Umbilical deployment modeling for tethered UAV detecting oil pollution from ship

Oil slick detection and guiding of oil recovery ship by using on board tethered UAV need a non-linear dynamic model for the aerial umbilical including variable length domain and material elasticity. Considering the flight phases constraints and the system definition, two continuous models are presented using a Lagrangian approach or an updated Lagrangian one, both including different kinds of boundary condition at the umbilical bottom end. At the winch position, during a take-off or landing (TOL) phase flight, a geometrical singularity occurs in the Lagrangian approach while in the updated Lagrangian one, a difference exists between the unstrained curvilinear coordinate velocity and the strained umbilical material point velocity. Properties of internal strain energy and non-linear strain measure permit to characterize the regularity of the longitudinal and transversal umbilical displacements. From the continuous models we deduce the discrete finite-element models. Numerical examples with until eleven nodes are given, including the case of an emergency flight phase. Applications of this captive aerial detection system are equally discussed.