[quote="$1"]
[quote="$1"]
... playing with fins in different ways the most significant thing was the size of the fin and its front to rear position in the box. [/quote]
MrJ,
My compliments, on the above observation. You are spot-on!
[/quote]
cheers Mr Thraikill! its nice to be acknowledged by an industry professional
[quote="$1"]
.....You didnt mention how much flex difference there were between fins and your style and types of waves. A heavier surfer that surfs hard on rail in steep surf loads fins a lot more than a light surfer, surfing horizontally in soft waves. Your mileage may vary.
[/quote]
yes, I'm a lighweight, slightly built, even footed with my surfing tending to be rather horizontal. My plastic fin observations made in powerful waves carrying a lot of water - Middle Peak Steamer Lane Santa Cruz. However these waves tend to be slopey rather than tubing.
[quote] I also believe discussions on Swaylocks have had an influence. Cheers. [/quote]
http://www2.swaylocks.com/forums/fish-fin-arrangements-please-explain
I posted my twin-fin/twinzer observations on the fish fin thread partly with this thread in mind.
this post was all based on experience rather than theory. I haven't been able to follow all the theory on this thread, however I think this thread has explained to me why the twin fin is faster than the single fin (short board comparison only) - the fins on the rail contain the water that would otherwise escape sideways?
Could someone explain to me why the thruster has more drive than the twin-fin?
From what Ive heard Lane is plenty powerfull. But again, you didnt mention flex difference in fins. Cannot over emphisize this. I can almost guarantee you that if you made two identical sets of fins for the same board and only varied the flex in the fins you would feel it. One might be better, one might be worse. None would be right or wrong, just different. There are few absolutes. There is a Lane guy here goes by CJ3 he should post about this topic...he's in the water almost everyday and experiments a lot...he knows.
On rail, a thruster has two fins thrusting, in a twin only one. BB explained earlier here that there are other affects going on with thrusters too. On rail, a quad has two fins thrusting too, but the second fin is better positioned to thrust. This last statement can be controversial, and there are reasons why, some valid, some not so valid.
I should note that making a good thruster is much easier than making a good quad. Experience really counts in making good quads. I was talking to a guru about this, he mentioned how Stretch's quads weren't positioned correctly during the time Stretch made shaper of the year and put quads back on the map. In essence, the marketing machine's "Quad King" wasnt making them optimally either. Then there is McKee who has a different arragement all together. Ironically, making a good single is not easy either. I was told when you can design and make a really really good single, youve graduated to a much higher level.
So which fin set up does what? Depends on who you ask!
[quote="$1"]
....................., I'll get right to the results, see next paragraph. For those interested, and I hope some are, and will want to actually check my model and numbers, please work though the iillustrations below. It's not a very complex model. It's crude, but hopefully not unreasonable.
.............
........
[/quote]
Overall I get it.
But there are two issues that bother me.
First:
Using Carswells data, you appear to be taking the positive lift coefficients for the referenced fin. His plots indicate max lift for the negative coefficients as well as a net negative lift at 0 deg AOA. Since this happens for both the calculated and empirical data.
I suspect, Carswell’s frame of reference is opposite to the conventional notation shown in your diagram. If true you, the negative lift coefficients represent lift identified in your model .
As a result the lift coefficients corresponding to your example would increase to a max of Cl= 1.5 at 30 deg.
Second:
As much as I like the BB diagram which indicates flow symmetrically radiating away from the tail of the board. I believe the pattern is not parallel to the board’s stringer and should be at some angle due to cross-flow created by traversing the wave or rotating the board during a turn.
I know you intentionally simplified this part of the model, so this should not be a ‘deal breaker’.
However, if the flow is allowed to ‘spread’ by equal amounts on both sides of the stringer, both side fins will generate the same amount of thrust. (yes/no?) and both are propelling the board forward.
Your argument leads us to believe that increased ‘shedding angle’ B will increase the net AOA (A) for each side fins and generate increasing thrust. ( sounds logical)
If each side fin is producing equal amounts of thrust while the board is traveling straight ahead. Does that mean thrusters improve the glide or top speed of a board, while traveling straight ?
If you tweak the bottom of the board to create more lateral flow (shedding flow B) at the tail and increase the Toe angle of the fins accordingly, are you flirting with a ‘perpetual motion’ design?
The extreme example of fins toed 90 deg would provide max thrust in the forward direction IF aligned with flow at the tail. Hard to swallow, huh?
Regards,
-bill
Hi Bill,
… reference
I used the flat side of the asymmetrically foiled fin as reference. I guess you could use the foiled side of the fin, it might be an interesting exercise.
Also, another point regarding Carswell's data, it's accurate, in that it likely reflects the important relationships, but I'm not sure it's meant to be used in precise design, as explained by him in the paper. His numbers are likely off somewhat, but I'm pretty confident that his relationships do reflect reality, and to some extent his numbers too, but with some caution. He also offers a correction factor.
… flow diagrams
I can't speak for BillBarnfield, but my guess would be that his diagram was meant to be suggestive or qualitative – basically a departure point, meant more to illustrate the nature of the way the flow sheds, though shed is my term. Perhaps he'll jump back in and clarify. That's why I wrote, the angle was not 'inconsistent' with that in his diagram.
… incident flow
Regarding the incident flow, I believe that you are right, and suggested as much in a prior post, see diagrams in a reply above to BillBarnfield. Admittedly, the diagram should have been done in 3-D. I am not convinced that the flow is shedding equally, or symmetrically, however. In general the orientation of a surfboard on a wave suggests otherwise. I'm inclined to believe far more is headed towards the wave-side rail. In fact, make that far far more, but without data, who knows. This would impact the thrust from each fin. So assuming such a condition exists, where the fins are providing different magnitudes of propulsion, and possibly one drag the other not – you get a sort of thrust differential. Again, I don't know at this point.
Also, if this kind of shedding exists, it really does change the way bottom contours, and the various fin gizmos, and fin configuration gizmos are actually operating, as compared to a non-shedding view, or a limited shedding view.
… perpetual motion
Yes, this at first glance does suggest the trap of a 'perpetual motion design', but here the power is from the flow in the wave. The force of gravity is the constraint -i.e. holds the board in place, its orientation adjusted by the surfer's posture etc. The problem is of course, if this was as useful as one might be lead to believe, you would likely see its application elsewhere. This is why, I suggested that it may be playing a role in a feedback mechanism, which has particular utility in surfing, see below. As the transverse speed of the board increases, the net direction of the flow will likely shift the contribution of the fin back into the negative region -i.e. where drag begins to dominate, as opposed to propulsion.
… taking it to its logical conclusion -i.e. applications
It is possible to find empirical or practical examples where taking the 'thruster hypothesis' to its full conclusion causes problems. That's why I'm inclined to approach it all as a series of trade-offs. As stated by a number (a lot actually, heck most) of people who have posted, a proper assessment of the value of the thruster configuration can not be made unless 'turning' is a part of it – a large part of it. Of course, that wasn't the point of this thread, but it rapidly became its point.
By the way, it should be stated that virtually any (reasonable?) fin configuration, from single to multi-fin configurations, potentially can, at some point during turning generate the kind of propulsion describe here – its magnitude and when it's likely to kick in. will differ based on design, of course. It's a part of fins do in general.
… staying connected
In a nutshell, I don't think speed is the real issue in surfing, acceleration is. That is, it's more important to be able to get to where you want to be, and stay there, then just going real fast. Shortboards addressed this issue, and the thruster configuration is an important option is that solution set. But it's not merely acceleration, it's staying 'connected' to the flow in the wave. Constantly, rocketing off is a pain, so different design elements have been employed which makes things more user-friendly, that is they will assist the surfer in maintaining this connection with less effort on his part.
kc
Added on 08/07/09... my apologies, I was slow in getting this finished... didn't think it required a new post.
That only considers the thrust/drag contributions of the fins. You can always lift the toe of the board up enough to make the flow positive AOA on both fins. However, the hull drag increases the more nose-up you ride. And that generally overwhelms the overall thrust/drag problem. Hulls ride with the least drag the more nose-down you angle them. This is often inconsistent with a thruster, in which the nose must be kept up enough so that fins are at positive AOAs because you are “shedding” strongly enough.
Again, there is a solution to this problem that allows you to keep three fins AND keep the nose down whenever you want to…if you can follow the logic it should do best in smaller waves where drag and thruster are more of the issue, and control is less of an issue.
Aloha Zeffenell
As you noted, my drawing was a super simplified image to try and get people thinking about the true water flow splitting and flowing off both sides of the board, rather then common surfboard theory being so singularly influenced by the all to familiar image, of the water coming off of one side of the board at an extreme angle to the centerline. When in reality it is flowing near equally off both sides of the board at once. And of course out the rear! I used a symmetrical view and hoped, as this discussion has, to expand on that as needed. But if people couldn't accept the simple view it would be very hard to discuss anything further.
In my drawing, there is a central line drawn around which the water "splits". It wasn't meant to be absolutely rigid nor was I intending to say that all the water flows exactly this way all the time. I was mostly just trying to establish it's existence first. I am in agreement with you that this splitting of the flow, doesn't always sit in the dead center of the board. The split is mostly regulated by where the riders downward force is located on the deck side. Depending on the rider then, the splitting of the flow will be happen in different places during different rider positions or manuevers.
To support and balance the downward force of the rider there must be a reciprocal upward force from the water that is centered underneath the rider to counter balance him. So, if the rider is pressing the rail deep into a bottom turn he is having to overcome the buoyancy of the board and the lifting forces of the water underneath the board. He will also have to sink the tail deeper then the nose to engage the rockers arc so as to turn the board. This will cause him to shift his downward force further back on the board and more to the inside rail.
The reciprocal or counter acting upward force from the water will then also shift underneath this area of the board where the downforce is. And my drawing, if I were redrawing for this situation, would then have the red lines shifted so that the center of the split, would be off center of the board and somewhere under the downward force.
But even in this situation. The water flow would still be upward, backward and outward as my original drawing shows. Just the center of the split and it's angle on the board would be a bit different. And I don't think it would be as different as some might think.
[quote] However, if the flow is allowed to ‘spread’ by equal amounts on both sides of the stringer, both side fins will generate the same amount of thrust. (yes/no?) and both are propelling the board forward. [/quote]
Yes! I don't think the thrust would be exactly the same but pretty close depending on the specifics of the turn. See my newer drawing below. It is hard to draw to proper perspective so hopefully everyone will understand the drawing. The tail is shifted into the wave so the fins are all viewed at odd angles. The tail fin doesn't have Cant. As you can see there is significant flow hitting the side fins on the inside sides. The compression ( for lack of a better term at the moment) of the water between the fins and board bottom provides exceptional lift to counter the riders down force. The Cant and Toe In allows the water to expand rapidly (for lack of a better term) out the back of the board, such that tremendous thrust is gained with little drag.
[img_assist|nid=1044473|title=Water Flow 2|desc=|link=none|align=left|width=640|height=480]
Janklow, this is why I wouldn't use the term tip drag as I don't think there is very much drag compared to the other forces. And while there is surely some drag that term sounds too negative for all the positive stuff that is happening.
[quote] Your argument leads us to believe that increased ‘shedding angle’ B will increase the net AOA (A) for each side fins and generate increasing thrust. ( sounds logical)
If each side fin is producing equal amounts of thrust while the board is traveling straight ahead. Does that mean thrusters improve the glide or top speed of a board, while traveling straight ?
If you tweak the bottom of the board to create more lateral flow (shedding flow B) at the tail and increase the Toe angle of the fins accordingly, are you flirting with a ‘perpetual motion’ design?
The extreme example of fins toed 90 deg would provide max thrust in the forward direction IF aligned with flow at the tail. Hard to swallow, huh?
Regards,
-bill
[/quote]
I can't answer for Kcasey and please excuse my butting in....... But I don't subscribe to often stated opinion that tri fins are slow going straight. Besides the fact that one is vary rarely going perfectly straight, if ever, I think a properly designed and set up tri fin, is always faster then a single fin. When we were making the switch from single fins to tri fins and the fin positions hadn't been fully sorted out yet there were many problems. So as I have mentioned before, I just kept grinding the fins off on the same boards and each time changing only one or two factors. I tried every possible combination multiple times on multiple boards till I felt they were surfing well and more importantly, I understood what each change or factor actually did to the performance of the boards. Did it all without the math too! Ha!
I am not much into the math, I am more into "tank testing" and my tank just happens to be exceptional for this purpose. One of the things we all complained about was that the boards were too fast and were very hard to get to slow down for tube rides and such. Pressing down on the tail of a single fin stalled it. Pressing down on a tri fin accelerated it! We all got used to this in time and were able to add more rocker and narrow up the tails a bit more and change our surfing to suit the added speed of the boards. Once I had the fins sorted out, I never had complaints about tri fins being slow going straight or otherwise.
Whoops Double post deleted
Hey Bill that new diagram is a KEEPER! Thanks for taking the time to sketch it.
I like the tank too...I'd much rather use the tank than the calculator.
THis model is confusing. Vs to too steep and at zero AOA there is still lift and even less drag. But Im not a math guy.
That model would more likely match a top turn, not a bottom turn. At the top, you often slow down during sharp turns, but now youve got tons of potential to work with.
There is way too much emphasis here regarding thrust to the point of mentioning perpetual motion. Geez guys, the energy comes from the gravity/wave and the surfer's ability to harness this energy. Thrust happens when there is enough kinetic energy and this only happens when wave and potential energy has been converted.
Perpetual motion? Tow you and your board behind a boat on the flats. Let go of the rope. You'll slow immediately and sink.
The whole point of modern fin setups is to provide just enough thrust (or a lot depending on your taste) to 1) overcome the effects of drag and 2) to compensate for energy losses at the bottom of the wave, making modern hi-perf surfing possible. Modern hi-perf surfing has mostly to do with creating and mainting kinectic energy, which comes from capturing it from gravity and wave. Fins is what makes this possible. As I stated before, fins are energy transducers. Certainly not perpetual motion machines.
The whole point of modern fin setups is to provide just enough thrust (or a lot depending on your taste) to 1) overcome the effects of drag and 2) to compensate for energy losses at the bottom of the wave, making modern hi-perf surfing possible.
Actually that's incomplete.
1. directional control
2. hold
3. facilitate maneuverability
4. overcome affects of higher drag (ie more thrust) from setups that provide improved #3
5. compensate for energy losses at the bottom (energy transducing)
but I digress.............
The reason I have issues with these models is that as far as I know, no one has ever accurately determined what angle "B" is. And B appears to be one of the central issues if not THE central issue. So either you assume various values of B or just guess. Either way, you dont really know for sure. I gets even more complicated when you look at both rail fins and also consider that the outside fin is in and out of the surface water AT THE SAME TIME. That's why Im a firm believer in using 'the tank' and just 'believing' what you feel. Whether that belief is right or wrong is really the basis of argument of this thread, putting aside ignorance.
IMO, BB's intuitive knowledge of the subject matter is undeniable. And he makes cool sketches most of us can understand....Kudos!
EDIT: B also varies with depth/distance away from board as well!
EDIT2: B also varies with speed!!! I wonder how high we can count the variables!!!!!!!!!
This is an interesting thread. I’ve read almost every attempt to disect how fins work. I can agree however that “believing what you feel” is the way to go. I don’t want to stray too far from the subject but I personaly spend about 95% of my time on a wave doing turns. Weather it’s a bottom turn or a cut back or a snap(Yes the right amount of cavitation is nice at times). The board is on rail 95% of the time. Personaly I design a surfboard first (Rocker, template, thickness, bottom design, foam flow) then choose the right fins to compliment the design. Every surfboard has a certain arc that it wants to travel. Placing the fins that allow the board to travel the arc of turn it wants creats a hydrodynamicly effecient partnership between the two.
I would love to read a dicussion about rocker, bottom designs and template as that is what mostly makes a board work. Bad rocker flow or a board that is too thin would have a far greater effect on drag then bad foil on fins.
MW
By the way, I enjoyed looking at the cool diagrams. =)
Great thread.
Seeing this photo brought it to mind , so i thought I’d add it for fun.
Probably copyright , used without permission from NZ Adventure Magazine .
That shows clearly that the bottom is the main lifting/control surface.
Also it shows how thin the sheet of water traveling across the bottom is, and its force vectors.
Which makes it obvious how little effect the sheet hitting the outside fins has, relative to the volume/mass of all the water and work the bottom and submerged fins are engaged in.
M_Woo, I see that you are a new member – welcome!- but a friendly word of advice, use the reply button under a post if you want to direct your comments to that post. This isn't mandatory, but unless you do, you might have a situation where some kook decides they are directed at him... like here... and start spewing.
on turning in general...
Turns don't generate force, force or forces generate turns. Irritating huh. A statement like that has got to start the eyes glazing. But it's true. The term 'turn' is used to describe the consequence(s) of an application of a force. Turn describes a change in the direction of some motion, but it takes a force to change the direction of motion.
[img_assist|nid=1043289|title=.|desc=|link=none|align=center|width=560|height=411]
Figure 1 is a diagram I've used a number of times to illustrate a typical wetted surface of a board on a wave. And when I've done so I've usually then gone on about the forces of planing, see figure 2. Planing refers to the forces developed on an solid object by a moving fluid, in this case the liquid water, but also on an object which has a particular kind of shared contact with two differing fluids, in this case water and air.
[img_assist|nid=1043290|title=.|desc=|link=none|align=left|width=429|height=530]
Believe it or not, but these two diagrams also apply to the kind of 'on rail' turning I believe you're referring to. Planing is still the issue, but now the angle-of-attack of the bottom surface relative to the flow is very high. In fact if you took the diagram in BillBarnfield's post (the colorful one in this thread) and rotated accordingly, you'd basically have simplified first attempt at an illustration of a high angle-of-attack planing -i.e. a surfer 'on rail' at some point during a deep bottom turn for instance. Or just check out the pictures posted by NuclearFishin, and those aren't even a bottom turns.
So depending on what you believe is making a board turn, we may or may not have much to say to each other, or for that matter how to relate rocker, template, bottom contour or fin configuration to turning. But that shouldn't stop you from posting or replying, heck, it has never stopped me.
By the way I kind of agree with your last statement on what makes a surfboard work, but I'm inclined to believe that design in general has moved beyond the rudiments, and is now mostly concerned with making surfboards more user-friendly. That's not to imply there's some book somewhere that's going to explain the fundamental dynamics - though opinions would appear to differ on that. Nevertheless, if you want to move beyond just pure “creative?” guessing, I believe having some basic physical model in mind can be of great value. But again, opinions seem to differ on that too.
Anyway, welcome.
kc
nice shots… they are fun… came in handy too (see post to M_Woo)
kc
Aloha Kcasey,
Mahalo for your tips on the reply! Do you design surfboards? Your mathmatical skills are awesome! You have surfboard design down to a mathmatical formula! =) If you do design surfboards I was just wondering if you create a mathmatical formula formula for every custom shape you do? Or is that just guess work based on what you know based on Weight X hight X skill X waveX foot size?
The subject here in this thread is like starting a conversation about religion or oil! haha. I’m just curious. Are you sure of all the variables in your formulas? Is there anything left out? Water is such a unstable variable considering that we are sometimes even riding through foam. What water temp. are your tests based on and what speed is the board going? I’m sure density in water changes with temp. Also chop, wind speed and if the wind is off shore or on shore must play into this. Then, how much board are you dealing with? A 9’0 or a 5’8? Also, How much curve the template in a board has and where the apex is in realtionship to the rocker. This has a direct effect on how the board goes on rail. The last photos of Dave is a great example of " balance" in a surfboard design. Looks like a quad set up. What ever it is the rail is burried up to the nose. Sick shot.
My point is is that there are soooooo many variables in what maks a board work. You could NEVER figure it out with math. It’s like trying to disect soul. You coud never bring up a discussion about only fins or a fin set up with out laying down all of the varibles.
Just a simple question. How fast does a normal surfer surf?
Sorry if I’m a newbie on swaylocks. Just came across it lately. Been shaping for sometime though.=)
I’d like to ask you a really great question. What percent in your opinion does each of these variables make up a surfboard. In order and percent. Rocker, template, bottom design, foam flow, fin setup.
Complete respect in what your discussion is about and you seem very passionate about the math behind surfboard design.
Mahalo,
MW
“Do you design surfboards?”
I haven’t touched a planer in a little under ten years. In fact
last year I sold off my last few rolls of glass, a bunch of other
build related stuff, and one of my planers.
“Your mathmatical skills are awesome!”
You flatter me, but if my mathematical skills were that awesome,
I suspect my answer to your next question would be different. And
anyway, its not really about the math, its more about the physical
approach. And my skills in that area are equally un-awesome.
“You have surfboard design down to a mathmatical formula! =)
If you do design surfboards I was just wondering if you create a
mathmatical formula formula for every custom shape you do? Or is that
just guess work based on what you know based on Weight X hight X
skill X waveX foot size?”
I have no mathematical plug-in model of the kind I believe you’re
referring to. But if you meant do I have a physical model in mind,
that is having some idea of what makes a surfboard go, which you can
relate to design, and maybe take forward, yes I guess I do.
“The subject here in this thread is like starting a
conversation about religion or oil! haha. I’m just curious. Are you
sure of all the variables in your formulas? Is there anything left
out? Water is such a unstable variable considering that we are
sometimes even riding through foam. What water temp. are your tests
based on and what speed is the board going? I’m sure density in water
changes with temp. Also chop, wind speed and if the wind is off shore
or on shore must play into this. Then, how much board are you dealing
with? A 9’0 or a 5’8? Also, How much curve the template in a board
has and where the apex is in realtionship to the rocker. This has a
direct effect on how the board goes on rail. The last photos of Dave
is a great example of " balance” in a surfboard design.
Looks like a quad set up. What ever it is the rail is burried up to
the nose. Sick shot.”
It’s only akin to religion or oil(?) if you want it to be. If you
want to design boards that move though foam, that somehow deal with
changes in water density, surface tension, etc. or something that
surfs well in chop – go for it. But, I’m arguing that you’ll be
that much farther ahead with some basic understanding of the dynamics
involved. Then again, maybe not – so just start guessing – it has
worked in the past.
“My point is is that there are soooooo many variables in what
maks a board work. You could NEVER figure it out with math. It’s like
trying to disect soul. You coud never bring up a discussion about
only fins or a fin set up with out laying down all of the varibles.”
Life is modeling. All is abstraction. Sounds mystical, but its
not. An abstraction captures essentials, but is never complete. If it
was complete, it would be the thing it’s abstracting. Even your
memories and experiences are incomplete. There is always a level of
detail which goes unnoticed, undocumented, unrecorded. So don’t trust
your memories or experiences? Also, because something is incomplete
now doesn’t mean that it will continue to be, at least become less incomplete in the future.
Still, I don’t see anyone anytime soon coming up with a formula
for a surfboard design, especially one based on first principles. But
so what? Because you can say that something is incomplete, only means
just that it’s incomplete. If you’ve decided that there are just too
many variables, then the job is done for you. Let the kooks who think
otherwise waste their time, and vice versa.
“Just a simple question. How fast does a normal surfer surf?
“
I don’t believe surfing is about speed. I believe it’s about
being able to get to where you need to get in the right amount of
time – or in a word, acceleration. The velocity of breaking wave is
constantly changing, as is the flow up its face, and as is the surfer
riding on its face – its all acceleration. The move to shorter
boards addressed this issue, as have many of the other design
elements which now are commonly found in surfboards, like multi-fin
configurations.
“I’d like to ask you a really great question. What percent in
your opinion does each of these variables make up a surfboard. In
order and percent. Rocker, template, bottom design, foam flow, fin
setup.”
Bottom (area) surface comes first, but constrained by an optimum
width range. That is, empirically the width range (maximum) of 50
centimeters plus or minus, seems to be what we humans like, (based on
what we like to do when surfing), the exact value depending on the
kind of conditions the board is being design for, and for whom its
being designed (“whom” as in the kind of surfer the designer has
in mind.) The minimum surface area, though it depends on
conditions, seems to fall around .4 meters squared. Also, start with
something flat, finless and virtually without volume… and then add
whatever it takes to make it work for you or for whom you had in
mind, that is give it the right amount user-friendliness (which by
the way is relative.) In the picture below, I think the hat is
optional (at least I think it’s a hat?), but I’m sure opinions will differ.
“Complete respect in what your discussion is about and you
seem very passionate about the math behind surfboard design.”
One of my passions is surfing, and when I not surfing, another one
is thinking about surfing. I would like to be building too, and
hopefully will again soon. But as it relates to my posts – that I
tend to be a bit more physical in my approach. is probably something
that just comes with the package…people are what they are.
By the way, questions are great, and I’m flattered that you seem to
have had a number about me, but I don’t speak for nor represent
Swaylocks or any of its members, well, other than myself. Hopefully in
the furture you won’t hold back on “assertions”, you know the
kind of statements people may actually find they differ with. It’s not the only
kind of exchange that happens on this forum, but its definitely one
of the ”fun” kind.
kc