Several mathematical models are developed for a hose-drogue refueling system in an attempt to represent the physical system accurately and to subsequently observe the dynamic response of the system under different initial conditions. The mathematical models examined include a flexible hose model and a model which includes elastic bending effects. The equations of motion include aerodynamic, gravitational, and tensile forces, and solutions of the refueling system are found using fewer assumptions than in previous work.

Once the equations of motion are developed, they are separated into equilibrium and perturbation portions. Solutions of the nonlinear equilibrium tension distribution are obtained by solving the equations in closed form using a two point boundary value problem solver program. The solution to the linear equilibrium tension distribution is found and compared to the nonlinear solutions. Results indicate that the behavior of the solutions is similar, but the linear solution gives larger values of tension near the hose attachment point.

The perturbation equation is discretized using a finite difference scheme and the resulting first order differential matrix equation is integrated to calculate the dynamic response for given parameters and initial conditions with the various equilibrium tension distribution solutions. Results show negligible differences between the different tension values upon substitution and it is therefore recommended that the linear approximation to the equilibrium tension distribution be used in analysis of this hose-drogue refueling system because of the ease in obtaining solutions with this method.