Chapter 13 · reward round
Submarine Trim
Hold the boat inside the gold band until the survey bar fills. Drag the boat down to flood and sink, up to blow and rise — or hold the pump buttons.
Play Submarine Trim
Dive 1: Neutral means ρ_sub = ρ_water.
↓ flood · ↑ blow · Space run · R resetReady
How the physics works
The dry boat is 1000 kg and it displaces a fixed 1.20 m³. Only the ballast water changes m, so the pump is a direct handle on the average density of the whole boat.
Upthrust is the weight of the displaced water. V is fixed, so the only thing that changes the upthrust as you descend is ρwater — which is exactly what the halocline does to you.
Substituting m = ρsubV into W = mg collapses the whole vertical balance into one density difference. Δρ = 0 holds depth, its sign decides sink or rise and its size decides how fast.
In uniform water this is P = ρgh. In layered water the gauge pressure is the running integral of the profile, which is why the crush depth on dive 4 is not a round number. Absolute pressure adds the 101.3 kPa of atmosphere above the surface.
With Cd = 0.90, A = 1.4 m² and b = 480 N·s/m, a 25 kg trim error settles at about 0.35 m/s, so a small early correction beats a big late one. Every other number: g = 9.81 m/s², dry hull 1000 kg, V = 1.20 m³, ballast 0–340 kg, pump 46 kg/s, fixed step 1/120 s, semi-implicit Euler.