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22 pages, 12585 KiB  
Article
Preparation and Characterization of Atomic Oxygen-Resistant, Optically Transparent and Dimensionally Stable Copolyimide Films from Fluorinated Monomers and POSS-Substituted Diamine
by Zhenzhong Wang, Xiaolei Wang, Shunqi Yuan, Xi Ren, Changxu Yang, Shujun Han, Yuexin Qi, Duanyi Li and Jingang Liu
Polymers 2024, 16(19), 2845; https://doi.org/10.3390/polym16192845 - 9 Oct 2024
Viewed by 409
Abstract
Optically transparent polyimide (PI) films with good atomic oxygen (AO) resistance have been paid extensive attention as thermal controls, optical substrates for solar cells or other components for low Earth orbit (LEO) space applications. However, for common PI films, it is usually quite [...] Read more.
Optically transparent polyimide (PI) films with good atomic oxygen (AO) resistance have been paid extensive attention as thermal controls, optical substrates for solar cells or other components for low Earth orbit (LEO) space applications. However, for common PI films, it is usually quite difficult to achieve both high optical transparency and AO resistance and maintain the intrinsic thermal stability of the PI films at the same time. In the current work, we aimed to achieve the target by using the copolymerization methodology using the fluorinated dianhydride 9,9-bis(trifluoromethyl)xanthene-2,3,6,7-tetracarboxylic dianhydride (6FCDA), the fluorinated diamine 2,2-bis [4-(4-aminophenoxy)phenyl]hexafluoropropane (BDAF) and the polyhedral oligomeric silsesquioxane (POSS)-containing diamine N-[(heptaisobutyl-POSS)propyl]-3,5-diaminobenzamide (DABA-POSS) as the starting materials. The fluoro-containing monomers were used to endow the PI films with good optical and thermal properties, while the silicon-containing monomer was used to improve the AO resistance of the afforded PI films. Thus, the 6FCDA-based PI copolymers, including 6FCPI-1, 6FCPI-2 and 6FCPI-3, were prepared using a two-step chemical imidization procedure, respectively. For comparison, the analogous PIs, including 6FPI-1, 6FPI-2 and 6FPI-3, were correspondingly developed according to the same procedure except that 6FCDA was replaced by 4,4′-(hexafluoroisopropylidene)diphthalic anhydride (6FDA). Two referenced PI homopolymers were prepared from BDAF and 6FDA (PI-ref1) and 6FCDA (PI-ref2), respectively. The experimental results indicated that a good balance among thermal stability, optical transparency, and AO resistance was achieved by the 6FCDA-PI films. For example, the 6FCDA-PI films exhibited good thermal stability with glass transition temperatures (Tg) up to 297.3 °C, good optical transparency with an optical transmittance at a wavelength of 450 nm (T450) higher than 62% and good AO resistance with the erosion yield (Ey) as low as 1.7 × 10−25 cm3/atom at an AO irradiation fluence of 5.0 × 1020 atoms/cm2. The developed 6FCDA-PI films might find various applications in aerospace as solar sails, thermal control blankets, optical components and other functional materials. Full article
(This article belongs to the Special Issue Polymer Thin Films and Their Applications)
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Figure 1
<p>Preparation of PI and referenced PI resins.</p>
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<p>GPC plots of PI resins.</p>
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<p>XRD spectra of PI resins.</p>
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<p><sup>1</sup>H-NMR spectra of 6FPI resins in DMSO-d<sub>6</sub>.</p>
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<p><sup>1</sup>H-NMR spectra of 6FCPI resins in DMF-d<sub>7</sub>.</p>
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<p>FTIR spectra of PI films.</p>
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<p>TGA and DTG curves of PI films in nitrogen. (<b>a</b>) 6FPI; (<b>b</b>) 6FCPI.</p>
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<p>DSC curves of PI films.</p>
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<p>DMA curves of PI films.</p>
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<p>TMA curves of PI films.</p>
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<p>UV-Vis spectra of PI films.</p>
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<p>Appearance of PI films before and after AO exposure (doze: 5.0 × 10<sup>20</sup> atoms/cm<sup>2</sup>). (<b>a</b>–<b>c</b>): 6FPI-1~6FPI-3 films: left: pristine film; right: film after AO exposure; (<b>d</b>–<b>f</b>): 6FCPI-1~6FCPI-3 films: left: pristine film; right: film after AO exposure; (<b>g</b>) 6FPI-1-AO; (<b>h</b>) 6FPI-2-AO; (<b>i</b>) 6FPI-3-AO; (<b>j</b>) 6FCPI-1-AO; (<b>k</b>) 6FCPI-2-AO; (<b>l</b>) 6FCPI-3-AO.</p>
Full article ">Figure 13
<p>Comparison of UV-Vis spectra of PI films before and after AO exposure. (<b>a</b>) 6FPI; (<b>b</b>) 6FCPI.</p>
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<p>SEM and EDS images of pristine 6FCDA-PI films. (<b>a</b>) 6FCPA-1, (<b>b</b>) 6FCPI-2 and (<b>c</b>) 6FCPI-3.</p>
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<p>SEM and EDS images of 6FCDA-PI films after AO exposure (5.0 × 10<sup>20</sup> atoms/cm<sup>2</sup>). (<b>a</b>) 6FCPA-1-AO, (<b>b</b>) 6FCPI-2-AO and (<b>c</b>) 6FCPI-3-AO.</p>
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<p>XPS spectra of Si2p and O1s for 6FCPI films. (<b>a</b>) 6FCPI-1 and 6FCPI-1-AO; (<b>b</b>) 6FCPI-2 and 6FCPI-2-AO; (<b>c</b>) 6FCPI-3 and 6FCPI-3-AO.</p>
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17 pages, 677 KiB  
Article
Periodic and Quasi-Periodic Orbits in the Collinear Four-Body Problem: A Variational Analysis
by Abdalla Mansur, Muhammad Shoaib, Iharka Szücs-Csillik, Daniel Offin, Jack Brimberg and Hedia Fgaier
Mathematics 2024, 12(19), 3152; https://doi.org/10.3390/math12193152 - 9 Oct 2024
Viewed by 391
Abstract
This paper investigated the periodic and quasi-periodic orbits in the symmetric collinear four-body problem through a variational approach. We analyze the conditions under which homographic solutions minimize the action functional. We compute the minimal value of the action functional for these solutions and [...] Read more.
This paper investigated the periodic and quasi-periodic orbits in the symmetric collinear four-body problem through a variational approach. We analyze the conditions under which homographic solutions minimize the action functional. We compute the minimal value of the action functional for these solutions and show that, for four equal masses organized in a linear configuration, these solutions are the minimizers of the action functional. Additionally, we employ numerical experiments using Poincaré sections to explore the existence and stability of periodic and quasi-periodic solutions within this dynamical system. Our results provide a deeper understanding of the variational principles in celestial mechanics and reveal complex dynamical behaviors, crucial for further studies in multi-body problems. Full article
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Figure 1
<p>Graphs of <math display="inline"><semantics> <mrow> <mi>A</mi> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>A</mi> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>+</mo> <mi>B</mi> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </semantics></math>.</p>
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<p>The polynomial <math display="inline"><semantics> <msub> <mi>P</mi> <mn>39</mn> </msub> </semantics></math> is positive when <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>∈</mo> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>0.238</mn> <mo>)</mo> <mo>∪</mo> <mo>(</mo> <mn>0.387</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> </semantics></math> and is negative when <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>∈</mo> <mo>(</mo> <mn>0.238</mn> <mo>,</mo> <mn>0.387</mn> <mo>)</mo> </mrow> </semantics></math>.</p>
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<p><math display="inline"><semantics> <mrow> <msup> <mi>ϕ</mi> <mrow> <mo>″</mo> </mrow> </msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> is positive when <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>∈</mo> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>0.238</mn> <mo>)</mo> <mo>∪</mo> <mo>(</mo> <mn>0.387</mn> <mo>,</mo> <mn>0.4644</mn> <mo>)</mo> </mrow> </semantics></math>.</p>
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<p>Configuration of the symmetric collinear four-body (SC4BP) problem.</p>
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<p>Examples of Poincaré surface of sections in case <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>&lt;</mo> <mi>M</mi> </mrow> </semantics></math> for energy levels <math display="inline"><semantics> <mrow> <mo>−</mo> <mn>0.077</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mn>9.8</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 5 Cont.
<p>Examples of Poincaré surface of sections in case <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>&lt;</mo> <mi>M</mi> </mrow> </semantics></math> for energy levels <math display="inline"><semantics> <mrow> <mo>−</mo> <mn>0.077</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mn>9.8</mn> </mrow> </semantics></math>.</p>
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<p>Poincaré surface of sections in case <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>&lt;</mo> <mi>M</mi> </mrow> </semantics></math> for energy level 15.</p>
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<p>Poincaré surface of section for energy level <math display="inline"><semantics> <mrow> <mo>−</mo> <mn>0.077</mn> </mrow> </semantics></math>.</p>
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17 pages, 1325 KiB  
Article
Thrust Model and Trajectory Design of an Interplanetary CubeSat with a Hybrid Propulsion System
by Alessandro A. Quarta
Actuators 2024, 13(10), 384; https://doi.org/10.3390/act13100384 - 1 Oct 2024
Viewed by 401
Abstract
This paper analyzes the performance of an interplanetary CubeSat equipped with a hybrid propulsion system (HPS), which combines two different types of thrusters in the same deep space vehicle, in a heliocentric transfer between two assigned (Keplerian) orbits. More precisely, the propulsion system [...] Read more.
This paper analyzes the performance of an interplanetary CubeSat equipped with a hybrid propulsion system (HPS), which combines two different types of thrusters in the same deep space vehicle, in a heliocentric transfer between two assigned (Keplerian) orbits. More precisely, the propulsion system of the CubeSat considered in this work consists of a combination of a (low-performance) photonic solar sail and a more conventional solar electric thruster. In particular, the characteristics of the solar electric thruster are modeled using a recent mathematical approach that describes the performance of the miniaturized engine that will be installed on board the proposed ESA’s M-ARGO CubeSat. The latter will hopefully be the first interplanetary CubeSat to complete a heliocentric transfer towards a near-Earth asteroid using its own propulsion system. In order to simplify the design of the CubeSat attitude control subsystem, we assume that the orientation of the photonic solar sail is kept Sun-facing, i.e., the sail reference plane is perpendicular to the Sun-CubeSat line. That specific condition can be obtained, passively, by using an appropriate design of the shape of the sail reflective surface. The performance of an HPS-based CubeSat is analyzed by optimizing the transfer trajectory in a three-dimensional heliocentric transfer between two closed orbits of given characteristics. In particular, the CubeSat transfer towards the near-Earth asteroid 99942 Apophis is studied in detail. Full article
(This article belongs to the Special Issue Dynamics and Control of Aerospace Systems)
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Figure 1

Figure 1
<p>Variation with <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>∈</mo> <mo>[</mo> <mn>0.75</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>1.25</mn> <mo>]</mo> <mspace width="0.166667em"/> <mi>AU</mi> </mrow> </semantics></math> of the auxiliary function <span class="html-italic">F</span> defined in Equation (<a href="#FD2-actuators-13-00384" class="html-disp-formula">2</a>).</p>
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<p>Variation with <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>∈</mo> <mo>[</mo> <mn>0.75</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>1.25</mn> <mo>]</mo> <mspace width="0.166667em"/> <mi>AU</mi> </mrow> </semantics></math> of the maximum magnitude of the HPS-induced thrust vector <math display="inline"><semantics> <mi mathvariant="bold-italic">T</mi> </semantics></math>.</p>
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<p>Thrust bubble (when <math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>) as a function of the Sun-CubeSat distance <span class="html-italic">r</span>. The ticks in the color bar are in millinewtons. (<b>a</b>) Case of <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>=</mo> <mn>0.75</mn> <mspace width="0.166667em"/> <mi>AU</mi> </mrow> </semantics></math>; (<b>b</b>) Case of <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>=</mo> <mn>1</mn> <mspace width="0.166667em"/> <mi>AU</mi> </mrow> </semantics></math>; (<b>c</b>) Case of <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>=</mo> <mn>1.25</mn> <mspace width="0.166667em"/> <mi>AU</mi> </mrow> </semantics></math>.</p>
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<p>Variation with <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>∈</mo> <mo>[</mo> <mn>0.75</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>1.25</mn> <mo>]</mo> <mspace width="0.166667em"/> <mi>AU</mi> </mrow> </semantics></math> of propellant mass flow rate when the throttle function is <math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>; see the right side of Equation (<a href="#FD9-actuators-13-00384" class="html-disp-formula">9</a>).</p>
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<p>Ecliptic projection and isometric view of the rapid transfer trajectory towards asteroid 99942 Apophis when the initial CubeSat mass is <math display="inline"><semantics> <mrow> <msub> <mi>m</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>30</mn> <mspace width="0.166667em"/> <mi>kg</mi> </mrow> </semantics></math>. The <span class="html-italic">z</span>-axis of the isometric view is exaggerated to highlight the three-dimensionality of the trajectory. Black line → CubeSat transfer trajectory; blue line → Earth’s orbit; red line → asteroid’s orbit; filled star → perihelion; blue dot → starting point; red square → arrival point; orange dot → the Sun.</p>
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<p>Time variation in the thrust angles <math display="inline"><semantics> <mi>α</mi> </semantics></math> and <math display="inline"><semantics> <mi>δ</mi> </semantics></math> along the rapid transfer trajectory towards asteroid 99942 Apophis when the initial CubeSat mass is <math display="inline"><semantics> <mrow> <msub> <mi>m</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>30</mn> <mspace width="0.166667em"/> <mi>kg</mi> </mrow> </semantics></math>. Blue dot → starting point; red square → arrival point.</p>
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<p>Time variation in the mass <span class="html-italic">m</span> and solar distance <span class="html-italic">r</span> along the rapid transfer trajectory towards asteroid 99942 Apophis when the initial CubeSat mass is <math display="inline"><semantics> <mrow> <msub> <mi>m</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>30</mn> <mspace width="0.166667em"/> <mi>kg</mi> </mrow> </semantics></math>. Blue dot → starting point; red square → arrival point.</p>
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<p>Results of the parametric study of the Earth–Apophis, orbit-to-orbit, rapid transfer as a function of the value of the initial CubeSat mass <math display="inline"><semantics> <msub> <mi>m</mi> <mn>0</mn> </msub> </semantics></math> (step of <math display="inline"><semantics> <mrow> <mn>1</mn> <mspace width="0.166667em"/> <mi>kg</mi> </mrow> </semantics></math>, green dots).</p>
Full article ">Figure A1
<p>Artistic representation of the ESA’s M-ARGO CubeSat approach to a potential near-Earth asteroid. Image: © ESA.</p>
Full article ">Figure A2
<p>Miniaturized electric thruster: variation of <math display="inline"><semantics> <mrow> <mo movablelimits="true" form="prefix">max</mo> <mrow> <mo>(</mo> <mrow> <mo>∥</mo> <msub> <mi mathvariant="bold-italic">T</mi> <mi>e</mi> </msub> <mo>∥</mo> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math> and <math display="inline"><semantics> <msub> <mi>I</mi> <mrow> <mi>sp</mi> </mrow> </msub> </semantics></math> with <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>∈</mo> <mo>[</mo> <mn>0.75</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>1.25</mn> <mo>]</mo> <mspace width="0.166667em"/> <mi>AU</mi> </mrow> </semantics></math>.</p>
Full article ">Figure A3
<p>Artistic concept of the NASA’s Near-Earth Asteroid Scout (NEA Scout) approaching the target asteroid. The solar sail-based CubeSat failed to make contact with ground station after launch, and the mission NEA Scout was considered lost in December 2022. Image credit: NASA.</p>
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<p>Photonic solar sail in a Sun-facing configuration: variation of the thrust magnitude <math display="inline"><semantics> <mrow> <mo>∥</mo> <msub> <mi mathvariant="bold-italic">T</mi> <mi>s</mi> </msub> <mo>∥</mo> </mrow> </semantics></math> with the solar distance <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>∈</mo> <mo>[</mo> <mn>0.75</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>1.25</mn> <mo>]</mo> <mspace width="0.166667em"/> <mi>AU</mi> </mrow> </semantics></math>, according to Equation (<a href="#FD18-actuators-13-00384" class="html-disp-formula">A9</a>). The solar sail characteristics (in terms of sail area and sail force coefficients) are consistent with the system installed onboard of the NASA’s NEA Scout CubeSat.</p>
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19 pages, 6333 KiB  
Article
Notes on Towed Self-Propulsion Experiments with Simulated Managed Ice in Traditional Towing Tanks
by José Enrique Gutiérrez-Romero, Blas Zamora-Parra, Samuel Ruiz-Capel, Jerónimo Esteve-Pérez, Alejandro López-Belchí, Pablo Romero-Tello and Antonio José Lorente-López
J. Mar. Sci. Eng. 2024, 12(10), 1691; https://doi.org/10.3390/jmse12101691 - 24 Sep 2024
Viewed by 458
Abstract
Efficiency estimation of a propeller behind a vessel’s hull while sailing through ice floes, together with the ship’s resistance to motion, is a key factor in designing the power plant and determining the safety measures of a ship. This paper encloses the results [...] Read more.
Efficiency estimation of a propeller behind a vessel’s hull while sailing through ice floes, together with the ship’s resistance to motion, is a key factor in designing the power plant and determining the safety measures of a ship. This paper encloses the results from the experiments conducted at the CEHINAV towing tank, which consisted of analyzing the influence of the concentration at the free surface of artificial blocks, simulating ice, in propeller–block interactions. Thrust and torque were measured for a towed self-propelled ship model through simulated broken ice blocks made of paraffin wax. Three block concentrations of different block sizes and three model speeds were studied during the experimentation. Open-water self-propulsion tests and artificial broken ice towed self-propulsion tests are shown and compared in this work. The most relevant observations are outlined at the end of this paper, as well as some guidelines for conducting artificial ice-towed self-propulsion tests in traditional towing tanks. Full article
(This article belongs to the Special Issue Ice-Structure Interaction in Marine Engineering)
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<p>Scheme of the configuration in the testing zones.</p>
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<p>(<b>a</b>) Zoomed-in detail of the propeller and double-rudder configuration; (<b>b</b>) Image of the scaled model used during the experimentation.</p>
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<p>Plan of hull lines for the side and top view of the Spanish Army’s Research Vessel Hespérides, for which the calculations are conducted in this work.</p>
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<p>(<b>a</b>) Propeller used during the experimental tests with paraffin wax blocks; (<b>b</b>) Propeller installed at the vessel stern.</p>
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<p>(<b>a</b>) Top view of the 30% coverage; (<b>b</b>) Top view of the 45% coverage; (<b>c</b>) Top view of the 60% coverage.</p>
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<p>Obtained values of thrust and torque coefficients (<span class="html-italic">K<sub>T</sub></span>, <span class="html-italic">K<sub>Q</sub></span>), and propeller open water efficiency (<span class="html-italic">η</span><sub>0</sub>), as a function of the advance coefficient (<span class="html-italic">J</span>).</p>
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<p>Comparison between thrust and torque at different speeds and the same coverage (<span class="html-italic">C</span>1 = 30%): (<b>a</b>) Test speed of 0.22 m/s; (<b>b</b>) Test speed of 0.33 m/s; (<b>c</b>) Test speed of 0.53 m/s.</p>
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<p>(<b>a</b>) Comparison of thrust at 0.53 m/s for the three studied free surface coverages (<span class="html-italic">C</span>1 = 30%; <span class="html-italic">C</span>2 = 45%; <span class="html-italic">C</span>3 = 60%); (<b>b</b>) Comparison of torque at 0.53 m/s for the three studied free surface coverages (<span class="html-italic">C</span>1 = 30%; <span class="html-italic">C</span>2 = 45%; <span class="html-italic">C</span>3 = 60%).</p>
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<p>(<b>a</b>) Thrust versus percentage of block coverage. Thrust mean values are represented by the red squares, while the black hollow diamonds represent individual tests; (<b>b</b>) Mean thrust versus model speed.</p>
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<p>(<b>a</b>) Mean torque over coverage percentage. Mean torque values are represented by the red squares, while individual tests are represented by the black hollow diamond markers. (<b>b</b>) Mean torque versus model speed.</p>
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<p>Mean thrust in Newtons (N) versus mean torque (N·cm).</p>
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<p>Towing force values <span class="html-italic">F<sub>x</sub></span> as a function of model speed and the percentage of coverage.</p>
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<p>Delivered power <span class="html-italic">P<sub>D</sub></span> values as a function of the coverage percentage and model speed.</p>
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<p>(<b>a</b>) Usual configuration for a towing tank test to measure ship resistance to motion in calm water. (<b>b</b>) Redesigned configuration to perform towing tank tests with artificial ice blocks on the free surface.</p>
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<p>Resistance set-up used during experimental tests. Adapted from [<a href="#B36-jmse-12-01691" class="html-bibr">36</a>].</p>
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<p>Sequence of a block colliding with one of the rudders during a test. (<b>a</b>) Block near the port side of the model. (<b>b</b>) Block under the model’s hull on the port side. (<b>c</b>) Block colliding with port rudder of the model.</p>
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14 pages, 8196 KiB  
Article
Pitching Stabilization Control for Super Large Ships Based on Double Nonlinear Positive Feedback under Rough Sea Conditions
by Chunyu Song, Qi Qiao and Jianghua Sui
J. Mar. Sci. Eng. 2024, 12(9), 1657; https://doi.org/10.3390/jmse12091657 - 16 Sep 2024
Viewed by 424
Abstract
Due to the rapid development of a global navigation satellite system and the rapid growth of ships, the traditional control algorithms are not suitable; hence, the longitudinal rocking phenomenon generated by external disturbances is more serious when a ship is sailing. This paper [...] Read more.
Due to the rapid development of a global navigation satellite system and the rapid growth of ships, the traditional control algorithms are not suitable; hence, the longitudinal rocking phenomenon generated by external disturbances is more serious when a ship is sailing. This paper takes a mathematical model of the super large oil tanker “KVLCC2”’s longitudinal motion as the controlled plant, establishing a multi-input multi-output instability control system, using the root trajectory shaping method and a weighting matrix to ensure the stability of its transfer function’s mathematical model. An improved closed-loop gain-shaping algorithm is utilized to design a simple robust controller. And a dual nonlinear positive feedback control algorithm is added to the control system to further improve the controller’s pitching stabilization performance and reduce the controller’s output energy. In order to verify that the controller has a consistently strong robustness, simulation experiments are carried out by adding a level 6, 7 and 8 wind wave model and a perturbation link to the control system, respectively. The results show that when the value of the hysteresis constant is taken as 0.25, the output values of the heave displacement and the pitch angle are greatly reduced, and the longitudinal rocking phenomenon is significantly improved. The dual nonlinear positive feedback control algorithm enhances the ship’s pitching stabilization control capability and further reduces the controller’s output energy, which provides technical support for the smooth and efficient sailing of super large ships under changing sea conditions. Combined with a global navigation satellite system, this algorithm provides a new method for pitching stabilization control of super large ships. Full article
(This article belongs to the Special Issue Global Navigation Satellite System for Maritime Applications)
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<p>Ship motion coordinate system.</p>
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<p>Stabilizing root trajectory after forming.</p>
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<p>Simple robust controller design framework.</p>
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<p>Structure of the feed-forward control system.</p>
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<p>Perturbation system.</p>
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<p>Linear feedback under level 6 sea conditions.</p>
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<p>Nonlinear positive feedback under level 6 sea conditions.</p>
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<p>Linear feedback under level 7 sea conditions.</p>
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<p>Nonlinear positive feedback under level 7 sea conditions.</p>
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<p>Linear feedback under level 8 sea conditions.</p>
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<p>Nonlinear positive feedback under level 8 sea conditions.</p>
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18 pages, 7240 KiB  
Article
Artificial Neural Network-Based Route Optimization of a Wind-Assisted Ship
by Cem Guzelbulut, Timoteo Badalotti, Yasuaki Fujita, Tomohiro Sugimoto and Katsuyuki Suzuki
J. Mar. Sci. Eng. 2024, 12(9), 1645; https://doi.org/10.3390/jmse12091645 - 14 Sep 2024
Viewed by 569
Abstract
The International Maritime Organization aims for net-zero carbon emissions in the maritime industry by 2050. Among various alternatives, route optimization holds an important place as it does not require any additional component-related costs. Especially for wind-assisted ships, the effectiveness of different sailing systems [...] Read more.
The International Maritime Organization aims for net-zero carbon emissions in the maritime industry by 2050. Among various alternatives, route optimization holds an important place as it does not require any additional component-related costs. Especially for wind-assisted ships, the effectiveness of different sailing systems can be improved significantly through route optimization. However, finding the ship’s optimal route is computationally expensive when the totality of possible weather conditions is taken into consideration. To determine the optimal route that minimizes energy consumption, an energy model based on the environmental conditions, ship route and ship speed was built using artificial neural networks. The energy consumed for given input data was calculated using a ship dynamics model and a database was generated to train the artificial neural networks, which predict how much energy is consumed depending on the route followed in given environmental conditions. Then, such networks were exploited to derive the optimal routes for all the relevant operational conditions. It was found that route optimization can reduce the overall ship energy consumption depending on the weather conditions of the environment by up to 9.7% without any increase in voyage time and by up to 35% with a 10% delay in voyage time. The proposed methodology can be applied to any ship by training real weather conditions and provides a framework for reducing energy consumption and greenhouse gas emissions during the service life of ships. Full article
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<p>Description of coordinate systems.</p>
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<p>Progressive route updates.</p>
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<p>Definition of parameters for describing the V-shaped route.</p>
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<p>Workflow of the proposed route optimization method.</p>
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<p>Investigation of the controller effectiveness: (<b>a</b>) Wind speed and direction distribution on a map showing three reference routes, and (<b>b</b>) the comparison of the simulated routes with controller and reference routes, (<b>c</b>) the variation in the propeller speed and (<b>d</b>) the rudder angle along the route.</p>
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<p>Investigation of the controller effectiveness: (<b>a</b>) Wind speed and direction distribution on a map showing three reference routes, and (<b>b</b>) the comparison of the simulated routes with controller and reference routes, (<b>c</b>) the variation in the propeller speed and (<b>d</b>) the rudder angle along the route.</p>
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<p>(<b>a</b>) Artificial neural network model used in the study. (<b>b</b>–<b>d</b>) Regression performance of the artificial neural network model for training, test and validation data.</p>
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<p>The distribution of wind speed and direction in (<b>a</b>) Case 1, (<b>b</b>) Case 2 and (<b>c</b>) Case 3.</p>
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<p>The distribution of wind speed and direction in (<b>a</b>) Case 1, (<b>b</b>) Case 2 and (<b>c</b>) Case 3.</p>
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<p>The effect of a different number of divisions on the (<b>a</b>) optimal route, (<b>b</b>) propeller power and (<b>c</b>) ship speed in Case 1.</p>
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<p>The effect of a different number of divisions on the (<b>a</b>) optimal route, (<b>b</b>) propeller power and (<b>c</b>) ship speed with a voyage time constraint in Case 1.</p>
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<p>The effect of different numbers of divisions on the (<b>a</b>) optimal route, (<b>b</b>) propeller power and (<b>c</b>) ship speed with a voyage time constraint in Case 2.</p>
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<p>The effect of a different number of divisions on the (<b>a</b>) optimal route, (<b>b</b>) propeller power and (<b>c</b>) ship speed with a voyage time constraint in Case 3.</p>
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<p>Variation in trajectory, propeller power and ship speed depending on the allowance to time delays of 3%, 5% and 10% for (<b>a</b>) the first, (<b>b</b>) second and (<b>c</b>) third cases.</p>
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<p>Comparison of the straight route and optimal routes in terms of energy consumption depending on the allowance of time delay for Case 1, Case 2 and Case 3.</p>
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18 pages, 3464 KiB  
Article
This Ship Prays: The Southern Chinese Religious Seascape through the Handbook of a Maritime Ritual Master
by Ilay Golan
Religions 2024, 15(9), 1096; https://doi.org/10.3390/rel15091096 - 10 Sep 2024
Viewed by 699
Abstract
Long kept in the British Library, a liturgical manuscript from the port of Haicheng, Fujian, holds details of the rich system of beliefs that Chinese sailors held. Originally untitled, the text by the shelfmark OR12693/18 is usually referred to as “Libation Ritual (for [...] Read more.
Long kept in the British Library, a liturgical manuscript from the port of Haicheng, Fujian, holds details of the rich system of beliefs that Chinese sailors held. Originally untitled, the text by the shelfmark OR12693/18 is usually referred to as “Libation Ritual (for Ship Safety)” ([An Chuan] Zhuoxian Ke [(安船)酌献科]). Formerly, it was given scholarly attention mostly due to its addended lists of maritime placenames, which follows Qing-era sea routes across China’s coasts and to the South China Sea. Further inquiry into the manuscript’s terminology, deity names, and maritime knowledge confirms its deep relation to sailors’ lore. By tracing this text into a wide range of sources, this paper demonstrates how manuscript OR12693/18 reflects a cohesive maritime system of beliefs and knowledge. Manifested within the prayer are a hierarchical pantheon, ritual practices, and a perceived sacred seascape. Moreover, it is evident that the manuscript belonged to a tradition of sailing ritual masters who were regular members of the crew onboard junks. As such, this paper offers an analysis of a religious-professional tradition with trans-local aspects, shedding new light on seafaring in pre-modern China. Full article
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<p>End of the prayer in ACZK (<b>right</b>) and start of the western sea route list (<span class="html-italic">wang xiyang</span> 往西洋, <b>left</b> page, from <a href="#B35-religions-15-01096" class="html-bibr">OR12693/18</a> (<a href="#B35-religions-15-01096" class="html-bibr">n.d.</a>) <span class="html-italic">Zhuoxian Ke</span>, p. 35.</p>
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<p>Stern side of a tribute ship (<span class="html-italic">feng chuan</span> 封船), in a drawing from <a href="#B45-religions-15-01096" class="html-bibr">Baoguang Xu</a> (<a href="#B45-religions-15-01096" class="html-bibr">1720, p. 8.2a</a>).</p>
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<p>Invocation of Mazu, the Heavenly Concubine (<span class="html-italic">Tianfei Niangniang</span> 天妃娘娘, second column from the right) followed by her family members (<a href="#B35-religions-15-01096" class="html-bibr">OR12693/18</a> (<a href="#B35-religions-15-01096" class="html-bibr">n.d.</a>) <span class="html-italic">Zhuoxian Ke</span>, p. 15).</p>
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<p>“Holy Places for Ship Rituals” (Chuan Jiao Sheng Wei 船醮聖位), appendix to the liturgical manuscript “Lingbao-sect Calamity Averting Ship Worship Ritual” (Lingbao Rangzai Ji Chuan Ke 靈寶禳災祭船科), dated 1749. It presents a list of deities, some corresponding to the ship and others to sacred shrines along the coast. Notice on the bottom-right: “our ships’ wooden dragon” (<span class="html-italic">ben chuan mulong</span> 本船木龍). Photo by Prof. Hsieh Tsung-hui. See (<a href="#B17-religions-15-01096" class="html-bibr">Hsieh 2014, p. 43</a>).</p>
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<p>ACZK, the continued route to the Western Ocean, showing places of worship, including Boshui 泊水 (in a red rectangle). The deity and temple names are written in half-sized characters. Luo’an Head (Luo’an Tou 羅鞍頭, circled in red) is a junction; every time it repeats marks the start of a different route, out of nine total in the Xiyang (<a href="#B35-religions-15-01096" class="html-bibr">OR12693/18</a> (<a href="#B35-religions-15-01096" class="html-bibr">n.d.</a>) <span class="html-italic">Zhuoxian Ke</span>, p. 36).</p>
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<p>Beginning of the “down south” route (left page). The Water Immortals Palace is circled in red. The half-sized letters underneath read “Water Immortal Kings” (Shuixian Wang 水仙王). In <a href="#B35-religions-15-01096" class="html-bibr">OR12693/18</a> (<a href="#B35-religions-15-01096" class="html-bibr">n.d.</a>) <span class="html-italic">Zhuoxian Ke</span>, p. 41.</p>
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<p>Last pages of the “up north” route, ending the entire text of ACZK (<a href="#B35-religions-15-01096" class="html-bibr">OR12693/18</a> (<a href="#B35-religions-15-01096" class="html-bibr">n.d.</a>) <span class="html-italic">Zhuoxian Ke</span>, p. 44).</p>
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14 pages, 1114 KiB  
Editorial
Advances in Navigability and Mooring
by Marko Perkovič
J. Mar. Sci. Eng. 2024, 12(9), 1601; https://doi.org/10.3390/jmse12091601 - 10 Sep 2024
Viewed by 434
Abstract
Considerable technological progress has been made in ship handling and mooring in recent years, especially progress generated by the needs imposed by the introduction of ever larger ships. These advancements exploit the economic scale and environmental efficiency of larger vessels, but also present [...] Read more.
Considerable technological progress has been made in ship handling and mooring in recent years, especially progress generated by the needs imposed by the introduction of ever larger ships. These advancements exploit the economic scale and environmental efficiency of larger vessels, but also present unique challenges, particularly in narrow waterways and harbour approaches. Precise navigation in these environments requires highly accurate hydrographic measurements, high-quality electronic charts, and advanced navigation systems, such as modern electronic chart display and information systems (ECDIS). Safe and efficient port operations also depend on the optimised allocation of port resources and comprehensive queuing strategies. Modern ships are increasingly susceptible to interference with Global Navigation Satellite Systems (GNSS) and Automatic Identification Systems (AIS), necessitating the development of resilient technologies and procedures to ensure navigational safety. In addition, climate change is exacerbating the challenges of ship handling in ports, as larger vessels are particularly vulnerable to sudden gusts of wind and have difficulty maintaining their position in the quay in strong crosswinds. Training and simulation are crucial to overcoming these challenges. Ship-handling simulators are invaluable for training purposes, but development is still needed to accurately simulate tilt and lean effects, especially when ships are sailing in narrow channels with following currents and changing winds. Improving the accuracy of these simulators will improve the preparation of seafarers for real-life conditions and ultimately contribute to safer and more efficient ship operations. Full article
(This article belongs to the Special Issue Advances in Navigability and Mooring)
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<p>Engine power limiter of a mechanically driven type engine (changing a set of governor’s fuel index).</p>
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<p>Main engine propulsion power vs. vessel size expressed in TEU.</p>
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24 pages, 14060 KiB  
Article
Multi-Objective Route Planning Model for Ocean-Going Ships Based on Bidirectional A-Star Algorithm Considering Meteorological Risk and IMO Guidelines
by Yingying Wang, Longxia Qian, Mei Hong, Yaoshuai Luo and Dongyv Li
Appl. Sci. 2024, 14(17), 8029; https://doi.org/10.3390/app14178029 - 8 Sep 2024
Viewed by 683
Abstract
In this study, a new route planning model is proposed to help ocean-going ships avoid dangerous weather conditions and ensure safe ship navigation. First, we integrate ocean-going ship vulnerability into the study of the influence of meteorological and oceanic factors on navigational risk. [...] Read more.
In this study, a new route planning model is proposed to help ocean-going ships avoid dangerous weather conditions and ensure safe ship navigation. First, we integrate ocean-going ship vulnerability into the study of the influence of meteorological and oceanic factors on navigational risk. A multi-layer fuzzy comprehensive evaluation model for weather risk assessment is established. A multi-objective nonlinear route planning model is then constructed by comprehensively considering the challenges of fuel consumption, risk, and time during ship navigation. The International Maritime Organization (IMO) guidelines are highlighted as constraints in the calculations, and wind, wave, and calm water resistance to ships in the latest ITTC method is added to the fuel consumption and sailing time in the objective function. Finally, considering the large amount of data required for ocean voyages, the bidirectional A* algorithm is applied to solve the model and reduce the planning time. Furthermore, our model is applied to the case of an accident reported in the Singapore Maritime Investigation Report, and the results show that the model-planned route is very close to the original planned route using the Towing Manual, with an average fit of 98.22%, and the overall meteorological risk of the model-planned route is 11.19% smaller than the original route; our model can therefore be used to plan a safer route for the vessel. In addition, the importance of risk assessments and the IMO guidelines as well as the efficiency of the bidirectional A* algorithm were analyzed and discussed. The results show that the model effectively lowers the meteorological risk, is more efficient than the traditional route planning algorithm, and is 86.82% faster than the Dijkstra algorithm and 49.16% faster than the A* algorithm. Full article
(This article belongs to the Section Marine Science and Engineering)
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<p>Hierarchical structure of the risk index.</p>
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<p>The arithmetic process of bidirectional A* algorithm.</p>
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<p>Dividing the Towing Manual planned route into TMrouteA and TMrouteB.</p>
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<p>Gaussian membership function image of wave height.</p>
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<p>Gaussian membership function image of visibility.</p>
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<p>Gaussian membership function image of vessel age.</p>
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<p>Risk regionalization result maps selected from 1 May 2022 to 12 May 2022.</p>
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<p>Risk regionalization result maps selected from 20 June 2022 to 5 July 2022.</p>
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<p>IBA*routeA from 1 to 12 May 2022.</p>
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<p>IBA*routeB from 16 June to 7 July 2022.</p>
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<p>The routes of Realroute, TMrouteB, and IBA*routeB from 26 June to 2 July 2022.</p>
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<p>Box plots for Realroute, TMrouteB, and IBA*routeB.</p>
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<p>Comparison of the actual route and planned route of the validation case.</p>
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<p>Average risk value of planned routes under different propulsion efficiency scenarios.</p>
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<p>Average risk value of planned routes under different roughness allowance factor scenarios.</p>
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<p>IBA*routeB and WrouteB from 16 June to 7 July 2022.</p>
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16 pages, 1450 KiB  
Article
Venus Magnetotail Long-Term Sensing Using Solar Sails
by Alessandro A. Quarta
Appl. Sci. 2024, 14(17), 8016; https://doi.org/10.3390/app14178016 - 7 Sep 2024
Viewed by 409
Abstract
Propellantless propulsion systems, such as the well-known photonic solar sails that provide thrust by exploiting the solar radiation pressure, theoretically allow for extremely complex space missions that require a high value of velocity variation to be carried out. Such challenging space missions typically [...] Read more.
Propellantless propulsion systems, such as the well-known photonic solar sails that provide thrust by exploiting the solar radiation pressure, theoretically allow for extremely complex space missions that require a high value of velocity variation to be carried out. Such challenging space missions typically need the application of continuous thrust for a very long period of time, compared to the classic operational life of a space vehicle equipped with a more conventional propulsion system as, for example, an electric thruster. In this context, an interesting application of this propellantless thruster consists of using the solar sail-induced acceleration to artificially precess the apse line of a planetocentric elliptic orbit. This specific mission application was thoroughly investigated about twenty years ago in the context of the GeoSail Technology Reference Study, which analyzed the potential use of a spacecraft equipped with a small solar sail to perform an in situ study of the Earth’s upper magnetosphere. Taking inspiration from the GeoSail concept, this study analyzes the performance of a solar sail-based spacecraft in (artificially) precessing the apse line of a high elliptic orbit around Venus with the aim of exploring the planet’s induced magnetotail. In particular, during flight, the solar sail orientation is assumed to be Sun-facing, and the required thruster’s performance is evaluated as a function of the elliptic orbit’s characteristics by using both a simplified mathematical model of the spacecraft’s planetocentric dynamics and an approximate analytical approach. Numerical results show that a medium–low-performance sail is able to artificially precess the apse line of a Venus-centered orbit in order to ensure the long-term sensing of the planet’s induced magnetotail. Full article
(This article belongs to the Section Aerospace Science and Engineering)
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<p>Artistic impression of the magnetosphere of Venus (top part of the figure), Earth (middle part), and Mars (bottom part). The topology of the induced magnetosphere of Venus and Mars is substantially different from that of the Earth, whose internal magnetic field interacts with the solar wind charged particles. Image: European Space Agency (ESA).</p>
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<p>Artistic impression of the ESA’s Venus Express orbiting around the second planet of the Solar System. Using the installed onboard magnetometer and low-energy particle detector, the spacecraft observed Venus’s magnetotail on 15 May 2006 at a distance of about 1.5 planet’s radii downstream of Venus. Image: ESA—D. Ducros.</p>
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<p>Conceptual scheme of a GeoSail-type mission scenario applied to a Venus-centered case. The solar sail-induced thrust rotates the apse line of the spacecraft (elliptic) science orbit in order to maintain the apocytherion inside Venus’s induced magnetotail. The spacecraft and Venus move around the Sun along the same plane <math display="inline"><semantics> <mi mathvariant="script">P</mi> </semantics></math>. The artificial precession of the apse line can be maintained, theoretically, for a very long period of time.</p>
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<p>Scheme of the solar sail-based spacecraft’s science orbit around Venus, in which the initial direction of the planetocentric orbit apse line coincides with the Venus–Sun line. In particular, initially, the Sun belongs to the positive direction of the first axis of a classical perifocal reference frame. The Sun–Venus distance <math display="inline"><semantics> <msub> <mi>r</mi> <mrow> <mi>S</mi> <mi>V</mi> </mrow> </msub> </semantics></math> is a constant of motion, and its value is high enough to assume that the Sun rays arrive parallel to the solar sail-based spacecraft.</p>
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<p>Sketch of a Sun-facing solar sail in a Venus-centered mission scenario in which the direction of the incoming Sun rays is coincident with the elliptic orbit apse line. Note that the Sun belongs to the apse line of the science orbit at a distance approximately equal to <math display="inline"><semantics> <msub> <mi>r</mi> <mrow> <mi>S</mi> <mi>V</mi> </mrow> </msub> </semantics></math>, which is considered a constant of motion.</p>
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<p>Variation of the dimensionless components of the solar sail-induced propulsive acceleration vector with the spacecraft true anomaly <math display="inline"><semantics> <mi>ν</mi> </semantics></math>, according to Equations (<a href="#FD14-applsci-14-08016" class="html-disp-formula">14</a>) and (<a href="#FD15-applsci-14-08016" class="html-disp-formula">15</a>).</p>
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<p>Variation of <math display="inline"><semantics> <mi>ω</mi> </semantics></math> with <math display="inline"><semantics> <mi>ν</mi> </semantics></math> obtained by the numerical integration of the Lagrange planetary equations (black line), when <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mi>p</mi> </msub> <mo>=</mo> <mn>1.3</mn> <mspace width="0.166667em"/> <msub> <mi>R</mi> <mi>V</mi> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mi>a</mi> </msub> <mo>=</mo> <mn>6</mn> <mspace width="0.166667em"/> <msub> <mi>R</mi> <mi>V</mi> </msub> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mi>c</mi> </msub> <mo>≃</mo> <mn>0.363</mn> <mspace width="0.166667em"/> <mi>mm</mi> <mo>/</mo> <msup> <mi mathvariant="normal">s</mi> <mn>2</mn> </msup> </mrow> </semantics></math>. The red dashed line indicates the rotation of the Venus–Sun line during the spacecraft’s revolution around the planet. Note how the black and red dashed lines overlap when <math display="inline"><semantics> <mrow> <mi>ν</mi> <mo>=</mo> <mn>2</mn> <mi>π</mi> <mspace width="0.166667em"/> <mi>rad</mi> </mrow> </semantics></math>.</p>
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<p>Variation of the dimensionless semimajor axis and the eccentricity with <math display="inline"><semantics> <mi>ν</mi> </semantics></math>, as obtained by the numerical integration of Lagrange planetary equations (in Gaussian form), when <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mi>p</mi> </msub> <mo>=</mo> <mn>1.3</mn> <mspace width="0.166667em"/> <msub> <mi>R</mi> <mi>V</mi> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mi>a</mi> </msub> <mo>=</mo> <mn>6</mn> <mspace width="0.166667em"/> <msub> <mi>R</mi> <mi>V</mi> </msub> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mi>c</mi> </msub> <mo>≃</mo> <mn>0.363</mn> <mspace width="0.166667em"/> <mi>mm</mi> <mo>/</mo> <msup> <mi mathvariant="normal">s</mi> <mn>2</mn> </msup> </mrow> </semantics></math>.</p>
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<p>Parametric study of the required solar sail characteristic acceleration <math display="inline"><semantics> <msub> <mi>a</mi> <mi>c</mi> </msub> </semantics></math> as a function of the pericytherion <math display="inline"><semantics> <msub> <mover accent="true"> <mi>r</mi> <mo>˜</mo> </mover> <mi>p</mi> </msub> </semantics></math> and apocytherion <math display="inline"><semantics> <msub> <mover accent="true"> <mi>r</mi> <mo>˜</mo> </mover> <mi>a</mi> </msub> </semantics></math> dimensionless radii: (<b>a</b>) surface plot of <math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mi>c</mi> </msub> <mo>=</mo> <msub> <mi>a</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <msub> <mover accent="true"> <mi>r</mi> <mo>˜</mo> </mover> <mi>p</mi> </msub> <mo>,</mo> <msub> <mover accent="true"> <mi>r</mi> <mo>˜</mo> </mover> <mi>a</mi> </msub> <mo>)</mo> </mrow> </mrow> </semantics></math>; (<b>b</b>) contour plot of <math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mi>c</mi> </msub> <mo>=</mo> <msub> <mi>a</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <msub> <mover accent="true"> <mi>r</mi> <mo>˜</mo> </mover> <mi>p</mi> </msub> <mo>,</mo> <msub> <mover accent="true"> <mi>r</mi> <mo>˜</mo> </mover> <mi>a</mi> </msub> <mo>)</mo> </mrow> </mrow> </semantics></math>.</p>
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<p>Dimensionless apocytherion radius <math display="inline"><semantics> <msub> <mover accent="true"> <mi>r</mi> <mo>˜</mo> </mover> <mi>a</mi> </msub> </semantics></math> as a function of the dimensionless pericytherion radius <math display="inline"><semantics> <msub> <mover accent="true"> <mi>r</mi> <mo>˜</mo> </mover> <mi>p</mi> </msub> </semantics></math> when the solar sail required characteristic acceleration is <math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mi>c</mi> </msub> <mo>∈</mo> <mrow> <mo>{</mo> <mn>0.1</mn> <mo>,</mo> <mn>0.15</mn> <mo>,</mo> <mn>0.2</mn> <mo>}</mo> </mrow> <mspace width="0.166667em"/> <mi>mm</mi> <mo>/</mo> <msup> <mi mathvariant="normal">s</mi> <mn>2</mn> </msup> </mrow> </semantics></math>.</p>
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<p>Schematic concept of the (simplified) cylindrical shadow model, which was used to determine the solar sail’s required performance in the presence of a period of eclipse.</p>
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<p>The required solar sail’s characteristic acceleration <math display="inline"><semantics> <msub> <mi>a</mi> <mi>c</mi> </msub> </semantics></math> as a function of the pericytherion <math display="inline"><semantics> <msub> <mover accent="true"> <mi>r</mi> <mo>˜</mo> </mover> <mi>p</mi> </msub> </semantics></math> and apocytherion <math display="inline"><semantics> <msub> <mover accent="true"> <mi>r</mi> <mo>˜</mo> </mover> <mi>a</mi> </msub> </semantics></math> dimensionless radii in the presence of a period of eclipse: (<b>a</b>) contour plot of <math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mi>c</mi> </msub> <mo>=</mo> <msub> <mi>a</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <msub> <mover accent="true"> <mi>r</mi> <mo>˜</mo> </mover> <mi>p</mi> </msub> <mo>,</mo> <msub> <mover accent="true"> <mi>r</mi> <mo>˜</mo> </mover> <mi>a</mi> </msub> <mo>)</mo> </mrow> </mrow> </semantics></math>; (<b>b</b>) case of <math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mi>c</mi> </msub> <mo>∈</mo> <mrow> <mo>{</mo> <mn>0.1</mn> <mo>,</mo> <mn>0.15</mn> <mo>,</mo> <mn>0.2</mn> <mo>}</mo> </mrow> <mspace width="0.166667em"/> <mi>mm</mi> <mo>/</mo> <msup> <mi mathvariant="normal">s</mi> <mn>2</mn> </msup> </mrow> </semantics></math>.</p>
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<p>Function <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mi>ω</mi> <mo>(</mo> <mi>ν</mi> <mo>)</mo> </mrow> </semantics></math>, in the presence of a period of eclipse, when <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mi>p</mi> </msub> <mo>=</mo> <mn>1.3</mn> <mspace width="0.166667em"/> <msub> <mi>R</mi> <mi>V</mi> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mi>a</mi> </msub> <mo>=</mo> <mn>6</mn> <mspace width="0.166667em"/> <msub> <mi>R</mi> <mi>V</mi> </msub> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mi>c</mi> </msub> <mo>≃</mo> <mn>0.42</mn> <mspace width="0.166667em"/> <mi>mm</mi> <mo>/</mo> <msup> <mi mathvariant="normal">s</mi> <mn>2</mn> </msup> </mrow> </semantics></math>. The black line indicates the output of an orbit simulator, while the red dashed line indicates the rotation of the Venus–Sun line during the spacecraft revolution around the planet.</p>
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21 pages, 2250 KiB  
Article
Optimization of Controllable-Pitch Propeller Operations for Yangtze River Sailing Ships
by Wuliu Tian, Xiao Lang, Chi Zhang, Songyin Yan, Bing Li and Shuo Zang
J. Mar. Sci. Eng. 2024, 12(9), 1579; https://doi.org/10.3390/jmse12091579 - 6 Sep 2024
Viewed by 595
Abstract
The Yangtze River’s substantial variation in water depth and current speeds means that inland ships face diverse operational conditions within a single voyage. This paper discusses the adoption of controllable-pitch propellers, which adjust their pitch to adapt to varying navigational environments, thereby optimizing [...] Read more.
The Yangtze River’s substantial variation in water depth and current speeds means that inland ships face diverse operational conditions within a single voyage. This paper discusses the adoption of controllable-pitch propellers, which adjust their pitch to adapt to varying navigational environments, thereby optimizing energy efficiency. We developed an optimization framework to determine the ideal pitch angle and rotation speed (RPM) under different sailing conditions. The energy performance model for inland ships was enhanced to account for the open-water efficiency of CPPs across various pitch angles and RPMs, considering the impacts of current and shallow water, among other factors. The optimization approach was refined by incorporating an improved genetic algorithm with an annealing algorithm to enhance the initial population, applying the K-means clustering algorithm for population segmentation, and using multi-parent crossover from diverse clusters. The efficacy of the optimization method for CPP operations was validated by analyzing three operational scenarios of a Yangtze sailing ship. Additionally, key components of the ship performance model were calibrated through experimental tests, demonstrating an anticipated fuel consumption reduction of approximately 5% compared to conventional fixed-pitch propellers. Full article
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Figure 1
<p>Controllable-pitch propeller force diagram [<a href="#B38-jmse-12-01579" class="html-bibr">38</a>].</p>
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<p>The simplified CPP ship fuel consumption modeling process in this study.</p>
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<p>The proposed CPP operation optimization method in this study.</p>
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<p>Conventional genetic algorithm optimization process.</p>
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<p>The further improved method for generating the initial genetic algorithm population by adding the annealing algorithm.</p>
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<p>Schematic diagram of the further developed crossover strategy.</p>
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<p>Comparison of the ship resistance for the case-study ship, with a draft of 2.4 m; the blue line is experimental data, and the red line is the results from the calibrated formula.</p>
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<p>The SFOC at different engine loads as percentages of the maximum continuous rating (MCR) for the case-study ship.</p>
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<p>Comparison of measured and calculated open-water efficiency: the black curve represents the experimental measurements, while the curves in various colors correspond to calculations from OpenProp software.</p>
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<p>Open-water efficiency for pitch angles of service pitch angle <math display="inline"><semantics> <mrow> <msup> <mrow> <mo>+</mo> <mn>3</mn> </mrow> <mrow> <mo>°</mo> </mrow> </msup> </mrow> </semantics></math> (<b>left</b>) and <math display="inline"><semantics> <mrow> <msup> <mrow> <mo>+</mo> <mn>7</mn> </mrow> <mrow> <mo>°</mo> </mrow> </msup> </mrow> </semantics></math> (<b>right</b>).</p>
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<p>Open-water efficiency for pitch angles of service pitch angle <math display="inline"><semantics> <mrow> <msup> <mrow> <mo>−</mo> <mn>5</mn> </mrow> <mrow> <mo>°</mo> </mrow> </msup> </mrow> </semantics></math> (<b>left</b>) and <math display="inline"><semantics> <mrow> <msup> <mrow> <mo>−</mo> <mn>3</mn> </mrow> <mrow> <mo>°</mo> </mrow> </msup> </mrow> </semantics></math> (<b>right</b>).</p>
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<p>Open-water efficiency at different pitch angles for the case-study CPP; service pitch angles of <math display="inline"><semantics> <mrow> <msup> <mrow> <mo>−</mo> <mn>3</mn> </mrow> <mrow> <mo>°</mo> </mrow> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msup> <mrow> <mo>+</mo> <mn>3</mn> </mrow> <mrow> <mo>°</mo> </mrow> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msup> <mrow> <mo>+</mo> <mn>4</mn> </mrow> <mrow> <mo>°</mo> </mrow> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msup> <mrow> <mo>+</mo> <mn>5</mn> </mrow> <mrow> <mo>°</mo> </mrow> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msup> <mrow> <mo>+</mo> <mn>6</mn> </mrow> <mrow> <mo>°</mo> </mrow> </msup> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msup> <mrow> <mo>+</mo> <mn>7</mn> </mrow> <mrow> <mo>°</mo> </mrow> </msup> </mrow> </semantics></math> are presented from left to right.</p>
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<p>Optimization iteration for segment 3 of scenario 1; the blue dots are the mean fitness, and the black dots indicate the best fitness.</p>
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<p>Optimal pitch angle and RPM of scenario 1.</p>
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<p>Optimization iteration at a speed of 4 kn in scenario 2; the blue dots are the mean fitness, and the black dots indicate the best fitness.</p>
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<p>Optimal pitch angle and RPM for scenario 2.</p>
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<p>Optimization results of scenario 3.</p>
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22 pages, 15104 KiB  
Article
Hydrodynamic Analysis of Different Formation Configurations of Catamaran in Regular Head Waves
by Zhifan Zhang, Bo Jiang, Longkan Wang, Shengren Wei, Tao Li, Guiyong Zhang and Zhi Zong
J. Mar. Sci. Eng. 2024, 12(9), 1577; https://doi.org/10.3390/jmse12091577 - 6 Sep 2024
Viewed by 401
Abstract
When undertaking long-distance missions at sea, vessels aim to achieve an extended operational range through drag reduction and energy efficiency, while enhanced wave resilience also provides substantial benefits. In this work, the Delft-372 catamaran is utilized to investigate the feasibility of drag reduction [...] Read more.
When undertaking long-distance missions at sea, vessels aim to achieve an extended operational range through drag reduction and energy efficiency, while enhanced wave resilience also provides substantial benefits. In this work, the Delft-372 catamaran is utilized to investigate the feasibility of drag reduction and roll mitigation for catamaran formation sailing in waves, analyzing the effects of three different formation configurations and varying spacings. The overset grid method was employed to simulate vessel motions, while the Volume of Fluid (VOF) method captured the free surface. First, the numerical results of the catamaran’s resistance, pitch, and heave motion amplitudes under different wave conditions were compared with experimental data to verify the accuracy of the CFD numerical method, and a grid convergence analysis was performed. Next, numerical models of the Delft-372 catamaran were constructed in parallel, tandem, and lateral formations under wave conditions. The results of the single-ship simulation were employed as a benchmark to analyze the impact of different formation configurations and varying lateral and longitudinal spacings on the resistance, pitch, and heave motions of the catamarans. The study also examined the effects of wave interference between vessels and the combined influence of external waves on individual and overall hydrodynamic performance. Results indicated that the tandem formation outperformed the parallel and lateral formations, with optimal performance observed at the longitudinal distance of 1 LPP. Generally, during navigation, the follower catamaran should ideally be positioned in the trough of the stern wave of the leader catamaran. Full article
(This article belongs to the Section Ocean Engineering)
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Figure 1
<p>The flocking of ducks.</p>
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<p>The 3D model of the Delft-372 catamaran: (<b>a</b>) bow view and (<b>b</b>) stern view.</p>
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<p>Overset domain and background domain. (<b>a</b>) Regional division and (<b>b</b>) mesh around the slice and mesh differences between regions.</p>
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<p>Domain and hull grid. (<b>a</b>) Computational domain mesh, (<b>b</b>) overset domain mesh, and (<b>c</b>) hull surface mesh.</p>
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<p>Domain and hull grid. (<b>a</b>) Computational domain mesh, (<b>b</b>) overset domain mesh, and (<b>c</b>) hull surface mesh.</p>
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<p>Heave and pitch motion responses of the Delft-372 catamaran with Fr = 0.7 in head waves. (<b>a</b>) Heave RAO and (<b>b</b>) pitch RAO [<a href="#B29-jmse-12-01577" class="html-bibr">29</a>].</p>
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<p>Added resistance coefficient of the Delft-372 catamaran with Fr = 0.7 in head waves [<a href="#B29-jmse-12-01577" class="html-bibr">29</a>].</p>
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<p>The geometric configuration of catamarans in different formations: (<b>a</b>) tandem formation, (<b>b</b>) lateral formation, and (<b>c</b>) parallel formation.</p>
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<p>The resistance and lateral force of the catamaran under different lateral distances.</p>
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<p>The heave and pitch amplitudes of the catamaran under different lateral distances.</p>
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<p>The free surface deformations of parallel formation at different lateral distances: (<b>a</b>) SP/<span class="html-italic">B</span> = 0.25, (<b>b</b>) SP/<span class="html-italic">B</span> = 0.5, (<b>c</b>) SP/<span class="html-italic">B</span> = 0.75, (<b>d</b>) SP/<span class="html-italic">B</span> = 1, (<b>e</b>) SP/<span class="html-italic">B</span> = 1.5, and (<b>f</b>) SP/<span class="html-italic">B</span> = 2.</p>
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<p>The free surface deformations of parallel formation at different lateral distances: (<b>a</b>) SP/<span class="html-italic">B</span> = 0.25, (<b>b</b>) SP/<span class="html-italic">B</span> = 0.5, (<b>c</b>) SP/<span class="html-italic">B</span> = 0.75, (<b>d</b>) SP/<span class="html-italic">B</span> = 1, (<b>e</b>) SP/<span class="html-italic">B</span> = 1.5, and (<b>f</b>) SP/<span class="html-italic">B</span> = 2.</p>
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<p>Comparison of the total resistance coefficients for each catamaran in the two-ship system.</p>
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<p>Comparison of the motion characteristics for each catamaran in the two-ship system. (<b>a</b>) Heave amplitude and (<b>b</b>) pitch amplitude.</p>
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<p>Comparison of the total resistance coefficients for each catamaran in the three-ship system.</p>
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<p>Comparison of the motion characteristics for each catamaran in the three-ship system. (<b>a</b>) Heave amplitude and (<b>b</b>) pitch amplitude.</p>
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<p>The sketch of the wave profile along the centerline.</p>
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<p>The free surface deformations of tandem formation in the two- and three-ship systems. (<b>a</b>) Two-ship system and (<b>b</b>) three-ship system.</p>
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<p>Comparison of the total resistance coefficients for each catamaran in lateral formation.</p>
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<p>Comparison of the motion characteristics for each catamaran in lateral formation. (<b>a</b>) Heave amplitude and (<b>b</b>) pitch amplitude.</p>
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<p>The free surface deformations of lateral formation in different longitudinal and lateral distances: (<b>a</b>) ST/<math display="inline"><semantics> <mrow> <msub> <mi>L</mi> <mi mathvariant="italic">PP</mi> </msub> </mrow> </semantics></math> = 0.5, SP/<span class="html-italic">B</span> = 0.25; (<b>b</b>) ST/<math display="inline"><semantics> <mrow> <msub> <mi>L</mi> <mi mathvariant="italic">PP</mi> </msub> </mrow> </semantics></math> = 1, SP/<span class="html-italic">B</span> = 0.5; (<b>c</b>) ST/<math display="inline"><semantics> <mrow> <msub> <mi>L</mi> <mi mathvariant="italic">PP</mi> </msub> </mrow> </semantics></math> = 1.25, SP/<span class="html-italic">B</span> = 0.75; (<b>d</b>) ST/<math display="inline"><semantics> <mrow> <msub> <mi>L</mi> <mi mathvariant="italic">PP</mi> </msub> </mrow> </semantics></math> = 1.5, SP/<span class="html-italic">B</span> = 1.</p>
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19 pages, 7505 KiB  
Article
Stereo Particle Image Velocimetry Measurement of the Flow around SUBOFF Submarine under Yaw Conditions
by Mo Chen, Nan Zhang, Ziyan Li, Junliang Liu, Lan Yu, Wentao Zheng and Xuan Zhang
J. Mar. Sci. Eng. 2024, 12(9), 1576; https://doi.org/10.3390/jmse12091576 - 6 Sep 2024
Viewed by 1525
Abstract
To gain a better understanding of the complex flow dynamics and stealth characteristics of submarines under maneuvering conditions, flow field experiments were conducted on the SUBOFF submarine model in the large low-speed wind tunnel at the China Ship Scientific Research Center (CSSRC). The [...] Read more.
To gain a better understanding of the complex flow dynamics and stealth characteristics of submarines under maneuvering conditions, flow field experiments were conducted on the SUBOFF submarine model in the large low-speed wind tunnel at the China Ship Scientific Research Center (CSSRC). The three-dimensional velocity field above the hull at 6° and 9° yaw angles was captured using the stereo particle image velocimetry (SPIV) system. The experimental Reynolds numbers were selected as ReL = 0.46 × 107 and ReL = 1.08 × 107. The wake of the sail and the junction between the sail root and the hull were analyzed in detail, focusing on the core flow of the sail-tip vortex. The results revealed that at a larger yaw angle, the vorticity magnitude and turbulent kinetic energy (TKE) of the wake increased, and the downwash effect of the sail-tip vortex center became more pronounced. Furthermore, a higher Reynolds number resulted in an even more significant downwash of the vortex center, accompanied by a slight deviation towards the suction side. These experimental findings can contribute to the enrichment of the benchmark database for validating and improving numerical simulations of submarine wakes. Full article
(This article belongs to the Section Ocean Engineering)
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<p>DARPA SUBOFF submarine model.</p>
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<p>Measurement planes and coordinate system.</p>
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<p>Diagram of the wind tunnel SPIV experimental scenario.</p>
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<p>Diagram of the SPIV system.</p>
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<p>Diagram of SPIV experimental setup.</p>
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<p>The wind tunnel SPIV experiment.</p>
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<p>Experimental results of ensemble-averaged velocities and vorticity magnitude (<span class="html-italic">ψ</span> = 6°, <span class="html-italic">x</span>/<span class="html-italic">L</span> = 0.595): (<b>a</b>) &lt;<span class="html-italic">U<sub>x</sub></span>&gt;/<span class="html-italic">U<sub>∞</sub></span>; (<b>b</b>) &lt;<span class="html-italic">U<sub>y</sub></span>&gt;/<span class="html-italic">U<sub>∞</sub></span>; (<b>c</b>) &lt;<span class="html-italic">U<sub>z</sub></span>&gt;/<span class="html-italic">U<sub>∞</sub></span>; (<b>d</b>) &lt;<span class="html-italic">U<sub>xyz</sub></span>&gt;/<span class="html-italic">U<sub>∞</sub></span>; (<b>e</b>) &lt;<span class="html-italic">ω<sub>xyz</sub></span>&gt;<span class="html-italic">L</span>/<span class="html-italic">U<sub>∞</sub></span>.</p>
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<p>Experimental results of ensemble-averaged velocities and vorticity magnitude (<span class="html-italic">ψ</span> = 6°, <span class="html-italic">x</span>/<span class="html-italic">L</span> = 0.818): (<b>a</b>) &lt;<span class="html-italic">U<sub>x</sub></span>&gt;/<span class="html-italic">U<sub>∞</sub></span>; (<b>b</b>) &lt;<span class="html-italic">U<sub>y</sub></span>&gt;/<span class="html-italic">U<sub>∞</sub></span>; (<b>c</b>) &lt;<span class="html-italic">U<sub>z</sub></span>&gt;/<span class="html-italic">U<sub>∞</sub></span>; (<b>d</b>) &lt;<span class="html-italic">U<sub>xyz</sub></span>&gt;/<span class="html-italic">U<sub>∞</sub></span>; (<b>e</b>) &lt;<span class="html-italic">ω<sub>xyz</sub></span>&gt;<span class="html-italic">L</span>/<span class="html-italic">U<sub>∞</sub></span>.</p>
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<p>Experimental results of ensemble-averaged velocities and vorticity magnitude (<span class="html-italic">ψ</span> = 9°, <span class="html-italic">x</span>/<span class="html-italic">L</span> = 0.595): (<b>a</b>) &lt;<span class="html-italic">U<sub>x</sub></span>&gt;/<span class="html-italic">U<sub>∞</sub></span>; (<b>b</b>) &lt;<span class="html-italic">U<sub>y</sub></span>&gt;/<span class="html-italic">U<sub>∞</sub></span>; (<b>c</b>) &lt;<span class="html-italic">U<sub>z</sub></span>&gt;/<span class="html-italic">U<sub>∞</sub></span>; (<b>d</b>) &lt;<span class="html-italic">U<sub>xyz</sub></span>&gt;/<span class="html-italic">U<sub>∞</sub></span>; (<b>e</b>) &lt;<span class="html-italic">ω<sub>xyz</sub></span>&gt;<span class="html-italic">L</span>/<span class="html-italic">U<sub>∞</sub></span>.</p>
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<p>Experimental results of ensemble-averaged velocities and vorticity magnitude (<span class="html-italic">ψ</span> = 9°, <span class="html-italic">x</span>/<span class="html-italic">L</span> = 0.818): (<b>a</b>) &lt;<span class="html-italic">U<sub>x</sub></span>&gt;/<span class="html-italic">U<sub>∞</sub></span>; (<b>b</b>) &lt;<span class="html-italic">U<sub>y</sub></span>&gt;/<span class="html-italic">U<sub>∞</sub></span>; (<b>c</b>) &lt;<span class="html-italic">U<sub>z</sub></span>&gt;/<span class="html-italic">U<sub>∞</sub></span>; (<b>d</b>) &lt;<span class="html-italic">U<sub>xyz</sub></span>&gt;/<span class="html-italic">U<sub>∞</sub></span>; (<b>e</b>) &lt;<span class="html-italic">ω<sub>xyz</sub></span>&gt;<span class="html-italic">L</span>/<span class="html-italic">U<sub>∞</sub></span>.</p>
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<p>Distribution of the sail-tip vortex center positions in the tail view: (<b>a</b>) <span class="html-italic">x</span>/<span class="html-italic">L</span> = 0.595; (<b>b</b>) <span class="html-italic">x</span>/<span class="html-italic">L</span> = 0.818.</p>
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<p>Distribution of the ensemble-averaged resultant velocity near the leeward and windward sides of the sail-tip vortex: (<b>a</b>) <span class="html-italic">x</span>/<span class="html-italic">L</span> = 0.595; (<b>b</b>) <span class="html-italic">x</span>/<span class="html-italic">L</span> = 0.818.</p>
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<p>Distribution of the ensemble-averaged vertical velocity near the leeward and windward sides of the sail-tip vortex: (<b>a</b>) <span class="html-italic">x</span>/<span class="html-italic">L</span> = 0.595; (<b>b</b>) <span class="html-italic">x</span>/<span class="html-italic">L</span> = 0.818.</p>
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<p>Distribution of the normal Reynolds stresses and TKE near the leeward and windward sides of the sail-tip vortex for <span class="html-italic">x</span>/<span class="html-italic">L</span> = 0.595: (<b>a</b>) ⟨<span class="html-italic">u<sub>x</sub>u<sub>x</sub></span>⟩; (<b>b</b>) ⟨<span class="html-italic">u<sub>y</sub>u<sub>y</sub></span>⟩; (<b>c</b>) ⟨<span class="html-italic">u<sub>z</sub>u<sub>z</sub></span>⟩; (<b>d</b>) TKE.</p>
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<p>Distribution of the normal Reynolds stresses and TKE near the leeward and windward sides of the sail-tip vortex for <span class="html-italic">x</span>/<span class="html-italic">L</span> = 0.818: (<b>a</b>) ⟨<span class="html-italic">u<sub>x</sub>u<sub>x</sub></span>⟩; (<b>b</b>) ⟨<span class="html-italic">u<sub>y</sub>u<sub>y</sub></span>⟩; (<b>c</b>) ⟨<span class="html-italic">u<sub>z</sub>u<sub>z</sub></span>⟩; (<b>d</b>) TKE.</p>
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<p>Distribution of the ensemble-averaged vorticity magnitude near the leeward and windward sides of the sail-tip vortex: (<b>a</b>) <span class="html-italic">x</span>/<span class="html-italic">L</span> = 0.595; (<b>b</b>) <span class="html-italic">x</span>/<span class="html-italic">L</span> = 0.818.</p>
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<p>Distribution of the ensemble-averaged lateral velocity near the upper and lower sides of the sail-tip vortex: (<b>a</b>) <span class="html-italic">x</span>/<span class="html-italic">L</span> = 0.595; (<b>b</b>) <span class="html-italic">x</span>/<span class="html-italic">L</span> = 0.818.</p>
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<p>Distribution of the TKE near the upper and lower sides of the sail-tip vortex: (<b>a</b>) <span class="html-italic">x</span>/<span class="html-italic">L</span> = 0.595; (<b>b</b>) <span class="html-italic">x</span>/<span class="html-italic">L</span> = 0.818.</p>
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19 pages, 2692 KiB  
Article
Impact of Pitch Angle Limitation on E-Sail Interplanetary Transfers
by Alessandro A. Quarta
Aerospace 2024, 11(9), 729; https://doi.org/10.3390/aerospace11090729 - 6 Sep 2024
Viewed by 362
Abstract
The Electric Solar Wind Sail (E-sail) deflects charged particles from the solar wind through an artificial electric field to generate thrust in interplanetary space. The structure of a spacecraft equipped with a typical E-sail essentially consists in a number of long conducting tethers [...] Read more.
The Electric Solar Wind Sail (E-sail) deflects charged particles from the solar wind through an artificial electric field to generate thrust in interplanetary space. The structure of a spacecraft equipped with a typical E-sail essentially consists in a number of long conducting tethers deployed from a main central body, which contains the classical spacecraft subsystems. During flight, the reference plane that formally contains the conducting tethers, i.e., the sail nominal plane, is inclined with respect to the direction of propagation of the solar wind (approximately coinciding with the Sun–spacecraft direction in a preliminary trajectory analysis) in such a way as to vary both the direction and the module of the thrust vector provided by the propellantless propulsion system. The generation of a sail pitch angle different from zero (i.e., a non-zero angle between the Sun–spacecraft line and the direction perpendicular to the sail nominal plane) allows a transverse component of the thrust vector to be obtained. From the perspective of attitude control system design, a small value of the sail pitch angle could improve the effectiveness of the E-sail attitude maneuver at the expense, however, of a worsening of the orbital transfer performance. The aim of this paper is to investigate the effects of a constraint on the maximum value of the sail pitch angle, on the performance of a spacecraft equipped with an E-sail propulsion system in a typical interplanetary mission scenario. During flight, the E-sail propulsion system is considered to be always on so that the entire transfer can be considered a single propelled arc. A heliocentric orbit-to-orbit transfer without ephemeris constraints is analyzed, while the performance analysis is conducted in a parametric form as a function of both the maximum admissible sail pitch angle and the propulsion system’s characteristic acceleration value. Full article
(This article belongs to the Special Issue Advances in CubeSat Sails and Tethers (2nd Edition))
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Figure 1

Figure 1
<p>Conceptual scheme of a centrifugal deployment of an E-sail-propelled spacecraft, in which the main central body, the conducting tethers, and the remote units are sketched. The conducting tethers deployment takes place substantially in the so-called “sail nominal plane”, which is indicated with a shaded green disk in the right part of the figure. (<b>a</b>) Centrifugal deployment of the E-sail, where the spin direction is indicated by curved orange arrows; (<b>b</b>) final (fully deployed) E-sail configuration.</p>
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<p>Artistic impression of a CubeSat equipped with a spinning, single-tether E-sail, which can be used to obtain the first in situ measurement of the propulsive acceleration given by this fascinating propulsion system. In the artistic image, the CubeSat with a deployed (single) conducting tether covers a high-elliptic Lunar orbit which allows the vehicle to move outside Earth’s magnetosphere. Image courtesy of Mario F. Palos.</p>
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<p>Description of a Sun-facing configuration and a generic case in which the sail nominal plane is inclined with respect to the radial direction. (<b>a</b>) Sun-facing configuration in which the sail nominal plane is perpendicular to the Sun–spacecraft line; (<b>b</b>) case of a generic sail pitch angle different from zero, in which the E-sail-induced thrust vector has a non-zero transverse component.</p>
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<p>Radial-Transverse-Normal reference frame (RTN) of unit vector <math display="inline"><semantics> <msub> <mover accent="true"> <mi mathvariant="bold-italic">i</mi> <mo stretchy="false">^</mo> </mover> <mi mathvariant="normal">R</mi> </msub> </semantics></math> (radial), <math display="inline"><semantics> <msub> <mover accent="true"> <mi mathvariant="bold-italic">i</mi> <mo stretchy="false">^</mo> </mover> <mi mathvariant="normal">T</mi> </msub> </semantics></math> (transverse), and <math display="inline"><semantics> <msub> <mover accent="true"> <mi mathvariant="bold-italic">i</mi> <mo stretchy="false">^</mo> </mover> <mi mathvariant="normal">N</mi> </msub> </semantics></math> (normal). The plane <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mover accent="true"> <mi mathvariant="bold-italic">i</mi> <mo stretchy="false">^</mo> </mover> <mi mathvariant="normal">R</mi> </msub> <mo>,</mo> <msub> <mover accent="true"> <mi mathvariant="bold-italic">i</mi> <mo stretchy="false">^</mo> </mover> <mi mathvariant="normal">T</mi> </msub> <mo>)</mo> </mrow> </semantics></math> coincides with the plane of the spacecraft osculating orbit, while the spacecraft inertial velocity vector has a positive component along the direction of <math display="inline"><semantics> <msub> <mover accent="true"> <mi mathvariant="bold-italic">i</mi> <mo stretchy="false">^</mo> </mover> <mi mathvariant="normal">T</mi> </msub> </semantics></math>.</p>
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<p>Sketch of the normal unit vector <math display="inline"><semantics> <mover accent="true"> <mi mathvariant="bold-italic">n</mi> <mo stretchy="false">^</mo> </mover> </semantics></math> and the propulsive acceleration vector <math display="inline"><semantics> <msub> <mi mathvariant="bold-italic">a</mi> <mi>p</mi> </msub> </semantics></math> in the RTN reference frame. The scheme introduces the sail pitch angle <math display="inline"><semantics> <msub> <mi>α</mi> <mi>n</mi> </msub> </semantics></math> and the sail clock angle <math display="inline"><semantics> <mi>δ</mi> </semantics></math>, which are the two (scalar) E-sail’s control terms.</p>
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<p>Force bubble in the unconstrained case (<math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mi>n</mi> </msub> <mo>∈</mo> <mrow> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>90</mn> <mo>]</mo> </mrow> <mspace width="0.166667em"/> <mi>deg</mi> </mrow> </semantics></math>) when <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>=</mo> <msub> <mi>r</mi> <mo>⊕</mo> </msub> </mrow> </semantics></math>. The direction of propagation of the solar wind coincides with the direction of the <span class="html-italic">z</span>-axis, that is, the Sun belongs to the vertical axis.</p>
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<p>Force bubble in the constrained case when <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>=</mo> <msub> <mi>r</mi> <mo>⊕</mo> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <msub> <mi>n</mi> <mo movablelimits="true" form="prefix">max</mo> </msub> </msub> <mo>∈</mo> <mrow> <mo>{</mo> <mn>30</mn> <mo>,</mo> <mn>45</mn> <mo>,</mo> <mn>60</mn> <mo>,</mo> <mn>75</mn> <mo>}</mo> </mrow> <mspace width="0.166667em"/> <mi>deg</mi> </mrow> </semantics></math>.</p>
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<p>Time variation in the control angles <math display="inline"><semantics> <mrow> <mo>{</mo> <msub> <mi>α</mi> <mi>n</mi> </msub> <mo>,</mo> <mspace width="0.166667em"/> <mi>δ</mi> <mo>}</mo> </mrow> </semantics></math> in an unconstrained Earth–Mars transfer with <math display="inline"><semantics> <msub> <mi>a</mi> <mi>c</mi> </msub> </semantics></math> = 1 mm/s<sup>2</sup>. Blue dot → starting point; red square → arrival point.</p>
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<p>Time variation in the control angles <math display="inline"><semantics> <mrow> <mo>{</mo> <msub> <mi>α</mi> <mi>n</mi> </msub> <mo>,</mo> <mspace width="0.166667em"/> <mi>δ</mi> <mo>}</mo> </mrow> </semantics></math> in an unconstrained Earth–Venus transfer with <math display="inline"><semantics> <msub> <mi>a</mi> <mi>c</mi> </msub> </semantics></math> = 1 mm/s<sup>2</sup>. Blue dot → starting point; red square → arrival point.</p>
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<p>Time variation in the control angles <math display="inline"><semantics> <mrow> <mo>{</mo> <msub> <mi>α</mi> <mi>n</mi> </msub> <mo>,</mo> <mspace width="0.166667em"/> <mi>δ</mi> <mo>}</mo> </mrow> </semantics></math> in an unconstrained Earth–Mercury transfer with <math display="inline"><semantics> <msub> <mi>a</mi> <mi>c</mi> </msub> </semantics></math> = 1 mm/s<sup>2</sup>. Blue dot → starting point; red square → arrival point.</p>
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<p>Ecliptic projection and isometric view of the unconstrained optimal transfer trajectory in an Earth–Mars scenario with <math display="inline"><semantics> <msub> <mi>a</mi> <mi>c</mi> </msub> </semantics></math> = 1 mm/s<sup>2</sup>. Black line → optimal transfer trajectory; blue line → Earth’s orbit; red line → target planet’s orbit; filled star → planet’s perihelion; blue dot → starting point; red square → arrival point; orange dot → the Sun.</p>
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<p>Ecliptic projection and isometric view of the unconstrained optimal transfer trajectory in an Earth–Venus scenario with <math display="inline"><semantics> <msub> <mi>a</mi> <mi>c</mi> </msub> </semantics></math> = 1 mm/s<sup>2</sup>. See the caption of <a href="#aerospace-11-00729-f011" class="html-fig">Figure 11</a> for the legend.</p>
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<p>Ecliptic projection and isometric view of the unconstrained optimal transfer trajectory in an Earth–Mercury scenario with <math display="inline"><semantics> <msub> <mi>a</mi> <mi>c</mi> </msub> </semantics></math> = 1 mm/s<sup>2</sup>. See the caption of <a href="#aerospace-11-00729-f011" class="html-fig">Figure 11</a> for the legend.</p>
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<p>Simulation results of the constrained case when <math display="inline"><semantics> <msub> <mi>a</mi> <mi>c</mi> </msub> </semantics></math> = 1 mm/s<sup>2</sup>. The dimensionless term <span class="html-italic">D</span> is defined in Equation (<a href="#FD11-aerospace-11-00729" class="html-disp-formula">11</a>). (<b>a</b>) Earth–Mars scenario; (<b>b</b>) Earth–Venus scenario; (<b>c</b>) Earth–Mercury scenario.</p>
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<p>Time variation in the control angles <math display="inline"><semantics> <mrow> <mo>{</mo> <msub> <mi>α</mi> <mi>n</mi> </msub> <mo>,</mo> <mspace width="0.166667em"/> <mi>δ</mi> <mo>}</mo> </mrow> </semantics></math> in a constrained Earth–Mars transfer with <math display="inline"><semantics> <msub> <mi>a</mi> <mi>c</mi> </msub> </semantics></math> = 1 mm/s<sup>2</sup> and <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <msub> <mi>n</mi> <mo movablelimits="true" form="prefix">max</mo> </msub> </msub> <mo>=</mo> <mn>30</mn> <mspace width="0.166667em"/> <mi>deg</mi> </mrow> </semantics></math>. Blue dot → starting point; red square → arrival point.</p>
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<p>Numerical results, in terms of minimum flight time <math display="inline"><semantics> <msub> <mi>t</mi> <mi>f</mi> </msub> </semantics></math>, of the trajectory optimization in an Earth–Mars scenario, where <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <msub> <mi>n</mi> <mo movablelimits="true" form="prefix">max</mo> </msub> </msub> <mo>∈</mo> <mrow> <mo>[</mo> <mn>30</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>90</mn> <mo>]</mo> </mrow> <mspace width="0.166667em"/> <mi>deg</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mi>c</mi> </msub> <mo>∈</mo> <mrow> <mo>[</mo> <mn>0.6</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>1</mn> <mo>]</mo> </mrow> <mspace width="0.166667em"/> <mi>mm</mi> <mo>/</mo> <msup> <mi mathvariant="normal">s</mi> <mn>2</mn> </msup> </mrow> </semantics></math>.</p>
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<p>Curve levels of the dimensionless parameter <math display="inline"><semantics> <mrow> <mi>D</mi> <mo>=</mo> <mi>D</mi> <mo>(</mo> <msub> <mi>α</mi> <msub> <mi>n</mi> <mo movablelimits="true" form="prefix">max</mo> </msub> </msub> <mo>,</mo> <mspace width="0.166667em"/> <msub> <mi>a</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> </semantics></math> in an Earth–Mars scenario, where <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <msub> <mi>n</mi> <mo movablelimits="true" form="prefix">max</mo> </msub> </msub> <mo>∈</mo> <mrow> <mo>[</mo> <mn>30</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>90</mn> <mo>]</mo> </mrow> <mspace width="0.166667em"/> <mi>deg</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mi>c</mi> </msub> <mo>∈</mo> <mrow> <mo>[</mo> <mn>0.6</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>1</mn> <mo>]</mo> </mrow> <mspace width="0.166667em"/> <mi>mm</mi> <mo>/</mo> <msup> <mi mathvariant="normal">s</mi> <mn>2</mn> </msup> </mrow> </semantics></math>.</p>
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18 pages, 8249 KiB  
Article
Astodrimer Sodium Nasal Spray versus Placebo in Non-Hospitalised Patients with COVID-19: A Randomised, Double-Blinded, Placebo-Controlled Trial
by Stephen Winchester, Alex Castellarnau, Kashif Jabbar, Meera Nadir, Kapila Ranasinghe, Xavier Masramon, George R. Kinghorn, Isaac John and Jeremy R. A. Paull
Pharmaceutics 2024, 16(9), 1173; https://doi.org/10.3390/pharmaceutics16091173 - 6 Sep 2024
Viewed by 994
Abstract
Background/Objectives: Dendrimer-based astodrimer sodium nasal spray was assessed for its ability to reduce SARS-CoV-2 load in outpatients with COVID-19, which remains a severe illness for vulnerable groups. Methods: This was a randomised, double-blind, placebo-controlled clinical investigation evaluating the efficacy of astodrimer nasal spray [...] Read more.
Background/Objectives: Dendrimer-based astodrimer sodium nasal spray was assessed for its ability to reduce SARS-CoV-2 load in outpatients with COVID-19, which remains a severe illness for vulnerable groups. Methods: This was a randomised, double-blind, placebo-controlled clinical investigation evaluating the efficacy of astodrimer nasal spray in reducing SARS-CoV-2 viral burden in the nasopharynx of outpatients with COVID-19. Non-hospitalised adults with SARS-CoV-2 infection were randomised 1:1 to astodrimer or placebo four times daily from Day 1 to Day 7. Nasopharyngeal swabs for SARS-CoV-2 load determination were self-obtained daily from Day 1 to Day 8. The primary endpoint was an area under the curve of SARS-CoV-2 RNA copies/mL through Day 8 (vAUCd1–8). The primary analysis population was the modified intent-to-treat population (mITT: all randomised participants exposed to the study treatment who had at least one post-baseline viral load determination). Safety analyses included all randomised participants exposed to the study treatment. Study registration: ISRCTN70449927; Results: 231 participants were recruited between 9 January and 20 September 2023. The safety population comprised 109 and 113 participants randomised to astodrimer and placebo, respectively, with 96 and 101 participants in the mITT. Astodrimer sodium nasal spray reduced the SARS-CoV-2 burden (vAUCd1–8) vs. placebo in non-hospitalised COVID-19 patients aged 16 years and over (−1.2 log10 copies/mL × Day). The reduction in SARS-CoV-2 load was statistically significant in those aged 45 years and older (−3.7, p = 0.017) and the effect increased in older age groups, including in those aged 65 years and older (−7.3, p = 0.005). Astodrimer sodium nasal spray increased the rate of viral clearance and helped alleviate some COVID-19 symptoms, especially loss of sense of smell. Overall, 31 participants (14%) had ≥1 adverse event (AE). Four AEs were deemed possibly related to treatment. Most AEs were of mild severity and occurred at similar rates in both treatment arms. Conclusions: Astodrimer nasal spray reduces viral burden and accelerates viral clearance, especially in older populations, and is well tolerated. Full article
(This article belongs to the Special Issue Inhaled Treatment of Respiratory Infections, 2nd Edition)
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Figure 1

Figure 1
<p>Representation of astodrimer sodium dendrimer structure and mechanism of antiviral action.</p>
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<p>Schematic of study design.</p>
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<p>CONSORT flow diagram.</p>
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<p>SARS-CoV-2 RNA load from Day 1 through Day 8 (vAUC<sub>d1–8</sub>) by treatment and age group. Compared using least squares means difference. * <span class="html-italic">p</span> &lt; 0.05.</p>
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<p>Proportion of participants with negative RT-qPCR test at or by Day 8, by treatment and age group. Compared using Fisher’s exact text. * <span class="html-italic">p</span> &lt; 0.05.</p>
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<p>Time in days from baseline to negative RT-qPCR (55 Y+). Compared using log-rank test. * <span class="html-italic">p</span> &lt; 0.05.</p>
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<p>SARS-CoV-2 RNA load at each determination by treatment and age group: (<b>a</b>) all ages (mITT), (<b>b</b>) 45 Y+ and (<b>c</b>) 65 Y+. Compared using least squares means difference. * <span class="html-italic">p</span> &lt; 0.05.</p>
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<p>SARS-CoV-2 RNA load at each determination by treatment and age group: (<b>a</b>) all ages (mITT), (<b>b</b>) 45 Y+ and (<b>c</b>) 65 Y+. Compared using least squares means difference. * <span class="html-italic">p</span> &lt; 0.05.</p>
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<p>Proportion of participants with (<b>a</b>) loss of sense of smell (anosmia), (<b>b</b>) loss of sense of taste (ageusia) and (<b>c</b>) loss of sense of smell (anosmia) and/or taste (ageusia) on any given day after starting study treatment by age analysis group. Compared using Fisher’s exact text. * <span class="html-italic">p</span> &lt; 0.05.</p>
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<p>Proportion of participants with (<b>a</b>) loss of sense of smell (anosmia), (<b>b</b>) loss of sense of taste (ageusia) and (<b>c</b>) loss of sense of smell (anosmia) and/or taste (ageusia) on any given day after starting study treatment by age analysis group. Compared using Fisher’s exact text. * <span class="html-italic">p</span> &lt; 0.05.</p>
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