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

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

Initial conditions: and. Here: Equations of motion: Mathematical modelling in the field of kites

Stability of energy production here w is wind speed and E is energy production

Flight optimization T  a Δ Δ a 1. Creating the table of tests 2. Determining Pareto-set 3. Choosing constraints on objectives.

Choice of test points Equidistant grid LP τ : all coordinates of all points are different

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