~~PACIFIC BEE~~ STABILITY
POST # 31 HOW LIGHT IS LIGHT ENOUGH ?
Laurent wrote;
Sven,
The question I am asking myself though is; how far do I have to go?
Aloha Laurent,
So, i.e. how much light is “light enough”?
This in relation to the calculation of proper RM versus construction weight
I think you have 2 sorts of light enough ;
- A. The total platform relative to driving power SA /Displ ratio
This can simply be derived from a spreadsheet containing all figures from existing proa’s.
I suggest make one, I used Jzerro as benchmark , and upgraded Pacific Bee as far as realistic.
53ft UNAMA has say 20% better figures as a starter.
If you donot respect those figures ; you will obviously have a slow proa. that would take away the fun of the pacific proa concept.
- B The lightness of the ama & beam construction to seek a high variable RM range.
This is the most important feature of proa design. It makes or breaks swiftness ,sea/wave handling, safety, on board comfort ,and does away with an otherwise ugly loaded platform and helm issues.
Another way of putting this lightness is design displacement percentage 75% vaka displacement , 25% ama displacement .
But this approach does not work if you have a very variable RM [ RMvar] , if you make up a RM spreadsheet or a RM diagram for that matter you get a max & min RM figure, so now you can design the ama displacment volume according to the RM related loading .
So although you initially may design the vaka & ama to a certain displacement volume , it does not mean that you have to load the ama to that waterline constantly.
Note ; as soon as the ama leave the water ,that ama/beam weight [including all waterballast] shall be added to the vaka weight in the spreadsheet. My RMvar spreadsheet calculated all RM “as if the ama is just soaring”, hence the ama displacement volume for the RM calculation is not important.
The ama displacement is important for reserve buoyancy [backwinding incidents] ,[ballast tank volume]
Other considerations - The Proa at rest shall show a high ama [ tanks empty] , with all interior beds floors tables, countertops –level-
- how light, is light enough. ; the simple answer is ; you cannot go light enough [within construction safety considerations]. But a very very light construction will become , due exotic materials very expensive.
For 53ft UNAMA we will use; [a moderate expensive construction]
Vaka & Ama certified plywood ; Bruynzeel being the best quality , next best Joubert . combined w/ RedWestern Cedar & Sitka Spruce .
Decks light plywood ,Corecell ,plywood sandwich. Local reinforcement blocking in way of fittings.
Beams A-grade Sitka Spruce. Carbon fibre battens + local carbon fibre reinforcements. [ see Bieker Brown system]
Mast; A-grade Sitka spruce & local Carbon fibre reinforcements. End result is stiffer,stronger & lighter than full Carbon.
interior , light aircraft plywood.
- As for RM , first make the proa platform as light as structural realistic , than fiddle around with RM, with waterballast [be sure to build in enough tankage] ,till you find a nice balance to handle the driving force.
design the rigging loads to maximum reachable dynamic loads + safety factor.
- Lightness versus use. Is it to be a speedster, weekender , passagemaker, charter platform…… it are decisions which obviously influences the choice of design ,hence material & weight.
A very very quick pacific proa is unfortunately automatically an expensive one. , so it is obvious the balance needs to be found between expensive building materials, say; full carbon and cheap junk plywood.
The “enough” material answer also lies in checking out Jzerro against Pacific Bee [ex Cimba]. Jzerro was build a fair bit lighter than the original Cimba . The first few years I could simply not match Jzerro’s speed, now after lightening & changing many things, and also increasing the power a lot, Iam finally near the speed of Jzerro, [with the ultimate check the speedo which reads sustained speeds of 18 to 18,5 kn this in slight to moderate waves]
Can we derive ratios from this to upscale Pacific Bee or Jzerro ? Hmmm, IMHO the answer shall have to be no. upscaling to the bigger proa at 53ft it has totally different lines and ratios, also the ultimate speed will not be much quicker , it will reach that speed easier and remain in that groove longer, as such the average is higher. Example; in close quarters Pacific Bee outperforms Des Jours Meilleurs, that’s proven. But on a long stretch he will gradually pull away from me for sure.
Bottom line is ;save every pound you can find, specifically in the vaka construction. i.e. have a strong keel system, lighter topsides and deck/wing. Small interior stuff & gear , get them really light.
Ama & Beams have to be very strong , especially the ama gets a lot of abuse & pounding.
More pacific proa’s can be found too heavy than too light
Ok ,so far. [I think most of this you knew already]
Cheers Sven
Thanks Sven!
I have put together a spreadsheet with information that I could gather on different proas and made nice graphs etc, to compare… I agree with you that the scaling up and down is always a source of worry…
I understand the concept of having a variable righting moment depending on course and windspeed and how much canvas you carry.
The hard part I am struggling with is to find a rule of thumb formula, realistic enough to be meaningful, to calculate the heeling moment of the wind in the sails… If I know the surface area of the sails, the shape of the sail and the windspeed, how much heeling moment (T.m or lbs.ft) does it generate?
Instead, I am using some formulas that estimate at what wind speed you will lift the windward hull out of the water. It is clearly stated as approximate by the authors.
The one I use is from Kelsall and is;
Stability = 15.8 x squareroot(D x CLtoLeeCL / (SA x He))
Where:
D is Displacement in lbs
CLtoLeeCL is distance between the Center Line of the boat to lee hull to Center Line in ft (for catamaran or proas, for trimarans, it is from main hull to ama)
SA is Sail Area in sq.ft
He is Height of the center of effort of wind above WaterLine in ft
OBVIOUSLY, it has to be adapted for proas!!! The Centerline to lee hull centerline is clearly an estimate of the distance between the CG (which is supposed to be on the centerline of the craft for anything OTHER than a proa) and the center of buoyancy when you lift the mainhull or windward hull. For proas, instead we have to take Ama CL to Vaka centerline x % displacement on ama. This is the distance between the true lateral position of the CG
and the vaka centerline.
That stability number is supposed to be the windspeed at which you will lift the windward hull…
Do you have a better way to calculate the following:
“with this sail plan (surface area and shape), and this windspeed, I will generate a heeling moment of so much”.
That is what I am lacking…
Cheers,
Laurent
PS: I am also considering right now a 25% displacement in the ama, with 370 lt of ballast full, for a total displacement, ballasted of 2.7 tons, on a 45 ft, with 20.5 ft CL to CL…
Do you have a better way to calculate the following:
“with this sail plan (surface area and shape), and this windspeed, I will generate a heeling moment of so much”.
Laurent,
Another formula to look at is in John Shuttleworths article “Multihull Design Considerations for Seaworthiness”:
http://www.john-shuttleworth.com/Articles/NESTalk.html
“Stability in wind.”
Cheers
Rob
Am I correct that, even with a very basic and strong construction, the ama should be well within the 25%?
Am I correct that, even with a very basic and strong construction, the ama should be well within the 25%?
Aloha Mark
75% vaka 25% ama volume will be a good starter for the Rm spreadsheet [ as long as the submersed ama = 120 % volume [ for safety]
cheers Sven
Thanks Sven!
Aloha Laurent
I understand the concept of having a variable righting moment depending on course and windspeed and how much canvas you carry.
The hard part I am struggling with is to find a rule of thumb formula, realistic enough to be meaningful,
I wouldn’t bother to much about trying to find that right formula, IMHO the spreadsheets ; Rm & proa will compare best , and will give you that meaningful data.
OBVIOUSLY, it has to be adapted for proas!!! Correct !!! as such they don’t work
That stability number is supposed to be the windspeed at which you will lift the windward hull…
Do you have a better way to calculate the following:
“with this sail plan (surface area and shape), and this windspeed, I will generate a heeling moment of so much”.That is what I am lacking… As I decided to approach this matter in a different way, I don’t bother about all those formulas which in the end [ real world of handling the pproa platform] do not apply
In [real life] I simply , type down the sail setup , next I register the ama lift , and amount of waterballast , so you gather data to evaluate over say a year. by that time you know precisely , in relation to the true wind, how much power you want to generate for the next trip. add sails, add ballast , Voila…..again , you have enough driving power versus displacement , next thing is to sail it , and find out which suit of sails fit best versus the amount of waterballast pumped in or out.
Cheers SvenCheers,Laurent
PS: I am also considering right now a 25% displacement in the ama, with 370 lt of ballast full, for a total displacement, ballasted of 2.7 tons, on a 45 ft, with 20.5 ft CL to CL…
Hey Laurent,
If you wanted to roughly estimate the heeling moment, then you need (1) the amount of lift the rig produces and (2) the position of the center of effort. Estimating (1) is pretty easy:
F = 1/2 * rho * v^2 * c_L * A
I’d recommend doing it in metric units, and then converting it back to foot-pounds or whatever you need when you’re done. (Unit conversions are easy to do with google; just type something like “5 newton meters in foot pounds” and it’ll calculate it for you; in most cases you will have to type the full name of the units for google to recognize it).
F = lift in Newtons
rho = Density of the fluid; dry air at 20°C has a density of 1.2kg/m^3
v = flow velocity in m/s (the speed of the APPARENT wind)
c_L = lift coefficient, for a bermuda rig with a small jib I’d use something like 1.6 for the jib and 1.0 for the main when close-hauled. If you are using a genoa, the c_L for the genoa will be lower, maybe something closer to 1.2 - 1.4. The values in the literature vary widely on that point.
(2) You can get a rough estimate of the height of the center of effort by simply multiplying the height of the jib by ~0.4. If your main has a large gap beneath the boom, then you should add that distance seperately, but for the main you can also use the same factor of 0.4 times the height of the luff of the sail, and then add the height of the boom to that. Then just multiply the lift of each sail by the corresponding height of the center of effort, and you have a rough value for the heeling moment for each of the two sails. Add them together and you are done. If you want a more detailed and accurate procedure, then I recommend having a look at “Principles of Yacht Design” (around page 158).
Sven is right though that any sort of estimate is going to be pretty rough; thorough simulations (which only an expert can do properly) or actual measurements on the full sized rig are the only way to get the real values. That said, the procedure above will get you in the right ballpark.
I hope this helps!
Cheers,
Marco
POST # 31 HOW LIGHT IS LIGHT ENOUGH ?
Mast; A-grade Sitka spruce & local Carbon fibre reinforcements. End result is stiffer,stronger & lighter than full Carbon.
Aloha Sven,
I am near to placing an order for a HM carbon mast for my 9.5 metre proa currently in build. However I would love to know more about your proposal for using carbon reinforced spruce???.....I would love to save some cost, I like working in wood and labour time is not a big issue if I get a better overall result….
Current mast size is 85mm ID with 3mm walls.
Cheers,
Rob
Marco,
That’s exactly what I was looking for.
I knew the formula below, but I did not have any idea of what value to use for the Lift coefficient. For the height as well, 40% seems reasonable. I have seen lower values like 1/3 of mast height in other litterature, but obviously it will depend as well on the main sail shape, fully battened with fat head vs. “traditional” triangular shape, for instance.
Lift coefficient is for the… Lift force, which by definition is perpendicular to apparent wind direction, and we should look at drag force, but I am sure that the drag coefficient is much more difficult to assess… Anyway, on close haul, lift force is most definitely a good approximation of the heeling force.
I will have a better look at “Principles of Yacht Design” as well.
Thanks,
Laurent
Hey Laurent,
If you wanted to roughly estimate the heeling moment, then you need (1) the amount of lift the rig produces and (2) the position of the center of effort. Estimating (1) is pretty easy:
F = 1/2 * rho * v^2 * c_L * A
I’d recommend doing it in metric units, and then converting it back to foot-pounds or whatever you need when you’re done. (Unit conversions are easy to do with google; just type something like “5 newton meters in foot pounds” and it’ll calculate it for you; in most cases you will have to type the full name of the units for google to recognize it).
F = lift in Newtons
rho = Density of the fluid; dry air at 20°C has a density of 1.2kg/m^3
v = flow velocity in m/s (the speed of the APPARENT wind)
c_L = lift coefficient, for a bermuda rig with a small jib I’d use something like 1.6 for the jib and 1.0 for the main when close-hauled. If you are using a genoa, the c_L for the genoa will be lower, maybe something closer to 1.2 - 1.4. The values in the literature vary widely on that point.(2) You can get a rough estimate of the height of the center of effort by simply multiplying the height of the jib by ~0.4. If your main has a large gap beneath the boom, then you should add that distance seperately, but for the main you can also use the same factor of 0.4 times the height of the luff of the sail, and then add the height of the boom to that. Then just multiply the lift of each sail by the corresponding height of the center of effort, and you have a rough value for the heeling moment for each of the two sails. Add them together and you are done. If you want a more detailed and accurate procedure, then I recommend having a look at “Principles of Yacht Design” (around page 158).
Sven is right though that any sort of estimate is going to be pretty rough; thorough simulations (which only an expert can do properly) or actual measurements on the full sized rig are the only way to get the real values. That said, the procedure above will get you in the right ballpark.
I hope this helps!
Cheers,
Marco
Hey Laurent,
If you wanted to roughly estimate the heeling moment, then you need (1) the amount of lift the rig produces and (2) the position of the center of effort. Estimating (1) is pretty easy:
F = 1/2 * rho * v^2 * c_L * A
There’s a handy calculator for this on Wolfram Alpha at: http://www.wolframalpha.com/widgets/gallery/view.jsp?id=75ef1bba53e412ef97e4a241fa588ddd If you can’t cut and paste this go to Wolfram and search “airfoil lift calculator.”
I use a rule of thumb, actually an isolated case, as a touchstone/shortcut: At a lift coefficient of 1.0, a 17 kt wind will create a force of 1 lb/sq ft of sail area. You can check this on the calculator; it’s accurate. Now, if you want to consider a change in lift coefficient or area, it will effect the formula linearly—100 sq ft will develop 100 lbs force. If you want to change wind velocity, there’s a squared relationship; half the wind speed (8.5 kts) will yield 1/4 the force, double the wind speed (34 kts) will quadruple the force.
For hydrofoils, as water is 800X as dense as air, you multiply the force by 800 and the touchstone still holds.
Another rule of thumb, only roughly accurate, is that the resultant force from a boomed sail is perpendicular to the boom. This is usually accurate to ~4-5 degrees which is pretty darn inaccurate for calculating, but good for interpolating photos, plus gives you (and any student sailing with you) a decent handle on just what the sail is doing, and how the resultant’s direction effects sailing.
Last, many multihull designers don’t do precise calcs on the rig’s drive, but rather work backwards from the hulls’ righting moment. We know this precisely under two conditions, knowing only the mass of the boat and its center of gravity. First is at rest, where RM = 0. Not very helpful, but it holds up one end of the line when you graph it. 😊 The other is when the ama just flies, where RM is at its maximum and is precisely equal to mass times the distance between CG and CB. It is possible with only this to “guestimate” power from the rig necessary to exceed max RM and therefore the biggest rig you need consider for a given set of conditions.
Dave