Presets
Playback
Trim
Ballast tank fill, payload and vertical thruster.
Ocean and start
Water density, an optional thermocline, drag and the start depth.
Layers
Model checks
The science
Archimedes and trim
A rigid hull of volume V = 8 m3 displaces water of density rho and feels the buoyant force B = rho V g. Its weight is W = m g with m = 7640 kg + ballast fill x 1120 kg + payload change. Neutral trim means B = W, i.e. ballast fill = (rho V - M) / capacity. The "Find neutral trim" button solves exactly this; the check below re-solves it by bisection.
Motion with drag
Vertical motion obeys m dv/dt = B - W + T - Cd v |v| (T = 62 N per percent of thruster, quadratic drag, v positive when rising). A constant net force F gives a terminal speed v_t = sqrt(F / Cd). In the 3D lab the water density is uniform, so neutral buoyancy is neutral equilibrium: the craft stays at whatever depth you put it.
Thermocline (2D-only option)
Real oceans are stratified. With the thermocline slider the density rises smoothly by delta rho across a layer centred at 200 m: rho(z) = rho0 + delta rho (1 + tanh((z - 200)/60)) / 2. A craft that is light compared with the dense layer and heavy compared with the upper layer now has a restoring force and settles at the equilibrium depth where rho(z*) V = m (green dashed line), found by bisection.
Pressure
Absolute pressure is p = p0 + integral of rho g dz, with p0 = 101,325 Pa; about 1 atm per 10 m of seawater. It is shown in the last graph and checked against the closed form for constant density.
Simplifications
The hull is incompressible (a real hull and the water itself compress slightly with depth), there is no added mass, no horizontal motion and no waves. Educational model of an unmanned research vehicle.
What to try
- Press Find neutral trim: net force drops to zero and the vehicle hangs in place.
- Pick Heavy: dive and watch the speed rise to the terminal value where drag equals the net force.
- Pick Stratified ocean: the vehicle sinks, overshoots slightly and settles at the equilibrium depth inside the thermocline.
- Pick Fresh-water lake and compare the neutral ballast fill with seawater.