Prismatic Coefficient

[BTScow]

Perhaps the hardest thing about being a beginner is not having the hard won experience of comparison. I am designing a 24' double ender, wholly inspired by Phil Rhodes. I am checking my numbers and come up with a Cp of .27 . Hmmmm, I say to myself, recheck my calculations and go back to the books. I am to understand that if an easily driven is what a guy wants, than a low Cp is the ticket, but at the sacrifice of boat speed.

My question is this; What is it I have done? Supposing I have done my arithmetic correctly will the boat be a dog? I understand performance is the culmination of factors. Before I go back to the drawing board I was hoping someone could help me wrap my mind around the significance of this number, and the conclusions to be drawn.

Many thanks in advance.

BT

[jehardiman]

How are you calculating CP? That is waaay too low as you surmise. Normally, appendages are not included, and that includes the deadwood in a full keel vessel with a lot of sternpost drag. I would expect a CP of about 0.6 and a block of about 0.4

[Guest625101138]

Originally Posted by BTScow

...... I am to understand that if an easily driven is what a guy wants, than a low Cp is the ticket, but at the sacrifice of boat speed.

..

BT

No a light displacement, easily driven hull will have a prismatic coefficient around 0.65 for operation near hull speed.

For example racing kayaks have PC around 0.65 as they are intended to be fast for modest power input. The only reason ocean kayks have a lower value is for stability. Their need for beam is to have static stability.

What displacement do you have, what is the length and what speed do you want to achieve?

Rick W.

[Ad Hoc]

Yup...sounds like a typo in your calculations and/or understanding of prismatic Coeff. See here for more:
Prismatic Coefficient

[BTScow]

Many thanks to all that have replied. In an effort to get the bottom of my mystery, I will try an answer some of the questions asked. Firstly, I have used the following formula for calculating Cp=(disp. ft^3)/(max area of underbody, ft^2)(LWL). I will go back and recheck my square ft. measurements of the below water line underbody. The boat is 25'3" with a lwl of 24', displ. is about 2000lbs. I would like to get 6 knots out of her.

[Guest625101138]

Originally Posted by BTScow

Many thanks to all that have replied. In an effort to get the bottom of my mystery, I will try an answer some of the questions asked. Firstly, I have used the following formula for calculating Cp=(disp. ft^3)/(max area of underbody, ft^2)(LWL). I will go back and recheck my square ft. measurements of the below water line underbody. The boat is 25'3" with a lwl of 24', displ. is about 2000lbs. I would like to get 6 knots out of her.

Lowest drag hull for given conditions in calm water operation has prismatic coefficient of 0.66. There will probably be other drivers that dictate what you end up with.

Rick W

[BTScow]

Found my mistake. Evidently I have a Cp of 52%. Thoughts? Conclusions? Thanks to all who helped.

[messabout]

Rick; Please explain more about your suggested Cp numbers. You have us in the mid zero point six range. Any kayak that I am familiar with has a Cp in the low zero point 50s. I will bet a Fosters that your HPV has a Cp much smaller than the optimum 0.66 that you mention. I thought I knew what I had been calculating for all this time, but perhaps I have much to learn.

[Guest625101138]

Originally Posted by messabout

Rick; Please explain more about your suggested Cp numbers. You have us in the mid zero point six range. Any kayak that I am familiar with has a Cp in the low zero point 50s. I will bet a Fosters that your HPV has a Cp much smaller than the optimum 0.66 that you mention. I thought I knew what I had been calculating for all this time, but perhaps I have much to learn.

These are not "suggested" numbers. They are the numbers that give the lowest drag hull for my operating conditions.

I use externally stabilised monohulls like these:
http://www.boatdesign.net/gallery/sh...//ppuser/18624
http://www.boatdesign.net/gallery/sh...//ppuser/18624
So I do not need inherent stability in the load carrying hull. It is designed purely for minimum resistance and the form stability is close to zilch in both cases. Both have a PC of 0.64.

This one is keel stabilised but has some form stability as well:
http://www.adventuresofgreg.com/HPB/...019-795780.JPG
It has a PC of 0.6.

I have attached some information from the One Ocean Kayak site - refer last line. Hulls with low PC are slower and driven by stability constraint not low drag.

Rick W

[willfox]

Dont Know if anyone uses Larsson but looking at the optimum Cp for a Fn of 0.306 which is 6 knots for this vessel, gives only just above 0.5. Which way do you work out the optimum?

[Guest625101138]

Originally Posted by willfox

.... Which way do you work out the optimum?

Lets call it the lowest drag hull rather than optimum because it is no good having the least resistance if it is upside down more often than upright.

The PC of 0.66 was the result of 8000 iterations using Godzilla for calm saltwater at a temperature of 12C. That is for a hull displacing 909kg with a LWL of 7.5m designed for 6kts.

What is done above the waterline will have bearing on performance when wind and waves come into play but having the lowest drag for calm water translates well to heavier going.

Rick W

[Guest625101138]

Originally Posted by messabout

Rick; ... I will bet a Fosters that your HPV has a Cp much smaller than the optimum 0.66 that you mention. ........

The cost to mail the Fosters is not worth it. I prefer wine these days anyhow.

The main point to consider with my hulls is the maximum beam. When the hull is 0.225m maximum beam on a length of 7.2m it does not take much taper to get quite full ends. It is the small beam that most contributes to the low resistance.

A lot of my effort has been spent on working out how to achieve a stable boat while keeping a narrow BWL. Ocean kayaks do not use training wheels so need inherent stability. Some of the outriggers canoes are close to the shape I have. They tend to have a steadier thrust than a rowing shell. The later have a long glide and the speeds varies a lot from thrust to glide. I think they typically have lower PC than I have.

Rick W

[Ad Hoc]

"...Lets call it the lowest drag hull rather than optimum because it is no good having the least resistance if it is upside down more often than upright.."

Willfox
It all depends upon your criteria/eon. If you are designing with one sole objective in mind, then you can select an "ideal " design and ignore all the other factors, since that is your objective.

No design is ideal, nor optimum. Every design, with a criteria of more than one, is a compromise of many factors. To select one and use this as a carte blanche statement for all designs just points to a lack of understanding of what compromises are required to ensure a boat with a varying and often wide ranging requirements, are satisfied.

Not many people cannot do this, because they are constantly focusing on one aspect and do not wish to compromise this position for fear of being subjected to criticism for making such a stance. A design with one objective is easy, a design with many is much more difficult and cannot be reduced to a one liner.

Just focus on your own objective...then formulate your solution accordingly..

[messabout]

We get some Aussie wine here in the states. An inexpensive one is called Yellow Tail. I suspect that you have some vintners who produce very nice stuff. Thank you for allowing me to weasel out on the wager. The Fosters that I might get in the U.S. may not be the real thing anyway.

On contemplating the details of your HPV, I rescind my scepticism. Yes the very long skinny boats will have an unusually high Cp for the reasons that you stated.

The Cp thing is entirely fascinating as it can be seen to be entwined with displacement, displacement length ratio, speed length ratio, and a few more things, no doubt.

I concede that Skenes has dated information. His Cp best values are dependant on S/L figures and at S/L = 1.2 his Cp is about 0.56. The graphs consider wavemaking resistance in terms of pounds per ton of displacement. The graph is said to be based on model testing by Taylor. Light weight boats such as your Godzilla model call for even lower Cp by his standards.

Tom Speer has posted a very cogent and succinct note, in another thread, about Cp. His post is still up in this section.

[jehardiman]

Originally Posted by BTScow

Found my mistake. Evidently I have a Cp of 52%. Thoughts? Conclusions? Thanks to all who helped.

0.52 sounds a lot better, but is still a little low unless the displacement/length ratio is very high. As has been pointed out in the side discussion between Rick and Messabout as well as Ad hoc's points, there are other ratio's given the length and desired speed that conspire to move "optimum" Cp around.

FWIW, I think the first turn around the design spiral for a heavy displacement sailboat with a S/L of ~1.2 should have a CP of about 0.54 with the maximum section loacated about the same aft of the fwd perp. Of course the ballast ratio, SA/D and D/L will move this around a bit as you crank on through, especially the aft quarter buttocks.