Underwater Undulatory Swimming (UUS)

The Underwater Undulatory Swimming, which can be referred as the fifth stroke in the swimming world.
It is more commonly called the Dolphin kick. Those are used by freedivers with the monofin in the Constant Weight disciplines.

The UUS has been studied and analized through a lot of publication. It was not analyzed only through swimmer motion analyze, but also compare to fish using their tail to swim.

To actually analyze and compare that, scientists use vortices that results from swimming motion. R. Aurellano described and observed them, using different methods [Arellano R. 1999] [Arellano R. and all 2002].

Through the transcription of his and others work, we will first describe how we can perform the UUS then we are going to explain how we can maximized the thrust resulting from them.

Studies on aquatic animal locomotion ( [Rosen M. W. 1959] [Gray J. 1968] [F.E. Fish , J. J. Rohr 1999] ) observed vortices during aquatic motion in the water.

Let’s explore the role of vortices in propulsion.

Vortices and propulsion

Vortices are whirlpool created by changes of pressure during a motion underwater. Under specific condition, those vortices could contribute to the swimmer thrust.

Those vortices apply to undulatory body has been studied on swimming animal.

On one of this study, Gray J. (1968) observed :

« When a flexible undulating body acquires forward momentum, a corresponding amount of backward momentum must be acquired by the water; this backward momentum is concentrated in a vortex wake and appears in the form of a jet of fluid expelled from the wake »[Gray J. 1968]

First description of USS

Using [Gray J. 1968] analyze on the subject, [Arellano R. 1999] describes two parts od the UUS.

• The Downward kick, creating a main vortex.
• The Upward kick, creating a secondary vortex.

The main vortex is generated a the beginning of the downward kick when the feet are at the highest and is liberated when the feet change direction for the upward kick.

The secondary vortex is generated at the beginning of the upwardkick when the feet are at the lowest and it is detached when the feet change direction for the downward kick [Arellano R. 1999].

( see detailed description of the kick in Detailed description of USS below)

Aquatic animal locomotion

On « Water flow about a swimming fish » [Rosen M. W. 1959] identify two kinds of vortex. Main vortices behind the fish. Secondary vortices on the side of the fish. On the following demonstration, the use of « main vortices » and « secondary vortices » will be according to [Rosen M. W. 1959] definition.

She established a link between the two of them, let’s develop that below.

The secondary vortices are going to be very interesting for us.
A secondary vortex starts at the beginning of the movement, builds up as he follows the body until It releases him self when the direction of the kick changes.
[Rosen M. W. 1959] describe those phase as « structure of vortex ». She also describe a link between all the vortices as they cross each other during the motion.

When the tail is crossing the main vortex, the secondary vortices feed this vortex. By the 3^rd Law of Newton this result in a reaction, a thrust propelling the fish forward.[Rosen M. W. 1959] (p75 – EVOLUTION OF A VORTEX – FINAL EXPANSION).

Despite the interpretation of [Rosen M. W. 1959] saying that «This is not a Karman vortex street. », the analyze of the thrust origin comes in adequacy with the interpretation of Theodore Von Karman vortex streets.
Karman vortex streets could be described as the fact that alternate separation of the vortices or whirlpool can create a periodic thrust.

Specially when [Karman v. T. 1963] in « Aerodynamics » reminded how the unstable vortex street of his first theory^[1] could be stable despite their asymmetric disposition (in triangle in a undulatory body).
He « showed how the creation of such a vortex system can represent the mechanism of the wake drag. » [Karman v. T. 1963]

This mechanism of the wake drag is simply our main vortex alimented by the secondary vortices. For an undulatory body they are build up along the body, feed the main vortex and create the thrust with the 3^rd Law of Newtopn in reaction of the wake drag.

Karman interpretation is still use on the scientific literature, as [Ungerechts B.E. and all 1998] does by quoting [Lighthill M. J. 1973] :

« According to [Lighthill M. J. 1973], the creation of [a main vortex]^[2] is a fundamental basis for thrust production in thunniform locomotion, since «between [the secondary vortices]^[3] a jet-like motion is induced ». » [Ungerechts B.E. and all 1998]

[Arellano R. 1999] identify those vortices as main and secondary when they are the results of the same physics reason.

Let’s transfer the undulatory swimming of fish to a swimmer

From fish to swimmer

If a fish is symmetrical or almost, the downward kick and upward kick are physically different, the muscles, the joints, the shape etc… for each movement are different. From that result the fact that the downward kick is generally stronger than the upward kick. Therefore, [Arellano R. 1999], identify the vortex resulting from the downward kick stronger as the main and the other as secondary.

Those secondary vortices can be enhanced and therefor I could increase the thrust. By having a longer body to undulate, we should be able to build up more the secondary vortices to nourish our main vortices.

[Videler J. J. and all 1999] describes this phenom as (using the term proto-vortex or body vortex for secondary vortex and tail vortex for main vortex) :

« Body undulations create semicircular flows driven by pressure differences. These flows centre around the inflection points of the body, forming a [secondaty vortex]^[4] that is shed at the tail tip. […]
This [secondary vortex]^[5] contributes to the wake and hence to the momentum transferred by the fish to the water. […]
If the [secondary vortex]^[5] merges with the [main vortex]^[6], its circulation contributes to the total circulation in the [main vortex]^[6] and, hence, to thrust. […]
This suggests that the body can contribute substantially to thrust production. » [Videler J. J. and all 1999]

Those information comes reinforce the reason why a swimmer like Micheal Phelps lokk like his whole body undulate.

But

In a learning process of UUS I will recommend to follow the advice given on Last adjustments below and to be follow by a coach who as the required expertise to teach the expansion of the movement.

If we want to get close to fish propulsion and to there efficiency there is also another aspect really important to emphasize : The Upward Kick – Anteversion (Illustration 9).

Dolphin propulsion has been analyzes through different studies [Lighthill M. J. 1973] [Ungerechts B. E. 1982] [Ungerechts B.E. and all 1998] [F.E. Fish , J. J. Rohr 1999] , and sometimes compare to swimmers UUS [Ungerechts B. E. 1982] [Ungerechts B.E. and all 1998]; without describing all the aspect of those studies, one particular point was pointed by [Ungerechts B. E. 1982].
During his study he pointed out that the upward kick was way more used by dolphin than swimmers. This statement is confirm by [Arellano R. 1999] who observed smaller vortex after the upward kick.
In order to improve this aspect, emphasizing the fact that the upward kick has as much importance as the downward kick to swimmers/freedivers could be a way to improve their UUS.

Now let’s describe this motion in details to execute our UUS with the adequate technique.

Detailed description of USS

Initial position

The Initial position for a dolphin kick is a streamline (Illustration 8), or « arrow position ». In this position we want to have a perfect streamline between :

• Hand, head, shoulder line, hips/waist and feet

During our UUS, we will keep the streamlined hand/head/shoulder line fix.

Initial motion

In a first place the swimmer will alternate anteversion and retroversion of the hips (Illustration 9).

This first movement will gave the swimmer the proper momentum to start using his leg muscle properly.

At this stage, hip’s movements will start to make our lower body undulate.

To finish the movement the swimmer uses his muscle to enhance the thrust:

The Downward Kick – Retroversion (Illustration 10)

During the retroversion of his hips, the swimmer push his leg downward (swimming horizontally) or forward (swimming vertically), using his core and gluteus muscles^[7] to do the retroversion of his hips.

In the same time, the swimmer uses his quadriceps to finish the movement with the all leg.

Illustration 10 describes this part of the dolphin kick.
You can notice the heel on yellow going down using the quadriceps.
You can notice the hips in red going up using the core and gluteus muscles.
From picture 1 the swimmer is using his quadriceps to straight his leg bend previously by the resistance of the water (explained above). Between picture 5 and 6 we can notice that the heel are not going down anymore. At this point he swimmer extend his ankle to accelerate the water and increase the thrust coming by the creation of vortices.

We can notice that the leg, and more specifically the feet are behaving like fish tail. This effect is amplify by the use of fins.

The Upward Kick – Anteversion (Illustration 11)

During the anteversion of his hips, the swimmer brings back his leg upward (swimming horizontally) or backward (swimming vertically), using his lower back muscles to do the anteversion of his hips.

In the same time, the swimmer uses his hamstring to finish the movement with the all leg.

Illustration 11 describes this part of the dolphin kick.
You can notice the heel on yellow going up using the hamstring.
You can notice the hips in red going down using the lower back muscles.
On picture 4 and 5 we observe that the anteversion of the hips is barely noticeable and that the knees are bending. During this part the swimmer already started to do his retroversion and the knees are bending due to the resistance of the water.

Last adjustments

Let’s remind that during this process the upper body stay still (green dot Illustration 10 and Illustration 11).
This body position can be call to controversy :
Indeed, if we observe swimmer as Michael Phelps which is probably one of the best swimmer about UUS of all time, we observe that he is using his whole body to do his UUS.
If he appears to undulate using the chest (hand/arm/head/shoulder line staying fix), there is another way to analyze this motion.

In order to increase is dolphin amplitude and to give a longer undulatory body, Michael Phelps simply enhance the amplitude of his hips retroversion/anteversion eithier by pushing his pelvis forward using his core and gluteus muscles or pulling his bottom more backward still using his lower back.

The first step being a control of your hips area with the basic retroversion/anteversion movement then apply it it the water.
Then slowly with training enhance the amplitude of your retroversion/anteversion.
Strengthened the lower back, core and gluteus muscles will be a major factor to improve your USS, either by stretching of the hips area than muscle power or stamina.

As we can observe on Illustration 11, a swimmer like Micheal Phelps already have a huge control, flexibility (amplitude) and power on his hips movement.

In a process of learning I will recommend to fix the upper body in order to control the UUS better. When the swimmer/freediver has a good control of his upper body, he can start to enhance the amplitude of his movement.
The risk by doing it to early in the learning process is to have a swimmer using his all body to undulate (hand/head/ shoulder line included).
This will results in an increase of the body cross-sectional area, the pressure drag and a loss of efficiency.( remember that in school we learn addition before multiplication !)

Now that we know how the propulsion is created in UUS, let’s extrapolate those research to freestyle kick then in monofin and bi-fin use.

Notes

• ^[1]Despite that the vortex are called by T. v. Karman, he never claimed to have discovered this phenomenon. Henri-Bernard (1974-1939) a french physicist observed that from the point of view of an experimental physicist. [Karman v. T. 1963].
• ^[2]Written as « vortex-wake » by [Ungerechts B.E. and all 1998].
• ^[3]Written as « the vortices with altered sense of rotation » by [Ungerechts B.E. and all 1998] from [Lighthill M. J. 1973].
• ^[4]Written as « proto-vortex » by [Videler J. J. and all 1999]
• ^[5]Written as « body vortex » by [Videler J. J. and all 1999].
• ^[6]Written as « tail vortex » by [Videler J. J. and all 1999]
• ^[7]Gluteus Muscles are the group of muscles of the buttocks.

References

• [Rosen M. W. 1959] : Moe William Rosen , Water flow about a swimming fish (p), 1959.
• [Karman v. T. 1963] : Theodore von Karman, Aerodynamics (p), 1963.
• [Gray J. 1968] : James Gray, Animal Locomotion (p29-46), 1968.
• [Lighthill M. J. 1973] : Michael James Lighthill, Aquatic animal locomotion, 1973.
• [Ungerechts B. E. 1982] : Bodo E. Ungerechts, A Comparison of the Movements of the Rear Parts of Dolphins and Butterfly Swimmers (p), 1982.
• [Ungerechts B.E. and all 1998] : Bodo E. Ungerechts, Dan Daly, J.P. Zhu, What dolphins tell us about hydrodynamics, 1998.
• [Arellano R. 1999] : Raul Arellano, Vortices and Propulsion (p53-65), 1999.
• [Videler J. J. and all 1999] : J. J. VIDELER, U. K. MÜLLER AND E. J. STAMHUIS, AQUATIC VERTEBRATE LOCOMOTION: WAKES FROM BODY WAVES, 1999.
• [F.E. Fish , J. J. Rohr 1999] : F.E. Fish , J. J. Rohr, Review of Dolphin Hydrodynamics and Swimming Performance (p), 1999.
• [Arellano R. and all 2002] : Raúl Arellano, Susana Pardillo, Arantxa Gavilán, Underwater undulatory swimming: Kinematic characteristics, vortexgeneration and application during the start, turn and swimming strokes, 2002.