# A pedagogical example for stem using the glauert inflow equation, mathematica and python

Ganguli, R (2019) A pedagogical example for stem using the glauert inflow equation, mathematica and python. In: AIAA Scitech 2019 Forum, 7-11 January 2019, San Diego, California.

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Official URL: https://dx.doi.org/10.2514/6.2019-0867

## Abstract

The prediction of inflow velocity through the rotor disk is an important problem for helicopters. In forward flight, the resulting Glauert inflow equation is an irrational algebraic equation which is typically solved using the Newton-Raphson numerical method. We present a closed form solution of the Glauert inflow equation by using the theory of equations in algebra to convert the irrational equation to the rational form. Superfluous or extraneous roots introduced into the rational form are then eliminated and the inflow velocity is obtained in forward flight for a given thrust coefficient, flight speed and rotor disk angle of attack. This problem is solved using the symbolic programming language Mathematica and the results are verified by writing a Python code. The problem is useful as a benchmark solution in helicopter aerodynamics for comparing numerical solutions of the Glauert inflow equation. It can also be used as an example problem for STEM education to illustrate algebra, numerical methods and symbolic and scientific computer programming. Â© 2019, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.

Item Type: Conference Paper AIAA Scitech 2019 Forum American Institute of Aeronautics and Astronautics Inc, AIAA cited By 0; Conference of AIAA Scitech Forum, 2019 ; Conference Date: 7 January 2019 Through 11 January 2019; Conference Code:225819 Algebra; Angle of attack; Aviation; Problem oriented languages, Algebraic equations; Benchmark solutions; Closed form solutions; Helicopter aerodynamics; Irrational equations; Numerical solution; Symbolic programming language; Thrust coefficients, Numerical methods Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering) 29 Oct 2020 09:59 29 Oct 2020 09:59 http://eprints.iisc.ac.in/id/eprint/65390