Swimming Stroke Fluid Dynamics Simulator (2D)

Stroke

Stroke rate 50 /min

Stroke smoothness (technique) 50%

Swimmer mass 75 kg

Live motion

Velocity

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Average velocity

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Thrust force

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Drag force

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Energy over distance

Distance swum

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Work expended

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Cost of transport

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Avg thrust power

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m·dv/dt = F_thrust(t) − ½ρ_water·Cd·A·v². The average thrust power is held fixed as you move the smoothness slider — only the shape of the stroke changes, so any speed gain comes purely from spreading propulsion more evenly across the cycle.

How it works

The swimmer is a single point mass obeying Newton's second law along the direction of travel: m·dv/dt = F_thrust(t) − F_drag(v), with quadratic fluid drag F_drag = ½·ρ_water·Cd·A·v² (ρ_water = 1000 kg/m³).

Thrust is generated in pulses timed to the stroke cycle. The smoothness slider blends between a peaky, rectified-sine pulse (0%, like a single hard pull per stroke) and a constant push (100%, propulsion spread continuously through catch, pull and finish) — the blend is built so the average thrust power stays identical at every setting.

Because drag grows with v², a velocity that oscillates around a mean value produces more average drag than a constant velocity at that same mean (Jensen's inequality: mean(v²) ≥ mean(v)²). So a peaky stroke burns the same average power but reaches a lower average speed and a higher cost of transport than a smooth one — exactly what elite swimmers exploit by spreading propulsion across the whole stroke instead of a single hard yank.

Stroke rate changes how often the pulses arrive, which reshapes the velocity ripple without changing the average power input.
Mass changes how quickly the body accelerates but not the long-run average speed for a given thrust and technique.

Drag the sliders — watch the velocity trace and cost-of-transport respond