Biomechanics and Medicine in Swimming XI

Extending the Critical Force Model to Approach
Critical Power in Tethered Swimming, and its
Relationship to the Indices at Maximal Lactate
Steady-State
Pessôa Filho, d.M., denadai, B.s.
Paulista State University, Brazil
This study aimed at comparing tethered-power (CP Teth ), assessed using
the critical force model, to the power at maximal lactate steady state
(P TethMLSS ), and critical velocity (CV) to the velocity at maximal lactate
steady state (v MLSS ). Ten swimmers were submitted to measurements of
the CP Teth (linear and non-linear adjustments of impulse against time),
CV (linear plotting of time and velocity in the 200, 400 and 800-m),
P TethMLSS (3-4 trials ranging from 95 to 105% of non-linear Fcrit),
and v MLSS (3-4 trials ranging from 85 to 95% of the 400-m free-crawl
performance). Estimated CP Teth and P TethMLSS were obtained from the
tethered-force equation times hydrofoil velocity. The results showed that
neither CV (1.19 ± 0.11m·s -1 ) nor CP Teth (98±22W) matches the statements
for maximal lactate steady state, once differences (p ≤ 0.05) were
noted in relation to v MLSS (1.17 ± 0.10m·s -1 ) and P TethMLSS (89±15W),
respectively.
Keywords: critical tethered-force; tethered swimming; maximal lactate
steady state; swimming hydrodynamics
IntroductIon
Time to exhaustion is linearly related to the steady-load applied while
swimming at full-tethered conditions (Ikuta et al., 1996). These authors
defined critical force (Fcrit), the slope of the linear plot between impulse
and maximal sustainable time, as the tethered force that could
be maintained without fatigue. Despite the fact, that the measurements
of endurance pulling force provide good relationships to long-distance
performance (Swaine, 1996) and to blood lactate accumulation index
(Ikuta et al., 1996), the relationship between pulling force and swimming
intensity at maximal lactate steady-state (MLSS) remains to be
established.
The MLSS corresponds to the highest constant workload that can
be maintained over time without continuous blood lactate accumulation
(Beneke et al., 2001). The time to exhaustion-based model is a simple,
rapid and non-invasive test to evaluate endurance capacity, but the accuracy
of indirect tests to estimate MLSS has been questioned. Dekerle
et al. (2005) suggested that the determination of critical velocity (CV)
leads to an overestimation of the metabolic rate associated with MLSS,
and that the differences between these variables tend to be greater with
the improvement of aerobic performance. Although Ikuta et al. (1996)
did not measure the force or velocity at MLSS, they assumed its correspondence
to the Fcrit based on the correlations between this parameter
and endurance indices obtained under free crawl condition.
It should be noted that the interchangeable use of MLSS and CV
(or critical power, CP) to represent the upper limit of heavy exercise
domain has been refuted either in cycling (Pringle & Jones, 2002) or in
swimming (Dekerle et al., 2009). Despite the slight differences between
these variables, CP leads to an overestimation of physiological rate associated
to MLSS (Pringle & Jones, 2002; Dekerle et al., 2003). Thus,
it was postulated that exercising just above MLSS is hardly tolerable
once it induces to a continuous increasing in blood lactate concentration
and VO 2 (Pringle & Jones, 2002; Dekerle et al., 2009). Nevertheless,
this slight difference between MLSS and CV (or PC) should be interpreted
with caution, due to methodological limitations of modeling CV
(or PC) (Dekerle et al., 2003) and of the precise control of load under
MLSS testing procedures (Pringle & Jones, 2002).
The assessment of stroke force by means of tethered swimming is
chaPter2.Biomechanics
simple and versatile, besides it has provided a great deal of specificity for
swimmer evaluation, training and free swimming performance ( Johnson
et al., 1993; Rouard et al., 2006). Furthermore, according to Kjendlie
& Thorsvald (2006), force measurement with tethered swimming is
highly reliable and shows low values of variation for test-retest protocol.
Thus, assuming tethered swimming as a steady-force environment, one
of the purposes of this study was to compare and to relate the values of
power output at MLSS (PTethMLSS ) in relation to the critical force (PF crit
) model. Another purpose was to proceed with the same analysis for
reciprocal tests under free crawl swimming, allow for further comparisons
through the two swimming conditions (non- and full-tethered),
as for blood lactate concentration at MLSS, and for amplitude of the
differences between P Fcrit vs. P TethMLSS and velocity at MLSS (v MLSS )
vs. CV.
Methods
Ten well-trained male swimmers (16.6 ± 1.4 years, 69.8 ± 9.5kg, 175.8
± 4.6cm) were submitted to four independent tests in order to measure
the P TethC , CV, P TethMLSS and v MLSS . They were informed of all test protocols
and we obtained their informed consent. The study was approved
by the local Ethics Committee.
The active drag force (Fr) in maximal free crawl swimming was estimated
based on subjects body mass, using drag proportionality coefficient
(A = ((0.35 x mass)) + 2), according to Toussaint et al. (1998). This
procedure is not a direct measurement of active body drag, and it takes
into account an early assumption that the resistance is related to the
square of the swimming velocity (Fr = Av 2 ) (Toussaint et al., 1998). On
a practical note, this approach provides a good deal of applications for
hydrodynamics assessment on poolside throughout the training season.
To estimate Fcrit, loads ranging from 75 to 100% of the Fr in the
pulley-rope system were attached to the swimmer. Three trials lasting 3
to 15 minutes were performed until exhaustion, i.e. the instant that the
swimmer was not able to generate force enough to prevent him from
being pulled back by the load. The impulse (load times trials duration, N
x s) was plotted against trials duration by means of a linear curve fitting
(i = a + b(t)), and a non-linear two-parameter equation (t = a/(i – b)),
where the slope gives Fcrit in both adjustments (Ikuta et al., 1996). The
load related to MLSS intensity was obtained in three to four trials ranging
from 95 to 105% of non-linear Fcrit. The greatest fraction that did
not elicit a lactate accumulation above 1mmol.L -1 between 10 th and 30 th
minutes was considered the tethered-force at MLSS (F MLSS ). Blood
samples (~25µl) from ear lobe were analyzed for lactate concentration
([La]) using an automated analyzer (YSI 2300, Yellow Springs, Ohio,
USA). The test was interrupted by 30s break for blood sampling at the
10 th and 30 th minutes, as suggested by Beneke et al. (2001).
To approach mechanical tethered-power (P Teth ) from Fcrit and
F MLSS , we considered two assumptions. First, the hydrofoil moves backward
with uniform velocity during the entire stroke. Second, an external
and constant loading generates an opposing load force (F Load ) equal to
the tethered-force of hydrofoil (F Teth ). Thus, added weight must prevent
the swimmer from moving forward (v = 0) according to F Load + Fr –
F Teth = 0, where Fr approaches zero in this condition. This statement
for hydrofoil motion in tethered swimming is an unequivocal rewrite of
the mechanical assumption for hydrofoil described by de Groot & van
Ingen Schenau (1988). Therefore, the relationship between forward and
backward forces in steady state condition equals:
F Load = F Teth = 0,5Cx Hydr × ρ × S Hydr × u 2 (1)
where F Load and F Teth are noted in Newtons; Cx Hydr is the drag coefficient
for hydrofoil (~2.2), p is the water density (~1000kg/m 3 ), S Hydr
is the hydrofoil plane area (estimated from hand and forearm volume
powered by two thirds, i.e. V Hydr 2/3 ), and u 2 is the squared hydrofoil velocity
(v Hydr, m·s -1 ). The volume of hand and forearm was determined
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