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In the context of competitive freestyle swimming, the leg position during the flutter kick can either partially exit the water or remain fully submerged. The leg's motion affects both propulsion and drag, thus impacting overall velocity.

At swim practice, my coach told me to keep both legs underwater but I timed myself and I'm faster with the legs partially exiting the water. I'm interested in the math explaining this.

What I tried: Consider the drag force formula

$$F_d=\frac{1}{2}C_d\rho Av^2$$

where $F_d$ is the force of drag. I think I want to maximize drag because I'm kicking in the opposite direction that I'm swimming. $C_d$ is the coefficient of drag, $\rho$ is the fluid density, $A$ is the surface area, and $v$ is the velocity.

I think the reason why I'm faster with the kick where both legs partially exit the water is because $v^2$ is so much higher. The legs are moving through air first before striking the water and moving the swimmer forwards.

I’m not sure if this explanation is entirely logical, or if there are additional reasons why having the legs partially exit the water results in a better performance.

EDIT: This is for sprinting the 50 freestyle, so it's a 25 second race.

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  • $\begingroup$ Your legs entering and exiting the water boundary may create vortex-like structures right around your legs. It may be easier to push off these structures than to push purely against the fluid viscosity itself... $\endgroup$
    – James
    Commented Oct 1 at 5:00
  • $\begingroup$ Why is pushing off vortex-like structures instead of fluid viscosity easier? $\endgroup$
    – Bird Boi
    Commented Oct 3 at 4:00
  • $\begingroup$ Jelly fish swims faster by using their own past vortices too youtube.com/watch?v=UKB87pdfiiQ $\endgroup$
    – James
    Commented Oct 5 at 17:30
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    $\begingroup$ I'd like to try it out, copying the jellyfish. With freestyle kick, would the idea be to use the past vortex of one leg to help the other leg? And to create higher pressure in the water like the jellyfish does inside its bell, should I move the knees closer during the middle of the kick and keep them further apart at the beginning and end? $\endgroup$
    – Bird Boi
    Commented Oct 5 at 19:34
  • $\begingroup$ Sorry, I could swim enough to save myself in a flood, but probably not win any swimming competitions. sports.stackexchange.com may have more experts on this topic... All the best! $\endgroup$
    – James
    Commented Oct 5 at 19:48

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Swim with legs partially exiting the water is in fact faster. You just need to watch the 50m Freestyle race at the Olympics https://www.youtube.com/watch?v=qVOn_SgHH3U. All the swimmers have the legs partially out of water. This is because you are pushing more water after you. According to the third Newton law, the force you make on the water is the force the water makes on you, momentum must preserve so the higher water you displace, the faster you go.

But this mechanism is turbulent. You create vortex in water so a lot of heat is dissipated. This means that this mechanism is not very efficient, you are wasting your energy in creating vortex. That's why long-distance swimmers keep legs inside the water in they trials. See as an example the 1500m Freestyle race at the Olympics https://www.youtube.com/watch?v=4Uw-zg0Xtys&t=421s.

So take the advise of your trainer and keep the legs underwater if you want you swim most efficiently, but forget about this technique if you want to win a short race.

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  • $\begingroup$ Interesting (+1) Can a (small) object kick a whirlpool from the side (e.g. youtu.be/B9w3vX48rhQ?si=qAEVAIHVA8JpwtQ5&t=22 ) and push itself away from this whirlpool by this kick? $\endgroup$
    – James
    Commented Oct 1 at 16:24
  • $\begingroup$ Nice explanation! If training for the 50 free, since we want to maximize vorticity, should I build a mind-muscle connection to laterally rotate the ankle, knee, and hip while kicking? I'm thinking rotation in every direction - x, y, z, so the knee would trace out a helix, but am not sure if this is the best path to maximize vorticity. $\endgroup$
    – Bird Boi
    Commented Oct 2 at 2:26
  • $\begingroup$ You don't want to maximize vorticity, you want to maximize the momentum of water displaced. Vorticity is the price you pay to maximize it. The payment is profit to gain velocity, but cost more energy. Ideally, it would be better to maximize momentum without creating voritcity, but we can't make it because our body have evolved to walk, not to swim. Fish have evolved to maximize water displacement without creating vortex, flippers have more surface than fingers, so they can push back more water. In conclusion, no, don't rotate your ankle, focus in push water behind you. $\endgroup$
    – Padisi
    Commented Oct 2 at 12:15
  • $\begingroup$ James: I don't know, the problem with this vortex is that the pressure gradient is very high, so the attraction force to the center is very high. Theoretically its possible to escape, but I don't know how much energy would it cost, and if a fish can make it. I guess that this depend on the fish and the vortex. Is like escape from a planet by jumping. Theoretically possible, but in practice you need to build a damn rocket to do it. $\endgroup$
    – Padisi
    Commented Oct 2 at 12:21

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