The presentation that I am going to make today is technical, and it also will be practical. I would like to know how many of you are coaches? Raise your hands. How many of you consider yourselves coaching scientists? How many here are engineers? Okay, there’s a few.
Before we go any further, I do need to thank a few people for helping me out these past several years. Of course, there are Guy Edson and John Leonard, two wild and crazy guys that are crazy enough to invite me, a non-swimmer non coach, here to speak, and I appreciate the support they have given me.
USA Swimming I want to thank too because they sponsored my research this past year and hopefully will next year. Steve Roush has been very supportive, and Scott Riewald, the new Director of Biomechanics there, has just been great to work with. He has helped me out quite a bit. Even before he left Northwestern University and started the job there in Colorado, we were talking on the phone about where we were going to go with this. So, Scott, thank you as well.
Ernie Maglischo has also been very supportive. Ernie and I talk a lot on the phone and have lunch occasionally and share ideas and information. And what impresses me about Ernie is, you know, he’s really at the peak of his profession. I’m not saying he’s old, I’m just saying that he is at the peak of his profession. And he is still open to new ideas, which is unusual for somebody that is really one of the pillars of the field. Sometimes they get set in their ways and they are not open to new ideas, and Ernie has really impressed me with his openness.
I would also like to thank Joel Stager, and Nan, you can thank him for me. About five years ago, when I published my first paper in swimming, Joel was the one that published it in the JSR, and he kind of went against the grain to do that, and he believed in what I was doing and he helped to get me started.
And last but not least, I would like to thank Dr. Monica Schloder. Monica is a longtime friend of mine. She was my daughter’s first swim coach. She taught her to swim at the age of three. She has been very supportive of me as well. As a matter of fact, she was the one that first suggested that I get a copy of Ernie’s book and start looking at it and start figuring out ways that I could apply engineering principles to swimming. So thank you Monica.
I have listened to several other presentations during this conference and after listening to some of them, I feel compelled to change my presentation just a little bit. I want to take a few minutes, I really feel that it is necessary, to defend technology a little bit. And you probably already know what I am speaking about. There is a certain percentage of coaches or people that kind of pooh-pooh science and say, well we don’t need no stinking rocket science. We’ll go with our feelings and so on and so forth. If I can borrow a quote that Joel Stager used yesterday of Doc Councilman, whom I have the utmost respect for, Doc said, “Science has provided me with a framework within which the art of coaching can be performed.” And that is really how I feel about swimming. It’s a blend of science and art. It is similar to the field of architecture. Architecture is also a blend of science and art. If you let a pure scientist design a building or a monument it will be a square block. It will stand up and it will be very functional, it will be ugly and not very creative. If you let a pure artist design a building or a monument it will be something really graceful and curvy and just fantastic to look at, but it might not stand up.
Okay, there has to be a framework around or inside that structure based upon scientific principles to keep it standing. And that is kind of how I view swimming. It’s a blend of science and art. So to those of you that say it’s just science, I say consider the artistic side. And to those of you that say it’s just an art, I say consider the scientific side.
The title of my presentation is “Swimming Ain’t Rocket Science, Or Is It?” Obviously, since I am an engineer, I am going to be talking about the technical side of swimming, not the artistic side. The answer to title question is that swimming is not rocket science yet, but it will be. I am going to show you some principals and techniques today that engineers apply in rocket science. I am an engineer, and I design gas turbine engines using the principals of rocket science. I am going to show you some techniques that we use in that world and apply them to swimming.
Excuse me, but I am going to take off my coat. I haven’t worn a jacket in two years, and my wife made me buy this for this occasion., So excuse me while I take it off. Besides, us engineers are not known for the way we dress anyway. By the way do you know the difference between an engineer and a scientist? The best way to tell the difference is to explain a little story to you. Three scientists were sent out to measure the height of a flagpole. They were out there with a ladder, and they had a tape measure and they were taking their measurements and dropping their tape and falling off the ladder and they were trying to compute a standard deviation and everything, and an engineer saw what they were doing. He walked out and pulled the flagpole out of the ground, laid it flat on the ground, took a tape measure, measured it and it was twelve feet nine inches. He went over to the scientists and said “It’s thirteen feet long.” One scientist looked at another and said “Isn’t that just like an engineer. We’re supposed to measure the height and he gives us the length.” So, us engineers are kind of practical. And I think you are going to see that the results of my study are pretty practical too.
Okay, what I am going to discuss first of all is a few definitions. I am going to talk about one particular tool today called computational fluid dynamics, or CFD for short. It’s a tool that I use every day at work, and it is a tool that I have applied to swimming.
I have done a CFD analysis of a swimmer’s hand and arm. Okay, so here are two definitions, pretty simple really. I’ll just let you read them for yourself. The point that I am trying to make is this: one interpretation of these two definitions is that swimming is a subset of rocket science. So computational fluid dynamics, what is it? Well, it is an analytical method. It is a technique that we use to analyze flow either around something or through something and we do it on a computer, and you can sort of think of it as a desktop wind tunnel. We input information into the computer. What kind of object we are analyzing, in this case it is a hand and an arm. And then we specify what velocity the hand is moving at or the fluid is moving at, and then this program solves the equations of fluid dynamics for us. And from that solution, we get things like velocity and acceleration and pressure. And we can compute lift forces and drag forces and coefficients.
Here are some of the existing applications of CFD. CFD has been used in all of these industries. In the sports industry, it’s been used by the bobsledders to optimize their bobsled shapes. Of course, it is used a lot in the race car industries and the aerospace industry. Probably the best way to explain CFD is to show you some examples.
Now, I have this one up here to begin with. Everyone knows what this is. It’s a space shuttle. This is not just a pretty picture that is what I want to emphasize. All of these colors are contour plots in either pressure or velocity or heat and they have all been calculated using a CFD model. And the CFD model consists not only of the shuttle, but all of the air around the shuttle. And the solution of the air around the shuttle has been removed so that you can actually see what is happening to the shuttle. CFD was very important in the design of the space shuttle, because engineers could not replicate the reentry of the shuttle into space. They couldn’t get both the speed and the thermal conditions right to analyze it in a wind tunnel. So they had to rely on computational fluid dynamics to do that for them.
Those of you that are old enough to remember when the shuttle first went into space, you remember there was a lot of concern about the tiles on the shuttle. And computational fluid dynamics is what they used to design that. Here is another example that you will recognize, the Harrier jump jet. Those lines on there are all calculated. The CFD model consists of not only the jet itself but the air all around it and those lines are probably, I don’t know for sure, but it looks like they are colored according to velocity. Here is a cross section of a wing. This is the solution for a wing with its flaps and slats out, and these are plots of the speed of the air around the wing. You can see there is a stagnation point, right there, where it is red, where the speed is very, very slow and then as the air comes around the wing it gets going really fast, right there.
Those of you that drive a Ford Taurus will recognize this picture. Those are contour plots, probably of pressure, with streamlines of flow. And how engineers would use this is they would look at it and say, “Oh the flow is very smooth and it’s not too turbulent. It’s a good design.” Or they might look at pressure plots and say, “Man we’ve got way too much pressure in this area, we need to change the design.” And this becomes really important when you are analyzing race cars. Of course, the racing industry has a lot more money than the swimming industry, and so they spend big bucks doing this sort of analysis. And this not only tells them how to fashion their cars aerodynamically, they can take the loads applied from this and do stress and vibration analysis on their cars as well to get optimum designs.
CFD can also be used for mundane things like air conditioning duct design. The medical industry uses it to evaluate the heat transfer in laser surgery. There is a whole field in that. Can you imagine two high-speed trains approaching a tunnel at one-hundred-fifty miles an hour from opposite directions. Engineers designing the tunnels and the trains want to know what happens to the pressure in that tunnel, and how does it interact with the trains when the trains enter the tunnel at the same time. I am going to skip through some.
I have got a lot of different examples, but I think you are kind of getting the idea. Let me get to some examples that are a little more related to swimming. These are two bodies submerged in water. They both have a velocity. The big one is moving in this direction and the little one is moving in this direction, and as they near each other you can see how the pressure on one is effected by the other.
The next example is a good demonstration of something that has not been discussed, as far as I know of, in the swimming community, and that is interference drag. If you take the drag of one object and you take the drag of another object over here, they both have their separate drags. If you bring them together the drag of the two combined is different than the sum of the two drags. That is called interference drag. And that happens a lot in swimming and nobody’s ever quantified it. That is one of the things on my list to do with computational fluid dynamics. For instance, that type of interaction would occur as your arm is going by your chest, it would occur as your hand is going by your thigh, it would occur as one leg is passing the other. It makes a big difference in aircraft design. It’s very critical how engines are placed on a wing or next to the fuselage. And that is something that nobody has addressed so far in swimming, and if I don’t burn out on this stuff I hope to have a chance to look at it.
Here is something that is also a little more related to swimming. This is a ship plowing through water, and all of you are familiar with a bow wave by the swimmers head. These contour lines are contours of the displacement of the surface of the water. And you can see here, the water is being pushed up just like you see by a swimmers head. The ship is moving in this direction and here is a wave trough. This could just as easily be a swimmers body being modeled through water.
Here’s a couple more that also have direct applications to swimming that demonstrate some concepts that I want to get across. This is a CFD model of a torpedo. And the model consists of a torpedo, the walls on either side, the floor and then in this whole area are the fluid elements of the model, which, again, have been removed for clarity. A couple things that I want to point out. First of all, do you see that color along the side there? That is the surface of the water. The torpedo is causing those waves. You might think that the torpedo is a long way from the wall, but it’s not far enough. And that is why in computational fluid dynamics, when you model an object in water, you have a big body of water around it so you don’t influence the solution. Those contours, I believe, are pressure contours. And you can see how the pressure on the floor there is effected by the torpedo.
Now, I imagine that a swimmer doing a butterfly kick near the pool bottom is going to get an interaction with the bottom and with their kick, and that kick interaction is going to be different whether the swimmer is swimming on their side or on their stomach. And there are other people in this room that are better qualified to address that issue than I am. But this is a good demonstration of how maybe walls and the bottom of the people have more influence on how a swimmer goes through the water than you might think. Here is another example: This a ship going through a tow tank. Again, I want to point out a couple of things. The ship there is effecting the pressure in the water clear out here ahead of it. Also you have the wave profiles, and you’ve got these contour pressures along the side here. In this case I would say in this tow tank the walls are too close to the ship to get an accurate solution.
Okay, so, now let’s look at CFD applied to swimming. There are a lot of different ways CFD can be applied to swimming. I am going to talk to you today about the CFD analysis of a swimmers hand and arm. But there are other ways it can be used. CFD can be used to model a swimmers body, calculate wave drag, calculate not only passive drag, but as computers get a little faster, we could also use it to calculate active drag. In other words, we could change the shape of a swimmers body going through the water. We could use it to maximize body component propulsion. By “component”, I mean you can look at a hand or an arm or a foot or a head position, look at the drag of a head, look at interference drag, lots of different things.
CFD can also be used to separate lift and drag into its various components, and by that I mean there are actually six different types of drag that a swimmer encounters in the water. I usually only see about three of those types mentioned in the literature. But swimming will enable us to separate the total drag into pressure and form drag, friction drag, etc. I could actually calculate with this model what portion of the drag or lift is due to the skin friction against the arm. I can’t model the hair that would be beyond the scope of my ability right now. But, I could model a smooth arm or a swimsuit. What I would need would be a coefficient of roughness. I don’t know if anyone has determined the roughness of skin yet or not, but if they have, I can put that in the model and tell you reasonable close how much of the drag is actually caused by skin friction. My goal, in the next couple years probably, is to develop the optimum stroke.
So, what I want to do now is show you today what I have done so far. I am going to show you the results that I have to date. And then I am going to have some conclusions for the scientists in the auditorium, and I am going to have some conclusions for the coaches. Then I am going to talk a little bit about the future.
Okay, this is part of the model for the CFD model of the hand and arm. I say part of the model because this is the rest of the model, but that little black speck there is the hand and arm. This is a dome, the red part here is the bottom of the dome, it’s flat, and the blue part is the top of the dome, which is hemispherically shaped. Everything in between is water. The reason that it is so big is that I don’t want the hand to interact with the boundaries and vice versa. Here’s how this works. I apply a velocity to a boundary and then let the program calculate the pressure and velocity in this area to tell me what the solution is.
Here is a close-up of the hand and arm. On the bottom of the dome, and one thing I want to point out is, how very fine the cells are down here. We call these things cells. The reason is, we want to capture what’s happening very accurately close to the hand and arm. I have analyzed this model so far for steady flow conditions. Next year I will progress into unsteady flow, because I realize that swimmers very rarely move their arms at a constant velocity or orientation. But I wanted to start out with steady flow for several reasons. One is it is a baseline upon which to build and I can’t determine the effects of the acceleration or rotation of the arm relative to steady state unless I do the steady state first. The other reason is that most of the testing that has been done has been done for steady state conditions. Most of you are probably familiar with Berger’s study or Schleihauf’s results or some of the work that Doc did or Ernie did. Most of that was for steady state flow.
I did look at variable angles of attack, and I looked at varying water turbulence, which is something that nobody has done yet, as far as I know. The turbulence of the water effects the lift and drag coefficients. By water turbulence I mean, is the water calm, is it churning, are there vortices in it. And that can be measured by two different parameters. One is turbulence intensity, which is (I won’t give you the math equation) basically a reflection of how much the velocity varies with time. If the velocity is totally constant and isn’t fluctuating then the turbulence intensity is zero. If you look at a mountain stream where there are all sorts of things going on, the turbulence there is very high.
The other measure of turbulence is the turbulence length, and that is physically what the size of balls of turbulence might be. These two turbulence variables can be input into a CFD program and we can determine the effects of turbulence on the solution. Here’s how the program works: I input into the program a velocity on this surface here. And then on this surface and everywhere else inside the dome the computer program calculates the velocity and pressures according to the laws of physics. This direction, the angle of attack is zero. There is a picture of the arm at a forty-five degree angle of attack. You see, the water is moving this way and here is the original axis, and that angle is forty-five degrees. Okay, so what can we look at from this analysis? We are going to discuss the results next.
Well, we are going to look at flow path lines. We can actually see how water moves around the hands, and where it goes afterward and what it does. We can look at contour plots on the hand and arm and we can see what the pressures are. And finally, we can calculate lift and drag coefficients.
So, let me show you some other color pictures. CFD, it is computational fluid dynamics, but sometimes we call it colorful fluid dynamics. As boring as we engineers usually are, we do like to use color and it kind of spices things up. Plus, this would be very difficult to understand without the use of color. The water is moving in this direction here, it hits this surface, the angle of attack is zero, the velocity is exactly two meters per second coming in. Of course as it gets close to the hand, that changes. The turbulence intensity for this analysis was 1 % and the turbulence length was about 0.10 meters. As a reference, the ICAR flume has a turbulence intensity of 4% and a turbulence length of .10 meters. I don’t know what it is in a swimming pool (that might be a good master’s thesis for somebody to do) because obviously, as I will show you later it makes a big difference what the turbulence is.
There are a couple of things that I want to point out. The water starts out coming over the surface nice and smooth, but it can’t quite stay on the surface, and it gets about here and all hell breaks loose. Right here you have a vortex starting to form. By the way, these lines are colored according to time. The time involved in this was .22 second, so anything in red has moved through a time of .22 second.
By the way, since we are a small cozy group, if you have any questions along the way, please ask. If you don’t, I might get a little worried that everybody’s asleep. Last Sunday in church there were two little girls in front of us and one of them leaned over to the other and said “How come we have to be so quiet in church?” and the other one said “Because people are sleeping.”
So are there any questions so far?
(Question.) Um, yeah, it is going to depend on the angle of attack, but it moves, it moves fast in some places and slow in others.
(Question.) No you are seeing a change in speed. Let me show you some other plots, and I think it will become a little clearer. Here’s the path flow lines at a forty-five degree angle of attack. Now you can see not only some of the water coming around, but some of the water decides it’s going to go down the surface a ways before it comes out. And in this area here, the flow has totally left the hand surface. And that has very important consequences, which I am going to cover in just a second.
Yes Joel. (Question.) Well, actually, I did it for multiple speeds. I did it for speeds between about 0.4 meters per second up to 3 meters per second. As far as the separation goes, you’ll see more turbulence and more confusion and more separation with higher velocities, but maybe not as much as you expect.
(Another person asks a question.) Um, say in freestyle, the average hand speed can vary between, and Scott correct me if I am wrong, one and one-half and three and one-half meters per second. Is that about right? Scott said the average is a little bit over two, but it depends where you’re at in the stroke cycle.
Okay, here is an angle of attack of ninety degrees. You can see here that the water comes over and totally leaves the hand here. This is called boundary layer separation, and it is very critical because boundary layer separation determines what type of flow you have. If the boundary layer doesn’t separate, then you can invoke Bernoulli’s principle and use it to explain lift. Once the boundary layer separates, then all bets are off. Bernoulli’s principle is derived using certain assumption. One of the assumptions is ideal flow. Once the boundary layer separates, the flow is no longer ideal.
Okay, so this shows that Bernoulli’s equation is not the best model to explain this lift. Now that doesn’t mean that lift isn’t generated, and that has been one source of confusion I have seen in the swimming community. You don’t need Bernoulli’s equation to have lift. You just use a different equation to describe that lift. You know, twenty or thirty-something years ago when Doc Counsilman first came up with the idea of lift applied to swimming, he was exactly right about there being lift. But the best way to describe that lift is with Newton’s law, not Bernoulli’s equation.
Any kayakers in the group? Okay Joel, that figures. Then you know what a hydraulic is. If you go white water kayaking, and you go around a big old rock in the middle of the stream, there is usually a vortex on the other side of that rock, and you don’t want to be caught in that vortex because you might never get out. Well, this hand is a perfect example of a big old rock in the stream and that is a vortex right there. And again these stream lines are colored by time, and you can see that some flow lines come right over and keep on going, but the ones that come right over here, they just keep on going around and around and around. If I were to have plotted this for a minute you would just see a mass of particles just keep going around and around there.
When we do wind tunnel tests, there is something called an oil film analysis that we do. We put oil on the object of what we are testing and that oil flows over the surface. It flows very slowly over the surface because it’s in the boundary layer and it’s not going to go anywhere real fast. And we have the ability, using CFD, to model that and this is one of those models. You can see, it comes around the surface and it gets right about here before leaving the surface to go into these vortices. This black area is where the boundary layer is totally separated from the arm.
Here is another picture that demonstrates a point that I want to make. That is, that these analyses are highly three dimensional. This plot demonstrates that. This shows there is a line of fluid particles here that are going directly into the hand and what happens is, they not only go to the side but they go up and over. They are going to seek the point of lowest pressure.
Here’s how tip vortices can form off of the fingertips. This is a common occurrence on airplane wings, and it also happens on your hand as it goes through water. We can also get pressure contours, so if we were designing something at work we would plot pressure contours of our engine or parts of our engine, where the flow is going by, and we would look and say, oh we have too much pressure there or, oh the boundary layer separates there. We have got to change our design.
Here is a close-up. This kind of gives you an idea of how detailed of information you can get with these models. This is a plot of the wake behind the hand and arm in a certain location. You can tell a lot about the drag from looking at the wake behind an object. This is another tool that we use to help us in our designs. By the way, these are velocity contours, so you can see, even quite a ways behind the hand, the fluid is affected. See I told you we called it colorful fluid dynamics. This is the bottom of the dome, and then this is a vertical surface rising from it. I wanted to know what was the velocity of the fluid directly behind the hand and arm, not right next to it but just a little ways behind. So I created the surface in the model and then plotted contour plots on it. As you can see there’s areas of stagnation right directly behind the hand, which is what we would expect.
Now we are slowly working our way into things that can be a little more practical to coaches, but I am still talking to scientists a little bit longer. Bear with me. Those of you that have studied the literature of Schleihauf, Maglischo, Counsilman, Berger, and Wood, this sort of plot might look familiar. This is a plot of drag coefficient versus angle of attack. I have done it for the hand, the arm and the hand and the arm together. Just a couple things I want to point out, first of all, no matter how the arm is oriented, like this, it basically has a constant drag coefficient. This amount of difference between .72 and .6 as far as I am concerned is the same.
This is a plot of the 2-D lift coefficient. This is the coefficient of lift in one direction between zero and ninety degrees, that is with the thumb leading, and between one-hundred and eighty and ninety degrees and this is with the little finger leading. Notice the arm in red has very little lift. Now here the axial direction coefficient, which is perpendicular to the direction of flow. I want to point out here that it has some fairly significant coefficients. Some of the experiments that have been done with flow models have only been done using lift in two-dimensions rather than three. I want to skip through some of these and get to the good stuff here.
This is a plot of 3-D lift coefficients for just parts of the hand. Actually, I can divide this up even further. If you wanted to know what the drag of your little finger was, I could tell you what that was. What I want to point out here is, that with the hand and arm in the position shown, the fingers peak at thirty degrees and the wrist peaks at sixty degrees. If you could somehow get those to peek out at the same angle of attack, depending on how you hold your fingers, relative to your palm, you could get more propulsion.
(Question). I can. Not actively, no. Well I could, actively, if I wanted to plan ahead and get a bunch of work stations and couple them together and really do some serious number crunching.
(Question.) The hand, for these analyses, is an extension of the wrist. It could be placed in a different fashion, and I will get into that a little bit more towards the end of where I want to go with this.
This is called a polar diagram, and what this shows is a plot of drag coefficient versus lift coefficient, and I have compared the arm and hand with the just the hand, just the fingers, and two airfoils. The red airfoil is square, which really isn’t a practical air foil, and the green air foil has an aspect ratio of three to one. It is three times longer than it is wide. Neither one of those are very realistic air foils, but they are close (in their plan view) to the hand. What this plot shows is that the hand doesn’t have flow characteristics anywhere close to an airfoil. I know that this may seem like a small thing, but being an engineer I really don’t like reading that the hand is an airfoil and that it acts like an airfoil. It really doesn’t, so please don’t call it an airfoil.
Okay, I did examine the effects of turbulence, both turbulence length and turbulence intensity. You can see that in the ICAR flume a turbulence intensity at 5% is going to have a drag coefficient significantly higher than say if you had 1% or even less. The same applies to lift, and I’m not going to show it because I am running out of time. What I want to show next, is a comparison of my analytical results with experiments. This is a plot of the hand drag coefficients, plotted versus Schleihauf’s data and Berger’s data. I have adjusted their data by five or ten degrees because of how they defined the angle of attack was slightly different from mine, and from each other. The green there is 10% turbulence intensity, the blue is 1%, and you can see both of their data fall within that range. That is hand drag. Here is hand lift. You can see that Berger’s data is on the high side and Schleihauf’s is on the low side. But overall, it’s a pretty good comparison.
Now there are reasons that Sschleihauf’s is on the low side. Schleihauf only determined 2-D lift. There is a reason that Berger’s is on the high side. Berger’s model penetrated the surface of the water and so her hand generated wave drag. So when she calculated drag coefficients, the wave drag was included in that. I didn’t have time to run a CFD model with a free surface, which would enable me to calculate just how much wave drag there would be. But I could very easily calculate a 2-D lift coefficient just like Schleihauf did, and you can see that it compares much better.
Okay this is a combined hand and arm drag, and both of these models here in the middle are Berger’s, and you can see they are on the high side. Berger drug a hand and arm through a tow tank. The water wasn’t flowing and the arm was moving. You would expect the turbulence to be quite low, and these results are higher than you would have expected for that experiment. They are closer to the 10 % rather than the 1% and again, that’s due to the wave drag.
Here is Berger’s data again with 3-D lift coefficients. Also she calculated her coefficients based upon total surface area rather than projected surface area. In my CFD model that is no problem, I can do it either way. And that is why some of these numbers might look a little smaller than some previous ones.
Finally, Trevor Wood, back in the seventies, did some work with wind tunnels and his arm model was a hand and half of a forearm. I was able to go into my model and figure out what a full arm would be versus a half arm and adjust his data to account for that. After doing that, here is where his data falls. Again, I was getting pretty good comparisons. I really didn’t expect to get this good of correspondence between the analysis and test. We don’t usually get this good of a correspondence at work, so I was thrilled, really, to see this. Here is Wood’s wind tunnel data for a 2-D lift. He did not compute 3-D lift.
Okay, so let me summarize the points that I want to make to the scientists in the room. First, is that lift is definitely out there, and Doc was absolutely right. That was probably one of the most important things that has happened in this century for swimming, is acknowledging that lift existed. But that lift is not due to Bernoulli’s equation. It has to be described, because of the boundary layer of separation, with Newtonian mechanics. Another thing is that even simple arm motion causes a 3-D flow. You can’t have a 3-D object without having a 3-D flow. In other words, a lift coefficient should not be a 2D coefficient. A third thing is that the hand is not an airfoil, it is not even close, so those of you that are writing books……..where is Ernie? Is he gone? A fourth thing is that water turbulence increases drag and lift. Finally, I think that I have shown, at least to my satisfaction, that we know how to model a swimmer’s hand and arm using CFD (because of the good correlation we got with the experiment). So those are the conclusions that I want to give to the scientists in the room.
Now, let’s talk a little bit to the coaches. By the way, those two are not mutually exclusive, of course. At least they shouldn’t be.
(Question.) That is just what I am going to talk about next, beautiful. What I did to get a little more practical about this, I went in and calculated the peek hand propulsive force at different stroke angles. And here is how I define stroke angle. If a swimmer is swimming the free style and he moves his/ her arm directly down, that is a zero degree stroke angle. Say we go over here and stroke forty-five degrees from this line, which is a plus forty-five degrees. If then we stroke this way, this would be a minus forty-five degrees. So, for each stroke angle, I took the lift and drag forces and resolved them into the propulsive direction, in the direction that the swimmer is moving. I plotted the peak hand force, and the red is the total lift and drag resolved into propulsive force, the blue is that force just from lift, and the green is that force just from drag. The reason that I plotted those two is because I know there is a lift versus drag controversy going on that I want to address.
I am going to spend a little bit of time on this because it really says a lot. Notice that the peek hand propulsive force really is pretty much constant between a minus seventy-five degree stroke angle to a plus forty-five degree stroke angle. And what that is saying is, for all these stroke angles in between, there is a combination of stroke angle and angle of attack which basically gives a constant propulsive force. Remember the angle of attack is how your hand is oriented to the flow direction. The stroke angle is how your arm is moving.
(Question.) Okay. There’s two angles. There’s the stroke angle, say my body is moving this way. The stroke angle is the angle from the direction that I am heading, that I am stroking relative to that direction. The angle of attack is the angle the hand is hand as I am moving it along that angle.
(Question.) No, well what I have done is for each stroke angle, I have analyzed moving the hand at different angles of attack. I have taken the angle of attack that gives me the most propulsive force in the direction that I am heading, and I have plotted it on that graph.
(Question.) Okay, each of these points represents the maximum from a series of analyses. I did an analysis at a zero degree angle of attack. I held my hand this way and pulled that way, I held my hand this way and pulled that way, I held my hand this way and pulled that way and I held my hand this way and pulled that way and whatever gave me the most propulsive force in the direction that I wanted to go, that’s what I plotted on that graph.
(Question.) No, I haven’t gotten to what these percentages mean yet. Those percentages are the portion of that total propulsive force that comes from drag. Here we go. Percentage propulsion from drag is noted above. So, when I am pulling straight down, 100% of the force is coming from drag. When I am pulling from an angle of forty-five degrees, 57% of it is coming from drag. When I am pulling from an angle of minus seventy-five degrees, which is almost this way, 17% is coming from drag.
(Question.) This is a stroke angle minus seventy-five degrees and this chart doesn’t tell you what angle of attack gave me that peak. I just analyzed a bunch of angles of attack, and whichever one gave me the maximum amount of propulsion, I plotted it on here. I think you guys are trying to jump ahead of me, that’s what I think the problem is. This is hand position for maximum propulsion at different stroke angles. Remember at each stroke angle, I analyzed the hands at various angles of attack. These are cross sections of the hand. This is the forward motion of the swimmer. Imagine yourself as a swimmer and you are looking down and you are seeing how your hand is sweeping across your body. This would be the insweep and this would be the out sweep. These are the angles of attack that give the most force at each stroke angle. And what surprised me is, up until about plus or minus sixty degrees, the best orientation of the hand, regardless of which direction you are pulling, is facing straight backwards.
(Question.) Within that stroke angle, the percentage of propulsion due to drag varied from 48% due to drag here, to 57% due to drag here, to in the middle 100% due to drag. I know there is this lift versus drag controversy going on, and these results reflect on that controversy. He can get about the same propulsion over a whole range of stroke angle.
I’m sorry, I should have said he or she. I have one swimmer in my family and that is my daughter, so I should really be saying she. By the way, I tried swimming once and the other swimmers were so concerned about my health that they inquired to the coach about if I was going to be all right. I gave it up. You know, I used to be fairly athletic, but I was never a swimmer. I thought well, I’ll just get in the pool and I can breathe every stroke. I used to run marathons, I know it’s hard to believe looking at me now, but I’ll just breathe every other stroke, no problem. I just died. I couldn’t do it. So, I have a healthy respect for swimmers. Now where was I?
Okay, let me just summarize this. The peak propulsive force for the hand is practically constant between the stroke angles of minus seventy-five degrees and sixty degrees, if the hand is held at an optimum angle of attack. There is a little bit of an advantage with the pinky leading. The best orientation for the hand between stroke angles of plus or minus forty degrees is, from a practical standpoint, facing directly back towards the feet.
And finally, the percentage of hand propulsive force due to drag can vary between 0%, that’s right there, and 100%. Okay, let me quickly go on to the arm. The arm is really not too exciting, it’s basically all drag.
(Question.) I don’t know the answer to that question, and the reason I don’t is because this analysis was for steady state analysis. And it doesn’t take into account the difference of the length of the stroke, whether this way or that way. It also doesn’t take into account the acceleration or the motion of the water prior to reaching it. So these conclusions based upon a steady state analysis. What I am going to do in the coming year is to analyze unsteady flow and look at the effects of acceleration and of deceleration. That will probably take me about a year because I just do this as a hobby.
Here’s a summary for coaches, and remember I’m qualifying this because it is based upon steady state.
S-shaped or straight strokes can develop equal amounts of propulsion. The best propulsion can be obtained by keeping the palm facing straight back, no matter which angle you are stroking at. And propulsive forces may be drag or lift dominant. Okay, now, having given those declarative statements, let me put up a quote given by Mark Twain. Okay, yes.
(Question.) Yeah, I would say there’s probably several advantages to going at an angle. One is that the stroke is longer. Two is the still water idea, first brought up by Doc, which is, if you are pushing straight back the whole direction, you start to have water moving in front of you and you are getting less and less push on it, whereas, if you are changing the angle of attack, you are probably going to get more push from it. That will come out in my future research. Those are some of the things that I will be looking at. This is about a three-year project because I will be working part-time on it. Yes.
(Question.) You can have lift without invoking Bernoulli’s principle. You can use Newton’s law to come up with lift. You don’t have to use the classical circulation calculations that aerodynamics engineers use for wings, where the boundary layers on wings do not separate usually until the very, very end. That is why they can use Bernoulli’s equation to calculate that lift for very small angles of attack, but once the boundary layer separates, all bets are off and you have to go back to Newton.
(Question.) Yes, there is definitely lift, and as you can see there can be a lot of lift. It’s just that Bernoulli’s principle is the wrong way mathematically to describe that lift.
(Question.) Yes, with Newton’s law. No, you can do a lot of things with Newton’s law. You can start out and you can develop a lot of equations from Newton’s law.
Okay, so, the reason that I have this up is that I want to caution people that this is just the start of my work. And there’s a lot more to do, and I’m really excited about this research. I think it’s going to improve our knowledge in swimming, and I think we’re going to take a giant step forward, especially once we’ll be able to look at the rotation of the arm and acceleration. Some should be some really good stuff that has never been done before.
(Question.) Well, Bernoulli’s equation can be derived from Newton’s law. Think of Bernoulli’s equation as a subset of Newton’s law. Bernoulli’s equation applies to ideal flow, and ideal flow means that the flow has to follow the boundary and can’t separate.
(Question) No, you’ll still have the difference in pressure, you just can’t use Bernoulli’s equation to describe that difference in pressure. It’s kind of a small subtle point really, but to an engineer it is important. But remember that Doc was absolutely right, that lift is there, and it’s very important.
(Question.) Yes, I have no rotation of the arm involved.
(Question.) It assumes that the arm is far enough away from the surface for wave drag to not contribute. But, my conclusions are based upon the arm not changing its orientation as it moves. In other words, we are not allowing the arm to rotate as it really would in true swimming. That will be done in the future.
(Question.) Yeah, that’s something that could be very significant, or it might be that for these velocities, it’s not significant. I frankly don’t know, but it’s going to be interesting to look at. For instance, I could put in this model a model of a chest or a thigh of whatever, and have one object go by the other and see what the effects are.
(Question.) Well, if you’re a yachtsman, you probably know your boat moves ahead through the water and the waves follow right along with you at a certain velocity. The same goes for swimmers. In the breaststroke, for instance, if you pause long enough, those waves can catch up with you and actually give you a little boost. If you have ever been in a boat and you slow down all of a sudden, the waves catch up to you and the boat kind of goes like this. If that’s what you are talking about, that’s possible.
(Question.) Yeah, and the common denominator is we can use the CFD analysis. I did it for different intensities. I did it for very low intensities and very high intensities. In using this, if somebody does a flume study versus a water tank study, I can go to CFD and say okay, well the flume has these effects because of turbulence and the water tank has these effects.
(Question.) Swimming pool turbulence is really a tough one to answer. I mean there is just so much going on in the pool. It’s a stochastic process.
All right, I am sorry for running over. By the way, thank you very much. I just want to say one thing real quick. This presentation is not about me(I’m not selling books or promoting clinics). This presentation is about CFD. I want to encourage all of you to go back to wherever you live and talk to your swim club parents in technical professions, and talk to your professors in your engineering departments and get them involved. There is so much work here that can be done, and I can’t do it all. I think it’s a rea gold mine for swimming research. Thank you very much.