I'm going to stick to my guns here, please don't think this is flippant or sarcastic. I tried hard to eliminate any trace of these types of phrasings in my reply. FYI, I'm a Naval Architect out of Michigan and got an A in model testing :-) Jed wrote: While it's my belief that the boat actually turns around the boat/paddler's center or gravity when at rest, descibing this as it's center of floatation is close enough for me. With regard to turning the boat by turning both ends, this is true *as long as the boat is not moving* The COG and COF are the same the same for longitudinal and transverse axes, (not vertical though) otherwise the boat will trim/list until they are, however the boat turns about the point where the volume of water forward and aft of the COF are equal. The effort (force x lever arm) required to rotate the hull is the same, no matter which end or anywhere along the hull it is applied. Also the COG/COF changes during the sweep as your body moves forward and back. but different forces come into play when the boat is moving. I agree that the dynamic forces added to the system by the fact that the boat is moving complicate the model, but your statement "as long as the boat is not moving" is wrong. When the boat is moving the hull still rotates around the COF. What is happening and I don't think you realize it, is that the amount of effort (the push away from the bow) the paddler is able to impart on the outward sweep is noticeably less than the amount of effort they are able to bring to bear in pulling in at the end of the sweep. I'm not sure if this is a result of the lever arm becoming shorter quicker (the COF moving towards the point where the paddle is planted in the water) as the boat moves forward (it follows that the lever arm gets longer faster as the COF passes the paddle for the finish of the draw) or the body can't push out as hard when you are leaning forward (leading arm sorta' over the shoulder) as pull in, when finishing the sweep and the arms are below your shoulders and pulling in. Probably a combination of both. Another thought; the amount of time that you spend in the forward part of the sweep is less since the boat is moving forward (less time = less work, since work = force x time) When the boat is *moving forward* there exists a bow wave that has a similar effect as pushing the bow deeper into the water, retarding any tendency for the bow to move left or right appreciably. The bow wave is a result of water being displaced to the side. Forward motion of the hull through a fluid actually creates lift! This is why we need bow lines when motoring down the highway. :-) Makes no difference though, since the hull has to rotate around the COF. The bow wave does not anchor the bow. Your forward lean does move the COF/COG forward and increases the trim by the bow (and decreases the lever arm), then as you sit up during the sweep the bow rises to a more even trim. I expect that the amount the lever arm is shortened during the initial part of the sweep is greater than the shorting of the lever arm during the end since we typically can lean forward farther than leaning back. Again another example of why the first part of the sweep doesn't work as well as the last half. The first part of a forward sweep is pushing against this bow wave and having little effect. The middle part of the sweep cannot turn the boat either because the bow wave again fights any effort to move the bow left or right. So the middle part of the sweep tends to move you forward. But the last part of the sweep is acting against the stern that is not "anchored" by a bow wave and may in fact be in a wave trough. This makes it possible to pull the stern towards the paddle during the last phase of the forward sweep, in effect performing a stern draw. This is wrong, if true, your thesis would have the hull turning around the stern at the beginning and middle of the sweep and around the bow at the end. Just isn't so. Even a stern draw rotates the hull around the COF. A clear example of this can be seen by taking your boat up to speed, say about 4 knots. Then try to turn the boat by doing only the first 1/2 of a forward sweep. Count the number of 1/2 sweeps that are required to turn the boat 180 degrees. Then perform the same test only this time use only the last 1/2 of the sweep stroke. To keep things easy, try to do the turns with no edging of the boat and be sure to take the last 1/2 of the sweep all the way to the stern. Think hit the boat with the paddle. Most people find that the boats turn with significantly fewer strokes when they use the last 1/2 of the sweeps ompared to the first 1/2 of the sweep stroke. A perfect example of being able to input less work into the system with the initial weaker outward push than with the final inward pull. Putting the boat up on edge significantly reduces the amount of overall work required, and allows the momentum of the hull to assist the turn due to the asymmetry of the hull when on edge. I'd sure like other Naval Architects to weigh in here, am I that far off base? John Blackburn *************************************************************************** PaddleWise Paddling Mailing List - Any opinions or suggestions expressed here are solely those of the writer(s). 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Yes, as John Blackburn wrote, the Center of Gravity and the Center of Flotation are on the same vertical axis (as opposed to close to it as Jed suggested). However, contrary to his hypothesis, the hull does not pivot around the COF unless the hull is both completely symmetrical and the COF is also not moving. A hull pivots around its Center of Lateral Resistance. To provide an extreme example (that should serve to make this distinction obvious) imagine a light round flying saucer shape floating on the water. At one point on the saucer's edge imagine attaching a large fixed fin that radiates out from the edge (is oriented to line up with the center of the saucer). This big fin penetrates the water deeply and in effect becomes a fixed vertical skeg to the smooth flat shallow saucer. To keep the saucer level we will counterweight it opposite the skeg side (to keep the center of flotation in the exact center of the saucer shape for this example). Now who would like to get in this skegged floating saucer and try to make it spin it around its COF (which is still the center of the saucer). Note: the center of Lateral Resistance of this "skegged saucer boat" would be directly down the center of the saucer only if it were pushed from directly behind the skeg or 180 degrees around the saucer from the skeg. However, if you pushed this "boat" from the "side" you would probably find that you would have to push somewhere out on the skeg to get this object to move directly away from your push without rotating. So in this instance the Center of Lateral Resistance is no where near the Center of Flotation/Center of Gravity axis even when it is not in motion. Now for a more moving imagination example, lets consider a more traditional hull shape that is symmetrical on each end so both the COF/COG and COLR are in the middle of the hull when it is stationary. When pushed sideways from the center it will move evenly sideways without rotating. Now if we put this hull in motion along the long axis (in either direction) the end that is pushing the water apart will experience greater water pressure (than when not moving) and the end that is withdrawing from the water will experience less (than when standing) water pressure on that end. This will be true at all speeds (but the relationship will vary with different speeds). If you apply a side force directly to the center of this now moving hull you will find that the stern is easier to push over than the bow and the hull will rotate about the new Center of Lateral Resistance that has shifted towards the leading end. If you move the point of the center of your sideways force forward to the point that pushes the hull sideways without rotating it you have found the new Center of Lateral resistance for that particular hull (at that speed, in that direction). As you can, I hope, see the pressure changes around a moving hull move the Center of Lateral Resistance (the pivot point) but not the Center of Flotation/Center of Gravity. Next think of the wind as the force moving a kayak sideways and you should understand why most hulls weathercock when moving even though they might be neutral to a side wind when stationary. As was discussed by others, shifting the center of gravity by leaning forward or backward will shift the COF/COG in the direction the weight is shifted. This change in trim will also add more lateral resistance in the weight shifted direction and less lateral resistance in the end that rises some out of the water. So the Center of Lateral Resistance is shifted by moving the COF/COG. Gee, maybe we could invent some device to shift the COF/COG (and therefore the COLR) to help compensate for the conditions we find ourselves in. Any suggestions as to how we might do this? Matt Broze (who flunked out of college) http://www.marinerkayaks.com *************************************************************************** PaddleWise Paddling Mailing List - Any opinions or suggestions expressed here are solely those of the writer(s). You must assume the entire responsibility for reliance upon them. All postings copyright the author. Submissions: PaddleWise_at_PaddleWise.net Subscriptions: PaddleWise-request_at_PaddleWise.net Website: http://www.paddlewise.net/ ***************************************************************************
Matt Broze wrote: > ...<snip>... > > Gee, maybe we could invent some device to shift the COF/COG (and therefore > the COLR) to help compensate for the conditions we find ourselves in. Any > suggestions as to how we might do this? Hmmm. Let's see.... Oh, I know! How about a sliding seat?!? Now if we could just figure out how to make one that is *comfortable* we would have a winner. :-) Dan Hagen *************************************************************************** PaddleWise Paddling Mailing List - Any opinions or suggestions expressed here are solely those of the writer(s). You must assume the entire responsibility for reliance upon them. All postings copyright the author. Submissions: PaddleWise_at_PaddleWise.net Subscriptions: PaddleWise-request_at_PaddleWise.net Website: http://www.paddlewise.net/ ***************************************************************************
From: "Matt Broze" <mkayaks_at_oz.net> > However, contrary to his hypothesis, the hull does not pivot > around the COF unless the hull is both completely symmetrical > and the COF is also not moving. > > A hull pivots around its Center of Lateral Resistance. Strictly speaking, the hull can be seen as pivoting around any point. Rotation is rotation and the rotation is the same regardless of inertial reference frame chosen. Naval architects normally choose to use the center of gravity for convenience. If you play with physics problems, you'll quickly discover that choosing a good point of reference (or origin) can make a solution easier. For hulls, choosing the center of gravity can make a lot of problems simpler, hence the preference. Aerospace engineers are split on the issue. Some use a reference point in front of and below the aircraft, some use the center of gravity while others use the wing quarter-chord. In every case, the choice reduces the complexity for the task at hand and reduces the likelyhood of error. Yours truly, in his aircraft engineering days had to convert all these data to a common reference point to determine aircraft loads (and thus stresses etc.) This lead to many arguments among the various groups (until we agreed I was doing it right :-). Matt's example of the saucer is an interesting one, as he makes a good case for focusing attention on the center of lateral resistance. However, if you shift your focus, you can get the same results for any center of rotation. Over two-thousand years ago, Aristarchus of Samos pointed out that an earth-centered universe with the planets revolving around the sun and the sun and moon revolving around the earth explained the retrograde motion of the planets as seen from earth. When Galileo was on trial for espousing the sun-centered view of the universe, Tycho Brahe presented Aristarchus' model as an alternative that didn't match Galileo's but solved the same problem, thus making Galileo look bad. What is remarkable is that with so many of the era's prominent scientists looking on, no one seemed to notice that the two models were identical, but taken from a different reference point. Rotation was confusing then as it is now. So how you see things depends on how you look. But the answer should be the same. Mike *************************************************************************** PaddleWise Paddling Mailing List - Any opinions or suggestions expressed here are solely those of the writer(s). You must assume the entire responsibility for reliance upon them. All postings copyright the author. Submissions: PaddleWise_at_PaddleWise.net Subscriptions: PaddleWise-request_at_PaddleWise.net Website: http://www.paddlewise.net/ ***************************************************************************
Mike said > Strictly speaking, the hull can be seen as pivoting around any point. > Rotation is rotation and the rotation is the same regardless of > inertial reference frame chosen. G'Day, Mike, You put forward an intriguing proposition and I'll try hard not to misinterpret but looking at Matt and John's explanations I don't think they are saying the same thing with different frames of reference. Their use of phrases such as rotating around various points (John) and "pivot point" (Matt) were fairly specific and I think in the context of the discussion could be taken as synonymous. Surely also they are both using a common frame of reference (latitude and longitude)? John discussed the boat rotating around the center of flotation (COF) rather than the bow which I interpret as meaning that the COF was a pivot point, while Matt was saying that the center of lateral resistance was the pivot point and didn't necessarily correspond with the COF. If the frame of reference were latitude and longitude in both cases then the physical ramifications of each interpretation would be quite different. I found Matt's explanation of center of lateral resistance (the pivot point) very clear. John's points about effective arm extension differences in moving vs stationary boats were compelling. Much appreciated your historical references which I hadn't heard before. All the best, PeterO *************************************************************************** PaddleWise Paddling Mailing List - Any opinions or suggestions expressed here are solely those of the writer(s). You must assume the entire responsibility for reliance upon them. All postings copyright the author. Submissions: PaddleWise_at_PaddleWise.net Subscriptions: PaddleWise-request_at_PaddleWise.net Website: http://www.paddlewise.net/ ***************************************************************************
From: "PeterO" <rebyl_kayak_at_iprimus.com.au> > Mike said > > Strictly speaking, the hull can be seen as pivoting around any point. > > Rotation is rotation and the rotation is the same regardless of > > inertial reference frame chosen. > > G'Day, > > Mike, You put forward an intriguing proposition and I'll try hard not to > misinterpret but looking at Matt and John's explanations I don't think they > are saying the same thing with different frames of reference. Their use of > phrases such as rotating around various points (John) and "pivot point" > (Matt) were fairly specific and I think in the context of the discussion > could be taken as synonymous. Surely also they are both using a common frame > of reference (latitude and longitude)? Their frames of reference are implicitly the centers of rotation they discuss, which are a few centimeters apart. One is the same as the other with a bit of translation involved. > If the frame of > reference were latitude and longitude in both cases then the physical > ramifications of each interpretation would be quite different. Long and lat are not the reference frame, so that's why you're likely confused. While the two approaches may result in slightly different answers for some things, the answers are equivalent. For example, if they both applied numbers to calculations, they might discover that they came up with the same forces but different moments (torques). However, the difference in the moments would be the relevant force times the distance between the two centers they chose. If they tried to use the answers to see how the kayak would respond (i.e F=ma or the rotational equivalent M = I x alpha where I is the moment of mass [equiv to mass but for rotation] and alpha is angular acceleration), they'd get the same answer assuming they correctly calculated the effects of where the center of gravity is relative to their chosen center of rotation (i.e. recalculate "I" about the center of rotation and not about the center of gravity). If they chose the center of gravity, such effects disappear, making the calculations simpler - hence why naval architects often use CG. > I found Matt's explanation of center of lateral resistance (the pivot point) > very clear. > John's points about effective arm extension differences in moving vs > stationary boats were compelling. They are. I'm not saying they are wrong - in fact they are just looking at the same thing from two perspectives. I'm just being a bug and trying to emphasize that the chosen center of rotation is somewhat arbitrary and that one shouldn't try to be definitive about which point is relevant. Mike *************************************************************************** PaddleWise Paddling Mailing List - Any opinions or suggestions expressed here are solely those of the writer(s). You must assume the entire responsibility for reliance upon them. All postings copyright the author. Submissions: PaddleWise_at_PaddleWise.net Subscriptions: PaddleWise-request_at_PaddleWise.net Website: http://www.paddlewise.net/ ***************************************************************************
Boy is my face red! Both Matt and Nick are correct, The boat does turn around it's COLR, not COF! I was using the wrong term. Just goes to show you what 34 years between classes and your first application of that knowledge will do. My apologies to everyone, I was suffering from an attack of CRS (can't remember stuff), an age related problem that, until now, I only thought affected my mother :-)) If you substitute COLR for COF in my argument, then I think everything holds together: 1. As you move forward through the water the COLR moves towards the initiation of the sweep, effectively reducing the lever arm and hence the amount of effort you are able to input to the turn initially, and increasing the amount of effort you get in the last half; and 2. The force the body is able to exert on the initial outward sweep with the arm extended over the shoulder is less than it can during the inward pull at the end of the sweep with the arm below the shoulder. At least it feels that way to me, and 3. Matts comments on pressure distribution are also right on the mark with a higher pressure at the bow and lower at the stern moving the COLR forward. And that's why the the first part of the sweep doesn't work as well as the last part. Thanks to everyone for their comments and corrections. I like a good technical discussion. John Blackburn *************************************************************************** PaddleWise Paddling Mailing List - Any opinions or suggestions expressed here are solely those of the writer(s). You must assume the entire responsibility for reliance upon them. All postings copyright the author. Submissions: PaddleWise_at_PaddleWise.net Subscriptions: PaddleWise-request_at_PaddleWise.net Website: http://www.paddlewise.net/ ***************************************************************************
At 11:37 AM -0800 1/9/02, John Blackburn wrote: > >The COG and COF are the same the same for longitudinal and transverse >axes, (not vertical though) otherwise the boat will trim/list until they >are, however the boat turns about the point where the volume of water >forward and aft of the COF are equal. The effort (force x lever arm) >required to rotate the hull is the same, no matter which end or anywhere >along the hull it is applied. Also the COG/COF changes during the sweep >as your body moves forward and back. Don't we have a terminology problem here? It seems like we are using COF (center of flotation) as the equivalent of COB (center of buoyancy). The COG (C. O. Gravity) and the COB will always be vertically aligned, but COF is the geometric center of the waterplane. I.e. if you made a paper cutout of the shape of the waterline, COF would be it's geometric center. COB is the geometric center of the submerged volume, not just the waterplane. COF is a center of area, where COB is a center of volume. As an extreme example to show the difference, imagine a bottle held underwater at a 45 degree angle so that just the neck is above water. The COF will be the center of the small ellipse at the surface, where the COB will be somewhere in the middle of the bottle several inches away from the COF. In a kayak the COF and COB tend to be close but they usually are not in the same place. COF is the location of the axis about which trim will change if you shift weight fore and aft. It does not move (much) when you change the trim where COB and COG do change substantially. Not trying to pick nits, just want to make sure we are all on the same page. -- Nick Schade Guillemot Kayaks 824 Thompson St Glastonbury, CT 06033 (860) 659-8847 *************************************************************************** PaddleWise Paddling Mailing List - Any opinions or suggestions expressed here are solely those of the writer(s). You must assume the entire responsibility for reliance upon them. All postings copyright the author. Submissions: PaddleWise_at_PaddleWise.net Subscriptions: PaddleWise-request_at_PaddleWise.net Website: http://www.paddlewise.net/ ***************************************************************************
> (i.e F=ma or the rotational equivalent M = I x alpha where I is the > moment of mass [equiv to mass but for rotation] and alpha is angular > acceleration), they'd get the same answer assuming they correctly > calculated the effects of where the center of gravity is relative to > their chosen center of rotation (i.e. recalculate "I" about the > center of rotation and not about the center of gravity) Soooo Pete, concentrate on the last part of your sweep when the boat is underway. ;-) steve Alder Creek Kayak & Canoe N 45º 39' 47" 250 NE Tomahawk Isle Dr. W 122º 36' 16" Portland, OR 97217 Web: www.aldercreek.com Phone: 503.285.0464 Email: aldercreek_at_qwest.net *************************************************************************** PaddleWise Paddling Mailing List - Any opinions or suggestions expressed here are solely those of the writer(s). You must assume the entire responsibility for reliance upon them. All postings copyright the author. Submissions: PaddleWise_at_PaddleWise.net Subscriptions: PaddleWise-request_at_PaddleWise.net Website: http://www.paddlewise.net/ ***************************************************************************
From: "Alder Creek Kayak & Canoe" <aldercreek_at_qwest.net> > Soooo Pete, concentrate on the last part of your sweep when the boat is > underway. ;-) Yes, I'm guilty of straying from the topic. Peter, I'll help you with your sweep if I can see it firsthand. What's the cheapest way to get from T.O. to Sydney? Island hopping in my kayak may be a bit excessive; then there's the problem of all that land between here and the Pacific.... Mike *************************************************************************** PaddleWise Paddling Mailing List - Any opinions or suggestions expressed here are solely those of the writer(s). You must assume the entire responsibility for reliance upon them. All postings copyright the author. Submissions: PaddleWise_at_PaddleWise.net Subscriptions: PaddleWise-request_at_PaddleWise.net Website: http://www.paddlewise.net/ ***************************************************************************
Nick Schade wrote: <SNIP> >>>>>>In a kayak the COF and COB tend to be close but they usually are not in the same place. COF is the location of the axis about which trim will change if you shift weight fore and aft. It does not move (much) when you change the trim where COB and COG do change substantially. Not trying to pick nits, just want to make sure we are all on the same page<<<<<<<< I was using the terms given by John (and I think how he meant them) and assumed that Center of Flotation was a term that was being used interchangeably with the Center of Buoyancy (which I think was what John meant too). After searching around in several books I couldn't find Center of Flotation mentioned at all. However, on searching for it with Google I see Nick is correct (or at least he agrees with the sources I found anyhow) and the Center of Flotation is the center of the waterplane area. I also continued to use the same abbreviations as John did for consistency although I believed that CG, CB, CF are the more widely used abbreviations. Sorry for any confusion. I guess I should have stayed in college. ;-) Without other forces acting on them I believe the CB and CG will come to rest on the same vertical axis. The Center of Flotation is of interest as it stays near the axis a boat will pivot around when it is pitching (rocking end for end) as well as being the axis for changing trim. In the future does anyone object to using nautical terms as defined at http://www.oneoceankayaks.com/smhydro/hydro.htm#lcb ? I think the excellent graphics on this site help make the definitions clearer. I disagree with several of the "design" sections conclusions or I'd probably have added and promoted this website with a link to it from our website long ago. Matt Broze http://www.marinerkayaks.com *************************************************************************** PaddleWise Paddling Mailing List - Any opinions or suggestions expressed here are solely those of the writer(s). You must assume the entire responsibility for reliance upon them. All postings copyright the author. Submissions: PaddleWise_at_PaddleWise.net Subscriptions: PaddleWise-request_at_PaddleWise.net Website: http://www.paddlewise.net/ ***************************************************************************
I had to check a naval architecture text to make sure I wasn't blowing smoke. I understood what Matt and John were saying, but figured some of the disagreement between them could have been due to misinterpretation of terminology. I have my own description of some of these terms at http://www.guillemot-kayaks.com/Design/ParticularDescr.html. I just added a few more abbreviations to the page because there seem to be many in standard use. And then of course there are different interpretations of what different abbreviations mean. Nick At 1:06 AM -0800 1/11/02, Matt Broze wrote: >Nick Schade wrote: ><SNIP> >>>>>>>In a kayak the COF and COB tend to be close but they usually are not >in the same place. COF is the location of the axis about which trim >will change if you shift weight fore and aft. It does not move (much) >when you change the trim where COB and COG do change substantially. > >Not trying to pick nits, just want to make sure we are all on the same >page<<<<<<<< > >I was using the terms given by John (and I think how he meant them) and >assumed that Center of Flotation was a term that was being used >interchangeably with the Center of Buoyancy (which I think was what John >meant too). After searching around in several books I couldn't find Center >of Flotation mentioned at all. However, on searching for it with Google I >see Nick is correct (or at least he agrees with the sources I found anyhow) >and the Center of Flotation is the center of the waterplane area. >I also continued to use the same abbreviations as John did for consistency >although I believed that CG, CB, CF are the more widely used abbreviations. >Sorry for any confusion. I guess I should have stayed in college. ;-) >Without other forces acting on them I believe the CB and CG will come to >rest on the same vertical axis. The Center of Flotation is of interest as it >stays near the axis a boat will pivot around when it is pitching (rocking >end for end) as well as being the axis for changing trim. >In the future does anyone object to using nautical terms as defined at >http://www.oneoceankayaks.com/smhydro/hydro.htm#lcb ? I think the excellent >graphics on this site help make the definitions clearer. I disagree with >several of the "design" sections conclusions or I'd probably have added and >promoted this website with a link to it from our website long ago. > >Matt Broze >http://www.marinerkayaks.com -- Nick Schade Guillemot Kayaks 824 Thompson St Glastonbury, CT 06033 (860) 659-8847 *************************************************************************** PaddleWise Paddling Mailing List - Any opinions or suggestions expressed here are solely those of the writer(s). You must assume the entire responsibility for reliance upon them. All postings copyright the author. Submissions: PaddleWise_at_PaddleWise.net Subscriptions: PaddleWise-request_at_PaddleWise.net Website: http://www.paddlewise.net/ ***************************************************************************
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