Sounding Rocket Trajectory Simulation And Optimization With-Books Pdf

SOUNDING ROCKET TRAJECTORY SIMULATION AND OPTIMIZATION WITH
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their mean value and the standard deviation Further The results are a vehicle and a payload that are the most. details are described in 1 complex and challenging projects MORABA has. constructed and launched to date, 3 TRAJECTORY SIMULATION. As described in section 2 the SHEFEX 2 mission will. be launched by a two stage sounding rocket The, workflow to simulate a trajectory in ASTOS is intuitive. and in line with the logic of the mission design, engineer The first steps are performed in the Model. Browser the GUI that links all the models of the, ASTOS library. Figure 2 Batch mode inspector, 3 1 Modelling the Vehicle.
2 SHEFEX Define the environment either from a list of already. The Sharp Edge Flight Experiment is a DLR German available models or linking external data from txt or. Aerospace Centre program to investigate aerodynamic Excel files. behaviour and thermal protection problems and develop Define the vehicle components stages with. solutions for re entry vehicles at hypersonic velocities structural and propellant mass payload fairing etc. using unconventional shapes comprising multi facetted Define the propulsion systems thrust mass flow or. surfaces with sharp edges Sounding rockets provide a Isp profile jet damping. useful facility to obtain experimental flight data for Define the aerodynamic models used in the course. period of several orders greater than possible with shock of the mission through coefficient and inertia tables. tunnels The first SHEFEX sounding rocket launch Define the list of phases based on the thrust and. comprising an experiment with an asymmetric form at coast arcs. re entry velocities of Mach 6 7 was launched from the. Andoya Rocket Range ARR Norway in October, 2005 The success of this mission led to the definition. and approval of the SHEFEX 2 mission, Figure 3 Artistic impression of SHEFEX2. SHEFEX 2 was originally conceived as a payload with Figure 4 SHEFEX case in Model Browser. small passive stabilizing fins to be flown on a VSB 30. with a conventional parabolic trajectory which would The most important task of the model definition is the. have provided velocities in the order of Mach 8 The phase list it is required to define a new phase every. greater velocity together with a re entry elevation angle time a discontinuity is present in the physical vehicle. in the order of 75 degrees would have resulted in a A discontinuity could be a new aerodynamic. short experiment time An alternative solution was then configuration the jettisoning of a module or an. found in the VS 40 motor combination together with a important point of the mission In the specific case of. precession control of the spinning second stage to the SHEFEX 2 missions. provide a conventional trajectory of the first stage Starting the engine with the vehicle still fixed at the. together with a suppressed trajectory of the exo ramp. atmospheric burning second stage The result is a flatter The vehicle is moving along the inclined rail due to. re entry angle of about 35 degrees and a velocity of the thrust force. Mach 10 which still provides in the order of 60 seconds Thrust arc of the first stage until burn out. of experiment time between 100 and 20 kilometres Coast arc until the separation of the first stage. altitude Coast arc until the ignition of the second stage. required to compute the re pointing manoeuvre, Re pointing manoeuvre to produce a suppressed The altitude profile is almost identical Figure 6. trajectory see section 2 Several other auxiliary functions have been compared. Thrust arc of the second stage till burn out and and the matching between the ASTOS computation and. separation the MORABA reference trajectory is very good This. Coast arc until 100 km altitude result validates the ASTOS 6DOF computation for. Experiment phase until 20km altitude sounding rocket applications. Re entry until ground impact, 3 4 Atmosphere effect. 3 2 Simulation and visualization, An accurate analysis of the ASTOS results Figure 6.
As soon as the mission is modelled the simulation can reveals an important difference in the Mach profile. be easily performed with the pressing of a button in the when the vehicle is flying at high altitude above 100. GUI of ASTOS km The Mach number is the ratio between the vehicle. Also the trajectory visualization is managed through the speed and the speed of sound the speed of sound is. graphical interface hundreds of auxiliary functions are computed by the atmosphere model as function of the. automatically computed by ASTOS and can be arranged altitude The altitude and the vehicle speed profiles are. in the Viewer according to the user requirements almost identical between ASTOS and the reference tool. the atmosphere model is the guilty party, 3 3 ASTOS computation verification Both ASTOS and the reference tool are using the US. Standard 62 model 4 but it seems that the, ASTOS has been extensively used for the computation. interpretation of this model for high altitudes is not. of launcher trajectory where the simulation and, optimization of a point mass 3DOF is accurate enough. This result directs the attention to the importance of the. in firsts phases of a mission design, atmosphere model for the correct simulation of. According to this experience a 3DOF simulation has. sounding rocket trajectories, been performed and the results compared with a 6DOF.
The influence of the atmosphere can be estimated by a. simulation Fig 5, comparison between simulations performed with the. several models present in the ASTOS library, Figure 5 Comparison 3 6DOF simulation. Figure 7 Atmosphere influence, The comparison shows that the 3DOF and the 6DOF. simulations are quite different a simple 3DOF The Figure 7 presents the altitude profile zoomed in the. simulation seems not accurate enough for this sounding max apogee area of the trajectory The different. rocket mission A second comparison is performed atmosphere models produce a difference in the order of. between the ASTOS simulation 6DOF and the 2 3 km, reference trajectory computed by MORABA 3. 4 IMPACT DISPERSION ANALYSIS, In chapter 3 4 the influence of the atmosphere has been.
assessed in relation to the altitude profile of the. trajectory but one of the most critical aspects of a. sounding rocket simulation is the computation of the. impact point This position is required for technical and. safety issues among others the placement of a mobile. tracking station the payload recovery and the, verification that the rocket will not exit from the impact. Figure 6 ASTOS verification, The batch mode capability of ASTOS see chapter 1 1. can be merged with the extensive data available from. the GRAM99 atmospheric model 5 to compute a, dispersion analysis function of the atmosphere The visualization capability of ASTOS can be. characteristics density and temperature Figure 8 In appreciated in Figure 9 where the altitude and Mach. fact the GRAM99 model contains not only information number information are plotted over a physical map of. on the atmosphere functions density pressure the Earth surface In the field of the safety assessment. temperature composition but also the dispersion of the possibility to use a map of the Earth population. these functions i e the one sigma value density as a background can be appreciated This map. was produced with the upmost recent data at the present. date from GPWv3 6, Figure 8 Atmospheric dispersion analysis. Having assessed the power and flexibility of the batch. mode in this first exercise a more comprehensive Figure 10 Impact positions on population map. Monte Carlo analysis has been conducted on a wider. spectrum As post processing analysis ASTOS computes the. The atmosphere uncertainties are not the only source of distribution profile of the output variables selected by. dispersion in the computation of the impact position the user In Figure 11 the distribution of the trajectory. other variables cannot be precisely identified or range is presented. measured in a sounding rocket mission either, Launch ramp elevation.
Launch azimuth, Drag coefficients, Vehicle mass, Thrust value. Thrust misalignment, Based on the experience of MORABA the dispersion Figure 11 Range distribution. values for all these variables have been inserted in the. batch mode of ASTOS Figure 2 A set of simulations The analysis computed shows an asymmetric Gaussian. has been performed and automatically post processed to bell with the peak at the nominal value 550km This. provide an indication of the impact region and Monte Carlo analysis is based on 10000 simulations the. extension computation time on a Pentium 2 4GHz was 20 hours. 5 OPTIMIZATION, ASTOS was designed in 1989 for trajectory. optimization since then many simulation features have. been added to the tool but the optimization field is still. the playground of this software, Just to clarify one important point. For simulation the models should be as complex as, For optimization the models should be as complex.
as required, Figure 9 3D trajectory and impact positions The important phase of the mission from the scientific. point of view is the hypersonic re entry of SHEFFEX2. The optimization goal is therefore to maximize the time. the rocket stays at an altitude range between 100km and. 20km with Mach number higher than 7 Figure 13 presents a 3D visualization of the two. The problem characteristics are summarized in Table 1 trajectories the reference and the optimized from a. different point of view North West Even if the, duration of the optimized trajectory the lower one is. Open parameters Constraints, longer see Figure 12 the range constraint has not been. violated see Figure 13, Initial pitch, Required time after. Duration of coast arcs The increased experiment duration presents one evident. jettison of first and, Pitching maneuver side effect the maximum Mach number reached.
second stage, decreases from 9 to 8, This is a classical situation in the design of a mission it. Goal Maximize the experiment duration is not possible to gain in all the aspects of the trajectory. Table 1 Optimization summary Of course it would be possible to change the weight of. the cost function and to add more constraints in order to. The reference trajectory has been provided by obtain a different result. MORABA 3 but the mission design of SHEFEX2 is This makes the optimization an interactive process. not concluded yet so it is probable that the flying where the engineer and the computer work together to. trajectory will differ from the one presented in this reach the best compromise in the mission design. 6 CONCLUSION, 5 1 Results ASTOS is a software tool for trajectory simulation and. Even if the modifiable parameters are few the optimization completely data driven through GUI. optimization has tailored the trajectory to a completely The simulation results are in line with the MORABA. different altitude profile Figure 12 reference tool. The batch mode capability of ASTOS can be used to, perform an interesting impact dispersion analysis. The optimized trajectory can increase the experiment. time by 25 without any violation of the mission, constraints. The computation time for a trajectory simulation less. than 10 seconds is in line with the ground segment. requirements, REFERENCES, Figure 12 Optimized vs reference trajectory.
The launch pad elevation is slightly lower 1 5 degree 1 Wiegand A et al 2008 ASTOS User Manual. the coast arc before the second stage ignition is longer Version 6 0 0 Astos Solutions GmbH. These modifications produce a lower apogee and Unterkirnach Germany. increase the flatness of the Mach profile in the 2 Wiegand A et al 2008 ASTOS Model Library. experiment arc Figure 12 Version 6 0 0 Astos Solutions GmbH. The optimized trajectory allows an experiment time of Unterkirnach Germany. 86 seconds it was 69 in the reference trajectory 3 Jung W Scheuerpflug F 2009 Private. Conversation and emails DLR MORABA, 4 U S Standard Atmosphere 1962 U S Government. Printing Office Washington D C 1962, 5 Justus C G Global Reference Atmospheric Model. 1999 GRAM 99 NASA MSFC 1999, 6 Center for International Earth Science Information. Network CIESIN Columbia University and, Centro Internacional de Agricultura Tropical. CIAT 2005 Gridded Population of the World, Version 3 GPWv3 Palisades NY.
Socioeconomic Data and Applications Center, SEDAC Columbia University. SOUNDING ROCKET TRAJECTORY SIMULATION AND OPTIMIZATION WITH trajectory data and the latter to provide a The atmosphere uncertainties are not the only source of

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