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Mathematical modelling in the field of kites
• Calculation of kites strength, shape and aerodynamic coefficients Material Science, Solid
mechanics, Aerodynamics, Aeroelasticity
• Finding kites trajectory, speed and attitude Multi-body dynamics
• Laddermill control Stability, optimization and
optimal control
• Problems of aerodynamics Airflow around the kite Finding the aerodynamic
coefficients• Problems of aeroelasticity
Finding the shape of the kite under air load
Finding the aerodynamic coefficients
• Problems of solid mechanics Prediction of fatigue and failure
of kite materials and structure Prediction of life cycle length
![Page 2: Mathematical modelling in the field of kites Calculation of kites strength, shape and aerodynamic coefficients Material Science, Solid mechanics, Aerodynamics,](https://reader036.vdocuments.us/reader036/viewer/2022062517/56649efd5503460f94c11803/html5/thumbnails/2.jpg)
Mathematical modelling in the field of kites
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Mathematical modelling in the field of kites
![Page 4: Mathematical modelling in the field of kites Calculation of kites strength, shape and aerodynamic coefficients Material Science, Solid mechanics, Aerodynamics,](https://reader036.vdocuments.us/reader036/viewer/2022062517/56649efd5503460f94c11803/html5/thumbnails/4.jpg)
![Page 5: Mathematical modelling in the field of kites Calculation of kites strength, shape and aerodynamic coefficients Material Science, Solid mechanics, Aerodynamics,](https://reader036.vdocuments.us/reader036/viewer/2022062517/56649efd5503460f94c11803/html5/thumbnails/5.jpg)
Mathematical modelling in the field of kites
• What’s next?
Courtesy of Rensselaer Polytechnic Institute
Courtesy of University of California in Irwing
Courtesy of Ecole Polytechnique de Montréal
![Page 6: Mathematical modelling in the field of kites Calculation of kites strength, shape and aerodynamic coefficients Material Science, Solid mechanics, Aerodynamics,](https://reader036.vdocuments.us/reader036/viewer/2022062517/56649efd5503460f94c11803/html5/thumbnails/6.jpg)
Step 32
Step 155
Step 806
The pictures of the airflow around 6*3 pt plate in a 30*30 pt region
Mathematical modelling in the field of kites
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![Page 8: Mathematical modelling in the field of kites Calculation of kites strength, shape and aerodynamic coefficients Material Science, Solid mechanics, Aerodynamics,](https://reader036.vdocuments.us/reader036/viewer/2022062517/56649efd5503460f94c11803/html5/thumbnails/8.jpg)
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Here:
Equations of motion:
Mathematical modelling in the field of kites
![Page 9: Mathematical modelling in the field of kites Calculation of kites strength, shape and aerodynamic coefficients Material Science, Solid mechanics, Aerodynamics,](https://reader036.vdocuments.us/reader036/viewer/2022062517/56649efd5503460f94c11803/html5/thumbnails/9.jpg)
Stability of energy production
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here w is wind speed and E is energy production
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![Page 10: Mathematical modelling in the field of kites Calculation of kites strength, shape and aerodynamic coefficients Material Science, Solid mechanics, Aerodynamics,](https://reader036.vdocuments.us/reader036/viewer/2022062517/56649efd5503460f94c11803/html5/thumbnails/10.jpg)
Flight optimization
T
a
Δ
Δ
a
1. Creating the table of tests
2. Determining Pareto-set
3. Choosing constraints on objectives.
![Page 11: Mathematical modelling in the field of kites Calculation of kites strength, shape and aerodynamic coefficients Material Science, Solid mechanics, Aerodynamics,](https://reader036.vdocuments.us/reader036/viewer/2022062517/56649efd5503460f94c11803/html5/thumbnails/11.jpg)
Choice of test pointsEquidistant grid LPτ: all coordinates of all points are different
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Mathematical modelling in the field of kites
• Calculation of kites strength, shape and aerodynamic coefficients Material Science, Solid
mechanics, Aerodynamics, Aeroelasticity
• Finding kites trajectory, speed and attitude Multi-body dynamics
• Laddermill control Stability, optimization and
optimal control
• Problems of aerodynamics Airflow around the kite Finding the aerodynamic
coefficients• Problems of aeroelasticity
Finding the shape of the kite under air load
Finding the aerodynamic coefficients
• Problems of solid mechanics Prediction of fatigue and failure
of kite materials and structure Prediction of life cycle length