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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Mater.</journal-id>
<journal-title>Frontiers in Materials</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Mater.</abbrev-journal-title>
<issn pub-type="epub">2296-8016</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">1096839</article-id>
<article-id pub-id-type="doi">10.3389/fmats.2023.1096839</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Materials</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Design and advanced computational approaches based comprehensive structural parametric investigations of rotary-wing UAV imposed with conventional and hybrid computational composite materials: A validated investigation</article-title>
<alt-title alt-title-type="left-running-head">Raja et al.</alt-title>
<alt-title alt-title-type="right-running-head">
<ext-link ext-link-type="uri" xlink:href="https://doi.org/10.3389/fmats.2023.1096839">10.3389/fmats.2023.1096839</ext-link>
</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Raja</surname>
<given-names>Vijayanandh</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1551659/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>AL-bonsrulah</surname>
<given-names>Hussein A. Z.</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1688829/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Gnanasekaran</surname>
<given-names>Raj Kumar</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/2125495/overview"/>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Eldin</surname>
<given-names>Sayed M.</given-names>
</name>
<xref ref-type="aff" rid="aff4">
<sup>4</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<uri xlink:href="https://loop.frontiersin.org/people/2017591/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Rajendran</surname>
<given-names>Parvathy</given-names>
</name>
<xref ref-type="aff" rid="aff5">
<sup>5</sup>
</xref>
<xref ref-type="aff" rid="aff6">
<sup>6</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1373328/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Baskaran</surname>
<given-names>Balamurali</given-names>
</name>
<xref ref-type="aff" rid="aff7">
<sup>7</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/2096750/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Sakthivel</surname>
<given-names>Pradesh</given-names>
</name>
<xref ref-type="aff" rid="aff8">
<sup>8</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/2158968/overview"/>
</contrib>
</contrib-group>
<aff id="aff1">
<sup>1</sup>
<institution>Department of Aeronautical Engineering</institution>, <institution>Kumaraguru College of Technology</institution>, <addr-line>Coimbatore</addr-line>, <addr-line>Tamil Nadu</addr-line>, <country>India</country>
</aff>
<aff id="aff2">
<sup>2</sup>
<institution>Al-Amarah University College</institution>, <addr-line>Maysan</addr-line>, <country>Iraq</country>
</aff>
<aff id="aff3">
<sup>3</sup>
<institution>Iraqi Ministry of Oil</institution>, <institution>Midland Refineries Company</institution>, <addr-line>Najaf Refinery</addr-line>, <addr-line>Najaf</addr-line>, <country>Iraq</country>
</aff>
<aff id="aff4">
<sup>4</sup>
<institution>Center of Research</institution>, <institution>Faculty of Engineering</institution>, <institution>Future University in Egypt</institution>, <addr-line>New Cairo</addr-line>, <country>Egypt</country>
</aff>
<aff id="aff5">
<sup>5</sup>
<institution>School of Aerospace Engineering</institution>, <institution>Universiti Sains Malaysia</institution>, <addr-line>Nibong Tebal</addr-line>, <addr-line>Penang</addr-line>, <country>Malaysia</country>
</aff>
<aff id="aff6">
<sup>6</sup>
<institution>Faculty of Engineering &#x26; Computing</institution>, <institution>First City University College</institution>, <addr-line>Petaling Jaya</addr-line>, <addr-line>Selangor</addr-line>, <country>Malaysia</country>
</aff>
<aff id="aff7">
<sup>7</sup>
<institution>Department of Mechanical Engineering</institution>, <institution>SNS College of Engineering</institution>, <addr-line>Coimbatore</addr-line>, <addr-line>Tamil Nadu</addr-line>, <country>India</country>
</aff>
<aff id="aff8">
<sup>8</sup>
<institution>Department of Aeronautical Engineering</institution>, <institution>Rajalakshmi Engineering College</institution>, <addr-line>Chennai</addr-line>, <country>India</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/502825/overview">Natrayan L</ext-link>., Saveetha University, India</p>
</fn>
<fn fn-type="edited-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/2098404/overview">Sathish Kumar Palaniappan</ext-link>, King Mongkut&#x2019;s University of Technology North Bangkok, Thailand</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/2098429/overview">Prabhu Paramasivam</ext-link>, Mettu University, Ethiopia</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/2099777/overview">Lakshmipathy R</ext-link>., KCG College of Technology, India</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/2099882/overview">Subash Thanappan</ext-link>, Ambo University, Ethiopia</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Sayed M. Eldin, <email>sayed.eldin22@fue.edu.eg</email>
</corresp>
<fn fn-type="other">
<p>This article was submitted to Polymeric and Composite Materials, a section of the journal Frontiers in Materials</p>
</fn>
</author-notes>
<pub-date pub-type="epub">
<day>30</day>
<month>01</month>
<year>2023</year>
</pub-date>
<pub-date pub-type="collection">
<year>2023</year>
</pub-date>
<volume>10</volume>
<elocation-id>1096839</elocation-id>
<history>
<date date-type="received">
<day>12</day>
<month>11</month>
<year>2022</year>
</date>
<date date-type="accepted">
<day>02</day>
<month>01</month>
<year>2023</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2023 Raja, AL-bonsrulah, Gnanasekaran, Eldin, Rajendran, Baskaran and Sakthivel.</copyright-statement>
<copyright-year>2023</copyright-year>
<copyright-holder>Raja, AL-bonsrulah, Gnanasekaran, Eldin, Rajendran, Baskaran and Sakthivel</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p>
</license>
</permissions>
<abstract>
<p>This work aims to design a rotary-wing unmanned aerial system (RUAS) that monitors the pollutants and minimizes their concentration in the atmosphere. This RUAS could be well suited for implementation in cities such as New Delhi and Ghaziabad, where air pollution is a major concern. This RUAV&#x2019;s well-thought-out design and use would be good for the environment also a step forward in the technology of UASs. Therefore, an advanced approach in design as well as innovative computational composite materials development based on structural analysis of this RUAS has been made. The major components involved in this comprehensive investigation are the fuselage, main rotor and tail rotor of RUAS. The aerodynamic parameters on RUAS have been estimated through the advanced technique adopted computational fluid dynamics approach using ANSYS Fluent 17.2. The finite element analysis (FEA) of the RUAS imposed under two different approaches enforced on lightweight composite materials has been estimated through ANSYS Structural 17.2. Firstly, the advanced computational platform for the development of composite materials has been created through the ANSYS Composite Preprocessor tool 17.2, wherein computational moldings of the fuselages of RUAV are framed. The computational moldings are greatly supported and so the conventional polymer matrix composites, metal matrix based composites, and advanced hybrid composites are well prepared. A ll of these uniquely framed materials have undergone computational structural investigations, and the material suitable for RUAVs has thus been selected. The computational tests are validated with advanced experimental outcomes, which furthermore enhanced the reliability of this proposed work. Additionally, the main rotor and entire RUAV are also computationally investigated under aerodynamic loading conditions through fluid structure interaction (FSI) approach. At last, the suitable lightweight material for all the parts of RUAS is shortlisted through innovative integrated computational engineering analyses.</p>
</abstract>
<kwd-group>
<kwd>computational composites</kwd>
<kwd>deformation analysis</kwd>
<kwd>RUAV</kwd>
<kwd>stresses</kwd>
<kwd>structural effects</kwd>
<kwd>composite material</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec id="s1">
<title>1 Introduction</title>
<p>The purpose of this study is to implement and evaluate a Rotary Wing Unmanned Aerial Vehicle (RUAV) for use in atmospheric pollution removal. The mission profile for this RUAV calls for a vertical takeoff, lengthy hover, and landing. The development of RUAV relied on a number of historical and standard pieces of information. After the initial conceptual design phase, this RUAV underwent extensive computer evaluations and computations to guarantee its reliability and practicality. The decision to use rotary wings was made. Because long periods of hovering and close observation of a location would not be possible with a fixed-wing structure, and <italic>vice versa</italic>. Compared to fixed-wing aircraft, rotary-wing RUAVs have the advantage of greater payload capacity. A rotary-wing aircraft would be more stable in high winds. Up until now, the military has made use of aircraft with medium-sized rotating wings (like helicopters) for tasks like border patrol, traffic monitoring, espionage, inspection, rescue, etc. The ultimate goal of this study is to put into practice a layout that is functional in residential and public settings. The planned RUAVs are very similar to helicopters, but they have some special features that set them apart. The sprayer mechanism is part of the 22.5&#xa0;kg payload that may be carried by this RUAV.</p>
<sec id="s1-1">
<title>1.1 Literature survey</title>
<p>Numerous articles concerning our application and UAVs are carefully examined, and information is gathered for earlier studies. The key findings from several study articles are briefly presented in the following passages. According to a study by Wienczyslaw et al., a helicopter&#x2019;s fuselage design, aerodynamic characteristics, and general effectiveness should be maximized during high-speed flight. Four types of fuselages were morphed and examined to determine the aerodynamic coefficients using a CFD (computational fluid dynamics) technique. In addition, this study used interactive design and numerical optimization based on the multi-objective genetic algorithm. To calculate the impacts of the main and tail rotors on the flow field, cumulative distribution function computations were performed (<xref ref-type="bibr" rid="B31">Stalewski and Zoltak, 2012</xref>). With the aid of precise geometric information for the blades in a given range, <xref ref-type="bibr" rid="B30">Slavik (2004)</xref> discussed the preliminary analysis of the propeller thrust and the power coefficients according to the forward ratio. This method can be improved further by considering the impacts of the Mach number tip, the aerodynamics of airfoils, and investigating the impact of blade numbers.</p>
<p>The conception and basic design of a small helicopter were covered by <xref ref-type="bibr" rid="B6">Krenik and Weiand (2016)</xref> The investigation was conducted progressively. It began with the estimation of component weights using common weight models. The VSAERO software was used to estimate the fuselage&#x2019;s aerodynamics. The HOST tool was used to estimate the control dynamics of rotor blades. There is also justification for several other parameters, including energy ratio, blade loading, blade twist, etc. A novel idea for a universal helicopter design was investigated and numerically implemented. <xref ref-type="bibr" rid="B5">Kania et al. (2007)</xref> described the airfoil design with maximum efficiency appropriate for helicopter rotor blades. The airfoil was numerically designed, analyzed, and empirically validated by the authors using wind tunnel testing. The outcomes are attained because the newly developed rotor blade airfoils of the ILH3XX series and the tail rotor blade airfoils of the ILT212 series are more effective than the other airfoils already in use. <xref ref-type="bibr" rid="B32">Tamer et al. (2011)</xref> discussed how to design and optimize the helicopter rotor blades with the least amount of power needed. The rotor diameter, number of blades, and airfoil needed inputs were selected using historical data and the xBEM tool. The CAMRAD JA analysis tool and the CONMIN algorithm were coupled to produce the desired design optimization outcome in this study. The xBEM was used to perform the aerodynamic evaluations of the optimized blades. This rotor blade optimization offers a practical method for rotorcraft design to improve several factors, including maximum performance, improved stability, reduced vibration, and lower cost. For the structural size of a rotorcraft fuselage, Dominik B et al. adopted an integrated design technique. The linear-elastic ANSYS solver was used to analyze static calculations of the fuselage airframe. The sizing procedure was carried out under various loading circumstances. This study also covered the aerodynamic loading brought on by the primary rotor&#x2019;s interactions with other parts (<xref ref-type="bibr" rid="B27">Schwinn et al., 2018</xref>). <xref ref-type="bibr" rid="B7">Li and Chen (2010)</xref> and others created a new mathematical framework to analyze helicopters in great detail. The model was created with six degrees of freedom, linked flap-lag-torsion elastic rotor blade motion, coupled unstable aerodynamics with dynamic stall, and high-order dynamic wake models. Discrete beam elements were created from the rotor blade. The Galerkin approach of weighted residuals was the foundation for formulating the finite element analysis. The structural operator is validated between the UMARC model and the UH-60 helicopter. They decided to put up with one another. The fundamental method for designing helicopters was created by <xref ref-type="bibr" rid="B8">Luka (2016)</xref> This technique uses statistical modeling of the key characteristics of the performance and size of currently existing, comparable helicopters, as well as the usage and development of the rotary wing performance equation. Data from current helicopters were gathered, and the parameters determined by statistical modeling were compared. The typical difference was 20.78%, which was satisfactory for a test design. The performance of the helicopter&#x2019;s rotor tip blade was examined by <xref ref-type="bibr" rid="B3">Barakos (2013)</xref> The three main varieties on the rotor blade have been identified as parabolic tips, tapped tops, and BERP tips. Data on the rotor tips of helicopters from the past and now have been examined. The failure to achieve the ideal tip form was likely caused by the absence of the tools required for proper evaluation. Modern, high-resolution CFD techniques can now provide a more thorough understanding of the aerodynamics of blades and tips and will soon advance quickly enough to improve the design process.</p>
<p>Basset et al. Analyzed and outlined the techniques used in the past and present to pre-size rotary-wing UAVs that were done on earlier UAV initiatives like MAVDEM, ExDro, and CAPECON. The most recent CREATION, the Onera UAV project, was developed with helpful input from earlier initiatives. The development of a numerical approach for the analysis and validation of rotorcraft performance characteristics and environmental impact is the main goal of CREATION (<xref ref-type="bibr" rid="B33">Tremolet&#x2019;s, 2014</xref>). <xref ref-type="bibr" rid="B38">Zhang et al. (2021)</xref> discussed the simulation of UAV collisions, which helps determine the safety of the UAV. Utilizing LS-Dyna software, high-accuracy finite element modeling was completed. The UAV was tested at various positions and angles to forecast the crash&#x2019;s impact. Experiments were also used to validate the FE model&#x2019;s findings. The structural layout of a UAV driven by solar energy was given by <xref ref-type="bibr" rid="B4">Chen et al. (2018)</xref> The author examined the strength of a high-end, long-range UAV during cruising and gusts. It was discovered that flutter-induced vibrations significantly contributed to the UAV&#x2019;s fatigue life. The UAV would sustain structural damage at 22.5&#xa0;m/s, according to the outcomes of the numerical calculations. <xref ref-type="bibr" rid="B13">Mo&#xeb;ll and Nordin (2008)</xref> suggested the helicopter&#x2019;s comprehensive design approach. All theoretical formulas were deduced, and explicit step-by-step design instructions were provided. This strategy aims to make computer-based design more accessible. The design process is extremely simple when using the design tool, and it takes only a little time from the start of a full concept. <xref ref-type="bibr" rid="B2">Atmaca et al. (2018)</xref> provided a succinct description of the behaviour and CFD analysis of a flock of UAVs. Each UAV creates aerodynamic forces while flying in flocks, which affects the other UAVs. The aerodynamic properties of UAV flocks were examined using CFD analysis. The CFD results showed that for sustained flying, flocks of UAVs need to maintain a specified distance from one another. The structural study of UAV airframes was the focus of Aadya Mishra et al. In all UAV designs, the airframe is one of the primary structural elements. UAV aerodynamics and structural integrity are both influenced by the airframe. The finite element method was used to keep track of its physical characteristics and vibrations. The structural analyses for fixed-wing and multi-copter UAVs were addressed in this paper, which showed how every moving part of the airframe might be examined for multi-copter UAVs (<xref ref-type="bibr" rid="B12">Mishra et al., 2020</xref>). <xref ref-type="bibr" rid="B25">Romeo and Frulla (2002)</xref> worked on creating long-endurance, high-altitude unmanned aerial vehicles at the Turin Polytechnic University. A preliminary design was created, and a HELIPLAT setup was performed. The monoplane Heliplat has two vertical tails, rudders, a very large horizontal stabilizer, and eight brushless motors. Estimates of wing lift distribution, pressure distribution, and the consequences of high aspect ratio wings were made using the VSAERO software. It was shown that the UAV performed better when the aspect ratio grew. Using the NASTRAN programme, the entire structure underwent a finite element analysis. The structural analysis of the UAV&#x2019;s wing and the landing gear was described by <xref ref-type="bibr" rid="B15">Park et al. (2011)</xref> After conducting a finite-element analysis and evaluating its structural performance, a composite target drone air vehicle was developed. The wing study also includes a static strength analysis and buckling investigation. The landing gear underwent a dynamic examination and a static strength analysis. The test showed that the wing tip deflection exceeded the finite element by 17%. The outcome is material and geometry flaws that develop throughout production. A tilt-rotor UAV design was created by <xref ref-type="bibr" rid="B26">Saharudin (2016)</xref> followed by structural analysis and validation. Additionally, a structural analysis of the wing of the UAV was conducted. The shear stress, bending stress, moment of inertia, stress-strain curve, etc., were calculated theoretically. A suitable material and a secure structural design for the wing were discovered from the outcomes of the finite element analysis. The important information collected from the literature surveys is listed in <xref ref-type="table" rid="T1">Table 1</xref>, <xref ref-type="table" rid="T2">Table 2</xref>, <xref ref-type="table" rid="T3">Table 3</xref>. After these tables, the next section is dealt the complete analytical procedures involved in the proposed design of RUAV. Thirdly, the imposed methodology and its problem formulations are provided. Fourthly, the four computational structural results are incorporated under the results and discussions section.</p>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Estimation of pitch angle chord length of main rotor blade.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Sl. No</th>
<th align="center">Location (inch)</th>
<th align="center">Pitch angle (&#x03B8;) (&#x00B0;)</th>
<th align="center">Chord length (inch)</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">1</td>
<td align="center">1.8</td>
<td align="center">54.78657</td>
<td align="center">3.561260085</td>
</tr>
<tr>
<td align="center">2</td>
<td align="center">3.6</td>
<td align="center">35.30548</td>
<td align="center">3.453365022</td>
</tr>
<tr>
<td align="center">3</td>
<td align="center">5.4</td>
<td align="center">25.27119</td>
<td align="center">2.910749385</td>
</tr>
<tr>
<td align="center">4</td>
<td align="center">7.2</td>
<td align="center">19.49657</td>
<td align="center">2.448313271</td>
</tr>
<tr>
<td align="center">5</td>
<td align="center">9</td>
<td align="center">15.81407</td>
<td align="center">2.09449821</td>
</tr>
<tr>
<td align="center">6</td>
<td align="center">10.8</td>
<td align="center">13.2804</td>
<td align="center">1.823554354</td>
</tr>
<tr>
<td align="center">7</td>
<td align="center">12.6</td>
<td align="center">11.4371</td>
<td align="center">1.611924912</td>
</tr>
<tr>
<td align="center">8</td>
<td align="center">14.4</td>
<td align="center">10.03851</td>
<td align="center">1.442982594</td>
</tr>
<tr>
<td align="center">9</td>
<td align="center">16.2</td>
<td align="center">8.942221</td>
<td align="center">1.305393753</td>
</tr>
<tr>
<td align="center">10</td>
<td align="center">18</td>
<td align="center">8.060376</td>
<td align="center">1.191362196</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>Estimation of Pitch angle &#x26; Chord length of Tail rotor blade.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Sl. No</th>
<th align="center">Location (inch)</th>
<th align="center">Pitch angle (&#x00B0;)</th>
<th align="center">Chord length (inch)</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">1</td>
<td align="center">0.422925</td>
<td align="center">56.79289</td>
<td align="center">0.922823375</td>
</tr>
<tr>
<td align="center">2</td>
<td align="center">0.84585</td>
<td align="center">37.36388</td>
<td align="center">0.929423767</td>
</tr>
<tr>
<td align="center">3</td>
<td align="center">1.268775</td>
<td align="center">26.97569</td>
<td align="center">0.798084295</td>
</tr>
<tr>
<td align="center">4</td>
<td align="center">1.6917</td>
<td align="center">20.89335</td>
<td align="center">0.677897024</td>
</tr>
<tr>
<td align="center">5</td>
<td align="center">2.114625</td>
<td align="center">16.98155</td>
<td align="center">0.583306212</td>
</tr>
<tr>
<td align="center">6</td>
<td align="center">2.53755</td>
<td align="center">14.27757</td>
<td align="center">0.509771211</td>
</tr>
<tr>
<td align="center">7</td>
<td align="center">2.960475</td>
<td align="center">12.30487</td>
<td align="center">0.451799418</td>
</tr>
<tr>
<td align="center">8</td>
<td align="center">3.3834</td>
<td align="center">10.80541</td>
<td align="center">0.405231071</td>
</tr>
<tr>
<td align="center">9</td>
<td align="center">3.806325</td>
<td align="center">9.628621</td>
<td align="center">0.367135167</td>
</tr>
<tr>
<td align="center">10</td>
<td align="center">4.22925</td>
<td align="center">8.681205</td>
<td align="center">0.335455702</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="T3" position="float">
<label>TABLE 3</label>
<caption>
<p>Important input parameters involved in CFD analysis.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th colspan="2" align="center">CFD inputs</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">Solver</td>
<td align="center">Pressure based</td>
</tr>
<tr>
<td align="center">Scheme</td>
<td align="center">Coupled</td>
</tr>
<tr>
<td align="center">Turbulence model</td>
<td align="center">Standard k-epsilon</td>
</tr>
<tr>
<td align="center">Element type</td>
<td align="center">Tetrahedral</td>
</tr>
<tr>
<td align="center">Inlet</td>
<td align="center">Velocity inlet</td>
</tr>
<tr>
<td align="center">Outlet</td>
<td align="center">Pressure outlet</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
</sec>
<sec id="s2">
<title>2 Proposed design&#x2013;Rotary wing UAV</title>
<p>The design flow of RUAV consists of several stages. The planned RUAV will be having a body like helicopter, one main rotor, and a nozzle mechanism for dropping payload. The historical relationships and literature survey gave the necessary data for the RUAV design calculations. With the help of design calculations, the conceptual design model of RUAV has been made using CATIA software. For ensuring the quality of design and for the optimization of the design, the CAD (computer aided drafting) model has been incorporated to ANSYS 17.2 Fluent for CFD analyzes, and the results will be obtained to get an optimized and efficient model of RUAV.</p>
<sec id="s2-1">
<title>2.1 Weight and thrust&#x2014;Calculations</title>
<p>From the historical data, the relationship between payload weight and maximum take-off weight is derived that is graphically represented in <xref ref-type="fig" rid="F1">Figure 1</xref>. The payload weight is assumed as 22.5&#xa0;kg to carry the cleaner for air pollution at large terminals like railway stations, bus stands, Temples, churches, etc., Based on the defence applications, the UAV&#x2019;s speed is assumed as 25&#xa0;m/s and the atmospheric velocity is measured as 3&#xa0;m/s.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Historical relationship derived for proposed rotary wing UAV.</p>
</caption>
<graphic xlink:href="fmats-10-1096839-g001.tif"/>
</fig>
<p>The payload weight is assumed as 22.5&#xa0;kg to carry the cleaner for air pollution at large terminals like railway stations, bus stands, temples, churches, etc., From <xref ref-type="fig" rid="F1">Figure 1</xref>, the historical relationship between overall weight of RUAV and its payload weight has been framed that is given in Eq. <xref ref-type="disp-formula" rid="e1">1</xref> (<xref ref-type="bibr" rid="B11">Mathaiyan et al., 2021</xref>; <xref ref-type="bibr" rid="B14">Murugesan et al., 2021</xref>; <xref ref-type="bibr" rid="B24">Raja et al., 2021</xref>; <xref ref-type="bibr" rid="B28">Senthilkumar et al., 2021</xref>; <xref ref-type="bibr" rid="B21">Raja et al., 2022a</xref>; <xref ref-type="bibr" rid="B36">Vijayanandh et al., 2022a</xref>; <xref ref-type="bibr" rid="B20">Raja et al., 2022b</xref>; <xref ref-type="bibr" rid="B23">Raja et al., 2022c</xref>; <xref ref-type="bibr" rid="B22">Raja et al., 2022d</xref>; <xref ref-type="bibr" rid="B18">Raja M. K. et al., 2022</xref>; <xref ref-type="bibr" rid="B37">Wang et al., 2022</xref>; <xref ref-type="bibr" rid="B19">Raja et al., 2023</xref>).<disp-formula id="e1">
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<label>(1)</label>
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<p>Based on the defence applications, the UAV&#x2019;s speed is assumed as 25&#xa0;m/s and the atmospheric velocity is measured as 3&#xa0;m/s.</p>
</sec>
<sec id="s2-2">
<title>2.2 Diameter of the main rotor</title>
<p>The thrust and power required by the main rotor of RUAV are expressed in Eqs <xref ref-type="disp-formula" rid="e2">2</xref>, <xref ref-type="disp-formula" rid="e3">3</xref>. The air enters the stream tube with velocity Vc and then acquires an additional velocity Vi as it passes through the helicopter rotor disk, and finally, it forms the wake with a velocity Vc &#x2b; Vi. Applying the principles of conservation for mass, momentum, and energy like in the hover we get: The thrust force is equal to,<disp-formula id="e2">
<mml:math id="m3">
<mml:mrow>
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<mml:mo>&#x3d;</mml:mo>
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<mml:mo>&#x2d9;</mml:mo>
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<mml:mo>&#x3d;</mml:mo>
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</mml:mrow>
<mml:mo>.</mml:mo>
<mml:mn>2</mml:mn>
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<label>(2)</label>
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<p>At vertical climb without inclusion of drag, the thrust force is equal to, <inline-formula id="inf1">
<mml:math id="m4">
<mml:mrow>
<mml:mi>&#x03F1;</mml:mi>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">V</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">V</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
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<mml:mo>.</mml:mo>
<mml:mn>2</mml:mn>
<mml:msub>
<mml:mi mathvariant="normal">V</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. Let us assume the thrust of the propeller is generated 100% greater than the overall weight of the rotary wing UAV, Thus, <inline-formula id="inf2">
<mml:math id="m5">
<mml:mrow>
<mml:mi>&#x03F1;</mml:mi>
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<mml:mi mathvariant="normal">v</mml:mi>
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<mml:mo>.</mml:mo>
<mml:mn>2</mml:mn>
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<mml:mi mathvariant="normal">v</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
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<mml:mo>&#x2a;</mml:mo>
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<mml:mn>1.2256</mml:mn>
<mml:mo>&#x2a;</mml:mo>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
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<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
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</inline-formula>. Finally, the diameter of the main rotor is estimated as 36 inch (<xref ref-type="bibr" rid="B11">Mathaiyan et al., 2021</xref>; <xref ref-type="bibr" rid="B14">Murugesan et al., 2021</xref>; <xref ref-type="bibr" rid="B24">Raja et al., 2021</xref>; <xref ref-type="bibr" rid="B28">Senthilkumar et al., 2021</xref>; <xref ref-type="bibr" rid="B21">Raja et al., 2022a</xref>; <xref ref-type="bibr" rid="B36">Vijayanandh et al., 2022a</xref>; <xref ref-type="bibr" rid="B20">Raja et al., 2022b</xref>; <xref ref-type="bibr" rid="B23">Raja et al., 2022c</xref>; <xref ref-type="bibr" rid="B22">Raja et al., 2022d</xref>; <xref ref-type="bibr" rid="B18">Raja M. K. et al., 2022</xref>; <xref ref-type="bibr" rid="B37">Wang et al., 2022</xref>; <xref ref-type="bibr" rid="B19">Raja et al., 2023</xref>). The power consumed is given by the product of the thrust and the total velocity through the rotor disk, that is,<disp-formula id="e3">
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<mml:mi mathvariant="normal">P</mml:mi>
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<label>(3)</label>
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<mml:mrow>
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</sec>
<sec id="s2-3">
<title>2.3 Estimation of main rotor&#x2019;s pitch</title>
<p>The typical relationship between mechanical power required and its subordinates of drone design parameters is given in Eq. <xref ref-type="disp-formula" rid="e4">4</xref> (<xref ref-type="bibr" rid="B11">Mathaiyan et al., 2021</xref>; <xref ref-type="bibr" rid="B14">Murugesan et al., 2021</xref>; <xref ref-type="bibr" rid="B24">Raja et al., 2021</xref>; <xref ref-type="bibr" rid="B28">Senthilkumar et al., 2021</xref>; <xref ref-type="bibr" rid="B21">Raja et al., 2022a</xref>; <xref ref-type="bibr" rid="B36">Vijayanandh et al., 2022a</xref>; <xref ref-type="bibr" rid="B20">Raja et al., 2022b</xref>; <xref ref-type="bibr" rid="B23">Raja et al., 2022c</xref>; <xref ref-type="bibr" rid="B22">Raja et al., 2022d</xref>; <xref ref-type="bibr" rid="B18">Raja M. K. et al., 2022</xref>; <xref ref-type="bibr" rid="B37">Wang et al., 2022</xref>; <xref ref-type="bibr" rid="B19">Raja et al., 2023</xref>).<disp-formula id="e4">
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<label>(4)</label>
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<mml:mo>&#x21d2;</mml:mo>
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<mml:mi mathvariant="normal">t</mml:mi>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mi mathvariant="normal">h</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
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<mml:mo>&#x3d;</mml:mo>
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<mml:mtext>&#x2009;</mml:mtext>
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<mml:msup>
<mml:msub>
<mml:mi mathvariant="normal">R</mml:mi>
<mml:mrow>
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<p>Eq. 5 is representing the dynamic thrust relationship for drone, wherein the design parameters of propellers are plays major role. To proceed further, the additional unknowns presented are reduced through comparative relationship approach (<xref ref-type="bibr" rid="B11">Mathaiyan et al., 2021</xref>; <xref ref-type="bibr" rid="B14">Murugesan et al., 2021</xref>; <xref ref-type="bibr" rid="B24">Raja et al., 2021</xref>; <xref ref-type="bibr" rid="B28">Senthilkumar et al., 2021</xref>; <xref ref-type="bibr" rid="B21">Raja et al., 2022a</xref>; <xref ref-type="bibr" rid="B36">Vijayanandh et al., 2022a</xref>; <xref ref-type="bibr" rid="B20">Raja et al., 2022b</xref>; <xref ref-type="bibr" rid="B23">Raja et al., 2022c</xref>; <xref ref-type="bibr" rid="B22">Raja et al., 2022d</xref>; <xref ref-type="bibr" rid="B18">Raja M. K. et al., 2022</xref>; <xref ref-type="bibr" rid="B37">Wang et al., 2022</xref>; <xref ref-type="bibr" rid="B19">Raja et al., 2023</xref>). <disp-formula id="equ104">
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<mml:mo>&#x3d;</mml:mo>
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</mml:mrow>
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<mml:mi mathvariant="normal">R</mml:mi>
</mml:mrow>
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</p>
<p>From the literature survey it was found that propeller hub thicknesses are varies from 48.9&#xa0;mm to 50&#xa0;mm, the internal diameter of hub is 32&#xa0;mm, and external diameter of hub is 50&#xa0;mm. From the base of pitch description, the pitch relationship is expressed in Eq. <xref ref-type="disp-formula" rid="e6">6</xref> (<xref ref-type="bibr" rid="B11">Mathaiyan et al., 2021</xref>; <xref ref-type="bibr" rid="B14">Murugesan et al., 2021</xref>; <xref ref-type="bibr" rid="B24">Raja et al., 2021</xref>; <xref ref-type="bibr" rid="B28">Senthilkumar et al., 2021</xref>; <xref ref-type="bibr" rid="B21">Raja et al., 2022a</xref>; <xref ref-type="bibr" rid="B36">Vijayanandh et al., 2022a</xref>; <xref ref-type="bibr" rid="B20">Raja et al., 2022b</xref>; <xref ref-type="bibr" rid="B23">Raja et al., 2022c</xref>; <xref ref-type="bibr" rid="B22">Raja et al., 2022d</xref>; <xref ref-type="bibr" rid="B18">Raja M. K. et al., 2022</xref>; <xref ref-type="bibr" rid="B37">Wang et al., 2022</xref>; <xref ref-type="bibr" rid="B19">Raja et al., 2023</xref>).<disp-formula id="e6">
<mml:math id="m13">
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<mml:mo>&#x3d;</mml:mo>
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<mml:mi mathvariant="normal">i</mml:mi>
<mml:mi mathvariant="normal">o</mml:mi>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
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<mml:mi mathvariant="normal">e</mml:mi>
<mml:mi mathvariant="normal">r</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
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<mml:mi mathvariant="normal">c</mml:mi>
<mml:mi mathvariant="normal">o</mml:mi>
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<mml:mtext>&#x2009;</mml:mtext>
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<mml:mi mathvariant="normal">o</mml:mi>
<mml:mi mathvariant="normal">l</mml:mi>
<mml:mi mathvariant="normal">u</mml:mi>
<mml:mi mathvariant="normal">t</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
<mml:mi mathvariant="normal">o</mml:mi>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mi mathvariant="normal">s</mml:mi>
</mml:mrow>
<mml:mi mathvariant="normal">s</mml:mi>
</mml:mfrac>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x3d;</mml:mo>
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</mml:mrow>
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<mml:mi mathvariant="normal">o</mml:mi>
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<mml:mi mathvariant="normal">i</mml:mi>
<mml:mi mathvariant="normal">o</mml:mi>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
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<label>(6)</label>
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<mml:mrow>
<mml:mi mathvariant="normal">M</mml:mi>
<mml:mi mathvariant="normal">R</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>984.252</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>61.29999997548</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>16</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi mathvariant="normal">i</mml:mi>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mi mathvariant="normal">c</mml:mi>
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</mml:mrow>
</mml:math>
</disp-formula>
</p>
</sec>
<sec id="s2-4">
<title>2.4 Estimation of pitch angle and chord of the main rotor</title>
<p>For specific locations on the rotor blade, the pitch angle and chord length are determined using <xref ref-type="disp-formula" rid="e7">Formulae 7</xref>, <xref ref-type="disp-formula" rid="e8">8</xref>. For sample calculation the 10% of radius, i.e., r &#x3d; 1.8 inch, has been picked (<xref ref-type="bibr" rid="B11">Mathaiyan et al., 2021</xref>; <xref ref-type="bibr" rid="B14">Murugesan et al., 2021</xref>; <xref ref-type="bibr" rid="B24">Raja et al., 2021</xref>; <xref ref-type="bibr" rid="B28">Senthilkumar et al., 2021</xref>; <xref ref-type="bibr" rid="B21">Raja et al., 2022a</xref>; <xref ref-type="bibr" rid="B36">Vijayanandh et al., 2022a</xref>; <xref ref-type="bibr" rid="B20">Raja et al., 2022b</xref>; <xref ref-type="bibr" rid="B23">Raja et al., 2022c</xref>; <xref ref-type="bibr" rid="B22">Raja et al., 2022d</xref>; <xref ref-type="bibr" rid="B18">Raja M. K. et al., 2022</xref>; <xref ref-type="bibr" rid="B37">Wang et al., 2022</xref>; <xref ref-type="bibr" rid="B19">Raja et al., 2023</xref>).<disp-formula id="e7">
<mml:math id="m15">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b8;</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">M</mml:mi>
<mml:mi mathvariant="normal">R</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mi mathvariant="normal">a</mml:mi>
<mml:mi mathvariant="normal">r</mml:mi>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mi mathvariant="normal">t</mml:mi>
<mml:mi mathvariant="normal">a</mml:mi>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mi mathvariant="normal">g</mml:mi>
<mml:mi mathvariant="normal">e</mml:mi>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mi mathvariant="normal">t</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mfrac>
<mml:msub>
<mml:mi mathvariant="normal">p</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">M</mml:mi>
<mml:mi mathvariant="normal">R</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mo>&#x2a;</mml:mo>
<mml:mi mathvariant="normal">&#x3c0;</mml:mi>
<mml:mo>&#x2a;</mml:mo>
<mml:mi mathvariant="normal">r</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(7)</label>
</disp-formula>
<disp-formula id="equ7">
<mml:math id="m16">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b8;</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">M</mml:mi>
<mml:mi mathvariant="normal">R</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mi mathvariant="normal">a</mml:mi>
<mml:mi mathvariant="normal">r</mml:mi>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mi mathvariant="normal">t</mml:mi>
<mml:mi mathvariant="normal">a</mml:mi>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mi mathvariant="normal">g</mml:mi>
<mml:mi mathvariant="normal">e</mml:mi>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mi mathvariant="normal">t</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mfrac>
<mml:mn>16</mml:mn>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mo>&#x2a;</mml:mo>
<mml:mi mathvariant="normal">&#x3c0;</mml:mi>
<mml:mo>&#x2a;</mml:mo>
<mml:mn>1.8</mml:mn>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x21d2;</mml:mo>
<mml:msub>
<mml:mi>&#x3b8;</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">M</mml:mi>
<mml:mi mathvariant="normal">R</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>54.76</mml:mn>
<mml:mi mathvariant="normal">&#x00B0;</mml:mi>
</mml:mrow>
</mml:math>
</disp-formula>
</p>
<p>The chord length is expressed in Eq. <xref ref-type="disp-formula" rid="e8">8</xref>,<disp-formula id="e8">
<mml:math id="m17">
<mml:mrow>
<mml:msub>
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<mml:mrow>
<mml:mi mathvariant="normal">M</mml:mi>
<mml:mi mathvariant="normal">R</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>8</mml:mn>
<mml:mo>&#x2a;</mml:mo>
<mml:mi>&#x3c0;</mml:mi>
<mml:mo>&#x2a;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mi>sin</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>&#x3b8;</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2a;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>tan</mml:mi>
<mml:mrow>
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<mml:mrow>
<mml:mi>&#x3b8;</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
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<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>1.2</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2a;</mml:mo>
<mml:mi>tan</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>&#x3b8;</mml:mi>
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</mml:mfenced>
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</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2b;</mml:mo>
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<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
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</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2a;</mml:mo>
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<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>&#x3b8;</mml:mi>
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</mml:mfenced>
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</mml:mfrac>
</mml:mrow>
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</mml:mrow>
<mml:mo>&#x2a;</mml:mo>
<mml:mi mathvariant="normal">r</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mo>&#x2a;</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">C</mml:mi>
<mml:mi mathvariant="normal">L</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(8)</label>
</disp-formula>
</p>
<p>The estimated C<sub>L</sub> is 0.5617034. Therefore,<disp-formula id="equ8">
<mml:math id="m18">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">b</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">M</mml:mi>
<mml:mi mathvariant="normal">R</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>8</mml:mn>
<mml:mo>&#x2a;</mml:mo>
<mml:mi mathvariant="normal">&#x3c0;</mml:mi>
<mml:mo>&#x2a;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mi>sin</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mn>54.7588</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2a;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>tan</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mn>54.7588</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>1.2</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2a;</mml:mo>
<mml:mi>tan</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mn>54.7588</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>1.2</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2a;</mml:mo>
<mml:mi>tan</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mn>54.7588</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2a;</mml:mo>
<mml:mn>1.8</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mo>&#x2a;</mml:mo>
<mml:mn>0.5617034</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x21d2;</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">b</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">M</mml:mi>
<mml:mi mathvariant="normal">R</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>3.558</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi mathvariant="normal">i</mml:mi>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mi mathvariant="normal">h</mml:mi>
</mml:mrow>
</mml:math>
</disp-formula>
</p>
<p>As similar as previously shown calculations, the other sectional calculations are determined. The complete design data of main rotor blade is listed in <xref ref-type="table" rid="T1">Table 1 </xref>(<xref ref-type="bibr" rid="B11">Mathaiyan et al., 2021</xref>; <xref ref-type="bibr" rid="B14">Murugesan et al., 2021</xref>; <xref ref-type="bibr" rid="B24">Raja et al., 2021</xref>; <xref ref-type="bibr" rid="B28">Senthilkumar et al., 2021</xref>; <xref ref-type="bibr" rid="B21">Raja et al., 2022a</xref>; <xref ref-type="bibr" rid="B36">Vijayanandh et al., 2022a</xref>; <xref ref-type="bibr" rid="B20">Raja et al., 2022b</xref>; <xref ref-type="bibr" rid="B23">Raja et al., 2022c</xref>; <xref ref-type="bibr" rid="B22">Raja et al., 2022d</xref>; <xref ref-type="bibr" rid="B18">Raja M. K. et al., 2022</xref>; <xref ref-type="bibr" rid="B37">Wang et al., 2022</xref>; <xref ref-type="bibr" rid="B19">Raja et al., 2023</xref>).</p>
</sec>
<sec id="s2-5">
<title>2.5 Estimation of diameter and pitch of the tail-rotor</title>
<p>From the historical data and literature survey the relationship between main rotor and tail rotor was obtained, which is expressed in Eq. <xref ref-type="disp-formula" rid="e9">9</xref> (<xref ref-type="bibr" rid="B11">Mathaiyan et al., 2021</xref>; <xref ref-type="bibr" rid="B14">Murugesan et al., 2021</xref>; <xref ref-type="bibr" rid="B24">Raja et al., 2021</xref>; <xref ref-type="bibr" rid="B28">Senthilkumar et al., 2021</xref>; <xref ref-type="bibr" rid="B21">Raja et al., 2022a</xref>; <xref ref-type="bibr" rid="B36">Vijayanandh et al., 2022a</xref>; <xref ref-type="bibr" rid="B20">Raja et al., 2022b</xref>; <xref ref-type="bibr" rid="B23">Raja et al., 2022c</xref>; <xref ref-type="bibr" rid="B22">Raja et al., 2022d</xref>; <xref ref-type="bibr" rid="B18">Raja M. K. et al., 2022</xref>; <xref ref-type="bibr" rid="B37">Wang et al., 2022</xref>; <xref ref-type="bibr" rid="B19">Raja et al., 2023</xref>).<disp-formula id="e9">
<mml:math id="m19">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">D</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">T</mml:mi>
<mml:mi mathvariant="normal">R</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0.149</mml:mn>
<mml:mo>&#x2a;</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">D</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">M</mml:mi>
<mml:mi mathvariant="normal">R</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>0.079</mml:mn>
</mml:mrow>
</mml:math>
<label>(9)</label>
</disp-formula>
<disp-formula id="equ9">
<mml:math id="m20">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">D</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">T</mml:mi>
<mml:mi mathvariant="normal">R</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0.149</mml:mn>
<mml:mo>&#x2a;</mml:mo>
<mml:mn>0.91172</mml:mn>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>0.079</mml:mn>
<mml:mo>&#x21d2;</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">D</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">T</mml:mi>
<mml:mi mathvariant="normal">R</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0.21484618871</mml:mn>
<mml:mi mathvariant="normal">m</mml:mi>
</mml:mrow>
</mml:math>
</disp-formula>
</p>
<p>The <inline-formula id="inf3">
<mml:math id="m21">
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<mml:msub>
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<mml:mrow>
<mml:mi mathvariant="normal">T</mml:mi>
<mml:mi mathvariant="normal">a</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
<mml:mi mathvariant="normal">l</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mi mathvariant="normal">i</mml:mi>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mi mathvariant="normal">d</mml:mi>
<mml:mi mathvariant="normal">u</mml:mi>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mi mathvariant="normal">e</mml:mi>
<mml:mi mathvariant="normal">d</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is assumed as 25&#xa0;m/s so the rotational velocity is estimated with the help of power required relationship that is expressed in Eq. <xref ref-type="disp-formula" rid="e10">10</xref>. The estimation of power for tail rotor consumed is given by the product of the thrust and the total velocity through the rotor disk, that is,<disp-formula id="e10">
<mml:math id="m22">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">P</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">T</mml:mi>
<mml:mi mathvariant="normal">R</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mi mathvariant="normal">T</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">V</mml:mi>
<mml:mi mathvariant="normal">c</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">V</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mi mathvariant="normal">T</mml:mi>
<mml:mo>.</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">V</mml:mi>
<mml:mi mathvariant="normal">c</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mi mathvariant="normal">T</mml:mi>
<mml:mo>.</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">V</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
<label>(10)</label>
</disp-formula>
</p>
<p>The <inline-formula id="inf4">
<mml:math id="m23">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="normal">T</mml:mi>
<mml:mi mathvariant="normal">h</mml:mi>
<mml:mi mathvariant="normal">r</mml:mi>
<mml:mi mathvariant="normal">u</mml:mi>
<mml:mi mathvariant="normal">s</mml:mi>
<mml:mi mathvariant="normal">t</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi mathvariant="normal">F</mml:mi>
<mml:mi mathvariant="normal">o</mml:mi>
<mml:mi mathvariant="normal">r</mml:mi>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mi mathvariant="normal">e</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="normal">T</mml:mi>
<mml:mi mathvariant="normal">R</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi mathvariant="normal">i</mml:mi>
<mml:mi mathvariant="normal">s</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mn>55.5116</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi mathvariant="normal">N</mml:mi>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> Therefore, <inline-formula id="inf5">
<mml:math id="m24">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">P</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">T</mml:mi>
<mml:mi mathvariant="normal">R</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>55.51163</mml:mn>
<mml:mo>&#x2a;</mml:mo>
<mml:mn>27</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mo>&#x21d2;</mml:mo>
<mml:mn>1498.81401</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi mathvariant="normal">W</mml:mi>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> Additionally, another power required relationship of tail rotor is expressed in Eq. <xref ref-type="disp-formula" rid="e11">11</xref>.<disp-formula id="e11">
<mml:math id="m25">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">P</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">T</mml:mi>
<mml:mi mathvariant="normal">R</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mi mathvariant="normal">k</mml:mi>
<mml:mo>&#x2a;</mml:mo>
<mml:msup>
<mml:msub>
<mml:mi mathvariant="normal">R</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">T</mml:mi>
<mml:mi mathvariant="normal">R</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mn>3</mml:mn>
</mml:msup>
<mml:mo>&#x2a;</mml:mo>
<mml:msup>
<mml:mi mathvariant="normal">D</mml:mi>
<mml:mn>4</mml:mn>
</mml:msup>
<mml:mo>&#x2a;</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">p</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">T</mml:mi>
<mml:mi mathvariant="normal">R</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
<label>(11)</label>
</disp-formula>
<disp-formula id="equ10">
<mml:math id="m26">
<mml:mrow>
<mml:mn>1498.81401</mml:mn>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>5.3</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mo>&#x2a;</mml:mo>
<mml:mo>&#x2a;</mml:mo>
<mml:msup>
<mml:msub>
<mml:mi mathvariant="normal">R</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">T</mml:mi>
<mml:mi mathvariant="normal">R</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mn>3</mml:mn>
</mml:msup>
<mml:mo>&#x2a;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>8.4585</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mn>4</mml:mn>
</mml:msup>
<mml:mo>&#x2a;</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">p</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">T</mml:mi>
<mml:mi mathvariant="normal">R</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x21d2;</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">p</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">T</mml:mi>
<mml:mi mathvariant="normal">R</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>55245697333303.7712</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
</mml:mrow>
<mml:msup>
<mml:msub>
<mml:mi mathvariant="normal">R</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">T</mml:mi>
<mml:mi mathvariant="normal">R</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mn>3</mml:mn>
</mml:msup>
</mml:mfrac>
</mml:mrow>
</mml:math>
</disp-formula>
</p>
<p>The thrust production relationship of tail rotor is expressed in Eq. <xref ref-type="disp-formula" rid="e12">12</xref> and then the pitch relationship is mentioned in Eq. <xref ref-type="disp-formula" rid="e13">13</xref> (<xref ref-type="bibr" rid="B11">Mathaiyan et al., 2021</xref>; <xref ref-type="bibr" rid="B14">Murugesan et al., 2021</xref>; <xref ref-type="bibr" rid="B24">Raja et al., 2021</xref>; <xref ref-type="bibr" rid="B28">Senthilkumar et al., 2021</xref>; <xref ref-type="bibr" rid="B21">Raja et al., 2022a</xref>; <xref ref-type="bibr" rid="B36">Vijayanandh et al., 2022a</xref>; <xref ref-type="bibr" rid="B20">Raja et al., 2022b</xref>; <xref ref-type="bibr" rid="B23">Raja et al., 2022c</xref>; <xref ref-type="bibr" rid="B22">Raja et al., 2022d</xref>; <xref ref-type="bibr" rid="B18">Raja M. K. et al., 2022</xref>; <xref ref-type="bibr" rid="B37">Wang et al., 2022</xref>; <xref ref-type="bibr" rid="B19">Raja et al., 2023</xref>).<disp-formula id="e12">
<mml:math id="m27">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">T</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">T</mml:mi>
<mml:mi mathvariant="normal">R</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>4.392399</mml:mn>
<mml:mo>&#x2a;</mml:mo>
<mml:msup>
<mml:mn>10</mml:mn>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>8</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mo>&#x2a;</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">R</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">T</mml:mi>
<mml:mi mathvariant="normal">R</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2a;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msup>
<mml:mi mathvariant="normal">d</mml:mi>
<mml:mn>3.5</mml:mn>
</mml:msup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:msqrt>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="normal">p</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
<mml:mi mathvariant="normal">t</mml:mi>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mi mathvariant="normal">h</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="normal">T</mml:mi>
<mml:mi mathvariant="normal">R</mml:mi>
</mml:mrow>
</mml:msub>
</mml:msqrt>
</mml:mfrac>
<mml:mo>&#x2a;</mml:mo>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:mn>4.23333</mml:mn>
<mml:mo>&#x2a;</mml:mo>
<mml:msup>
<mml:mn>10</mml:mn>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>4</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mo>&#x2a;</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">R</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">T</mml:mi>
<mml:mi mathvariant="normal">R</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2a;</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">p</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">T</mml:mi>
<mml:mi mathvariant="normal">R</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">V</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(12)</label>
</disp-formula>
<disp-formula id="equ11">
<mml:math id="m28">
<mml:mrow>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
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<label>(13)</label>
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</sec>
<sec id="s2-6">
<title>2.6 Estimation of pitch angle and chord of the tail rotor</title>
<p>As similar as main rotor calculation procedure, the tail rotor design parameters are determined. At 10% of radius, r &#x3d; 0.422925 inch (<xref ref-type="bibr" rid="B11">Mathaiyan et al., 2021</xref>; <xref ref-type="bibr" rid="B14">Murugesan et al., 2021</xref>; <xref ref-type="bibr" rid="B24">Raja et al., 2021</xref>; <xref ref-type="bibr" rid="B28">Senthilkumar et al., 2021</xref>; <xref ref-type="bibr" rid="B21">Raja et al., 2022a</xref>; <xref ref-type="bibr" rid="B36">Vijayanandh et al., 2022a</xref>; <xref ref-type="bibr" rid="B20">Raja et al., 2022b</xref>; <xref ref-type="bibr" rid="B23">Raja et al., 2022c</xref>; <xref ref-type="bibr" rid="B22">Raja et al., 2022d</xref>; <xref ref-type="bibr" rid="B18">Raja M. K. et al., 2022</xref>; <xref ref-type="bibr" rid="B37">Wang et al., 2022</xref>; <xref ref-type="bibr" rid="B19">Raja et al., 2023</xref>).<disp-formula id="equ13">
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<mml:mi mathvariant="normal">e</mml:mi>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mi mathvariant="normal">t</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
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<mml:mrow>
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<p>The chord length of the tail rotor is,<disp-formula id="equ14">
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<mml:mo>&#x3d;</mml:mo>
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<mml:mrow>
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<mml:mrow>
<mml:mi>&#x3b8;</mml:mi>
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<mml:mo>&#x2a;</mml:mo>
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<mml:mrow>
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<mml:mrow>
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<mml:mrow>
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<mml:mrow>
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</mml:mrow>
<mml:mrow>
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<mml:mrow>
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<mml:mrow>
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<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
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<p>The estimated C<sub>L</sub> is 0.539538. Therefore,<disp-formula id="equ15">
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<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">b</mml:mi>
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<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
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<mml:mo>&#x2a;</mml:mo>
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<mml:mrow>
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<mml:mrow>
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<mml:mrow>
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<mml:mrow>
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<mml:mi mathvariant="normal">n</mml:mi>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mi mathvariant="normal">h</mml:mi>
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<p>As similar as previously shown calculations, the other sectional calculations are determined. From the literature survey, the needful other details are found out, which are: propeller hub thickness is 10&#xa0;mm&#x2013;11.1&#xa0;mm, internal diameter of hub is 6.35&#xa0;mm, and external diameter of hub is 10&#xa0;mm (<xref ref-type="bibr" rid="B11">Mathaiyan et al., 2021</xref>; <xref ref-type="bibr" rid="B14">Murugesan et al., 2021</xref>; <xref ref-type="bibr" rid="B24">Raja et al., 2021</xref>; <xref ref-type="bibr" rid="B28">Senthilkumar et al., 2021</xref>; <xref ref-type="bibr" rid="B21">Raja et al., 2022a</xref>; <xref ref-type="bibr" rid="B36">Vijayanandh et al., 2022a</xref>; <xref ref-type="bibr" rid="B20">Raja et al., 2022b</xref>; <xref ref-type="bibr" rid="B23">Raja et al., 2022c</xref>; <xref ref-type="bibr" rid="B22">Raja et al., 2022d</xref>; <xref ref-type="bibr" rid="B18">Raja M. K. et al., 2022</xref>; <xref ref-type="bibr" rid="B37">Wang et al., 2022</xref>; <xref ref-type="bibr" rid="B19">Raja et al., 2023</xref>).</p>
</sec>
<sec id="s2-7">
<title>2.7 Estimation of the distance, which is between the main rotor shafts to the tail rotor shaft</title>
<p>Estimation of the distance that is between the main rotor shafts to the tail rotor shaft has been uniquely framed and also expressed in Eq. <xref ref-type="disp-formula" rid="e14">14</xref>. The other conventional as well as modified relationships relevant with main rotor are expressed in Eqs <xref ref-type="disp-formula" rid="e15">15</xref>, <xref ref-type="disp-formula" rid="e16">16</xref> (<xref ref-type="bibr" rid="B11">Mathaiyan et al., 2021</xref>; <xref ref-type="bibr" rid="B14">Murugesan et al., 2021</xref>; <xref ref-type="bibr" rid="B24">Raja et al., 2021</xref>; <xref ref-type="bibr" rid="B28">Senthilkumar et al., 2021</xref>; <xref ref-type="bibr" rid="B21">Raja et al., 2022a</xref>; <xref ref-type="bibr" rid="B36">Vijayanandh et al., 2022a</xref>; <xref ref-type="bibr" rid="B20">Raja et al., 2022b</xref>; <xref ref-type="bibr" rid="B23">Raja et al., 2022c</xref>; <xref ref-type="bibr" rid="B22">Raja et al., 2022d</xref>; <xref ref-type="bibr" rid="B18">Raja M. K. et al., 2022</xref>; <xref ref-type="bibr" rid="B37">Wang et al., 2022</xref>; <xref ref-type="bibr" rid="B19">Raja et al., 2023</xref>).<disp-formula id="e14">
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</sec>
<sec id="s2-8">
<title>2.8 Estimation of overall length of the rotary wing UAV</title>
<p>The overall length of fuselage of RUAV is uniquely expressed in Eq. <xref ref-type="disp-formula" rid="e17">17</xref>, in which the conceptualization of RUAV has been played the major role (<xref ref-type="bibr" rid="B11">Mathaiyan et al., 2021</xref>; <xref ref-type="bibr" rid="B14">Murugesan et al., 2021</xref>; <xref ref-type="bibr" rid="B24">Raja et al., 2021</xref>; <xref ref-type="bibr" rid="B28">Senthilkumar et al., 2021</xref>; <xref ref-type="bibr" rid="B21">Raja et al., 2022a</xref>; <xref ref-type="bibr" rid="B36">Vijayanandh et al., 2022a</xref>; <xref ref-type="bibr" rid="B20">Raja et al., 2022b</xref>; <xref ref-type="bibr" rid="B23">Raja et al., 2022c</xref>; <xref ref-type="bibr" rid="B22">Raja et al., 2022d</xref>; <xref ref-type="bibr" rid="B18">Raja M. K. et al., 2022</xref>; <xref ref-type="bibr" rid="B37">Wang et al., 2022</xref>; <xref ref-type="bibr" rid="B19">Raja et al., 2023</xref>).<disp-formula id="e17">
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<label>(17)</label>
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<sec id="s2-9">
<title>2.9 Estimations of fuselage dimensions</title>
<p>The nature of this UAV is unmanned one so unwanted space for crew has been removed and thus the shape and dimensions of the fuselage of the RUAV is used form the standard symmetrical aerofoil. The implemented aerofoil is NACA-0024. The comprehensive fineness ratios between design parameters of fuselage of RUAV are derived in Eqs <xref ref-type="disp-formula" rid="e18">18</xref>, <xref ref-type="disp-formula" rid="e19">19</xref>, <xref ref-type="disp-formula" rid="e20">20</xref> (<xref ref-type="bibr" rid="B11">Mathaiyan et al., 2021</xref>; <xref ref-type="bibr" rid="B14">Murugesan et al., 2021</xref>; <xref ref-type="bibr" rid="B24">Raja et al., 2021</xref>; <xref ref-type="bibr" rid="B28">Senthilkumar et al., 2021</xref>; <xref ref-type="bibr" rid="B21">Raja et al., 2022a</xref>; <xref ref-type="bibr" rid="B36">Vijayanandh et al., 2022a</xref>; <xref ref-type="bibr" rid="B20">Raja et al., 2022b</xref>; <xref ref-type="bibr" rid="B23">Raja et al., 2022c</xref>; <xref ref-type="bibr" rid="B18">Raja M. K. et al., 2022</xref>; <xref ref-type="bibr" rid="B37">Wang et al., 2022</xref>; <xref ref-type="bibr" rid="B19">Raja et al., 2023</xref>).<disp-formula id="e18">
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<mml:mi mathvariant="normal">v</mml:mi>
<mml:mi mathvariant="normal">e</mml:mi>
<mml:mi mathvariant="normal">r</mml:mi>
<mml:mi mathvariant="normal">a</mml:mi>
<mml:mi mathvariant="normal">l</mml:mi>
<mml:mi mathvariant="normal">l</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi mathvariant="normal">L</mml:mi>
<mml:mi mathvariant="normal">e</mml:mi>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mi mathvariant="normal">g</mml:mi>
<mml:mi mathvariant="normal">t</mml:mi>
<mml:mi mathvariant="normal">h</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi mathvariant="normal">o</mml:mi>
<mml:mi mathvariant="normal">f</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi mathvariant="normal">t</mml:mi>
<mml:mi mathvariant="normal">h</mml:mi>
<mml:mi mathvariant="normal">e</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi mathvariant="normal">R</mml:mi>
<mml:mi mathvariant="normal">U</mml:mi>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mi mathvariant="normal">V</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0.20</mml:mn>
</mml:mrow>
</mml:math>
<label>(20)</label>
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<disp-formula id="equ23">
<mml:math id="m48">
<mml:mrow>
<mml:mo>&#x21d2;</mml:mo>
<mml:mi mathvariant="normal">L</mml:mi>
<mml:mi mathvariant="normal">e</mml:mi>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mi mathvariant="normal">g</mml:mi>
<mml:mi mathvariant="normal">t</mml:mi>
<mml:mi mathvariant="normal">h</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi mathvariant="normal">B</mml:mi>
<mml:mi mathvariant="normal">e</mml:mi>
<mml:mi mathvariant="normal">t</mml:mi>
<mml:mi mathvariant="normal">w</mml:mi>
<mml:mi mathvariant="normal">e</mml:mi>
<mml:mi mathvariant="normal">e</mml:mi>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi mathvariant="normal">N</mml:mi>
<mml:mi mathvariant="normal">o</mml:mi>
<mml:mi mathvariant="normal">s</mml:mi>
<mml:mi mathvariant="normal">e</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi mathvariant="normal">t</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
<mml:mi mathvariant="normal">p</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi mathvariant="normal">t</mml:mi>
<mml:mi mathvariant="normal">o</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi mathvariant="normal">f</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
<mml:mi mathvariant="normal">r</mml:mi>
<mml:mi mathvariant="normal">s</mml:mi>
<mml:mi mathvariant="normal">t</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mi mathvariant="normal">o</mml:mi>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mi mathvariant="normal">e</mml:mi>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mi mathvariant="normal">t</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mi mathvariant="normal">g</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi mathvariant="normal">p</mml:mi>
<mml:mi mathvariant="normal">o</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mi mathvariant="normal">t</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi mathvariant="normal">o</mml:mi>
<mml:mi mathvariant="normal">f</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi mathvariant="normal">w</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mi mathvariant="normal">g</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi mathvariant="normal">a</mml:mi>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mi mathvariant="normal">d</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi mathvariant="normal">f</mml:mi>
<mml:mi mathvariant="normal">u</mml:mi>
<mml:mi mathvariant="normal">s</mml:mi>
<mml:mi mathvariant="normal">e</mml:mi>
<mml:mi mathvariant="normal">l</mml:mi>
<mml:mi mathvariant="normal">a</mml:mi>
<mml:mi mathvariant="normal">g</mml:mi>
<mml:mi mathvariant="normal">e</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0.20</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mo>&#x2a;</mml:mo>
<mml:mn>64.61</mml:mn>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>12.922</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi mathvariant="normal">i</mml:mi>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mi mathvariant="normal">h</mml:mi>
<mml:mi mathvariant="normal">e</mml:mi>
<mml:mi mathvariant="normal">s</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>32.822</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mi mathvariant="normal">m</mml:mi>
</mml:mrow>
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</p>
<p>At hovering, the thrust force is equal to weight. <inline-formula id="inf6">
<mml:math id="m49">
<mml:mrow>
<mml:mi mathvariant="normal">T</mml:mi>
<mml:mi mathvariant="normal">h</mml:mi>
<mml:mi mathvariant="normal">r</mml:mi>
<mml:mi mathvariant="normal">u</mml:mi>
<mml:mi mathvariant="normal">s</mml:mi>
<mml:mi mathvariant="normal">t</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi mathvariant="normal">o</mml:mi>
<mml:mi mathvariant="normal">r</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi mathvariant="normal">L</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
<mml:mi mathvariant="normal">f</mml:mi>
<mml:mi mathvariant="normal">t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mi mathvariant="normal">W</mml:mi>
<mml:mi mathvariant="normal">e</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
<mml:mi mathvariant="normal">g</mml:mi>
<mml:mi mathvariant="normal">h</mml:mi>
<mml:mi mathvariant="normal">t</mml:mi>
<mml:mo>;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> So, the known relationships are expressed in Eqs <xref ref-type="disp-formula" rid="e21">21</xref>, <xref ref-type="disp-formula" rid="e22">22</xref>.<disp-formula id="e21">
<mml:math id="m50">
<mml:mrow>
<mml:mi mathvariant="normal">T</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mover accent="true">
<mml:mi mathvariant="normal">m</mml:mi>
<mml:mo>&#x2d9;</mml:mo>
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<mml:mi mathvariant="normal">w</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mover accent="true">
<mml:mi mathvariant="normal">m</mml:mi>
<mml:mo>&#x2d9;</mml:mo>
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<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:msub>
<mml:mi mathvariant="normal">V</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mi mathvariant="italic">&#x03F1;</mml:mi>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:msub>
<mml:mi mathvariant="normal">V</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:msub>
<mml:mi mathvariant="normal">V</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>2</mml:mn>
<mml:mi mathvariant="italic">&#x03F1;</mml:mi>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">V</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:math>
<label>(21)</label>
</disp-formula>
<disp-formula id="e22">
<mml:math id="m51">
<mml:mrow>
<mml:mi mathvariant="normal">T</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>2</mml:mn>
<mml:mi>&#x3c1;</mml:mi>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">V</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">h</mml:mi>
<mml:mi mathvariant="normal">o</mml:mi>
<mml:mi mathvariant="normal">v</mml:mi>
<mml:mi mathvariant="normal">e</mml:mi>
<mml:mi mathvariant="normal">r</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mi mathvariant="normal">t</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
<mml:mi mathvariant="normal">p</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mo>&#x3d;</mml:mo>
<mml:mi mathvariant="normal">W</mml:mi>
<mml:mi mathvariant="normal">e</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
<mml:mi mathvariant="normal">g</mml:mi>
<mml:mi mathvariant="normal">h</mml:mi>
<mml:mi mathvariant="normal">t</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi mathvariant="normal">o</mml:mi>
<mml:mi mathvariant="normal">f</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi mathvariant="normal">t</mml:mi>
<mml:mi mathvariant="normal">h</mml:mi>
<mml:mi mathvariant="normal">e</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi mathvariant="normal">R</mml:mi>
<mml:mi mathvariant="normal">U</mml:mi>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mi mathvariant="normal">V</mml:mi>
</mml:mrow>
</mml:math>
<label>(22)</label>
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<disp-formula id="equ24">
<mml:math id="m52">
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mi>&#x3c1;</mml:mi>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">V</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">h</mml:mi>
<mml:mi mathvariant="normal">o</mml:mi>
<mml:mi mathvariant="normal">v</mml:mi>
<mml:mi mathvariant="normal">e</mml:mi>
<mml:mi mathvariant="normal">r</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mi mathvariant="normal">t</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
<mml:mi mathvariant="normal">p</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>57.065</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mo>&#x2a;</mml:mo>
<mml:mn>9.81</mml:mn>
<mml:mo>&#x21d2;</mml:mo>
<mml:mi mathvariant="italic">&#x03F1;</mml:mi>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">V</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">h</mml:mi>
<mml:mi mathvariant="normal">o</mml:mi>
<mml:mi mathvariant="normal">v</mml:mi>
<mml:mi mathvariant="normal">e</mml:mi>
<mml:mi mathvariant="normal">r</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mi mathvariant="normal">t</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
<mml:mi mathvariant="normal">p</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>279.903825</mml:mn>
<mml:mo>&#x21d2;</mml:mo>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0.65252</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:msup>
<mml:mi mathvariant="normal">m</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:math>
</disp-formula>
<disp-formula id="equ25">
<mml:math id="m53">
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">V</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">h</mml:mi>
<mml:mi mathvariant="normal">o</mml:mi>
<mml:mi mathvariant="normal">v</mml:mi>
<mml:mi mathvariant="normal">e</mml:mi>
<mml:mi mathvariant="normal">r</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mi mathvariant="normal">t</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
<mml:mi mathvariant="normal">p</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>279.903825</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>0.79972521428571428571428571428572</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>350</mml:mn>
<mml:mo>&#x21d2;</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">V</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">h</mml:mi>
<mml:mi mathvariant="normal">o</mml:mi>
<mml:mi mathvariant="normal">v</mml:mi>
<mml:mi mathvariant="normal">e</mml:mi>
<mml:mi mathvariant="normal">r</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mi mathvariant="normal">t</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
<mml:mi mathvariant="normal">p</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>18.71</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi mathvariant="normal">m</mml:mi>
<mml:mo>/</mml:mo>
<mml:mi mathvariant="normal">s</mml:mi>
</mml:mrow>
</mml:math>
</disp-formula>
</p>
</sec>
<sec id="s2-10">
<title>2.10 Estimation of C<sub>L</sub> and C<sub>D</sub> for main rotor</title>
<p>For vertical climb, we know that, Lift &#x3d; Weight &#x2b; Drag; The relevant aerodynamic forces and their associates are mentioned in Eqs <xref ref-type="disp-formula" rid="e23">23</xref>, <xref ref-type="disp-formula" rid="e24">24</xref>, <xref ref-type="disp-formula" rid="e25">25</xref>. The parasite drag area (<inline-formula id="inf7">
<mml:math id="m54">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">P</mml:mi>
<mml:mo>.</mml:mo>
<mml:mi mathvariant="normal">D</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>) is expressed in Eq. <xref ref-type="disp-formula" rid="e23">23</xref> (<xref ref-type="bibr" rid="B11">Mathaiyan et al., 2021</xref>; <xref ref-type="bibr" rid="B14">Murugesan et al., 2021</xref>; <xref ref-type="bibr" rid="B24">Raja et al., 2021</xref>; <xref ref-type="bibr" rid="B28">Senthilkumar et al., 2021</xref>; <xref ref-type="bibr" rid="B21">Raja et al., 2022a</xref>; <xref ref-type="bibr" rid="B36">Vijayanandh et al., 2022a</xref>; <xref ref-type="bibr" rid="B20">Raja et al., 2022b</xref>; <xref ref-type="bibr" rid="B23">Raja et al., 2022c</xref>; <xref ref-type="bibr" rid="B22">Raja et al., 2022d</xref>; <xref ref-type="bibr" rid="B18">Raja M. K. et al., 2022</xref>; <xref ref-type="bibr" rid="B37">Wang et al., 2022</xref>; <xref ref-type="bibr" rid="B19">Raja et al., 2023</xref>).<disp-formula id="e23">
<mml:math id="m55">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">P</mml:mi>
<mml:mo>.</mml:mo>
<mml:mi mathvariant="normal">D</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mi mathvariant="normal">k</mml:mi>
<mml:mo>&#x2a;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">m</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">m</mml:mi>
<mml:mi mathvariant="normal">t</mml:mi>
<mml:mi mathvariant="normal">o</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mn>1000</mml:mn>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mfrac bevelled="true">
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:mfrac>
</mml:msup>
</mml:mrow>
</mml:math>
<label>(23)</label>
</disp-formula>Where, k varying from 9 (for old helicopters) to 2.5 for current low-drag helicopters<disp-formula id="equ26">
<mml:math id="m56">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">P</mml:mi>
<mml:mo>.</mml:mo>
<mml:mi mathvariant="normal">D</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>2.5</mml:mn>
<mml:mo>&#x2a;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mn>57.065</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>1000</mml:mn>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mfrac bevelled="true">
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<mml:mi mathvariant="normal">A</mml:mi>
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<p>The estimation of parasite drag is given in Eq. <xref ref-type="disp-formula" rid="e24">24</xref> and lift is mentioned in Eq. <xref ref-type="disp-formula" rid="e25">25</xref>.<disp-formula id="e24">
<mml:math id="m57">
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<label>(24)</label>
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</mml:msub>
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<label>(25)</label>
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<p>From the equilibrium force equation, the following steps are estimated.<disp-formula id="equ28">
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</p>
</sec>
<sec id="s2-11">
<title>2.11 Estimation of C<sub>L</sub> of tail&#x2013;Rotor</title>
<p>Another force balance equation is given in Eq. <xref ref-type="disp-formula" rid="e26">26</xref>, wherein drag is very low compared than main rotor so the tail rotor is assumed to be zero (<xref ref-type="bibr" rid="B11">Mathaiyan et al., 2021</xref>; <xref ref-type="bibr" rid="B14">Murugesan et al., 2021</xref>; <xref ref-type="bibr" rid="B24">Raja et al., 2021</xref>; <xref ref-type="bibr" rid="B28">Senthilkumar et al., 2021</xref>; <xref ref-type="bibr" rid="B21">Raja et al., 2022a</xref>; <xref ref-type="bibr" rid="B36">Vijayanandh et al., 2022a</xref>; <xref ref-type="bibr" rid="B20">Raja et al., 2022b</xref>; <xref ref-type="bibr" rid="B23">Raja et al., 2022c</xref>; <xref ref-type="bibr" rid="B22">Raja et al., 2022d</xref>; <xref ref-type="bibr" rid="B18">Raja M. K. et al., 2022</xref>; <xref ref-type="bibr" rid="B37">Wang et al., 2022</xref>; <xref ref-type="bibr" rid="B19">Raja et al., 2023</xref>).<disp-formula id="e26">
<mml:math id="m62">
<mml:mrow>
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<mml:mi mathvariant="normal">t</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
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<mml:mi mathvariant="normal">e</mml:mi>
<mml:mo>&#x2b;</mml:mo>
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<label>(26)</label>
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<mml:mfenced open="[" close="]" separators="|">
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<mml:mrow>
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<mml:mrow>
<mml:mn>1.2256</mml:mn>
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<mml:mo>&#x2a;</mml:mo>
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<mml:mi>&#x3c9;</mml:mi>
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<mml:mrow>
<mml:mo>&#x21d2;</mml:mo>
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</mml:msub>
<mml:mo>&#x3d;</mml:mo>
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<mml:mrow>
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<mml:mrow>
<mml:msup>
<mml:mi mathvariant="normal">&#x3c9;</mml:mi>
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<mml:mo>;</mml:mo>
<mml:mi mathvariant="normal">I</mml:mi>
<mml:mi mathvariant="normal">f</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi mathvariant="normal">&#x3c9;</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>6</mml:mn>
<mml:mo>&#x2a;</mml:mo>
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<mml:mo>&#x2b;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>4</mml:mn>
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</mml:mrow>
<mml:mn>24</mml:mn>
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<mml:mo>&#x3d;</mml:mo>
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<mml:mrow>
<mml:mi mathvariant="normal">m</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="normal">s</mml:mi>
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<mml:mo>;</mml:mo>
<mml:mi mathvariant="normal">s</mml:mi>
<mml:mi mathvariant="normal">o</mml:mi>
<mml:mo>;</mml:mo>
<mml:mtext>&#x2009;</mml:mtext>
<mml:msub>
<mml:mi mathvariant="normal">C</mml:mi>
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</sec>
<sec id="s2-12">
<title>2.12 Airfoil selection</title>
<p>The rotor blades should produce more lift with less drag in order to attain efficient flight. Reynolds number is taken as 1,000,000 for main rotor and 200,000 for tail rotor. Several airfoils are collected and plotted with their respective C<sub>D</sub> values. The C<sub>L</sub> required for main rotor blade is 0.561 and for tail rotor blade is 0.539. NACA 2412 is found to be the suitable airfoil for both main and tail rotor blades as it generates the required C<sub>L</sub> with the least C<sub>D</sub> among the other airfoils at given conditions. The comparative graphs of airfoils are depicted below (<xref ref-type="bibr" rid="B11">Mathaiyan et al., 2021</xref>; <xref ref-type="bibr" rid="B14">Murugesan et al., 2021</xref>; <xref ref-type="bibr" rid="B24">Raja et al., 2021</xref>; <xref ref-type="bibr" rid="B28">Senthilkumar et al., 2021</xref>; <xref ref-type="bibr" rid="B21">Raja et al., 2022a</xref>; <xref ref-type="bibr" rid="B36">Vijayanandh et al., 2022a</xref>; <xref ref-type="bibr" rid="B20">Raja et al., 2022b</xref>; <xref ref-type="bibr" rid="B23">Raja et al., 2022c</xref>; <xref ref-type="bibr" rid="B22">Raja et al., 2022d</xref>; <xref ref-type="bibr" rid="B18">Raja M. K. et al., 2022</xref>; <xref ref-type="bibr" rid="B37">Wang et al., 2022</xref>; <xref ref-type="bibr" rid="B19">Raja et al., 2023</xref>). The design includes the rotor blades with hub, and the payload mechanism along with the landing gear. From the theoretical calculations, the CAD model is designed using CATIA software. <xref ref-type="fig" rid="F2">Figure 2</xref> is the drafted representation of RUAV with dimensions.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>A typical representation of design draft of RUAV model.</p>
</caption>
<graphic xlink:href="fmats-10-1096839-g002.tif"/>
</fig>
</sec>
</sec>
<sec id="s3">
<title>3 Proposed methodologies&#x2013;Computational engineering analyses</title>
<sec id="s3-1">
<title>3.1 Computational models</title>
<p>For the preliminary CFD analysis, the CAD model of the RUAV is imported. The CFD analysis is carried out using ANSYS 17.2 Fluent tool. A cylindrical fluid domain is created as the computational domain. Upstream and downstream of the model 2C (two times of the characteristic length), 6C (six times of the characteristic length) is given respectively.</p>
</sec>
<sec id="s3-2">
<title>3.2 Discretization of models</title>
<p>For the structural analysis of the RUAV&#x2019;s fuselage, hybrid meshing is done with more than 5,000 elements for half fuselage model and 10,000 elements for full fuselage model. Similarly, the main rotor and full fuselage are also discretized. Through hybrid mesh facility, both uniform and non-uniform meshes are framed with the consideration of design. <xref ref-type="fig" rid="F3">Figures 3</xref>, <xref ref-type="fig" rid="F4">4</xref> are depicting the different mesh cases for finite element analysis such as half fuselage, full fuselage, and main rotor and complete RUAV.</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Mesh elements of half fuselage model&#x2013;isometric view.</p>
</caption>
<graphic xlink:href="fmats-10-1096839-g003.tif"/>
</fig>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>A typical isometric representation of discretized structure of RUAV.</p>
</caption>
<graphic xlink:href="fmats-10-1096839-g004.tif"/>
</fig>
</sec>
<sec id="s3-3">
<title>3.3 Boundary conditions</title>
<p>For inlet and outlet conditions velocity inlet and pressure outlet are chosen, and it is set as 25&#xa0;m/s, 0 Pascal, respectively. The pressure load obtained from the CFD analysis has been imported to the ANSYS structural section for the estimation of structural behaviour of the RUAV&#x2019;s fuselage. The uniformly distributed load has been applied over the fuselage. Finally, the comprehensive imposed boundary conditions on the fuselage models, and entire RUAV are revealed in <xref ref-type="fig" rid="F5">Figures 5</xref>, <xref ref-type="fig" rid="F6">6</xref>.</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>Detailed boundary conditions imposed on full fuselage model for FEA.</p>
</caption>
<graphic xlink:href="fmats-10-1096839-g005.tif"/>
</fig>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>Imposed boundary conditions on RUAV.</p>
</caption>
<graphic xlink:href="fmats-10-1096839-g006.tif"/>
</fig>
</sec>
<sec id="s3-4">
<title>3.4 Solver descriptions and governing equations</title>
<p>CFD analyses have been conducted using ANSYS Fluent tool. The authors have applied pressure based - incompressible flow solver. For getting accurate results, second order upwind spatial discretization has been used. Governing equations are the mathematical formulae which helps to perform the computational simulations. For modeling, they manage the expected behaviour of fluids in the surface provided by the code. Governing equations are the theoretical approximations for describing the fluid flow, structural representations and their components. The stress relationships of orthotropic materials (O.T) are provided in Eqs <xref ref-type="disp-formula" rid="e27">27</xref>&#x2013;<xref ref-type="disp-formula" rid="e29">29</xref> and for isentropic materials in Eqs <xref ref-type="disp-formula" rid="e30">30</xref>&#x2013;<xref ref-type="disp-formula" rid="e32">32</xref>.<disp-formula id="e27">
<mml:math id="m65">
<mml:mtable class="align" columnalign="left">
<mml:mtr>
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<mml:msubsup>
<mml:mrow>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi mathvariant="normal">&#x3c3;</mml:mi>
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<mml:mo>.</mml:mo>
<mml:mi mathvariant="normal">T</mml:mi>
</mml:mrow>
</mml:msubsup>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3c5;</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">r</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi mathvariant="normal">p</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="normal">O</mml:mi>
<mml:mo>.</mml:mo>
<mml:mi mathvariant="normal">T</mml:mi>
</mml:mrow>
</mml:msubsup>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>2</mml:mn>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3c5;</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">q</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi mathvariant="normal">p</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="normal">O</mml:mi>
<mml:mo>.</mml:mo>
<mml:mi mathvariant="normal">T</mml:mi>
</mml:mrow>
</mml:msubsup>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3c5;</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">r</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi mathvariant="normal">q</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="normal">O</mml:mi>
<mml:mo>.</mml:mo>
<mml:mi mathvariant="normal">T</mml:mi>
</mml:mrow>
</mml:msubsup>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3c5;</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">p</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi mathvariant="normal">r</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="normal">O</mml:mi>
<mml:mo>.</mml:mo>
<mml:mi mathvariant="normal">T</mml:mi>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3b5;</mml:mi>
<mml:mi mathvariant="normal">r</mml:mi>
<mml:mi mathvariant="normal">o</mml:mi>
</mml:msubsup>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:math>
<label>(29)</label>
</disp-formula>
<disp-formula id="e30">
<mml:math id="m68">
<mml:mrow>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3c3;</mml:mi>
<mml:mi mathvariant="normal">p</mml:mi>
<mml:mi mathvariant="normal">p</mml:mi>
</mml:msubsup>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">E</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mi mathvariant="normal">M</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3c5;</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mi mathvariant="normal">M</mml:mi>
</mml:mrow>
<mml:mi mathvariant="normal">p</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2b;</mml:mo>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3c5;</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mi mathvariant="normal">M</mml:mi>
</mml:mrow>
<mml:mi mathvariant="normal">p</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>2</mml:mn>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3c5;</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mi mathvariant="normal">M</mml:mi>
</mml:mrow>
<mml:mi mathvariant="normal">p</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3b5;</mml:mi>
<mml:mi mathvariant="normal">p</mml:mi>
<mml:mi mathvariant="normal">p</mml:mi>
</mml:msubsup>
<mml:mo>&#x2b;</mml:mo>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">E</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mi mathvariant="normal">M</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3c5;</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mi mathvariant="normal">M</mml:mi>
</mml:mrow>
<mml:mi mathvariant="normal">p</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2b;</mml:mo>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3c5;</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mi mathvariant="normal">M</mml:mi>
</mml:mrow>
<mml:mi mathvariant="normal">p</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>2</mml:mn>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3c5;</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mi mathvariant="normal">M</mml:mi>
</mml:mrow>
<mml:mi mathvariant="normal">p</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3b5;</mml:mi>
<mml:mi mathvariant="normal">q</mml:mi>
<mml:mi mathvariant="normal">p</mml:mi>
</mml:msubsup>
<mml:mo>&#x2b;</mml:mo>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">E</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mi mathvariant="normal">M</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3c5;</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mi mathvariant="normal">M</mml:mi>
</mml:mrow>
<mml:mi mathvariant="normal">p</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2b;</mml:mo>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3c5;</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mi mathvariant="normal">M</mml:mi>
</mml:mrow>
<mml:mi mathvariant="normal">p</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>2</mml:mn>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3c5;</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mi mathvariant="normal">M</mml:mi>
</mml:mrow>
<mml:mi mathvariant="normal">p</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3b5;</mml:mi>
<mml:mi mathvariant="normal">r</mml:mi>
<mml:mi mathvariant="normal">p</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:math>
<label>(30)</label>
</disp-formula>
<disp-formula id="e31">
<mml:math id="m69">
<mml:mrow>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3c3;</mml:mi>
<mml:mi mathvariant="normal">q</mml:mi>
<mml:mi mathvariant="normal">p</mml:mi>
</mml:msubsup>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">E</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mi mathvariant="normal">M</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3c5;</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mi mathvariant="normal">M</mml:mi>
</mml:mrow>
<mml:mi mathvariant="normal">p</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2b;</mml:mo>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3c5;</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mi mathvariant="normal">M</mml:mi>
</mml:mrow>
<mml:mi mathvariant="normal">p</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>2</mml:mn>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3c5;</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mi mathvariant="normal">M</mml:mi>
</mml:mrow>
<mml:mi mathvariant="normal">p</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3b5;</mml:mi>
<mml:mi mathvariant="normal">p</mml:mi>
<mml:mi mathvariant="normal">p</mml:mi>
</mml:msubsup>
<mml:mo>&#x2b;</mml:mo>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">E</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mi mathvariant="normal">M</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3c5;</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mi mathvariant="normal">M</mml:mi>
</mml:mrow>
<mml:mi mathvariant="normal">p</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2b;</mml:mo>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3c5;</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mi mathvariant="normal">M</mml:mi>
</mml:mrow>
<mml:mi mathvariant="normal">p</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>2</mml:mn>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3c5;</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mi mathvariant="normal">M</mml:mi>
</mml:mrow>
<mml:mi mathvariant="normal">p</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3b5;</mml:mi>
<mml:mi mathvariant="normal">q</mml:mi>
<mml:mi mathvariant="normal">p</mml:mi>
</mml:msubsup>
<mml:mo>&#x2b;</mml:mo>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">E</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mi mathvariant="normal">M</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3c5;</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mi mathvariant="normal">M</mml:mi>
</mml:mrow>
<mml:mi mathvariant="normal">p</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2b;</mml:mo>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3c5;</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mi mathvariant="normal">M</mml:mi>
</mml:mrow>
<mml:mi mathvariant="normal">p</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>2</mml:mn>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3c5;</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mi mathvariant="normal">M</mml:mi>
</mml:mrow>
<mml:mi mathvariant="normal">p</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3b5;</mml:mi>
<mml:mi mathvariant="normal">r</mml:mi>
<mml:mi mathvariant="normal">p</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:math>
<label>(31)</label>
</disp-formula>
<disp-formula id="e32">
<mml:math id="m70">
<mml:mrow>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3c3;</mml:mi>
<mml:mi mathvariant="normal">r</mml:mi>
<mml:mi mathvariant="normal">p</mml:mi>
</mml:msubsup>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">E</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mi mathvariant="normal">M</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3c5;</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mi mathvariant="normal">M</mml:mi>
</mml:mrow>
<mml:mi mathvariant="normal">p</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2b;</mml:mo>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3c5;</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mi mathvariant="normal">M</mml:mi>
</mml:mrow>
<mml:mi mathvariant="normal">p</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>2</mml:mn>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3c5;</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mi mathvariant="normal">M</mml:mi>
</mml:mrow>
<mml:mi mathvariant="normal">p</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3b5;</mml:mi>
<mml:mi mathvariant="normal">p</mml:mi>
<mml:mi mathvariant="normal">p</mml:mi>
</mml:msubsup>
<mml:mo>&#x2b;</mml:mo>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:mfrac>
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<label>(32)</label>
</disp-formula>
</p>
</sec>
<sec id="s3-5">
<title>3.5 Validational studies&#x2013;Through experimental test</title>
<p>To test the reliability of the imposed advanced computations procedures through ANSYS Workbench 17.2, the experimental test based validation test on the attained computational outcomes are mandatory. Thus, high-speed jet facility based experimental test results and this work imposed computational procedures based outcomes are compared with each other. The typical high-speed jet facility is revealed in <xref ref-type="fig" rid="F7">Figure 7</xref>.</p>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>Test setup for high pressure load development.</p>
</caption>
<graphic xlink:href="fmats-10-1096839-g007.tif"/>
</fig>
<p>The experimental tests are conducted at normal atmospheric condition at outside and high-pressurized conditions at inside the jet-path. The typical experimental test setup long with test specimen is revealed in <xref ref-type="fig" rid="F23">Figure 23</xref>.</p>
<p>The given high pressure is 40&#xa0;bar so the aluminium based test specimen is broken due to high aerodynamic load but the CFRP based test specimen is retained its structural integrity. The imposed test specimens of aluminium alloy and the typical structural failure of aluminium alloy based test specimen is revealed in <xref ref-type="fig" rid="F8">Figure 8</xref>. From the previous experimental results, it was found that the ultimate stress of the woven CFRP is 3,500&#xa0;MPa and the ultimate stress of the enhanced aluminium alloy is 690&#xa0;MPa. After successful conduction of experimental tests, the computational tests are computed in ANSYS Workbench 17.2. The design data of experimental test-up and computational test specimen are exactly given in the generation of computational platform of high-speed jet path associated with computational test specimen. The pressure inlet based computational simulation is carried out on the discretized model and so the needful pressure variation on the test specimen has been found. The typical aerodynamic pressure distribution in and over the test specimen is shown in <xref ref-type="fig" rid="F9">Figure 9</xref>. The computed aerodynamic pressure on the model is transferred into computationally developed aluminium alloy and CFRP based composite models thorough system coupling approach in ANSYS Workbench 17.2. Additionally, the FEA based solver is incorporated in this advanced computation and thereafter the ultimate equivalent stresses are obtained on both the models under imposed as well as transferred aerodynamic loading conditions. The structural outcomes of aluminium alloy and CFRP based composite models are projected in <xref ref-type="fig" rid="F10">Figures 10</xref>, <xref ref-type="fig" rid="F11">11</xref> respectively.</p>
<fig id="F8" position="float">
<label>FIGURE 8</label>
<caption>
<p>Test specimen after structural failure.</p>
</caption>
<graphic xlink:href="fmats-10-1096839-g008.tif"/>
</fig>
<fig id="F9" position="float">
<label>FIGURE 9</label>
<caption>
<p>Imported pressure on the computational test specimen.</p>
</caption>
<graphic xlink:href="fmats-10-1096839-g009.tif"/>
</fig>
<fig id="F10" position="float">
<label>FIGURE 10</label>
<caption>
<p>Ultimate Equivalent stress of Aluminium Alloy.</p>
</caption>
<graphic xlink:href="fmats-10-1096839-g010.tif"/>
</fig>
<fig id="F11" position="float">
<label>FIGURE 11</label>
<caption>
<p>Ultimate equivalent stress of CFRP woven based test specimen.</p>
</caption>
<graphic xlink:href="fmats-10-1096839-g011.tif"/>
</fig>
<p>From this computational procedure, it is found that the maximum equivalent stress of the woven CFRP is obtained as 2,853.3&#xa0;MPa and the maximum equivalent stress of the enhanced aluminium alloy is 2,157.7&#xa0;MPa. The current authors confirmed that, the imposed advanced FSI technique is developed breaking stress on aluminium alloy and allowable stress for CFRP test specimen. The experimental test setup also provided the broken test specimen of aluminum alloy and unbroken test specimen of CFRP. Thus, these imposed computational procedures can give reliable outcomes so it is finalized to impose on the various components of RUAV.</p>
</sec>
<sec id="s3-6">
<title>3.6 Validations studies&#x2013;Grid convergence tests</title>
<p>The second sensitivity test has been computed in this work, in which grid finalization based focal is chosen as primary factor. The deformations based computational outcomes are played the vital contributors on these grid convergence tests. Firstly, the deformation developed by the full fuselage model is investigated for various grid cases. The comprehensive sensitivity outcomes are shown in <xref ref-type="fig" rid="F12">Figure 12</xref>. From <xref ref-type="fig" rid="F12">Figure 12</xref>, 35,000 elements are finalized as suitable discrete counts for the production of reliable outcomes.</p>
<fig id="F12" position="float">
<label>FIGURE 12</label>
<caption>
<p>Total deformation on full fuselage of RUAV with Epoxy-Carbon-Woven-Wet.</p>
</caption>
<graphic xlink:href="fmats-10-1096839-g012.tif"/>
</fig>
</sec>
</sec>
<sec sec-type="results|discussion" id="s4">
<title>4 FEA results and discussions</title>
<p>Finite Element Analysis (FEA) is the simulation of a physical model using numerical mathematical equations referred to as the Finite Element Method (FEM). Engineers use FEM to reduce the production of physical prototypes and run computational analysis to optimize their designs. FEA is the primary computational analysis technique in industries (<xref ref-type="bibr" rid="B1">Arul Prakash et al., 2022</xref>; <xref ref-type="bibr" rid="B35">Vijayanandh et al., 2022b</xref>; <xref ref-type="bibr" rid="B34">Vijayanandh et al., 2022c</xref>; <xref ref-type="bibr" rid="B9">Madhavi et al., 2022</xref>; <xref ref-type="bibr" rid="B10">Malavika et al., 2022</xref>; <xref ref-type="bibr" rid="B16">Prabhu et al., 2022</xref>; <xref ref-type="bibr" rid="B17">Raj Kumar et al., 2022</xref>; <xref ref-type="bibr" rid="B29">Sivaguru et al., 2022</xref>).</p>
<sec id="s4-1">
<title>4.1 Results of half RUAV fuselage&#x2013;Various perspectives&#x2013;I</title>
<p>ANSYS structural software is used here to run and visualize the results of finite element analysis of a RUAV&#x2019;s fuselage. Initially, the half span of the fuselage has been analyzed with 8 different materials and from that, the best performing 5 materials have been imposed on the entire fuselage. Further to fine-tune the material, hybrid composites have been imposed on the fuselage. The hybrid composites are created by fusing the best performing individual materials. The materials used for analysis are epoxy-E-glass-UD, epoxy-S-glass-UD, epoxy-carbon-UD-prepreg, epoxy-carbon-UD-wet, epoxy-carbon-woven-prepreg, epoxy-carbon-woven-wet, epoxy-e-glass-wet, and aluminum alloy. As per the aforesaid structural boundary conditions and transferred aerodynamic loading conditions, the computational structural investigations are carried on two different fuselage models. Since the aerodynamic conditions are complicated in nature, the two models based structural investigations are computed. Through these two models based detailed outcomes, this paper can give exact material for aerodynamic load resistor in real-time applications. The important structural outcomes of both half, full fuselage, main rotor, and entire RUAV models are systematically shown in <xref ref-type="fig" rid="F13">Figures 13</xref>&#x2013;<xref ref-type="fig" rid="F30">30</xref>.</p>
<fig id="F13" position="float">
<label>FIGURE 13</label>
<caption>
<p>Total deformation on half fuselage of RUAV with Epoxy-Carbon-Woven-Wet.</p>
</caption>
<graphic xlink:href="fmats-10-1096839-g013.tif"/>
</fig>
<fig id="F14" position="float">
<label>FIGURE 14</label>
<caption>
<p>Total deformation on half fuselage of RUAV with GFRP and its associate materials.</p>
</caption>
<graphic xlink:href="fmats-10-1096839-g014.tif"/>
</fig>
<fig id="F15" position="float">
<label>FIGURE 15</label>
<caption>
<p>Equivalent stress on half fuselage of RUAV with GFRP and its associate materials.</p>
</caption>
<graphic xlink:href="fmats-10-1096839-g015.tif"/>
</fig>
<fig id="F16" position="float">
<label>FIGURE 16</label>
<caption>
<p>Total deformation on half fuselage of RUAV with CFRP and its associate materials.</p>
</caption>
<graphic xlink:href="fmats-10-1096839-g016.tif"/>
</fig>
<fig id="F17" position="float">
<label>FIGURE 17</label>
<caption>
<p>Equivalent stress on half fuselage of RUAV with CFRP and its associate materials.</p>
</caption>
<graphic xlink:href="fmats-10-1096839-g017.tif"/>
</fig>
<fig id="F18" position="float">
<label>FIGURE 18</label>
<caption>
<p>Total deformation on full fuselage of RUAV with Epoxy-Carbon-Woven-Wet.</p>
</caption>
<graphic xlink:href="fmats-10-1096839-g018.tif"/>
</fig>
<fig id="F19" position="float">
<label>FIGURE 19</label>
<caption>
<p>Total deformation on full fuselage of RUAV with GFRP and its associate materials.</p>
</caption>
<graphic xlink:href="fmats-10-1096839-g019.tif"/>
</fig>
<fig id="F20" position="float">
<label>FIGURE 20</label>
<caption>
<p>Equivalent stress on full fuselage of RUAV with GFRP and its associate materials.</p>
</caption>
<graphic xlink:href="fmats-10-1096839-g020.tif"/>
</fig>
<fig id="F21" position="float">
<label>FIGURE 21</label>
<caption>
<p>Total deformation on full fuselage of RUAV with CFRP and its associate materials.</p>
</caption>
<graphic xlink:href="fmats-10-1096839-g021.tif"/>
</fig>
<fig id="F22" position="float">
<label>FIGURE 22</label>
<caption>
<p>Equivalent stress on full fuselage of RUAV with CFRP and its associate materials.</p>
</caption>
<graphic xlink:href="fmats-10-1096839-g022.tif"/>
</fig>
<fig id="F23" position="float">
<label>FIGURE 23</label>
<caption>
<p>CFRP woven wet&#x2013;Total deformation.</p>
</caption>
<graphic xlink:href="fmats-10-1096839-g023.tif"/>
</fig>
<fig id="F24" position="float">
<label>FIGURE 24</label>
<caption>
<p>Equivalent stress&#x2013;GFRP-FR-4-Woven.</p>
</caption>
<graphic xlink:href="fmats-10-1096839-g024.tif"/>
</fig>
<fig id="F25" position="float">
<label>FIGURE 25</label>
<caption>
<p>Comprehensive report of total deformation of main rotor of RUAV.</p>
</caption>
<graphic xlink:href="fmats-10-1096839-g025.tif"/>
</fig>
<fig id="F26" position="float">
<label>FIGURE 26</label>
<caption>
<p>Comprehensive report of equivalent elastic stress of main rotor of RUAV.</p>
</caption>
<graphic xlink:href="fmats-10-1096839-g026.tif"/>
</fig>
<fig id="F27" position="float">
<label>FIGURE 27</label>
<caption>
<p>CFRP-woven-prepreg&#x2013;Total deformation.</p>
</caption>
<graphic xlink:href="fmats-10-1096839-g027.tif"/>
</fig>
<fig id="F28" position="float">
<label>FIGURE 28</label>
<caption>
<p>FR-4 based woven composite&#x2013;equivalent elastic stress.</p>
</caption>
<graphic xlink:href="fmats-10-1096839-g028.tif"/>
</fig>
<fig id="F29" position="float">
<label>FIGURE 29</label>
<caption>
<p>Comprehensive report of total deformation of RUAV.</p>
</caption>
<graphic xlink:href="fmats-10-1096839-g029.tif"/>
</fig>
<fig id="F30" position="float">
<label>FIGURE 30</label>
<caption>
<p>Comprehensive report of equivalent elastic stress of RUAV.</p>
</caption>
<graphic xlink:href="fmats-10-1096839-g030.tif"/>
</fig>
<p>Different lightweight conventional and hybrid composite materials have been developed by advanced composite development tool and so imported on RUAV fuselage shapes also analyzed through advanced engineering simulations. Since total deformations are plays major role in FEA approaches, the computational outcomes of deformed structures of various lightweight materials are revealed in <xref ref-type="fig" rid="F13">Figures 13</xref>&#x2013;<xref ref-type="fig" rid="F17">17</xref>. In addition to the deformations, and equivalent elastic stresses are investigated for both of the traditional and advanced composite aerospace materials. The comprehensive outcomes of various lightweight materials are revealed in <xref ref-type="fig" rid="F14">Figures 14</xref>&#x2013;<xref ref-type="fig" rid="F17">17</xref>. From the results of half fuselage simulation, three best performing materials have been sorted. They are Epoxy-Carbon-Woven-Wet, Epoxy-Carbon-Woven-Prepreg, and Aluminium alloy (<xref ref-type="bibr" rid="B1">Arul Prakash et al., 2022</xref>; <xref ref-type="bibr" rid="B35">Vijayanandh et al., 2022b</xref>; <xref ref-type="bibr" rid="B34">Vijayanandh et al., 2022c</xref>; <xref ref-type="bibr" rid="B9">Madhavi et al., 2022</xref>; <xref ref-type="bibr" rid="B10">Malavika et al., 2022</xref>; <xref ref-type="bibr" rid="B16">Prabhu et al., 2022</xref>; <xref ref-type="bibr" rid="B17">Raj Kumar et al., 2022</xref>; <xref ref-type="bibr" rid="B29">Sivaguru et al., 2022</xref>).</p>
</sec>
<sec id="s4-2">
<title>4.2 Results of full RUAV fuselage&#x2013;Various perspectives&#x2013;II</title>
<p>The best performing two materials from the full fuselage simulation are Epoxy-Carbon-Woven-Wet and Aluminium alloy. For this second modified computation, the same boundary conditions are imposed and thereafter the primary structural outcomes are computed. In the fine-tuning process with the hybrid composites, Epoxy-Carbon-Woven-Wet with Aluminium alloy produced the favorable output. The displaced structure of full fuselage of RUVA for important lightweight material is revealed in <xref ref-type="fig" rid="F18">Figure 18</xref>. The comprehensive FEA outcomes are revealed in <xref ref-type="fig" rid="F19">Figures 19</xref>&#x2013;<xref ref-type="fig" rid="F22">22</xref>.</p>
<p>
<xref ref-type="fig" rid="F19">Figures 19</xref>&#x2013;<xref ref-type="fig" rid="F22">22</xref> describe the graphical representation of different output values of RUAV&#x2019;s full fuselage analysis. Based on the extensive structural analysis, Epoxy-Carbon-Woven-Wet has been observed as the suitable individual composite material and Epoxy-Carbon-Woven-Wet with Aluminium alloy has been observed as the suitable hybrid composite material.</p>
</sec>
<sec id="s4-3">
<title>4.3 FSI investigation on main rotor of RUAV&#x2014;Various perspectives&#x2013;III</title>
<p>Fluid Structure Interaction (FSI) investigation has been carried out on the main rotor of RUAV under the given aerodynamic loadings and aforesaid boundary conditions. The major polymer matrix composites and relevant aerospace alloys are used as platform of this computational structural analysis. <xref ref-type="fig" rid="F23">Figures 23</xref>&#x2013;<xref ref-type="fig" rid="F26">26</xref> are demonstrate the important structural computational outcomes of RUAV&#x2019;s main rotor under different lightweight materials.</p>
</sec>
<sec id="s4-4">
<title>4.4 FSI investigation on complete RUAV&#x2014;Various perspectives&#x2013;IV</title>
<p>The complete RUAV has been subjected to a FSI study using the aforementioned aerodynamic loadings and boundary conditions. This computational structural study is based on the main polymer matrix composites and important aerospace alloys. The important computational structural outcomes of complete RUAV under various lightweight materials are revealed in <xref ref-type="fig" rid="F27">Figures 27</xref>&#x2013;<xref ref-type="fig" rid="F30">30</xref>.</p>
<p>From comprehensive main rotor <xref ref-type="fig" rid="F25">Figures 25</xref>, <xref ref-type="fig" rid="F26">26</xref>, as well as comprehensive <xref ref-type="fig" rid="F29">Figures 29</xref>, <xref ref-type="fig" rid="F30">30</xref>, the following observations are obtained: CFRP-UD-Wet is stiffer for main rotor construction; GFRP-E-Fabric is good to provide high lifetime for main rotor construction; CFRP-Woven-Wet is stiffer for entire RUAV construction; KFRP-UD-49 is good to provide high lifetime for main rotor construction.</p>
</sec>
</sec>
<sec sec-type="conclusion" id="s5">
<title>5 Conclusion</title>
<p>The design development, aerodynamic, and structural characteristics of the RUAV are the primary focuses of this study endeavor. In addition to the data that were obtained, comprehensive CFD and FEA computations were carried out in order to estimate the performance of the RUAV through advanced Fluid Structure Interaction based computational investigations. According to the findings of the CFD investigations, the maneuverings can be accomplished by elevating the main rotor&#x2019;s tilt angle in order to cause an increase in the side forces. The multiple reference frame analysis attempted to determine whether or not the force produced by the tail rotor is sufficient to counteract the force generated by the main rotor. The material that would work best for the design of the RUAV&#x2019;s fuselage was identified through the use of finite element analysis. The Epoxy-Carbon-Woven-Prepreg and aluminium alloy provided the most satisfying results to the loads in the half fuselage analysis. The Epoxy-Carbon-Woven-Wet and Aluminum alloy provided the most satisfying results to the loads in the half fuselage analysis. Thus, Epoxy-Carbon-Woven-Wet with Aluminum Alloy produced the favorable results in the structural aspects in terms of total deformation, equivalent stress, equivalent elastic strain, strain energy, and normal stress among the hybrid composites that were analyzed. Finally, Carbon Fiber based polymer matrix composite is shortlisted as best material for rotary wing UAV under all kind of complicated aerodynamic loading conditions. Finding the best material for the RUAV&#x2019;s primary rotor is a secondary goal of this forced FSI research. The primary rotor of the RUAV is analyzed because it is the part that is put under the most stress. This was demonstrated by prior test results. Eleven categories of substances were considered during the study. Total deformation, equivalent stress, equivalent elastic strain, and normal stress were all considered extensively during the research. Total deformation and equivalent elastic strain were found to be lowest for the aluminium alloy, and equivalent stress and normal stress were found to be lowest for the Epoxy-S Glass Unidirectional based composites. The following insights can be gleaned by looking at the comprehensive main rotor results: CFRP-Woven-Wet is stiffer for the entire RUAV construction; KFRP-UD-49 is good to provide high lifetime for main rotor construction; CFRP-UD-Wet is stiffer for the construction of the main rotor; GFRP-E-Fabric is good to provide high lifetime for the construction of the main rotor; and CFRP-UD-Wet is stiffer for the construction of the main rotor.</p>
</sec>
</body>
<back>
<sec sec-type="data-availability" id="s6">
<title>Data availability statement</title>
<p>The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.</p>
</sec>
<sec id="s7">
<title>Author contributions</title>
<p>Conceptualization, VR and PS; methodology, VR, RG, and BB; software, VR and RG; validation, VR and HAL-B.; formal analysis, VR and HAL-B; investigation, VR, BB, and RG; resources, VR, PS, and BB; data curation, VR and RG; writing&#x2014;original draft preparation, VR; writing&#x2014;review and editing, PS, BB, and VR; visualization, SE, HAL-B, and PR; supervision, PR and SE; project administration, SE and PR; funding acquisition, SE. All authors have read and agreed to the published version of the manuscript.</p>
</sec>
<sec id="s8">
<title>Funding</title>
<p>This work was partially funded by the research center of the Future University in Egypt, 2022.</p>
</sec>
<ack>
<p>These computing resources were generously provided by the Aircraft Design and Analyses Laboratory in the Department of Aeronautical Engineering at Kumaraguru College of Technology (KCT) in Coimbatore-641049, Tamil Nadu, India. Therefore, the authors of this piece appreciate the support of the company&#x2019;s upper management and the industry&#x2019;s finest.</p>
</ack>
<sec sec-type="COI-statement" id="s9">
<title>Conflict of interest</title>
<p>HAL-B was empolyed by the Iraqi Ministry of Oil, Midland Refineries Company.</p>
<p>The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec sec-type="disclaimer" id="s10">
<title>Publisher&#x2019;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
<ref-list>
<title>References</title>
<ref id="B1">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Arul Prakash</surname>
<given-names>R.</given-names>
</name>
<name>
<surname>Vijayanandh</surname>
<given-names>R.</given-names>
</name>
<name>
<surname>Naveen Kumar</surname>
<given-names>K.</given-names>
</name>
<name>
<surname>Raj Kumar</surname>
<given-names>G.</given-names>
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