# Active drag, part 1: what it is and why it has to be inferred

> Passive drag is a force you can hang a weight against. Active drag is a quantity defined by subtraction. The first of five posts on how swimming resistance is measured.

- Source: https://swimas.co.nz/blog/active-drag-1-what-it-is/
- In plain English (ELI5): https://swimas.co.nz/blog/active-drag-1-what-it-is/eli5/
- Author: V. Karpov, swimas (Swimming Art & Science), New Zealand
- Published: 18 Oct 2026
- Topics: Active drag, Biomechanics; strokes: FR, BK, BR, FL

How much does the water truly hold a swimmer back? The question defies an easy answer, because the very medium that resists the swimmer's motion is also what propels them forward. When a swimmer is towed in a fixed streamlined position, drag can be measured directly from the force needed to sustain a constant speed. In swimming, however, the body's shape is in constant flux: its parts move in different directions while propulsive and resistive forces act at the same time. A swimmer's motion reveals only the net outcome of this interplay. At a steady average speed these opposing forces balance out over a complete stroke cycle, leaving their individual sizes unknown. Estimating active drag therefore demands assumptions about how to untangle propulsion from resistance. Because different methods rest on different assumptions, they can give starkly different estimates for the same swimmer. This leaves a coach with a practical question: when a test shows lower drag, has the swimmer's resistance really fallen, or has something shifted in the measurement itself?

Swimmers' resistance has been measured since the first towing experiments of the early 1900s, and the drag of a swimming body has been estimated since the 1970s, yet the question remains far from settled. The discrepancies are striking: on the same swimmers, two methods have differed by almost a factor of two, and across studies the published values of active drag run from about passive drag to three times passive drag. This post, the first of five, examines why the resistance of a body that is swimming is a different and much harder problem than that of a body being towed, explores what resistance is for a human body in water, and traces how the field arrived at its present state. The following posts take the measurement methods one family at a time (parts 2 to 4) before asking whether they agree and what a coach can actually draw from them (part 5). The series is a narrative review of selected work, not a systematic search: my own recalculations are derived from published tables, and wherever I note that something was not found, that applies to the sources I read.

## Passive drag: a well-posed question

Tow a swimmer who holds a fixed streamlined position, and the resisting force becomes a well-defined physical quantity. It depends on speed, posture, depth, and body size and shape, and it can be measured with a weight over a pulley, a dynamometer or a flume. Repeatability can be checked, though the literature reports two different kinds of figures. A swimmer held on a tether in a flume gave correlations of 0.98 across three repeats in one session (Roberts et al., 2003), which shows that the repeats rose and fell together, but not how far apart they were. With swimmers towed 0.6 m under the surface of a pool, the coefficient of variation over five repeats, a direct measure of that spread, did not exceed 15.1 per cent (Cortesi & Gatta, 2015). Posture matters in measurable ways: head position changes passive drag by 4 to 11 per cent, and arms extended overhead rather than held at the sides lower it by about 18 per cent (Cortesi & Gatta, 2015).

The trouble is that there is no clear relationship between a swimmer's passive and active drag (Wilson & Thorp, 2003). In the largest data set on the subject, 797 swimmers tested by Kolmogorov et al. (1997), the drag coefficient while swimming did not correlate at all with the drag coefficient while towed ($r = -0.09$). This does not mean that body size or shape are irrelevant, only that the two coefficients are not interchangeable. Whatever resistance a swimming body meets, it is not the resistance of the same body held still.

## Active drag: a question defined by subtraction

**Figure 1.** Passive drag is what a towed body feels. Active drag is defined by subtraction: propulsion and resistance act on the same body, and its motion shows only their net effect.

Two panels side by side. Left, passive drag: a swimmer towed or gliding in a fixed streamlined posture, one tow force forward and one drag force back. One unknown force, measured directly: hang a weight and read the steady speed; repeatable, with r = 0.98 between repeats (Roberts 2003). Right, active drag: a swimming swimmer whose limbs both propel and resist, with propulsion and resistance arrows; at constant speed they sum to zero over a cycle. Two unknown forces on one body, whose motion shows only their sum; every method is a set of assumptions that lets the sum be split, hence the disagreements.


Unlike a towed body, a swimming body is never rigid. The arms and legs that generate propulsion are also the parts that generate resistance; the trunk pitches and rolls; and the speed of the centre of mass rises and falls within every stroke cycle. In Kolmogorov's measurements on nine swimmers from the world top ten, the difference between the highest and the lowest speed in a cycle was about 8 to 9 per cent of the mean speed in front crawl, about 10 per cent in backstroke, 30 to 35 per cent in butterfly and about half the mean speed in breaststroke (Kolmogorov, 2008). These fluctuations are the net force at work: at every instant propulsion and resistance act together, on the same moving limbs, and no instrument measures the two apart. Measurements at single parts of the body come closest: pressure sensors on the hands and flow measurements around the arms and legs. Yet these capture only what happens at that part, not the force on the whole body (more below). To get drag from them, one has to fall back on the same force balance as the other methods: the hands' mean propulsion is taken for the whole of it and set equal to the mean drag (part 4). Ultimately, "active drag" is defined as the resistive part of a force balance that can only be split under assumptions.

## Three kinds of resistance

Whatever the method, the resistance it seeks to isolate stems from three physical mechanisms that act on any body moving through water.

**Skin friction** arises from the viscosity of water: in the thin boundary layer next to the body, water is dragged along with it, and the resulting shear stress holds the body back. It depends on the wetted area, the roughness of the surface and the state of the boundary layer (laminar or turbulent). It grows somewhat more slowly than the square of speed, at about v<sup>1.8</sup> at a swimmer's Reynolds numbers, according to the ITTC-1957 friction line, an empirical formula for the friction of a smooth flat plate used in naval architecture, which Webb et al. (2011) applied to a swimmer.

Treating the body as a flat plate allows one to estimate how far back the boundary layer stays laminar. Over a smooth plate the flow stays laminar up to a Reynolds number of about half a million, counted from the leading edge. For a swimmer that is just the first 0.3 m at 1.5 m/s and 0.2 m at 2 m/s, so only some 10 per cent of the skin would be under laminar flow, and where the layer turns turbulent the shear on the skin rises sharply (Polidori et al., 2006). On a real body the transition may come elsewhere: skin is not a smooth plate, the water a swimmer meets is not still, and the curves of the body speed the flow up and slow it down. Fitting a drag model to towing data, Mollendorf et al. (2004) put the start of the transition within a few centimetres of the swimmer's leading edge, the head in their tows, with the flow transitional over most of the body. Still, these figures are an estimate from theory, not a direct measurement on swimmers.

**Figure 2.** The boundary layer of a flat plate as long as a gliding swimmer, a textbook model (after Polidori et al., 2006) drawn along the body. From the fingertips the layer is laminar and thin; from a Reynolds number of 5·105, about 0.28 m from the fingertips at 1.5 m/s and 0.21 m at 2 m/s, it turns turbulent over a transition zone, drawn up to 106, and thickens, and the shear on the skin rises steeply. On a swimmer the transition has not been measured, and the body's curves change the flow, which separates at the neck and the small of the back (Figure 3). The layer is drawn four times thicker than it is.

An animated side view of a swimmer gliding under water in a streamline, the water coming from the left; from the fingertips to the toes the body is 2.74 m long. Above and below the body the boundary layer is drawn as a blue band, four times thicker than it is. Dots ride in the water, each at its own distance from the skin, also drawn four times larger, and at the speed the water has there, coloured from ochre where it is slow through teal to blue where it moves with the stream; the water is drawn about half as fast as it goes. Over the hands the layer is laminar and very thin, and the dots at the skin barely move. From a Reynolds number of 5·10<sup>5</sup> it turns turbulent over a transition zone, drawn up to 10<sup>6</sup>, and thickens towards the feet, where it is about 4.5 cm thick; the dots in it wander across it, those at the skin move faster than over the hands, and dots from the open water are taken into the thickening layer and slow down. The speed rises from 1.5 to 2.0 m/s, holds, and falls back, and the transition moves from 0.28 m to 0.21 m from the fingertips and back: the laminar part is 10 per cent of the body's length at 1.5 m/s and 8 per cent at 2.0 m/s. Under the body, on the same scale, a chart of the shear stress on the skin along the body, 0 to 12 pascals. In the laminar part it falls from high values at the fingertips to about 1 Pa at 1.5 m/s (about 2 Pa at 2.0 m/s); across the transition zone, shaded, it rises to about 4 Pa (about 7.5 Pa), and then falls slowly to about 3 Pa (about 5 Pa) at the toes. The curves for 1.5 and 2.0 m/s are drawn dashed, the current speed's over them. Flat-plate formulas in water at 27 °C, a textbook model rather than a measurement on a swimmer: the laminar layer's thickness after Polidori et al.'s integral solution and its shear after Blasius, the turbulent layer after the one-seventh power law, the two blended smoothly across the transition zone. A legend under the scene names the water, the boundary layer and the dots' colours, from still water to the stream's speed.


On a swimming person, skin friction has never been measured on its own: none of the studies of free swimming reviewed here separates it experimentally from pressure drag. Instead it is estimated in four ways. The first uses the flat-plate formula above, by which Webb et al. (2011) put friction at 8 per cent of one swimmer's passive drag at 1.55 m/s. The second computes the whole flow field around a three-dimensional model of a swimmer: gliding 0.9 m below the surface, friction was 8 per cent of the drag with the arms along the trunk and 13 per cent with the arms extended forward, its absolute value nearly the same in both positions (Marinho et al., 2009). Other computations of an underwater glide put the frictional share at 16 to 27 per cent, depending on the model (Bixler et al., 2007; Zaïdi et al., 2010). The third changes the surface itself and measures the difference, which is how shaving and swimwear are tested (below). The fourth relies on boundary-layer theory: Polidori et al. (2006) modelled the swimmer as a flat surface at a skin temperature of 33 °C and computed the shear stress in pool water from 20 to 30 °C. They found about 20 to 22 N of friction for a fully submerged swimmer at 2.8 m/s, and about 5 to 6 N at 2 m/s with half the body under water, some 4 to 5 per cent of total drag. Warmer water, which warms the boundary layer and lowers its viscosity, reduced friction by up to 1.5 per cent at high speeds, about 0.4 N between 20 and 30 °C. Most of these estimates make friction the smallest of the three components: Wilson (2018) puts surface drag under 5 per cent of the total, whereas Pendergast et al. (2005) assigned it a quarter.

Small as it is, friction is precisely what shaving and swimwear aim to reduce, though the evidence on how far they succeed is mixed. When nine college swimmers shaved their arms, legs and trunk, a 366 m breaststroke swim at about 90 per cent effort cost them 9 per cent less oxygen, left 20 per cent less lactate in their blood, and carried them 12 per cent further per stroke. In tethered swimming, where the body does not travel through the water, shaving changed nothing, whereas in a push-off glide the shaved swimmers lost speed more slowly (Sharp & Costill, 1989).

Suits whose fabric mimics shark skin are meant to cut friction itself. The scales of fast sharks carry fine ribs along the flow, riblets, and in the laboratory riblets genuinely lower friction: across experiments in water and air, as summarised by Koeltzsch et al. (2002), they reduce drag by up to about 10 per cent compared with a smooth surface. Imitating the shark more closely did not help: in an oil channel, rows of staggered finlets modelled on shark scales lowered the turbulent shear stress on a test plate by up to 7.3 per cent against a smooth reference, whereas plain straight ribs in the same tests lowered it by 9 per cent (Bechert et al., 2000). In the pool, that gain all but vanished. On the MAD system, swimming with the arms alone, the legs on a pull buoy, 13 swimmers in a FastSkin suit covering the trunk and legs met 2 per cent less active drag, a difference that was not statistically significant, against the 7.5 per cent the manufacturer had claimed from passive drag tests (Toussaint et al., 2002). Because friction forms so small a part of active drag, the authors concluded, "the possible effect on total drag of using friction-reducing fabrics can only be small" (p. 8). Roberts et al. (2003) tested the same suit in two ways. Towed in a flume, swimmers met the same passive drag in it as in briefs at speeds up to 2.5 m/s. Then nine swimmers swam three 183 m freestyle trials, at a moderate, a moderately hard and a hard effort of their own choosing: in the suit they went 2 per cent faster on average, but used 4 per cent more oxygen and ended with 10 per cent more lactate, and at the same speeds, 1.4 and 1.6 m/s, the two suits made no difference. So the suit did not make swimming easier: the swimmers chose to go faster and paid for it, which the authors attributed to the swimmers' expectations. And on a mannequin towed in a flume, low-drag suits lowered surface drag by only about 2 per cent (Wilson, 2018).

Friction also gave biology one of its longest-running puzzles. In 1936 Gray (as cited in Fish, 2006) modelled a dolphin as a rigid body with a turbulent boundary layer, calculated the power it would need at 10.1 m/s, found that more than its muscles could give, and proposed that the dolphin keeps the flow laminar through its own movement, which speeds up the water over the rear half of its body. "Gray's paradox" steered research into dolphin hydrodynamics, including their skin, for sixty years, even though the paradox rested on shaky numbers, with two weak points independent of each other. First, the speed of 10.1 m/s came from a dolphin seen swimming alongside a ship: it may have been riding the ship's bow wave, which would have done part of the work, so that the dolphin itself did not produce that power. Second, even if the dolphin did swim that fast on its own, it can hold such a speed only briefly, like a sprinter, whereas its muscle power was estimated from an oarsman's long, sustained effort; over a short burst, muscles can give considerably more power (Fish, 2006).

**Pressure drag**, also called form drag, is the part of resistance governed by the body's shape. At the very front of the body the oncoming water is brought to a halt, and the pressure there is highest. The water then speeds up to pass around the body, and along the sides its pressure drops below that of the undisturbed water; behind the widest part the flow must slow down again to fill the space the body leaves, and the pressure rises once more. Already slowed by skin friction, the thin boundary layer next to the skin cannot push on against this rising pressure: it separates from the surface, and behind the line of separation the body trails a wake in which the pressure stays low. High pressure in front and low pressure behind add up to a net force holding the body back. The separated layers roll up into eddies; behind a bluff body they break away from one side and then the other and drift off downstream, as Figure 3 shows schematically. So pressure drag too owes its existence to viscosity: in an ideal fluid without it, the flow would close smoothly behind a body deep under water, and there would be no resistance at all (d'Alembert's paradox).

How large pressure drag is depends less on the size of a body than on its shape, and above all on its rear: on where the flow separates and how wide a wake it leaves. For the same frontal area, the drag coefficient of a flat plate across the flow is 1.28, of a ball up to 0.5, and of a streamlined wing section just 0.045 (NASA Glenn Research Center, 2025). These are values for simple shapes, not for a swimmer's body, but they show how much shape matters. A hand held out of a moving car's window shows the same: palm to the wind it is pushed back hard, turned edge-on it slices through. Because pressure differences scale with the dynamic pressure, $\tfrac{1}{2}\rho v^2$, pressure drag grows roughly with the square of speed, as long as the flow separates at the same place.

For a swimmer, this is what a streamline is for. One hand stacked on the other with the head between the arms presents a single narrow leading edge to the water instead of a head, two hands and two shoulders, and a straight body with the legs together and the toes pointed lets the flow stay attached down to the feet instead of breaking away early at the hips, behind bent knees or past feet not fully pointed. Even a tight streamline, however, cannot keep the flow attached everywhere. In a computed flow round a gliding swimmer the flow broke away behind the back of the head, under the chin and in the hollow of the lower back (Sato & Hino, 2010), and tufts on the suits of French national-team swimmers gliding at 2.2 m/s showed it separating over the back and on the buttocks (Zaïdi et al., 2010). In that computation pressure drag came to about six times friction, whereas on a ship's hull pressure drag is usually under 30 per cent of the friction drag (Sato & Hino, 2010). A lifted head, sinking hips or a trunk inclined to the flow presents a wider, blunter front and leaves a broader wake: while swimming, the trunk is inclined about 10 to 12 degrees to the flow, against 4 to 6 degrees when towed faster than 1 m/s (Zamparo et al., 2009); the measured effects of head and arm position on passive drag are given above. Yet the same mechanism also works for the swimmer: a palm set squarely against the water gets much of its grip from pressure drag.

Where the flow separates depends also on the state of the boundary layer, and here turbulence offers one distinct advantage: a turbulent layer clings to the body longer before separating, so the wake, and with it pressure drag, is smaller. On a smooth sphere a laminar layer separated at about 82 degrees from the front stagnation point; once the layer turned turbulent before separating, at Reynolds numbers above about 3·10<sup>5</sup>, it stayed attached to about 120 degrees, and the drag coefficient fell from about 0.5 to below 0.1 (Achenbach, 1972). The dimples on a golf ball are there to trip the layer so that this happens within the speeds of a driven ball (Bearman & Harvey, 1976). On a swimmer the effect is weaker and less clear-cut. In a towing tank a swimmer's head at the surface showed such a drop in drag, though there it was tied to the bow wave turning into a smooth sheet; under the surface the head's drag coefficient fell by only 6 per cent, and a whole mannequin showed no drop at all, though in a cap over which the flow had already changed it met about 7 per cent less drag at 1.7 and 1.8 m/s than in one over which it had not (James, 2016). In towing tests at 2.2 m/s, suits covering the body from the shoulders to the knees or to the ankles met about 10 and 5 per cent less drag than briefs; when the measured drag was split by fitting a model, friction came out higher and pressure and wave drag lower, which Mollendorf et al. (2004) put down to the suit tripping the boundary layer and keeping the flow attached longer, an effect swimwear makers sometimes seek by design (Polidori et al., 2006). No direct measurement of the boundary layer itself on a swimmer was found in the sources reviewed.

**Figure 3.** Pressure drag. Above, three bodies with the same frontal area: the water piles up ahead of each (high pressure), and behind the plate and the ball it breaks away into a wake of eddies (low pressure); behind the streamlined section it closes again. Their drag coefficients are from NASA Glenn Research Center (2025). Below, a swimmer gliding. In a streamline, drawn after a computed flow and tufts on swimmers (Sato & Hino, 2010; Zaïdi et al., 2010), the pressure is higher where the water meets the body and in its hollows and lower over its bulges, and the flow still separates at the neck and the small of the back and from the buttocks back. With the head lifted, the hips sunk and the knees bent, the front is wider and the wake wider and turbulent; this posture is drawn schematically.

An animated figure in two parts. The water comes from the left, drawn as dotted streamlines moving with it. Above, three bodies of the same frontal height in the same stream, each with its drag coefficient for the same frontal area and a bar of that length: a plate across the flow, 1.28; a ball, up to 0.5; a streamlined section, 0.045. A shaded patch ahead of each body marks the high pressure where the water piles up (+). Behind the plate the flow breaks away at its edges and leaves a wake wider than the plate; behind the ball it breaks away a little before the widest point and leaves a wake about as wide as the ball. In both wakes, shaded and at low pressure (−), eddies are shed from each side in turn and drift away. Behind the streamlined section the streamlines close again and the wake is a thin line. Below, the same swimmer gliding in two postures, one above the other, with a legend: an ochre line for pressure higher than in the open water, a blue line for lower, a shaded pocket with a curl for separated flow, and shading for slowed water. The streamline, the arms stretched, the head between them, the body and legs straight, is drawn after a computed flow round a gliding swimmer and tufts on swimmers' suits (Sato and Hino 2010; Zaïdi et al. 2010). The water stops at the fingertips and at the crown of the head. Along the back the pressure is lower over the back of the head, higher at the nape, lower over the shoulder blades, higher in the small of the back, lower over the buttocks, higher behind the knees, lower over the calves and higher at the heels; underneath it is higher on the upper chest and lower over the widest part of the chest. Small pockets of separated flow, drawn larger than they are, sit behind the back of the head, under the chin and over the small of the back. From behind the buttocks slowed water wraps the legs, about 0.23 m deep by the shins, and trails behind the feet, with no eddies shed in turn. With the head lifted, the hips sunk and the knees bent, the body meets the water with a wider front, a larger pocket forms behind the head, the flow breaks away at the hips, and a wider, turbulent wake trails behind the legs: its edge ragged and shifting, a few large eddies rolling up off the buttocks and the knees at irregular moments, either way round, stretching and breaking up downstream among many small ones, with no row shed in turn; this posture is schematic, as no published computation or measurement shows its flow.


**Wave drag** arises at the free surface: a body moving along it makes waves, the waves carry energy away, and the force that supplies that energy is wave drag. This is the component that sets swimming apart from, say, cycling or flying: like a ship, a swimmer travels along the boundary between water and air. Yet a ship has a rigid hull that can be shaped into an efficient hydrodynamic form, and a separate engine to drive it. A swimmer's body must serve as both hull and engine, and to move at all it must keep changing shape, giving up its streamline with every stroke.

The head pushes the water ahead of it up into a bow wave; behind it the surface drops into a trough and rises again into the next crest, and so on along the body and behind it, as behind a boat. For waves on deep water that keep pace with the swimmer, their length $\lambda$ is set by the speed $v$: $\lambda = 2\pi v^2/g$, where $g$ is the acceleration due to gravity, 9.81 m/s². That gives about 1.1 m at 1.3 m/s, 1.9 m at 1.72 m/s and 2.5 m at 2 m/s. At low speed several short waves fit along the body. As speed rises they stretch until, at the so-called hull speed, a single wave is as long as the body: the swimmer lies cradled in the trough between their own bow and stern crests, and to go any faster they must literally swim uphill, climbing their own bow wave (Barbosa, 2018). Hull speed is $v = \sqrt{g L/2\pi}$, where $L$ is the body's length; this corresponds to a Froude number, $\mathrm{Fr} = v/\sqrt{g L}$ (speed divided by the square root of gravity times body length), of about 0.4. For a swimmer 1.9 m tall it is 1.72 m/s, so taller swimmers have a higher hull speed, and young swimmers gain it as they grow. Borrowed from naval architecture, hull speed is a useful heuristic for seeing why wave drag rises so steeply, not a hard limit on a swimmer's speed.

Swimmers do go faster than their hull speed, but at a steep price. Elite men's front crawl sprinters swim at Froude numbers of up to 0.46 (Kolmogorov, 2008); in the London 2012 Olympic finals the medallists in the 400 m freestyle swam at about their hull speed, those in the 50 m about a fifth faster than theirs (Barbosa, 2018). That is why wave drag depends on the Froude number and, over the range of swimming speeds, grows faster than the square of speed. Being a surface effect, however, it falls off quickly with depth (the numbers are below), and it can be shared. A swimmer drafting close behind another moves through water the leader has already set moving and makes smaller waves: half a metre behind the leader, the follower's drag coefficient is about 56 per cent of the leader's, six metres behind still about 84 per cent (Barbosa, 2018).

**Figure 4.** Hull speed. The wave a swimmer makes at the surface grows longer with speed: λ = 2πv²/g, where λ is the wavelength, v the speed and g the acceleration due to gravity. At the hull speed it is as long as the body (λ = L, where L is the body's length; a Froude number of about 0.40, 1.72 m/s for a swimmer 1.9 m tall), and the swimmer lies in the trough between his own bow and stern crests; to go faster he must climb his bow wave (after Barbosa, 2018). Elite crawl sprinters reach a Froude number of 0.46 (Kolmogorov, 2008).

An animated side view of a front crawl swimmer 1.90 m tall at the surface, with the wave he makes; wave heights are exaggerated. The speed rises from 1.30 m/s (Froude number 0.30) to 1.72 m/s and holds, rises to 1.99 m/s (0.46) and holds, and falls back to 1.72 m/s. The wavelength λ, marked from crest to crest above the water, follows λ = 2πv²/g, where v is the speed and g the acceleration due to gravity: 1.08 m at 1.30 m/s, shorter than the body; 1.90 m at 1.72 m/s, equal to the body length marked under the swimmer, with the bow crest at his head, the next crest at his feet and the trough between them ("hull speed: λ = L, the swimmer in his own trough"); 2.53 m at 1.99 m/s, longer than the body, the swimmer pitched a little nose up ("climbing his own bow wave"). A scale of the Froude number v/√(gL), where L is the body's length, from 0.30 to 0.50 marks the hull speed at 0.40 and elite crawl sprinters at 0.46, with a marker moving to the current value.


**Figure 5.** The three components as a function of speed, drawn schematically. Friction grows somewhat more slowly than v² (about v1.8), pressure drag about as v², and wave drag faster (about $v^{2.9}$ for a passive mannequin below 2 m/s; Vennell et al., 2006). How large the wave share is at sprint speed is contested.

A schematic chart of passive drag: resistance in newtons, 0 to 100, against swimming speed, 0.8 to 2.2 metres a second. Three components are stacked: friction at the bottom, pressure (form) drag on it, and wave drag on top; the total rises ever more steeply with speed. Friction grows about as speed to the power 1.8, pressure drag about as its square, and wave drag faster still. A note gives the wave share as published: 20 per cent for crawl at 2.0 m/s (Pendergast 2005) to 60 per cent in passive towing (Vennell 2006; Webb 2011). The shares are drawn after Webb et al. 2011 at 1.55 m/s; the magnitudes are illustrative, not measured.


There is little consensus on how much each component contributes at race pace.

- Pendergast et al. (2005) estimated that in front crawl at 2 m/s, resistance is about 25 per cent friction, 55 per cent pressure drag and 20 per cent wave drag.
- Flume tests of a passive mannequin (Vennell et al., 2006) found total resistance at the surface up to 2.4 times that of the same body fully submerged, with wave drag reaching 50 to 60 per cent of the total at 1.7 m/s and falling below 5 per cent at depths of 0.5 to 0.7 m.
- Webb et al. (2011), applying naval-architecture methods to one swimmer's passive drag at 1.55 m/s, attributed 59 per cent to waves, 33 per cent to the wake and 8 per cent to friction.
- Wilson and Thorp (2003), splitting published active-drag curves into three terms, put the waves at 10 to 20 per cent at 1 m/s and 30 to 40 per cent at 1.9 m/s, pressure drag remaining the largest part. Later Wilson (2018), citing both that paper and Vennell et al. (2006), gave the waves 60 to 70 per cent at maximal speed and pressure drag 30 to 40 per cent, the share the 2003 paper had given the waves.
- Measurements on swimmers at the Australian Institute of Sport (Tor et al., 2015) found total resistance 20 per cent lower at a depth of 0.5 m and 24 per cent lower at 1.0 m, with the wave component down 70 per cent and nearly 100 per cent respectively. Dickson et al. (2020), meanwhile, found no further fall in a mannequin's wave resistance below 0.4 m at 2.5 m/s and, in simulations at 0.4 m depth and 1.0 m/s, a 10 to 66 per cent increase in wave resistance from deviations in body pitch.

Whatever the precise shares, two conclusions hold in the sources reviewed. First, resistance grows roughly as the square of speed, so that even a modest gain in speed demands a disproportionate increase in force. Second, wave-making can steepen that curve further: Vennell et al. (2006) fitted an exponent of 2.3 for a mannequin at the surface against 2.0 submerged. Fitted exponents also vary with posture, technique and the speed range tested; across the passive-drag literature reviewed by Havriluk (2005), they span 1.66 to 2.42. This becomes crucial later on, because nearly every method of estimating active drag assumes an exponent of exactly two.

> **Aside: Why so few animals swim at the surface**
>
> Travelling along the boundary of water and air is so costly that the animals that live by swimming avoid it. Fish, dolphins, seals and penguins travel under water, and those that breathe air come up only to breathe; wave drag becomes negligible once a body is more than two to three of its own diameters below the surface (Hertel, 1966, as cited in Fish, 2000). Fast dolphins even take to the air: above a certain speed, a run of leaps costs them less than swimming just under the surface (Au & Weihs, 1980).
>
> The animals that do swim at the surface are mostly semiaquatic, such as ducks, muskrats, mink and otters, and they pay for it in drag, energy and speed. A harbour seal towed at the surface met 2.5 times the drag it met submerged at the same speed (Williams & Kooyman, 1985, as cited in Fish, 2000). Paddling, the way surface swimmers move, is the costliest way for a mammal to swim, and a surface swimmer can hardly go faster than its hull speed, at which its bow wave grows as long as its body and the animal is "effectively trapped in a wave trough" (Fish, 2000, p. 686). Ducklings get round this in two ways: they rise out of the water and plane, reaching four times their hull speed (Aigeldinger & Fish, 1995), or they line up behind their mother to ride her wave (Yuan et al., 2021).
>
> People swim at the surface because they have to breathe, not because it is fast. As noted above, an elite front crawl sprinter swims at a Froude number of up to about 0.46 (Kolmogorov, 2008), around and just beyond the hull speed of a body that long (a Froude number of about 0.4), where wave drag rises most steeply. So after the start and each turn swimmers stay under water for a while: the body still carries the speed of the dive or the push-off, and below the surface it loses less of it to waves. Some swimmers, kicking dolphin-style under water on their backs and on their fronts, proved faster than on the surface, and the rules now limit the underwater part to 15 m in freestyle, backstroke and butterfly.


## Splitting propulsion from resistance

The same three mechanisms act on a swimmer moving under their own power, yet in free swimming even their sum, the total resistance, cannot be measured apart from propulsion. Observations of the flow show why. Unlike a towed body, a swimmer's hands and feet keep changing speed and direction, so the flow around them never settles into a steady pattern (Matsuuchi et al., 2009; Takagi et al., 2016). In a flume, as a front crawl swimmer's hand reversed its sideways sweep, the vortex it had been carrying was shed into the water while a new vortex of opposite rotation formed around the hand, and the pair drove a jet of water backwards (Matsuuchi et al., 2009). Where force, pressure and flow were recorded at the same time, on a robotic hand and on the hand of a sculling swimmer, the peak forces came as a vortex formed on the back of the hand and the pressure there fell. Those peaks far exceeded what steady-flow calculations predict: 11.9 N of drag against 6.9 N on the robot, 49.4 N against 22.8 N on the swimmer (Takagi et al., 2013; Takagi, Shimada, et al., 2014).

The legs show a similar picture. In the dolphin kick, a pair of counter-rotating vortices with a jet between them followed the downbeat of the feet, consistent with a vortex ring (Miwa et al., 2006). Computations do reproduce such rings (Pacholak et al., 2014), although a quasi-three-dimensional measurement of the wake captured the vortex pair and the jet but not a closed ring (Shimojo et al., 2019). Furthermore, a vortex shed behind the bending knee was met again by the legs on the next upbeat, which the authors read as the swimmer recapturing its energy (Hochstein & Blickhan, 2011). The same structures blur the bookkeeping of forces: when a robotic arm drew a hand straight back, broadside to the water, the hand shed vortices alternately from either edge like any bluff body, and the drag it met *was* the swimmer's propulsion (Takagi, Nakashima, et al., 2014). Propulsion and resistance arise in the same disturbed water, from the same movements, at the same instants; for unsteady self-propulsion Ungerechts and Klauck (2006) state it as a principle that the sources of drag and thrust cannot be separated.

Consequently, every method is, at heart, an argument. It introduces assumptions under which the net force can be split, and it reports the resistive part under those assumptions. Nearly every method of measuring active drag rests on two core assumptions.

The first is the steady-state assumption. If a swimmer holds the same average speed from one stroke cycle to the next, the mean propulsive force over a cycle equals the mean resistive force: a direct consequence of Newton's second law and beyond dispute. The assumption lies in the next step: most methods treat the swimmer as a body travelling steadily at that mean speed and apply steady-flow relations to the cycle averages. Within every cycle, however, the body and the water around it keep accelerating and decelerating, and the instantaneous resistance depends on these accelerations, not only on speed. The water that must be accelerated with the body, its added mass ($M_\mathrm{A}$), enters the force balance as an inertial term, $(m + M_\mathrm{A}) \cdot \mathrm{d}v/\mathrm{d}t$, which acts only while the speed changes and is not drag; for sprinters accelerating from rest, the added mass has been estimated at 28.7 ± 15.2 per cent of body mass (Carmigniani et al., 2025), close to the 25 per cent measured on fully submerged swimmers in a glide (Caspersen et al., 2010, as cited in Carmigniani et al., 2025), while Kolmogorov's in-situ tests gave 10 to 14 per cent, close to the theoretical value for an elongated spheroid of the same volume moving along its long axis (Kolmogorov, 2008). The value, then, depends on how it is estimated. As Toussaint (2002) observed, "most, if not all, studies assume that the swimmer is swimming at constant speed, treating drag as a stationary process" (pp. 20–21), even though the speed within a cycle is anything but constant.

The second is the power law: resistance is assumed to scale as $D = k \cdot v^{n}$, where $D$ is the drag, $v$ the speed, $k$ a constant for the given swimmer and $n$ the exponent, almost always taken as 2 (the textbook $D = \tfrac{1}{2} \cdot \rho \cdot C_\mathrm{d} \cdot A \cdot v^2$, where $\rho$ is the density of water, $C_\mathrm{d}$ the drag coefficient and $A$ a reference area of the body). Yet as the section on the three kinds of resistance showed, measured exponents often depart from two, and the wave component alone can grow nearer the cube of speed (about $v^{2.9}$ for a passive mannequin; Vennell et al., 2006).

Beneath these two lies a more fundamental problem, which several authors have pointed out. Simulating undulating fish and a robotic fin, Bale et al. (2014) showed that the total hydrodynamic force on a self-propelled body can be split unambiguously into "thrust" and "drag" only for restricted classes of motion, and that towed drag and "frozen-shape" drag give the wrong answer in general. Hochstein et al. (2014) concluded that "due to the intertwining of drag and propulsion in swimming there is no satisfactory method for a direct experimental determination of active drag". Webb et al. (2011) suggested that active drag "may be viewed as a composite quantity that includes both the resistive drag of the swimmer and the propulsive thrust generated for a given speed and stroke rate" (p. 133). Illustrating this, Mason et al. (2014) compared three computational routes to the instantaneous drag profile within a cycle: two gave nearly identical curves, the third a 40 to 65 per cent wider range for the same resultant force, leaving the authors to choose between them on plausibility. The data alone do not dictate the split.

Keep this in mind through the rest of the series. When two methods disagree, neither need be wrong: they may simply be measuring two different composite quantities that share one name, active drag.

## A short history of trying

Over more than a century, swimmers' resistance has been approached from several sides: through the swimmer's breathing, through pads under the hands, and through towing, tethers and flumes. The timeline shows when each method appeared and when methods were first compared on the same swimmers.

**Figure 6.** Ninety years of trying. Methods above the line; comparisons on the same swimmers below it.

A timeline from 1930 to 2025, the scale widening after 1985. Above the line, the methods: Karpovich, passive towing (1933); Counsilman, forces in crawl (1955); di Prampero et al., energetic extrapolation (1974); Clarys, form against technique (1979); the MAD system, Hollander et al. (1986); the SPM or VPM, Kolmogorov and Duplishcheva (1992); 797 swimmers, Kolmogorov et al. (1997); flume residual thrust, Takagi (1999); assisted towing, Alcock and Mason (2007); the HRM, Kolmogorov (2008); NABA, Webb et al. (2011); MRT, Narita et al. (2017); robotic VPM and its reliability, Gonjo and Olstad (2022); the Sacilotto review and Kolmogorov's single-swim stand (2023); tethered residual thrust, Cortesi (2024). Below the line, comparisons on the same swimmers: MAD against VPM, Toussaint, Roos and Kolmogorov (2004); MAD against ATM, Formosa et al. (2012); the AIS workshop, VPM, ATM and RTM on 13 swimmers (2013); MRT against MAD, Narita et al. (2018); hand pressure sensors against VPM, Morais et al. (2023).


Passive drag was the first thing anyone measured. The earliest experiments simply pulled people through the water and recorded the force needed: first from a rowing boat (du Bois-Reymond, 1905, as cited in Toussaint et al., 2004) and later with a winch on the shore (Liljestrand & Stenström, 1920, as cited in Toussaint et al., 2004). Karpovich (1933, as cited in Havriluk, 2005) published "Water Resistance in Swimming" from towing experiments; Counsilman (1955, as cited in Kolmogorov et al., 1997) measured forces in two variants of the crawl; and in the 1970s Clarys and colleagues towed large groups of swimmers and related resistance to body form (Clarys et al., 1974, as cited in Kolmogorov et al., 1997). Clarys (1979, as cited in Kolmogorov et al., 1997) concluded that body size and shape govern passive drag but not active drag, so that active drag is a matter of technique, a conclusion still widely cited in the literature.

The first estimates of active drag itself were indirect: di Prampero et al. (1974, as cited in Zamparo et al., 2009) measured oxygen uptake while a swimmer held a constant speed against a known aiding or hindering external force, and extrapolated to the force that would bring the metabolic cost down to resting level. Their active drag came out at two to three times passive drag.

In 1986 a Dutch group built the MAD system (Hollander et al., 1986): a row of fixed underwater pads on a rod connected to a force transducer that records each push, which the swimmer pushes off with the hands while swimming front crawl with the arms alone, the legs on a pull buoy. For the first time propulsive force was measured directly. The values came out close to passive drag and far below the energetic estimates. Toussaint's later work on propelling efficiency, and the finding by Toussaint et al. (1988, as cited in Kolmogorov et al., 1997) that an Olympic champion's drag was much lower than an average swimmer's, made MAD the reference instrument of the 1990s.

Kolmogorov's group took another route. Kolmogorov and Duplishcheva (1992) published in English the small perturbation method, whose development Kolmogorov dates to the end of the 1980s (Kolmogorov, 2025): two maximal swims, one free and one towing a calibrated body, with active drag computed from the speed loss on the assumption of equal power. Its formula, $D = F_\mathrm{b} \cdot v_2 \cdot v_1^2 \,/\, (v_1^3 - v_2^3)$, where $D$ is the active drag at the free speed $v_1$, $v_2$ the speed with the load and $F_\mathrm{b}$ the load's own drag at $v_2$, became the algebra the whole perturbation family shares: assisted and resisted towing rest on it too (part 3). It worked in all strokes in an ordinary pool. Its results were near passive drag, and in some swimmers below it. Over the five years before the 1992 Olympics Kolmogorov's group tested 797 swimmers (Kolmogorov et al., 1997); it went on to apply the method to seasonal monitoring (Kolmogorov et al., 2000), to combine it with an instantaneous force balance (Kolmogorov, 2008) and, in 2011, to build a hydrodynamic stand over a lane of a 50 m pool that gives active drag from a single 50 m swim. The swimmer tows the calibrated body, hung from a slider on a cable above the lane, from the 3 m to the 23 m mark, where it is released, and then swims on free, so that one swim gives both the loaded and the free speed (Kolmogorov, 2023).

Japanese researchers opened yet another route, through a flume: Takagi et al. (1999), after a Japanese version in 1998, built a method of their own. Tethered to a force sensor, the swimmer swims in place against the current at a stroke rate fixed in advance. In still water the whole propulsive force goes into the tether; as the current is speeded up step by step, part of the propulsive force is spent on the drag of the swimming body, and less of it reaches the tether (the residual thrust). Assuming the propulsive force stays the same at a fixed stroke rate, the drag at each flow speed is the difference between the two tether forces. Their values came out above passive drag and cast doubt on the $v^2$ assumption. Later versions let propulsion fall as the flow rises (part 4).

The 2000s brought the first comparisons on the same swimmers: MAD against the perturbation method (Toussaint et al., 2004); the assisted towing method of the Australian Institute of Sport (Alcock & Mason, 2007) and its comparison with MAD (Formosa et al., 2012); and the naval-architecture approach (Webb et al., 2011). Then, at a 2013 AIS workshop, Toussaint, Kolmogorov, Wilson and the AIS group tested perturbation, assisted and resisted towing side by side and concluded that "the results from different methods of active drag testing certainly are not generally in agreement with one another" (Mason, Kolmogorov, et al., 2013), even though in one of the two groups tested assisted towing ranked the swimmers in nearly the same order as the perturbation method ($r = 0.96$; details in part 5). Ranking swimmers alike, however, does not by itself mean that the numbers agree.

The past decade has added refined residual-thrust methods (Cortesi et al., 2024; Narita et al., 2017; Narita, Nakashima, & Takagi, 2018); two further comparisons on the same swimmers, flume residual thrust against MAD (Narita, Ogita, et al., 2018) and hand pressure sensors against the perturbation method (Morais et al., 2023); a detailed reliability study of the perturbation method with a robotic resistance device (Gonjo & Olstad, 2022); and a comprehensive narrative review (Sacilotto et al., 2023).

More than a century after the first towing experiments, the field has a dozen methods, a handful of direct comparisons, and no agreed reference. Why that is, and whether it matters in practice, is the subject of the next four posts.

## What this part establishes

Passive drag is a well-defined physical force that can be measured repeatably. Active drag, in effect, is not measured but inferred: every method records some other quantity and computes drag under its own assumptions, which other methods do not share. A figure for active drag therefore means little without its method, its protocol and its error, and two numbers from two different methods cannot be taken, without checking, for two measurements of the same quantity. The next post begins with the two oldest approaches, at opposite ends of the scale: the energetic method, which reads drag from a swimmer's breathing, and the MAD system, which gives the hands something solid to push against.

## The methods at a glance

Every method in the series records something that can be measured and computes drag from it under an assumption. The table is a map for the posts that follow; each row is taken up in its own part.

| Method | What is recorded | What is computed | Main assumption | Suited to |
|---|---|---|---|---|
| Energetic method (part 2) | Oxygen uptake at a fixed speed, with known external forces assisting or resisting the swimmer | The assisting force at which the metabolic cost of swimming would fall to resting, taken as drag | Cost rises in a straight line with the external force, efficiency unchanged | Drag tied to metabolic cost, at aerobic speeds |
| MAD system (part 2) | The force on fixed pads, arms only, at several constant speeds | The mean pad force as drag; a drag-speed curve | Cycle-averaged force balance; pushing off pads stands in for the free arm stroke | A front crawl drag curve with known repeatability, arms only |
| Small perturbation method (part 3) | Mean speeds of a free and a loaded maximal swim; the load's own drag | Drag at the free speed, $D = F_\mathrm{b} \cdot v_2 \cdot v_1^2/(v_1^3 - v_2^3)$, where $v_1$ is the free speed, $v_2$ the loaded speed and $F_\mathrm{b}$ the load's drag at $v_2$ | Equal power in both swims; $D = k \cdot v^2$ with $k$ constant | One number at top speed, any stroke, in a pool |
| Assisted and resisted towing (part 3) | The tow force at a set speed a little above or below maximal; the free speed | The perturbation equation with $v_2$ the towed speed; denominator $v_2^3 - v_1^3$ for assistance, $v_1^3 - v_2^3$ for resistance, the applied force entered as a positive magnitude | Equal power towed and free; $D = k \cdot v^2$ with $k$ constant | Top speed, with the force through the cycle |
| Residual thrust in a flume (part 4) | Tether force at a fixed stroke rate at eight flow speeds | The drag coefficient, and the drag at the self-propelled speed, from a fitted model | The model's propulsion and drag parameters stay the same across the speeds tested | Drag near the free speed, where a flume is available |
| Residual thrust in a pool (part 4) | The force fully tethered; force and speed in semi-tethered swims | Drag as the difference between the two forces | Propulsion is the same tethered and moving | Sprinters, without a flume |
| Hydrodynamic reaction method (part 4) | Trunk speed; body volume and posture from video; coefficients from flume tests | The frontal drag of the body through the cycle | Position-specific drag coefficients and an unsteady correction apply to the reconstructed stroke; propelling segments left out | The body's own resistance within the cycle |

## Terms used in the series

The same few quantities recur in every post, and the literature does not always keep them apart.

| Symbol | What it is | Unit |
|---|---|---|
| $D$ | Drag, the resisting force of the water; $D_\mathrm{p}$ passive drag, of a body towed in a fixed posture | N |
| $F_\mathrm{p}$ | Propulsive force | N |
| $T$ | Residual thrust, propulsion minus drag, found from the tether tensions (positive forwards) | N |
| $v$, $U$ | Swimming speed; $U$ the speed of the flow in a flume | `m/s` |
| $k = D/v^2$ | Drag factor, when drag is taken to grow as the square of speed | `kg/m` |
| $C_\mathrm{d}$ | Drag coefficient, $D/(\tfrac{1}{2} \cdot \rho \cdot A \cdot v^2)$, without units, where $\rho$ is the density of water; its value depends on the reference area $A$ chosen (a frontal area, a body volume to the power 2/3, or another) | – |
| $P_\mathrm{D} = D \cdot v$ | Power spent against drag; what it includes depends on what the author counts in $D$ (part 4) | W |
| Mechanical power | The swimmer's whole external mechanical output: the power against drag and the power lost to moving water | W |
| Metabolic power | The rate of metabolic energy use; oxygen uptake measures its aerobic part, and hard swimming adds an anaerobic part | W |

## The series

1. What active drag is and why it has to be inferred (this post)
2. [Pads and masks: the MAD system and the energetic method](/blog/active-drag-2-pads-and-masks/)
3. [Two swims, one power: the perturbation family](/blog/active-drag-3-two-swims-one-power/)
4. [Residual thrust and the hydrodynamic reaction](/blog/active-drag-4-residual-thrust/)
5. [Why the methods disagree, and what a coach can use](/blog/active-drag-5-why-they-disagree/)

## References

- Achenbach, E. (1972). Experiments on the flow past spheres at very high Reynolds numbers. *Journal of Fluid Mechanics, 54*(3), 565–575. https://doi.org/10.1017/S0022112072000874
- Aigeldinger, T. L., & Fish, F. E. (1995). Hydroplaning by ducklings: Overcoming limitations to swimming at the water surface. *Journal of Experimental Biology, 198*, 1567–1574.
- Alcock, A., & Mason, B. (2007). Biomechanical analysis of active drag in swimming. In H.-J. Menzel & M. H. Chagas (Eds.), *Proceedings of the XXV International Symposium on Biomechanics in Sports* (pp. 212–215). https://ojs.ub.uni-konstanz.de/cpa/article/view/438
- Au, D., & Weihs, D. (1980). At high speeds dolphins save energy by leaping. *Nature, 284*(5756), 548–550. https://doi.org/10.1038/284548a0
- Bale, R., Shirgaonkar, A. A., Neveln, I. D., Bhalla, A. P. S., MacIver, M. A., & Patankar, N. A. (2014). Separability of drag and thrust in undulatory animals and machines. *Scientific Reports, 4*, Article 7329. https://doi.org/10.1038/srep07329
- Barbosa, T. M. (2018). Hydrodynamics. In G. J. Mullen (Ed.), *Swimming science: Optimizing training and performance* (pp. 12–39). University of Chicago Press. https://doi.org/10.7208/chicago/9780226287980.001.0001
- Bearman, P. W., & Harvey, J. K. (1976). Golf ball aerodynamics. *Aeronautical Quarterly, 27*(2), 112–122. https://doi.org/10.1017/S0001925900007617
- Bechert, D. W., Bruse, M., & Hage, W. (2000). Experiments with three-dimensional riblets as an idealized model of shark skin. *Experiments in Fluids, 28*(5), 403–412. https://doi.org/10.1007/s003480050400
- Bixler, B., Pease, D., & Fairhurst, F. (2007). The accuracy of computational fluid dynamics analysis of the passive drag of a male swimmer. *Sports Biomechanics, 6*(1), 81–98. https://doi.org/10.1080/14763140601058581
- Carmigniani, R., Coloretti, V., Brunel, T., Bosetto, P., Fantozzi, S., Cortesi, M., & Zamparo, P. (2025). A novel method for assessing added mass in front crawl swimming. *Journal of Biomechanics, 189*, Article 112816. https://doi.org/10.1016/j.jbiomech.2025.112816
- Cortesi, M., & Gatta, G. (2015). Effect of the swimmer's head position on passive drag. *Journal of Human Kinetics, 49*(1), 37–45. https://doi.org/10.1515/hukin-2015-0106
- Cortesi, M., Gatta, G., Carmigniani, R., & Zamparo, P. (2024). Estimating active drag based on full and semi-tethered swimming tests. *Journal of Sports Science and Medicine, 23*(1), 17–24. https://doi.org/10.52082/jssm.2024.17
- Dickson, T. A. J., Taunton, D., Banks, J., Hudson, D., & Turnock, S. (2020). *Quantifying the wave resistance of a swimmer* [Preprint]. bioRxiv. https://doi.org/10.1101/2020.06.22.164236
- Fish, F. E. (2000). Biomechanics and energetics in aquatic and semiaquatic mammals: Platypus to whale. *Physiological and Biochemical Zoology, 73*(6), 683–698. https://doi.org/10.1086/318108
- Fish, F. E. (2006). The myth and reality of Gray's paradox: Implication of dolphin drag reduction for technology. *Bioinspiration & Biomimetics, 1*(2), R17–R25. https://doi.org/10.1088/1748-3182/1/2/R01
- Formosa, D. P., Toussaint, H. M., Mason, B. R., & Burkett, B. (2012). Comparative analysis of active drag using the MAD system and an assisted towing method in front crawl swimming. *Journal of Applied Biomechanics, 28*(6), 746–750. https://doi.org/10.1123/jab.28.6.746
- Gonjo, T., & Olstad, B. H. (2022). Reliability of the active drag assessment using an isotonic resisted sprint protocol in human swimming. *Scientific Reports, 12*(1), Article 13085. https://doi.org/10.1038/s41598-022-17415-5
- Havriluk, R. (2005). Performance level differences in swimming: A meta-analysis of passive drag force. *Research Quarterly for Exercise and Sport, 76*(2), 112–118. https://doi.org/10.1080/02701367.2005.10599273
- Hochstein, S., & Blickhan, R. (2011). Vortex re-capturing and kinematics in human underwater undulatory swimming. *Human Movement Science, 30*(5), 998–1007. https://doi.org/10.1016/j.humov.2010.07.002
- Hochstein, S., Pacholak, S., Brücker, C., Siebert, T., & Blickhan, R. (2014). Drag reduction by underwater undulatory swimming? An experimental and numerical approach. In B. Mason (Ed.), *Proceedings of the XIIth International Symposium on Biomechanics and Medicine in Swimming*. Australian Institute of Sport.
- Hollander, A. P., de Groot, G., van Ingen Schenau, G. J., Toussaint, H. M., de Best, H., Peeters, W., Meulemans, A., & Schreurs, A. W. (1986). Measurement of active drag during crawl arm stroke swimming. *Journal of Sports Sciences, 4*(1), 21–30. https://doi.org/10.1080/02640418608732094
- James, M. C. (2016). *On the search to reduce a swimmer's resistance: Surface-piercing bluff bodies over the critical Re-Fr range* [Doctoral dissertation, University of Southampton].
- Koeltzsch, K., Dinkelacker, A., & Grundmann, R. (2002). Flow over convergent and divergent wall riblets. *Experiments in Fluids, 33*(2), 346–350. https://doi.org/10.1007/s00348-002-0446-3
- Kolmogorov, S. (2023). Development of the technology to measure active drag of swimmers by the method of small perturbations. *Journal of Biomechanics, 149*, Article 111486. https://doi.org/10.1016/j.jbiomech.2023.111486
- Kolmogorov, S., Lyapin, S., Rumyantseva, O., & Vilas-Boas, J. P. (2000). Technology for decreasing active drag at the maximal swimming velocity. In R. Sanders & Y. Hong (Eds.), *Proceedings of XVIII International Symposium on Biomechanics in Sports: Applied program – Application of biomechanical study in swimming* (pp. 39–47). The Chinese University Press. https://ojs.ub.uni-konstanz.de/cpa/article/view/2152
- Kolmogorov, S. V. (2008). Kinematic and dynamic characteristics of steady-state non-stationary motion of elite swimmers. *Russian Journal of Biomechanics, 12*(4), 56–70.
- Kolmogorov, S. V. (2025). *Energeticheskoe obespechenie, gidromekhanika i biomekhanika sportivnogo plavaniia: Ot issledovanii k trenerskoi praktike i… obratno* [Energy supply, hydromechanics and biomechanics of competitive swimming: From research to coaching practice and… back]. Editus.
- Kolmogorov, S. V., & Duplishcheva, O. A. (1992). Active drag, useful mechanical power output and hydrodynamic force coefficient in different swimming strokes at maximal velocity. *Journal of Biomechanics, 25*(3), 311–318. https://doi.org/10.1016/0021-9290(92)90028-Y
- Kolmogorov, S. V., Rumyantseva, O. A., Gordon, B. J., & Cappaert, J. M. (1997). Hydrodynamic characteristics of competitive swimmers of different genders and performance levels. *Journal of Applied Biomechanics, 13*(1), 88–97. https://doi.org/10.1123/jab.13.1.88
- Marinho, D. A., Reis, V. M., Alves, F. B., Vilas-Boas, J. P., Machado, L., Silva, A. J., & Rouboa, A. I. (2009). Hydrodynamic drag during gliding in swimming. *Journal of Applied Biomechanics, 25*(3), 253–257. https://doi.org/10.1123/jab.25.3.253
- Mason, B., Kolmogorov, S., Wilson, B., Toussaint, H., Sinclair, P., Schreven, S., Sacilotto, G., Dominguez, R., & Hazrati, P. (2013). Comparison between active drag values estimated using both the velocity perturbation method and the A.I.S. assisted towing method. In T.-Y. Shiang, W.-H. Ho, P. C. Huang, & C.-L. Tsai (Eds.), *Proceedings of the 31st International Conference on Biomechanics in Sports*. https://ojs.ub.uni-konstanz.de/cpa/article/view/5559
- Mason, B. R., Sacilotto, G. B., Hazrati, P., & Franco, R. (2014). Three different calculations to compute a swimmer's instantaneous active drag profile and variations in the parameter values that arise as a consequence. In B. Mason (Ed.), *Proceedings of the XIIth International Symposium for Biomechanics and Medicine in Swimming* (pp. 168–174). Australian Institute of Sport.
- Matsuuchi, K., Miwa, T., Nomura, T., Sakakibara, J., Shintani, H., & Ungerechts, B. E. (2009). Unsteady flow field around a human hand and propulsive force in swimming. *Journal of Biomechanics, 42*(1), 42–47. https://doi.org/10.1016/j.jbiomech.2008.10.009
- Miwa, T., Matsuuchi, K., Shintani, H., Kamata, E., & Nomura, T. (2006). Unsteady flow measurement of dolphin kicking wake in sagittal plane using 2C-PIV. *Revista Portuguesa de Ciências do Desporto, 6*(Suppl. 2), 64–66.
- Mollendorf, J. C., Termin, A. C., Oppenheim, E., & Pendergast, D. R. (2004). Effect of swim suit design on passive drag. *Medicine & Science in Sports & Exercise, 36*(6), 1029–1035. https://doi.org/10.1249/01.MSS.0000128179.02306.57
- Morais, J. E., Barbosa, T. M., Garrido, N. D., Cirilo-Sousa, M. S., Silva, A. J., & Marinho, D. A. (2023). Agreement between different methods to measure the active drag coefficient in front-crawl swimming. *Journal of Human Kinetics, 86*, 41–49. https://doi.org/10.5114/jhk/159605
- Narita, K., Nakashima, M., & Takagi, H. (2017). Developing a methodology for estimating the drag in front-crawl swimming at various velocities. *Journal of Biomechanics, 54*, 123–128. https://doi.org/10.1016/j.jbiomech.2017.01.037
- Narita, K., Nakashima, M., & Takagi, H. (2018). Effect of leg kick on active drag in front-crawl swimming: Comparison of whole stroke and arms-only stroke during front-crawl and the streamlined position. *Journal of Biomechanics, 76*, 197–203. https://doi.org/10.1016/j.jbiomech.2018.05.027
- Narita, K., Ogita, F., Nakashima, M., & Takagi, H. (2018). Comparison of active drag using the MRT-method and the MAD-system in front crawl swimming. *Proceedings, 2*(6), Article 287. https://doi.org/10.3390/proceedings2060287
- NASA Glenn Research Center. (2025, September 9). *Shape effects on drag*. Beginner's Guide to Aeronautics. https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/shape-effects-on-drag/
- Pacholak, S., Hochstein, S., Rudert, A., & Brücker, C. (2014). Unsteady flow phenomena in human undulatory swimming: A numerical approach. *Sports Biomechanics, 13*(2), 176–194. https://doi.org/10.1080/14763141.2014.893609
- Pendergast, D., Mollendorf, J., Zamparo, P., Termin, A., II, Bushnell, D., & Paschke, D. (2005). The influence of drag on human locomotion in water. *Undersea & Hyperbaric Medicine, 32*(1), 45–57.
- Polidori, G., Taiar, R., Fohanno, S., Mai, T. H., & Lodini, A. (2006). Skin-friction drag analysis from the forced convection modeling in simplified underwater swimming. *Journal of Biomechanics, 39*(13), 2535–2541. https://doi.org/10.1016/j.jbiomech.2005.07.013
- Roberts, B. S., Kamel, K. S., Hedrick, C. E., McLean, S. P., & Sharp, R. L. (2003). Effect of a FastSkin suit on submaximal freestyle swimming. *Medicine & Science in Sports & Exercise, 35*(3), 519–524. https://doi.org/10.1249/01.MSS.0000053699.91683.CD
- Sacilotto, G., Sanders, R., Gonjo, T., Marinho, D., Mason, B., Naemi, R., Vilas-Boas, J. P., & Papic, C. (2023). “Selecting the right tool for the job” a narrative overview of experimental methods used to measure or estimate active and passive drag in competitive swimming. *Sports Biomechanics, 22*(12), 1572–1589. https://doi.org/10.1080/14763141.2023.2197858
- Sato, Y., & Hino, T. (2010). CFD simulation of flows around a swimmer in a prone glide position. *Japanese Journal of Sciences in Swimming and Water Exercise, 13*(1), 1–9. https://doi.org/10.2479/swex.13.1
- Sharp, R. L., & Costill, D. L. (1989). Influence of body hair removal on physiological responses during breaststroke swimming. *Medicine and Science in Sports and Exercise, 21*(5), 576–580.
- Shimojo, H., Gonjo, T., Sakakibara, J., Sengoku, Y., Sanders, R., & Takagi, H. (2019). A quasi three-dimensional visualization of unsteady wake flow in human undulatory swimming. *Journal of Biomechanics, 93*, 60–69. https://doi.org/10.1016/j.jbiomech.2019.06.013
- Takagi, H., Nakashima, M., Ozaki, T., & Matsuuchi, K. (2013). Unsteady hydrodynamic forces acting on a robotic hand and its flow field. *Journal of Biomechanics, 46*(11), 1825–1832. https://doi.org/10.1016/j.jbiomech.2013.05.006
- Takagi, H., Nakashima, M., Ozaki, T., & Matsuuchi, K. (2014). Unsteady hydrodynamic forces acting on a robotic arm and its flow field: Application to the crawl stroke. *Journal of Biomechanics, 47*(6), 1401–1408. https://doi.org/10.1016/j.jbiomech.2014.01.046
- Takagi, H., Nakashima, M., Sato, Y., Matsuuchi, K., & Sanders, R. H. (2016). Numerical and experimental investigations of human swimming motions. *Journal of Sports Sciences, 34*(16), 1564–1580. https://doi.org/10.1080/02640414.2015.1123284
- Takagi, H., Shimada, S., Miwa, T., Kudo, S., Sanders, R., & Matsuuchi, K. (2014). Unsteady hydrodynamic forces acting on a hand and its flow field during sculling motion. *Human Movement Science, 38*, 133–142. https://doi.org/10.1016/j.humov.2014.09.003
- Takagi, H., Shimizu, Y., & Kodan, N. (1999). A hydrodynamic study of active drag in swimming. *JSME International Journal Series B: Fluids and Thermal Engineering, 42*(2), 171–177. https://doi.org/10.1299/jsmeb.42.171
- Tor, E., Pease, D. L., & Ball, K. A. (2015). How does drag affect the underwater phase of a swimming start? *Journal of Applied Biomechanics, 31*(1), 8–12. https://doi.org/10.1123/jab.2014-0081
- Toussaint, H. M. (2002). Biomechanics of propulsion and drag in front crawl swimming [Keynote lecture]. In K. E. Gianikellis (Ed.), *Proceedings of the XXth International Symposium on Biomechanics in Sports* (pp. 13–22). University of Extremadura. https://ojs.ub.uni-konstanz.de/cpa/article/view/613
- Toussaint, H. M., Roos, P. E., & Kolmogorov, S. (2004). The determination of drag in front crawl swimming. *Journal of Biomechanics, 37*(11), 1655–1663. https://doi.org/10.1016/j.jbiomech.2004.02.020
- Toussaint, H. M., Truijens, M., Elzinga, M.-J., van de Ven, A., de Best, H., Snabel, B., & de Groot, G. (2002). Effect of a Fast-skin 'body' suit on drag during front crawl swimming. *Sports Biomechanics, 1*(1), 1–10. https://doi.org/10.1080/14763140208522783
- Ungerechts, B. E., & Klauck, J. (2006). Consequences of unsteady flow effects for functional attribution of swimming strokes. *Revista Portuguesa de Ciências do Desporto, 6*(Suppl. 2), 109–111.
- Vennell, R., Pease, D., & Wilson, B. (2006). Wave drag on human swimmers. *Journal of Biomechanics, 39*(4), 664–671. https://doi.org/10.1016/j.jbiomech.2005.01.023
- Webb, A., Banks, J., Phillips, C., Hudson, D., Taunton, D., & Turnock, S. (2011). Prediction of passive and active drag in swimming. *Procedia Engineering, 13*, 133–140. https://doi.org/10.1016/j.proeng.2011.05.063
- Wilson, B., & Thorp, R. (2003). Active drag in swimming. In J.-C. Chatard (Ed.), *Biomechanics and medicine in swimming IX* (pp. 15–20). Publications de l'Université de Saint-Étienne.
- Wilson, B. D. (2018). Technology for within stroke analysis in swimming. *ISBS Proceedings Archive, 36*(1), 1024–1027. https://commons.nmu.edu/isbs/vol36/iss1/253
- Yuan, Z.-M., Chen, M., Jia, L., Ji, C., & Incecik, A. (2021). Wave-riding and wave-passing by ducklings in formation swimming. *Journal of Fluid Mechanics, 928*, Article R2. https://doi.org/10.1017/jfm.2021.820
- Zaïdi, H., Fohanno, S., Taïar, R., & Polidori, G. (2010). Turbulence model choice for the calculation of drag forces when using the CFD method. *Journal of Biomechanics, 43*(3), 405–411. https://doi.org/10.1016/j.jbiomech.2009.10.010
- Zamparo, P., Gatta, G., Pendergast, D., & Capelli, C. (2009). Active and passive drag: The role of trunk incline. *European Journal of Applied Physiology, 106*(2), 195–205. https://doi.org/10.1007/s00421-009-1007-8