{"id":11801,"date":"2025-01-07T23:58:17","date_gmt":"2025-01-08T04:58:17","guid":{"rendered":"https:\/\/blogs.mathworks.com\/student-lounge\/?p=11801"},"modified":"2025-02-21T10:14:26","modified_gmt":"2025-02-21T15:14:26","slug":"simulating-water-propelled-aircraft-for-airbus-sloshing-rocket-workshop","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/student-lounge\/2025\/01\/07\/simulating-water-propelled-aircraft-for-airbus-sloshing-rocket-workshop\/","title":{"rendered":"Simulating Water-Propelled Aircraft for Airbus Sloshing Rocket Workshop"},"content":{"rendered":"<div class=\"rtcContent\">\n<h2 id=\"H_3386\" style=\"margin: 20px 10px 5px 4px; padding: 0px; line-height: 20px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 20px; font-weight: bold; text-align: left;\">Introduction<\/h2>\n<div style=\"margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left;\">This work was developed by <a href=\"https:\/\/www.linkedin.com\/in\/piercarlo-mirto-4413a3228\/\"><span style=\"text-decoration: underline;\">Piercarlo Mirto<\/span><\/a> and <a href=\"https:\/\/www.linkedin.com\/in\/vincenzo-junior-di-rosa\/\"><span style=\"text-decoration: underline;\">Vincenzo Junior Di Rosa<\/span><\/a> master\u2019s students in Aerospace Engineering at the University of Naples Federico II. This was their contribution to the AirSloths team&#8217;s project presented to the <a href=\"https:\/\/sloshing.euroavia.eu\/\"><span style=\"font-weight: bold;\">Airbus Sloshing Rocket Workshop (<\/span><span style=\"font-weight: bold; text-decoration: underline;\">ASRW<\/span><span style=\"font-weight: bold;\">)<\/span><\/a> 2023 competition. Team AirSloths secured first position in the 2023 final, held in Belgrade.<\/div>\n<div style=\"margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left;\">The code aims to simulate the aircraft model&#8217;s flight and let the team optimize its geometry to maximize the flight range. Figure 1 shows the desired flight path.<\/div>\n<div style=\"margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left;\"><\/div>\n<div style=\"margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: center;\"><img decoding=\"async\" loading=\"lazy\" class=\"imageNode\" style=\"vertical-align: baseline; width: 320px; height: 319px;\" src=\"https:\/\/blogs.mathworks.com\/student-lounge\/files\/2025\/01\/25jan7_1.png\" alt=\"\" width=\"320\" height=\"319\" \/><\/div>\n<div style=\"margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: center;\">Figure 1 &#8211; Desired aircraft flight<\/div>\n<h3 id=\"H_0990\" style=\"margin: 15px 10px 5px 4px; padding: 0px; line-height: 18px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 17px; font-weight: bold; text-align: left;\"><\/h3>\n<div style=\"margin-bottom: 20px; padding-bottom: 4px;\">\n<div style=\"margin: 0px; padding: 10px 0px 10px 5px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: bold; text-align: start;\"><span style=\"font-weight: bold;\">Table of Contents<\/span><\/div>\n<div style=\"margin: -1px 0px 0px; padding: 10px 0px 10px 7px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: start;\"><a href=\"#H_3386\">Introduction<br \/>\n<\/a><a href=\"#H_2e0b\">Motivation<br \/>\n<\/a><a href=\"#H_74df\">Water-Propelled aircraft<br \/>\n<\/a><a href=\"#H_5502\">Aircraft mathematical modeling<br \/>\n<\/a> <a href=\"#H_742f\">Architecture setup<br \/>\n<\/a> <a href=\"#H_9ec1\">Inertial properties evaluation<br \/>\n<\/a> <a href=\"#H_99f4\">Aerodynamics modeling<br \/>\n<\/a> <a href=\"#H_4b3b\">Propulsion modeling<br \/>\n<\/a><a href=\"#H_5d45\">Flight simulation<br \/>\n<\/a> <a href=\"#H_37bb\">Aircraft dynamics modeling<br \/>\n<\/a> <a href=\"#H_9cfd\">Initial conditions<br \/>\n<\/a> <a href=\"#H_97ff\">Simulation results<br \/>\n<\/a><a href=\"#H_4a47\">Conclusions<\/a><\/div>\n<\/div>\n<h2 id=\"H_2e0b\" style=\"margin: 20px 10px 5px 4px; padding: 0px; line-height: 20px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 20px; font-weight: bold; text-align: left;\">Motivation<\/h2>\n<div style=\"margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left;\">The ASRW 2023 competition demands teams develop a low-cost reusable rocket-powered aerospace vehicle that is destabilized by the movement of water stored in an unpressurized tank located on the rear side of the vehicle. The vehicle design shall incorporate mechanisms to manage the dynamic forces introduced by the sloshing water to maximize its range, time of flight, and liquid payload capacity.<\/div>\n<div style=\"margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left;\">To achieve this goal of maximum range, endurance, and stable flight, the AirSloths team developed the simulation with MATLAB and Simulink to study the effect of tail contribution and optimize the vehicle design. This code was developed with the following assumptions:<\/div>\n<ul style=\"margin: 10px 0px 20px; padding-left: 0px; font-family: Helvetica, Arial, sans-serif; font-size: 14px;\">\n<li style=\"margin-left: 56px; line-height: 21px; min-height: 0px; text-align: left; white-space: pre-wrap;\">Complete aircraft is a rigid body.<\/li>\n<li style=\"margin-left: 56px; line-height: 21px; min-height: 0px; text-align: left; white-space: pre-wrap;\">There is zero sloshing.<\/li>\n<li style=\"margin-left: 56px; line-height: 21px; min-height: 0px; text-align: left; white-space: pre-wrap;\">There is zero latency in avionics.<\/li>\n<li style=\"margin-left: 56px; line-height: 21px; min-height: 0px; text-align: left; white-space: pre-wrap;\">Aircraft has longitudinal symmetry.<\/li>\n<\/ul>\n<div style=\"margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left;\">The main idea was to actively regulate the pitching moment law to alter the trajectory, a concept which led to a non-conventional design for the lifting surfaces, consisting of a foldable V-tail (Figure 2). Hence, the control law translated into an opening-angle change with the elevation angle, to smoothly change the configuration from a &#8220;rocket&#8221; (tail &#8220;closed&#8221;) into a &#8220;glider&#8221; (tail &#8220;open&#8221;). The aircraft must pitch down until it reaches a point after the apogee where the speed is enough to smoothly land through a pull-up maneuver. This tailplane also plays a crucial role in counteracting the destabilizing effects of liquid sloshing, ensuring a controlled descent.<\/div>\n<div style=\"margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left;\">This code contains additional files that can be accessed via the <a href=\"https:\/\/github.com\/VincenzoPiercarlo\/Simulating-Water-Propelled-Aircraft-for-ASRW\">GitHub repository<\/a>.<\/div>\n<h2 id=\"H_74df\" style=\"margin: 20px 10px 5px 4px; padding: 0px; line-height: 20px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 20px; font-weight: bold; text-align: left;\">Water-Propelled aircraft<\/h2>\n<div style=\"margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: center;\"><img decoding=\"async\" loading=\"lazy\" class=\"imageNode\" style=\"vertical-align: baseline; width: 440px; height: 250px;\" src=\"https:\/\/blogs.mathworks.com\/student-lounge\/files\/2025\/01\/25jan7_2.png\" alt=\"\" width=\"440\" height=\"250\" \/><\/div>\n<div style=\"margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: center;\">Figure 2 &#8211; Aircraft model CAD<\/div>\n<div style=\"margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left;\">The water rocket glider developed by the AirSloths team was engineered using lightweight and durable materials, mainly polar wood and polystyrene + carbon fiber reinforcement. The propulsion system utilized a 2-liter PET bottle, filled with 0.7 liters of water, pressurized to 10 bars, which provided the necessary thrust for takeoff. The sloshing tank was 3-D printed. The aircraft\u2019s flight computer measures key parameters such as altitude and elevation angle, with the latter being used to adjust the folding angle of the tailplane for precise control throughout the flight mission.<\/div>\n<div style=\"margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left;\"><\/div>\n<h2 id=\"H_5502\" style=\"margin: 3px 10px 5px 4px; padding: 0px; line-height: 20px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 20px; font-weight: bold; text-align: left;\">Aircraft mathematical modeling<\/h2>\n<h3 id=\"H_742f\" style=\"margin: 15px 10px 5px 4px; padding: 0px; line-height: 18px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 17px; font-weight: bold; text-align: left;\">Architecture setup<\/h3>\n<div style=\"margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left;\">To start modeling our aircraft, we used <a href=\"https:\/\/github.com\/VincenzoPiercarlo\/Simulating-Water-Propelled-Aircraft-for-ASRW\/blob\/main\/defineAircraftComponents.mlx\"><span style=\"font-family: monospace;\">defineAircraftComponents.mlx<\/span><\/a> to construct a data structure <a href=\"#M_01b1\">aircraftParts<\/a> to store the assigned geometric properties of the components. The defineAircraftComponents function was complemented with <a href=\"https:\/\/github.com\/VincenzoPiercarlo\/Simulating-Water-Propelled-Aircraft-for-ASRW\/blob\/main\/defineMaterialDensities.mlx\"><span style=\"font-family: monospace;\">defineMaterialDensities.mlx<\/span><\/a> to define densities of various component materials.<\/div>\n<div style=\"background-color: #f5f5f5; margin: 10px 15px 10px 0; display: inline-block;\">\n<div class=\"inlineWrapper\">\n<div id=\"M_01b1\" style=\"border-radius: 4px; padding: 6px 45px 4px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: #212121; font-family: Menlo, Monaco, Consolas, 'Courier New', monospace; font-size: 14px; border: 0.666667px solid #d9d9d9;\"><span style=\"white-space: pre;\">aircraftParts = defineAircraftComponents(defineMaterialDensities);<\/span><\/div>\n<\/div>\n<\/div>\n<div style=\"margin: 10px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left;\">Now that all aircraft components have been defined, we can create the aircraft model, as <a href=\"#M_5f16\">aircraftConfiguration<\/a> data structure, using <a href=\"https:\/\/github.com\/VincenzoPiercarlo\/Simulating-Water-Propelled-Aircraft-for-ASRW\/blob\/main\/buildAircraft.mlx\"><span style=\"font-family: monospace;\">buildAircraft.mlx<\/span><\/a>. The algorithm describes the latter as a system of material points.<\/div>\n<div style=\"background-color: #f5f5f5; margin: 10px 15px 10px 0; display: inline-block;\">\n<div class=\"inlineWrapper\">\n<div id=\"M_5f16\" style=\"border-radius: 4px; padding: 6px 45px 4px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: #212121; font-family: Menlo, Monaco, Consolas, 'Courier New', monospace; font-size: 14px; border: 0.666667px solid #d9d9d9;\"><span style=\"white-space: pre;\">aircraftConfiguration = buildAircraft(aircraftParts);<\/span><\/div>\n<\/div>\n<\/div>\n<h3 id=\"H_9ec1\" style=\"margin: 15px 10px 5px 4px; padding: 0px; line-height: 18px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 17px; font-weight: bold; text-align: left;\">Inertial properties evaluation<\/h3>\n<div style=\"margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left;\">Inertial properties of aircraft was calculated using <a href=\"https:\/\/github.com\/VincenzoPiercarlo\/Simulating-Water-Propelled-Aircraft-for-ASRW\/blob\/main\/setupInertia.mlx\"><span style=\"font-family: monospace;\">setupInertia.mlx<\/span><\/a>.<\/div>\n<div style=\"background-color: #f5f5f5; margin: 10px 15px 10px 0; display: inline-block;\">\n<div class=\"inlineWrapper\">\n<div style=\"border-radius: 4px; padding: 6px 45px 4px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: #212121; font-family: Menlo, Monaco, Consolas, 'Courier New', monospace; font-size: 14px; border: 0.666667px solid #d9d9d9;\"><span style=\"white-space: pre;\">inertialData = setupInertia(aircraftConfiguration);<\/span><\/div>\n<\/div>\n<\/div>\n<div style=\"margin: 10px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left;\">The tail arm length, distance between the Horizontal Tail (HT) and the aircraft Center of Gravity (CG), was one of the main design optimization object .<\/div>\n<div style=\"background-color: #f5f5f5; margin: 10px 15px 10px 0; display: inline-block;\">\n<div class=\"inlineWrapper\">\n<div style=\"border-left: 0.666667px solid #d9d9d9; border-right: 0.666667px solid #d9d9d9; border-top: 0.666667px solid #d9d9d9; border-bottom: 0px none #212121; border-radius: 4px 4px 0px 0px; padding: 6px 45px 0px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: #212121; font-family: Menlo, Monaco, Consolas, 'Courier New', monospace; font-size: 14px;\"><span style=\"white-space: pre;\">aircraftConfiguration.r_G = inertialData.r_G;<\/span><\/div>\n<\/div>\n<div class=\"inlineWrapper\">\n<div style=\"border-left: 0.666667px solid #d9d9d9; border-right: 0.666667px solid #d9d9d9; border-top: 0px none #212121; border-bottom: 0.666667px solid #d9d9d9; border-radius: 0px 0px 4px 4px; padding: 0px 45px 4px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: #212121; font-family: Menlo, Monaco, Consolas, 'Courier New', monospace; font-size: 14px;\"><span style=\"white-space: pre;\">aircraftConfiguration.HT.Arm = inertialData.r(7,1) &#8211; aircraftConfiguration.r_G(1);<\/span><\/div>\n<\/div>\n<\/div>\n<h3 id=\"H_99f4\" style=\"margin: 15px 10px 5px 4px; padding: 0px; line-height: 18px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 17px; font-weight: bold; text-align: left;\">Aerodynamics modeling<\/h3>\n<div style=\"margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left;\">To perform the aerodynamic analysis, a total of 8 configurations of the aircraft was prepared with the folding angle variation between 0 to 75 degrees. Here, 0 degree folding angle converts aircraft to rocket mode and 75 degree relates to fully opened wings for gliding.<\/div>\n<div style=\"margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left;\">To obtain the aerodynamics coefficients of the aircraft, <a href=\"https:\/\/www.pdas.com\/datcom.html\"><span style=\"text-decoration: underline;\">Digital Datcom<\/span><\/a> was used. This Digital Datcom data was imported with built-in <a href=\"https:\/\/in.mathworks.com\/help\/releases\/R2024b\/aerotbx\/ug\/datcomimport.html?searchPort=53145\"><span style=\"text-decoration: underline;\">datcomimport<\/span><\/a> function of MATLAB. The imported data is available in the <a href=\"https:\/\/github.com\/VincenzoPiercarlo\/Simulating-Water-Propelled-Aircraft-for-ASRW\/blob\/main\/setupAerodynamics.mlx\"><span style=\"text-decoration: underline;\">setupAerodynamics.mlx<\/span><\/a>.<\/div>\n<div style=\"background-color: #f5f5f5; margin: 10px 15px 10px 0; display: inline-block;\">\n<div class=\"inlineWrapper\">\n<div id=\"M_1191\" style=\"border-radius: 4px; padding: 6px 45px 4px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: #212121; font-family: Menlo, Monaco, Consolas, 'Courier New', monospace; font-size: 14px; border: 0.666667px solid #d9d9d9;\"><span style=\"white-space: pre;\">aerodynamicData = setupAerodynamics();<\/span><\/div>\n<\/div>\n<\/div>\n<div style=\"margin: 10px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left;\">This imported data is finally modeled in the form of lookup tables in the <a href=\"https:\/\/github.com\/VincenzoPiercarlo\/Simulating-Water-Propelled-Aircraft-for-ASRW\/blob\/main\/simulateFlight.slx\">Simulink model<\/a>. The aerodynamic coefficients used in the simulation are:<\/div>\n<ul style=\"margin: 10px 0px 20px; padding-left: 0px; font-family: Helvetica, Arial, sans-serif; font-size: 14px;\">\n<li style=\"margin-left: 56px; line-height: 21px; min-height: 0px; text-align: left; white-space: pre-wrap;\"><span style=\"vertical-align: -6px;\">$ C_D $<\/span>: Drag coefficient<\/li>\n<li style=\"margin-left: 56px; line-height: 21px; min-height: 0px; text-align: left; white-space: pre-wrap;\"><span style=\"vertical-align: -6px;\">$ C_L $<\/span>: Lift coefficient<\/li>\n<li style=\"margin-left: 56px; line-height: 21px; min-height: 0px; text-align: left; white-space: pre-wrap;\"><span style=\"vertical-align: -6px;\">$ C_M $<\/span>: Pitching moment coefficient<\/li>\n<li style=\"margin-left: 56px; line-height: 21px; min-height: 0px; text-align: left; white-space: pre-wrap;\"><span style=\"vertical-align: -10px;\">$ C_{M_0} $<\/span>: Pitching moment coefficient at zero angle of attack<\/li>\n<li style=\"margin-left: 56px; line-height: 21px; min-height: 0px; text-align: left; white-space: pre-wrap;\"><span style=\"vertical-align: -10px;\">$ C_{M_q} $<\/span>: Pitching moment coefficient derivative with respect to the pitch rate (q). It indicates the change in pitch moment due to the aircraft\u2019s rotation.<\/li>\n<li style=\"margin-left: 56px; line-height: 21px; min-height: 0px; text-align: left; white-space: pre-wrap;\"><span style=\"vertical-align: -8px;\">$ C_L^{\\mathrm{(tail)}} $<\/span>: Lift coefficient for the tailplane. It is the key of the control law.<\/li>\n<\/ul>\n<h3 id=\"H_4b3b\" style=\"margin: 15px 10px 5px 4px; padding: 0px; line-height: 18px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 17px; font-weight: bold; text-align: left;\">Propulsion modeling<\/h3>\n<div style=\"margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left;\">This aircraft is powered by water propulsion. To calculate the thrust profile, first, speed profile of the exhaust flow was computed using the <a href=\"https:\/\/waterrocketsimulator.github.io\/\">Water Rocket Simulator<\/a>. This speed profile was discretized and fed to a function called<a href=\"https:\/\/github.com\/VincenzoPiercarlo\/Simulating-Water-Propelled-Aircraft-for-ASRW\/blob\/main\/massflowRate.mlx\"> <span style=\"font-family: monospace;\">massflowRate.mlx<\/span><\/a> to compute the mass evolution. The mass evolution was calculated by integrating the mass flow <span style=\"vertical-align: -5px;\">$ \\dot{m}=\\rho VA $<\/span> over time, where <span style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: #212121;\">\u03c1<\/span>, <span style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: #212121;\">V<\/span>, and <span style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: #212121;\">A<\/span> are the water density, speed of the water at the nozzle, and section area of the nozzle respectively. This mass evolution data was used to calculate the <a href=\"#M_8e61\">thrust profile<\/a>.<\/div>\n<div id=\"M_8e61\" style=\"margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: center;\"><img decoding=\"async\" loading=\"lazy\" class=\"imageNode\" style=\"vertical-align: baseline; width: 321px; height: 318px;\" src=\"https:\/\/blogs.mathworks.com\/student-lounge\/files\/2025\/01\/25jan7_3.png\" alt=\"\" width=\"321\" height=\"318\" \/><\/div>\n<div style=\"margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: center;\">Figure 3 &#8211; Thrust Profile<\/div>\n<div style=\"margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left;\">Finally, the thrust profile along with eccentricity was modeled with <a href=\"https:\/\/github.com\/VincenzoPiercarlo\/Simulating-Water-Propelled-Aircraft-for-ASRW\/blob\/main\/setupPropulsion.mlx\"><span style=\"font-family: monospace;\">setupPropulsion.mlx<\/span><\/a><span style=\"font-family: monospace;\">. <\/span>The eccentricity is important to calculate the pitching moment due to the thrust itself.<\/div>\n<div style=\"background-color: #f5f5f5; margin: 10px 15px 10px 0; display: inline-block;\">\n<div class=\"inlineWrapper\">\n<div id=\"M_6e8e\" style=\"border-radius: 4px; padding: 6px 45px 4px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: #212121; font-family: Menlo, Monaco, Consolas, 'Courier New', monospace; font-size: 14px; border: 0.666667px solid #d9d9d9;\"><span style=\"white-space: pre;\">propulsionData = setupPropulsion(aircraftConfiguration);<\/span><\/div>\n<\/div>\n<\/div>\n<h2 id=\"H_5d45\" style=\"margin: 3px 10px 5px 4px; padding: 0px; line-height: 20px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 20px; font-weight: bold; text-align: left;\">Flight simulation<\/h2>\n<div style=\"margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left;\">To evaluate the gliding performance of the aircraft, a Simulink model, <a href=\"https:\/\/github.com\/VincenzoPiercarlo\/Simulating-Water-Propelled-Aircraft-for-ASRW\/blob\/main\/simulateFlight.slx\"><span style=\"font-family: monospace;\">simulateFlight.slx<\/span><\/a>, was developed. It models, simulates, and compares the performance of two different configurations to study the effect of aircraft tail:<\/div>\n<ul style=\"margin: 10px 0px 20px; padding-left: 0px; font-family: Helvetica, Arial, sans-serif; font-size: 14px;\">\n<li style=\"margin-left: 56px; line-height: 21px; min-height: 0px; text-align: left; white-space: pre-wrap;\"><span style=\"font-weight: bold;\">Glider Configuration<\/span>: models the aircraft dynamics with the tail deployment. Along with the trajectory, it also returns the aircraft attitude <span style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: #212121;\">\u03b8<\/span> to represent the aircraft orientation as well.<\/li>\n<li style=\"margin-left: 56px; line-height: 21px; min-height: 0px; text-align: left; white-space: pre-wrap;\"><span style=\"font-weight: bold;\">Non-Gliding Configuration:<\/span> models the aircraft dynamics like glider configuration except the tail contribution.<\/li>\n<\/ul>\n<div style=\"margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: center;\"><img decoding=\"async\" loading=\"lazy\" class=\"imageNode\" style=\"vertical-align: baseline; width: 683px; height: 362px;\" src=\"https:\/\/blogs.mathworks.com\/student-lounge\/files\/2025\/01\/25jan7_4.png\" alt=\"\" width=\"683\" height=\"362\" \/><\/div>\n<div style=\"margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: center;\">Figure 4 &#8211; Simulink model<\/div>\n<div style=\"margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left;\">Along with the aircraft dynamics modeling of both configurations, stop conditions were also modeled to make sure that the aircraft did not attain a negative altitude. Finally, for the visualization 3 DOF Animation block was used.<\/div>\n<div style=\"margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left;\"><\/div>\n<h4 id=\"H_37bb\" style=\"margin: 10px 10px 5px 4px; padding: 0px; line-height: 18px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 15px; font-weight: bold; text-align: left;\">Aircraft dynamics modeling<\/h4>\n<div style=\"margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left;\">For both, Gliding and Non-Gliding configurations, aircraft dynamics were modeled with the following key sub-systems:<\/div>\n<ul style=\"margin: 10px 0px 20px; padding-left: 0px; font-family: Helvetica, Arial, sans-serif; font-size: 14px;\">\n<li style=\"margin-left: 56px; line-height: 21px; min-height: 0px; text-align: left; white-space: pre-wrap;\"><span style=\"text-decoration: underline;\">Forces and Moments<\/span>: To model forces and moments, <a href=\"#M_1191\"><span style=\"text-decoration: underline;\">Aerodynamic data<\/span><\/a> and <a href=\"#M_6e8e\"><span style=\"text-decoration: underline;\">Propulsion data<\/span><\/a> were imported to Simulink through lookup tables. This data was complemented with various flight data parameters to calculate Forces and Moments. It also has a pitching moment filter to consider the first 0.064s of the flight when the aircraft is still getting out of the launch tube, designed to absorb the aggressive pitch impulse and provide the aircraft with appropriate directions.<\/li>\n<li style=\"margin-left: 56px; line-height: 21px; min-height: 0px; text-align: left; white-space: pre-wrap;\"><span style=\"text-decoration: underline;\">Equations of motion<\/span>: To model the equation of motion with variable mass and inertia, the <a href=\"https:\/\/in.mathworks.com\/help\/releases\/R2024b\/aeroblks\/customvariablemass3dofwindaxes.html?searchPort=61930\">Custom Variable Mass 3DOF (Wind Axes) <\/a>block was used. It was supplemented by the variable <a href=\"https:\/\/github.com\/VincenzoPiercarlo\/Simulating-Water-Propelled-Aircraft-for-ASRW\/blob\/main\/massflowRate.mlx\">mass data <\/a>and <a href=\"https:\/\/github.com\/VincenzoPiercarlo\/Simulating-Water-Propelled-Aircraft-for-ASRW\/blob\/main\/setupInertia.mlx\">inertia data<\/a>, essential for simulating dynamic changes in the vehicle\u2019s mass and inertia during flight or movement. This block also models the gravitational forces. This subsystem provides the effect of the forces and moments on the aircraft in terms of various aircraft states.<\/li>\n<\/ul>\n<div style=\"margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: center;\"><img decoding=\"async\" loading=\"lazy\" class=\"imageNode\" style=\"vertical-align: baseline; width: 710px; height: 374px;\" src=\"https:\/\/blogs.mathworks.com\/student-lounge\/files\/2025\/01\/25jan7_5.png\" alt=\"\" width=\"710\" height=\"374\" \/><\/div>\n<div style=\"margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: center;\">Figure 5 &#8211; Aircraft dynamics modeled in both configuration<\/div>\n<div style=\"margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: center;\"><\/div>\n<h4 id=\"H_9cfd\" style=\"margin: 10px 10px 5px 4px; padding: 0px; line-height: 18px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 15px; font-weight: bold; text-align: left;\">Initial conditions<\/h4>\n<div style=\"margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left;\">The competition requirements governed the initial condition of the vehicles. For the ASRW competition 2023, the rocket had to be launched at an elevation angle of 88 degrees. All other parameters were considered zero except the initial speed to simplify the numerical complexities.<\/div>\n<table style=\"margin: 3px; border: 0.666667px solid #bfbfbf; border-collapse: collapse;\">\n<tbody>\n<tr style=\"background-color: #f5f5f5;\">\n<td style=\"border: 0.666667px solid #bfbfbf; vertical-align: top;\">\n<div style=\"margin: 2px 10px 2px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: break-spaces; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: center;\"><span style=\"font-weight: bold;\">Parameters<\/span><\/div>\n<\/td>\n<td style=\"border: 0.666667px solid #bfbfbf; vertical-align: top;\">\n<div style=\"margin: 2px 10px 2px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: break-spaces; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: center;\"><span style=\"font-weight: bold;\">Initial Values<\/span><\/div>\n<\/td>\n<\/tr>\n<tr style=\"background-color: rgba(0, 0, 0, 0);\">\n<td style=\"border: 0.666667px solid #bfbfbf; vertical-align: top;\">\n<div style=\"margin: 2px 10px 2px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: break-spaces; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left;\">Initial location [xE0, yE0, ze0]<\/div>\n<\/td>\n<td style=\"border: 0.666667px solid #bfbfbf; vertical-align: top;\">\n<div style=\"margin: 2px 10px 2px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: break-spaces; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: center;\">[0 0 0]<\/div>\n<\/td>\n<\/tr>\n<tr style=\"background-color: rgba(0, 0, 0, 0);\">\n<td style=\"border: 0.666667px solid #bfbfbf; vertical-align: top;\">\n<div style=\"margin: 2px 10px 2px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: break-spaces; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left;\">Launch elevation angle (theta0)<\/div>\n<\/td>\n<td style=\"border: 0.666667px solid #bfbfbf; vertical-align: top;\">\n<div style=\"margin: 2px 10px 2px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: break-spaces; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: center;\">88 degrees<\/div>\n<\/td>\n<\/tr>\n<tr style=\"background-color: rgba(0, 0, 0, 0);\">\n<td style=\"border: 0.666667px solid #bfbfbf; vertical-align: top;\">\n<div style=\"margin: 2px 10px 2px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: break-spaces; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left;\">Pitch speed (q0)<\/div>\n<\/td>\n<td style=\"border: 0.666667px solid #bfbfbf; vertical-align: top;\">\n<div style=\"margin: 2px 10px 2px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: break-spaces; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: center;\">0<\/div>\n<\/td>\n<\/tr>\n<tr style=\"background-color: rgba(0, 0, 0, 0);\">\n<td style=\"border: 0.666667px solid #bfbfbf; vertical-align: top;\">\n<div style=\"margin: 2px 10px 2px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: break-spaces; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left;\">Angle of attack (alpha0)<\/div>\n<\/td>\n<td style=\"border: 0.666667px solid #bfbfbf; vertical-align: top;\">\n<div style=\"margin: 2px 10px 2px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: break-spaces; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: center;\">0<\/div>\n<\/td>\n<\/tr>\n<tr style=\"background-color: rgba(0, 0, 0, 0);\">\n<td style=\"border: 0.666667px solid #bfbfbf; vertical-align: top;\">\n<div style=\"margin: 2px 10px 2px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: break-spaces; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left;\">Linear speed (V0)<\/div>\n<\/td>\n<td style=\"border: 0.666667px solid #bfbfbf; vertical-align: top;\">\n<div style=\"margin: 2px 10px 2px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: break-spaces; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: center;\">0.1<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div style=\"margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left;\"><\/div>\n<h4 id=\"H_97ff\" style=\"margin: 10px 10px 5px 4px; padding: 0px; line-height: 18px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 15px; font-weight: bold; text-align: left;\">Simulation results<\/h4>\n<div style=\"background-color: #f5f5f5; margin: 10px 15px 10px 0; display: inline-block;\">\n<div class=\"inlineWrapper\">\n<div id=\"H_7af1\" style=\"border-radius: 4px; padding: 6px 45px 4px 13px; line-height: 18.004px; min-height: 0px; white-space: nowrap; color: #212121; font-family: Menlo, Monaco, Consolas, 'Courier New', monospace; font-size: 14px; border: 0.666667px solid #d9d9d9;\"><span style=\"white-space: pre;\">results = sim(<span style=\"color: #a709f5;\">&#8220;simulateFlight.slx&#8221;<\/span>);<\/span><\/div>\n<\/div>\n<\/div>\n<div style=\"margin: 10px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: center;\"><img decoding=\"async\" loading=\"lazy\" class=\"imageNode\" style=\"vertical-align: baseline; width: 545px; height: 467px;\" src=\"https:\/\/blogs.mathworks.com\/student-lounge\/files\/2025\/01\/25jan7_6.gif\" alt=\"SimultioGIF.gif\" width=\"545\" height=\"467\" \/><\/div>\n<div id=\"H_4686\" style=\"margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left;\">Simulation results show that the gliding configuration with the tail activated provided a range advantage of 6.545 m compared to the non-gliding mode configuration. Also, both configurations achieved a maximum altitude of 8.4987 meters.<\/div>\n<h2 id=\"H_4a47\" style=\"margin: 3px 10px 5px 4px; padding: 0px; line-height: 20px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 20px; font-weight: bold; text-align: left;\">Conclusions<\/h2>\n<div style=\"margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left;\">The simulation shows that the glider gains range through a pull-up maneuver, aided by the tailplane design, ensuring stable flight without stalling. The goal of achieving instability at the apex, leading to a rapid pitch-down for gaining airspeed, was successfully met. Also, this airspeed generates the necessary lift from the wings and tailplane for a smooth landing. Thrust eccentricity also proved effective, enhancing the range by 6.54 meters and controlling the elevation angle at the apex.<\/div>\n<div style=\"margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: #212121; font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: 400; text-align: left;\">Although the simulation results were approximate, they were close to the flight test results (<a href=\"https:\/\/www.youtube.com\/watch?v=y8TNEQP7Qss\"><span style=\"text-decoration: underline;\">AirSloths Flight Tests Video<\/span><\/a>) and were used iteratively to test and improve the overall design. Team AirSloths&#8217; code utilized multiple capabilities of the <a href=\"https:\/\/www.mathworks.com\/products\/aerospace-toolbox.html\"><span style=\"text-decoration: underline;\">Aerospace Toolbox<\/span><\/a> and <a href=\"https:\/\/in.mathworks.com\/products\/aerospace-blockset.html\"><span style=\"text-decoration: underline;\">Aerospace Blockset<\/span><\/a> to analyze the vehicle design and simulate the flight. There are many features and examples available that may help you accelerate your aerospace vehicle design, so don\u2019t miss browsing them.<\/div>\n<\/div>\n<p><script type=\"text\/javascript\">var css = ''; var head = document.head || document.getElementsByTagName('head')[0], style = document.createElement('style'); head.appendChild(style); style.type = 'text\/css'; if (style.styleSheet){ style.styleSheet.cssText = css; } else { style.appendChild(document.createTextNode(css)); }<\/script><a href=\"https:\/\/blogs.mathworks.com\/student-lounge\/files\/2025\/01\/25jan7.mlx\"><button class=\"btn btn-sm btn_color_blue pull-right add_margin_10\">Download Live Script<\/button><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<div class=\"overview-image\"><img src=\"https:\/\/blogs.mathworks.com\/student-lounge\/files\/2025\/01\/25jan7_6.gif\" class=\"img-responsive attachment-post-thumbnail size-post-thumbnail wp-post-image\" alt=\"\" decoding=\"async\" loading=\"lazy\" \/><\/div>\n<p>\nIntroduction<br \/>\nThis work was developed by Piercarlo Mirto and Vincenzo Junior Di Rosa master\u2019s students in Aerospace Engineering at the University of Naples Federico II. This was their contribution to&#8230; <a class=\"read-more\" href=\"https:\/\/blogs.mathworks.com\/student-lounge\/2025\/01\/07\/simulating-water-propelled-aircraft-for-airbus-sloshing-rocket-workshop\/\">read more >><\/a><\/p>\n","protected":false},"author":183,"featured_media":11795,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[6,8],"tags":[18,746],"_links":{"self":[{"href":"https:\/\/blogs.mathworks.com\/student-lounge\/wp-json\/wp\/v2\/posts\/11801"}],"collection":[{"href":"https:\/\/blogs.mathworks.com\/student-lounge\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.mathworks.com\/student-lounge\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.mathworks.com\/student-lounge\/wp-json\/wp\/v2\/users\/183"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.mathworks.com\/student-lounge\/wp-json\/wp\/v2\/comments?post=11801"}],"version-history":[{"count":3,"href":"https:\/\/blogs.mathworks.com\/student-lounge\/wp-json\/wp\/v2\/posts\/11801\/revisions"}],"predecessor-version":[{"id":11906,"href":"https:\/\/blogs.mathworks.com\/student-lounge\/wp-json\/wp\/v2\/posts\/11801\/revisions\/11906"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/blogs.mathworks.com\/student-lounge\/wp-json\/wp\/v2\/media\/11795"}],"wp:attachment":[{"href":"https:\/\/blogs.mathworks.com\/student-lounge\/wp-json\/wp\/v2\/media?parent=11801"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.mathworks.com\/student-lounge\/wp-json\/wp\/v2\/categories?post=11801"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.mathworks.com\/student-lounge\/wp-json\/wp\/v2\/tags?post=11801"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}