# How does moving your legs propel you forward in swimming?

• CuriousBanker
In summary: There are two ways to overcome friction: by increasing the area of contact, or by decreasing the surface area. Your arms and legs work together to overcome the friction between them. When you swim forward, you are pulling water back with your arms which creates a lot of resistance. This resistance is greater than the resistance of your air-breathing muscles when you move your arm forward, so you are propelled forward. However, your legs also contribute to your forward motion. When you kick your legs, the action of the legs creates a downward force which moves you forward. The more you kick, the more force is applied and the faster you will move forward

#### CuriousBanker

Ok, so I know why your arms move you forward in swimming. You are pulling the water back which pushes you forward a lot because there is a lot of resistance, and then you are moving your arm forward in the air which offers little resistance to push you back. So the amount you push back in the water is greater than the amount the air pushes you back when you move your arm forward.

But what about the legs? There are two things I am confused about:

1)How does moving your legs vertically propel you forward at all? I don't know how a downward kick can move you forward. If I were to kick the ground right now, it would not move me forward.
2) If kicking your legs down propels you forward, shouldn't bringing your leg back to the original position move you backward? For instance, if I were to floor the gas pedal in my car while it was in drive for 5 seconds, it would move me a distance forward. If I were to then throw my car in reverse and floor the pedal for 5 seconds, it would move me back to my starting point. So how come kicking down propels you forward, while kicking up does move you backward?

Sorry if I did not explain my question clearly enough.

On a side note with my retarded thinking...how do lubricants work to make something easier to pull or move around? Like if something is stuck in something else, you use lube to free it up. But by adding lube, you are decreasing the space to pull the thing out. I know that was stated confusingly. But like let's say my finger is stuck in a bottle, and there is only like 1/100 of a inch of space between my finger and the bottle, making it hard to pull my finger out. By adding 1/200th of an inch of lube to make the bottle slippery, I am decreasing the free space by 50%...so how is it easier to pull out after that?

CuriousBanker said:
Ok, so I know why your arms move you forward in swimming. You are pulling the water back which pushes you forward a lot because there is a lot of resistance, and then you are moving your arm forward in the air which offers little resistance to push you back. So the amount you push back in the water is greater than the amount the air pushes you back when you move your arm forward.

But what about the legs? There are two things I am confused about:

1)How does moving your legs vertically propel you forward at all? I don't know how a downward kick can move you forward. If I were to kick the ground right now, it would not move me forward.
2) If kicking your legs down propels you forward, shouldn't bringing your leg back to the original position move you backward? For instance, if I were to floor the gas pedal in my car while it was in drive for 5 seconds, it would move me a distance forward. If I were to then throw my car in reverse and floor the pedal for 5 seconds, it would move me back to my starting point. So how come kicking down propels you forward, while kicking up does move you backward?

Sorry if I did not explain my question clearly enough.
First a disclaimer--I'm an amateur swimmer, not a coach or sports physiologist, so I'm essentially guessing here. Having said that, IMO there are two effects. First, you swim on the surface so kicking up displaces little water compared to down. Second, your scenario might apply underwater if your leg swung like a stick on a hinge, but if you watch a good swimmer you see that they use a subtle undulating motion all the way down through the feet. Each leg mimics (with smaller amplitude) the motion of the dolphin kick used in the butterfly stroke. The undulating motion is essentially a traveling wave that moves down the length of the body, propelling you forward.

Hi CuriousBanker. It is better to confine your thread to one topic, to keep responses focused and to attract the interest of those who may wish to follow it.

The swimming question has two parts to its answer, I'll address one of them: fluid friction.

A fact of fluid friction is that the faster your velocity through a Newtonian fluid, the greater the friction you must overcome. It's easy to slowly wade through a shallow swimming pool, but try sprinting and you'll very quickly tire. (For water, I think drag is proportional to v3 or v4, someone is sure to look it up and tell us in detail. ). So if you try to move your leg downwards very quickly, the water exerts a large force upwards against your leg opposing your effort. Then, if you more slowly retract your leg upwards, the water exerts a significantly lesser force downwards against your movement. On balance, you encounter a large force upwards for a short period of time then partially countered by a lesser force downwards for a longer period. Fortunately for pool owners, the mathematics and water viscosity consistently seems to work in favour of you being able to kick your way out of drowning.

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If a force is exerted on a body, it will move.
Gravitational force in exerted on any mass.
When you are on a solid ground, the ground will exert a force on you to counter the gravity.

On water, bouyancy will keep a boat afloat.
So the boat does not need additional force to counter the gravity.

When you are swimming, the bouyancy does not guarantee you afloat.
You need extra force, additional to bouyancy.
Going forward also require applied force too.

The resultant of forces produced by your legs and hands is forward motion and afloat.

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Considering the arms: You can use them for diving, too - while you can use the air here, it is not required. See NascentOxygen's post for an explanation.

how do lubricants work to make something easier to pull or move around?
They reduce the coefficient of friction.

I'm more proficient in Swimming than I am in physics, but I am a long time swimmer and I have spent a lot of time both in and out of the pool thinking about this very topic! "The Science of Swimming" is a great book written by a sports scientist which does this topic justice should you have further questions. This is also much of the source for the following:

For your legs:
- for a front crawl swimmer the leg mostly moves at the knee. Because your leg is like a swing arm pivoting at the knee, areas of your leg further from your knee travel in a longer arc, therefore displacing a greater amount of water. Most of the propulsion is generated by the flat surface of your foot as it moves through this arc (good swimmers keep the foot parallel to the shin, reason for which will be seen below).

- The amount of forward thrust generated by your kick is proportional to the sine of the angle between your propulsive surface (i.e. foot and shin, mostly) and your direction of travel (your body should remain horizontal, i.e. parallel to direction of travel). So, your kicking imparts the most propulsion if your lower leg is at right angle to your direction of travel and moving towards horizontal with your body, and the least amount of propulsion when your lower leg is already at horizontal and moving towards either up or down (this is assuming you are several feet underwater and you knee somehow bends both ways to 90 degrees. read on).

- while swimming front crawl, your lower leg has a better arc going up than down because of how our knees bend (indeed, one only gets a good "downward" kick by moving the hip in unison). The up direction also has much less resistance as your leg travels through air, not water. Extending your leg fully through this arc, i.e. all the way up, then down, results in a big "slapping" effect on the water, which is a total waste of energy. Good swimmers keep their feet and legs mostly below / at the surface of the water to create a "churning" effect. Any additional momentum generated by moving your leg through the air does not help forward propulsion as that momentum is dispersed into the water when the angle between your lower leg and body (i.e. direction of travel) is at 0, therefore the slap does not impart forward momentum (additionally it wastes energy running into water rather than accelerating while already in water).

- an efficient front crawl kick ( or double kick) uses the hip joint to pivot the knee slightly lower into the water to allow more downward arc as you fully extend your leg. IF you didn't do this, your "down" stroke would simply return your foot parallel to direction of travel and impart no real foward momentum. On the up stroke, your hip moves upwards returning to parallel with your body while your knee also contracts going to around 20-30 degrees, depending on your style. Synchronizing hip movement greatly enhances the effectiveness of the up stroke by extending the effective swing arm length.

Marcusl: Hip synchronization might give the appearance that a double kick is two "mini" dolphin kicks that create a standing wave moving down the body. However that is not the case, which can be observed if you watch carefully the rhythm of each kick. A dolphin kick has a "one-two" stroke pattern while using legs in unison, for butterfly this is two kicks per arm stroke but one kick is small and one is larger. A front crawl kick also has a "one-two" pattern but the legs are not synchronous, the pattern is just "left up, right down" and "left down, right up". Basically the idea here is that if both legs were doing a desynchronous dolphin kick there would be 4 unique steps in one complete cycle, i.e. "left up little kick, right down little kick; left down big kick, right up big kick" or "left up big kick, right down little kick"... and etc, depending on how far apart you desynchronize both leg cycles.

Nascent oxygen: if you watch swimmers you will see that their legs move more slowly down than up. This is because the basic construction of our knee allows better up movement than down while swimming. The reason swimmers stay afloat was mentioned by azizlwl - basically, good swimming technique has your body horizontal to the surface of water. You can float on your back or stomach without moving by simply being horizontal. Good technique takes advantage of this by training the swimmer to use their arm-stroke to solely generate forward momentum, in effect reaching your arm forwards, "grabbing" a pocket of water with your flat palm and pushing it past your body, keeping the movement of your arm totally parallel to your body. Outstretching your arm with palm facing downwards and trying to "push" the water down at the beginning of your arm-stroke is a great way to through out your shoulder muscle and not travel anywhere.

A butterfly kick is much more of a whip-like motion, which as mentioned earlier produces a wave that travels down the length of your body. Sperm and flagella bacteria use this motion as well, and really good swimmers seem to have very "elastic" and symmetrical undulations.

As I mentioned before, good swimmers stay horizontal to the surface of water to maintain good bouyancy. An additional factor is that staying horizontal minimizes the cross-sectional area they expose to the direction of travel, which minimizes drag. Use your head and the beginning of your front crawl arm stroke to "break" the water like the aerospike on a missile breaks the air ahead of it, reducing drag for the body that follows.

Naturally movement through water creates a vacuume behind you that slows you down. Very interestingly, it has been found through experiments measuring resistance and thrust of swimmers that kicking assists a swimmer to travel forward more by reducing the vacuum or suction behind them than it does by producing forward thrust. The legs thrash the water making it turbid, which I suppose helps "fill in" the water behind you as you go.

Thats not to say that kicking does not propel you forward, rather, the amount by which kicking propels you forward is less than the amount by which suction slows you down if you try front crawl using only your arms.

Hi H2bro, thank you for the detailed lesson on kicking. I wasn't trying to say that the flutter and dolphin kicks are the same, but to make the point that the leg doesn't move stiffly back and forth. The leg moves in a coordinated way at the hip, knee and ankle. You can see it in this video of Michael Phelps, starting at minute 1:40 where it shows him from the side. He has a wave motion all the way down to his ankles and feet and even his toes flex; it is most visible in the dolphin, less so in the flutter kick partly because the camera is far away and there are a lot of bubbles.
http://www.youtube.com/watch?v=ax77_hHq9Dc
Maybe the downstroke is faster, but it certainly looks like he is exerting more force downwards than upwards.

I looked around a bit for a slow motion shot of a swimmer kicking without great success, but there's a short clip here--starting at 3:50 to 4:15, she has what looks like a traveling wave down her leg.
http://www.youtube.com/watch?v=YlhGqEy8MBc
It seems like these motions must be important.

EDIT: Actually, addressing NascentOxygen, up and down strokes must take be of the same duration since both legs complete one cycle at the same time but out of phase.

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CuriousBanker said:
1)How does moving your legs vertically propel you forward at all? I don't know how a downward kick can move you forward. If I were to kick the ground right now, it would not move me forward.
2) If kicking your legs down propels you forward, shouldn't bringing your leg back to the original position move you backward? For instance, if I were to floor the gas pedal in my car while it was in drive for 5 seconds, it would move me a distance forward. If I were to then throw my car in reverse and floor the pedal for 5 seconds, it would move me back to my starting point. So how come kicking down propels you forward, while kicking up does move you backward?

Sorry if I did not explain my question clearly enough.

I'm totally guessing here remembering my childhood swimming days. After H2Bro's explanation this may sound unnecessary.

Even though kicking legs may propel a swimmer forward, but that forward motion, IMHO, is very small. The main purpose of kicking, again IMHO, is to keep balance in the water, to stay afloat in water. If you don't kick your feet, the feet will sink in water making works by hands more difficult.
Well, I don't have pool around to try it out.

Hey marcusl,

Nice videos. From what it looked like on the video, phelps has a flutter kick as I described. The lady seems to keep her knee more relaxed, you can actually see it bend backwards somewhat. I suppose the lady's legs do look wavelike, personally I haven't reached that level of kicking myself ;)

Neandethal00, kicking does help keep balance during a front crawl as the kicks offset the small amount of torque imparted by the arm-stroke. Kicking might do something to help you keep afloat, but its really not the purpose or the idea behind it. It's quite easy to float with little or no movement at all.

In fact, your feet sink down in the water when you lift your head up. Keep your head down and your feet will stay up. All about being horizontal.

On a related note (for some reason this is still not hitting home for me) how does a propeller work on a boat or helicopter? On a helicopter, how does spinning sideways make the helicopter go up? For a boat, how does the propeller spinning sideways push it forward.

Also, since it is a similar motion, I never understood how turning a screwdriver pushes it into a wall. If you push forward when screwing I get it. But how does twisting something in a circle move it forward?

Sorry, I don't know what is wrong with my brain that I am having a hard time with this.

When you get down to it, all these propulsion mechanisms behave in a similar way to a wedge or inclined plane. The force that the swimmer / 'screwer' / propellor exerts on the medium it's in has two components - one in the direction that the water / wood / air is pushed backwards and another force at right angles to that direction. This one has no effect because it's usually balanced out by another force in the opposite direction so the only force that can produce movement is the one pushing the medium backwards.
The other classic example of this happening is when you squeeze an orange pip between finger and thumb. The pip is slightly tapered and the sideways force between finger and thumb is almost canceled out but a small force turns up to push the pip out at high speed in a forward direction.

This is usually described in terms of Vectors and the Maths may bring on the pains. If you want to delve into simple Vector theory then I suggest that you google around until you find something at an acceptable level. The same vector ideas can be used for forces and motion. Sometimes, people find it easier to see how vectors apply to motion. Swimming across a moving river will produce a diagonal motion that is the result of the two motion (velocity) vectors. The actual angle of travel and overall speed will depend upon the magnitudes of the two velocities.

Now could someone tell me why I swim like a brick when I try breast stroke kicks. I look soooo sad!

The way I understand/visualize it is in how you're generating a sort of vortex similar to a fish underwater. When generating that vortex it flows in a direction with a rotating force that pushes against the fin (or feet for a person) and then the fin pushes back against the original force producing the effect which pushes you through the water.

Another visual aid: If you go to a stream and place a generally strait stick into the current you initially get two vortexes vying for the higher pressure zone, then you get steady vortex shedding and a turbulent flow. The faster the current the more violent the flow and more difficult it is to keep the stick steady. The stick wants to drop into the lower pressure zone (the vortex spinning with less force against the back side of the stick) because of the steady force applied to the front of the cylindrical body.

Now if you imagine those vortexes being created by the force exerted by your legs and arms... you're basically creating high pressure vorticies that act in a smooth manner of propulsion (depending on how well you can swim). And with those you are A: Creating a vortex ... B: pushing off against that vortex ... C: repeating.

Cheap and easier physical visual aid is as simple as making coffee and having a stirring spoon. Add in some cream, apply force via your hand, then stop and watch the two vortices continue to push the spoon.

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Nstanch, you know, I hadn't much considered how vortices would affect movement while swimming, though I'm sure they must because it's quite noticeable to have little "twisters" come off the ends of your hands as you go along.

Now that I think about it, they might become significant in butterfly and breast stroke.

CuriousBanker: you can also think about this: when you use a piece of paper or a book or some flat surface and flap it back and forth in your hands to "fan" something, like a fire, why does air feel to come straight away from the fanning motion? You'd think air would just get pushed side to side, right?

You could also look up "Archimedes Screw" - maybe that would illustrate well for you.

Well during the fanning motion, on the first half of the swing, air is being pushed at my face on an angle. On the second half of the swing (first half being from the cocked back position to my face, second from my face to cocked forward), I am sure air is being pushed backwards, I just can't feel it because I only have one face.

try an experiment...

tape two pieces of paper hanging from a desk or shelf, but so the pieces of paper face each other. Tape them say a few feet apart.

Then use a binder or book to fan one paper. Make sure your "fan" is right between the two pieces of paper, aimed so the midpoint of the swing lines up with the middle of a paper. What happens?

edit: by fan I mean wave the book with your hand keeping your arm steady.

I mean I know you're right. I also know that swimming works. I just wanted to know why, not by using analogies but by using physical laws

But some posters on this thread have done a good job explaining. Unfortunately my ignorance in this field makes me unable to understand most of it. I don't really understand vortices. But I kinda get it now a little bit. So than you all very much

Also another explaining could be this: I think force=v^3 or something like that in water. So maybe you kick really hard on the way down and not so hard on the way up? So the force on the way down is more than the force on the way up?

CuriousBanker said:
Also another explaining could be this: I think force=v^3 or something like that in water. So maybe you kick really hard on the way down and not so hard on the way up? So the force on the way down is more than the force on the way up?

The amount of force applied kicking down, generating the vortex, distances itself from you while losing energy in its interaction with the rest of the water as it pushes against you, and you against it. In other words, the longer you take to kick up or push against the remainder of that force, the less force there will be. Now, if you kick down very hard (say in a speed run), you would want kick up, and repeat, to maximize the energy that you're both generating and being pushed by and pushing against

Imagine someone kicking downwards. Only downwards. Then waiting until their momentum essentially stopped. Compare how far and how fast they would end up moving in a 200 meter swim compared to someone who is pacing themselves by kicking up and down in a fluid like manner (no pun intended).

Really, the current math around this (as far as I'm concerned) isn't adequate and (literally) doesn't really exist. If you can figure out three dimensional fluid dynamic mathematics then you win a million dollars (Clay Institute of Mathematics reward for advancement on Navier-Stokes equations). Personally, just thinking about three dimensional flow of a vortex gives me an actual headache. Thought experiments on it feel like they're sucking the energy out of my damn brain :tongue2: .

Best approach, for me at least, is to visually study the behavior of fluids. From there you get an intuitional understanding that advanced from the basics, then upwards. Either way, fluids are a very difficult and confusing/frustrating field of thought.

H2Bro said:
Nstanch, you know, I hadn't much considered how vortices would affect movement while swimming, though I'm sure they must because it's quite noticeable to have little "twisters" come off the ends of your hands as you go along.

Now that I think about it, they might become significant in butterfly and breast stroke.

The thing with vortices and the human physical form is that we aren't really aquatically dynamic in our shape. An obvious example being a freestyle swim and how quickly the vortices "crumble" due to our various other movements in the water. Like how a smoke ring does fine on its own until the balance of forces disrupts and disbands the motion.

Most aquatic creatures compliment these forces with both their shape and motions. Even snakes utilize the dynamics of the water well when swimming. They seem to "wiggle" their bodies to compliment the flow and to generate the most speed as they snap at each vortex like a whip. Like with the stick in the water and the vortex shedding... except they contour their bodies with the alternating high and low pressure zones in that snap or whip like motion of their tails. Most fish do the same, but far more efficiently given the shape of their tails.

Also, the breast stroke and butterfly would be the best way to implicate (or at least mess around) with this concept. I found it easier to visualize and "feel" when doing underwater dolphin drills.

Edit: Another factor in how we swim rather poorly compared to submerged creatures is that, if submerged and attempting to freestyle, you obviously won't do well on account of having to bring our arms and hands back to the front... what with air resistance being far less slowing than water. You can sort of compare it to two people in a row boat rowing against the motion of the other person.

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Ntstanch said:
Also, the breast stroke and butterfly would be the best way to implicate (or at least mess around) with this concept. I found it easier to visualize and "feel" when doing underwater dolphin drills.

I see it coming into play during the breast stroke where your hands move towards the center of the body near the end of the stroke, before pushing up against the water to clear your mouth for air.

Would 'pushing' water together like this, before pushing 'against' it, increase the effectiveness of the force transferred to your upward motion? Or would this go against the "incompressible" aspect of water?

Also, by having the stroke "reset" by moving hands towards center, the vortices are led towards the area your body is about to travel through increasing turbidity and decreasing resistance. Your thoughts?

Human body I think is more remarkable for characteristics making it well suited to aquatic activity compared to a lack of such characteristics. You know, hairless bodies, webbed fingers and toes, the 'dive' reflex for infants, so on. Not so sure about the "aquatic ape" hypothesis but we certainly have SOME adaptations that are useful.

Edit: I think two of my 'geusses' at at odds with each other - vortices are unlikely to help you push off as well as glide through at the same time! if you could hint at what you think is going it I'd appreciate.

I am curious about the vortices here. I was told once that vortices were formed by 'a flow of energy' (in an argument to explain the existence of life, as it happens). Could it be here that the vortices are the symptom of an energy gradient rather than the cause of propulsion?

Also I was under the impression that vortices increase drag. Does this mean they are an undesirable thing for a swimmer? This video suggests natural swimmers have laminar flow

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H2bro, Those are both "Tall orders" on my part, as I'm still trying to convince myself and understand their dynamics. Also been busy lately. I'll try and think of a way to explain my thinking on your questions, but can't promise anything.

Except for the pushing off the wall. In this case you're pushing off a solid, then going into a dolphin like kick where the importance of a vortex in general comes into play. When "pushing off" a vortex you're guiding your body and using unique motions to utilize the force of the spin in the vortex to continue propelling yourself on what otherwise would get you no where... or at least veer away from you and disperse its energy as it travels away.

(Edit: Pushing off the wall, and pushing off the vortices, isn't so different in my mind. One is a solid and not going to give way or waste much of that energy. The vortex will however waste energy while being pushed against as all that energy doesn't concentrate in key areas as if it were helping us swim faster. Fins, flippers, big feet - etc... help you to not waste that energy though. Oh, and chimps are terrible swimmers, their bone density and muscle mass usually results in them sinking. So score one for homo-sapiens... However, that muscle and bone density is also why they're terrifyingly powerful and can dent/bend the frame of a car tire by bashing it with their fists. :P )

Until I really get a solid foundation in the whole concept the theory becomes mostly private as not to confuse or waste anyone time (aside from my own).

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Rooted said:
I am curious about the vortices here. I was told once that vortices were formed by 'a flow of energy' (in an argument to explain the existence of life, as it happens). Could it be here that the vortices are the symptom of an energy gradient rather than the cause of propulsion?

I'm not really interested in this sort of topic. Sorry.

Rooted said:
Also I was under the impression that vortices increase drag. Does this mean they are an undesirable thing for a swimmer? This video suggests natural swimmers have laminar flow

A vortex, or vortices, can increase or decrease drag. It's a spinning streamline flow... depends where you're at and how you're utilizing the flow. Though I think this is more a case for gases than fluids. Gases being much quicker and much more difficult to imagine in general. As for the video, streamline flow is important, but have you ever seen anything in the water lay still and swim quickly? The motions are, from what I can tell, the key to efficient swimming. The idea is that vortices are an important part of this efficiency.

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CuriousBanker said:
Ok, so I know why your arms move you forward in swimming. You are pulling the water back which pushes you forward a lot because there is a lot of resistance, and then you are moving your arm forward in the air which offers little resistance to push you back. So the amount you push back in the water is greater than the amount the air pushes you back when you move your arm forward.

But what about the legs? There are two things I am confused about:

<snip>

Swimming (or any propulsive locomotion based on a repeating cycle of movement) is surprisingly tricky to explain- after all, why can't you simply reverse your motion and swim backwards?

Pucell's excellent paper is a great place to start:

http://jila.colorado.edu/perkinsgroup/Purcell_life_at_low_reynolds_number.pdf [Broken]

and Lighthill's book "Mathematical Biofluiddynamics' has a considerable amount of information and current (as of 1975) theoretical approaches to solving the problem of aquatic locomotion, but I can't claim to understand very much of it.

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Purcell's paper is not directly relevant here because bacteria swim at *very* low Reynolds numbers where our experience fails to apply. Purcell states that a swimming bacterium is equivalent to a human sitting in a swimming pool of molasses and moving no part of his/her body more rapidly than 1 cm/minute! As just one difference, micro-organisms do not generate the vortices that are an important part of how we swim. Having said that, it is a remarkable paper.

marcusl said:
<snip> As just one difference, micro-organisms do not generate the vortices that are an important part of how we swim.

Wrongedy-wrong. See flagellar locomotion and nematode swimming. Gray and Hancock's 1955 paper has some nice detail. And again, Lighthill's book is comprehensive.

Unless you mean that having arms and legs makes human swimming radically distinct from other forms of aquatic locomotion.

I'm speaking of vortices in the fluid, not rotational motion of a flagellum. At the low Reynolds numbers that Purcell considers, inertia effects are negligible compared to viscous effects (he points out that inertial forces die away in distance of order 0.1 Angstrom!). How are vortex rings sustained in that regime?

marcusl said:
How are vortex rings sustained in that regime?

I'm kind of lost, but wouldn't a vortex waste more energy while it is spreading out... while the ring contains itself far more efficiently?

The issue I raised is only that Purcell's paper does not describe human swimming but rather that of bacteria for whom inertial forces in the fluid are negligible. I believe in that case that the fluid cannot support vortices of the sort you described for human swimming and that have been observed shedding off of the tails of fish.

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marcusl said:
I'm speaking of vortices in the fluid, not rotational motion of a flagellum. At the low Reynolds numbers that Purcell considers, inertia effects are negligible compared to viscous effects (he points out that inertial forces die away in distance of order 0.1 Angstrom!). How are vortex rings sustained in that regime?

As I mentioned, Purcells' paper is a *starting* point, kind of like how frictionless surfaces and massless pulleys are used in introductory mechanics. Since you (apparently) don't have access to Lighthill:

http://maeresearch.ucsd.edu/~elauga/research/references/LaugaPowers09_RPP.pdf

and
http://www.pnas.org/content/early/2011/07/28/1106904108.full.pdf

Figure 8 of #2 is instructive, as vortices are clearly present. In the fluid. More than 0.1 Angstrom away.

Thank you, I will read these.