Active drag, part 5: why the methods disagree, and what a coach can use

The previous four posts walked through roughly a dozen ways of measuring a force that, as the first post explained, cannot be measured directly in free swimming, only calculated indirectly. This final post answers the questions that may interest a practising coach. Do these methods agree with one another? Why do they diverge? How far can each of them be trusted? And what should you actually do when handed a number labelled “active drag”?

Same swimmers, different methods

Comparing figures across different laboratories is next to pointless, as differences in the methods and differences in the swimmers get tangled together. The truly instructive studies are the rare few that tested two or more protocols on the exact same athletes. Here is what they revealed:

• MAD pads vs. the small perturbation method (six high-level swimmers, arms only in both): 67 newtons on the pads against 53 newtons by the small perturbation method. For individual swimmers, the second method yielded anywhere from 44 to 122 per cent of their pad reading.
• MAD pads vs. an assisted-towing winch (nine swimmers towed faster than their own top speed): 82 newtons on the pads against 148 newtons on the winch, 45 per cent lower on the pads.
• The small perturbation method vs. both versions of the winch (thirteen swimmers split into two groups at an Australian Institute of Sport workshop): in one group, the assisted-towing winch produced higher numbers than the small perturbation method for every single swimmer. In the second group, the small perturbation method yielded the lowest numbers instead, and scores across the different protocols bore almost no relation to one another. Even the rank order of the methods by magnitude flipped between the two groups.
• Assisted vs. resisted winch on the exact same rig (ten swimmers): group averages came out at 105 and 91 newtons, a difference that was not statistically significant, yet an individual swimmer’s score in one mode said virtually nothing about their score in the other.
• Residual thrust in a flume vs. MAD pads (six swimmers, arms only): drag measured 19 to 47 per cent higher in the flume.
• Pool tether vs. planimetry (two studies by the same research group): in the first study, the results nearly matched; in the second, planimetry yielded noticeably lower figures. Neither paper explains why.
• Hand pressure sensors vs. the small perturbation method (18 junior swimmers): across the group, the average difference was just 6 per cent. For an individual swimmer, however, the sensors could read roughly 20 per cent lower or 30 per cent higher.

The overarching picture is clear: group averages sometimes align, but an individual swimmer’s results across different tests almost never do.

Do the methods at least agree on who has more drag?

Two bathroom scales that disagree about your weight can still be useful, as long as they agree on who in the family is heavier. A coach mostly needs exactly that: who meets more drag, and whether one swimmer’s drag has changed. So do the methods at least put swimmers in the same order? Sometimes yes, often no.

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Three slope charts, one above another. In each, a swimmer’s active drag in newtons by one method is marked on a left axis and by the other on a right axis, on one scale, and the two points are joined by a line.

Top, the AIS workshop’s 10 m group, perturbation method on the left, assisted towing on the right; r = 0.96, and 0.94 for the coefficient k. The four women (pale lines) all lie below the three men, and every line rises to the right: the towed value is higher for every swimmer. Woman A 51 and 75 N, B 58 and 93, C 38 and 60, D 54 and 83; man E 85 and 123, F 84 and 105, G 87 and 113.

Middle, MAD on the left, perturbation method on the right, arms only, a swimmer’s perturbation tests averaged against MAD at the same speed; r about 0.31, rank correlation 0.09, computed. Lines cross. B 71.3 and 87.1 N, C 47.1 and 40.9, E 81.4 and 71.1, R 75.7 and 34.3, S 67.8 and 67.8, T 73.6 and 46.2. Singled out: R, second highest on the pads and lowest by the perturbation method, and B, fourth on the pads and highest by the perturbation method.

Bottom, assisted towing on the left, resisted towing on the right; r about −0.35 from the thesis’s table, rank correlation −0.67, computed (the text of the thesis gives 0.32). Lines cross in a tangle. Swimmer 1 92.9 and 83.5 N, 2 91.5 and 124.9, 3 106.5 and 81.6, 4 77.5 and 100.5, 5 92.5 and 86.8, 6 115.3 and 95.8, 7 159.0 and 74.8, 8 94.7 and 61.7, 9 86.5 and 96.7, 10 142.6 and 86.3. Singled out: 7, highest assisted and second lowest resisted, and 2, third lowest assisted and highest resisted.

• The small perturbation method and a winch towing a little faster than the swimmer, on the same day over 10 metres: almost the same order, though the winch gave bigger numbers for everyone. Much of that agreement came from the group itself: it mixed four women and three men, and the women were below the men under both methods. Among the women the order matched; among the men it did not.
• The MAD pads and the small perturbation method: the order fell apart. One swimmer had the second highest drag of six on the pads and the lowest by the small perturbation method, because he swam the swim with the float with about a third less power. Another was fourth on the pads and first by the small perturbation method.
• The winch helping and the winch holding back, on one machine: the order, if anything, flipped. The swimmer with the most drag when helped was second from the bottom when held back, and one of the lowest when helped had the most when held back. The thesis gives a correlation of 0.32 between the two, but its own table of swimmers gives a negative one.

Why? Partly the swimmers themselves. A swimmer who eases off when the rope helps gets too high a number; the same swimmer easing off when the rope holds him back gets too low a number. So swimmers who ease off and swimmers who keep their effort end up in opposite orders. Nobody measured their power, so this is still a guess.

What follows for a coach: never compare a number from one method with a number from another, not even to say who has more drag. Compare swimmers only with the same test, and only when the gap is bigger than the test’s own error, and follow one swimmer with one test.

A map of the published values

Place all the methods side by side and a distinct pattern emerges. One cluster yields values close to passive drag: the MAD pads, the small perturbation method, the resisting winch, and the assisted winch when configured to let speed fluctuate naturally within each stroke cycle. A second cluster yields roughly 1.5 to 3.3 times passive drag: the breathing method, residual thrust in both a flume and a pool, planimetry, and the constant-speed towing winch. Twenty years ago, researchers were already attributing this divide to the protocols themselves rather than the swimmers.

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A chart of active drag as a multiple of passive drag in front crawl, one row per method. Ratios are as reported by the sources or computed from their tables. A solid bar is a range of individual values; a dashed bar is a span across studies, conditions or estimates; a dot is a ratio of reported means; nothing is drawn where a source gives neither. The perturbation row is front crawl alone (with backstroke and butterfly the individual ratios run from 0.60 to 1.99, in breaststroke from 1.03 to 2.98). The rows differ in participants, speed, task and passive posture, so the chart is a descriptive map, not two families of methods or a correction factor.

Method	Low	High	Range	Ratio of means	Note
MAD system, arms only (van der Vaart 1987)	0.65	1.00	across studies		MAD 24 kg/m against 24 to 38 kg/m for passive drag in other swimmers
SPM / VPM, towed body (Kolmogorov 1992)	0.60	1.62	individual, 24 swimmers	1.03	70.4 against 68.1 N; 10 of 24 below 1
Resisted towing, RTM (Mason 2013; Hazrati 2016)	0.53	1.34	individual, 23 swimmers	0.94	77 against 81 N; 89 against 95 N
Assisted towing, fluctuating (Mason 2013; Hazrati 2016)	0.70	1.70	individual, 23 swimmers	1.10	89 against 81 N; 106 against 95 N
NABA (Webb 2011, one swimmer)	1.26	1.33	three tows	1.29	134 against 104 N; passive with the arms at the sides
Semi-tethered residual thrust (Cortesi 2024)	1.21	1.98	individual, 14 men	1.52	k = 37.3 against 24.6 kg/m
Residual thrust and standing start (Carmigniani 2025)	1.79	1.85	three estimates		k = 47.7 to 49.2 against 26.6 kg/m
Planimetric estimate (Gatta 2015; Zamparo 2009)	1.50	2.00	across studies		1.5 by definition; 1.7 to 2.0 by speed
Flume residual thrust, MRT (Narita 2018)	1.52	2.64	individual, 7 men at 1.3 m/s	1.91	77.3 against 40.5 N; 1.57 at 1.1 m/s
Energetic extrapolation (Pendergast 2005; Zamparo 2009)	1.50	2.20	across studies, computed		2 to 3 in older summaries
Assisted towing, constant speed (Formosa 2010)				2.89; 3.31	men 228 against 79 N, women 164 against 50 N

It is important to recognise that this grouping is a broad observation rather than a strict statistical boundary. The underlying studies differ in swimmers, speeds and motor tasks, and even passive drag baselines were measured in varying postures. Indeed, some individual readings in the “lower” cluster reach 1.3 to 1.7 times passive drag, straying into the “upper” cluster’s territory. Far stronger proof of divergence comes from the head-to-head comparisons on identical swimmers outlined above.

Seven reasons for the gap

Several mechanisms drive this divergence simultaneously, and their relative weight shifts from one protocol to the next:

1. The equal-power assumption. This is the primary culprit wherever two swims are compared. If power output in the second swim drops by 15 per cent, the resulting drag calculation is off by 30 per cent. In one detailed error analysis, breaches of this assumption accounted for 36 newtons out of a total uncertainty of 38 newtons. Moreover, the direction of the bias is predictable: an assisted winch pulling forward overstates drag, whereas a towed resisting load understates it.
2. The size of the load. As we saw in the third post, a light load protects the equal-power assumption but magnifies stopwatch error; a heavy load does the exact opposite. Research groups operating at a 4 to 6 per cent slowdown and groups operating at an 18 to 50 per cent slowdown are simply measuring different things. Worse still, most published protocols do not report their timing precision at all.
3. The velocity exponent. Nearly every method assumes drag grows precisely with the square of velocity (an exponent of 2). Empirical measurements, however, yield exponents ranging anywhere from 1.6 to 2.9. The resulting error is moderate, around 10 per cent, but it is systematic, always pushing the calculation in the same direction.
4. Hardware that alters technique. Fixed pads dictate stroke length; a winch cable smooths out natural intracyclic velocity fluctuations; and in a flume, the athlete swims to a metronome while held between two tethers. Every such apparatus shifts the outcome, and none allows the swimmer to move entirely naturally.
5. The reference area you divide by. Different authors calculate the dimensionless drag coefficient by dividing force by entirely different reference areas: total body surface area, frontal projection, or body volume raised to the power of two-thirds. Furthermore, those areas themselves are often rough estimates. A cleaner approach is to report force divided simply by velocity squared (in kilograms per metre), as some authors already do.
6. Surface waves. Swimming at the surface above a certain velocity can make wave-making resistance the largest component of passive drag, and it grows faster than the square of speed. How large a share wave drag claims during active swimming remains contested: some estimate it at roughly 12 per cent of total drag at 1.89 metres per second, while others view that figure as a clear underestimate.
7. The definition itself. As discussed in the first and fourth posts, the average drag of a self-propelling body exists only within the confines of a theoretical model. Furthermore, one major scientific school explicitly treats the output of the small perturbation method as total propulsive force rather than body drag. Part of the spread across the literature is simply a clash of definitions.

How far can any of this be trusted?

Repeatability has been established for only a handful of methods. On the MAD pads, measurements across two consecutive days agree to within roughly 1.5 newtons. The constant-speed towing winch repeats almost flawlessly. Repeatability for the small perturbation method hinges heavily on load size: with the lightest load, typical error reached 23 per cent, whereas with moderate loads it dropped to between 3 and 4 per cent. For half of the methods (the breathing method, the pool tether and the hydrodynamic reaction method) the reviewed literature contains no repeatability data whatsoever.

Even so, high repeatability does not guarantee a true answer. Bathroom scales that consistently read two kilograms heavy are highly repeatable, yet entirely wrong. Tellingly, the highest repeatability in the field belongs to the constant-speed winch: the very apparatus that constrains the swimmer most heavily and systematically violates the equal-power assumption.

Data from 1991 illustrate what happens when repeatability figures are missing. Tested via the small perturbation method, national-team swimmers saw their calculated drag shift by 1.5 to more than 2 times over a span of one to four weeks at nearly identical speeds. The authors attributed this to adjustments in stroke technique. Perhaps so, but without baseline repeatability figures, there is no way to rule out, or even estimate, how much of that swing was simply measurement noise.

What to do with a number

Imagine taking a child’s temperature using three different thermometers: one in the mouth, one under the arm, and one on the forehead. Each gives a different reading, and each is valid on its own terms, but comparing readings only makes sense if you stick to the same thermometer. Active drag works the same way: any given figure is the output of a specific protocol, not an absolute property of the swimmer. Compare only like with like: the exact same method, load magnitude, load direction, distance, velocity exponent and reference area, all on the same athlete.

Match the tool to your specific question:

• You want a complete drag curve in freestyle, and an altered, arms-only stroke is acceptable: the MAD pads provide a directly measured mechanical force with known repeatability.
• You want a single number at top speed, in any stroke, at minimal cost: the small perturbation method will do the job, provided you respect its pitfalls. Log the exact percentage of slowdown and your timing precision, run multiple trials, and compare a swimmer only against themselves.
• You have access to a flume and want to see how leg kick, stroke rate and stroke length affect drag across different velocities: that is a job for the residual thrust method.
• You have a resistance device in a standard pool: the pool tether protocol provides a solid estimate while simultaneously cross-checking its model against measured free-swimming speed. Keep loads at or below roughly 75 per cent of maximal stationary thrust. Above all, do not replace actual testing with a crude “1.5 times passive drag” rule of thumb: in that same research group’s follow-up study, that shortcut fell roughly 17 per cent below the measured tether value.
• You need drag tied directly to metabolic energy cost: use the breathing method, keeping to aerobic speeds.

When tracking a swimmer over time, respect the arithmetic of error. To be 95 per cent confident that a change is genuine, the shift must be nearly three times larger than the typical error of a single test, because each of the two tests being compared brings its own margin of error. A test with a 4 per cent typical error can only reliably detect a shift of roughly 11 per cent or more. Averaging multiple trials lowers that threshold. If a method’s typical error has never been published, only your own repeated trials can tell you whether an observed change is real. Why go to all this trouble? Because in a simple mathematical model, reducing active drag by 10 per cent at a given speed allows a swimmer producing the same power to travel roughly 3.6 per cent faster. (Treat that as an illustration of the maths, however, not a guaranteed return on any specific technical tweak.)

The exact same discipline is required when evaluating a change in stroke technique. In the breaststroke study discussed in the third post, researchers compared breathing every stroke cycle against breathing every second cycle, running just one free and one loaded swim per condition. While group averages showed no difference, individual swimmers’ calculated drag when breathing every second cycle plummeted by nearly 85 newtons or jumped by almost 52 newtons. Six swimmers recorded lower drag breathing every second cycle; nine recorded lower drag breathing every cycle. With only a single pair of swims per condition, swings like these are indistinguishable from the test’s inherent noise. Each technical variation must be swum multiple times, ideally across two separate days.

Finally, whenever you read or publish an active drag figure, the figure needs its accompanying methodological details: the exact protocol; load direction and magnitude alongside timing precision; the assumed or measured velocity exponent; the reference area used; pool depth and surface conditions; and at least a basic check on the equal-power assumption (even if only stroke rate and stroke length across both swims). Without those particulars, two numbers cannot be meaningfully compared, even if they come from the very same laboratory.

What would settle the debate

The existing literature makes it fairly clear what the field still lacks:

1. An independent repeatability check of the classic small perturbation method conducted outside Kolmogorov’s own group, using accurately measured top speeds, calibrated loads and a strict 4 to 6 per cent slowdown.
2. Direct or indirect measurement of power output across both swims to disentangle the two competing explanations for why heavy loads underestimate drag.
3. An independent cross-comparison of the hydrodynamic reaction method against any other established protocol, as it remains the only method that calculates instantaneous frontal body drag within the stroke cycle.
4. Empirical measurement of the velocity exponent for each individual protocol, rather than blindly assuming it equals two.
5. A consensus on terminology, so that a reader knows immediately whether a paper is reporting total propulsive force or net resistance on the body itself.

What to remember

The first post opened with a coach’s practical question: when a test shows lower drag, is the swimmer genuinely slicing through the water more cleanly, or has something merely shifted in the measurement itself? Five posts later, we have a clear answer, though it comes with strict conditions. A shift in the numbers can be interpreted as a real change in the swimmer only if the exact same method and protocol were executed at a comparable speed, and only if the shift exceeds the minimum detectable change for that specific test. Even then, crossing that threshold merely rules out random measurement noise; it does not automatically prove that better technique lowered drag. You still have to weigh whether the swimmer’s effort changed, or how well the model’s underlying assumptions held up on the day. Conversely, a discrepancy between two different methods says nothing whatsoever about changes in the swimmer, and may not even reflect the same physical quantity.

Within those boundaries, however, each method answers its own specific question well enough to be practical, and none becomes arbitrary merely because it relies on a theoretical model. After all, a clearly defined model with a known margin of error is precisely what turns a raw number into a working tool.

The series

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

The sources for this post are listed in the full version.