  Recent major oil-spills were tracked using observations with sufficient
altitudes over the sea surface, to detect oil slick locations. For oil-spill
responders, we propose a captive Unmanned Aerial System, UAS acting like a
periscope over a ship or supply vessel. The system is composed of an umbilical
deployed from ship deck, and there are few studies that have examined
elasticity within cable dynamic during take-off or landing (TOL) and normal
flight phases. Therefore, the safest approach for the control-commands of the
system is through umbilical dynamic modelling. We give a time-dependant
finite-element formulation, using improved elastic non-linear cable elements.
Two kinds of boundary condition, natural or essential, are discussed for
roll-in or roll-out of the umbilical. A numerical convergence and a validation
with an exact solution are provided, using two examples for the flight
parameters. Finally, sensitivity of the model potentially extends its capacity
for the system equilibrium prediction, under wind primary influence.
