higher velocities. at higher The velocities. orientation The of theorientation rocket did of notthe appearrocket did tohave not appear a noticeable to have impact a noticeable on the consideration at higher velocities. The orientation of the rocket did not appear to have a noticeable results,impact ason no the patterns results, oras trendsno patterns appeared or trends in the appeared data. in the data. impact on the results, as no patterns or trends appeared in the data. 9.9. AnalysisAnalysis andand Discussion:Discussion: ManufacturingManufacturing ImplicationsImplications ofof ErrorError AnalysisAnalysis 9. Analysis and Discussion: Manufacturing Implications of Error Analysis TheThe errorerror analysisanalysis discusseddiscussed inin SectionSection8 8 provides provides some some guidance guidance for for the the production production of of the the next next The error analysis discussed in Section 8 provides some guidance for the production of the next generationgeneration ofof smallsmall modularmodular rocketsrockets inin orderorder to to avoid avoid the the pitfalls pitfalls encountered encountered in in the the current current study. study. generation of small modular rockets in order to avoid the pitfalls encountered in the current study. 1.1. The skin frictionfriction studystudy showsshows thethe inﬂuenceinfluence ofof thethe surfacesurface roughnessroughness ofof thethe parts,parts, whichwhich isis 1. The skin friction study shows the influence of the surface roughness of the parts, which is controlled primarilyprimarily byby varyingvarying thethe layerlayer thicknessthickness andand thethe buildbuild speed.speed. DesignersDesigners shouldshould controlled primarily by varying the layer thickness and the build speed. Designers should consider their choice of process settings on the skin friction, eventually finding the optimal consider their choice of process settings on the skin friction, eventually finding the optimal design settings to balance easier manufacturing with increased performance. design settings to balance easier manufacturing with increased performance. 2. Payload ejection time can be controlled mainly by the choice of engines for the flights. 3-D 2. Payload ejection time can be controlled mainly by the choice of engines for the flights. 3-D printing produces custom geometry, so accommodating a variety of engines is a simple matter. printing produces custom geometry, so accommodating a variety of engines is a simple matter. Aerospace 2017, 4, 17 21 of 25

consider their choice of process settings on the skin friction, eventually finding the optimal design settings to balance easier manufacturing with increased performance. 2. Payload ejection time can be controlled mainly by the choice of engines for the flights. 3-D printing produces custom geometry, so accommodating a variety of engines is a simple matter. The information collected in this study could aide in the proper selection of engines for the types of rocket in this study. 3. Clearly, the launch rail friction had an impact on the results of this experiment. A better launch method should be used for these types of rockets, including tray or tube launching, in future launches. 4. The influence of the angle of attack variations increases with velocity, so designers should make sure that the airframes are as symmetric and well balanced as possible. They should also be checked for printing errors before launching to ensure that no unbalance exists in the geometry.

10. Analysis and Discussion: Design Modularization The main purpose of this study was to develop, design, and test an airframe design based on feature modularization into complex parts, instead of part modularization into subassemblies. The rocket airframes used in this study were built in three parts; the booster, the payload, and the nose cone. In a real aircraft, such as a sounding rocket or missile, the booster section would contain all the propulsion components, the payload section would contain the warhead or instruments, and the nose cone would carry the guidance system and computer. Based on the need of the mission and the sizes of the AM equipment available, the number and scope of the complex parts can be adjusted. The rockets used in this study were deliberately manufactured out of polylactic acid (PLA) because it biodegradable and fully recyclable; if any rockets were lost, the pollution to the environment would be minimal. Rockets made from the standard ABS would be significantly lighter but are not at all environmentally-friendly or as easily recyclable. The modularization technique dramatically reduced the effort in creating the designed experiment used in this study. Two different booster and two different payload designs were made, then combined into four separate unique rocket designs that had significantly different performances. If the experimental design had not called for measurable and predictable combinations of the factors, there is virtually no limit to the unique designs that could be made. Production time was very brief as well, requiring around 10 h to design, verify, set up, print, and assemble the rockets. While most commercial model rocket producers would likely be able to produce rockets much faster, this depends on months or years of design, testing, and preparation to produce stock parts. The design modularization technique can produce a successful launch of a completely unique design 10 h after the original idea is proposed. The benefits of this technique to the manufacturing of airframes in general is obvious. When compared to the cost of commercially available alternatives to the rockets used in this study, the modular designs were very cost efficient. Not including the labor of the authors, each of the rockets required about 100 g of material (including supports and waste) and about 8 h of electricity at 30 W, a total of about $2.25 per airframe. Even if the designer chose to use expensive proprietary filament instead of open source filament (as was used in this study), the cost would remain under $10.00 per airframe. The motors for each launch cost about $6.00, but this should not be considered, as any rocket would require the same launch cost. Similar alternatives from the world of model rockets are shown in Table 12 (source: Amazon.com, February 2017). Clearly, the modular 3-D printed rockets are far more cost effective. Most of these have airframes made from cardboard or very thin plastic, unlike the strong airframes used in this study. In all cases, the airframe weight is comparable due to the ability to 3-D print the airframe as a complex hollow structure. Aerospace 2017, 4, 17 22 of 25

Table 12. Commercial model rocket alternatives.

Commercial Model Rocket Design Cost Estes 2452 Athena $12.07 Estes Hi-Flier $9.99 Estes Alpha III $24.99 Estes 7000 Bull Pup $15.43 Estes 2440 Magician $19.99

While the method could obviously be used to produce cheap customized model rockets, the greatest beneﬁt would be in the production of sounding rockets and military equipment. The model rockets provide an interesting and relatable case study for exploring this design method, but much further exploration and development of the method is needed before it would be trusted for more vital and complex applications. However, the beneﬁts are clear and this further development is certainly warranted.

11. Conclusions The present study explored a design modularization method that combines features into complex individual parts instead of parts into subassemblies. The results strongly suggest a number of general conclusions about the design modularization method and about the feasibility of the 3-D printing of rocket airframes, including:

Design modularization via combination of features into complex parts is a feasible design methodology for rockets and other airframe-based products;

3-D printing, particularly extrusion-based processes, is an excellent method for producing the complex multi-feature parts needed for optimized airframes;

It is possible and feasible to produce airframes that have excellent recyclability and low environmental impact by utilizing biodegradable materials in the design;

The airframe designs can be adjusted and customized nearly infinitely; The exact shape of the rocket fins and their combinations have a very significant influence on the performance and stability of the airframe;

AM and modular design greatly simplify the measurement and adjustment of the ﬁn inﬂuences on performance;

While the performance of the rockets fell short of the analytical predictions, the sources of the errors were very simple to identify due to the simpliﬁed design;

The print lines on 3-D printed parts seemed to provide an advantage, not a disadvantage, to the rockets as it reduced the drag coefﬁcient of the nose cone;

The payload ejection time was too short for the motors chosen, a factor that should be considered heavily in future studies;

The launch rail introduced a signiﬁcant amount of friction, causing the rockets to launch and burn out at slower speeds;

Five of the seven experimental responses produced data whose residuals followed a normal distribution without any statistical transforms, suggesting that very little random error is contained in the experiment. Aerospace 2017, 4, 17 23 of 25

In conclusion, this study was unique and was very successful as a detailed case study in modular design; very little research has been done in this area, and this study should provide background and motivation for further work. The performance of the modular rockets was very easily analyzed, with the sources of error easily found and explained; the modularization greatly eased analysis of the errors, as there were far fewer parts to consider. Future studies using modular design methods with AM can easily correct these sources of error, as the complex parts have great design and geometry freedom and are not limited by commercial part standards. In a standard design, it may be difﬁcult or impossible to correct sources of error found during experimentation if the design is dependent on a series of standard parts. Using part modularization, few or no standard parts are used, so inﬁnite adjustment and correction can be performed on designs in nearly real-time.

Supplementary Materials: The following is available online at http://www.mdpi.com/2226-4310/4/2/17/s1, Table S1: Flight data for rocket design A–D. Acknowledgments: No specific research grants or external funding were used in the completion of this work. The authors thank College of Engineering and Department of Industrial & Systems Engineering and Engineering Management, University of Alabama in Huntsville for providing laboratory space and materials for the completion of the experiments. Author Contributions: Rachel N. Hernandez led the effort to complete background research and digital models for 3-D printing and assisted with experimental design and experiment execution. Harpreet Singh provided background research, aerodynamic models, and assisted with experiment execution. Sherri L. Messimer provided advice and input concerning the experimental design and interpretation of results. Albert E. Patterson lead the research team, assisted with experimental design, performed the manufacturing of the samples, supervised and assisted with the experiments, and performed the data and error analyses. Rachel N. Hernandez and Albert E. Patterson wrote the initial proposal for lab space and resources to complete the work. All four authors contributed to the writing/editing of the paper. Conflicts of Interest: The authors declare no conflict of interest.

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