Designing a 9 meter sailing catamaran

@RX, OK, I understand. Thanks for the spreadsheet! The daggerboard will be rectangular (to keep the slot closed). But I suppose I can use the tapered formules when I use equal root and tip chord lengths. Therefore thickness will be equal over the whole board (but I will diminish crown and increase web towards the tip).

A few questions:
About inclined plate theory: when I use Cd and projected area (sin(alpha)) I get force in the long direction of the plate? The force I'd want to know is sidewards ?
was studying the spreadsheet, but was wondering:
What is Hollmann moment? Tried to find it on the internet, but couldn't find anything.
On the simplified page: modyfied moment is the moment corrected with non-lift related forces? What is the factor 2,25 in cell G25?
Adaption for my purpose: the spreadsheet uses 4,5 g (because it's a plane). I can set that to 1 and add the other forces.
Other forces: daggerboard is almost at CoG so pitching won't be a problem. Heaving does as the board is slanted outwards (above) by 15 degrees. Could I say that heave acceleration is 1 g?
Loads by rolling are rotational? So load on tip is higher? Could I calculate this by the difference in sideforce by a wind gust? With or without lever arms?

 

@Niclas, I didn;t knew of the calculator. And yes, doing it yourself gives more insight. But good to have a tool to check!

 

Pammie- For rectangular shape or constant chord, the formula is M=W x n (x^2/2B - x/2 + B/8). That is the part I accidentally erased. The standard method for a uniformly loaded cantelever beam is shown on the last page of the spreadsheet.

I first used the inclined plate theory when calculating the wind pressure on an inclined roof. It is downloadable from the net. I used a Cd for a flat plate which is less than 2 for a flat square plate.

Hollmann was a composite aircraft designer and has a doctorate degree. He was our consultant and according to his autobiography, was a consultant for NASA. I use his book (though outdated) as it contains most of the basics that holds true to date. Most calculations are now expounded with the modern explanations (and accuracy) but his book covered every aspect.

The spreadsheet gives 4.5 g as a sample. It is a measure of force that your body will encounter when subjected to vertical/rotational acceleration. It is also used in Class Rules. Your boat was designed for 2g at the LCoG I believe, in the condition you will operate on. Forward or aft of the centroid, it will be more according to the Rules. I haven't visited yet the rudder design.

Once you have established the loads and dimensions of the panel, you can use the LR or ISO method of tabulations and the required FoS for the material going to be used.

Heaving causes a load on the boat/appendage. That is vertical acceleration and covered in the Rules applicable to your design. Not in ISO I think. If slanted outward, the projected area will be minimal but you have to add this to the forward velocity pressure. If a standard foil shape, it is still a flat plate.

Rolling will be best calculated if you can find the roll characteristic of the boat when acted upon by the sail and dampened by the daggerboard. Might be minimal but counts a lot if you have a long slim daggerboard (like an Oar or a Paddle).

You are correct that rolling is rotational and the tip gets a greater load. You can average using the centroid of area. I recall the Wn for a triangular load/shape is Wn/3 (centroid) and Wn/2 for rectangular. You will notice that in standard cantelever formula Wl^2/2 in the spreadsheet load diagram. I guess for accuracy, we just have to plot the forces of a rotating body (propeller or oar) but that complicates things a bit. Until we do the calcs we would not know if it we have to increase the load factor.

 

I am attaching a method of construction comparing metal and composites. The rudder stock or spar is sized to handle all of the bending and shear loads, the skin to handle the pressure at the supported span. Usually, when the rudder has a high aspect ratio, ribs are inserted in between to reduce plate (skin) thickness. In composites, the aft spar provides stability for twist (torque).

The nose is heavily reinforced as it receives most of the impact and diminishes towards the stock/spar. The trailing edge receive some reinforcements also as it is thin. The skin thickness is sized according to dimensions of supported panel and its distance from the Neutral Axis.

 

Pammie- Do you have ISO 12215-8 Rudder? Might help in establishing baseline. I just browsed thru it but it seems it is not as detailed as we are discussing.

 

Yes I have. Had a quick look at it, though I used Larsson (which is based on ISO) for dimensioning the rudder stock and bearings. Rudder will be underhung 0,18 sqm each; tapered; naca 0015 to 0012. Rudderstock is 40 mm AISI 630 (with 315 sleeves) from Jefa + self-aligning bearings. Haven't designed the exact skin yet, but don't expect problems with that. 12215-8 will be helpfull with that. The reason I want to focus at the daggerboards is that I have access to CNC miller during Christmas holidays. I need those to be able to finish the daggerboard casing and the hull.

 

Preliminary daggerboard area is going to be 0,8 sqm.

I've been thinking about forces by rolling: Rolling with two hulls in the water has the rotation centre in the middle and a long (more or less perpendicular) distance from the daggerboard. Rolling over one hull (lifting a hull by windforce) goes very slow. I expect smaller than 30 degrees in 3 seconds. For the middle of a 1,6 board that means 0,4 m in 3 seconds.

 

One hull lifting out of water due to wind gust or setting of sails can be 1.5 second as seen on videos. Roll center would be just below the waterline. If the daggerboard is long, forces could be substantial. At the tip, angular velocity is much higher. The load diagram will change. Higher load on the tip (higher velocity) and lower load in the root (decreasing velocity). The reverse of a diminishing load towards tip (tapered wing).

Wing loads (airplanes) are like that. In straight flight, the wing supports the total weight. When banking, the load changes while rotating from the roll center. This is measured in negative/positive g's. This is probably the reason why the moment diagram is different from standard load diagram in the textbook.

 

Dear Pammie, experts and happy go lucky amateurs including lurkers ;-)
As always I am amazed at the amount of invaluable expert advice contributed. I hope you don't find this to be a hijacking post. You seem to keep up a good pace and have already moved on from hull preassures to rudder and board calcuations. Despite that, I was wondering if I might ask few questions, and add a few snippets of info. In the spirit of this thread of contributing detailed knowledge to amateurs of structural requirements and calculations for the construction of a boat/cat.
Like Pammie, I am trying to construct 9+m catamaran, and determin (calculate, adhere to rules or find benchmarks) the structural requirements. Only I am not sure if I will be able to actually build it. But at this point the learning part is the most omportant to me. The main difference to Pammies design, is that I have opted for a bridgedeck and 2' extra length.

Anway, even if this site has proven a veritable goldmine for quality info and links to papers, guides and other resources, I still haven't really found any complete descriptions of loadcases used for multihulls. So if someone would happen to have a link or a document to share, I would absolutely love to read it. Below I will try and attach 2 thesis papers from the reputable Chalmers technical institute, first one about slamming loads vis avi core materials, interestingly comparing calculations for ISO12215-5 with DNV among others. Second a partial FEA load case and laminating schedule optimization for a 24m racing trimaran. In this paper it was interesting to se the variation of fiber schedules fore to aft as well as the, to me, astonishingly high resulting loads on the deck areas. I have notices that the bows of multihulls fore of the main beams, seam to be an area of extreme stress (with many high profile cases of failure in large racing multis).

In the linked youtube fotage from a helicopter filming IDEC Sport Ultim trimaran (2016), at 1:23-1:26 into the video, you can really see the bow flexing sidways and then bounce back at a resonating frequency. Probably the kind of loading in large being responsible for those failures. The torsional flexing is often clearly visible in this kind of fotage, but not as often the bow flexing like in this example. Thought this might be of interest especially to you Pammie
Those posts are getting a little to long, so I'll take other questions i a new post. Hmmm...... second pdf to large... I'll se if I can find a way to work around that....

 

Ok, upploading the 2nd thesis as one text pdf, sorry for the sloppy layout. And then adding 5 screen shot size jpgs with all important tables and illustrations gathered. 2,3 and 4 being the most relevant. Table and illustration nubers left in text so it will be easy to find the coresponding ones in the jpgs. Hope it can be of interest.

 

Ok, so here are 3 questions.... i think. 1) I get the expert advice that one should pick one rule set and stick with it. Eg, 12215-5 vs 12215-7. But as a complementary calculation for trying to get a more in debth and accurate understanding of loads and safety factors, there are a pair of variations I would like to consider. 12215-5 rules for monohulls use panel loading formula that uses the hul width. The calculation Pammie upploaded in the spread sheet use hull width 1,1m. I am guessing th 4x0,275m value stems from one hull being max 0,55m at waterline and half a hull being 0,275. As pointed out it would make sense to take into account that the panel loading is individual to each hull. There for it would make sense to calculate 3 loadcases with different weight distributions between the hulls. Eg, 50/50, 75/25 and 100/0. As the formula for Pbase use the square root of displacement, it actually doesn't generate excessive values at asymetric hull loadings using 0,55m (individual) hull width, compared to using the width of both hulls. But still higher than the original 12215-5 ones. Also, with a 100/0 load distribution, a larger part of the panel will be submerged. Although I'm not sure if that impacts what panels should be calculated as below water line??? Does it make sense to do this?
2) Slamming loads depend a lot on angle and curvature of panels, but also on width. But usual loads on the bottom of hull from slamming, shouldn't be a problem, at least for panels on sailing cats. The global loads and fatigue resistance of the laminates might be more of an issue. But I am espescially interested in the slamming forces generated by braking waves i force 9-10 sea state. Those rougue super position ones that come from nowhere and wack the boat, sometimes even at an angle 45 degres off the main wave pattern. The effects seem brutal, sometimes making boats look more like a boiled egg thrown against a wall. That's why it's one of my main concerns for structural strength. If we put some of the most important factors aside, seamanship being one of the major ones, and make the asumption that the crew is making ideal desicions, letting us focus stricly on the engeneering aspect. I guess cats, especially those without keels, are somewhat different to monos in this respect. Pros, they tend to be faster surfing downwind and reducing speed difference between boat and breaking crests, reducing windspeed over deck, and also make steering easier if speed is kept throug water. 2, It can slide sideways more or less if boards are up. 3) Can accelerate fast even sideways, spreading the impact over time and generating less g. Cons, cats have larg deck areas and high freeboards= voulnurable surfaces often quite flat. Also if lightweight, it may also decellerate faster than a heavy balasted mono. What do you think of a rough estimate calculated as follows. Scenario: unexpected heavy winds not forseen in weather forcast. Not possible to outrun. Caught offshore. 9 Bueafort with gusts at storm strength 50 knots. Significant wave hight at around 25 feet (having long fetch). Meening there will likely be a few rougue ones at 45 feet. At those hights wave length is usualy around 10-15 times hight if still building, a little more up to 18 times for the lower waves. Say around 144m wave lenght. wave speed= period= square root of length =12m/s or about 24 knots. In most scenarions one would run bare pole with a drougue of some sort. If actually sailing with the wind on the beam, boards down, the risk of getting a nasty wack would be higher, and more likely situation in lower sea states but then again with similar speed difference between wave and hull as for running i larger waves (for small cats like Pammies, and my hypothetical one). In these conditions, the boat will be at its slowest in the wave valley after having had a wave pass under its hulls, then accelarating as the next wave catches upp, maxing at arround 12 knots average at the "drop in zone" near the crest, and then decellarating again on the back of the wave, slowing to around (guesstimate) 6 knots minimum. If the cat gets it bad, only accellerating half way, before getting smacked by a nasty breaker, there would be a speed difference of up to about 15 knots beween crest and boat. Do you think that would be around right, or way of as a guesstimate? Also, I ignored the possibility of the wave breaking from above, faling down on the cat, as cats are generaly quite high, and the breaking part of a 45 feet wave mostly isn't higher than the freeboards, (guess) making the impact horizontal. Any ideas on what loads that would be expected. As far as I understand, the impuls should be spread over a period of acceleration of the boat and dispersion of the wave around the object. Seems like a tuogh one to calculate. My best idea would be to make a drop test of the cat, fully loaded on its side from arround 2,5 meters. d=1/2*g*t(square) where t=v/g and estimated delta v beeing around 7m/s (14-15 knots) Then again a breaking crest should be less dense and disperse easier around the boat as it is mixed with some air and not surrounded but water like the patch of water in a drop test. Maybe making it possible to reduce hight for drop test to 1,5 or 2 m. Incidentaly 2m is the drop test option hight for CE marking small water craft, to avoid the hastle of all these calculations ;-) Any ideas, if I'm way off?
3) Pammie, you used a sestate coefficient Kdc 1, and craft type coefficient Ncgnh 1,2 as a base for panel loads. May I ask you what the definition for those values are. I first thought Kdc was given i Beaufort numbers.... but that was obviously way off :-D Do you think those values you chose, would be the same for me on a 9,9m bridgedeck offshore capable cat with max displacement around 2400kg?
Please accept my appologies for the long posts... I dont know why, but I allways do this.... don't know why i'm so lousy at keeping it short and neat :-/

 

@Niklas, all very interesting but I can't afford to have a look at it. After allmost one year my first hull still isn't finished. The engineering takes quite some time for me so can't do sidesteps and have to focus. If you need any specific information please ask.
Most rules use the concept that if plate load is OK, then so is structure. If you want to make big hulls don't worry about structural analysis anyway and don't mind about a few kilo's more. And if I may give an advise: buy a design, don't do it yourself. It takes a lot of time when you have to build the experience first.

 

Rolling forces V2: speed of the tip through the water. At 1,6 meter 30 degrees is 0,8 meter side ways movement in 1,5 second. So max speed is about 0,5 m/s. If the whole board would move at that speed as a flat plate F= 1025/2*0,8 (m2) * 2 (Cd) * 0,5^2 = 102,5 N. So can be ignored.

 

Rene: in your post #93, first line, between W and n: the x is x or a multiplier? I think last. This formula you mention is this the complete formula? For tapered is much more complex?
The adapted shear formule is WnCx/At-Wn/2. Correct?

In the calculation for shear the total height of the spar is used. But shouldn't that be the spar height minus crown and base height? When I compare to Annex H (12215) for stringers: this uses interlaminar shear stress between the plies for the shear in base and crown, and material shear stress in the web. Or is this incorparated in the formulas?

I changed the formula's to metric. In my situation: W = 2 * daggerboard load, B = 2 * length outside trunk.

I suppose I can calculate the part in the trunk at the same way, while ignoring the rigidity of the case itself?

See picture of my spreadsheet. Or spreadsheet itself.

A full (foolproof) board in max condition would be much to heavy. ISO12217 allows to reduce sailplan when this is described in the manual. Too much sail is just as dangerous as too much daggerboard depth. Or is there a (any) Rule against this? Question ofcourse is at which speed to reduce board? Boat speed at which to take first reef?

 

I can understand that you wish to learn and understand more.....reading the rules in more depth, will assist matters.

This is not accounted for in those rules.
This is what is considered a once in a life time wave and if you are to design for that....as such, there is little point in trying to look at panel sizes and angles and the loads for these panels. The loads from rouge waves will make the scantlings of your boat significantly different from any typical prescriptive set of rules like that which you cite.

You need to decide what is more important for you...your SOR...and design to that.