@inproceedings{LoebSchartnerDachwaldetal.2011, author = {Loeb, Horst W. and Schartner, Karl-Heinz and Dachwald, Bernd and Ohndorf, Andreas and Seboldt, Wolfgang}, title = {An Interstellar - Heliopause mission using a combination of solar/radioisotope electric propulsion}, series = {Presented at the 32nd International Electric Propulsion Conference}, booktitle = {Presented at the 32nd International Electric Propulsion Conference}, pages = {1 -- 7}, year = {2011}, abstract = {There is common agreement within the scientific community that in order to understand our local galactic environment it will be necessary to send a spacecraft into the region beyond the solar wind termination shock. Considering distances of 200 AU for a new mission, one needs a spacecraft travelling at a speed of close to 10 AU/yr in order to keep the mission duration in the range of less than 25 yrs, a transfer time postulated by ESA.Two propulsion options for the mission have been proposed and discussed so far: the solar sail propulsion and the ballistic/radioisotope electric propulsion. As a further alternative, we here investigate a combination of solar-electric propulsion and radioisotope-electric propulsion. The solar-electric propulsion stage consists of six 22 cm diameter "RIT-22"ion thrusters working with a high specific impulse of 7377 s corresponding to a positive grid voltage of 5 kV. Solar power of 53 kW BOM is provided by a light-weight solar array. The REP-stage consists of four space-proven 10 cm diameter "RIT-10" ion thrusters that will be operating one after the other for 9 yrs in total. Four advanced radioisotope generators provide 648 W at BOM. The scientific instrument package is oriented at earlier studies. For its mass and electric power requirement 35 kg and 35 W are assessed, respectively. Optimized trajectory calculations, treated in a separate contribution, are based on our "InTrance" method.The program yields a burn out of the REP stage in a distance of 79.6 AU for a usage of 154 kg of Xe propellant. With a C3 = 45,1 (km/s)2 a heliocentric probe velocity of 10 AU/yr is reached at this distance, provided a close Jupiter gravity assist adds a velocity increment of 2.7 AU/yr. A transfer time of 23.8 yrs results for this scenario requiring about 450 kg Xe for the SEP stage, jettisoned at 3 AU. We interpret the SEP/REP propulsion as a competing alternative to solar sail and ballistic/REP propulsion. Omiting a Jupiter fly-by even allows more launch flexibility, leaving the mission duration in the range of the ESA specification.}, language = {en} } @inproceedings{GrundmannLangeDachwaldetal.2015, author = {Grundmann, Jan Thimo and Lange, Caroline and Dachwald, Bernd and Grimm, Christian and Koch, Aaron and Ulamec, Stephan}, title = {Small Spacecraft in Planetary Defence Related Applications-Capabilities, Constraints, Challenges}, series = {IEEE Aerospace Conference}, booktitle = {IEEE Aerospace Conference}, pages = {1 -- 18}, year = {2015}, abstract = {In this paper we present an overview of the characteristics and peculiarities of small spacecraft missions related to planetary defence applications. We provide a brief overview of small spacecraft missions to small solar system bodies. On this background we present recent missions and selected projects and related studies at the German Aerospace Center, DLR, that contribute to planetary defence related activities. These range from Earth orbit technology demonstrators to active science missions in interplanetary space. We provide a summary of experience from recently flown missions with DLR participation as well as a number of studies. These include PHILAE, the lander recently arrived on comet 67P/Churyumov-Gerasimenko aboard ESA's ROSETTA comet rendezvous mission, and the Mobile Asteroid Surface Scout, MASCOT, now underway to near-Earth asteroid (162173) 1999 JU3 aboard the Japanese sample-return probe HAYABUSA-2. We introduce the differences between the conventional methods employed in the design, integration and testing of large spacecraft and the new approaches developed by small spacecraft projects. We expect that the practical experience that can be gained from projects on extremely compressed timelines or with high-intensity operation phases on a newly explored small solar system body can contribute significantly to the study, preparation and realization of future planetary defence related missions. One is AIDA (Asteroid Impact \& Deflection Assessment), a joint effort of ESA,JHU/APL, NASA, OCA and DLR, combining JHU/APL's DART (Double Asteroid Redirection Test) and ESA's AIM (Asteroid Impact Monitor) spacecraft in a mission towards near-Eath binary asteroid (65803) Didymos.}, language = {en} } @incollection{BorggrafeOhndorfDachwaldetal.2012, author = {Borggrafe, Andreas and Ohndorf, Andreas and Dachwald, Bernd and Seboldt, Wolfgang}, title = {Analysis of interplanetary solar sail trajectories with attitude dynamics}, series = {Dynamics and Control of Space Systems 2012}, booktitle = {Dynamics and Control of Space Systems 2012}, publisher = {Univelt Inc}, address = {San Diego}, isbn = {978-0-87703-587-9}, pages = {1553 -- 1569}, year = {2012}, abstract = {We present a new approach to the problem of optimal control of solar sails for low-thrust trajectory optimization. The objective was to find the required control torque magnitudes in order to steer a solar sail in interplanetary space. A new steering strategy, controlling the solar sail with generic torques applied about the spacecraft body axes, is integrated into the existing low-thrust trajectory optimization software InTrance. This software combines artificial neural networks and evolutionary algorithms to find steering strategies close to the global optimum without an initial guess. Furthermore, we implement a three rotational degree-of-freedom rigid-body attitude dynamics model to represent the solar sail in space. Two interplanetary transfers to Mars and Neptune are chosen to represent typical future solar sail mission scenarios. The results found with the new steering strategy are compared to the existing reference trajectories without attitude dynamics. The resulting control torques required to accomplish the missions are investigated, as they pose the primary requirements to a real on-board attitude control system.}, language = {en} } @inproceedings{PirovanoSeefeldtDachwaldetal.2015, author = {Pirovano, Laura and Seefeldt, Patric and Dachwald, Bernd and Noomen, Ron}, title = {Attitude and orbital modeling of an uncontrolled solar-sail experiment in low-Earth orbit}, series = {25th International Symposium on Space Flight Dynamics ISSFD}, booktitle = {25th International Symposium on Space Flight Dynamics ISSFD}, pages = {1 -- 15}, year = {2015}, abstract = {Gossamer-1 is the first project of the three-step Gossamer roadmap, the purpose of which is to develop, prove and demonstrate that solar-sail technology is a safe and reliable propulsion technique for long-lasting and high-energy missions. This paper firstly presents the structural analysis performed on the sail to understand its elastic behavior. The results are then used in attitude and orbital simulations. The model considers the main forces and torques that a satellite experiences in low-Earth orbit coupled with the sail deformation. Doing the simulations for varying initial conditions in attitude and rotation rate, the results show initial states to avoid and maximum rotation rates reached for correct and faulty deployment of the sail. Lastly comparisons with the classic flat sail model are carried out to test the hypothesis that the elastic behavior does play a role in the attitude and orbital behavior of the sail}, language = {en} } @inproceedings{DachwaldKahleWie2006, author = {Dachwald, Bernd and Kahle, Ralph and Wie, Bong}, title = {Solar sail Kinetic Energy Impactor (KEI) mission design tradeoffs for impacting and deflecting asteroid 99942 Apophis}, series = {AIAA/AAS Astrodynamics Specialist Conference and Exhibit}, booktitle = {AIAA/AAS Astrodynamics Specialist Conference and Exhibit}, doi = {10.2514/6.2006-6178}, pages = {1 -- 20}, year = {2006}, abstract = {Near-Earth asteroid 99942 Apophis provides a typical example for the evolution of asteroid orbits that lead to Earth-impacts after a close Earth-encounter that results in a resonant return. Apophis will have a close Earth-encounter in 2029 with potential very close subsequent Earth-encounters (or even an impact) in 2036 or later, depending on whether it passes through one of several so-called gravitational keyholes during its 2029-encounter. Several pre-2029-deflection scenarios to prevent Apophis from doing this have been investigated so far. Because the keyholes are less than 1 km in size, a pre-2029 kinetic impact is clearly the best option because it requires only a small change in Apophis' orbit to nudge it out of a keyhole. A single solar sail Kinetic Energy Impactor (KEI) spacecraft that impacts Apophis from a retrograde trajectory with a very high relative velocity (75-80 km/s) during one of its perihelion passages at about 0.75 AU would be a feasible option to do this. The spacecraft consists of a 160 m x 160 m, 168 kg solar sail assembly and a 150 kg impactor. Although conventional spacecraft can also achieve the required minimum deflection of 1 km for this approx. 320 m-sized object from a prograde trajectory, our solar sail KEI concept also allows the deflection of larger objects. In this paper, we also show that, even after Apophis has flown through one of the gravitational keyholes in 2029, solar sail Kinetic Energy Impactor (KEI) spacecraft are still a feasible option to prevent Apophis from impacting the Earth, but many KEIs would be required for consecutive impacts to increase the total Earth-miss distance to a safe value. In this paper, we elaborate potential pre- and post-2029 KEI impact scenarios for a launch in 2020, and investigate tradeoffs between different mission parameters.}, language = {en} } @inproceedings{HallmannHeideckerSchlottereretal.2016, author = {Hallmann, Marcus and Heidecker, Ansgar and Schlotterer, Markus and Dachwald, Bernd}, title = {GTOC8: results and methods of team 15 DLR}, series = {26th AAS/AIAA Space Flight Mechanics Meeting, Napa, CA}, booktitle = {26th AAS/AIAA Space Flight Mechanics Meeting, Napa, CA}, year = {2016}, abstract = {This paper describes the results and methods used during the 8th Global Trajectory Optimization Competition (GTOC) of the DLR team. Trajectory optimization is crucial for most of the space missions and usually can be formulated as a global optimization problem. A lot of research has been done to different type of mission problems. The most demanding ones are low thrust transfers with e.g. gravity assist sequences. In that case the optimal control problem is combined with an integer problem. In most of the GTOCs we apply a filtering of the problem based on domain knowledge.}, language = {en} } @inproceedings{DupratDachwaldHilchenbachetal.2013, author = {Duprat, J. and Dachwald, Bernd and Hilchenbach, M. and Engrand, Cecile and Espe, C. and Feldmann, M. and Francke, G. and G{\"o}r{\"o}g, Mark and L{\"u}sing, N. and Langenhorst, Falko}, title = {The MARVIN project: a micrometeorite harvester in Antarctic snow}, series = {44th Lunar and Planetary Science Conference}, booktitle = {44th Lunar and Planetary Science Conference}, year = {2013}, abstract = {MARVIN is an automated drilling and melting probe dedicated to collect pristine interplanetary dust particles (micrometeorites) from central Antarctica snow.}, language = {en} } @inproceedings{DachwaldSeboldtLoebetal.2007, author = {Dachwald, Bernd and Seboldt, Wolfgang and Loeb, Horst W. and Schartner, Karl-Heinz}, title = {A comparison of SEP and NEP for a main belt asteroid sample return mission}, series = {7th International Symposium on Launcher Technologies, Barcelona, Spain, 02-05 April 2007}, booktitle = {7th International Symposium on Launcher Technologies, Barcelona, Spain, 02-05 April 2007}, pages = {1 -- 10}, year = {2007}, abstract = {Innovative interplanetary deep space missions, like a main belt asteroid sample return mission, require ever larger velocity increments (∆V s) and thus ever more demanding propulsion capabilities. Providing much larger exhaust velocities than chemical high-thrust systems, electric low-thrust space-propulsion systems can significantly enhance or even enable such high-energy missions. In 1995, a European-Russian Joint Study Group (JSG) presented a study report on "Advanced Interplanetary Missions Using Nuclear-Electric Propulsion" (NEP). One of the investigated reference missions was a sample return (SR) from the main belt asteroid (19) Fortuna. The envisaged nuclear power plant, Topaz-25, however, could not be realized and also the worldwide developments in space reactor hardware stalled. In this paper, we investigate, whether such a mission is also feasible using a solar electric propulsion (SEP) system and compare our SEP results to corresponding NEP results.}, language = {en} } @inproceedings{Dachwald2005, author = {Dachwald, Bernd}, title = {Global optimization of low-thrust space missions using evolutionary neurocontrol}, series = {Proceedings of the international workshop on global optimization}, booktitle = {Proceedings of the international workshop on global optimization}, pages = {85 -- 90}, year = {2005}, abstract = {Low-thrust space propulsion systems enable flexible high-energy deep space missions, but the design and optimization of the interplanetary transfer trajectory is usually difficult. It involves much experience and expert knowledge because the convergence behavior of traditional local trajectory optimization methods depends strongly on an adequate initial guess. Within this extended abstract, evolutionary neurocontrol, a method that fuses artificial neural networks and evolutionary algorithms, is proposed as a smart global method for low-thrust trajectory optimization. It does not require an initial guess. The implementation of evolutionary neurocontrol is detailed and its performance is shown for an exemplary mission.}, language = {en} } @inproceedings{DachwaldBaturkinCoverstoneetal.2005, author = {Dachwald, Bernd and Baturkin, Volodymyr and Coverstone, Victoria and Diedrich, Ben and Garbe, Gregory and G{\"o}rlich, Marianne and Leipold, Manfred and Lura, Franz and Macdonald, Malcolm and McInnes, Colin and Mengali, Giovanni and Quarta, Alessandro and Rios-Reyes, Leonel and Scheeres, Daniel J. and Seboldt, Wolfgang and Wie, Bong}, title = {Potential effects of optical solar sail degredation on trajectory design}, series = {AAS/AIAA Astrodynamics Specialist}, booktitle = {AAS/AIAA Astrodynamics Specialist}, pages = {1 -- 23}, year = {2005}, abstract = {The optical properties of the thin metalized polymer films that are projected for solar sails are assumed to be affected by the erosive effects of the space environment. Their degradation behavior in the real space environment, however, is to a considerable degree indefinite, because initial ground test results are controversial and relevant inspace tests have not been made so far. The standard optical solar sail models that are currently used for trajectory design do not take optical degradation into account, hence its potential effects on trajectory design have not been investigated so far. Nevertheless, optical degradation is important for high-fidelity solar sail mission design, because it decreases both the magnitude of the solar radiation pressure force acting on the sail and also the sail control authority. Therefore, we propose a simple parametric optical solar sail degradation model that describes the variation of the sail film's optical coefficients with time, depending on the sail film's environmental history, i.e., the radiation dose. The primary intention of our model is not to describe the exact behavior of specific film-coating combinations in the real space environment, but to provide a more general parametric framework for describing the general optical degradation behavior of solar sails. Using our model, the effects of different optical degradation behaviors on trajectory design are investigated for various exemplary missions.}, language = {en} } @inproceedings{GehlerOberBloebaumDachwald2009, author = {Gehler, M. and Ober-Bl{\"o}baum, S. and Dachwald, Bernd}, title = {Application of discrete mechanics and optimal control to spacecraft in non-keplerian motion around small solar system bodies}, series = {Procceedings of the 60th International Astronautical Congress}, booktitle = {Procceedings of the 60th International Astronautical Congress}, publisher = {Elsevier}, address = {Amsterdam}, isbn = {978-161567908-9}, pages = {1360 -- 1371}, year = {2009}, abstract = {Prolonged operations close to small solar system bodies require a sophisticated control logic to minimize propellant mass and maximize operational efficiency. A control logic based on Discrete Mechanics and Optimal Control (DMOC) is proposed and applied to both conventionally propelled and solar sail spacecraft operating at an arbitrarily shaped asteroid in the class of Itokawa. As an example, stand-off inertial hovering is considered, recently identified as a challenging part of the Marco Polo mission. The approach is easily extended to stand-off orbits. We show that DMOC is applicable to spacecraft control at small objects, in particular with regard to the fact that the changes in gravity are exploited by the algorithm to optimally control the spacecraft position. Furthermore, we provide some remarks on promising developments.}, language = {en} } @inproceedings{DachwaldWurm2009, author = {Dachwald, Bernd and Wurm, P.}, title = {Design concept and modeling of an advanced solar photon thruster}, series = {Advances in the Astronautical Sciences}, booktitle = {Advances in the Astronautical Sciences}, publisher = {American Astronautical Society}, address = {San Diego, Calif.}, isbn = {978-087703554-1}, issn = {00653438}, pages = {723 -- 740}, year = {2009}, abstract = {The so-called "compound solar sail", also known as "Solar Photon Thruster" (SPT), holds the potential of providing significant performance advantages over the flat solar sail. Previous SPT design concepts, however, do not consider shadowing effects and multiple reflections of highly concentrated solar radiation that would inevitably destroy the gossamer sail film. In this paper, we propose a novel advanced SPT (ASPT) design concept that does not suffer from these oversimplifications. We present the equations that describe the thrust force acting on such a sail system and compare its performance with respect to the conventional flat solar sail.}, language = {en} } @incollection{Dachwald2017, author = {Dachwald, Bernd}, title = {Light propulsion systems for spacecraft}, series = {Optical nano and micro actuator technology}, booktitle = {Optical nano and micro actuator technology}, editor = {Knopf, George K. and Otani, Yukitoshi}, publisher = {CRC Press}, address = {Boca Raton}, isbn = {9781315217628 (eBook)}, pages = {577 -- 598}, year = {2017}, language = {en} } @inproceedings{DachwaldWurm2009, author = {Dachwald, Bernd and Wurm, P.}, title = {Mission analysis for an advanced solar photon thruster}, series = {60th International Astronautical Congress 2009, IAC 2009}, volume = {Vol. 8}, booktitle = {60th International Astronautical Congress 2009, IAC 2009}, publisher = {Elsevier}, address = {Amsterdam}, isbn = {978-161567908-9}, pages = {6838 -- 6851}, year = {2009}, abstract = {The so-called "compound solar sail", also known as "Solar Photon Thruster" (SPT), is a solar sail design concept, for which the two basic functions of the solar sail, namely light collection and thrust direction, are uncoupled. In this paper, we introduce a novel SPT concept, termed the Advanced Solar Photon Thruster (ASPT). This model does not suffer from the simplified assumptions that have been made for the analysis of compound solar sails in previous studies. We present the equations that describe the force, which acts on the ASPT. After a detailed design analysis, the performance of the ASPT with respect to the conventional flat solar sail (FSS) is investigated for three interplanetary mission scenarios: An Earth-Venus rendezvous, where the solar sail has to spiral towards the Sun, an Earth-Mars rendezvous, where the solar sail has to spiral away from the Sun, and an Earth-NEA rendezvous (to near-Earth asteroid 1996FG3), where a large orbital eccentricity change is required. The investigated solar sails have realistic near-term characteristic accelerations between 0.1 and 0.2mm/s2. Our results show that a SPT is not superior to the flat solar sail unless very idealistic assumptions are made.}, language = {en} } @inproceedings{GrundmannBauerBorchersetal.2019, author = {Grundmann, Jan Thimo and Bauer, Wlademar and Borchers, Kai and Dumont, Etienne and Grimm, Christian D. and Ho, Tra-Mi and Jahnke, Rico and Koch, Aaron D. and Lange, Caroline and Maiwald, Volker and Meß, Jan-Gerd and Mikulz, Eugen and Quantius, Dominik and Reershemius, Siebo and Renger, Thomas and Sasaki, Kaname and Seefeldt, Patric and Spietz, Peter and Spr{\"o}witz, Tom and Sznajder, Maciej and Toth, Norbert and Ceriotti, Matteo and McInnes, Colin and Peloni, Alessandro and Biele, Jens and Krause, Christian and Dachwald, Bernd and Hercik, David and Lichtenheldt, Roy and Wolff, Friederike and Koncz, Alexander and Pelivan, Ivanka and Schmitz, Nicole and Boden, Ralf and Riemann, Johannes and Seboldt, Wolfgang and Wejmo, Elisabet and Ziach, Christian and Mikschl, Tobias and Montenegro, Sergio and Ruffer, Michael and Cordero, Federico and Tardivel, Simon}, title = {Solar sails for planetary defense \& high-energy missions}, series = {IEEE Aerospace Conference Proceedings}, booktitle = {IEEE Aerospace Conference Proceedings}, doi = {10.1109/AERO.2019.8741900}, pages = {1 -- 21}, year = {2019}, abstract = {20 years after the successful ground deployment test of a (20 m) 2 solar sail at DLR Cologne, and in the light of the upcoming U.S. NEAscout mission, we provide an overview of the progress made since in our mission and hardware design studies as well as the hardware built in the course of our solar sail technology development. We outline the most likely and most efficient routes to develop solar sails for useful missions in science and applications, based on our developed `now-term' and near-term hardware as well as the many practical and managerial lessons learned from the DLR-ESTEC Gossamer Roadmap. Mission types directly applicable to planetary defense include single and Multiple NEA Rendezvous ((M)NR) for precursor, monitoring and follow-up scenarios as well as sail-propelled head-on retrograde kinetic impactors (RKI) for mitigation. Other mission types such as the Displaced L1 (DL1) space weather advance warning and monitoring or Solar Polar Orbiter (SPO) types demonstrate the capability of near-term solar sails to achieve asteroid rendezvous in any kind of orbit, from Earth-coorbital to extremely inclined and even retrograde orbits. Some of these mission types such as SPO, (M)NR and RKI include separable payloads. For one-way access to the asteroid surface, nanolanders like MASCOT are an ideal match for solar sails in micro-spacecraft format, i.e. in launch configurations compatible with ESPA and ASAP secondary payload platforms. Larger landers similar to the JAXA-DLR study of a Jupiter Trojan asteroid lander for the OKEANOS mission can shuttle from the sail to the asteroids visited and enable multiple NEA sample-return missions. The high impact velocities and re-try capability achieved by the RKI mission type on a final orbit identical to the target asteroid's but retrograde to its motion enables small spacecraft size impactors to carry sufficient kinetic energy for deflection.}, language = {en} } @techreport{BlandfordDachwaldDigeletal.2015, author = {Blandford, Daniel and Dachwald, Bernd and Digel, Ilya and Espe, Clemens and Feldmann, Marco and Francke, Gero and Hiecke, Hannah and Kowalski, Julia and Lindner, Peter and Plescher, Engelbert and Sch{\"o}ngarth, Sarah}, title = {Enceladus Explorer : Schlussbericht — Version: 1.0}, publisher = {FH Aachen}, address = {Aachen}, doi = {10.2314/GBV:86319950X}, year = {2015}, language = {de} } @article{LoebSchartnerDachwaldetal.2012, author = {Loeb, Horst Wolfgang and Schartner, Karl-Heinz and Dachwald, Bernd and Ohndorf, Andreas and Seboldt, Wolfgang}, title = {Interstellar heliopause probe}, series = {Труды МАИ}, journal = {Труды МАИ}, number = {60}, publisher = {Moskauer Staatliches Luftfahrtinstitut (МАИ)}, address = {Moskau}, pages = {2 -- 2}, year = {2012}, abstract = {There is common agreement within the scientific community that in order to understand our local galactic environment it will be necessary to send a spacecraft into the region beyond the solar wind termination shock. Considering distances of 200 AU for a new mission, one needs a spacecraft traveling at a speed of close to 10 AU/yr in order to keep the mission duration in the range of less than 25 yrs, a transfer time postulated by European Space Agency (ESA). Two propulsion options for the mission have been proposed and discussed so far: the solar sail propulsion and the ballistic/radioisotope-electric propulsion (REP). As a further alternative, we here investigate a combination of solar-electric propulsion (SEP) and REP. The SEP stage consists of six 22-cms diameter RIT-22 ion thrusters working with a high specific impulse of 7377 s corresponding to a positive grid voltage of 5 kV. Solar power of 53 kW at begin of mission (BOM) is provided by a lightweight solar array.}, language = {en} } @inproceedings{OhndorfDachwaldSeboldtetal.2011, author = {Ohndorf, Andreas and Dachwald, Bernd and Seboldt, Wolfgang and Schartner, Karl-Heinz}, title = {Flight times to the heliopause using a combination of solar and radioisotope electric propulsion}, series = {32nd International Electric Propulsion Conference}, booktitle = {32nd International Electric Propulsion Conference}, pages = {1 -- 12}, year = {2011}, abstract = {We investigate the interplanetary flight of a low-thrust space probe to the heliopause,located at a distance of about 200 AU from the Sun. Our goal was to reach this distance within the 25 years postulated by ESA for such a mission (which is less ambitious than the 15-year goal set by NASA). Contrary to solar sail concepts and combinations of allistic and electrically propelled flight legs, we have investigated whether the set flight time limit could also be kept with a combination of solar-electric propulsion and a second, RTG-powered upper stage. The used ion engine type was the RIT-22 for the first stage and the RIT-10 for the second stage. Trajectory optimization was carried out with the low-thrust optimization program InTrance, which implements the method of Evolutionary Neurocontrol,using Artificial Neural Networks for spacecraft steering and Evolutionary Algorithms to optimize the Neural Networks' parameter set. Based on a parameter space study, in which the number of thrust units, the unit's specific impulse, and the relative size of the solar power generator were varied, we have chosen one configuration as reference. The transfer time of this reference configuration was 29.6 years and the fastest one, which is technically more challenging, still required 28.3 years. As all flight times of this parameter study were longer than 25 years, we further shortened the transfer time by applying a launcher-provided hyperbolic excess energy up to 49 km2/s2. The resulting minimal flight time for the reference configuration was then 27.8 years. The following, more precise optimization to a launch with the European Ariane 5 ECA rocket reduced the transfer time to 27.5 years. This is the fastest mission design of our study that is flexible enough to allow a launch every year. The inclusion of a fly-by at Jupiter finally resulted in a flight time of 23.8 years,which is below the set transfer-time limit. However, compared to the 27.5-year transfer,this mission design has a significantly reduced launch window and mission flexibility if the escape direction is restricted to the heliosphere's "nose".}, language = {en} } @inproceedings{BorggraefeDachwald2010, author = {Borggr{\"a}fe, Andreas and Dachwald, Bernd}, title = {Mission performance evaluation for solar sails using a refined SRP force model with variable optical coefficients}, series = {2nd International Symposium on Solar Sailing}, booktitle = {2nd International Symposium on Solar Sailing}, pages = {1 -- 6}, year = {2010}, abstract = {Solar sails provide ignificant advantages over other low-thrust propulsion systems because they produce thrust by the momentum exchange from solar radiation pressure (SRP) and thus do not consume any propellant.The force exerted on a very thin sail foil basically depends on the light incidence angle. Several analytical SRP force models that describe the SRP force acting on the sail have been established since the 1970s. All the widely used models use constant optical force coefficients of the reflecting sail material. In 2006,MENGALI et al. proposed a refined SRP force model that takes into account the dependancy of the force coefficients on the light incident angle,the sail's distance from the sun (and thus the sail emperature) and the surface roughness of the sail material [1]. In this paper, the refined SRP force model is compared to the previous ones in order to identify the potential impact of the new model on the predicted capabilities of solar sails in performing low-cost interplanetary space missions. All force models have been implemented within InTrance, a global low-thrust trajectory optimization software utilizing evolutionary neurocontrol [2]. Two interplanetary rendezvous missions, to Mercury and the near-Earth asteroid 1996FG3, are investigated. Two solar sail performances in terms of characteristic acceleration are examined for both scenarios, 0.2 mm/s2 and 0.5 mm/s2, termed "low" and "medium" sail performance. In case of the refined SRP model, three different values of surface roughness are chosen, h = 0 nm, 10 nm and 25 nm. The results show that the refined SRP force model yields shorter transfer times than the standard model.}, language = {en} } @inproceedings{DachwaldKahleWie2007, author = {Dachwald, Bernd and Kahle, Ralph and Wie, Bong}, title = {Head-on impact deflection of NEAs: a case study for 99942 Apophis}, series = {Planetary Defense Conference 2007}, booktitle = {Planetary Defense Conference 2007}, pages = {1 -- 12}, year = {2007}, abstract = {Near-Earth asteroid (NEA) 99942 Apophis provides a typical example for the evolution of asteroid orbits that lead to Earth-impacts after a close Earth-encounter that results in a resonant return. Apophis will have a close Earth-encounter in 2029 with potential very close subsequent Earth-encounters (or even an impact) in 2036 or later, depending on whether it passes through one of several less than 1 km-sized gravitational keyholes during its 2029-encounter. A pre-2029 kinetic impact is a very favorable option to nudge the asteroid out of a keyhole. The highest impact velocity and thus deflection can be achieved from a trajectory that is retrograde to Apophis orbit. With a chemical or electric propulsion system, however, many gravity assists and thus a long time is required to achieve this. We show in this paper that the solar sail might be the better propulsion system for such a mission: a solar sail Kinetic Energy Impactor (KEI) spacecraft could impact Apophis from a retrograde trajectory with a very high relative velocity (75-80 km/s) during one of its perihelion passages. The spacecraft consists of a 160 m × 160 m, 168 kg solar sail assembly and a 150 kg impactor. Although conventional spacecraft can also achieve the required minimum deflection of 1 km for this approx. 320 m-sized object from a prograde trajectory, our solar sail KEI concept also allows the deflection of larger objects. For a launch in 2020, we also show that, even after Apophis has flown through one of the gravitational keyholes in 2029, the solar sail KEI concept is still feasible to prevent Apophis from impacting the Earth, but many KEIs would be required for consecutive impacts to increase the total Earth-miss distance to a safe value}, language = {en} } @inproceedings{GrundmannBodenCeriottietal.2017, author = {Grundmann, Jan Thimo and Boden, Ralf and Ceriotti, Matteo and Dachwald, Bernd and Dumont, Etienne and Grimm, Christian D. and Lange, Caroline and Lichtenheldt, Roy and Pelivan, Ivanka and Peloni, Alessandro and Riemann, Johannes and Spr{\"o}witz, Tom and Tardivel, Simon}, title = {Soil to sail-asteroid landers on near-term sailcraft as an evolution of the GOSSAMER small spacecraft solar sail concept for in-situ characterization}, series = {5th IAA Planetary Defense Conference}, booktitle = {5th IAA Planetary Defense Conference}, pages = {30 Seiten}, year = {2017}, language = {en} } @incollection{Dachwald2010, author = {Dachwald, Bernd}, title = {Solar sail dynamics and control}, series = {Encyclopedia of Aerospace Engineering}, booktitle = {Encyclopedia of Aerospace Engineering}, publisher = {Wiley}, address = {Hoboken}, doi = {10.1002/9780470686652.eae292}, year = {2010}, abstract = {Solar sails are large and lightweight reflective structures that are propelled by solar radiation pressure. This chapter covers their orbital and attitude dynamics and control. First, the advantages and limitations of solar sails are discussed and their history and development status is outlined. Because the dynamics of solar sails is governed by the (thermo-)optical properties of the sail film, the basic solar radiation pressure force models have to be described and compared before parameters to measure solar sail performance can be defined. The next part covers the orbital dynamics of solar sails for heliocentric motion, planetocentric motion, and motion at Lagrangian equilibrium points. Afterwards, some advanced solar radiation pressure force models are described, which allow to quantify the thrust force on solar sails of arbitrary shape, the effects of temperature, of light incidence angle, of surface roughness, and the effects of optical degradation of the sail film in the space environment. The orbital motion of a solar sail is strongly coupled to its rotational motion, so that the attitude control of these soft and flexible structures is very challenging, especially for planetocentric orbits that require fast attitude maneuvers. Finally, some potential attitude control methods are sketched and selection criteria are given.}, language = {en} } @inproceedings{SeboldtDachwald2003, author = {Seboldt, Wolfgang and Dachwald, Bernd}, title = {Solar sails for near-term advanced scientific deep space missions}, series = {Proceedings of the 8th International Workshop on Combustion and Propulsion}, booktitle = {Proceedings of the 8th International Workshop on Combustion and Propulsion}, pages = {14 Seiten}, year = {2003}, abstract = {Solar sails are propelled in space by reflecting solar photons off large mirroring surfaces, thereby transforming the momentum of the photons into a propulsive force. This innovative concept for low-thrust space propulsion works without any propellant and thus provides a wide range of opportunities for highenergy low-cost missions. Offering an efficient way of propulsion, solar sailcraft could close a gap in transportation options for highly demanding exploration missions within our solar system and even beyond. On December 17th, 1999, a significant step was made towards the realization of this technology: a lightweight solar sail structure with an area of 20 m × 20 m was successfully deployed on ground in a large facility at the German Aerospace Center (DLR) at Cologne. The deployment from a package of 60 cm × 60 cm × 65 cm with a total mass of less than 35 kg was achieved using four extremely light-weight carbon fiber reinforced plastics (CFRP) booms with a specific mass of 100 g/m. The paper briefly reviews the basic principles of solar sails as well as the technical concept and its realization in the ground demonstration experiment, performed in close cooperation between DLR and ESA. Next possible steps are outlined. They could comprise the in-orbit demonstration of the sail deployment on the upper stage of a low-cost rocket and the verification of the propulsion concept by an autonomous and free flying solar sail in the frame of a scientific mission. It is expected that the present design could be extended to sail sizes of about (40 m)2 up to even (70 m)2 without significant mass penalty. With these areas, the maximum achievable thrust at 1 AU would range between 10 and 40 mN - comparable to some electric thrusters. Such prototype sails with a mass between 50 and 150 kg plus a micro-spacecraft of 50 to 250 kg would have a maximum acceleration in the order of 0.1 mm/s2 at 1 AU, corresponding to a maximum ∆V-capability of about 3 km/s per year. Two near/medium-term mission examples to a near-Earth asteroid (NEA) will be discussed: a rendezvous mission and a sample return mission.}, language = {en} } @inproceedings{SchartnerLoebDachwaldetal.2009, author = {Schartner, Karl-Heinz and Loeb, H. W. and Dachwald, Bernd and Ohndorf, Andreas}, title = {Perspectives of electric propulsion for outer planetary and deep space missions}, series = {European Planetary Science Congress 2009}, booktitle = {European Planetary Science Congress 2009}, pages = {416 -- 416}, year = {2009}, abstract = {Solar-electric propulsion (SEP) is superior with respect to payload capacity, flight time and flexible launch window to the conventional interplanetary transfer method using chemical propulsion combined with gravity assists. This fact results from the large exhaust velocities of electric low-thrust propulsion and is favourable also for missions to the giant planets, Kuiper-belt objects and even for a heliopause probe (IHP) as shown in three studies by the authors funded by DLR. They dealt with a lander for Europa and a sample return mission from a mainbelt asteroid [1], with the TANDEM mission [2]; the third recent one investigates electric propulsion for the transfer to the edge of the solar system. All studies are based on triple-junction solar arrays, on rf-ion thrusters of the qualified RIT-22 type and they use the intelligent trajectory optimization program InTrance [3].}, language = {en} } @inproceedings{SpurmannOhndorfDachwaldetal.2009, author = {Spurmann, J{\"o}rn and Ohndorf, Andreas and Dachwald, Bernd and Seboldt, Wolfgang and L{\"o}b, Horst and Schartner, Karl-Heinz}, title = {Interplanetary trajectory optimization for a sep mission to Saturn}, series = {60th International Astronautical Congress 2009}, booktitle = {60th International Astronautical Congress 2009}, isbn = {9781615679089}, pages = {5234 -- 5248}, year = {2009}, abstract = {The recently proposed NASA and ESA missions to Saturn and Jupiter pose difficult tasks to mission designers because chemical propulsion scenarios are not capable of transferring heavy spacecraft into the outer solar system without the use of gravity assists. Thus our developed mission scenario based on the joint NASA/ESA Titan Saturn System Mission baselines solar electric propulsion to improve mission flexibility and transfer time. For the calculation of near-globally optimal low-thrust trajectories, we have used a method called Evolutionary Neurocontrol, which is implemented in the low-thrust trajectory optimization software InTrance. The studied solar electric propulsion scenario covers trajectory optimization of the interplanetary transfer including variations of the spacecraft's thrust level, the thrust unit's specific impulse and the solar power generator power level. Additionally developed software extensions enabled trajectory optimization with launcher-provided hyperbolic excess energy, a complex solar power generator model and a variable specific impulse ion engine model. For the investigated mission scenario, Evolutionary Neurocontrol yields good optimization results, which also hold valid for the more elaborate spacecraft models. Compared to Cassini/Huygens, the best found solutions have faster transfer times and a higher mission flexibility in general.}, language = {en} } @inproceedings{LoebSchartnerDachwaldetal.2007, author = {Loeb, Horst Wolfgang and Schartner, Karl-Heinz and Dachwald, Bernd and Seboldt, Wolfgang}, title = {SEP-Sample return from a main belt asteroid}, series = {30th International Electric Propulsion Conference}, booktitle = {30th International Electric Propulsion Conference}, pages = {1 -- 11}, year = {2007}, abstract = {By DLR-contact, sample return missions to the large main-belt asteroid "19, Fortuna" have been studied. The mission scenario has been based on three ion thrusters of the RIT-22 model, which is presently under space qualification, and on solar arrays equipped with triple-junction GaAs solar cells. After having designed the spacecraft, the orbit-to-orbit trajectories for both, a one-way SEP mission with a chemical sample return and an all-SEP return mission, have been optimized using a combination of artificial neural networks with evolutionary algorithms. Additionally, body-to-body trajectories have been investigated within a launch period between 2012 and 2015. For orbit-to-orbit calculation, the launch masses of the hybrid mission and of the all-SEP mission resulted in 2.05 tons and 1.56 tons, respectively, including a scientific payload of 246 kg. For the related transfer durations 4.14 yrs and 4.62 yrs were obtained. Finally, a comparison between the mission scenarios based on SEP and on NEP have been carried out favouring clearly SEP.}, language = {en} } @inproceedings{DachwaldMengaliQuartaetal.2007, author = {Dachwald, Bernd and Mengali, Giovanni and Quarta, Alessandro A and Macdonald, Malcolm and McInnes, Colin R}, title = {Optical solar sail degradation modelling}, series = {1st International Symposium on Solar Sailing}, booktitle = {1st International Symposium on Solar Sailing}, pages = {1 -- 27}, year = {2007}, abstract = {We propose a simple parametric OSSD model that describes the variation of the sail film's optical coefficients with time, depending on the sail film's environmental history, i.e., the radiation dose. The primary intention of our model is not to describe the exact behavior of specific film-coating combinations in the real space environment, but to provide a more general parametric framework for describing the general optical degradation behavior of solar sails.}, language = {en} } @article{Dachwald2005, author = {Dachwald, Bernd}, title = {Optimization of very-low-thrust trajectories using evolutionary neurocontrol}, series = {Acta Astronautica}, volume = {57}, journal = {Acta Astronautica}, number = {2-8}, publisher = {Elsevier}, address = {Amsterdam [u.a.]}, isbn = {1879-2030}, pages = {175 -- 185}, year = {2005}, abstract = {Searching optimal interplanetary trajectories for low-thrust spacecraft is usually a difficult and time-consuming task that involves much experience and expert knowledge in astrodynamics and optimal control theory. This is because the convergence behavior of traditional local optimizers, which are based on numerical optimal control methods, depends on an adequate initial guess, which is often hard to find, especially for very-low-thrust trajectories that necessitate many revolutions around the sun. The obtained solutions are typically close to the initial guess that is rarely close to the (unknown) global optimum. Within this paper, trajectory optimization problems are attacked from the perspective of artificial intelligence and machine learning. Inspired by natural archetypes, a smart global method for low-thrust trajectory optimization is proposed that fuses artificial neural networks and evolutionary algorithms into so-called evolutionary neurocontrollers. This novel method runs without an initial guess and does not require the attendance of an expert in astrodynamics and optimal control theory. This paper details how evolutionary neurocontrol works and how it could be implemented. The performance of the method is assessed for three different interplanetary missions with a thrust to mass ratio <0.15mN/kg (solar sail and nuclear electric).}, language = {en} } @inproceedings{SchoutetensDachwaldHeiligers2021, author = {Schoutetens, Frederic and Dachwald, Bernd and Heiligers, Jeannette}, title = {Optimisation of photon-sail trajectories in the alpha-centauri system using evolutionary neurocontrol}, series = {8th ICATT (International Conference on Astrodynamics Tools and Techniques) 23 - 25 June 2021, Virtual}, booktitle = {8th ICATT (International Conference on Astrodynamics Tools and Techniques) 23 - 25 June 2021, Virtual}, pages = {1 -- 15}, year = {2021}, abstract = {With the increased interest for interstellar exploration after the discovery of exoplanets and the proposal by Breakthrough Starshot, this paper investigates the optimisation of photon-sail trajectories in Alpha Centauri. The prime objective is to find the optimal steering strategy for a photonic sail to get captured around one of the stars after a minimum-time transfer from Earth. By extending the idea of the Breakthrough Starshot project with a deceleration phase upon arrival, the mission's scientific yield will be increased. As a secondary objective, transfer trajectories between the stars and orbit-raising manoeuvres to explore the habitable zones of the stars are investigated. All trajectories are optimised for minimum time of flight using the trajectory optimisation software InTrance. Depending on the sail technology, interstellar travel times of 77.6-18,790 years can be achieved, which presents an average improvement of 30\% with respect to previous work. Still, significant technological development is required to reach and be captured in the Alpha-Centauri system in less than a century. Therefore, a fly-through mission arguably remains the only option for a first exploratory mission to Alpha Centauri, but the enticing results obtained in this work provide perspective for future long-residence missions to our closest neighbouring star system.}, language = {en} } @inproceedings{SeefeldtBauerDachwaldetal.2015, author = {Seefeldt, Patric and Bauer, Waldemar and Dachwald, Bernd and Grundmann, Jan Thimo and Straubel, Marco and Sznajder, Maciej and T{\´o}th, Norbert and Zander, Martin E.}, title = {Large lightweight deployable structures for planetary defence: solar sail propulsion, solar concentrator payloads, large-scale photovoltaic power}, series = {4th IAA Planetary Defense Conference - PDC 2015, 13-17 April 2015, Frascati, Roma, Italy}, booktitle = {4th IAA Planetary Defense Conference - PDC 2015, 13-17 April 2015, Frascati, Roma, Italy}, pages = {24}, year = {2015}, language = {en} } @inproceedings{Dachwald2017, author = {Dachwald, Bernd}, title = {Radiation pressure force model for an ideal laser-enhanced solar sail}, series = {4th International Symposium on Solar Sailing}, booktitle = {4th International Symposium on Solar Sailing}, pages = {1 -- 5}, year = {2017}, abstract = {The concept of a laser-enhanced solar sail is introduced and the radiation pressure force model for an ideal laser-enhanced solar sail is derived. A laser-enhanced solar sail is a "traditional" solar sail that is, however, not solely propelled by solar radiation, but additionally by a laser beam that illuminates the sail. The additional laser radiation pressure increases the sail's propulsive force and can give, depending on the location of the laser source, more control authority over the direction of the solar sail's propulsive force vector. This way, laser-enhanced solar sails may augment already existing solar sail mission concepts and make novel mission concepts feasible.}, language = {en} } @article{PeloniCeriottiDachwald2016, author = {Peloni, Alessandro and Ceriotti, Matteo and Dachwald, Bernd}, title = {Solar-sail trajectory design for a multiple near-earth-asteroid rendezvous mission}, series = {Journal of Guidance, Control, and Dynamics}, volume = {39}, journal = {Journal of Guidance, Control, and Dynamics}, number = {12}, publisher = {AIAA}, address = {Reston, Va.}, issn = {0731-5090}, doi = {10.2514/1.G000470}, pages = {2712 -- 2724}, year = {2016}, abstract = {The scientific interest for near-Earth asteroids as well as the interest in potentially hazardous asteroids from the perspective of planetary defense led the space community to focus on near-Earth asteroid mission studies. A multiple near-Earth asteroid rendezvous mission with close-up observations of several objects can help to improve the characterization of these asteroids. This work explores the design of a solar-sail spacecraft for such a mission, focusing on the search of possible sequences of encounters and the trajectory optimization. This is done in two sequential steps: a sequence search by means of a simplified trajectory model and a set of heuristic rules based on astrodynamics, and a subsequent optimization phase. A shape-based approach for solar sailing has been developed and is used for the first phase. The effectiveness of the proposed approach is demonstrated through a fully optimized multiple near-Earth asteroid rendezvous mission. The results show that it is possible to visit five near-Earth asteroids within 10 years with near-term solar-sail technology.}, language = {en} } @inproceedings{Dachwald2004, author = {Dachwald, Bernd}, title = {Solar sail performance requirements for missions to the outer solar system and beyond}, series = {55th International Astronautical Congress 2004}, booktitle = {55th International Astronautical Congress 2004}, doi = {10.2514/6.IAC-04-S.P.11}, pages = {1 -- 9}, year = {2004}, abstract = {Solar sails enable missions to the outer solar system and beyond, although the solar radiation pressure decreases with the square of solar distance. For such missions, the solar sail may gain a large amount of energy by first making one or more close approaches to the sun. Within this paper, optimal trajectories for solar sail missions to the outer planets and into near interstellar space (200 AU) are presented. Thereby, it is shown that even near/medium-term solar sails with relatively moderate performance allow reasonable transfer times to the boundaries of the solar system.}, language = {en} } @incollection{DachwaldUlamecKowalskietal.2023, author = {Dachwald, Bernd and Ulamec, Stephan and Kowalski, Julia and Boxberg, Marc S. and Baader, Fabian and Biele, Jens and K{\"o}mle, Norbert}, title = {Ice melting probes}, series = {Handbook of Space Resources}, booktitle = {Handbook of Space Resources}, editor = {Badescu, Viorel and Zacny, Kris and Bar-Cohen, Yoseph}, publisher = {Springer}, address = {Cham}, isbn = {978-3-030-97912-6 (Print)}, doi = {10.1007/978-3-030-97913-3_29}, pages = {955 -- 996}, year = {2023}, abstract = {The exploration of icy environments in the solar system, such as the poles of Mars and the icy moons (a.k.a. ocean worlds), is a key aspect for understanding their astrobiological potential as well as for extraterrestrial resource inspection. On these worlds, ice melting probes are considered to be well suited for the robotic clean execution of such missions. In this chapter, we describe ice melting probes and their applications, the physics of ice melting and how the melting behavior can be modeled and simulated numerically, the challenges for ice melting, and the required key technologies to deal with those challenges. We also give an overview of existing ice melting probes and report some results and lessons learned from laboratory and field tests.}, language = {en} } @article{BaaderBoxbergChenetal.2023, author = {Baader, Fabian and Boxberg, Marc S. and Chen, Qian and F{\"o}rstner, Roger and Kowalski, Julia and Dachwald, Bernd}, title = {Field-test performance of an ice-melting probe in a terrestrial analogue environment}, series = {Icarus}, journal = {Icarus}, number = {409}, publisher = {Elsevier}, address = {Amsterdam}, doi = {10.1016/j.icarus.2023.115852}, pages = {Artikel 115852}, year = {2023}, abstract = {Melting probes are a proven tool for the exploration of thick ice layers and clean sampling of subglacial water on Earth. Their compact size and ease of operation also make them a key technology for the future exploration of icy moons in our Solar System, most prominently Europa and Enceladus. For both mission planning and hardware engineering, metrics such as efficiency and expected performance in terms of achievable speed, power requirements, and necessary heating power have to be known. Theoretical studies aim at describing thermal losses on the one hand, while laboratory experiments and field tests allow an empirical investigation of the true performance on the other hand. To investigate the practical value of a performance model for the operational performance in extraterrestrial environments, we first contrast measured data from terrestrial field tests on temperate and polythermal glaciers with results from basic heat loss models and a melt trajectory model. For this purpose, we propose conventions for the determination of two different efficiencies that can be applied to both measured data and models. One definition of efficiency is related to the melting head only, while the other definition considers the melting probe as a whole. We also present methods to combine several sources of heat loss for probes with a circular cross-section, and to translate the geometry of probes with a non-circular cross-section to analyse them in the same way. The models were selected in a way that minimizes the need to make assumptions about unknown parameters of the probe or the ice environment. The results indicate that currently used models do not yet reliably reproduce the performance of a probe under realistic conditions. Melting velocities and efficiencies are constantly overestimated by 15 to 50 \% in the models, but qualitatively agree with the field test data. Hence, losses are observed, that are not yet covered and quantified by the available loss models. We find that the deviation increases with decreasing ice temperature. We suspect that this mismatch is mainly due to the too restrictive idealization of the probe model and the fact that the probe was not operated in an efficiency-optimized manner during the field tests. With respect to space mission engineering, we find that performance and efficiency models must be used with caution in unknown ice environments, as various ice parameters have a significant effect on the melting process. Some of these are difficult to estimate from afar.}, language = {en} } @misc{FeldmannFranckeEspeetal.2022, author = {Feldmann, Marco and Francke, Gero and Espe, Clemes and Chen, Qian and Baader, Fabian and Boxberg, Marc S. and Sustrate, Anna-Marie and Kowalski, Julia and Dachwald, Bernd}, title = {Performance data of an ice-melting probe from field tests in two different ice environments}, doi = {10.5281/zenodo.6094866}, year = {2022}, abstract = {This dataset was acquired at field tests of the steerable ice-melting probe "EnEx-IceMole" (Dachwald et al., 2014). A field test in summer 2014 was used to test the melting probe's system, before the probe was shipped to Antarctica, where, in international cooperation with the MIDGE project, the objective of a sampling mission in the southern hemisphere summer 2014/2015 was to return a clean englacial sample from the subglacial brine reservoir supplying the Blood Falls at Taylor Glacier (Badgeley et al., 2017, German et al., 2021). The standardized log-files generated by the IceMole during melting operation include more than 100 operational parameters, housekeeping information, and error states, which are reported to the base station in intervals of 4 s. Occasional packet loss in data transmission resulted in a sparse number of increased sampling intervals, which where compensated for by linear interpolation during post processing. The presented dataset is based on a subset of this data: The penetration distance is calculated based on the ice screw drive encoder signal, providing the rate of rotation, and the screw's thread pitch. The melting speed is calculated from the same data, assuming the rate of rotation to be constant over one sampling interval. The contact force is calculated from the longitudinal screw force, which es measured by strain gauges. The used heating power is calculated from binary states of all heating elements, which can only be either switched on or off. Temperatures are measured at each heating element and averaged for three zones (melting head, side-wall heaters and back-plate heaters).}, language = {en} }