Prismatic Coefficient

I really do´nt mind cc or dd as long as the diver stays submerged.

 

I'm rather hoping he'll re-surface actually. I'm intrigued as to how he was going to justify some of his ideas....

 

If he is like many of the "others" on here, he'll just wax lyrically and metaphysically about...well take your pick, Daisy's, feelings of sadness, the cool breeze etc etc...and never answer and/or justify the comment...or even understand how to debate and discuss technical issues.

 

I've heard of this curve, but never actually seen it - do you know where I can get hold of a copy?

I have of course tried googling, but the only "Paris curves" I found were related to crack growth...

 

Well, Will, I guess I assessed you incorrectly, you are curious like a fishwife, hähh?

 

Not really, there is also an article about Paris Hilton and Rihanna in same dress shocker...

 

hehehe

 

And celebrities have nice curves or so the media would like everyone to think, one of my daughter in-laws was shocked to see I didn't know of Paris Hilton
But to business not idle chatter we have boat deisgn to discuss here

Probably a bit obscure for the internet.

Ship science papers, proceedings etc, J Paris a US Naval Architect has studied successful displacement craft and produced some useful guidelines on hull resistance. I will have his papers somewhere.

But it ties in with a knowledge of naval architecture so forgive the tutorial.

Boat design is always a compromise since there are always conflicting design paradigms however for the easiest driven hullform the simple approach is as follows

Choose the vessel parameters Length Draft Displacement Beam operational speed define a mid-ships section choose a half angle of entrance and a prismatic coefficient, autohull generators are in their element here.

Note for boats ideal (resistance related) Half angle(Ha) of entrance at WL is given by a general formulae approximately 50-(40 X SLR) where SLR is the speed length ratio but not much benefit going below around 9 degrees.

Sail boats differ from powered vessels and this is where Mr Paris comes into the picture he related ideal lateral plane coeff to Cp from observation of existing hulls.

Lateral plane coeff (CLP) is the immersed lateral plane area divided by LWL*D where D is depth of keel. Usual treatment of rudders in the area as for CLR include unless it’s a spade rudder, don’t include centerboard areas on CB craft etc.

Since series like the delft series are just the canoe body and in reality there are obvious idiosyncrasies with real vessels he suggests an ideal Cp for a related CLP as shown in the attached image from Teale which saves me plotting the data.


Suggestions for good books to read would be Yacht design by Gutelle. Creative naval architecture Smith, How to design a boat, Teale probably a few others. Trouble is when it comes to easily driven hulls most NA's are shy of sharing their findings since we all compete. Paper was by JE Paris.

Heavy displacement boats can be made reasonable performers with some knowledge. I have posted before on trawler resistance , there's some good info on trawler hull design which was also relative ( but not the new rule beaters).

I hope that helps anyway and I'd be interrested in what anyone else thinks too.

 

I graduated as a Naval Architect more than 20 years ago and have been designing yachts ever since. But I'm nevertheless happy to say that there's still a lot to be learnt!

The half-angle-formula was also new to me! Thanks!

 

And back to the original question. Please explain in ninth grade terms what the hell is prismatic coefficient? I'll take a stab at it as follows.............

Suppose you have a boat has an LOA of 36 feet, the beam is 8 feet, the static draft is 1.5 feet (18 inches). The immersed part of the boat would fit into a box that had dimensions of 36 x 8 x 1.5 feet. Find a block of wood that is 36 inches by 8 inches by 1.5 inches. Now we have a slug of wood that is a one 12th scale replica of the box into which the wet part of the boat would fit. Get out the saws, knives, and planes. Begin to whittle the block of wood into the shape of the boat. We are making the wet part of a model boat here. Save every chip or bit that you have removed from the original block. You could weigh or somehow measure the chips against the weight or measure of the original block of wood. If you had carved a displacement boat, the chips would come to somewhere between 40 and 50 percent of the original block. Let us say that the chips are 45 percent of the original. That leaves the wet part of the boat at 55% of the orginal block. You have a Cp of 0.55.

A little reflection about percentages of wood left after whittling will give you some insight into this concept. If the Cp is small, say 0.50 (we are talking displacement boats here) you can be sure that the ends are pretty sharp. Whereas if the Cp was 0.60 you could know that the ends of the boat are pretty blunt or tubby. A perfectly rectangular box would have a Cp of 1.00 because you have not removed anything from the ends. Why do we care about Cp anyway. Well there have been some pretty smart dudes that correlated Cp with speed. A kayak for example has a very low Cp and it operates very well in the realm of speed that one is able to paddle. As propulsive effort increases, perhaps with oars, or mechanical propulsion, then Cp ought to be somewhat larger than the slower boat. That means that the ends will be a bit fuller.

Planing boats will have a fat or flatter, wider section near or at the transom. Of course the Cp will be much larger as a result.

If you know or can can make a ballpark estimate of the Cp of a boat you can do preliminary design work on a cocktail napkin while you sip your martini. Please note the use of the words "ballpark estimate". First layout the mid section of the boat. Ain't that what we usually do? Take the measured area of the wet part. Now multiply by the Cp. You get a smaller number which is some where near the average area of the sum of all the section areas. Multiply by the presumed LWL and you have the total displacement of the cocktail napkin boat. You can do these calculations backwards by guessing at the total displacement of the boat that you intend to design. If the Cp is predetermined more or less you need only calculate the cubic capacity required to float the load. Divide that number by the LWL you have the required area of the mid section. ...almost....but not quite. You have to build the Cp into this deal. For example : if you needed an average section area of 500 square inches , you still must calculate the mid section correspondingly. That is to say divide the average section by the Cp and you will have the approximate area required for the mid section. 500/0.55 = 909 sq, inches. The simple math is fun and once you become familiar with the usual Cps of various boat types you can make you friends crazy while you sketch semi viable boats on cocktail napkins.

 

messabout - nice explanation, but in the first paragraph, I believe you're describing block coefficient- the fraction of the imaginary block occupied by the boat- as opposed to prismatic coefficient, where you start with a block already cut to the shape of the midship section.

 

Unfortunately you are confused here this is not Cp, read the earlier explanations

 

The "Paris Curve" and the half angle formula both exist, but I doubt many people who successfully design boats would use either.

You can see more about Cp and the Paris Curve here, from pages 95 to 100:

http://books.google.com/books?id=U0...&dq=how to design a boat#v=onepage&q=&f=false

 

Marshmat and Mike: Thanks for the heads up: Block vs Prismatic. I do know the difference and I delivered my explanation clumsily. That is misleadinmg for prospective readers who may not be up to speed about such stuff. I will attempt to be more careful next time. My only defense for this transgression is that I can type faster than I can think.

To set the record straight; The subject wood block is, first, to be formed from end to end in the exact shape of the mid section. Then and only then would you weigh or otherwise measure the beginning block of wood. Now the whittling and subsequent measuring of the chips will reveal the overall departure from the shape of the end to end mid section.

"The road to hell is paved with good intentions"

 

The half angle hypothesis has been mentioned by several authors, Gerr among others. The concept was chewed on at length by the early catamaran afficianados. Half angle influence was generally attributed to Newtonian physics with respect to acceleration of a particle. As in F=Ma. Supporting evidence is found in the performance comparison of long skinny boats and short fat boats of similar power.

Half angle may be influential but it is not the only thing with which we can agonize. The displacement curve may very well be influenced by the half angle. And the displacement curve is influenced by the prismatic or visa versa. Worse still, the mean water flow path rears its' ugly head when the boat is heeled or indeed when it encounters a wave set. When heeled most boats will exhibit a curved mean water path. More acceleration variables are to be considered. What the hell, there is also de-celeration to think about.

So it can be said that alphabet soup plays into design considerations. A/2, Cp, S/L, D/L, Dcurve, MFP, etc .. All that is fine but what about really big boats like a VLCC. They have nearly blunt bows. Where is half angle now? They have bodies that have almost the same section shape from stem to stern. That'll make the Cp approach unity. The only thing those beasts have going for them is long LWL, high aspect ratios and a lot of Maersk money. Maybe it is the money that trumps all the other stuff. All this is great fun to contemplate on a cold winters night.