sail area vs ballast

in building a 1/3 model of america's cup racer 'stars & stripes' 87 i need to work out the sail to ballast ratio. i expect to reduce the sail area to approx 1/3 of what it was: full-sized boat had 1830 sq ft.. one-third of that is 610 and my plan [now] is for 170 sq ft. or so.

ballast ratio on these boats is very high [70%]. can i reduce the ballast to 1/3 of 70% in the same proportion to the reduction in sail area, or should i stay with a figure that immerses the waterline at a particular level?

if the ballast sits the boat on her waterlines and the sail area is protortional to the full-sized racer, will she handle the same regardless the amount of ballast? thanks

 

Sail area scales as size^2, displacement scales as size^3. So your 1/3 scale model would have 1/9 the sail area (203 ft^2) and the weight would be 1/27 (3.7%) full size to get her to float on her lines.

The moment from the sails is proportional to area times height of the center of effort, so the applied moment will be 1/27 full scale but the righting moment will be 1/81 full size, so there's no way the boat will behave similarly to the full scale boat. Somehow you need to produce 3 times the righting moment or sail it in half the wind.

This is a fact of life - big boats have comparatively more stability than small boats. That's why small boats are built with wider proportions than big ones.

The only way I can see for you to get anything like similar performance would be to hang a deep bulb keel and shorten the rig.

 

thanks again, tom. i may have to name this project after you.

i can see where reducing the draft can seriously affect this boat by raising the center of gravity. reducing the height of the rig, of course, will help to counteract this.

maybe, a gunter rig won't be necessary at all. a mast height of 15' and a sail area of, say, 150 sq ft may suffice. i'm just guessing, of course, because i don't have the design capability to work it out on paper.

my venture 21 carries 170 sq ft of sail on a 6'10" beam, albeit with 400 lbs of ballast on the end of a swing keel. dinghy hulled, it is a bit tender and quite fast. otherwise, i don't have much to compare the ac model with.

do you think it will be necessary to build a weighted swing keel or daggerboard or is there a way to shorten the keel i have [to reduce draft] and compensate with internal ballast? in other words, what happens to the boat's handling when ballast is raised a couple of feet.

 

I think you need to make some estimates of the expected moments from the rig and the restoring moments from the hull. Take a look at Larsson & Eliasson's "Principles of Yacht Design". It's time to crunch the numbers.

 

i surfed around and found some sailboat calculators but they didn't give me the righting moments.

one problem that i encountered was using the displacement value that you suggested to float to the lwl. if i understand correctly you wrote that the 1/3 model will be 1/27 the displacement of the full-sized boat, making it 2000 lbs approx [stars & stripes was 56000 lbs].

this seemed like a lot and the calculator indicated the numbers to equal that of a "cruiser," which this boat definitely isn't. i tried it at 1000 lbs displ. and the figures were more reasonable. this gave a displ to lwl of 163 and lwl to beam of 3.5.

at 150 sq ft, the sail area to displacement is rated at 24. do these figures sound reasonable? i'm over my head here and don't have the background to make these calculations. i tried entering the parameters of this vessel as close as i could on a chined hull boatbuilding program and i remember the prismatic coefficient as being 49, but i don't know how accurate that would be. how can i figure all this out? thanks

 

options...

I think that you are out of options. There's only three left...

1• Either you'll have to learn, it's not incredibly complicated, but pretty involving. With that I mean that if you have no prior knowledge of yacht design you'll first need to undertand the language, and figure out the basic information about your bot that the ballast and rig calculations are based upon. The important thing is to understand the relationships, the formulas can always (almost) be found in suitable books.

2• Pay someone to do the numbers for you.

3• Guess and try (not recommended).

My suggestion is buy some good books on the subject (Larsson Eliasson is recommended by me too) and study the sections that concerns your situation.

As with so many things in life, there is no fast lane...

Good luck

Erik

 

thank you, erik, i believe you are correct. option #2 is the most logical, but it will probably involve all three optiions.

even if i figure out the data myself, i wouldn't have enough confidence in my ability to rely on the answers, and even if a more knowledgeable person crunches the numbers it will probably involve some experimentation.

for instance, putting the boat in the water and loading her with ballast, then weighing the ballast, should give the amount to float her to lwl. more problematic is sail area and configuration, and ballast configuration.

a BIG question is the keel. locally, our lakes have been as low as 17% of capacity the last few years. this means the less draft the better, but we can't compromise the boat too much. so, i would like to stay away from the swing keel idea but i don't know...i can really use some advice here and the numbers combined with knowledeable opinions are the best ways i know to arrive at this answer. that's why this forum is so terrific.

 

I think the most important question to ask here is why you are building a 1/3 scale of the "stars and stripes". Is the goal is to have a boat that looks like just like the "stars and stripes" or to have a boat that performs like it, or just to have an exact scale replica? If the answer is more than one of the above, then you need to weigh how important each factor is.

 

performance is the major factor. the particular requirements of the 12-meter class dictate a short waterline with long overhangs. since a component of the boat i desire includes electric power, an efficient design in an upright position is optimum. since i also sail, an efficient design while heeled is also desired. imho, this design can offer both.

and where else can one find a hull design that represents such an expenditure of money and engineering than a construction model for an ac racer?

of course i will compromise the maximum design paradigm a bit by adding a small cabin, reducing the mast height, and changing the ballast/keel. that's why i'm soliciting the opinions of the more knowledable and experienced people who frequent this list. and thanks to you all, i'm learning a good deal.
i think tom's suggestion to "crunch some numbers" is where we are right now, but i don't have the ability. i have, however, ordered some books as suggested.

 

Elsewhere in these forums I've posted some stability equations and concluded that you can scale a boat by scaling rig, length, and fairbody draft by a scale factor x and scaling beam, freeboard, and keel span by x^(2/3). When scaling from larger to smaller this will result in a boat that is wider, relatively, than the original. If you scale the rig by 0.33 and the beam of the boat by 0.48 you should be in good shape.

If that's all you need to know then feel free to stop here so my additional remarks don't confuse the issue.

If you don't want your boat to be relatively wider than the original you can use this concept in some other ways:

You could scale from the full sized boat in the manner I suggest, calculate the righting moment of the resulting beamy model, then calculate the righting moment of a model that is scaled down using a constant proportion. Either add draft to the latter, lowering the CG enough to bring the righting moment up to that of the beamy model, or reduce sail area to bring heeling moment down by the proportion of the two righting moments.

Or you could select a scale factor x such that x^(2/3) = the scale you really want. Scale using my method, producing a model that is both beamy and shorter than you want, then lengthen it by increasing the station spacing (leaving the sail area at the smaller dimentions or increasing it just slightly). This will produce a relatively light displacement version. Further increasing draft will make it faster to windward.

There is a table of similitude factors in Larsson based on the work of Barkla (deceased) [Fig. 2.1 in the first edition]. The reason I take a different approach is that theirs holds the midsection constant, and in my experience the ratio of waterline beam to fairbody draft should increase as a boat gets smaller. I'd also note that if you were to scale the whole keel (not just the span) by x^(0.7), as they propose, the keel area of your model might be too large.

The bottom line is that if you want to maintain the same length to beam ratio as the original your model will need more draft and a lower centrer of gravity than a scaled down version of the origional in order to achieve the same relative stability.

If you hire a designer consider Bruce Nelson. He was one of the designers of Stars & Stripes '87 and has had the benefit of working with Laurie Davidson leading up to the last America's Cup.

Good Luck!

 

If you are looking for performance, that is a dead end. Those boats are not designed for speed but to beat a rule. Formula designers are more lawyer than architect. I mean no offense, it's just the only way win. A Hobie Cat will beat a full size America's Cup boat in any breeze. A short waterline with long overhangs is one of the techiques to beat the rule. A long waterline is fast, therefore is penalized. All boats designed under a formula try to make a relatively slow boat measure slower. Some of the development formulas are better, but end up with designs that have plumb ends and other extreme features.

 

thanks for the opinions, fellas. stephen, i'll try to contact bruce nelson. it is looking more and more like a swing keel is going to be necessary in order to achieve a balance btwn minimum draft and windward performance.

gonzo, of course a planing hull is faster than a displacement one and, yes, the 12-meter rule encourages short lwl. but this doesn't mean 12-meter boats are dawgs. on the contrary, they are built to designs similar to the great herreshoff and sparkman & stephens cruisers and racers of yesteryear.

the long overhang/short lwl has the advantage of allowing quick tacks, necessary in ac dueling. they were used on the old cruisers to help the vessel rise to approaching and following seas, making for a seakindly ride. as mentioned, i like the short and efficient lwl hull shape for electric power, as well.

i own a racing dinghy [enterprise] and it is a superior sailing boat but very "corky" as planing craft tend to be. i'm looking for a displacement craft with superior characteristics, not another planing boat, and i think the 12-meter boats were among the best designed. certainly, they were less compromised by their designs than the boats now being built under the new international america's cup rule. so, the point is: performance is not only how fast you go. it's, also, how the boat handles.

and the problem is: what has to be done to a boat designed to be three times longer than the hull we have to make it sail?

 

If you want performance in a displacement hull, whether under sail or electric power, the way to go is a multihull.

It seems to me your impressions of the 12 metre vs the IAC class or other modern types is backwards. The reason they went to the IAC boats was to get away from the limited performance of the 12 metre's.

Given the size of boat you're talking about, if you want classic long overhangs a Universal Rule boat will probably give you more performance than one built to the International Rule.

I suggest you go out for a sail on a modern multihull, say one of the Corsair trimarans, and see what it's like. There's no comparison with heavy displacement monohulls in terms of either performance or comfort.

 

yes, i've often been aboard my friends trimarans in mexico. sailing a 40' trimarans is like riding a basketball court, they're so spacious, but i never thought of them as displacement craft. maybe because they're so fast, they seem to be planing.

i guess it depends on what you mean by performance. if speed is the criteria, 'stars & stripes 88' proved what a multihull can do. but there are other criteria that only monohulls satisfy. my criteria is the hull i happen to have and limited funds to purchase anything else i might want.

i think of the 12-meter boats as a natural limitation on the huge j-boats that preceeded them. the current iac designs with their dinghy sections don't appear to be as capable in adverse conditions as the older designs, but they are much faster and, as you mentiion, that's a reason for the change. of course, if this was an iac hull i wouldn't consider developing it into a pleasure boat.

 

The J-boats were designed to the Universal Rule, and it promotes boats that are a bit wider and lighter in displacment than the International Rule (metre boats).

When we took the R-boat Pirate out for a spin before commencing her restoration, there was a Santa Cruz 35 out for a demo sail. She only had up working sails, so the two boats were not all that different in size or displacement, etc. We literally sailed circles around the Santa Cruz in the light, steady air.

You might have better luck scaling up the lines of Pirate from the pond model (available from http://www.r-boat.org), as the lines of the hull matched Pirate but the keel was modified to make the scale yacht sail properly. Your keel would be somewhat in between and the size of your yacht is much closer to that of an R-boat than a 12-Metre.