Numerical Analysis of Glauert Inflow Formula for Single-Rotor Helicopter in Steady-Level Flight below Stall-Flutter Limit
This article addresses the numerical computation problem of induced inflow ratio based on the helicopter momentum theory in forward flight. The Glauert inflow formula (equation) is a nonlinear equation usually solved by the Newton–Raphson method in a relatively small number of iterations. However, m...
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MDPI AG
2023-02-01
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| Series: | Aerospace |
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| Online Access: | https://www.mdpi.com/2226-4310/10/3/238 |
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| author | Marjan Dodic Branimir Krstic Bosko Rasuo Mirko Dinulovic Aleksandar Bengin |
| author_facet | Marjan Dodic Branimir Krstic Bosko Rasuo Mirko Dinulovic Aleksandar Bengin |
| author_sort | Marjan Dodic |
| collection | DOAJ |
| description | This article addresses the numerical computation problem of induced inflow ratio based on the helicopter momentum theory in forward flight. The Glauert inflow formula (equation) is a nonlinear equation usually solved by the Newton–Raphson method in a relatively small number of iterations. However, many high-order convergence multipoint iterative methods have been developed over the last decade. The study examines several selected methods in terms of finding ones that provide a solution in only one iteration with acceptable accuracy. Furthermore, the influence of initial guesses on the accuracy of the obtained solutions has been investigated. In this regard, the practical range of parameters of the Glauert inflow equation for helicopters in forward flight is roughly determined by simplified modeling of a power and stall-flutter limitation. For these purposes, a basic low-fidelity longitudinal trim model of a single-rotor helicopter in steady-level flight is modified and numerically solved by a symbolic transformation of a system of 20+ nonlinear equations into a single nonlinear equation. |
| first_indexed | 2024-03-11T07:06:07Z |
| format | Article |
| id | doaj.art-f4b7c2882948441f931f5be1d932b0db |
| institution | Directory Open Access Journal |
| issn | 2226-4310 |
| language | English |
| last_indexed | 2024-03-11T07:06:07Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Aerospace |
| spelling | doaj.art-f4b7c2882948441f931f5be1d932b0db2023-11-17T08:58:17ZengMDPI AGAerospace2226-43102023-02-0110323810.3390/aerospace10030238Numerical Analysis of Glauert Inflow Formula for Single-Rotor Helicopter in Steady-Level Flight below Stall-Flutter LimitMarjan Dodic0Branimir Krstic1Bosko Rasuo2Mirko Dinulovic3Aleksandar Bengin4Section of Aerospace Engineering and Mechanics, Department of Military Mechanical Engineering, Military Academy, University of Defence in Belgrade, Veljka Lukica Kurjaka 33, 11042 Belgrade, SerbiaSection of Aerospace Engineering and Mechanics, Department of Military Mechanical Engineering, Military Academy, University of Defence in Belgrade, Veljka Lukica Kurjaka 33, 11042 Belgrade, SerbiaDepartment of Aerospace Engineering, Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Belgrade, SerbiaDepartment of Aerospace Engineering, Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Belgrade, SerbiaDepartment of Aerospace Engineering, Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Belgrade, SerbiaThis article addresses the numerical computation problem of induced inflow ratio based on the helicopter momentum theory in forward flight. The Glauert inflow formula (equation) is a nonlinear equation usually solved by the Newton–Raphson method in a relatively small number of iterations. However, many high-order convergence multipoint iterative methods have been developed over the last decade. The study examines several selected methods in terms of finding ones that provide a solution in only one iteration with acceptable accuracy. Furthermore, the influence of initial guesses on the accuracy of the obtained solutions has been investigated. In this regard, the practical range of parameters of the Glauert inflow equation for helicopters in forward flight is roughly determined by simplified modeling of a power and stall-flutter limitation. For these purposes, a basic low-fidelity longitudinal trim model of a single-rotor helicopter in steady-level flight is modified and numerically solved by a symbolic transformation of a system of 20+ nonlinear equations into a single nonlinear equation.https://www.mdpi.com/2226-4310/10/3/238Glauert inflow formulanumerical solutionmultipoint iterative methodsnonlinear equationssingle-rotor helicoptersteady-level flight |
| spellingShingle | Marjan Dodic Branimir Krstic Bosko Rasuo Mirko Dinulovic Aleksandar Bengin Numerical Analysis of Glauert Inflow Formula for Single-Rotor Helicopter in Steady-Level Flight below Stall-Flutter Limit Aerospace Glauert inflow formula numerical solution multipoint iterative methods nonlinear equations single-rotor helicopter steady-level flight |
| title | Numerical Analysis of Glauert Inflow Formula for Single-Rotor Helicopter in Steady-Level Flight below Stall-Flutter Limit |
| title_full | Numerical Analysis of Glauert Inflow Formula for Single-Rotor Helicopter in Steady-Level Flight below Stall-Flutter Limit |
| title_fullStr | Numerical Analysis of Glauert Inflow Formula for Single-Rotor Helicopter in Steady-Level Flight below Stall-Flutter Limit |
| title_full_unstemmed | Numerical Analysis of Glauert Inflow Formula for Single-Rotor Helicopter in Steady-Level Flight below Stall-Flutter Limit |
| title_short | Numerical Analysis of Glauert Inflow Formula for Single-Rotor Helicopter in Steady-Level Flight below Stall-Flutter Limit |
| title_sort | numerical analysis of glauert inflow formula for single rotor helicopter in steady level flight below stall flutter limit |
| topic | Glauert inflow formula numerical solution multipoint iterative methods nonlinear equations single-rotor helicopter steady-level flight |
| url | https://www.mdpi.com/2226-4310/10/3/238 |
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