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Description of the physical model

Description of the physical model. Forces applied to the vehicle : weight buoyancy drag The depth x(t) of the drogue can thus be described by the following differential equation: where M equals m + added mass of displaced fluid V is the total volume and ρ is the water density.

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Description of the physical model

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  1. Description of the physical model Forces applied to the vehicle : • weight • buoyancy • drag The depth x(t) of the drogue can thus be described by the following differential equation: where M equals m + added mass of displaced fluid V is the total volume and ρis the water density

  2. Description of the physical model If x(t)<surface cutoff depth the equation is a bit modified: where σis a surface effect coefficient σ≈ 1/20 surface cutoff depth ≈ 15cm

  3. Computation of the total volume V Contributions to the total volume: • Volume of the drogue • Volume of the trapped air bubbles The raw volume of the drogue only depends on the control position:

  4. Computation of the total volume V Taking into account the drogue’s elasticity, the actual volume of the drogue is given by:

  5. Computation of the total volume V We assume 1) ideal gas behavior for the air inside the trapped bubbles 2) constant temperature 3) no surface tension so that and consequently

  6. Computation of the total volume V Therefore the total volume is given by

  7. Summary of the physical parameters • cavity section • added mass of displaced fluid • drag • radial elasticity of the drogue • magnitude of the surface effect • surface cutoff

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