Inspection ROV Thrusters

What is modelled

A small ROV with N identical propeller thrusters on its surge axis. Each thruster follows the open-water propeller law, thrust T = KT rho n2 D4 with KT falling as the advance ratio J = v / (n D) rises. The hull drag is quadratic in speed. The balance gives the terminal speed through the water, and holding station in a current means cancelling the drag at the current speed. Power comes from the torque law and an ideal actuator disc gives the lower bound.

Equations

• Thrust T = KT(J) rho n2 D4, KT = 0.35 (1 - J/0.9); torque Q = KQ rho n2 D5.
• Drag 0.5 rho CdA v2; dynamics (m + 0.6 m) dv/dt = N T - drag.
• Momentum theory P_ideal = T^1.5 / sqrt(2 rho A), disc velocity sqrt(T / 2 rho A).
• Pressure dp/dz = rho g (1 + p/K), p = K (e^(rho g z / K) - 1).
• Endurance E / (N P_el + P_hotel), P_el = 2 pi n Q / 0.8.

Checks run in the page

• Terminal speed by RK4 against a bisection on thrust = drag.
• Slipstream kinetic-energy flux against the momentum-theory power and a figure of merit below 1.
• Compressible-water pressure integration against its closed form.
• n squared and n cubed scaling, the station-keeping rpm and the battery drain stepped in time.

Honest simplifications

Straight-line, steady-flow model: fixed open-water coefficients typical of small ducted-free propellers (not a tested thruster), no hull-thruster interaction or thrust deduction, a constant drag coefficient with no Reynolds dependence, added mass of 60 percent, neutral buoyancy, motor efficiency 0.8, no tether drag, no waves. A teaching estimate, not a vehicle design.

• Press Strong current and see whether the thrusters can still move the vehicle forward over the ground.
• Press Hover in light current and read the rpm needed to hold station.
• Press Deep dive, big battery and compare the pressure with the constant-density value.