Drogue dynamic model under bow wave in probe-and-drogue refueling

Probe-and-drogue refueling (PDR) is widely adopted owing to its simple requirement of equipment and flexibility, but it has an apparent drawback that the drogue position is susceptible to disturbances. There are three types of disturbances: atmospheric turbulence, trailing vortex of the tanker, and bow wave effect caused by the receiver. The former two disturbances are independent of the receiver, whereas the bow wave effect, which depends on the state of the receiver, greatly influences the docking within a close distance. As far as the authors know, little attention has been paid to the bow wave effect on docking control in existing literature. The existing literature related to the bow wave focuses on either qualitative static results obtained from experiments, or lookup tables based on computational fluid dynamics (CFD) analysis. These are inapplicable to the PDR docking controller design directly. This paper proposes a lower order dynamic model to describe drogue dynamics under the bow wave effect. The model consists of two components: one is a second-order transfer function matrix to describe the drogue dynamics, and the other is a nonlinear function vector to describe the bow wave effect model. A closed-loop simulation including the two components shows that the generated drogue dynamics are similar to those of a real experiment reported in an existing literature.