# Helicopter control and its general models (thesis)

- Hypothesis of the study
- Plan of the study
- DRA Research Puma XW241
- Input data
- Atmospheric conditions
- Introduction
- Mean sea level conditions
- Determination of the temperature
- Pressure modeling
- Density modeling
- Calculation of other parameters
- Validity of the model

- Lift coefficient
- Introduction
- Input data for the Helicopter DRA research Puma XW241
- Prandtl Lifting Line Theory
- The monoplane equation
- Solution of the monoplane equation
- Implementation on Matlab
- Interpretation of the results

- Lift and drag forces
- Introduction
- Input data
- Sufficient lift for takeoff
- Additional study: design of the wing
- Lift force calculation

- Pressure coefficient
- Introduction
- NACA airfoils
- Input data
- Theoretical model
- Results of the study
- Conclusion

- Helicopter noise reduction
- Introduction
- The Blade-vortex interaction
- Theoretical model
- Results of the investigation

- Calculation of helicopter power
- Introduction
- Motion of the helicopter and its elements
- Atmospheric parameters
- Results and interpretation

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.

[...] For a gas, it is common to use the law of Sutherland defined as follows: ? (V.13) Sutherland temperature (110,4 Reynolds Number By definition, the Reynolds number can be written as following: ? ? (V.14) V is the mean velocity of the object relative to the fluid L is the characteristic linear dimension Dynamic pressure The dynamic pressure can be found as: (V.15) Validity of the model The model had been checked with the following table issued from International Standard Atmosphere: Table International Standard Atmosphere In order to test the program, the altitude of 10058 meters has been entered as an input data in Matlab. We got the following output: 20 Figure output of the atmospheric conditions program for an altitude of 10058 meters The results are the same as in the table so the program works fine. It will be useful to computerize data issued from atmospheric conditions in the main program. [...]

[...] Thus, knowledge of the helicopter geometry, blade dynamics and other aerodynamic data which can only be got from real tests on wind-tunnel will be necessary. These tests, performed by companies, are very expensive and are often kept confidential so some information cannot be reached for this project. Nevertheless, the goal of this study is to improve the existing models (and, in our case, completely revise most of the parts) to get an even more accurate and understandable program by its user. [...]

[...] 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. [...]

[...] It represents the longitudinal tilt of the rotor tip path plane (as explained in the appendix D). The lateral flapping angle (blue) is decreasing with time at the opposite . It represents the lateral tilt of the rotor tip path plane (as explained in the appendix D). These two results mean that the nose of the aircraft rises relative to the tail and the helicopter tilts slightly to the side. Given the initial conditions (the force and the torque around the Z-axis), these graphics seem to be relevant. [...]

[...] Figure 34: Blade-vortex interaction in disc for different speeds in 2D 48 Figure 35: Blade-vortex interaction in disc for different speeds in 3D On the figures 34 and 35, we can note that the number of waves decreases when the speed increases. It corresponds to a reduced number of vortices inside the disc. Therefore, it seems that the helicopter is less disturbed at high speeds. It seems clear that the aircraft BVI depend on the helicopter wake. Significant research studies have been lead in order to reduce BVI. Therefore, many blades or rotor have been changed in their design as well as the fuselage of the helicopter. [...]