Helicopter control, nonlinear equations of motion for helicopters, aerodynamic behavior of the aircraft, NASA, Matlab, DRA Research Puma XW241, aircrafts performances, Prandtl lifting line theory, design of the wing, lift force, NACA airfoils, thesis
Simulations on helicopters are very useful for companies and research labs when one wants to make dynamic analysis, study the trajectory, investigate air combat, prepare pilot training and do many other tasks. The problem is that, regarding helicopters, very few investigations have been conducted and very few accurate programs which model their behavior exist in the scientific literature. Recent ones focus on quite rare flights in practice, as in the work of K. Sibiliski [Sibilski 1998 Sibilski 1999] in the late 90s, or enough incomplete in their modeling as the study lead by students from MH Lowenberg [Bedford and Lowenberg 2003, Bedford and Lowenberg 2004, Rezgui et al. 2006]. Meanwhile, the National Aeronautics and Space Administration (NASA) developed a program through the software Matlab whose name is "Minimum-Complexity Helicopter Simulation Math Model" (MCHSMM). This model is a flight simulator of a helicopter and has many advantages as it relies on basic data sources and does not require powerful computer tools. So, it allows low cost real-time simulations.
[...] We got the following results: Figure 50: evolution of velocities and angles for the third test The rotational velocities and as well as the Euler angles Ѳ φ and ψ are null which is relevant given the fact the helicopter is supposed to move straightly. The same statement 59 can be done for the longitudinal flapping angle and the lateral flapping angle . As for velocities, u is constant and equal to about 55 m/s (200 km/h) which is relevant with the initial conditions of the study. The velocity along the Z-axis may come from the force applied on the Z-axis and supposed to compensate the weight of the helicopter. [...]
[...] Plot from the implementation on Matlab Comparison with theory and interpretation Conclusion Helicopter noise reduction Introduction The Blade-vortex interaction Theoretical model Introduction X. Animation of the blade Explanation of some Matlab commands Results of the investigation Calculation of helicopter power Introduction Motion of the helicopter and its elements Atmospheric parameters Results and interpretation Conclusion and perspectives of the investigation Bibliography Appendix architecture of the DRA research Puma XW Appendix data issued from the book of Padfield Appendix explanation of the implementation on Matlab for the calculation of the lift coefficient Appendix determination of the motion of an helicopter System to which the Newton's laws of motion is applied Full nonlinear six-degree-of-freedom rigid body translational and rotational aircraft motion Euler rates Angular acceleration Translatory acceleration Euler angles Final rigid body equations Force and torque equations Forces Torques Model for main rotor Hovering Vertical descent Forward flight The rotor system and kinematics of a blade element (How to calculate ) Modeling for tail rotor Modeling for the empennage Appendix motors made by SAFRAN group for helicopters Abstract This document presents the theory relative to helicopters used for the implementation on Matlab. [...]
[...] In this example, the translational velocity of the helicopter (the norm of the vector of translational velocities composed by in red, in blue and in green) is increasing cyclically but not linearly. As for the rotational velocities (blue) and (green), we notice that the one around the Y-axis is decreasing whereas the two around the X and Z axis seem to be rather constant. This result is surprising given the initial conditions because no torque or force are applied along or around X and Y. [...]
[...] Lift and drag forces 1. Introduction A code has therefore been implemented in Matlab in order to calculate lift and drag forces required on the blades of the helicopter. The code also allows the chord length and the angle of attack to change along the span. The main inputs of this code are the tip chords, the span, the minimum/maximum angles of attack, the number of blade elements to consider, lift and drag data as well as some known and estimated helicopter characteristics. [...]
[...] The values reached by the power required by the aircraft are still below the power the two motors can provide so the results are fine and relevant with what was expected. Conclusion and perspectives of the investigation The studied model is not perfect and could suffer from some deficiencies. Indeed, the equations used in these models have been simplified with several hypotheses. So, the model could be more accurate with complex equations directly resulting from tests in laboratory. The results almost all seem to be coherent but they could not have been checked in some cases as no existing studies were found in the open literature as elements of comparison. [...]
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