Prismatic Coefficient

[hwsiii]

I understand props very well and most analysis of hulls, but for some reason I cannot seem to get it straight in my head on how to figure the prismatic coefficient of a hull form.
For some reason I seem to have a mental block that precludes me from understanding something so simple as this.
Could someone please explain this in 9th Grade english so I can get the jist of what I am missing.


H

[Mark Van]

Start with the area of the mid ship section. Multiply it by the LWL. Then take the volume of the actual hull. The prismatic coefficient is the ratio between those two numbers.

[MikeJohns]

The ratio of the volume of the displaced water to the volume of an imaginary shape made by extruding the largest cross section to the fore and aft static waterline extents.

In feet and tons its
(D X 35) / (L X A)

D is displ in tons multiply by 35 gives feet^3
L is LWL in ft
A is largest Xsectional area in ft^2

Cp is a very important measurement for the design of a hull and it should be chosen with care to match the operative speed length ratio for a displacment hull.

[Alik]

Prismatic coefficient CP is ratio of:
- volume displacement of hull (V) to
- volume of prism based on midship section, with height equal to waterline length (LWL)

CP=V/(w*LWL)

where w-area of midship section

[PAR]

Designers use several of these cute little things to help them understand the shape and employment of the hull type. What the prismatic coefficient does more then anything is tell the designer how fine the ends of the yacht are.

By way of a prismatic coefficient, there will be specifically targeted ranges for this coefficient on a particular yacht's S/L ratio, depending on it's expected performance envelope. It's part of the volumetric game playing, utilized working out an ideal underwater set of shapes, to incorporate into a specific set of design parameters. Did this help?

[rwatson]

Helped me a lot - thanks guys :-)

Once question - why do they call it a Prism ? is that because the 'midship section' is irregular (not necessarily square), though the theoretical 'top' of the shap would be flat (waterline)

[Alik]

Prism does not need to be square at base.
As well as cylinder does not need to have round base...

[MikeJohns]

For interest here's a plot of the design target relationship between CP and speed ratio for displacment craft.

For sailboats look also to the Paris curve that relates lateral plane and Cp.

[Ad Hoc]

If you're not so good with words...how about pictures?

[hwsiii]

Ad Hoc, can you please post the formula with that diagram.


H

[marshmat]

Care to explain/justify that generalization, ccdiver?

[daiquiri]

Displacement Hulls are misplaced on the water... as are their theoretical design formulas... They should be confined to museums where they are safe..
It is a very truthful summary ,of the character of displacement hull boats, and the nature of the theories that are the premis of their design.
Ccdiver, it depends... on what you want to achieve.
We are slowly and steadily going towards a future where oil wil be less and less available. So the energy efficiency will be a primary goal for ships and boats, not the speed. That's where displacement hulls are still unbeatable, if you consider the construction costs too.

Actually, we will probably have to move some models out of museums and put them in the water again, because some really efficient hulls have been created between the second half of the 19th and the first half of the 20th century, before the advent of planing V hulls.

[rwatson]

Displacement Hulls are misplaced on the water... as are their theoretical design formulas... They should be confined to museums where they are safe..

Oh sure - 85% of the worlds vital resources are moved by displacement hulls, and I prefer a boat you can put some gear in too.

And to intimate that displacement hulls are not safe ????

have you had a couple of heavy nights recently, need to get something off your liver :-) ?

[daiquiri]

I was not even talking about commercial vessels, but the savings there in going to planing designs would be even more massive. And you can carry a load ,,,

I would like to learn more about it. Can you elaborate or give an example?

[rwatson]

No need to get personal just because you are wrong watson..

I put a smile after my personal remark - but maybe you can tell me where I am 'wrong'

[apex1]

But faster is the point when the weather suddenly changes and you need to scramble for safety !
.

And that is where your philosophy shines? When weather suddenly changes, you are safer with a faster, lighter boat? Are you sure?

Costs of construction and materials for displacement hulls are more than double that of composite boats,


Joke of the week.................and then:


With all the materials laid out and the molds ready, I can single handedly build a composite planing hull less than 30' long in less than two weeks.
.

Well, that was a good one!





say for a first grader................

[PAR]

The lack of design experience and practical understanding is clearly evident here, Richard. Grandiose generalities on such a scale, that renders us all fools and uninformed, suggests we're all out of step but him . . .

[daiquiri]

Simple...
...

If I understood your words right, you are talking about a 40'x16'x3" box? And where do you go with that "boat"?
Could you please say few more words about the seaworthiness of that hull?

[apex1]

The lack of design experience and practical understanding is clearly evident here, Richard. Grandiose generalities on such a scale, that renders us all fools and uninformed, suggests we're all out of step but him . . .

;) We are Paul..........................;) Must go back to the asylum now, my nurse is waiting with the milk soup.

[Willallison]

Yikes!!
All that study... how could I have got it so wrong.....?;)

[Ad Hoc]

hwsiii

From the diagram, the longitudinal Cp = Volume / (Am x Lpp)

Volume = volume of hull at draft T
Am = midship section area (at given draft T, in figure)
Lpp = length between perpendiculars

[apex1]

Yikes!!
All that study... how could I have got it so wrong.....?;)

You did study??? To hammer a boat together you must study??? What did they tell you?
But now must really go back, they otherwise eat my milk soup and I will have no lullabye.

[apex1]

Sail your scows that you had to take out a mortgage on to spend a few weekends a year on, I'll fly on by in mine, that I built for less than your down payment, and spend 365 days a year on.. LOL

Good idea sugar!

And do´nt forget to leave the black, round thingy where it is, while you are sailing your fast built, advanced composite liveaboard racer!!!

That is the most important item in your dream..................








it is the bath tub plug!

[Willallison]

You did study??? To hammer a boat together you must study??? What did they tell you?
But now must really go back, they otherwise eat my milk soup and I will have no lullabye.

Q1. Yes
Q2. Apparently Not, so we've just learned
Q3. Nothing of any use, again as we've just learned....

That last bit... well ... I just don't get that....

[PAR]

Damn, I know all the time spent, pages dog eared, just to admit I still have much to learn.

It seems he's been "erased", which is probably his fate if caught 100 miles out in a 40' Cigarette, when conditions suddenly turn to a full gale and 20' seas.

[marshmat]

Yup, ccdiver is gone without a trace.

Paul, not sure if you checked ccdiver's profile, but the boat in question was nowhere near as strong or seaworthy as a 40' Cigarette. It wasn't much more than a box barge, five plywood sheet lengths long, two plywood sheet widths wide, by half a sheet width tall.

I had some fun on the walk in to work this morning going over what would happen if one tried to make a 20,000 TEU container liner plane.... reducto ad absurdium.

[terhohalme]

Damn, missed the fun. :(

[apex1]

That last bit... well ... I just don't get that....
As mentioned in post #19 Will,

I have to be back in my asylum at a given time, otherwise my nurse will give away my milk soup and does´nt sing me a lullaby, that weakens my libido further and makes me sad or agressive.


And to be constructive:
I understand props very well and most analysis of hulls, but for some reason I cannot seem to get it straight in my head on how to figure the prismatic coefficient of a hull form.
For some reason I seem to have a mental block that precludes me from understanding something so simple as this.
Could someone please explain this in 9th Grade english so I can get the jist of what I am missing.
H
was the thread..............................

[PAR]

I just noticed a new member named Dddiver, maybe we'll have some fun yet . . .

[Willallison]

Thanks Apex..

[apex1]

I just noticed a new member named Dddiver, maybe we'll have some fun yet . . .

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

[Willallison]

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

[Ad Hoc]

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.

[sorenfdk]

For sailboats look also to the Paris curve that relates lateral plane and Cp.

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...

[apex1]

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

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

[daiquiri]

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

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

[Ad Hoc]

hehehe ;)

[MikeJohns]

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...

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 :rolleyes:
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.

[sorenfdk]

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!

[messabout]

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.

[marshmat]

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.

[MikeJohns]

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...........


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

[Paul B]

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!

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=U0ihyQP1qMIC&printsec=frontcover&dq=how+to+design+a+boat#v=onepage&q=&f=false

[messabout]

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"

[messabout]

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.

[sorenfdk]

The "Paris Curve" and the half angle formula both exist, but I doubt many people who successfully design boats would use either.
http://books.google.com/books?id=U0ihyQP1qMIC&printsec=frontcover&dq=how+to+design+a+boat#v=onepage&q=&f=false

My company has survived in the yacht design business for almost 20 years without even knowing about Jay Paris' curve or the half angle formula, so you just might be right...:)

[MikeJohns]

......... All that is fine but what about really big boats like a VLCC. They have nearly blunt bows. Where is half angle now? ..............


That's not a boat..... that's a ship!
And a load carrier to boot, utterly different design paradigm.:) If you wanted to look at ships look to the clippers.

ADDED

The old bluff bowed sailing ships were also quite efficient for their speel length ratios which were usually significantly less than 1.

[MikeJohns]

My company has survived in the yacht design business for almost 20 years without even knowing about Jay Paris' curve or the half angle formula, so you just might be right...:)

Like any rule of thumb it's always where you start your design and then you will model resistance test a few variants of course.............don't you ;)

A huge amount of work was done refining and observing displacement craft in the first half of the 20th century then two things happened, fuel oil became cheap and engines became powerful in the commercial scene and in the sailing boat arena the racing rules started to drive hullshapes and fashion, now those boats have moved out of the displacment craft altogether and the leading edge testing is to optimize light displacment semi-planing performance with completely different pressure and flow fields.

Many power boat designers and Many displacement sailboat designers show a poor understanding of hull-form related to chosen speed length ratio's, in the commercial field where I have spent most of my design life you see the economics daily of a hull designed for SLR of 1 being pushed at 1.4 with a massive diesel and yet the boat's design is for 1/3 the power and 2/3 the speed.

[Willallison]

Many displacement sailboat designers show a poor understanding of hull-form related to chosen speed length ratio's, in the commercial field where I have spent most of my design life you see the economics daily of a hull designed for SLR of 1 being pushed at 1.4 with a massive diesel and yet the boat's design is for 1/3 the power and 2/3 the speed.

I think that's very much the case - probably more so - in the recreational arena too Mike. Witness the madness that has brought about the 'fast trawler'. Enormous diesels fitted to displacement hulls to satisfy a market segment with absolutely no common sense. The Grand Banks 42 comes to mind as an example......
Of course this madness eventually led to the virtual extinction of the true displacement cruiser (with a few notable exceptions) and we now see trawlers (hate that word) "fitted" with planing hulls... still sold as 'long-range cruisers'! As if by virtue of their otherwise traditional styling they are still sensible passagemakers. Few have a range of more than a couple of hundred miles for heavens sake.....

Phew... rant over.....:p

[Paul B]

Many displacement sailboat designers show a poor understanding of hull-form related to chosen speed length ratio's,

Since virtually every keelboat sails in "displacement mode" upwind maybe you would like to name who these "many..designers" are, and what their poor understanding is.

I know of quite a few designs of heavy steel yachts built by yards like Jongert and Royal Huisman that sail beautifully and were drawn without any regard to Paris Curves or half angle theories.

[apex1]

I think that's very much the case - probably more so - in the recreational arena too Mike. Witness the madness that has brought about the 'fast trawler'. Enormous diesels fitted to displacement hulls to satisfy a market segment with absolutely no common sense. The Grand Banks 42 comes to mind as an example......
Of course this madness eventually led to the virtual extinction of the true displacement cruiser (with a few notable exceptions) and we now see trawlers (hate that word) "fitted" with planing hulls... still sold as 'long-range cruisers'! As if by virtue of their otherwise traditional styling they are still sensible passagemakers. Few have a range of more than a couple of hundred miles for heavens sake.....
Phew... rant over.....:p

I would not call that a rant Will! That was a nice, honest and polite way to describe the mental illness of a much celebrated market, Trawlers. Or what Joe sixpack buys as a Trawler!

[MikeJohns]

Since virtually every keelboat sails in "displacement mode" upwind maybe you would like to name who these "many..designers" are, and what their poor understanding is....

Paul
I said Many and that does not mean all by any stretch of the imagination.

You of all people should not need to look far to see examnples of what I'm talking about just go into any yard and look around the boats on the hard.

If you'd like to open a new thread on this it might be informative.

Paris's observations are not a hard and fast rule either, they are more a rule of thumb and they allow a designer to make allowance for underwater variations to a canoe hull at the initail design stage. Naval architecture goes a lot further than this but you need to start somewhere.

I posted that as a helpful guide and was expecting some discussion I wasn't demanding that everyone use it ok?

[Paul B]

I said Many and that does not mean all by any stretch of the imagination.


Funny, I never mentioned ALL either. Nice attempt at distraction.

You said MANY designers show a poor understanding of hull form. To me MANY is more than one.

Seems you make these wild statements, yet cannot even name ONE designer that fits your description.

[MikeJohns]

Funny, I never mentioned ALL either. Nice attempt at distraction.

You said MANY designers show a poor understanding of hull form. To me MANY is more than one.

Seems you .. cannot even name ONE designer that fits your description.

Not funny , what distraction? Just look at your logic.

You know of "quite a few designs" wich are well designed and so do I but that's not what I said is it.

I didn't say ALL designers were amiss therefore it comes as no surprise that you know some that are good.

In the past you have talked of "the slow piggies" that can't get out of their own way, you have already identified those boats.

What's actually threatening to you here I wonder, perhaps the fact that medium heavy dispalcment craft could be good low resistance performers if well deisgned ?

Please try and contribute decently.

[Paul B]

You know of "quite a few designs" wich are well designed and so do I but that's not what I said is it.

What you said is Originally Posted by MikeJohns
Many displacement sailboat designers show a poor understanding of hull-form related to chosen speed length ratio's,.

I've simply asked you to name these designers so we all know whose work we should avoid using as data points for our own design work.

In the past you have talked of "the slow piggies" that can't get out of their own way, you have already identified those boats.?

Really? What boats or designers have I "identified" as having poor understanding of hull-form (sic) related to chosen speed length ratio's (sic)?

What's actually threatening to you here I wonder, perhaps the fact that medium heavy dispalcment craft could be good low resistance performers if well deisgned ?

I guess you missed the comment in my post about some of the steel yachts produced by Jongert and Royal Huisman, and my impression of their performance.



Maybe you should broaden your horizons and not reference the same book in so many of your arguments. If you are going to do so, maybe you should pick a better book on the subject. All you are doing is showing us all how little you really know about sailboats.

Obviously I bow to your superior knowledge of welding plates onto workboats.

[MikeJohns]

...........
Maybe you should broaden your horizons and not reference the same book.... how little you really know about sailboats....Obviously I bow to your superior knowledge.....

Where do you start when people trying to get a grip or a feel for something like prismatic coefficient.

If it is a technical discussion then you should always look for a decent paper but when it's something as fundamental as Cp it is a challenge to find material which popularizesa a subject sufficiently as to give an idea of the way it relates to hull design. John Teale is a Naval architect and his book is a good introduction for newbies as would Brewers primers or sorensons power boat primers, they are all aimed at the neophyte but Teale goes further.

Many other boat designers have other methods of arriving at a hullform which work but it doesn't make the methods mutually exclusive. Prof naval architecture material even uses different terms which only confuse people looking for a basic underestanding. If you would like more material just ask me for it please.

As for your dismissal of books I presume you refer to authors like Marchaj on seaworthiness?
I would note that in the past I have several times offered to give you papers or a technical discussion on several aspects of naval architecture but you have never taken me up on this.

You have a tendency to try and drive a thread that you find threatening into inane arguments and then start name calling. and I will not play this game. I have yet to understand just what put the bee in your bonnet here.

Instead post something helpfull on Cp or discuss your own design process with respect to this for a displacment boat.:)

[messabout]

Mlke: I cheerfully and respectfully defer to your experience and knowledge. I know that a VLCC is not a "boat". A lubberly transgression on my part, however 600 foot submarines are stubbornly referred to by their yankee crew as Boats.

The big cargo carrier is a floating object that displaces water when it is moving. Those big ones operate at very low S/L ratios of course. Even so they may be moving at 25 to 30 Kn. With impact velocities of that magnitude it seems to me that mass acceleration (of water) is more than a casual matter. I will also guess that those blunt nosed things are miserably wet in a seaway. I'll guess some more and opine that the scantlings of such boxy vessels must be signifigantly more robust because of the additional forward bouyancy. Would you comment on some of that please?

[MikeJohns]

...........
The big cargo carrier is a floating object that displaces water when it is moving. Those big ones operate at very low S/L ratios of course. Even so they may be moving at 25 to 30 Kn. With impact velocities of that magnitude it seems to me that mass acceleration (of water) is more than a casual matter. ................ Would you comment on some of that please?


Ships are long relative to the wave length of the generated waves and they are relatively deep. Block coefficient is more important here, Ships are also designed for a constant Service speed and are easier to optimize. Consequently there is a lot of effort in the design of a carrier as a pressure source and a sink separated by a long parallel mid body, the relative wave generation at bow and stern are chosen carefully along with bulb design (produces a wave train out of phase with the main hull). Then there’s wake….

Optimal block coefficient of a carrier can be quite high although the waterline entry may not be quite as bluff as you first think from looking at the upper stem and it ties in with the bulb-stem fairing, placement and design.Once the block coefficient gets over 0.8 parabolic bow shapes at the waterline entry become sensible and they are very bluff.

Forces are always high on ships bows and scantlings are set by class requirements with commercial shipping.

If you’re interested there’s a lot of material we could dive into here but probably better in a new thread. There are some very good books on modern ship design.
Here’s another graph which you might find interesting. from Ship Design Rawson & Tupper.

[BigCat]

:rolleyes: You guys are mean. In simple terms, the PC is how tapered a boat hull is under water. More volume in the ends = a 'blunter' boat, with a higher percentage of its underwater volume in the ends = a high PC. Less volume under water in the ends means less boat area underwater in the ends, ie. more tapered under water. A PC of 1.0 is not tapered in the ends at all- each slice of the loaf is the same area underwater. A PC of .49 is very fine, ie. very tapered - like an ocean kayak. A high PC (.65 to .70) is good if you are going to push the hull very fast. If you are going to push it slowly, by manpower, a low PC is better. Fast and slow are relative to the waterline length, not fast or slow in some absolute sense.

[Guest625101138]

.... If you are going to push it slowly, by manpower, a low PC is better. Fast and slow are relative to the waterline length, not fast or slow in some absolute sense.

You have given a simple description of prismatic coefficient that is easy to understand. However the additional information offered on manpowered craft is not correct. The reason you see low prismatic coefficient on something like an ocean kayak is driven by stability requirement not drag reduction or ease of pushing.

The minimum drag manpowered single person boat for sustainable effort will have a Cp around 0.65 for a male of average fitness. Racing kayaks approach this but are usually a little lower because going higher requires a lot of skill to stay upright. They are difficult to operate because of the low maximum beam but for a given effort they have considerably higher speed than a hull with a Cp of 0.49.

The reason lower Cp is seen on an ocean kayak has nothing to do with ease of "pushing". It is related to staying upright statically rather than with the aid of a paddle.

Rick W

[tspeer]

:rolleyes: You guys are mean. In simple terms, the PC is how tapered a boat hull is under water. More volume in the ends = a 'blunter' boat, with a higher percentage of its underwater volume in the ends = a high PC. Less volume under water in the ends means less boat area underwater in the ends, ie. more tapered under water. A PC of 1.0 is not tapered in the ends at all- each slice of the loaf is the same area underwater. A PC of .49 is very fine, ie. very tapered - like an ocean kayak. ...

There's another interpretation of PC, and that's how big the maximum cross section is for a given volume (which, of course, means a constant weight for the vessel). A PC of 1 has the smallest maximum cross section area. As the PC drops, the maximum cross section has to increase to make up for the volume lost at the ends (or anywhere else).

I think this interpretation helps to make sense of why higher speed craft tend to have larger PCs. One would think that blunter ends would increase the wave drag, and they might, but there's a benefit to be had from the reduction in maximum cross section. At some point, the benefit from one is outweighed by the penalty from the other, hence there being an optimum PC that is a function of Froude number.

[Mat-C]

There's another interpretation of PC, and that's how big the maximum cross section is for a given volume (which, of course, means a constant weight for the vessel). A PC of 1 has the smallest maximum cross section area. As the PC drops, the maximum cross section has to increase to make up for the volume lost at the ends (or anywhere else).

I think this interpretation helps to make sense of why higher speed craft tend to have larger PCs. One would think that blunter ends would increase the wave drag, and they might, but there's a benefit to be had from the reduction in maximum cross section. At some point, the benefit from one is outweighed by the penalty from the other, hence there being an optimum PC that is a function of Froude number.

Tad eluded to something similar elsewhere.... do you have a reference, or an equation for determing the optimum PC?
Thanks

[abhishek]

prisamatic coefficient = block coefficient of finess/mid ship area coefficient