# Active drag, part 2: pads and masks. The MAD system and the energetic method

> The two oldest approaches to active drag sit at opposite ends of the scale: breathing measurements say resistance is 1.6 to 3 times passive drag, fixed pads say it is about equal. Both have reasons.

- Source: https://swimas.co.nz/blog/active-drag-2-pads-and-masks/
- In plain English (ELI5): https://swimas.co.nz/blog/active-drag-2-pads-and-masks/eli5/
- Author: V. Karpov, swimas (Swimming Art & Science), New Zealand
- Published: 18 Oct 2026
- Topics: Active drag, Biomechanics; strokes: FR

Part 1 argued that active drag is a quantity defined by subtraction, and that every method is essentially a set of assumptions under which that subtraction can be performed. This post examines the two oldest families of methods. One measures the swimmer's breathing and extrapolates; the other replaces the water beneath the hands with instrumented pads and measures the push-off force directly. Measured against passive drag, their answers diverge sharply: active drag sits right around passive drag on the pads, yet reaches 1.6 to 3 times passive drag by the energetic method. The reasons for that gap are instructive for everything that followed.

## The energetic method: extrapolating to zero cost

Di Prampero et al. (1974, as cited in Zamparo et al., 2009) introduced the idea. A swimmer holds a fixed speed while a known horizontal force is applied through a pulley system, pulling them forwards in some trials and holding them back in others (the later studies of Pendergast et al., 2005, and Zamparo et al., 2009, used assisting forces only). Steady-state oxygen uptake is measured at each force. Because the relation between oxygen uptake and applied force is close to linear, the line can be extended back to resting oxygen uptake, and the force at which it crosses is the assisting force at which swimming would cost nothing extra, which is to say the force that would exactly cancel the water's resistance. That intercept, with its sign reversed, is taken as active drag.

**Figure 1.** The energetic method. The intercept of the oxygen-uptake line with resting uptake gives the assisting force that would cancel resistance.

A chart of oxygen uptake, 0 to 4 litres a minute, against an external horizontal force added at constant speed, from minus 100 newtons (assisting) to plus 50 (resisting). Measured points over the range from about minus 30 to plus 40 newtons lie on a straight line rising with the force. Extended down to the resting uptake, a dashed line, the line meets it at minus 80 newtons: the assisting force at which swimming would cost nothing, read as minus the active drag. Notes: the method assumes the efficiency stays the same across loads; van der Vaart et al. (1987) warned that "even small systematic errors are greatly magnified as a result of extrapolation"; it works at aerobic speeds only, where oxygen uptake is steady; its results come out at about two to three times passive drag.


The approach has two clear attractions. First, it leaves the swimmer's body position almost untouched: Zamparo et al. (2009) call it "a more 'ecological' approach" (p. 202) than the MAD and perturbation methods. Second, it links hydrodynamics directly to the energy cost of swimming, which is what an endurance physiologist ultimately cares about.

Yet its assumptions are heavy. The extrapolation is valid only if the swimmer's propelling efficiency and mechanical efficiency stay constant as the external force changes. Van der Vaart et al. (1987), of the Dutch group that built the MAD system (Hollander et al., 1986), judged that unrealistic: in other forms of locomotion efficiency rises with power output, and "even small systematic errors are greatly magnified as a result of extrapolation" (p. 546). The method also needs a steady oxygen uptake, which limits it to submaximal, aerobic speeds up to about 1.4 m/s (Seifert et al., 2015; Zamparo et al., 2009). Pendergast et al. (2005) extended it to race speeds by adding an anaerobic term estimated from blood lactate, but that extension has been validated mainly within the same group.

Its estimates are among the highest of any family: two to three times passive drag in the early studies (van der Vaart et al., 1987; Zamparo et al., 2009), about 1.6 to 2.1 times in more recent work. Across speeds, Pendergast et al. (2005) found a linear relation, $D_\mathrm{a} = 2.12 \cdot D_\mathrm{p} + 2.59$, where $D_\mathrm{a}$ is active and $D_\mathrm{p}$ passive drag in newtons, with $r = 0.99$. Zamparo et al. (2009) fitted $D_\mathrm{a} = 43.7 \cdot v^{1.60}$, active drag $D_\mathrm{a}$ in newtons against speed $v$ in metres a second, to six college swimmers over 0.6 to 1.4 m/s, pooling leg-kick trials at the lower speeds with full-stroke front crawl at the higher ones, and offered a mechanical explanation for an exponent below two: as speed rises the trunk inclines less, so the projected frontal area shrinks. The tabulation of van der Vaart et al. (1987) put the energetic estimates at 49 to 136 kg/m in terms of $F/v^2$, the force divided by the square of speed, against 24 to 38 kg/m for passive drag. No test-retest data for the energetic method were found in the sources I have read.

A related, cheaper estimate comes from planimetry. From the trunk inclination noted in part 1, about 10 to 12 degrees while swimming against 4 to 6 degrees when towed above 1 m/s, and the corresponding projected areas, Zamparo et al. (2009) estimated the ratio of active to passive drag; Gatta et al. (2015) instead measured the frontal area directly on video through the stroke cycle. Although the trunk-inclination estimate lands in the same region as the energetic values, its drag-speed fits explain only 42 to 49 per cent of the variance, against 83 per cent for measured drag. Narita, Nakashima, and Takagi (2018) criticised both planimetric approaches for ignoring limb movement and wave drag.

## The MAD system: measuring a force directly

Hollander et al. (1986) introduced the Measuring Active Drag (MAD) system. Fifteen or sixteen pads are mounted 1.30 to 1.35 m apart on a 22 to 23 m rod fixed 0.8 m below the surface along a lane. The rod is connected to a force transducer. With the legs supported by a pull buoy, the swimmer swims front crawl, pushing off each pad in turn. At constant speed the mean push force equals the mean resistance. Ten to sixteen swims at speeds from about 1.0 to 2.1 m/s map out the whole drag-speed curve, fitted as $D = A \cdot v^{n}$ by least squares, where $D$ is the drag, $v$ the speed, and $A$ and $n$ constants found for each swimmer (Toussaint et al., 2004; van der Vaart et al., 1987).

**Figure 2.** The MAD system. Each push on a pad is a pulse in the force trace; the mean of the trace at constant speed is taken as active drag. The trace is schematic, drawn to explain, not a recording.

An animation of the MAD system in four parts. At the top, the rod as a whole: 23 m long with 16 pads and a force transducer at its end, and the swimmer's place along it. Below, a painting of the swimmer seen from the side, the water cut away at the surface and the view going along with him: arms only, his legs together on a pull buoy, he swims over pads 1.35 m apart on a rod 0.8 m under the surface; each hand in turn lands on the upright face of a pad ahead of the shoulder, presses on it while the body passes over and leaves it behind the shoulder, the pad being pushed lit and an arrow showing the push; the arm then recovers over the water to the next pad. Third, the force the pads pass to the transducer: a pulse for each push, peaking at about 100 newtons in the slowest swim and 275 in the fastest, and a dashed line for its running mean, which at constant speed is the active drag. Fourth, a drag-speed chart: five swims at 1.2, 1.4, 1.6, 1.8 and 2.0 metres a second each add a point, from about 36 newtons at 1.2 to about 97 at 2.0, and a curve D = A·v^n is fitted through them, where D is the drag, v the speed, and A and n are fitted constants.


What the transducer records is the reaction of the pads. Under a force balance averaged over the cycle, its mean gives an estimate of drag for this modified, arms-only task, without any model of the swimmer's power, and it gives a full curve rather than a single point. And because the pads do not move, the swimmer loses no energy to accelerating water backwards, so the same measurement gives the useful mechanical power without the usual kinetic losses. Those advantages made the MAD system the reference instrument of the 1990s and the basis of Toussaint's influential work on propelling efficiency.

Its repeatability is well documented. Testing eleven swimmers on two consecutive days, Schreven et al. (2013) reported between-day intraclass correlations of 0.92 at 1.25 m/s and 0.94 at 1.55 m/s, with standard errors of measurement of just 1.4 and 1.7 N. They also showed that changing the pad spacing by 16 per cent (and hence the imposed stroke rate by 14 per cent) did not change the measured drag.

MAD values sit right at the level of passive drag. Van der Vaart et al. (1987) reported 53.2 ± 5.8 N at 1.48 m/s, a mean force $F$ over the square of speed, $F/v^2$, of 24.3 kg/m, indistinguishable from passive values. Toussaint's cohorts gave $K = D/v^2$, drag divided by the square of speed, of about 30 for men and 24 for women in 1988, and 27 and 22 in later groups (Toussaint, 2002). Individual exponents ranged from 2.08 to 2.82 (Toussaint et al., 2004), 1.84 to 2.89 (Schreven et al., 2013), 1.77 to 2.68 (Seifert et al., 2015) and 1.73 to 2.10 (Narita, Ogita, et al., 2018), a spread that already casts doubt on the universal assumption of $n = 2$.

The limitations are the very ones a coach would suspect, and Schreven et al. (2013) catalogue most of them. The method works only for front crawl, and only for the arms, whereas Hollander et al. (1988, as cited in Hazrati, 2016) estimated that the legs add up to 11.7 per cent of power. Because the hand presses on a rigid pad instead of catching yielding water, the force during the first part of the stroke, from hand entry to pad contact, is not measured at all. The stroke length is locked to the pad spacing, and with it, at a given speed, the stroke rate: at the same relative speed, stroke rate on the MAD system differs from free swimming by about 14 per cent (Seifert et al., 2015). Qualitative studies (Adé et al., 2009; Poizat et al., 2010) describe swimmers lifting the head to find the next pad, changing elbow angle, and struggling to turn their arms over fast enough at top speed. Toussaint et al. (2004) acknowledged that "the swimmer's technique is altered since the push off is made from fixed push off pads" (p. 1656), and Narita, Nakashima, and Takagi (2018) suggested that the structure "potentially underestimates drag". Electromyography during MAD swimming resembles that of free crawl (Clarys et al., 1988, as cited in Sacilotto et al., 2023), but Sacilotto's 2023 review still regards it as an open question whether pushing off fixed pads replicates or constrains normal stroke mechanics.

## Why the two families disagree

To sum up the divide: the energetic method gives two to three times passive drag in the early studies and about 1.6 to 2.1 times in more recent ones, whereas the MAD system returns about one times passive drag. Both cannot be right about the same physical quantity, yet the literature has lived with the gap for forty years. Three explanations are on the table.

The first lies in the energetic method's extrapolation. If efficiency rises with load, the true relation is curved, and the straight line extended back to resting uptake overshoots the intercept. Van der Vaart et al. (1987) raised this objection, and it has never been answered with data, because efficiency cannot be measured independently in the pool.

The second stems from the MAD system's structure. Rigid pads in place of yielding water, legs immobilised on a pull buoy, a catch that goes unmeasured and a stroke length fixed by the pad spacing could each lower the measured force relative to free swimming. The flume comparison on the same swimmers by Narita, Ogita, et al. (2018), covered in part 4, found that even arms-only drag measured by residual thrust was 19 to 47 per cent above MAD drag at the same speeds, and grew with a steeper exponent, which is consistent with the fixed pads removing some of the resistance that free swimming entails.

The third echoes the central argument of part 1: the two methods may not be after the same quantity at all. The energetic method asks what external force would make the swimmer's whole metabolic cost above rest vanish, a budget that includes the cost of moving water with the limbs. The MAD system asks what mean force the hands deliver to fixed points at a given speed. Part 4 will show that at least one school now explicitly treats the first of these as "total propelling force" and the second as closer to the "frontal component" of resistance (Kolmogorov, 2008, pp. 59–60).

What a coach can take from the two: the MAD system remains the method with a directly measured force and documented repeatability for a drag-speed curve in front crawl, at the cost of restricting the swimmer to an altered, arms-only stroke; the energetic method remains the way to infer drag from metabolic cost against an external force, at the cost of a linear extrapolation that cannot be checked directly and a speed ceiling of about 1.4 m/s. Neither tells you the resistance of your swimmer's own unconstrained stroke at race pace. To answer that question, the field turned to the perturbation methods, the subject of part 3.

## The series

1. [What active drag is and why it has to be inferred](/blog/active-drag-1-what-it-is/)
2. Pads and masks: the MAD system and the energetic method (this post)
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

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