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#### Double-Leg Kick (Dolphin Kick) Basics Part II: Kicking Tempo, Number, and Strouhal Number

First, don't forget to check out Double-Leg Kick (Dolphin Kick) Basics Part I: Kicking Depth. With depth out of the way, it is time to discuss double-leg kicking (DLK) tempo and distance per kick. Too often tempo and distance per kick are not discussed together, despite their clear association. This is odd since distance per stroke and stroke rate are commonly discussed together, kicking should not be different!

We have discussed both of these topics indirectly on Swimming Science, eloquently by Chris Plumb in Beep, Beep, Beep and in Groin Kick Syndrome: Part I. Now let us discuss them in more depth.

Tempo
DLK tempo and distance per kick (measured via kick number) has been studied extensively by Coach Bob Gillett. Coach Gillett has analyzed elite male and female swimmers and suggests both groups should have a kicking tempo around 0.45 (Gillett 2013), where Russell Mark (2012) notes a tempo around 0.40 is utilized. Many feel this kicking tempo is extremely fast, but one study by Cohen (2012) indicates faster kicking tempo is correlated with net higher streamline force. Surprisingly, ankle flexibility was not sensitive with streamline force! This suggests kicking tempo is superior to streamline than ankle flexibility!

Once again, using a tempo of 0.40 - 0.45 is recommended for elite dolphin kickers, but finding the ideal tempo for each person, the principle of individuality is a necessity. Unfortunately, too many poor dolphin kickers attempt kick with a large amplitude and slow kick, when a quicker tempo may fix their slow kicking! Some feel this tempo may not be necessary, as compared to cetaceans humans take a lot more kicks, even at the same velocity (von Loebbecke 2009). However, the applicability of comparing a human to a cetacean is questionable, as different biomechanics and fin/foot size also play a significant role.

Number
Coach Gillett also notes elite male and female flyers take approximately 9 and 11 kicks to reach 15-meters respectively (Gillett 2013). Unfortunately, this number varies slightly from back and fly swimmers, by approximately 1 kick, noted by Mark (2012).

Table-1 Mark (2012)

More research is needed on the ideal kick number for elite dolphin kickers, however the principle of individuality likely plays a large role for each swimmer.

Strouhal number
The Strouhal number is rarely discussed in coaching circles, but is a dominant discussion in research despite not being correlated [yet] with dolphin kicking performance (von Loebbecke 2009). For coaching, it is crucial to realize this number is somewhat combines underwater DLK tempo and velocity, unfortunately this isn't easily measurable at this time. However, with the increased use of underwater cameras and swimming technology, finding methods for measuring Stouhal number are likely around the corner.
In Physics it is expressed as: $mathrm{St}= {f Lover V},$. In this equation, f=frequency, L=body length or hydrallic diameter, and v=velocity.

Elite humans have a Strouhal number around 0.8 - 1.2, but more research on this value is necessary.

Conclusion
In the future, more sophisticated methods, like the Strouhal number, may be applicable for measuring skill level. Until then, finding your ideal kick tempo and number are necessary for underwater kicking success. This makes practicing at a fast pace essential for isolating and ingraining these aspects.

1. Cohen RC, Cleary PW, Mason BR. Simulations of dolphin kick swimming using smoothed particle hydrodynamics. Hum Mov Sci. 2012 Jun;31(3):604-19. doi: 10.1016/j.humov.2011.06.008. Epub 2011 Aug 12.
2. von Loebbecke A, Mittal R, Fish F, Mark R. A comparison of the kinematics of the dolphin kick in humans and cetaceans.
3. Hum Mov Sci. 2009 Feb;28(1):99-112. doi: 10.1016/j.humov.2008.07.005. Epub 2008 Nov 4.
4. von Loebbecke A, Mittal R, Fish F, Mark R. Propulsive efficiency of the underwater dolphin kick in humans. J Biomech Eng. 2009 May;131(5):054504. doi: 10.1115/1.3116150. von Loebbecke A, Mittal R, Mark R, Hahn J. A computational method for analysis of underwater dolphin kick hydrodynamics in human swimming. Sports Biomech. 2009 Mar;8(1):60-77. doi: 10.1080/14763140802629982.
5. B. Gillett Underwater Kicking and Foil Movement Personal communication. 2013 February 24.
6. M. Russell Dolphin Kicking. USA Swimming. 2012 April 12.
By Dr. G. John Mullen received his Doctorate in Physical Therapy from the University of Southern California and a Bachelor of Science of Health from Purdue University. He is the founder of the Center of Optimal Restoration, head strength coach at Santa Clara Swim Club, creator of the Swimmer's Shoulder System, and chief editor of the Swimming Science Research Review.

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1. ###### April 11, 2013

In the case of von Loebbecke & kicks per body length traversed, you could have just simplified the Strouhal number equation to

St=L / (lambda, or the dolphin kick wavelength), or St=L/(lambda)

which just tells you how far a swimmer goes forward with every doplhin kick compared to his/her body size

“unfortunately
this isn’t easily measurable at this time”

Kidding? In this case it’s ridiculously easy: just count how many kicks a person takes per 50m, and measure their body length.

In the other case of von Loebbecke & strouhal number, the “ratio of tip or toe speed to forward speed” it is a lot more difficult to do precisely, but you can still measure it roughly almost anywhere with some underwater video & some measuring sticks, combined with e.g. 15-50m dolphin kick time (–> the speed of the swimmer)

2. ###### April 12, 2013

Thanks for the input and the practical methods of measuring Strouhal number!