The Physics of Swimming: How Fluid Dynamics Powers Every Stroke

Water Doesn’t Want You in It

That’s not quite true, physically. But it feels true. If you’ve ever jumped into a pool and tried to sprint to the other end, you’ve experienced something that no amount of gym fitness prepares you for: water is roughly 800 times denser than air. Every movement you make has to push that mass aside. Every stroke has to overcome drag forces that scale with the square of your speed. Swimming fast is, from a physics perspective, absurdly expensive.

And yet. Humans swim. We swim recreationally, competitively, desperately. We’ve refined four competitive strokes over a century of Olympic competition, shaved seconds off world records through biomechanical analysis and suit technology, and built entire training programmes around the fluid dynamics of a human body moving through water at two metres per second.

The physics is beautiful. Also humbling. A dolphin does it better without thinking about it at all.

Buoyancy: Why You Float (Mostly)

Before you can swim, you have to not sink. That’s buoyancy, and it’s straightforward Archimedes: an object in a fluid experiences an upward force equal to the weight of the fluid it displaces.

The human body has an average density of about 950–1,050 kg/m³, depending on body composition. Muscle is denser than water (about 1,060 kg/m³). Fat is less dense (about 920 kg/m³). Bone is much denser (1,800+ kg/m³). Air in the lungs significantly reduces your effective density.

Fresh water has a density of 1,000 kg/m³. Seawater is about 1,025 kg/m³. So whether you float or sink depends on the balance: lean, muscular people with low body fat and empty lungs can sink. People with higher body fat percentages or full lungs tend to float. Take a deep breath and you’re probably buoyant. Exhale completely and you might not be.

This matters for swimming because a buoyant body sits higher in the water, exposing less frontal area below the surface. Less frontal area means less pressure drag. Female swimmers, who on average carry slightly higher body fat percentages than male swimmers, tend to ride higher in the water — a small but real hydrodynamic advantage that partially offsets differences in power output.

I find it interesting that the physics gives with one hand and takes with the other. More buoyancy means less drag. But the body composition that creates buoyancy — more fat — also typically means less muscle power. Elite swimming is about optimising the whole system, not just one variable.

Drag: The Three-Headed Monster

Drag is the central problem of swimming. Everything about stroke technique, body position, and racing strategy is ultimately about managing drag. There are three types, and they all matter.

Pressure drag (also called form drag) is the big one. It comes from the pressure difference between the front and back of your body as you move through water. Water piles up at your chest and head, creating high pressure. Behind you, the flow separates from your body and creates a low-pressure wake. The pressure difference pushes you backward. Pressure drag depends on your frontal cross-sectional area and your body’s streamlining. A swimmer in a streamlined position — arms extended overhead, body straight, head down — has dramatically less pressure drag than a swimmer with their head up and knees dropping.

Friction drag comes from the viscous shearing of water against your skin surface. Water molecules in contact with your skin are stationary (the no-slip condition, same as in aerodynamics), and each layer above moves progressively faster. This velocity gradient creates a shear stress on your body surface. Friction drag depends on total wetted surface area and surface roughness. This is why swimmers shave their bodies and wear smooth caps and suits — reducing surface roughness reduces friction drag.

Wave drag is the energy lost to creating surface waves as you swim. Your body moves near the air-water interface, and the pressure disturbances you create propagate as waves that carry energy away. Wave drag is negligible at slow speeds but becomes dominant as you approach a critical speed related to your body length — the hull speed, a concept borrowed from naval architecture.

Hull speed for a displacement body is approximately v = 1.34 × √L, where L is waterline length in feet and v is in knots. For a swimmer about 1.8 metres (6 feet) long, hull speed works out to roughly 2.2 m/s — which is remarkably close to the speed of Olympic freestyle sprinters. At this speed, the bow wave (from your head) and stern wave (from your feet) constructively interfere, creating a single large wave that the swimmer is essentially trapped in. Going faster requires climbing over your own bow wave, which demands disproportionately more power.

This is probably the single most important physics fact in competitive swimming. Elite sprinters are swimming at or near hull speed, where wave drag dominates and every additional tenth of a second of speed requires substantially more energy. The difference between a 47-second and a 48-second 100m freestyle is not 2% more effort. It’s more like 10–15% more power output, because of how steeply wave drag scales near hull speed.

Propulsion: Pushing Water Backward

Swimming propulsion is surprisingly poorly understood. I mean that — the biomechanics community has debated the relative contributions of different propulsive mechanisms for decades, and there isn’t complete consensus even now.

The simplest model is Newtonian: your hand and forearm push water backward, and by Newton’s third law, the water pushes you forward. The thrust equals the rate of backward momentum you impart to the water. Bigger hand surface area, faster hand speed, better angle of attack — more thrust.

But there’s more to it. Skilled swimmers don’t just push water straight back. They sculling — sweeping the hand through curved paths, constantly adjusting the pitch angle. This generates lift forces on the hand (the same kind of lift that keeps an aeroplane wing airborne), which can contribute to propulsion in the forward direction. The hand acts like a wing, not just a paddle.

How much propulsion comes from drag forces (pushing water back) versus lift forces (sculling) is the debate. Current thinking suggests it varies by stroke phase and by individual technique, but drag-based thrust probably dominates in most competitive strokes. The lift contribution is real but secondary.

There’s also the kick. In freestyle, the flutter kick contributes only about 10–15% of total propulsion for elite swimmers — its main role is keeping the legs high and the body streamlined, reducing pressure drag. In breaststroke, the kick is a major propulsive force, generating roughly 50% of the thrust through a whip-like motion that pushes water backward very effectively.

The Reynolds Number: Why Size Matters

Here’s where swimming physics gets really interesting. The flow regime around a swimming body is characterised by the Reynolds number — a dimensionless ratio of inertial forces to viscous forces:

Re = ρvL/μ

where ρ is fluid density, v is velocity, L is body length, and μ is dynamic viscosity.

For an adult human swimming at 1.5 m/s, Re is roughly 2–3 million. This is firmly in the turbulent regime. The flow around the body is chaotic, with eddies and vortex shedding and a turbulent wake. Drag is dominated by pressure effects and turbulent friction.

For a sperm cell swimming at maybe 50 micrometres per second, Re is about 0.00001. This is the extreme low-Reynolds-number regime, where viscous forces completely dominate. At this scale, inertia is irrelevant. If a sperm cell stopped moving its flagellum, it would coast for a distance of about 0.1 angströms before stopping — less than the diameter of an atom. The water at that scale might as well be honey. Or cold tar.

This matters because the physics of propulsion is completely different at different Reynolds numbers. The reciprocal stroke that works for a human — push water back with your hand, then swing your arm forward through the air — would produce zero net propulsion at low Reynolds number. At Re << 1, the fluid dynamics are time-reversible: the forward stroke and the return stroke would cancel exactly. This is called the Scallop Theorem, and it explains why bacteria and sperm cells use rotating flagella and corkscrew motions rather than back-and-forth paddling. They need non-reciprocal motions to move at all.

I think this is one of the most surprising results in fluid dynamics. The swimming strategy that works for you and me is physically impossible for a bacterium. Same fluid, same basic physics, completely different regime. Scale changes everything.

Starts and Turns: Where Races Are Won

In a 50m pool, a 200m freestyle race involves seven turns. Each turn takes the swimmer off the wall at 2.5–3.0 m/s — significantly faster than swimming speed — and the underwater streamline phase after each push-off can cover 10–15 metres before the swimmer surfaces. That means roughly half the race distance is covered in the push-off and underwater phases, not in surface swimming.

The physics of the push-off is simple: the swimmer plants their feet on the wall and extends their legs, applying a force of roughly 1,500–2,500 N over about 0.3 seconds. This imparts an impulse that accelerates the swimmer to wall departure speed. The subsequent underwater glide — body in a tight streamline, minimal frontal area — decelerates slowly because streamlined drag is much lower than surface swimming drag. There’s no wave drag underwater.

This is why underwater dolphin kicks after turns and starts have become so important in modern swimming. Swimmers stay submerged in the streamline position, performing undulatory kicks that maintain speed with much less drag than surface swimming. Some swimmers (notably backstrokers) can maintain speeds of 2.0+ m/s for 15 metres underwater — the maximum distance allowed by the rules before surfacing.

FINA (now World Aquatics) limits the underwater phase to 15 metres precisely because the physics advantage is so large. Without this rule, the fastest way to swim some races would be to stay underwater for the entire length, surfacing only to breathe — essentially turning swimming into underwater dolphin kicking with occasional gasps.

Why Humans Are Bad at This

Let me put it in perspective. Michael Phelps, arguably the greatest swimmer in history, swims 100 metres in about 47 seconds. That’s 2.13 m/s. A dolphin cruises at 3–5 m/s and can burst to 12 m/s. A sailfish — the fastest fish — can exceed 30 m/s.

The physics explains the gap. A dolphin’s body is a near-perfect fusiform shape, tapering smoothly at both ends, with a drag coefficient roughly one-tenth that of a human. Its tail fin generates thrust through the entire oscillation cycle, not just half of it. Its skin may have micro-turbulence-managing properties. It has no protruding limbs creating additional drag.

Humans evolved for bipedal locomotion on land. Our bodies are optimised for walking and running — long legs, upright posture, arms for balance and tool use. In water, all of those adaptations become liabilities. Our upright body creates a huge frontal area. Our arm recovery phase (above water in freestyle) creates no thrust. Our legs, shaped for push-off and stride, generate modest thrust with enormous energy cost when used as fins.

We swim because we’re clever enough to develop technique that partially compensates for our terrible hydrodynamic shape. But we’ll never be fast. Not by fish standards. The physics of our body plan won’t allow it.

The Elegant Inefficiency

I think swimming might be the sport where physics humbles us the most. On land, a trained sprinter converts maybe 25% of metabolic energy into forward motion. In water, a trained swimmer converts about 6–9%. The rest is lost to drag, waves, and turbulence — the fluid fighting back against a body that was never designed to move through it.

And yet there’s something I find genuinely beautiful about watching a great swimmer. The physics is working against them at every moment — drag scaling with the square of speed, wave resistance peaking near hull speed, the Reynolds number locking them into a turbulent regime where finesse matters more than brute force. Every aspect of elite technique — the catch, the pull, the rotation, the streamline, the kick timing — is an empirical negotiation with fluid dynamics, refined over a century of competition.

Eight hundred times the density of air. Two metres per second through it. Not bad, for an animal designed to walk upright on dry ground.