Wetted area vs. L/B at low speed.

Ok I've got for me what is a tough design question I'm trying to understand and am hoping for some insight.

I'm designing/planning a single person paddle craft in the genre of the wavewalk series of catamaran kayaks, and I am running into the dilemma of whats more important to speed for my use.: Wetted area or each each hulls length to beam ratio.

An article I found online ( www.oneoceankayaks.com/kayakpro/kayakgrid.htm#frianch ) makes it look like wave making resistance of narrow kayak hulls is not much at all ( under 1/2 lb of drag ) until you cross the 4 knot mark, wetted area being nearly all the drag until that speed.

Since my wife and I are not atheletes, I'm thinking by setting a max design speed of 4 knots, that I'm probably best off minimizing wetted area and making sure the cp stays in the low .60's.

With that in mind I calc'ed 3 different boats going from one extreme to another. They all displace the same, and are all perfectly round below the waterline, varying only in diameter, length, and at what point they begin to taper to each end.


#1__13 ft long, l/b 15.7:1, cp 0.62, wetted area 4957 in/sq, hull speed 4.8 knots
#2__9.2 ft long, l/b 9.1:1, cp 0.62, wetted area 4409 in/sq, hull speed 3.5 knots
#3__6.7 ft long, l/b 5.7:1, cp 0.62, wetted area 3654 in/sq, hull speed 3.0 knots

Besides #2 looking a bit funny and #3 looking REALLY funny, it does look like up to 4 knots #3 may be the easiest to move, except for that pesky l/b ratio which may well throw the whole thing off.
I have however, read more than once that the hull speed formula ( HS = 1.34 x √LWL ) doesn't really apply to catamarans correctly and should be adjusted up.

Thanks for any help/insight in understanding this.

Dean

 

A multi hull is almost surely going to have more wetted surface than a mono hull of the same displacement. Your Cp of 0.62 is characteristic of a very fast kayak or other human powered boat. A more realistic number is 0.55 or number in that vicinity. A boat with 0.62 is going to be very full at both ends and that is not the best deal for punching through a wave set. The fat ends do help avoid some of the pitching motion ( hobbyhorsing) that results from vigorous paddle strokes. Fat ends do contribute to pitching motion when paddling in a chop. If this is to be a serious cargo carrier in the Alaskan outback then OK for the large Cp.

A generality is to have the length to beam ratio somewhere around 5:1 more or less for a recreational kayak. A racer will have a lot larger number than that up to 10 to 1 or more but you have already stated that you are not athletes aspiring to Olympic status. Besides the ten to one type is so long and narrow that it is not much fun for general bird watching or other quiet pursuits.

A generality for a waterline in plan view is something like a long skinny parabola. That means that it will not be so fat at the ends. That is a compromise that takes into some wild assed account of wave making and wetted surface distribution.

A round bottom, round chine section is not the ultimate choice for mitigating wetted surface. ( Yes I know that I will get some flak from other members for saying that... but I can prove it) And rounded or cambered sections are certainly not the easiest to build either. A pure flat bottom like the ubiquitous Six Hour Canoe has the most wetted surface for a given displacement. A vee bottom is better but not the ultimate solution but the vee bottom does have some advantages in terms of structural considerations and eventual weight of the boat. Such a bottom is also not the most initially stable of the several choices. Kind of depends on the angles, displacement and other math fun and games.

 

Thank you for the reply!

What I took from it is that the best underwater shape would be a simple ( not to make! ) Parabola/Paraboloid?

Doing a quick calc gave me this:

#4__ 8.3 ft long, 7" radius, l/b 7.1, cp 0.50, wetted area 2952, hull speed 3.9 knots
#5__11.3 ft long, 6" radius, l/b11.3, cp 0.50, wetted area 3426, hull speed 4.5 knots
#6__ 13.5 ft long 5.5" radius l/b 14.72, cp 0.50, wetted area 3758, hull speed 4.9 knots.

Of these 3, it looks to me that #5 would be my best choice at 4 knots with a hull speed over design speed and less wetted area than #6. If that thinking is correct, the ideal would be would be about 1/2 way between #4 and #5, say 10.5 ft long, giving a hull speed comfortably over 4 knots with the least wetted area.

This craft will be used to explore rivers and streams mostly, with few significant waves. My biggest concern is that a paraboloid would have excessive rocker and with it insufficient directional stability.


I will be building this from glass over foam and own a hot wire cutter. I probably could do a true paraboloid by making a giant hand turned " lathe " and then cutting the finished piece lengthwise to make 2 perfect underwater shapes.

Thanks again for the help. This stuff is difficult for us newbs to fully understand.

Dean

 

Low Wetted Surface vs High L/B Ratio

In the Moth class before foils it was found that a section with more wetted surface but a higher L/B ratio was faster-see the notes and rough sketch below:

 

The parabola thing is just a general idea for the waterline as viewed from the top. You are quite correct that if the boat had excessive rocker it would not track well. Many good kayaks have a near straight keel line with only a little bit of upturn near the ends. Whitewater designs are a whole different deal because they need the ability to spin around within their own length.

Try not to get too deeply committed to the standard lore such as hull speed being a function of the square root of the length of the datum waterline. The physics of that rule is valid for certain types of hulls, not all types.

You can be pretty certain that a nine foot WL kayak will not likely be persuaded to go sq.rt 9 x 1.34. .....or 4.02 knots. More realistically something on the order of 2.5 knots for any extended period of time. Stretch the Waterline to ....say 14 feet and then you can probably maintain 4 knots for a mile or so if you are in fairly good physical shape. The 14 footer will glide between strokes while the nine footer will be less inclined to glide.

A really short boat is good for maneuvering and not much else except ease of storage. If you are into exploring tiny confined little gunk hole areas then a short boat is the solution. If you want to paddle with less effort and faster speeds then a longer boat is the ticket despite the wetted surface penalty. Why is that? Well a really short boat will necessarily be wider or deeper, or both, in order to satisfy the designed displacement. A longer one can be skinnier and will for sure be easier to propel and work more pleasingly than a stubby boat.

Conventional wisdom about wetted surface, prismatic coefficients, L/B, and D/L ratios and more is not to be ignored, however, there are so many variables about boats and hydrodynamics in general that we are well advised to proceed with a generous measure of caution. The application of math is reliable insofar as the math goes. Math does not lie. We do have to be pretty careful about how and when we apply our math to a case in which there are so many sneaky, large and small,l variables.

Sorry about all the pontificating DeaninMilwaukee. The best plan of all is to look at established designs for a serviceable kayak and stay pretty much within the same ball park. In fact there are some good plan sets for proven designs out there that are worth more than they cost.

 

Ok I think I'm following you. The parabola would have been tough to make anyway.

As you know, designing your own is half the fun, so I would like to do that rather than use someone else's plans. I am picking your brain here just to try to minimize design mistakes as much as I can, and thanks again for all the feedback.

Back to the original idea of all displace the same, and are all perfectly round below the waterline, varying only in diameter, length, and at what point they begin to taper to each end.

Adjusted to 10.5 ft to get hull speed over 4 knots I get:

#7__ 125" long, cp 0.54, l/b 10.4:1, wetted area 3651 in/sq, hull speed 4.3 knots

I think this is about as good as my plan form is going to get. I am hoping to keep total weight under 50 lbs. This version will use 10 cu/ft ( 15 lbs ) of foam with 4.4 under the waterline.

Dean

 

You make the sections perfectly round below the WL and the boat will be a bear to keep upright. That is if your boat is a monohull. Well OK if you are still persuaded to do a catamaran type, the round sections will be OK.

If you are doing a twin hull then you need to consider the interference waves that one hull applies to the other. In order to avoid the interaction of the bow and secondary waves you would need to keep the hulls separated by a considerable amount which make the boat not a practical kayak.

Weight is the enemy. Every pound of weight means that you have to push an equivalent pound of water out of the way. A 14 foot Guilemotte Tern model will weigh 33 pounds when built of 4mm okumee and sheathed with 6 ounce glass. Some of the Chesapeake Light Craft boats are in the same weight ball park.

Why not post a sketch of the boat you intend to build? We
can go from there with our conversation.

 

I will do that and thank you! I do intend to have bows like the wavewalk kayak to force the majority of the bow wave outwards. The spacing between my hulls will only be 12 " with a 36" total width. Until I have a proper sketch, check the wavewalk link to see what I'm emulating. : http://wavewalk.com/blog/new-700-series/

If you scroll down, there's quite a few images. Their hulls are not round bottom, but are otherwise similar to what I have in mind.

Dean

 

Ok. Here's my poorly rendered 3 view plus a foam model of an earlier version. Sharp corners and edges will be rounded in real life.


The model is similar, but it's proportions were 12 ft long with 10 inch wide hulls, now its 10.5 ft long and 12"wide. The seat is designed to adjust for and back on rails to allow the boat to sit level regardless of who's paddling.

Dean

 

Forgive this old curmudgeon for being so critical of your design work. No offense intended but I will venture that this design is not very promising. You have managed to make a complex building project when a more simple one will give you much better results.

A simple one is a monohull that is about 28 to 30 inches wide at the sheer line. the DWL width is about 26 inches wide if stability is the aim. Less than that, maybe 24 inches if a little less paddling effort is the aim. The bottom is not rounded. A flat bottom with chines beveled at about 35 to 40 degrees more or less. The bevels will be about 6 inches wide and rise about 5 inches. which gets the second chine above the waterline. Check out the wetted surface of such a simple section layout. You should be pleased with what you discover. Surprise? it has less wetted surface than a typical vee design.

The sheer line will turn up at the bow by several inches, the front ten or fifteen percent of the keel profile will turn up toward the waterline and the after end will also turn up a little bit. If you do not do that the boat will be difficult to turn.

Do not get too committed to minimum wetted surface. Do take that into account but it is not the summum bonum. When you get done with this simple design it will look a lot like a gazillion other kayaks and it will work better than the thing that you have drawn. It will also have more residual value than the catamaran when you decide to sell it.

If you are determined to build something different and are willing to take your chances with a less than optimum boat, then build what you have drawn. In any case, I wish you well and look forward to seeing pictures of the boat that you have built.

 

Thank you again for responding.

I do have a core reason for going to this more complex layout. : Very easy embarking and disembarking when dockside.
Secondary bonus, extra comfort due to not have to sit with your legs straight in front of you kayak style, plus the ability to easily stand and stretch at anytime.

In these points, my cat will do very well. The problem is to make it reasonably quick.

We already have some cheapy plastic kayaks, which are fun ( although very slow ) and have found through hard experience that my wife has a very difficult time exiting it dockside, with some tense moments entering as well.
Exiting, she needs to get a hold of something on the dock like a cleat and then worm her way up and out, ultimately body rolling onto the dock. Not fun at all. This problem will only get worse as we age.

With the cat design, stability is so high, she can just stand up and step out.
Check this wavewalk video, the one that inspired me to do a cat in the first place.
https://www.youtube.com/watch?v=bxQ4WTcmFUU

The wavewalk is reasonably quick and obviously very stable, so I want to build my own, optimized for our use.

Thanks again,
Dean

 

I finally got it in the water this past Sunday. Moved easily at 4 mph, ( gps), but didn't want to turn probably due to having no rocker at all. I am going to fix that this winter. It came in at 36.5 lbs.


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