How to use CP to adjust bow fineness

I know not to put all my faith in one parameter, but I'm a little perplexed as to how the prismatic coefficient can represent the fineness of the ends when it seems so influenced by the length of the mid-body. (CP increases with a longer mid-body independent of the ends.)

Specifically, with an expected speed/length ratio of 1.3 (and therefore target CP of .62), I adjusted the bow fineness of a 12.5 ft. paddleboard (yes, a lowly chunk of styrofoam) from a 20 degree half angle of entry down to 18 degrees, with a mild quadratic curve to the midsection. This would seem fairly fine, but the total CP is way high at .65 due to the long mid-body needed for stability. If I calculate the CP from an approximate mid-point of the craft forward, it's .61 which is just about on target. If I calculate for the approximate bow section only, it's a little low at .56.

Is it valid to use the front half of the craft only for CP where bow fineness is concerned? Even that half would be influenced by the mid-body length, so I wouldn't know where it should start.

I guess another way to ask this, is for what general shape of craft was the table of recommended CP to S/L ratios developed? If that can be answered, then I guess I can figure out how to "truncate" my particular craft appropriately before calculating CP. For instance, maybe I need to exclude any part of a mid-body that doesn't fit a continuous curve, bow to stern?

 

Did you have a look at this thread ?
http://www.boatdesign.net/forums/design-software/new-lines-prediction-program-45601.html
You can experiment with different parameters and see the influence.
Good luck
Uli

 

It is a long iterative process and not that simple.

Although the Cp defines the fineness of a ship, the midship section coefficient is necessary to complete the equation. The Froude number or Taylor's number guides you if a constant midship section (or parralel mid body) is beneficial. It also guides you on the optimum LCB position from which the Length of Entrance vs. the Length of Run can be plotted.

To find the optimum LCB position, you have to derive the Cb from the Cp, Cm inputs because the Watson and Gilfillian formula uses the Cb to plot the optimum LCB position.

With a known LCB position you can derive the Lr/L ratio using the Holtrop & Mennen formula after which you can derive the Le/Lr ratio given a trial Le input.

The half entrance angle cannot be defined arbitrarily as the half breadth needs to be multiplied by a factor of 1.2 or 1.36 depending on whether you have a form with or without a bulbous bow. I prefer the Linblad & Todd guide on half entrance angle range.

Attached is the basic setup to find the Lr ratio and the ITTC definition of Le/Lr ratio. I have a much more sophisticated sheet but that should suffice for now.

The ITTC definition of Hydrodynamics was originally posted by Daiquiri and Leo Lazauskas should be available in this forum.

 

Thanks. Yes, I'm looking at UliLines. I was trying to decide whether to use Freeship or Delftship, and it looks like UliLines will work just with Delftship, but if that's wrong, please advise.

Looks like entry angles are not easily dictated and recommendations vary widely with different sources. First, I want to follow some of the suggestions on how to take into account the mid-ship area that was throwing off the coefficients.

 

I consider entry angles as a tertiary input. Primary inputs such as length, breadth, displacement takes precedence, then the ratios and coefficients. Changing L/B ratios or even addition of parrallel mid body will affect the entrance angle.

I am attaching a bit more sophisticated spreadsheet to show you the hierarchy of inputs. I developed this to gain a quick visual of waterplane shape for every hull type. I got stuck because I could not find a way to derive entrance angle. It can be done but my math is limited. The waterplane curve is a 4th order polynomial curve. Taylors mathematical method is the only way.

Design is limited by boundaries. The spreadsheet narrows down the parameters but gives enough wiggle room. I use a much more sophisticated spreadsheet to take care of all the variables.

 

Thanks. That's quite sophisticated and sheds light on how entry angle and Cp are expected to change with vessel type and mid-body length. Previously I had only seen simple two-column tables with CP versus either Fn or S/L ratio. Intuitively I knew there was more to it, but had not seen it until now. I also just downloaded the full text of Saunder's Hydrodynamics in Ship Design, Vol. II, and that should be enlightening if I can understand any of it.