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

The previous four posts have described a dozen ways of measuring a force that, as part 1 argued, cannot be measured directly in free swimming, only inferred. This last post asks the questions that may interest a practising coach: do these methods agree, why do they diverge, how far can any of them be trusted, and what should a practitioner do with a reported number?

Comparisons on the same swimmers

Comparing active drag figures across laboratories inevitably mixes the method with the swimmer sample. The truly informative studies are the handful that apply two methods to the same people. They are grouped below into eight blocks; one block pairs two papers from the same group, and comparisons sharing data are not independent replications.

MAD against the perturbation method (Toussaint et al., 2004; six elite swimmers; arms only in both). At 1.64 m/s the MAD averaged 66.9 N against 53.2 N by the perturbation method, $p=0.029$, with individual perturbation values spanning from 44 per cent of the swimmer’s MAD value to 22 per cent above it. Regressing the drag discrepancy on the power discrepancy between the two perturbation swims gave $r^2=0.88$, though because both powers were derived from the same MAD curve, the regression is not an independent test of the cause. The authors offered the tentative conclusion that “both methods measure essentially the same active drag phenomenon”, while conceding that “the question which physical phenomenon is assessed with the MAD-system and which with VPM is not finally resolved” (p. 1661).

MAD against assisted towing (Formosa et al., 2012; nine club swimmers; towed 10 per cent above maximal speed). At 1.68 m/s, arms-only MAD averaged 82 N against 148 N for whole-stroke assisted towing, $p=0.002$. The paper calls this a 55 per cent variation, but the printed means show the MAD value to be 55 per cent of the towing figure, that is, 45 per cent lower.

Perturbation against assisted and resisted towing (Mason, Kolmogorov, et al., 2013; 13 swimmers in two groups tested on separate days at the AIS workshop). In the seven timed over 10 m, assisted towing exceeded the perturbation value for every swimmer while correlating tightly with it ($r=0.96$, largely because the group mixed women and men; see the next section), and resisted towing matched the perturbation mean (66.7 against 65.3 N). In the six timed over 20 m, however, the perturbation method gave the lowest values (76.0 N against 84.0 N assisted and 88.8 N resisted), and the correlations were weak ($r=0.38$ and −0.07). The authors concluded that “the results from different methods of active drag testing certainly are not generally in agreement with one another”.

Assisted against resisted towing on one apparatus (Hazrati, Mason, & Sinclair, 2014; ten swimmers). Means of 105 against 91 N, statistically indistinguishable, but correlated at only $r=0.32$ (by the thesis’s own table of individual values, about −0.35; see the next section), and with ten swimmers the comparison had only a 32 per cent chance of showing a true difference as significant (power 0.32; both figures from the thesis version of the study: Hazrati, 2016, Chapter 4). Accordingly, the authors caution that the lack of a significant difference “should be interpreted as being the result of high variability … rather than indicating consistency between the two methods” (Hazrati, Mason, & Sinclair, 2014, p. 107).

Flume residual thrust against MAD (Narita, Ogita, et al., 2018; six swimmers; arms only). Flume values exceeded the pads by 19 per cent at 1.0 m/s, 33 per cent at 1.2 m/s and 47 per cent at 1.4 m/s, with exponents of 2.53 against 1.90.

Pool residual thrust against planimetry (two studies from one group). In 14 sprinters, pool residual thrust came out at about 1.5 times passive drag, the very ratio built into the planimetric estimate (Gatta et al., 2015), with a Bland-Altman bias of just −2.4 N (Cortesi et al., 2024). In 16 other male sprinters, however, that agreement vanished (Carmigniani et al., 2025): k was 49.2 ± 6.3 kg/m by residual thrust (47.9 ± 5.7 kg/m from the regression line) and 47.7 ± 4.5 kg/m from a standing start, against 39.9 ± 5.0 kg/m by planimetry (p < 0.001), about 1.8 times the passive 26.6 kg/m. Neither paper explains the difference.

Naval-architecture variant against the perturbation formula (Webb et al., 2011; one swimmer; the formula applied to the same assisted tows). The means agreed (134 against 131 N), though in each towing condition the perturbation formula’s run-to-run spread was 2.6 to 5.1 times wider.

Hand pressure sensors against the perturbation method (Morais et al., 2023; 18 juniors). Drag coefficients agreed with a between-method coefficient of variation of 6 per cent and an ICC of 0.93, even though propulsive force from the sensors was about 10 per cent higher (68.8 against 62.8 N). Yet the agreement holds far better for the group mean than for one swimmer: from the mean difference and its confidence interval in their Table 2, the 95 per cent limits of agreement run from about −0.09 to +0.15 on a mean coefficient of about 0.5, so that one swimmer’s sensor value could lie some 20 per cent below or 30 per cent above the perturbation value. Moreover, both coefficients divide by the same frontal area and the same speed, which by itself raises their ICC.

Do the methods rank swimmers alike?

The comparisons above are about averages. A coach, though, rarely needs the number of newtons itself: the usual questions are which swimmer meets more drag, and whether one swimmer’s drag has changed. For those questions two methods could differ in their means by a factor of two and still both serve, as long as they put the swimmers in the same order; the difference would then be a matter of scale. The worse case is the reverse, similar means with the swimmers in a different order. The few studies that print each swimmer’s values let us see which of the two happens.

Two cautions come first. A correlation of the raw forces flatters agreement: faster and larger swimmers meet more drag under any method, and a group that mixes women and men spreads the values further, so even two methods that disagree swimmer by swimmer can correlate well. A coefficient that does not depend on speed, such as $k=D/v^2$, drag $D$ divided by the square of speed $v$, compared within a homogeneous group, is the fairer test. And the groups are small, six to ten swimmers in most comparisons, so each correlation is a rough estimate: with ten swimmers, $r=0.32$ is compatible with anything from −0.39 to 0.79 (the 95 per cent confidence interval).

Methods compared	Study; swimmers	$r$ of drag	$r$ of $k$, or of ranks	What it shows
Perturbation and assisted towing, 10 m section	Mason, Kolmogorov, et al., 2013; 4 women, 3 men	0.96	0.94 ($k$)	The order kept; the towed value higher in every swimmer; the women below the men under both
Perturbation and resisted towing, 10 m section	The same 7	0.72	0.21 ($k$)	The link in force goes mostly with speed
Perturbation and assisted towing, 20 m section	The same study; 6 men	0.38	0.57 ($k$)	Weak
Perturbation and resisted towing, 20 m section	The same 6	−0.07	−0.24 ($k$)	None
MAD and perturbation, arms only	Toussaint et al., 2004; 6	0.31 (computed)	0.09 (ranks, computed)	The order not kept
Assisted and resisted towing on one apparatus	Hazrati, 2016; 10	0.32 in the text; −0.35 from its table (computed)	−0.67 (ranks, computed)	The order, if anything, reversed
Hand pressure sensors and perturbation	Morais et al., 2023; 18 juniors		0.91 ($R^2=0.82$) for the drag coefficient	The order kept, though both coefficients share the frontal area and the speed
Passive and active drag coefficient	Kolmogorov et al., 1997; 797		−0.09	Passive drag does not predict active

“Computed” marks values I calculated from the papers’ tables of individual results; the others are the authors’. Of the other comparisons above, Formosa’s, Narita’s and Carmigniani’s report differences of means, not whether the order of swimmers holds.

Text description

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.

Behind the numbers are individual swimmers. In Toussaint’s group swimmer R met the second highest drag of the six on the pads, 75.7 N, and the lowest by the perturbation method, about 34 N; swimmer B, fourth on the pads, came first by the perturbation method with 87 N (Toussaint et al., 2004). The authors traced the gap to power: the difference between the two methods followed the swimmers’ loss of power in the loaded swim ($r=0.94$), and R swam that swim with about a third less power than the free one. In Hazrati’s thesis the swimmer with the highest drag under assisted towing, 159 N, had the second lowest under resisted towing, 75 N, while the swimmer third from the bottom under assisted towing, 91.5 N, had the highest under resisted towing, 124.9 N (Hazrati, 2016, Table 4.2). The thesis gives the correlation between the two methods as 0.32 (p. 95); its own table of individual values gives about −0.35, perhaps a lost sign or a different set of trials.

Even the closest agreement in the table owes much to the make-up of the group. In the AIS workshop’s 10 m group the four women were below the three men under both methods, and that alone drives the correlation up. Within the four women the order was the same under both methods; within the three men it was not (Mason, Kolmogorov, et al., 2013, computed from its tables). The same paper prints identical rows for swimmers G (10 m group) and J (20 m group) in its table of perturbation results, the same height, mass, speed, drag and power, most likely a copying slip, so one of the two groups’ figures rests on a wrong row.

Why does the order hold in one pair and not in another? It held where the two methods share an equation and an assumption and were run in the same conditions: the perturbation method and assisted towing over 10 m both rest on the equal-power algebra of part 3, and a swimmer who breaks the assumption in the same way under both errs in the same direction. It broke where swimmers respond to the apparatus in their own ways. The MAD system needs no equal power but changes the stroke itself, arms only on fixed pads, and swimmers adapt to it differently, while the perturbation value depends on how much power each swimmer keeps when loaded. Between assisted and resisted towing the equal-power error even changes sign: a swimmer who eases off when helped gets too high a value under assistance, and the same swimmer easing off when held back gets too low a value under resistance (the first of the reasons below). If some swimmers ease off and others do not, the two methods should order them in opposite ways, which would explain the negative correlation in Hazrati’s table. Power was not measured in either study, so this remains a hypothesis.

For a coach the consequences are practical:

• A value from one method cannot be compared with a value from another, not even as “more” or “less”: a swimmer high by one method can be low by another.
• Swimmers can be compared only within one method and protocol, and only when the difference exceeds the test’s own error (below).
• One swimmer is followed with one method, one protocol, one distance and one size of perturbation.
• A high correlation of raw forces is not yet agreement: ask for a coefficient that does not depend on speed, for the individual values, and for the make-up of the group by sex and size.

A map of the published values

Text description

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

Put the families side by side and a clear pattern appears. Two decades ago Wilson and Thorp (2003) noted the divide between MAD estimates and the higher semi-tethered figures of the 1980s and 1990s, attributing it “to a systematic difference in the methodologies” (p. 17) rather than to the swimmers. Extended to the methods developed since, the pattern holds. One cluster returns values near passive drag: the MAD system (Hollander et al., 1986; Toussaint, 2002), the perturbation method with a towed load (Kolmogorov & Duplishcheva, 1992; Kolmogorov et al., 1997), and resisted and fluctuating assisted towing (Hazrati, 2016; Mason, Kolmogorov, et al., 2013). The other returns about 1.5 to 3.3 times passive drag in its ratios of means and its spans across studies, individual values starting at about 1.2: energetic extrapolation (Zamparo et al., 2009), flume (Narita, Nakashima, & Takagi, 2018; Takagi et al., 1999) and pool residual thrust (Cortesi et al., 2024; Carmigniani et al., 2025), planimetry (Gatta et al., 2015; Zamparo et al., 2009), constant-speed assisted towing (Formosa et al., 2010). The naval-architecture estimate, about 1.3 times on one swimmer, sits between the two. To be sure, the pattern is descriptive, not a statistical result: the rows differ in swimmers, speed, task and the posture of the passive test; some give individual ranges and others spans of means across studies; individual ranges in the lower cluster reach 1.3 to 1.7 and overlap the upper one; the MAD comparison uses passive drag from other swimmers, and the naval-architecture row rests on one swimmer. The stronger evidence of disagreement is the paired comparisons on the same swimmers above.

Seven reasons for the gap

Several mechanisms contribute, and their relative weight shifts from one protocol to the next.

Equal power. The dominant factor wherever two separate swims are compared. By the estimate of Toussaint et al. (2004), a 15 per cent difference in power gives a 30 per cent error in drag, and in Hazrati’s uncertainty budget (Hazrati, 2016), with an assumed 7.5 per cent violation, the equal-power term is 36 N of a total of 38 N. The direction of the bias is predictable: assisted towing overestimates drag, loaded swims underestimate it. A second account, already suggested by Toussaint et al. (2004) and developed at length in Kolmogorov’s book (Kolmogorov, 2025, Chapter II), holds that an oversized load alters limb kinematics and lowers propelling efficiency rather than total power; it predicts the same sign of error, and existing data cannot separate the two.

Perturbation size. Gonjo and Olstad’s dose-response (calculated drag falling from 83.5 to 50.8 N as the load rose; Gonjo & Olstad, 2022) and the error analysis in part 3 (random error of about $\sqrt{2}\cdot \epsilon /\mathrm{\Delta }{v}_0$ at small $\mathrm{\Delta }{v}_0$) show that a small perturbation protects the equal-power assumption while magnifying timing error, and a large one does the reverse. Groups working at a 4 to 6 per cent speed loss and groups working at 18 to 50 per cent are simply not making the same measurement. Kolmogorov’s stand specifies a timing accuracy of 0.01 s at each mark crossing (Kolmogorov, 2023, p. 3); the basic test and most other protocols report none at all, and a reader needs it, or better the standard uncertainty of the segment times, to judge a result.

The exponent. The pool perturbation methods built on the shared algebra and the tethered methods assume $n=2$ (the naval-architecture variant being the exception). Yet measured curves give 1.73 to 2.89 on the pads (Narita, Ogita, et al., 2018; Schreven et al., 2013; Seifert et al., 2015; Toussaint et al., 2004), 2.53 in the flume (Narita, Ogita, et al., 2018), 1.60 by the energetic method (1.56 to 1.72 for Zamparo’s trunk-inclination estimate; Zamparo et al., 2009), and, for a passive mannequin in a flume, 2.3 at the surface and 2.9 for the wave component alone (Vennell et al., 2006). The resulting error is moderate, about 10 per cent by Toussaint’s estimate (Toussaint et al., 2004), but systematic.

Apparatus altering technique. Fixed pads that lock the stroke length; a towline that smooths the intra-cycle speed fluctuations; a metronome and a dual-tether belt in the flume. Each nudges the result in a partly predictable direction, and none captures the swimmer’s own unconstrained stroke.

Reference area. Coefficients are normalised variously to body surface area (0.02 to 0.06; Narita, Nakashima, & Takagi, 2018; Takagi et al., 1999), to frontal area (for example Barbosa et al., 2013; Morais et al., 2023), to body volume to the power 2/3 (group means of about 0.20 to 0.48 in Kolmogorov, 2025, Chapter II; individual values of 0.15 to 0.80 in Kolmogorov & Duplishcheva, 1992), or to wetted surface (Webb et al., 2011). The areas themselves carry substantial uncertainty: Clarys’s frontal-area formula (1979, as cited in Marinho et al., 2010, p. 74) has an $R^2$ of only about 0.70. Measured the same way, a streamlined swimmer’s frontal area is about 0.07 to 0.12 m² (0.113 m² in the juniors of Morais et al., 2023; 0.093 m² for the mannequin of Vennell et al., 2006), but the areas taken as a reference differ almost tenfold: about 0.15 to 0.20 m² for the immersed body’s volume to the power 2/3 (Kolmogorov, 2008), an effective area allowing for trunk incline that falls from 0.40 to 0.23 m² as speed rises from 0.6 to 1.4 m/s (Zamparo et al., 2009), and 0.65 to 0.75 m² in passive towing studies (Havriluk, 2005, as cited in Zamparo et al., 2009). For the same force in newtons, the choice of area alone can change a dimensionless coefficient several times over. Cortesi and colleagues report the dimensional $k=D/v^2$, drag $D$ divided by the square of speed $v$, in kg/m (Cortesi et al., 2024), which sidesteps the problem entirely and deserves imitation. Still, a different reference area changes only the dimensionless coefficient, not the force already obtained in newtons; the HRM’s exclusion of the propelling segments goes deeper, because it changes the body whose resistance is modelled (Kolmogorov, 2008).

Wave drag. At the surface and above Froude numbers of about 0.3, it can become the largest component of passive resistance and grows more steeply than $v^2$. A quadratic perturbation model can fold wave drag into its effective coefficient, but it cannot isolate that contribution or follow a change in its speed dependence between the two swims (the naval-architecture model treats waves as a separate term). How large it is in active swimming is itself contested: Toussaint et al. (2002) put it at about 12 per cent of total drag at 1.89 m/s (21 per cent in an example swimmer), an estimate Vennell et al. (2006) judged to “significantly under-estimate wave drag on active swimmers” (p. 670).

The definition. As Toussaint (2002) and Hochstein et al. (2014) emphasise, and as Cortesi et al. (2024) acknowledge for quasi-steady models, the cycle-averaged drag of a self-propelled body exists only as a model construct. Bale et al. (2014) showed that thrust and drag can be separated unambiguously only for certain classes of motion, and Mason et al. (2014), comparing three computational routes to the instantaneous drag profile with the same resultant, found two nearly identical profiles and a third with a 40 to 65 per cent wider range, and chose between them on plausibility. As part 4 showed, one major school now explicitly treats the perturbation result as the total propulsive force and calls the smaller frontal component the body’s resistance. Part of the spread in Figure 2 may therefore simply reflect differences in operational definitions.

How reliable is any of this?

Method and study	Repeatability measure	Value
MAD (Schreven et al., 2013)	between-day ICC; SEM	0.92 to 0.94; 1.4 to 1.7 N
Assisted towing, constant speed (Formosa et al., 2010)	ICC; typical error within a day	0.99; 2.5 N (4.9 %)
Assisted towing, constant speed +10 % (Formosa et al., 2012)	ICC within one session; typical error	0.91; 18.1 N (9.7 %)
Assisted towing, fluctuating (Hazrati et al., 2013; Hazrati et al., 2016)	ICC within a day (single trials) / between days (means of five trials)	0.80 to 0.85 / 0.92 to 0.93
Perturbation (Kolmogorov & Duplishcheva, 1992)	validity checks, not repeatability: towing check; two bodies	about 1 %; 50.2 vs 51.0 N
Perturbation (Toussaint et al., 2004)	repeat tests, at differing free speeds	up to about 36 % within a swimmer
Perturbation, modified tow (Wang et al., 2007)	SD of four repeats	3 to 9 N
Perturbation, robotic load (Gonjo & Olstad, 2022)	between-day ICC; typical error	0.40 to 0.97; 2.9 to 23.1 % by load
Perturbation: stand, swapped stand, basic test (Kolmogorov, 2023)	agreement of three set-ups in a fixed order: Pearson $r$; largest difference for one swimmer	same day 0.979, 2.3 %; next day 0.926, 5.2 % (recomputed ICC 0.98 and 0.91)
Hand sensors vs perturbation (Morais et al., 2023)	between-method ICC	0.93
Flume residual thrust (Narita et al., 2017)	variability of active drag in two swimmers	6.5 and 3.0 %
Energetic, pool residual thrust, HRM	test-retest	not identified in the reviewed sources

Two important cautions. First, the highest repeatability appears where the apparatus constrains the swimmer most, and it says nothing about validity: constant-speed towing reaches an ICC of 0.99, yet, as Hazrati argued from the changes in stroke rate and stroke length (Hazrati, 2016), it systematically violates equal power. Second, for half of the methods I found no repeatability data in the sources reviewed, so many reported “changes” in active drag cannot be told apart from noise. In the 1991 national-team data reported by Kolmogorov et al. (1992), individual swimmers’ perturbation drag changed by a factor of 1.5 to 2.3 over one to four weeks at nearly the same speed; the authors attributed this to changes in technique, but without a repeatability figure the share of measurement error can be neither excluded nor estimated.

What to do with a number

Treat any active drag value as the output of a specific protocol, not a property of the swimmer. Compare strictly like with like: the same method, the same direction and size of perturbation, the same distance, the same exponent and the same reference area, all in the same swimmer. A change of method can change not only the numbers but the order of swimmers (above). The AIS caveat that “the current method only allows intra-athlete comparisons” (Alcock & Mason, 2007, p. 214) was written about its own protocol, but for each of the methods reviewed here, comparing swimmers would require at least the same speed and task, a correction for body size and a known error.

Match the tool to the question.

• If you want a complete drag-speed curve in front crawl and can accept an altered, arms-only stroke, the MAD system offers a directly measured force and documented repeatability.
• If you want a single number at maximal speed in any stroke on a modest budget, the perturbation method works, provided its metrological trade-off is kept in view: report the speed loss and the timing precision, run several repeats, and keep comparisons within the individual swimmer.
• If you have a flume and want to see how the legs, stroke rate and stroke length change resistance across speeds, residual thrust is the tool.
• If you have an isokinetic resistance device in an ordinary pool, Cortesi’s semi-tethered protocol gives an estimate together with a check of the model against the measured free speed (Cortesi et al., 2024); their data suggest keeping the loads at or below about 75 per cent of maximal tether force, where the values agree better with the model. Do not replace the test with a flat 1.5 times passive drag: in the same group’s second study that shortcut came out about 17 per cent below the residual-thrust value (Carmigniani et al., 2025).
• If you need resistance tied to metabolic cost, the energetic method estimates drag from metabolic cost against an external force, at aerobic speeds.

When monitoring swimmers over time, respect the arithmetic of measurement error. In 12-year-old swimmers, Marinho (Marinho et al., 2010) found active drag changing by a non-significant 5 to 9 per cent over a training block against a between-swimmer standard deviation of 40 to 50 per cent of the mean; the spread between swimmers is routinely large (in Corrêa’s 17 juniors of the same maximal speed, the coefficient of variation of active drag was 44 per cent, much of it explained by body mass; Corrêa et al., 2007). Yet a wide spread between swimmers does not by itself mean poor repeatability; whether one swimmer’s change is real is decided only by the test’s own error. Compare a change with the uncertainty of the difference between two assessments, not with the spread of a single test: with independent, normally distributed errors of equal size and no systematic drift, the 95 per cent minimal detectable change is about $1.96\cdot \sqrt{2}\approx 2.77$ times the typical error of one assessment, so a test with a 4 per cent typical error needs a change of about 11 per cent (averaging repeats lowers the threshold, and between-day error must be estimated on its own). Where a method has no published typical error, it will not tell you whether a change is real; your own repeats will. And under the simplified relation $P=k\cdot v^3$, where $P$ is the power spent against drag, $v$ the speed and $k$ the drag factor, a 10 per cent reduction in $k$, that is, in drag at a given speed, at unchanged power raises speed by about 3.6 per cent; a model illustration, not a prediction for any specific change of technique.

Testing a change of technique demands the same discipline. Alves et al. (2024), already met in part 3, compared breathing every cycle with breathing every second cycle in breaststroke after six weeks of familiarisation, in 15 swimmers with one free and one loaded 25 m swim per condition. The group means did not differ (58.5 ± 30.5 against 60.3 ± 25.4 N; 95 per cent confidence interval of the difference −19.9 to +16.1 N), while individual drag when breathing every second cycle fell by up to about 85 N or rose by up to about 52 N: six swimmers had lower drag breathing every second cycle, nine breathing every cycle. With one pair of swims per condition and speed losses of 3 to 16 per cent, these individual changes cannot be told apart from the test’s own unmeasured noise. Repeat each version of the technique several times, ideally on two different days, and compare the difference with the uncertainty of the difference between the repeated series.

And whenever you read or publish a value, insist on the metadata: the method; the direction and size of the perturbation together with the timing precision; the assumed or fitted exponent; the reference area; the depth and surface conditions; and at least some check of equal power, even a proxy such as stroke rate and stroke length in both swims. Without that record two numbers cannot be compared, even from the same laboratory: at the 2013 AIS workshop the same methods came out in a different order of size in the groups timed over 10 m and 20 m (Mason, Kolmogorov, et al., 2013).

What would settle it

The sources reviewed make clear which pieces are still missing.

1. Kolmogorov (2023) came closest to a strict check, comparing the classic test with his stand on the following day. An independent test-retest of the classic perturbation method against itself, outside his group, with measured maximal speed, calibrated towed bodies, a 4 to 6 per cent speed loss and the ICC and typical error reported, would show how far the prescribed optimum is achievable in practice.
2. Measuring power in both perturbation swims, even by indirect biomechanical indicators, would separate the two explanations of underestimation under load.
3. No independent comparison of the HRM’s frontal component with any other method was found in the literature reviewed; since the HRM is the only method reviewed that computes the body’s own frontal drag within the cycle from the swimmer’s kinematics and flume coefficients, that is one of the largest gaps.
4. Measuring the drag-speed exponent for each method rather than assuming it to be two would remove one systematic error.
5. Finally, agreeing on names, so that a reader knows at a glance whether a reported “active drag” is the mean total propulsive force or the resistance of the body itself, would remove the part of the disagreement that has nothing to do with measurement.

Back to the question

Part 1 opened with a coach’s practical question: when a test shows lower drag, has the swimmer’s resistance really fallen, or has something shifted in the measurement itself? After five posts the series can give a clear but conditional answer. A change can be read as a change in the swimmer only when the same method and strictly the same protocol were used at a comparable speed, and when the change exceeds that test’s minimal detectable change. Even then, clearing the threshold rules out random test noise rather than proving that technique lowered drag: changes in the swimmer’s effort, or in how closely the model’s assumptions held on the day, must still be weighed. A difference between two methods, by contrast, says nothing about a change in the swimmer, and may not even be a difference in the same physical quantity. Within those limits each method answers its own question well enough to be useful, and none is arbitrary merely for depending on a model: a named model with a known error is precisely what turns a 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)

References

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