Studies of applied force versus speed in real paddlers allow us to analyze the limiting speed. Initially, we use the above-mentioned coefficient
kg/m, extracted from a field study [
4]. It is analogous and of the same order as other hydrodynamic studies at constant speed and propulsion [
1,
2,
3,
6], but it is a passive hydrodynamic drag coefficient. From the data of Gomes et al. [
9], for the competition paddling frequency, we have peak forces of 274 N and 153 N, for male and female categories, respectively, which transform to average forces of
N and
N, respectively, and where we have taken into account both the aquatic and aerial phases (factor 0.726 in men and 0.782 in women), as detailed in the previous
Section 3.4. The expression for the limiting velocity allows us to either obtain velocities from a known
d coefficient or to estimate the drag coefficient from the velocity data obtained in the study. Using the expression (
32) and the passive resistance coefficient
kg/m, we obtain velocities of
m/s and
m/s for males and females, respectively, appreciably above the average velocities obtained in the study
m/s and
m/s. Similar results can be obtained for the rest of the data at lower stroke frequencies. Regarding the kinematic–dynamic study over 200 m by Treus et al. [
15], the conclusions are similar. From their data, we take the fastest interval (between 50 and 100 m) corresponding to a force of
N and average velocity of
m/s for the male category. Such force, averaged as before and with a coefficient of
kg/m, can lead us to a much higher velocity, of value
m/s, analogous to those obtained for Gomes et al. [
9]. Similar results can also be obtained from more recent data [
10]. If, on the other hand, we extract drag coefficients from field data, we obtain
kg/m and
kg/m for males and females, respectively, from the data of Gomes et al. [
9] and
kg/m from that of Treus et al. [
15], being of the same order for the rest of the data or stroke frequencies and relatively constant by gender. We can evaluate the dynamic magnitudes from these force and drag coefficient estimates. We transfer the data to the expressions (
16). Using the remaining ones in
Figure 1, we obtain work to complete the acceleration interval of
J and
J and their corresponding estimated average power at
W and
W for males and females, respectively.
We have no data and cannot make any statements about the efficiency of the stroke. Additionally, the forces were obtained or correlated with accelerometry data measured in situ in the field studies. Therefore, the observed differences must have their origin in the simplifications assumed, which ultimately refer to the differences between active and passive hydrodynamic drag. From Pendergast’s studies of human locomotion in water [
23], it follows that active hydrodynamic drag is far superior to passive drag in all forms of human locomotion of this type. In particular for sprint canoeing, an estimate is made for active drag of the type
with the particularity of being a
free exponent expression sometimes used for hydrodynamic drag adjustments [
1]. A
phenomenological estimate tells us that in these settings,
higher exponents correspond to lower coefficients, and the equivalent expression with squared exponent corresponds to a considerably higher coefficient. For example, for velocities of
and
m/s, the active hydrodynamic drag for the above expression is
and
N and corresponds to coefficients of
and
kg/m if we use quadratic-type hydrodynamic drag expressions. We see that these are high estimates and well above the various passive hydrodynamic drag coefficients obtained in the literature. On the other hand, the curves obtained from the model suggest that the assumptions made and the resolution are not far fetched, as it is not difficult to find similar curves in the literature—for example, in the work of Leroyer [
17] by numerical calculation, in Begon’s [
18] where a kayak ergometer is modeled, or in Labbé [
22] or Buckmann’s [
24] works applied to Olympic rowing.