Biomechanics Part 1 by Dr. Scott Riewald (2002)


Published


Thank you guys for attending – it’s a good crowd.  I want to say at the onset that this is work that I have been doing with a gentleman by the name of Barry Bixler.  He has been a principal engineer working for Allied Signal and Honeywell Engineering for probably his entire career.  He is very familiar with the sport of swimming.  His daughter swims competitively but probably more importantly, he works in the aerodynamics or aeronautics industry. He is currently working with some of the technology and software packages that we are trying to apply to the sport of swimming.

 

The impetus of this project came about when Barry came to me and asked, is there any way that we can mesh this technology in athletics. We started from that point and type designed a project that would allow us to better understand propulsion and how it is generated by the upper body during the freestyle swimming stroke.

 

A lot of times stroke technique advances come from the “top-down approach” – you look at the best swimmer in the world, say Ian Thorpe, and see what he does.  Why does he swim so fast? Is it his high elbows? Is it his huge feet – how does the kick play a role in allowing a swimmer to go fast? You can look at Natalie Coglin underwater off her backstroke turns or her butterfly.  She has great mechanics. Obviously she goes fast, but why?

 

Observation is beneficial because you learn more about the strokes through watching the best swimmers, but there is an alternative to developing swimming technique. Let’s call this the “bottom-up” approach.  By trying to understand the fundamentals of fluid mechanics, fluid dynamics – how objects move through the water – and applying those principles to swimming, we can build from the bottom up and design the optimal stroke.

 

We chose to study propulsion generated by the hand and the arm. There has been some experimental research done on this subject over the past twenty years. There are some studies that show that propulsion comes from lift and drag forces. These experimental studies were effective in providing some information, but they are limited in terms of the accuracy of their information. I am integrating some new technology – so you can get a better picture of what is going on.

 

Take a plaster mold and a person’s forearm and instrument it with force sensors. Take that mold and drop it into a flume or tow it through a pool.  You are able to measure the forces that are produced on that object. Traditionally the literature discusses the two dominant types of propulsive forces you can generate – propulsive drag which is essentially grabbing onto the water and pushing it straight back and propulsive lift forces which are much the same as lift forces that cause an airplane to take off the ground.  This is Bernuli’s principle – air flying at different speeds over the two sides of the wing causes pressure differential between the underside and the topside of the wing that causes that plane to take off.  The hand is thought of in much the same way.  As it slices through the water it acts like a wing.  You have a pressure differential so even though the hand might be moving from side to side you are generating some propulsion that is making you go forward.

 

So you get this instrumented hand – put it in a flume, set an orientation and set the speed of the water. You get a set of forces as long as you know the speed of the water and you are able to define certain variables like the angle of attack, defined as the orientation of the hand and the arm to the oncoming water flow. So this is one way of defining the hand’s position in the water – you have the water flowing right to left at an angle of attack that is 45 degrees.

 

The second hand orientation is called the sweepback angle. Common in terms of airplanes, this angle defines the leading edge of your hand and arm movement as it goes through the water. By gathering this information – such as the speed of the water and the measurement of the forces acting on the arm – you are going to be able to come up with a look-up table. Once you have a look-up table with this data you are going to know which forces are acting on the hand and the forearm.

 

That has been the thinking behind these sorts of studies and really was a pretty slick way of getting these variables and even at USA Swimming, we took that information and used it to analyze stroke technique.  We digitized an athlete’s pulling pattern and we would be able to compute those angles. Go to that lookup table and you could see how much force they were generating – the velocity of the hand, how much propulsive force to get themselves to the pool etc.  We would use this information as a comparative tool to develop a good hand or a good force profile for a freestyle pull or a backstroke pull or a butterfly pull. We would compare one athlete to another and look at how things differed from the optimal force profile and give feedback to the athlete that hopefully would make him swim faster.

 

This method has been used for a number of years to help athletes who came through USA swimming to change their stroke technique.  They learned something new about the stroke and I believe that this probably helped a number of athletes get a little bit more effective in how they swam. But there is flaws in the information people are using to base their stroke technique on.

 

The scenario that was studied experimentally never ever occurs in an actual swimming stroke.  You never have a situation where the hand moves through the water with a constant orientation.  You never have a situation where the hand is moving at a constant velocity because there is acceleration; decelerations, rotations, and joint angles are changing. If you look to other areas of fluid dynamics –in aeronautics or the automobile industry, you find that if you start to introduce these unsteady variables some of those values can change by as much as 50%. So there is potential that you have a 50% error in some of the information you are giving back to an athlete.

 

I didn’t feel comfortable with that when I started at USA Swimming, so I phased out this digitized whole stroke force feedback to the athletes. The technology and the cost it would have taken to build a piece of equipment that could accelerate the hand through the water and get the profiles you wanted, especially as you rotated the hand through the water, would have been extremely expensive in the 70s. So there really wasn’t a whole lot more we could do back then.

 

The reason that you have these discrepancies or potential discrepancies between experiments that were done in the past and what happens in those dynamic situations is that there is not a causal relationship between the forces you generate and your hand velocity and position. There is not a direct cause and effect relationship between the two.  Just because you know the position and the velocity of the hand and the arm, doesn’t mean that you can accurately predict what forces are being generated.  There is a time component that is also important so it doesn’t only matter what your current position and velocity are, it also matters where you start and where you were shortly before that period. You also need to take into consideration the inertial characteristics of the arm – the mass, as well as the acceleration – there are all these factors that can potentially add some error into the analysis.

 

Only recently have a couple of researchers started to think about dynamic simulations, but have run into those roadblocks that I mentioned – cost and difficulty with instrumentation.  So if you had to ask the question – is this the proper way to teach stroke mechanics using this data, I would say there might be better ways. That was the kind of thinking behind the project that Barry and I set out on. What does body positions roll in terms of helping you to move through the water effectively?  The core of the body – it is very important – but how do you measure it?  This new technology is going to allow us to measure things that we couldn’t previously.

 

The technology that I am talking about is a software package called “Compensational Fluid Dynamics”.  It is a software package that essentially allows you to set up a wind tunnel in your computer. You can bring this big physical wind tunnel down to the size of your desktop and run simulations on if you wanted to. You can look at things like unsteady flow, or what happens if a body rotates – how does that impact the propulsion that can be generated. You can do this in different velocity of accelerations and decelerations of this model.

 

I’d like to give you some examples of where this technology is used in other areas. In the automotive industry it is huge.  Not only do they use this kind of technique to design and make vehicles more aerodynamic, they use it on things as intricate as the air flow through your engine, through your exhaust system. There are space shuttle parts that were actually designed using this type of software, looking at the stresses on the body, looking at the heat on the body, looking at how fluid flows past to help it with reentry back into the earth’s atmosphere.

 

So this is a valid technology.  It has been proven in other areas and can have some applications to swimming. We are going to focus on understanding propulsion mainly, but you can look at things like the kick. Does the kick really help or should you just let the legs hang back there because they are more of a nuisance than a help. What is the optimal body position to be the most streamline when you are swimming? You could use this type of technology to figure these things out.

 

This could help provide some scientific evidence behind different theories such as frictional properties.  The Speedo suits took the world by storm before the 2000 Olympics, but no one really knew a whole lot about them.  You can design a model to have the frictional characteristics of the Speedo suit or the TYR suits. What will be the performance benefit as well as the interference effects?  What happens when the hand passes six inches from the body during a pull versus when it is a foot and a half away from the body during a pull? We now have the technology that might allow us to address some of these questions as well as numerous other ones that might be kicking around your head.

 

We know from previous studies and from other areas of fluid dynamics and mechanics that there are things that are critical to propulsion. There is velocity, speed and direction as you are moving through the water. Consider angles – the angle of attack, the sweep back angle, the acceleration of the body through the water. And what about the way the water flows – whether it is a turbulent flow or whether it is lamina and everything is really smooth going around the hand and the arm.  These are all critical.  These are all things that you can control within the computer environment.

 

I want to explain how we designed this model. We took a standard adult male, 50 percentile male, and made a physical cast of plaster mold of his arm, digitized a bunch of points and then brought that whole model into a computer environment.  What you see here looks kind of like mesh – well it is.  Each one of those elements represents a place where we can observe computer properties of the fluid as it goes past. We can measure things like the temperature of the water, the speed of the water, the pressure at that point and use that information to then compute the forces that are being generated to propel this model for an athlete down the pool.

 

What is really neat about this type of simulation as well is that when you are working in the computer environment, you can chop this model up however you want. If you have a question about the contribution of the arm to propulsion, you can answer that question.  If you want to look at what the hand is doing or even what the fingers or the thumb are doing, you can look and break it down as specifically as you want. Some of the data that I am going to show you is going to be broken into a hand component and an arm component just to see how important each is to your swimming stroke.

 

We made this model which is actually this really small thing in the middle of this dome.  This dome represents a virtual pool.  The water is flowing through this dome.  It goes past the model and then we measure and we record how the fluid changes direction and what forces are generated.  This blue part here represents kind of our inlet boundary. We prescribe what speed and what direction the water is coming into this pool. We can say we want the speed to be 2 meters per second, traveling straight from this end to this end and it will do that.  Everywhere else in this pool there are no constraints so as the water comes past the hand maybe it deviates and changes direction and changes speed – we are able to record that.  We are not requiring that to fall into any sort of constraints.  That is important because we get a real accurate picture of what is really going on.

 

We replicated those experimental studies that had been done over the past twenty years to see if we were getting the same numbers using the computer model as they did. As we ran several simulations we found that there are three plots of our experimental simulated data: the green, red and blue plots. We plotted with two sets of data we collected experimentally from a physical model put in the flume or towed in the pool and found really good agreement between our results and theirs.

 

This is just to give you kind of a reference point – 90 degrees angle of attack would represent your hand and your forearm pulling straight back perpendicular to your body. They are oriented perpendicularly to the direction you are moving and you would expect to have the greatest propulsive drag force at that hand orientation.

 

So this was really encouraging to us because we were able to say our computerized world accurately represents what they measured experimentally. When we looked at the lift forces that were generated by various angles of attack, our data fell right on top of the experimental data that has been collected up to this point. We felt that we were then able to go on and look at some more complex situations.  But before I get to that, I want to point out some of what the other features are of this type of software.

 

We are looking here just at the arm; the hand is cut off. You can do things such as analyze the fluid flow around the arm and see it visually.  What you will notice here is that pockets of vortices form. This is turbulent flow and a separation here as the water comes past the arm – for lack of a better word we will call it a dry spot.  Actually it is a low-pressure area on the backside of the arm.  The same thing happens on the back side of the hand.  The bigger this area, the more propulsion you actually get. We can look at things for different flow conditions and kind of assess the size of this area and determine visually just one thing – one technique that is going to be more propulsive than another.

 

You can also look at how fluid flows past the model.  Here we are tracing actual water molecules as they go past the hand and past the arm in time. As you go to green, orange, yellow, and red, you get farther and farther along in time so we are tracking individual molecules.  You can see again, turbulence, separation – this separation happens to be greater at the hand.

 

We are looking at a bunch of steady state analysis that remain pretty consistent, but in terms of these, the hand generates more force than the arm does. You are going to find that that changes though, when you start to look at dynamics in relations. When you look more specifically at the hand, you see these vortices being formed – this to the scientist invalidates Bernoulli’s principle of generating lip forces with your hand. Bernoulli’s principle is based on the assumption that the water flowing past an object or the air going around a wing of an airplane remains laminar – remains smooth. There is no turbulence being formed. Just the fact that you see turbulence invalidates that theory.  It doesn’t mean that lift forces aren’t being generated, it is just that you can’t use those equations to compute how much lift force is actually generated for a certain hand position for a certain water speed.

 

Even when you would expect the hand to be most like an airplane wing, you still have turbulence so the hand is not like a wing. Just some added evidence to back that – here you see as each point represents increasing the angle of attack going from the flat surface to more angular presentations – the oncoming air and water flow – this is the profile you get for an ideal wing.  Here you are looking at the amount of lift that is generated.  Here you are looking at the drag that is generated.  As you change the angle of attach, the lift increases and the amount of drag you experience doesn’t really change a whole lot at all.  It is really nice when you are in an airplane and feels comfortable that the faster you go the more lift you are generating. But, at the same time you are not slowing the plane down very much. This is the same profile generated for the hand. You can see the vastly different shape of these two curves – again, the bottom line of the hand isn’t a very good representation of a wing.

 

One other thing that we were able to do in the steady state analyses was look at the contribution of the hand and the contribution of the arm.  The hand is shown here in the blue – the arm is shown in the red and then the combination of the hand and the arm is shown here as the green curve. The amount of drag propulsion generated by the hand far outweighs what is generated by the arm during the part of the most propulsive phase of the stroke.  You do have some situations at very low or very high angles of attack where the arm generates more propulsive drag force, but predominantly it is the hand that is doing the majority of the work.

 

Here we are looking at the lift forces that are generated and again you can see that the arm does very little if anything – zero lift force.  The hand though, through a 30 to 60-degree angle of attack, generates quite a bit of lift force. This again, validates the results from previous experimental studies that lift actually dominates your propulsion in some instances.  It provides even more propulsive force than the drag force that you generate.  Again, this is all for the steady state condition. So the initial conclusion that you can draw from the first phase of the study is that Bernoulli’s principle was disproved.  Lift forces can still be generated, but rules that govern these depend on Neutonion mechanics F = MA – for every action there is an equal and opposite reaction.

 

We came away feeling pretty good that the computational fluid dynamic model can accurately reproduce the experimental steady flow experiments that were done by research. If we had wanted to, we could have gone through all combinations of angles of attack, sweep back angles, and water velocities in this computer environment and create that same look up table with the same numbers in it that we already have. The important thing is that we validated the previous model and that information served as a launching pad to look at more complex and unknown areas of propulsion – namely, what happens when the hand and the arm accelerate and decelerate through the water.

 

So in phase two, we introduced these accelerations and decelerations.  As I mentioned, there are a couple of researchers who tried to do this in the past using physical models. Fehr did this but only looked at what was happening at very discrete points on the hand or the arm. They really couldn’t get a good picture of what was going on over the whole hand and arm. Sanders in 1999, tried to do this as well, but ran into those equipment constraints where he wasn’t able to accelerate the hand and arm as fast as he wanted through the water. As a result, things were all very low speed and not applicable to swimmers at all.

 

We used the same model and the same virtual pool.  One thing that we did do a little bit differently though was to pick just three angles of attack that you might see in the course of a swimming stroke – 60 degrees, 90 degrees and 135 degrees. These might correspond to an insweep, pushing straight back, and an outsweep phase of a stroke. We were seeing how things might be affected at each of those phases. We chose these three values for angle of attack, initial set of velocities and some final velocities, and the time over which those velocities changed.  That would give us an acceleration pattern.

 

One point that I want to make here, as an aside, is that there is a lot of talk concerning the hand and the arm as an anchor in the water. When you stroke, you pull the body past the arm. This is different than trying to get swimmers thinking about pulling their hand through the water.  I think that the former is the valid and correct way of teaching swimming.  That is the way I try to get athletes to think about their strokes. The fact is, though, that there is some movement of the hand through the water.  A lot of people site some studies that show that the hand a lot of times exits the pool farther down the pool than where it entered.  That happens, but if you look at where the hand touches the water as opposed to where it enters the water, there is some backward movement of the hand. The hand is never going to be a completely rigid attachment to anchor in the water and pull your body past it. There is always some movement.

 

So these philosophy profiles, representing the starting philosophies and finishing philosophies, represent data that we have actually collected on swimmers who have come through Colorado Springs over the past ten years. It is then entirely appropriate to say that there is going to be movement and acceleration of the hand and the arm through the water.  We chose four situations that represented the hand accelerating and, equally as important, when the hand and the arm decelerate through the water. Is that going to have a negative impact on an athlete’s performance? We compared the time history of the dynamic simulations with what we got in those quasi-steady results previous experiments and found some drastic differences as you might expect.  This is actually probably more of a scientific application, but there is a variable called the acceleration number that you can use to relate some of these variables. We were also able to see some things by visualizing flow around the hand and the arm.

 

Implications of these studies are going to be, hopefully, better teaching instruction, emphasizing the importance of acceleration. Drag in fact dominates the stroke so trying to stay away from sweeping patterns, S patterns, is the way to go.  The amount of propulsion that is generated by the arm equal to the amount of propulsion generated by the hand differs from the results we got. In these results, the hand greatly outweighed what you were getting from the arm.

 

So here is a graph which compares an unsteady simulation to what you got in those initial study simulations. We are looking at the amount of propulsive drag four studies generated.  We started here at an initial velocity of 5 meters per second.  We accelerated the hand through the water so that at the end of ¼ of a second it was moving 1 ½ meters per second, indicative of what you might see at the catch phase and the initial phase of a freestyle pull or a butterfly pull.  You can see that there are some drastic differences between the forces that were generated and dynamic conditions versus the steady state conditions. Here, we are looking at what happens from both the hand and the arm. And here there is probably a 40% difference in the amount of force that is being generated when you are incorporating these dynamic variables instead of just relying on the steady state information that we were using in the past.  Now kind of superimposing onto this, we look at the difference in lift forces that are generated. Again hand acceleration goes from 0.5 meters per second to 1 ½ meters per second. There is a difference but it is not nearly as comparable as the change you see in the amount of propulsive drag force. So lift force, while it is affected, is not affected nearly to the degree of the propulsive forces are.

 

If you want to look at just the hand, you see a couple of things.  You see that the drag force, propulsive drag, which is generated, does increase.  It is not anywhere close to the magnitude of the hand and the arm, but what you also see is that the entire changes in the lift forces that are generated come about at the hand. So we look at the next slide of what the arm is doing – these red curves lie right on top of each other.  It doesn’t generate any lift force from the steady states experiment and it still doesn’t generate any lift forces when you introduce these dynamic terms. However, the propulsive drag force that is generated by the arm does increase quite a bit. So the role of the forearm plays a bigger and bigger role as you start to introduce these unsteady terms.

 

To just briefly explain what the unsteady and quasi-steady terms mean – Quasi steady is those early experiments that were done in phase one. The reason it is called quasi study is to keep everything constant so the velocity is constant, the hand position is constant – even though there is still movement going on, nothing is changing.  Unsteady means that you are changing.  You are starting at one velocity and you are changing to another velocity. There is that dynamic component in the analysis. When you look at everything lumped together you can see the total hand and arm propulsive force in that unsteady situation greatly outweighs the total propulsive force that you had in the steady state – the quasi study simulation that we did.

 

Again, you are looking at a 40% increase in the amount of propulsive force. Is it reasonable to say that the past simulations with the freestyle and butterfly strokes were 40% off?  It may be. In the process of trying to implement some of this new data from those types of analyses we will see how that ties into teaching stroke mechanics. Equally as interesting is what happens when the hand and the arm start to decelerate in the water.  Obviously you think you probably won’t be generating as much force if you decelerate at all. But look at the steady state or the quasi study situation and the dynamic situation where you are decelerating.  You decelerate much faster and carry much less force in real life than what those early studies would have shown.  You also get to a point – if you happen to decelerate the hand for greater than 1/10th of a second – where you are actually generating forces that are slowing you down.

 

So 1/10th of a second is not very long, but if you are decelerating through that point, through that much time, you are generating some retarding forces even though your hand may still be moving in the proper direction. You think it would be helping you move down the pool but it would not.  So when you start deceleration in your stroke greater than .1 or .15 seconds it is actually slowing you down. Acceleration plays an important role in how well you are able to propel yourself down the pool.  You want to stay away from situations when the hand and the arm are slowing down.

 

There is a term that is used in other studies of fluid dynamics in the aeronautic industry – it is called an acceleration number. You can use that to relate your acceleration, the velocity and some variables – here we got the width of the arm and volume of the arm as in this turn over here. You can start to use this information to create a new set of look up tables so that if you know the acceleration, you know the velocity and you know these variables. You can start to get a feel for what the real forces are that act on the hand and the arm during a pull cycle.  The fact that all these curves lay right on top of each other, the different angles of attack, different finishing and starting velocities, there is a solid relationship there. That is science that you can use to help rebuild that database.  You can come up with a ratio relating the unsteady force to the new force to the quasi study force or the old force. You can come up with a situation where you have a slope of essentially an equation for a line – this ratio equals some constant times, this acceleration number plus another constant and you get this very linear relationship when you are looking at the drag forces that are generated.

 

So bottom line – what you can do is more force analysis and be able to accurately predict the propulsive drag forces that are generated. However, when you get into dealing with lift forces there is a lot more variability.  You saw how well those curves laid right on top of each other when we were looking at the drag forces, but when we are looking at lift, they don’t do that. For each different angle of attack you are going to need to come up with a new equation to describe that relationship.  We started the process of doing that, coming up with these equations to relate the new forces to the old ones, but there are a lot more simulations that we would actually have to do to get the full complement of information to analyze someone’s stroke correctly.

 

One of the things that I haven’t really talked about is axial flow in propulsion.  What I mean by axial flow is water flow from the elbow towards the fingertips.  You don’t think about that a lot when you are teaching mechanics, but these studies have shown that water in fact does move along this length of the arm. A recent study that was just published out of Holland showed that there are in fact pretty large pressure gradients along the back side of the arm that are caused by this fluid flowing from the elbow to the fingertips. This further decreases the pressure at the back of the hand and thereby increases that pressure differential from the front of the hand to the back of the hand. It is going to be most prominent in kind of a rotational axis as you set up that catch. For example – it is there partly because of that, but also when you are doing a straight back pull.  You do have a pressure gradient there as well so we are still in the process of trying to identify some specific teaching recommendations to augment that or take advantage of that. But the axial flow is something that is present and previous studies haven’t really investigated or even acknowledged it.

 

Another thing that you can do with the software when looking at unsteady types of simulations is to analyze the pressure.  They were looking at pressure on the pulling surface of the arm but probably more applicable is what is happening at the back of the arm.  I don’t have the slides to show you, but you would see the huge pressure differential between the front and the back of the arm as well as between the elbow and the fingertips. That further emphasizes that idea of water flowing from elbow to the hand and helping increase the pulling potential that the hand might have.

 

Here’s another cool picture where you can see how different the flows are of a hand that is accelerating through the water and a hand that is decelerating through the water.  There are some things that jump out at you that are pretty distinct. While you wouldn’t call this a completely laminar flow, it is moving through the water much more effectively than this hand that is decelerating. There’s a lot of turbulence that upsets the pressure differential between the palm and the back of the hand and that is what causes you to slow down.  The longer you decelerate, the larger this turbulence becomes and ultimately causes you to generate retarding forces.

 

So – some conclusions from this:

Unsteady forces are significantly different from steady state quasi-steady forces that were measured in previous experimental studies. We can start the process of updating some of these look up tables to provide better results so you can digitize an athletes stroke and be much more confident in the information you are giving back to an athlete. We will be able to say more accurately that these are the true force profiles that you are generating.

Accelerating your hand affects the propulsive drag force that you generate more than the propulsive lift forces.  So swimming is a propulsive drag dominated activity. There has been a lot of debate over the years as to whether the majority of propulsion comes from drag forces or from lift forces.  These simulations show, and I think it is validated by a lot of the top swimmers in the world, if you watch there stroke technique they are trying to grab onto the water and push it as opposed to having large sweeping motions – that is the way to go.

Unsteady flow, or acceleration, affects the arm more than it does the hand. At the end of these simulations the arm is generating just as much propulsive force as your hand is.  I know that there are a lot of coaches that have thought this for some time, but there are a lot of coaches that haven’t, so this is some information that you can use when you are teaching mechanics. Pulling mechanics should emphasize what is happening with the arm just as much as what is happening with the hand.

You can get a negative propulsive force when you decelerate the hand, even when the velocity of your hand is still moving towards your feet. This is something that is not very intuitive but comes out of these simulations.

 

I hope that there may be some information that you can take away from this and apply to your swimmers, now. But I think there are some greater and better things coming down the road. One of the reasons that I wanted to give you guys this talk is that again, we have gone through two phases of this, but the potential for this type of technology and the potential for conducting these simulations is essentially unlimited. As computers become more advanced we can start analyzing bigger and bigger models.  Maybe there will be a full body model some day. Or maybe we can start looking at the kick or maybe we can do some real time where you have an athlete in the water and you are getting this information live. What is important to understand is that there are great things going on and that the potential exists to better the state of USA Swimming.

 

So we are looking to the future and trying to get even more complex analyses, some real time feedback where an athlete can get this information right away.  We are not at that point now.  These simulations still take quite a bit of time to run. But again, as computers get faster and faster, I don’t see why we can’t develop some subject specific models. A model that is Tom Malchov for example – plug it into a computer and see what the best thing is going to be for Tom to do. There is potential on the horizon.

 

I just wanted to mention that this work was actually supported by the US Olympic Committee and a grant that they gave us. I just wanted to recognize their support.

 

Any questions you guys want to ask?

 

Question – I think because they are adjusting that – adjusting in and around the back of the wing to adjust the flow.

 

Question – yes, if they have a higher level of importance to the lift forces that were generated, but when you incorporate those accelerations, the drag force jumps up significantly. The lift force increases a little bit but not to the point that it creates any significant change.

 

Question – no, we are actually monitoring fluid flow through this.

 

Question – yes, I kind of passed over that slide, but yes we set all the physical properties of the water to be what they should be.

 

 

 

 

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