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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
Mathematical modelling in the field of kites
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Mathematical modelling in the field of kites
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
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
)()()(2
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0tir 0tiVInitial conditions: and .
Here:
Equations of motion:
Mathematical modelling in the field of kites
Stability of energy production
PEEPPwwP
EEww
here w is wind speed and E is energy production
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Flight optimization
T
a
Δ
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a
1. Creating the table of tests
2. Determining Pareto-set
3. Choosing constraints on objectives.
Choice of test pointsEquidistant grid LPτ: all coordinates of all points are different
0 0.4 0 .8
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irs
322
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