ROV Dive Envelope

What is modelled

A vehicle dives from the surface to a commanded depth, pings the seafloor with sonar and cruises forward under its thrusters. The page follows the depth, the battery energy and the sonar echo, and plots how pressure, sound speed, sunlight and endurance depend on depth and throttle.

Equations

• Pressure with slightly compressible seawater dp/dz = ρ(p) g, ρ = ρ0 eβ (p − p0), giving p = p0 − ln(1 − β ρ0 g z) / β.
• Sound speed (Mackenzie form, salinity 35) c = 1448.96 + 4.591 T − 0.05304 T² + 2.374×10−4 T³ + 0.016 z with a thermocline temperature profile; echo delay 2 ∫ dz / c(z).
• Light I = I0 e−K z and a lamp E = Φ / (4 π d²) e−K d.
• Thruster power ½ ρ Cd A v³ / η; endurance Ebattery / (Photel + Plamps + Pthrusters).

Checks run in the page

• Fourth-order stepping of the pressure equation against the closed form.
• A sonar front stepped through the sound speed profile against the integral of dz / c.
• Stepped light attenuation to the 1 % depth and the inverse-square lamp ratio.
• A 1 s battery drain against energy divided by power.

Honest simplifications

The thermocline, the attenuation coefficient, the vehicle drag area, efficiency and lamp efficiency are illustrative numbers; the ROV moves at a fixed speed and depth rate with no tether, currents or ballast dynamics; sonar refraction, spreading and bottom type are ignored. This is not dive-planning data.

• Press Canyon at 2,400 m and read the pressure in bar and the echo delay.
• Press Turbid harbour water and watch the sunlight vanish within a few metres.
• Press Full throttle sprint: thruster power grows as the cube of the speed and the endurance collapses.