doi: 10.5028/jatm.2012.04044412
Multidisciplinary Design Optimization of Sounding Rocket Fins Shape Using a Tool Called MDO-SONDA
Alexandre Nogueira Barbosa1*, Lamartine Nogueira Frutuoso Guimarães2 1,QVWLWXWRGH$HURQiXWLFDH(VSDoR±6mR-RVpGRV&DPSRV63±%UD]LO 2,QVWLWXWRGH(VWXGRV$YDQoDGRV±6mR-RVpGRV&DPSRV63±%UD]LO
Abstract:0XOWLGLVFLSOLQDU\GHVLJQRSWLPL]DWLRQLVDSURPLVLQJ¿HOGLQDHURVSDFHHQJLQHHULQJ+RZHYHUDGYDQFHVLQWKLV ¿HOGKDYHQRWEHHQDSSOLHG\HWWRLPSURYH%UD]LOLDQVRXQGLQJURFNHWVVXFKDVWKH967KHUHIRUHWRJLYHDSHUVSHF WLYHRIWKHPXOWLGLVFLSOLQDU\GHVLJQRSWLPL]DWLRQLQWKLVFRQWH[WWKLVZRUNSUHVHQWHGDFDVHVWXG\RIWKLVURFNHWZKLFK FRQVLVWVRIWKHVKDSHRSWLPL]DWLRQRILWV¿QV7RDFKLHYHWKLVJRDODVSHFLDOWRROFDOOHG0'2621'$ZKLFKLVWKHPDLQ FRQWULEXWLRQRIWKLVZRUNZDVGHYHORSHG,WVFXUUHQWYHUVLRQLQWHUDFWVZLWKWZRKLJK¿GHOLW\H[HFXWDEOHFRGHVRQHRI DHURG\QDPLFVDQGDQRWKHURIWUDMHFWRU\H[SORLWLQJWKHV\QHUJ\EHWZHHQERWKGLVFLSOLQHV7KH0'2621'$LVEDVHGRQ DPXOWLREMHFWLYHJHQHWLFDOJRULWKPZKRVHUHDORSHUDWRUZDVRULJLQDOO\GHVLJQHGLQWKLVZRUN%\XVLQJWKHSURSRVHGWRRO LWZDVIRXQGWKDWWKHGUDJGXHWRWKHURFNHW¿QVFRXOGEHUHGXFHGXSWR ZLWKRXWLQFUHDVLQJWKHFKDQFHVRIDGYHUVH HIIHFWVWKDWFRXOGOHDGWRXQVWDEOHEHKDYLRUV Keywords:6RXQGLQJURFNHW5RFNHW¿QGHVLJQ0XOWLGLVFLSOLQDU\GHVLJQRSWLPL]DWLRQ0XOWLREMHFWLYHJHQHWLFDOJRULWKPV
INTRODUCTION
At the end of the 1990s, among the Brazilian sounding respect to the entire project, promoted by low synergy between rockets, the VS-40 was presented as one that provides the best the design disciplines. conditions for experiments in microgravity (Ribeiro, 1999). 6LQFH ZKHQWKH¿UVW96ZDVODXQFKHGWKH Space systems are complex, i.e., their behavior is governed methodology that allows exploiting the synergy between by many distinct but interacting physical phenomena, and its design disciplines has not been used yet for Brazilian multidisciplinary, requiring balance among competing sounding rockets. A methodology called multidisciplinary objectives related to safety, reliability, performance, design optimization (MDO) replaces the traditional operability, and cost (Rowell and Korte, 2003). Over time, sequential methodology by synergic interactions between the advances in the engineering of complex systems have allowed design disciplines, promoting the overall gain in products to more quickly identify feasible solutions and exploit the performance, decreasing the design time (Floudas and synergy among the design disciplines (Rowell and Korte, Pardalos, 2009). +RZHYHUWKH96KDVQRWEHHQEHQH¿WHGE\VXFK Why should the VS-40 be revised? It promises the best advances yet. The interactions between the design disciplines conditions for microgravity experiments, but not widely of the VS-40 were processed in a sequential order, in which launched yet such as the VSB-30, also a Brazilian sounding those disciplines that act early in the conceptual design rocket, so that it could be more studied, and perhaps improved establish constraints on the others that follow later, leading E\FRQVLGHULQJFROOHFWHGÀLJKWGDWD7KH96ZDVUHFHQWO\ to a concept without regarding the trade-offs that may exist PRGL¿HGDWWKH*HUPDQ$HURVSDFH&HQWHU '/5 LQRUGHUWR between the design objectives. The plausible consequence SURYLGHWKHUHTXLUHGVWDELOLW\IRUDVSHFL¿FPLVVLRQEHFDXVH of such sequential methodology is a suboptimal design with it was not originally designed for carrying a payload with exposed canards, indicating that its design can be altered, if Received: 31/07/12 Accepted: 08/10/12 QHFHVVDU\WREHQH¿WLWVVWDELOLW\DQGSHUKDSVLWVSHUIRUPDQFH *author for correspondence: [email protected] /DVWO\LWKDVQRWEHHQEHQH¿WHGE\DGYDQFHVLQWKHHQJLQHHULQJ 3UDoD0DUHFKDO(GXDUGR*RPHV±9LODGDV$FiFLDV of complex systems, and it may have some subsystems that &(3 6mR-RVpGRV&DPSRV63±%UD]LO could be improved regarding its next launches at Brazilian
J. Aerosp. Technol. Manag., São José dos Campos, Vol.4, No 4, pp. 431-442, Oct.-Dec., 2012 431 %DUERVD$1*XLPDUmHV/1) territory carrying the Sub-orbital SARA, a Brazilian platform for microgravity experiments with an advantage, the payload for microgravity experiments. recovery operation associated with the VSB-30 is less costly Motivated by a search for VS-40 improvements, the use WKDQZLWKWKH96ZKRVHVSODVKGRZQLVDSSUR[LPDWHO\¿YH of the MDO was introduced in Brazilian sounding rockets. times more distant from the continent-ocean boundary than the Therefore, the objective of this paper was to provide a VSB-30, demanding more autonomy for the recovery means. perspective of the MDO application in this context based on a From 2004 to 2010, ten VSB-30 campaigns were case study of the VS-40. As case study, the shape optimization successfully performed, three of them in the Brazilian territory RI WKH 96 ¿QV ZDV SURSRVHG LQ RUGHU WR LPSURYH LWV *DUFLDHWDO, 2011). In contrast to the VSB-30, three VS-40 SHUIRUPDQFHE\UHGXFLQJWKHGUDJGXHWRWKH¿QVZLWKRXW campaigns has occurred so far, two of them in the Brazilian increasing the chances of adverse effects that could lead to WHUULWRU\WKH¿UVWRQHLQ 6DQWD0DULDFDPSDLJQ )LJD unstable behaviors. To perform the optimization, a computer DQGWKHVHFRQGRQHLQ /LYUDPHQWRFDPSDLJQ )LJE tool called MDO-SONDA (MDO of Sounding Rockets), ERWKDWWKH$OFkQWDUD/DXQFK&HQWHU &/$ LQ0DUDQKmR ,$( which was developed by Alexandre Nogueira Barbosa, was 2Q-XQHDPRGL¿HG96FDOOHG960 XVHG0'2621'$SUHVHQWDWLRQLQWKHOLWHUDWXUHZDV¿UVW carrying the Sharp Edge Flight Experiment (SHEFEX) II introduced by this paper. (Weihs HWDOD D*HUPDQSURMHFWZDVVXFFHVVIXOO\ launched at the Andøya Rocket Range in Northern Norway SOUNDING ROCKETS AND MICROGRAVITY '/5 DQGLW EHFDPHWKH¿UVW96 RSHUDWLRQLQ ENVIRONMENT DQRWKHUFRXQWU\ )LJF 7KH960¿QVVKDSH )LJF LV VLJQL¿FDQWO\ GLIIHUHQW IURP WKH WZR SUHYLRXV 96 Sounding rockets, such as the VS-40, are characterized by )LJVDDQGE 7KHQHZ¿QVZHUHGHVLJQHGDQGFRQVWUXFWHG WKHLUDSSOLFDWLRQDQGÀLJKWSUR¿OH$FFRUGLQJWR0RQWHQEUXFN IRU6+()(;,,DW'/5GXHWRWKHQHHGRIH[WHQGHG¿QVWR HWDO (2001), such rockets are constituted of solid fueled motors compensate for the aerodynamic effects of the small canards and a payload that carries instruments to take measurements at the payload, as can be seen in Fig. 1c (Weihs HWDO, 2008). DQGSHUIRUPVFLHQWL¿FH[SHULPHQWVGXULQJDSDUDEROLFÀLJKW In 1997, a recovery orbital platform called SARA Thus, the sounding term means taking measurements. for supporting short-orbital experiments in microgravity In comparison with the VSB-30, the VS-40 bi-stage can environment was proposed (Moraes and Pilchowski, 1997). provide a wide exposure to the microgravity environment, ,Q FRPSDULVRQ ZLWK D VXERUELWDO ÀLJKW ZKLFK SURYLGHV D characterized by a condition where an object is subjected few minutes of microgravity conditions, an orbital one can WRDJIRUFHOHVVWKDQȝJ /D1HYHDQG&RUUrD-U provide more than ten days before reentering the Earths achieved by moving in free fall, where there are no forces DWPRVSKHUH7KH6SDFH&DSVXOH5HFRYHU\([SHULPHQW 65( other than gravity acting on the object. ZKLFKLVDQ,QGLDQVSDFHFUDIW¿UVWODXQFKHGLQLVDYHU\ Payloads carried by rockets achieve the microgravity environment after the burnout of the rocket when the thrust force is zero and the payload is above the atmosphere. It is assumed that the Kármán line, at 100 km above the seawater surface, might be used as a reference for microgravity H[SHULPHQW SXUSRVHV WR GH¿QH WKH ERXQGDU\ EHWZHHQ WKH atmosphere and the outer space, from which the atmosphere becomes so thin that the drag force could be neglected.
FACTS ABOUT THE VS-40
In spite of the fact that the VS-40 provides more exposure to microgravity than the VSB-30, since the 21st century began, (a) (b) (c) rather than the VS-40, the VSB-30 has been most frequently Sources: (a) and (b) Institute of Aeronautics and Space, Brazil; XVHG IRU PLFURJUDYLW\ H[SHULPHQWV *DUFLD HW DO, 2011). F '/5 &HUWDLQO\EHFDXVHWKH96%KDVPHWPLVVLRQUHTXLUHPHQWV Figure 1. VS-40 launches.
432 J. Aerosp. Technol. Manag., São José dos Campos, Vol.4, No 4, pp. 431-442, Oct.-Dec., 2012 0XOWLGLVFLSOLQDU\'HVLJQ2SWLPL]DWLRQRI6RXQGLQJ5RFNHW)LQV6KDSH8VLQJD7RRO&DOOHG0'2621'$ similar example of such a kind of platform (Reddy, 2007). The current version is only prepared for optimization of $OVRDQH[DPSOHLVWKH5(;)UHH)O\HUWKH*HUPDQSURSRVDO WKHVKDSHRIURFNHW¿QV+RZHYHULWLVDQREMHFWRULHQWHGFRGH for application of SHEFEX derived technology, which ZULWWHQLQ&WKDWSURYLGHVVSHFL¿FIRUPVFODVVHVDQGREMHFWV is a reusable orbital return vehicle for experiments under to structure proper interfaces for further studies, including microgravity conditions (Weihs HWDO, 2008b). the shape optimization of other rocket subsystems, such as Thereafter, a platform called Sub-orbital SARA, which is DGGLWLRQDOVHWRI¿QVQRVHIDLULQJSURWXEHUDQFHVDQGFRQLFDO part of the road map to achieve the orbital mission purpose transitions between rocket stages of different diameters. of this platform, has been constructed to be launched by a The main aspects of the MDO-SONDA are architecture, VS-40, supporting an experimental module to be exposed to inputs, outputs, optimization algorithm, and how to proceed PLFURJUDYLW\HQYLURQPHQW /D1HYHDQG&RUUrD with the optimization. 7KH96ZDVRULJLQDOO\GHVLJQHGIRUÀLJKWTXDOL¿FDWLRQ of the S44 motor, which constitutes the fourth stage of the Architecture %UD]LOLDQODXQFKYHKLFOH 9/6 3HUHLUDDQG0RUDHV-U ,Q ZKHQWKH¿UVW96ZDVODXQFKHGWKH0'2 The architecture of the MDO-SONDA is described in methodology had recently been presented. two parts: the interaction between the objective function and 7KHVKDSHRSWLPL]DWLRQRIWKH96¿QVZLOOEHSUHVHQWHGWZRKLJK¿GHOLW\H[HFXWDEOHFRGHVRQHRIDHURG\QDPLFVDQG as a case study using such methodology to demonstrate its another of trajectory (Fig. 2a); and, the interaction between the application in the context of Brazilian sounding rockets. optimization algorithm and the objective function (Fig. 2b). However, before presenting the results of the optimization, the 7KHKLJK¿GHOLW\H[HFXWDEOHFRGHVDUH PLVVLOHGDWFRPDQG main aspects of the MDO-SONDA will be further depicted. rocket simulation (ROSI). The missile datcom is a widely used semi-empirical MULTIDISCIPLINARY DESIGN OPTIMIZATION OF aerodynamic prediction code, which estimates aerodynamic SOUNDING ROCKETS forces, moments, and stability derivatives for a wide range RIPLVVLOHFRQ¿JXUDWLRQVDVDIXQFWLRQRIWKUHHDWPRVSKHULF The MDO-SONDA was conceived to exploit the synergy descriptors: Mach number, altitude, and angle of attack (Sooy between the design disciplines of sounding rockets. Among and Schmidt, 2005). Its original version was developed in them, those that use physics-based engineering models are: )2575$1E\WKH0F'RQQHOO'RXJODV&RUSRUDWLRQ/DWHU propulsion, aerodynamics, heating, structures, controls, and the FORTRAN 90 version was documented by the U.S. Air trajectory. Its current version interacts in batch mode with Force (Blake, 1998). WZR KLJK¿GHOLW\ H[HFXWDEOH FRGHV RQH RI DHURG\QDPLFV The ROSI is also a FORTRAN code. It computes the motion and another of trajectory. Thus, it can exploit the synergy of a rigid body in a three-dimensional space, considering between these two disciplines. Interacting with at least two also its rotation in yaw, pitch, and roll axes (Ziegltrum, disciplines makes the MDO-SONDA able to demonstrate the *RPHV ,WVRULJLQDOYHUVLRQZDVGHYHORSHGE\ MDO methodology. Besides, it can support multiobjective '/5 =LHJOWUXP 6LQFHWKH VWKH526,KDVEHHQ problems. It can also investigate the trade-offs between the successfully used for the trajectory calculation of Brazilian design objectives. sounding rockets.
1st step 2nd 1st step Optimization Objective function algorithm assigns values to 3rd feeds interacts with interacts with 5th Evaluation Design calls of each cost variables function Missile DATCOM ROSI software 2nd software 4th feed Objective function returns Aerodynamic discipline Trajectory discipline (a) (b) Figure 2. Interactions of the MDO-SONDA.
J. Aerosp. Technol. Manag., São José dos Campos, Vol.4, No 4, pp. 431-442, Oct.-Dec., 2012 433 %DUERVD$1*XLPDUmHV/1)
The MDO-SONDA calls the executable codes in batch WKH¿UVWSDUWW\SLFDOÀLJKWHYHQWVDUH VWDJHLJQLWLRQEXUQRXW mode, which means to run to completion without manual spent stage separation, nose fairing ejection, and system release. intervention. The missile datcom provides to ROSI the Such events divide the trajectory calculation into phases, since
IROORZLQJ DHURG\QDPLF SURSHUWLHV GUDJ FRHI¿FLHQW &D), WKH\SURGXFHDEUXSWFKDQJHVLQWKHURFNHWFRQ¿JXUDWLRQ)RU
QRUPDOIRUFHFRHI¿FLHQWGHULYDWLYHZLWKDQJOHRIDWWDFN &1Į), LQVWDQFHWKHDHURG\QDPLFFRHI¿FLHQWVDUHJLYHQDVDIXQFWLRQ SLWFKLQJPRPHQWFRHI¿FLHQWGHULYDWLYHZLWKDQJOHRIDWWDFN of Mach and altitude for each change in rocket geometry, due
&0Į SLWFKLQJPRPHQWFRHI¿FLHQWGHULYDWLYHZLWKSLWFKUDWH to the separation of its parts, and jet plume, due to switching
&Mq UROOLQJ PRPHQW FRHI¿FLHQW GHULYDWLYH ZLWK UROO UDWH a motor on and off. Each phase is characterized by rocket
&lp), and center of pressure (Xcp). GH¿QLWLRQV ZKLFK GHQRWH WKH SKDVH FRQ¿JXUDWLRQV RI WKH
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DQG&OįDUHSDUDPHWHUVRIHDFKVLQJOH¿QWRGHWHUPLQHWKHUROO of the body, propulsion data, and mass and inertia properties rate of the rocket. Unfortunately, the missile datcom does not of each subsystem that still remains in the rocket during the
SURYLGH&OįEXWSURYLGHVWKHUROOLQJPRPHQWFRHI¿FLHQW &l). ÀLJKW8VLQJWKH+X\JHQV6WHLQHUWKHRUHPWKH0'2621'$ To use missile datcom calculation indirectly, it is assumed that computes the total mass and inertia properties of each phase
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EHXVHGWRHVWLPDWH&Oį(Eq. 1): Outputs 2Cl C1 Cld = , (1) 2d 0. 01c The MDO-SONDA provides an output interface for each The MDO-SONDA manages the process of each executable executable code and for the optimization results. Using such code, writes their inputs, and reads their outputs, coordinating interfaces, the user can save and analyze later the Pareto- their interaction. During the optimization loop, if they freeze optimal solutions by using the features of the output interface for any reason, their processes are, automatically, killed and for missile datcom and ROSI in order to verify and validate restarted but with different inputs. First, the MDO-SONDA WKH¿QDOUHVXOWV interacts with missile datcom, obtaining the aerodynamic FRHI¿FLHQWV7KHQLWZULWHVWKHFRHI¿FLHQWVLQWRWKHLQSXW¿OH Optimization algorithm of ROSI, which also receives the mass and inertia properties of the rocket, i.e., the changes of mass, center of gravity, Since it is expected that the objective functions have moment of inertia and product of inertia, computed by the many local minima and maxima and unknown functions MDO-SONDA due to spent stage separations, system releases gradient, the appropriate methods are, traditionally, genetic DQGSURSHOODQWFRQVXPSWLRQDORQJWKHURFNHWÀLJKW algorithms and simulated annealing, according to the logic 2QHPDMRUEHQH¿WRIWKH0'2621'$LVWRSURYLGHDdecision for choosing MDO, which was proposed by Rowell user-friendly interface to insert input values and to check, DQG.RUWH &RQVLGHULQJWKHWUDGLWLRQDODSSURDFKWKH graphically, outputs of both missile datcom and ROSI. It also MDO-SONDA is based on a multiobjective nongenerational SURYLGHVWKHYLVXDOL]DWLRQRIWKHLQSXW¿OHRIHDFKH[HFXWDEOH JHQHWLF DOJRULWKP %DUERVD DQG *XLPDUmHV 7KH code, which is automatically generated to make sure that there nongenerational approach is adequate for multiobjective issues, is not any apparent mistake. since it preserves individuals that are closer to the Pareto front 9DOHQ]XHOD5HQGyQDQG8UHVWL&KDUUH 7KHYHUVLRQRI Inputs this genetic algorithm approach, which was used in this work, is based on the proposal of Borges and Barbosa (2000). The The MDO-SONDA inputs can be grouped in three parts. nongenerational algorithm starts generating and assessing the 7KH¿UVWRQHFRQVLVWVRILQLWLDOFRQGLWLRQVÀLJKWHYHQWVDQG LQLWLDOSRSXODWLRQFRPSXWLQJWKH¿WQHVVRIHDFKLQGLYLGXDO URFNHWGH¿QLWLRQVZKLFKSURYLGHWKHHQWULHVWRHVWLPDWHWKH DQGUDQNLQJWKHSRSXODWLRQDFFRUGLQJWRLW7KHQSUHGH¿QHG DHURG\QDPLFFRHI¿FLHQWVDQGWRVLPXODWHWKHURFNHWWUDMHFWRU\ quantity of iterations is started, which will be satisfactory if The second are the elements of the optimization problem: all individuals become nondominated at the completion of GHVLJQREMHFWLYHVYDULDEOHVDQGFRQVWUDLQWV/DVWO\WKHWKLUG the optimization. Each iteration consists of selecting two ones are the optimization algorithm settings. With respect to individuals, denoted by parents, generating their offspring that
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LQFOXGHVWZRQHZVXEMHFWVFRPSXWLQJWKHLU¿WQHVVDQGVHOHFWLQJ method consists of parallel lines, vertical and equally spaced, WKHQHZLQGLYLGXDOZLWKWKHEHVW¿WQHVVDQGWHVWLQJWKHVHOHFWHG where each line corresponds to a design variable and the individual to decide on his/her inclusion into the population. maximum and minimum values of each variable are usually Despite the denomination given to this genetic algorithm, scaled to the upper and lower boundaries on their respective nongenerational, each iteration denotes a generation, since a OLQHV *ULQVWHLQHWDO 8VLQJWKLVDSSURDFKRQHYHUL¿HV new individual can be introduced into the population. In the graphically, whether the promising region of the search space version used in this work, new individuals are accepted only is reaching the lower and upper bounds or not. Then, if it does, if they are not bad than the worst individual in the population it suggests that the bounds should be extended. Otherwise, %DUERVDDQG*XLPDUmHV $OVRWKLVZRUNXVHGDUHDO it may suggest that the bounds should be more restrictive. RSHUDWRUWKDWSURGXFHVERWKGLYHUVL¿FDWLRQDQGLQWHQVL¿FDWLRQ Furthermore, the analyses of the optimization results may of the search for optimal solutions instead of the original binary expose unfeasible conditions that were not considered before operators, since the optimization problem of current interest is in the optimization problem. Thus, the optimization is also a based on continuous objective functions. learning process on the self-optimization problem. The proposed real operator works on a normalized search space. Firstly, appropriate values are assigned to its parameters: CASE STUDY
FRHI¿FLHQWRIPXWDWLRQ c), lower bound of mutation (Ninf), and upper bound of mutation (Nsup ZKHUHWKH¿UVWSDUDPHWHU This section presents the case study of the VS-40 by using is a real number and the last two are integers. Secondly, the the MDO-SONDA. Firstly, the elements of the optimization operator visits each solution that were previously chosen to SUREOHPZLOOEHGH¿QHG7KHQWKHVHWWLQJVRIWKHPXOWLREMHFWLYH JHQHUDWHDGHVFHQGDQWUXQQLQJWKHIROORZLQJVWHSV*LYHQD nongenerational genetic algorithm will be presented, and chosen solution, a variable (Y) of it that is a design variable is WKHVROXWLRQVWRLPSURYHWKH96¿QVZLOOEHFRPPHQWHG randomly chosen to suffer mutation. Thirdly, an integer (N) is Finally, a mission analysis considering a hypothetical payload randomly generated between Ninf and Nsup, and a real value (p) mass to microgravity experiment will be presented on the is randomly generated between zero and one. Finally, the new point of view of the trajectory discipline to evaluate the gain value of Y derives from the old one plus an increment (m), REWDLQHGZLWKWKHLPSURYHG¿QVLQFRPSDULVRQZLWKWKH96 which is given by Eq. 2: ZLWKLWVRULJLQDO¿QVWDNLQJLQWRDFFRXQWWKHLQÀXHQFHRIZLQG DQGGLVSHUVLRQIDFWRUVRIWKH96RQLWVÀLJKW -tv if p = 0; m = )tv(),1 - otherwise (2) Design problem statement where 7KHGHVLJQLVVXHPD\EHGH¿QHGDVIROORZV*LYHQWKH
- k original design of the VS-40 with a payload of 240 kg, and tce= $ 2 (3) assuming that this mass is the minimum acceptable for this ,Q(TZKHQWKHFRHI¿FLHQWRIPXWDWLRQc increases, URFNHWWKHJRDOLVWR¿QGDQLPSURYHGGHVLJQIRULWVWDLO¿QV WKH GLYHUVL¿FDWLRQ RI WKH VHDUFK GRHV WKH VDPH 7KH PRUH To achieve such a goal, two design objectives were pursued: GLYHUVL¿HGWKHPRUHJOREDOL]HGWKHRSWLPL]DWLRQLV+RZHYHU PLQLPL]DWLRQ RI WKH GUDJ IRUFH FDXVHG E\ WKH URFNHW ¿QV it is important to establish a compromise between both and maximization of the shortest interval between critical GLYHUVL¿FDWLRQDQGLQWHQVL¿FDWLRQLQRUGHUWRDYRLGH[FHVVLYH ÀLJKWHYHQWVZKLFKDUHWUDQVRQLFVSHHGPD[LPXPG\QDPLF HYDOXDWLRQVRIWKHREMHFWLYHIXQFWLRQLIGLYHUVL¿FDWLRQZHLJKV pressure, minimum static margin, and pitch-roll crossing. PRUHWKDQLQWHQVL¿FDWLRQRUSUHPDWXUHFRQYHUJHQFHRWKHUZLVH The second objective is commonly pursued to avoid subjecting the rocket to severe conditions that could induce an How to proceed with the optimization unstable behavior. The transonic speed refers to the range of Mach 0.8 to 1.4, in which severe instability can occur due to oscillating The optimization is a trial process. It consists of choosing shock waves and large acoustic energy release. The maximum the preliminary intervals for the design variables. The output dynamic pressure is often related to the point of maximum interface for optimization results uses a method for analyzing DHURG\QDPLFORDG,QGHHGWKH¿QVKDYHQHJOLJLEOHLQÀXHQFH multivariate data, which is called parallel coordinates. This on the instants of both the transonic speed and the maximum
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G\QDPLFSUHVVXUH7KHLUUHVSRQVHVDUHVLJQL¿FDQWO\UHODWHGWRWKH Table 1. Bounds of the design variables. rocket propulsion. The static margin is the position of the center Design variable Nominal /RZHUERXQG Upper bound of pressure, where the aerodynamic forces act, minus the position 1 (degrees) 0.6 0.42 0.6 of the center of gravity, both measured with respect to the nose 2 (m) 0 0 2.4843 tip as referential and positive in the direction of the rocket tail. 3 (m) 0.7095 0.7095 0.9095 If the static margin is negative, that is, the center of pressure 4 (m) 1.2513 1 1.2513 is ahead of the center of gravity, the rocket is aerodynamically 5 0.348038 0.348038 0.417646 unstable. If it is positive but too small, it increases the rocket 6 0.799168 0.719 0.959002 oscillations, which can affect the rocket performance. The pitch- 7 (m) 0.016783 0.011748 0.016783 roll crossing, that is, the crossing between the pitch and the roll rates, can lead to a physical phenomenon called roll resonance The optimization was subjected to the following side followed by the roll lock-in, where the roll rate deviates from its FRQVWUDLQWV UROOUDWH+]DQGVWDWLFPDUJLQFDOLEHUV GHVLUHGSDWK &RUQHOLVVHHWDO, 1979). These two latter critical Such constraints are necessary because excessive roll rate ÀLJKWHYHQWVDUHVLJQL¿FDQWO\DIIHFWHGE\WKH¿QVRIWKHURFNHW affects the structure, and too small static margin increases Before proceeding with the comments on the solutions to oscillations. Both situations can affect rocket performance. LPSURYHWKH96¿QVDQXQREYLRXVTXHVWLRQZDVDQVZHUHG ZKHQDWWHPSWLQJWRPLQLPL]HWKHGUDJGXHWR¿QVGRHVWKH Optimization settings and results second objective suffer as a result? It is also demonstrated that the MDO methodology can be used to investigate whether Table 2 presents the settings of the multiobjective design objectives are competing or not, leading to a more nongenerational genetic algorithm used in MDO-SONDA. It comprehensive understanding of the systems trade-offs. also shows that the neighborhood radius and the graduation Figure 3 describes the design variables. The VS-40 is a IDFWRUDUHSDUDPHWHUVRIWKH¿WQHVVIXQFWLRQZKLFKUHJXODWH ERG\WDLOURFNHWFRQ¿JXUDWLRQZLWKIRXULGHQWLFDOWDLO¿QV the distribution of solutions along the Pareto front (Borges DUUDQJHGLQDFUXFLIRUPJHRPHWU\,WV¿QVKDYHKH[DJRQDO and Barbosa, 2000). airfoil geometry and two segments. In this case study, only the Despite the small number of design variables, this case second segment was subjected to optimization (Fig. 3). Still, study showed that computational cost could become an the variation of mass and inertia properties related to the shape issue. A single simulation involving interactions between FKDQJHRIWKH¿QVZDVQHJOHFWHG aerodynamics and trajectory calculations takes 12 seconds 7KHLQWHUYDOVRIVKDSHYDULDWLRQRIWKH¿QVDUHHVWDEOLVKHG LQ D *+] 'XDO &RUH 6LQFH HYDOXDWLRQV RI WKH LQ7DEOHZKLFKGH¿QHVWKHFRQWLQXRXVGHVLJQVHDUFKVSDFH objective function were required for seven design variables, for optimization. the optimization took four hours.
b a a Var-4 1 Var-5 Var-6 Var-7 Side (i) Span station at (*) b Var-4 Var-5 Var-6 Side (ii) where
Note: (ii) is the mirror of (i). 0Var-51dd Var-4 0Var-61dd Var-2 (*)
Var-3 Second segment Fin panel
First segment 1.2513 m (area = 0.2279 m2)
Var-1 (deflection angle)
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Table 2. Optimization algorithm settings. 9 Nose tip Parameter Value 8 11 10 Fin profile Size of the population 20 7 9 8 Number of generations 600 6 7 Neighborhood radius 2 6 5 5 *UDGXDWLRQIDFWRU 0.5 Pareto-optimal 4 solutions &RHI¿FLHQWRIPXWDWLRQ 1.4 3 /RZHUERXQGRIPXWDWLRQ 1 4 2 Original fins Upper bound of mutation 6 3 1 2 Float-point precision 0.001 1 0
Shortest interval between critical flight events (s) -8 -7.5 -7 -6.5 -6 -5.5 -5 -4.5 We have found a Pareto front, demonstrating that the Drag force caused by fins (kN) PLQLPL]DWLRQRIWKHGUDJGXHWR¿QVDQGWKHPD[LPL]DWLRQ Figure 4. Optimization results. RI WKH VKRUWHVW LQWHUYDO EHWZHHQ FULWLFDO ÀLJKW HYHQWV DUH competing objectives (Fig. 4). on [-axis the total drag minus its value without computing the ,WVHHPVWKDWWKH¿WQHVVIXQFWLRQDVSURSRVHGE\%RUJHV ¿QVLQWKHGUDJFRHI¿FLHQWFDOFXODWLRQZKLFKLVN1 and Barbosa (2000), gave well-distributed points along the Thus, in terms of the total drag, the reduction was up to 5%. Pareto front (Fig. 4). However, despite the fact that population Regarding the parallel coordinates graph, the promising VL]HZDV¿[HGDW 7DEOH )LJRQO\SUHVHQWVDVHWRI area of the search space has reached the limits of almost the points. Indeed, in some of these points, there is more than one totality of the design variables (Fig. 5). solution with slight differences between them. In Fig. 5, regarding the line of Var-7, which is related to the Optimization results seem to be coherent. The interval WKLFNQHVVRIWKH¿QVWKHUHVXOWVVXJJHVWWKDWWKHORZHUERXQG between the transonic speed and the maximum dynamic KDVWREHUHGXFHG&HUWDLQO\WKHERXQGVKDYHWREHNHSWZKHQ SUHVVXUHHYHQWVLVVHFRQGVQRPDWWHUZKDW¿QVDUHXVHG they also want to avoid unfeasible solutions. Therefore, the The optimization could not lead to solutions that exceed such lower bound of Var-7 is kept, assuming that its reduction can LQWHUYDO )LJ $OVRWKHGUDJGXHWRWKHURFNHW¿QVFDQEH lead to structural issues. reduced up to 29% without increasing the chances of adverse Table 3 presents a Pareto-optimal solution associated effects that could lead to unstable behaviors (Fig. 4). There are with each point in Fig. 4. It is worth noting, based on Var-3 some chances that adverse effects increase when two or more and Var-4 values in Table 3 and the chord at the base of the FULWLFDOÀLJKWHYHQWVRFFXUDWWKHVDPHLQVWDQW)LJXUHVKRZV VHFRQGVHJPHQWRIWKH¿QSDQHODQGWKHDUHDRIWKH¿UVWRQH
7DEOH'LPHQVLRQVRI¿QVIRUWKH96 Solution* Variable 1 (m) Variable 2 (m) Variable 3 (m) Variable 4 (m) a (m) b (m) Variable 7 (m) Original 0.600 0.000 0.710 1.251 0.652 0.348 0.0168 1 0.587 2.429 0.793 1.167 0.584 0.382 0.0117 2 0.589 1.995 0.787 1.084 0.608 0.426 0.0118 3 0.550 1.995 0.787 1.084 0.597 0.418 0.0118 4 0.526 1.995 0.787 1.084 0.584 0.409 0.0118 5 0.427 1.995 0.787 1.084 0.577 0.409 0.0118 6 0.420 1.766 0.793 1.095 0.610 0.440 0.0117 7 0.420 1.995 0.812 1.095 0.626 0.423 0.0117 8 0.420 1.995 0.842 1.066 0.603 0.416 0.0118 9 0.421 1.995 0.862 1.089 0.622 0.421 0.0118 10 0.420 2.029 0.862 1.212 0.690 0.470 0.0117 11 0.422 1.855 0.905 1.196 0.684 0.461 0.0118 *solutions are ordered as in Fig. 4.
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1 Promising region boundary Dominated solutions Original fins Pareto-optimal solutions Normalized Interval
0 Var-1 Var-2 Var-3 Var-4 Var-5 Var-6 Var-7 Design variables Figure 5. Vizualization of the parallel coordinates. showed in Fig. 3, the Pareto-optimal solutions have from 2.8 Despite the fact that solutions providing the shortest to 19.6% more surface than the original panel. Surface area LQWHUYDO EHWZHHQ FULWLFDO ÀLJKW HYHQWV JUHDWHU WKDQ WZR often has more impact than geometry, increasing the drag, seconds are those safer than the solution number 1, for despite any attempts to reduce it by choosing an adequate PLVVLRQDQDO\VLVWKHLPSURYHG¿QVZHUHVHOHFWHGVLQFHLWLV geometry. However, the extended surface area of the Pareto- the Pareto-optimal solution that causes the largest reduction of optimal solutions does not seem to cause any disadvantage in the drag, increasing the rockets performance. FRPSDULVRQZLWKWKHRULJLQDO¿QV )LJXUHLVHYLGHQFHWKDWWKHRULJLQDO¿QVDUHQRWDGHTXDWH Mission analysis 7KHRULJLQDO¿QVRIWKH96KDYHUHFWDQJXODUSDQHOV )LJE $PRQJWKHSDQHOJHRPHWULHVIRU¿QVWKHUHFWDQJXODULVWKH The proposed mission to be analyzed is characterized by a one that provides more drag in supersonic speed, based on hypothetical payload of 240 kg, which is carried by the VS-40 equal surface area and span between the geometries (Fleeman, to be exposed to microgravity environment. If one suppose 'HVSLWHWKHUHGXFHGVXUIDFHDUHDRIWKHRULJLQDO¿QVLW the mission is scheduled for December, corresponding to the causes more drag than the Pareto-optimal solution number 11, WUDQVLWLRQEHWZHHQWKHGU\DQGUDLQ\SHULRGVLQ&/$ &DVWUR which has the largest surface area. and Fisch, 2007), when wind surface reduces gradually with Among the Pareto-optimal solutions, the drag increases as WKHRFFXUUHQFHRIUDLQWKHRSHUDWLRQZLOOEHEHQH¿WHG7KH WKHVXUIDFHDUHDLQFUHDVHVGHPRQVWUDWLQJWKHVWHDG\LQÀXHQFH goal is to evaluate what is the gain in the performance of the of the surface area (Fig. 6). However, the solution number 1 96ZLWKWKHLPSURYHG¿QVLQFRPSDULVRQZLWKLWVRULJLQDO is an outlier, since it causes less drag than solutions from 2 to ones considering this hypothetical mission. 7 but it has an area slightly extended with similar geometry The maximum expected gain can be estimated without (Fig. 4). Solutions are ordered as in Fig. 4. performing any optimization. The trajectory simulation ZLWKRXWFRPSXWLQJWKH¿QVLQWKHGUDJFRHI¿FLHQWFDOFXODWLRQ 8 provides an expected gain of 2.9% (Fig. 7). Despite the small Original solution 7.5 LQÀXHQFHRIWKH¿QVRQWKHSHUIRUPDQFHRIWKHURFNHWLQ PLFURJUDYLW\DVUHÀHFWHGE\WKHVPDOOH[SHFWHGJDLQLWZDV 7 11 seen that the conditions of a mission analysis can affect the 10 9 JDLQGXHWRLPSURYHPHQWRIWKHURFNHW¿QV 6.5 8 ,JQRULQJ WKH LQÀXHQFH RI WKH ZLQG DQG RI GLVSHUVLRQ 7 IDFWRUVRIWKH96RQLWVÀLJKWDWRWDOGUDJUHGXFWLRQRI 6 6 XVLQJWKHLPSURYHG¿QVFDXVHVDQHODSVHGÀLJKWWLPH {2,3,4,5} 5.5 gain in microgravity of 1.6% (Fig. 7). However, since the 1 Magnitude of the drag due to fins (kN) VS-40 is an unguided rocket, wind effects and dispersion 5 1.1 1.15 1.2 1.25 1.3 1.35 factors should be considered. The mission analysis consists Area of the fin panel (m2) of taking into account these factors in the evaluation of the )LJXUH'UDJGXHWR¿QVYHUVXV¿QSDQHODUHD 96FRQ¿JXUDWLRQVRQHZLWKWKHLPSURYHG¿QVDQGDQRWKHU
438 J. Aerosp. Technol. Manag., São José dos Campos, Vol.4, No 4, pp. 431-442, Oct.-Dec., 2012 0XOWLGLVFLSOLQDU\'HVLJQ2SWLPL]DWLRQRI6RXQGLQJ5RFNHW)LQV6KDSH8VLQJD7RRO&DOOHG0'2621'$
1020 The VS-40 with its original fins the wind weighting function, which had been previously The VS-40 with improved fins 1000 The VS-40 without computing fins drag calculated. The ballistic wind is hypothetical and constant in GLUHFWLRQDQGPDJQLWXGHIURPWKHJURXQGOHYHOWRDGH¿QHG 980 Gain of 2.9% upper limit of the effective atmosphere. In practice, the upper limit of the effective atmosphere is roughly 25 km (Hennigh, 960 Gain of 1.6% 1964). Finally, considering the ballistic wind, the splashdown 940 displacement caused by a unit wind, and the assumption that the response of the rocket is linear with the wind velocity, 920 the launch azimuth and elevation are adjusted. However, due
Elapsed flight time in microgravity (s) 900 to stochastic behavior of the wind, dispersion factors of the rocket, structural issues, geographical constraints, and rocket 880 80 80.5 81 81.5 82 82.5 83 83.5 84 84.5 85 assumption of the linear response to make the adjustments, Launch elevation (degrees) WKHIROORZLQJFRQVWUDLQWVVKRXOGEHFRQVLGHUHG ElA
)LJXUH(ODSVHGÀLJKWWLPHFDSDELOLW\LQPLFURJUDYLW\HQYLURQPHQW $]A_El&-ElR_DQG_$]A-$]R_ZKHUHElA
YDU\LQJZLWKODXQFKHOHYDWLRQ7KHXSSHUHOHYDWLRQLV and $]A are, respectively, the adjusted elevation and azimuth;
DFFRUGLQJWR&HQWURGH/DQoDPHQWRGH$OFkQWDUD and, ElR and $]R are, respectively, the reference elevation and azimuth. ZLWKWKHRULJLQDO¿QV7KHODXQFKD]LPXWKDQGHOHYDWLRQWKDW 8VLQJVDPSOHVRIZLQGSUR¿OHVFROOHFWHGDW&/$LQ SURYLGHWKHGHVLUDEOHSUREDELOLW\WRSURFHHGEULHÀ\ZLWKWKH December 2008, obtained with sensors, we have estimated PLVVLRQDUH¿UVWO\REWDLQHGE\FRQVLGHULQJWKHZLQGHIIHFW the probability of not violating such constraints for a range of 7KHQ¿[LQJWKHDGHTXDWHODXQFKD]LPXWKDQGHOHYDWLRQIRU launch azimuth and elevation values, given to one attempt of HDFK96 FRQ¿JXUDWLRQ WKH WKHRUHWLFDO GHYLDWLRQ RI WKH launch (Fig. 8). elapsed time in microgravity is estimated by considering Suppose the hypothetical mission cannot exceed two the dispersion factors of the rocket. Finally, the gain in the attempts of launch, given that the probability for one attempt SHUIRUPDQFHRIWKH96ZLWKWKHLPSURYHG¿QVLVHVWLPDWHG (P) can be expressed by Eq. 4: based on the average value of the elapsed time in microgravity, 1 n LQFRPSDULVRQZLWKLWVRULJLQDOFRQ¿JXUDWLRQ pP=-11^h -n (4) $ODUJHSHUFHQWDJHRIWKHWRWDOZLQGLQÀXHQFHRQWKH
URFNHWRFFXUVYHU\HDUO\LQÀLJKW'XULQJDQRSHUDWLRQLQWKH where, Pn is the probability, between 0 and 1, for n attempts Brazilian territory, to compensate for the wind effect, it is of launch. necessary to adjust the launch azimuth and elevation based on wind data, which are collected few moments before ,QRUGHUWRQRWH[FHHGWKHOLPLWRIDWWHPSWV¿[LQJPn at liftoff. Two types of wind sensing devices are provided, 0.98, for instance, the probability of not violating constraints rawinsondes to high altitudes and anemometer measurements of launch azimuth and elevation can be at least 0.9 (90%). RIZLQGVXUIDFHSUR¿OH7KHSURFHGXUHWRPDNHWKHODXQFK As the elapsed time in microgravity increases with the azimuth and elevation adjustments for sounding rockets, launch elevation (Fig. 7), let us select the maximum launch still adopted by the Brazilian launch centers, is based on HOHYDWLRQIRUHDFK96FRQ¿JXUDWLRQDVVRFLDWHGZLWK Hennigh (1964). It consists of determining, for a range of of nonviolation of the constraints. Based on Fig. 8, the VS-40 launch elevations, the wind weighting as a function of the ZLWK LPSURYHG ¿QV FDQ EH ODXQFKHG DW DQG ZLWK WKH altitude, and the splashdown displacements caused by a unit RULJLQDO¿QV7KHVHDUHWKHPD[LPXPODXQFKHOHYDWLRQV range- and cross-wind, respectively. Such displacements 7KHODXQFKD]LPXWKFDQEH¿[HGDWIRUERWKFRQ¿JXUDWLRQV are determined by considering the wind up to an upper The theoretical deviation of the elapsed time in microgravity limit of the effective atmosphere. The range-wind azimuth LVGHWHUPLQHGE\XVLQJ0RQWH&DUOR¶VPHWKRGZKLFKFRQVLVWV is given in the direction of the rocket launch tower, while of varying the dispersion factors, and computing their results WKHFURVVZLQGLVQRUPDOWRLW7KHQJLYHQDZLQGSUR¿OHDV on the trajectory of the rocket, assuming a normal distribution input, the procedure consists of evaluating the ballistic wind, RQWKHLUYDULDWLRQLQWHUYDOZKLFKLVGH¿QHGE\WKHLUUHVSHFWLYH combining data provided by the wind sensing devices with error. The aerodynamic coefficients are, for instance,
J. Aerosp. Technol. Manag., São José dos Campos, Vol.4, No 4, pp. 431-442, Oct.-Dec., 2012 439 %DUERVD$1*XLPDUmHV/1)
75 75 70 70 50 30 80 60 40 20 10 70 70 80
60 50 40 30 10 65 20 65
70 60 60 80 80 90
30 55 55 70 60 50 40 20 10
60 50 40 30 50 20 50 10 90 70 45 90 45 100 80 80 Launch azimuth (degrees) Launch azimuth (degrees) 40 40
40 30 20 70 60 50 10
35 35 90 90 60 50 40 30 20 10 30 30 80 80.5 81 81.5 82 82.5 83 83.5 84 84.5 85 80 80.5 81 81.5 82 82.5 83 83.5 84 84.5 85 Launch elevation (degrees) Launch elevation (degrees) (a) (b) Figure 8. Probability of not violating constraints of launch azimuth and elevation adjustment to compensate for the wind effect (%), given to RQHDWWHPSWRIODXQFK D 96ZLWKLWVRULJLQDO¿QV E 96ZLWKWKHLPSURYHG¿QV dispersion factors to be considered. Studies that evaluate the Table 5. Average value and error of the elapsed time in microgravity. accuracy of the missile datcom compared to experimental wind /DXQFKHOHYDWLRQ Elapsed time in microgravity (s) tunnel data shows that the results for aerodynamic drag are (degrees) :LWKRULJLQDO¿QV :LWKLPSURYHG¿QV predicted by missile datcom with an error, whose magnitude 81.5 922±138 939±134 is less than 20% for a variety of rocket geometries (Sooy and 82 932±138 949±129 Schmidt, 2005). At transonic speeds, where boundary layer shock interaction takes place, missile datcom does not have &RQVLGHULQJWKHPD[LPXPODXQFKHOHYDWLRQVWKHHODSVHG the capability to accurately represent such kind of interaction. WLPHJDLQLQPLFURJUDYLW\SURYLGHGE\WKHLPSURYHG¿QVFDQ Table 4 presents the dispersion factors that were assumed to increase from 1.6 to 2.9% (Table 5). As previously discussed, calculate the deviation of the elapsed time in microgravity. the expected gain does not seem to justify any attempt of FKDQJLQJWKH¿QVRIWKH96%HVLGHVWKHH[SHFWHGHUURULV Table 4. Dispersion factors error for each rocket stage. DSSUR[LPDWHO\¿YHWLPHVWKHJDLQLQPLFURJUDYLW\ 7DEOH 2Q Error the other hand, it was demonstrated that the factors associated Dispersion factor First stage Second stage with the mission analysis could affect the gain evaluation. It /DXQFKHUHOHYDWLRQHUURU GHJUHHV ±0.5 is expected that, by involving more subsystems and design /DXQFKHUD]LPXWKHUURU GHJUHHV ±3.0 GLVFLSOLQHVLQIXWXUHZRUNVVLJQL¿FDQWLPSURYHPHQWVLQWKH Head and cross wind (m/s) ±2.0 Brazilian sounding rockets can be demonstrated regarding Thrust variation (%) ±3.0 ±3.0 different applications, besides their application in microgravity Thrust misalignment in pitch and yaw experiments. (degrees) ±0.1 ±0.1 Aerodynamic drag (%) ±20.0 ±20.0 FUTURE WORKS Weight variation (%) ±1.0 ±1.0 Fin misalignment (degrees) ±0.01 ±0.01 In future works, at least four lines of development should Ignition time variation (s) ±2.0 be considered. First, new functionalities may be added to the MDO-SONDA. Interfaces might be created for graphical No predominant wind speed and direction have been FRPSDULVRQVRIWKHDHURG\QDPLFFRHI¿FLHQWVEHWZHHQSKDVH considered in the calculation of the deviation of the elapsed FRQ¿JXUDWLRQV'YLVXDOL]DWLRQRIWKHURFNHWDQGFXVWRPL]HG time in microgravity. Table 5 presents the deviation of the plots of the trajectory parameters. The user should be able to elapsed time in microgravity. customize the optimization problem and to set the interaction
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ZLWKDQHZKLJK¿GHOLW\H[HFXWDEOHFRGHE\XVLQJDQLQWHUIDFH why it should be revised. Before commenting the results of LQVWHDGRIDGGLQJWRRUUHSODFLQJDVSHFL¿FVXEURXWLQHLQ the optimization, the main aspects of the MDO-SONDA were MDO-SONDA. This latter should be able to recalculate the depicted. It was found that the minimization of the drag due mass and inertia properties of the rocket considering the WR¿QVDQGWKHPD[LPL]DWLRQRIWKHVKRUWHVWLQWHUYDOEHWZHHQ change of the shape that is being optimized. Data-mining FULWLFDOÀLJKWHYHQWVDUHFRPSHWLQJREMHFWLYHVOHDGLQJWRDPRUH methods might be included in the future to assist the user on comprehensive understanding of the VS-40 trade-offs. The drag searching for trade-offs, when the number of design variables GXHWRWKHURFNHW¿QVFRXOGEHUHGXFHGXSWR DQGZLWKDQ and objectives are such that the traditional methods of data LQWHUYDORIDWOHDVWRQHVHFRQGEHWZHHQFULWLFDOÀLJKWHYHQWV visualization are not enough to make them explicit. Also, the in order to avoid adverse effects that could lead to unstable MDO-SONDA should be compared with other codes. behaviors. However, in terms of the total drag, the reduction was 6HFRQG PRUH KLJK¿GHOLW\ FRGHV PD\ EH OLQNHG WR XSWRFDXVLQJDQHODSVHGÀLJKWWLPHJDLQLQPLFURJUDYLW\RI MDO-SONDA, involving more design disciplines. For ZLWKRXWLJQRULQJWKHLQÀXHQFHRIWKHZLQGDQGWKHGLVSHUVLRQ instance, teamwork involving experts in propulsion and factors of the rocket. Despite the small gain, it was demonstrated VWUXFWXUH PLJKW SURYLGH UHVSHFWLYHO\ VSHFL¿F FRGHV WR that the factors associated with the mission analysis could affect generate the thrust curve from the propellant variables and the gain evaluation. Finally, four lines of development for future to estimate the structural resistance of the rocket against works were suggested: the addition of new functionalities to DHURG\QDPLFORDGVGXULQJWKHÀLJKW)XUWKHUPRUHDQDQDO\VLV MDO-SONDA; the participation of more design disciplines, FDQEHSHUIRUPHGWRVWXG\WKHLQÀXHQFHRIWKHHUURURIWKH FRQWULEXWLQJZLWKWKHLUKLJK¿GHOLW\FRGHV WKHLPSURYHPHQWRI KLJK¿GHOLW\FRGHVRQWKHGHVLJQRSWLPL]DWLRQ the optimization mechanisms, adding sophisticated methods, Third, the optimization mechanisms may be more such as surrogate models; and the simultaneous optimization of GLYHUVL¿HG DQG VRSKLVWLFDWHG 0HPHWLF DOJRULWKPV DUH WKH two or more subsystems of the rocket. combination of two or more metaheuristics, cooperating or competing with each other, and surrogate models might REFERENCES improve the overall performance of the optimization by reducing the number of objective function evaluations. Parallel %DUERVD$1DQG*XLPDUmHV/1)³,QYHVWLJDWLQJ computing might be used together with such approaches for WKH(I¿FLHQF\RIWKH6XUURJDWHV%DVHGRQ1HXUDO1HWZRUNV large-scale optimization problems. The search for appropriate in Assisting Multi-objective Optimization of Test-problems parameter values related to the optimization mechanisms are 3HUIRUPHG E\ D 1RQJHQHUDWLRQDO *HQHWLF $OJRULWKP´ an issue for future works. ,Q 3URFHHGLQJV RI WKH UG ,QWHUQDWLRQDO &RQIHUHQFH RQ Finally, with respect to the last line of development to be Engineering Optimization, Rio de Janeiro. seen in future, two or more subsystems may be redesigned, simultaneously, to improve the rocket, for instance, two or more %ODNH:% ³0LVVLOH'DWFRP8VHU¶V0DQXDO± )RUWUDQ VHWVRI¿QV¿QVDQGQRVHIDULQJDQGVRRQ6HQVLWLYLW\DQDO\VLV 5HYLVLRQ´:ULJKW3DWWHUVRQ$LU)RUFH%DVH2KLR86$ can be executed to investigate the impact of any variations of the design variables on the its objectives. In addition, two %RUJHV&&+DQG%DUERVD+-&³$QRQJHQHUDWLRQDO or more missions with respect to the same rocket may be JHQHWLF DOJRULWKP IRU PXOWLREMHFWLYH RSWLPL]DWLRQ´ simultaneously considered at the same optimization process. LQ SURFHHGLQJV RI WKH &RQJUHVV RQ (YROXWLRQDU\ &RPSXWDWLRQ/D-ROODSS CONCLUSIONS &DVWUR/&DQG)LVFK*³(VWXGRGR0HLR$PELHQWH In this paper, a MDO application in the context of Brazilian $WPRVIpULFR 3URGX]LGR SDUD $WHQGHU R /DQoDPHQWR GR sounding rockets was demonstrated. As case study, the shape 96%9´,QVWLWXWRGH$HURQiXWLFDH(VSDoR6mR-RVp RSWLPL]DWLRQRI¿QVRIWKH96ZDVSUHVHQWHGUHJDUGLQJLWV GRV&DPSRV57) S next launches at the Brazilian territory to perform microgravity experiments. This paper began by introducing the concepts of &HQWUR GH /DQoDPHQWR GH $OFkQWDUD ³0DQXDO GH sounding rockets and the microgravity environment, which was 6HJXUDQoD 2SHUDFLRQDO GR &HQWUR GH /DQoDPHQWR GH followed by presenting facts about the VS-40, and explaining $OFkQWDUD´1R0$16*2%UD]LO
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