Sunken Treasures
Beneath the Blue

Scuba dive physics lab

Dive missions

Depth0.0m

Tank200bar

Dive time0:00

No-deco time99min

Treasure€0

Dive profile (depth vs time)

Net buoyancy0.0 N

BCD air0 L

Pressure / ppO21.00 atm / 0.21

Vertical speed0.0 m/min

Breathing (RMV)12 L/min

Light at depth R/G/B100/100/100 %

Bag

Controls
W/S swim forward / back (the diver swims where the camera looks) - A/D side-step - Shift hard kick (uses much more air)
R inflate BCD (rise) - F dump air (sink) - mouse drag or right stick: look - wheel: zoom
E grab / open chest - Q flashlight - P photo of marine life - L add air to the lift bag at the bronze bell
Goal: find the chest, collect treasure, photograph four species, enter the wreck, raise the bell, then ascend slowly (max 9 m/min) with a 3 minute safety stop at 5 m and 50 bar left.

Loading the wreck...

Dive report

The science

Experiments: simulation vs theory

Each test runs the simulator's own numerical code and compares it with an independent closed form or a published reference value. Tolerances are shown.

Settings and what-if

Water clarity 0.5x Lead weights 5.0 kg Gravity preset

Changing lead or water density changes the buoyancy force instantly - trim for neutral buoyancy at 5 m.

Pressure and Boyle's law

P(h) = P0 + rho g h -> 1 atm per 10.08 m of sea water P V = n R T -> V = V_surface / P_abs (BCD, wetsuit foam, lungs, bubbles) A bubble that leaves your regulator at 20 m grows to 3x its volume by the surface; a sealed lift bag does the same, so it accelerates as it rises. The wetsuit's foam gas compresses too, so you get heavier with depth (about 40% of the suit's lift is gone at 20 m).

Buoyancy and drag

F_net = rho g V_total - m_total g (Archimedes) m a = F_thrust - 1/2 rho (CdA)_f |v_f| v_f - 1/2 rho (CdA)_l |v_l| v_l + F_net (CdA)_f = 0.085 m2 (streamlined, head first), (CdA)_l = 0.42 m2 (broadside) apparent weight of treasure = m (1 - rho_water / rho_item) A 1 kg gold bar (19.3 g/cm3) feels like 0.95 kg in water; a bronze bell (8.8 g/cm3) of 22 kg still weighs about 19.5 kg-force, which is why it needs a lift bag. Simplifications: added mass is a fixed fraction, fin thrust is a smooth average (the kick animation is cosmetic), no currents.

Air consumption

VO2 = 0.30 + P_mech / (eta * 20.9 kJ/L) (eta = 0.15) RMV = 24 VO2 + 4 [L/min at surface pressure] gas drawn = RMV * P_abs -> air time = (200-50 bar) * 12 L / (RMV * P_abs) Doubling the depth roughly doubles the gas you breathe per minute because every breath is denser. Ideal-gas tank (real-gas compressibility ignored). RMV model is an illustrative approximation.

Nitrogen loading and the no-decompression limit

dP_t/dt = k (P_insp - P_t), k = ln2 / T_half P_t(t) = P_insp + (P_0 - P_insp) 2^(-t/T_half) (Haldane, exact step) tolerated ambient pressure P_tol = (P_t - a) b (Buhlmann ZH-L16 a, b) ceiling = depth where P_amb = max_i P_tol,i Five compartments (half-times 4, 12.5, 27, 54.3 and 109 min) use the published ZH-L16 N2 coefficients without gradient factors. This is an EDUCATIONAL model: never plan a real dive with it. Ascending faster than about 9 m/min is flagged.

Light under water (Beer-Lambert) and Snell's window

I(z) = I0 exp(-k z) k_red = 0.42, k_green = 0.065, k_blue = 0.028 m^-1 (clear water, typical) critical angle theta_c = asin(1 / n) = asin(1/1.333) = 48.6 deg Snell's window diameter at depth d = 2 d tan(theta_c) Red is gone by about 10 m, which is why the reef looks blue-green until the torch adds the colours back at short range (the torch path is only a metre or two). Looking up you see the whole sky squeezed into a 97 degree cone; outside it the surface is a mirror. The clarity slider scales all three coefficients.

Honest limitations

Single-diver rigid-body model with fixed gear; no currents, temperature, thermocline or exact Cd; fish and turtle motion is scripted (swim speeds are typical, not measured). Treasure values are illustrative. Models are baked in Blender; the model of the reference scene is stylised.

Sunken TreasuresBeneath the Blue

Dive missions–

Dive profile (depth vs time)

Dive report

Sunken Treasures
Beneath the Blue

Dive missions