Time 0:00Arrived 0At weir 0Tired / dead 0Median —Current 0 m/sFPS 0

Drag to orbit, wheel or pinch to zoom; the camera follows the lead fish and goes underwater when you orbit low. Fish swim upstream (right); the river flows to the left. Red dots on the map are fish, the grey bar is the weir, the dashed line is the fish ladder. Fish are drawn about 1.4x life size.

Salmon River Run: Swim Cost, Weir Leaps and Fish-Ladder Jets

Swimming against a current costs power with the cube of speed. Which speed gets a fish upstream cheapest, and can it clear a weir by leaping or by a ladder?

River and weir

Fish ladder

Fish and swimming

Time

Live readouts

Current vs what a fish can do

Cost of transport vs swim speed

Endurance (Brett-type curve)

Ladder jet vs the fish's burst capacity

Fish reaching the spawning gravel

Experiment: how many ladder steps?

Runs the whole school for 2 to 24 steps over the same weir height (fast-forward) and plots the share that reaches the gravel.

Independent numerical checks

Controls

Drag / one finger: orbit; wheel / pinch: zoom. "Camera" cycles follow-fish, weir overview and ladder close-up.
Presets set current, weir height and ladder; every slider stays editable. Time scale = simulated seconds per real second.
"Swim speed as multiple of current" is the fish's rule: 1.5 is the minimum-cost value for cubic drag; lower is slow and tiring over time, higher burns energy and fatigues faster.
Resting pockets: fish tuck behind boulders and recover when fatigue passes 60 %. Without them a fatigued fish is swept back.

The science

Swimming power. Drag power P = ½ ρ C_D S u³ with wetted area S = 0.42 L² and an effective C_D = 0.015 (an active-swimming allowance over a rigid body, illustrative), divided by an overall efficiency of 0.2, plus standard metabolism 0.4 W/kg with a Q₁₀ of 2.1 for temperature. In a current U the ground speed is u − U, so the cost per metre is P(u)/(u − U); with pure cubic drag its minimum is exactly u = 1.5 U, and standing metabolism pushes the optimum a little higher. The page checks the numeric minimum against 1.5 U.

Fatigue. Endurance follows a Brett-type curve log₁₀ t = A − B·u (u in body lengths per second), calibrated to 1 hour at 2.5 BL/s and 15 s at 6 BL/s (illustrative round numbers for adult sockeye, not a measurement). Fatigue accumulates by Miner's rule, dD = dt / t(u); at D = 1 the fish is exhausted and is swept downstream until it can rest and recover.

Leaping. A fish leaving the water at burst speed v and angle θ rises h = (v sin θ)² / 2g. A plunge pool must be deep enough: the usable height is scaled by min(1, depth / (1.25 h)). Burst capacity is about 10 body lengths per second, reduced for fish with a low energy reserve; each attempt costs a short burst of power and fatigue.

Fish ladder. A pool-and-weir ladder splits the weir height H into n equal drops Δh = H/n. Each drop drives a jet of about 0.85 √(2 g Δh) (Torricelli with a discharge loss); a fish must swim at that speed plus a margin for about 1.2 m, then rests in the next pool. Steps that are too tall give a jet faster than the fish can sustain for long enough: it fatigues and falls back. Entrance finding is a random process with a mean time you can set.

Limits. The river is a one-dimensional reach with a made-up current profile (riffles, a slower plunge pool, an impounded reach); no turbulence, temperature profile, predators, nets or migration-timing effects. All constants are illustrative; check species data before quoting numbers.

Models built with Blender (salmon, river bed, boulders, trees) and rendered with Three.js; weir and ladder are simple concrete blocks. Not an engineering design tool.