Discussion in 'Boat Design' started by Morelg, Aug 7, 2013.

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### MorelgJunior Member

Hi,

I know that this subject was discussed in the past but I couldn’t find an answer to my following question.
For the bottom loading (relative displacement trends for hard chine planning hull forms) Blont presented a chart with "extremely heavy", "heavy", "light" and "extremely light" lines. The X axis of his chart is LOA while the Y axis is (Displacement/(LOA X BOA)) X (LOA/BOA)^0.5. I would appreciate an explanation regarding the physical meaning for this expression as this does not seem to represent (Displacement/Planning area)
Thanks,
Morel

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### tom28571Senior Member

Where was this graph and equation published? Was is in Pro Boat?

It certainly does not take shape of the waterplane into account. It makes short-beamy or low LOA/BOA boats have a higher Y value. It works OK for boats with similar waterplane shapes and overhangs but the answer is not very precise.

Interesting that this thread is just following the one on comparing wooden homebuilt planing boats to commercially manufactured ones. Both are illustrations of the effects of bottom loading.

Edited to add: Assuming a good bottom design, bottom loading is the most important factor in determining low speed planing performance. Important at all speeds but particularly so in achieving planing in the first place. Bottom loading that is too high is the reason so many boats perform so poorly.

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### MorelgJunior Member

Hi,

Attached Blont's chard.
I would appreciate the physical interpretation of the (Displacement/(LOA X BOA)) X (LOA/BOA)^0.5 in this chart.
Thank all,

Morel

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### tom28571Senior Member

When I applied the formula to one of my 24' cruising powerboats, I got about 1 1/2# /sq ft less than I know it is, which I think may be pretty good for a general form. My boat also fits well below the extreme lightweight line on the graph.

If you are asking for the derivation of his formula, I'm sorry but I can't help there. I think it is a simple rectangular form with some modification to make it give reasonable results for the actual area of the typical planing powerboat waterplane. Its what you do when the actual area or shape of the waterplane is not known. All my guesses and someone else may have a better insight to it.

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Morel,

The answer is on the graph itself!

If you look on the upper right hand of each line (of heavy, light etc) you shall see a number ranging from 4.0 to 8.5 associated with each line. This is a non-dim ratio of Ap/vol^(2/3). The papers nomenclature shall define what Ap and V is, although it should be pretty obvious, but always best to confirm.

Once you understand what Ap is and the vol, you can then work out the same ratio for your own application and decide where in the 4.0-8.5 range your vessel sits. If it is not on one of the lines, you simply interpolate.

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### MorelgJunior Member

Regarding the meaning and definition of Ap/V^(2/3), this is perfectly understood. Indeed it is a dimensionless number which can be related to the bottom loading.
The question is regarding the ordinate. As you can see it is (Displacement/(LOA X BOA)) X (LOA/BOA)^0.5. It is not dimensionless but the dimension is lbs/ft^2. The physical interpretation of this number to the bottom loading is not understood to me i.e. why (Displacement/(LOA X BOA)) X (LOA/BOA)^0.5 is selected to be related to bottom loading?

THANKS,

Morel

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Morelg

Yes you're quite right, my apologies, I read your post too quickly, doh!

The Y-axis has the units, lb/ft^2, another way of saying this is pressure. Thus the graph provides an indication of the amount of bottom pressure for a given range of hull forms.

So a vessel of a given length, x- axis, with a given "fullness" in the 4.0-8.5 non-dim ratio shall yield a "typical" or "expected" bottom pressure in lb/ft^2.

However, most of this is now all mute, since most Class rules provide adequate bottom loading pressure for structural design. The quickest/easiest is that of DNV.

http://www.boatdesign.net/forums/boat-design/dnv-vertical-accelerations-formula-46622.html

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### MorelgJunior Member

Thanks again Ad Hoc, you are fast

I do understand all this and indeed the ordinate has the dimensions of pressure. But why is this selection related to bottom pressure? One could use for the ordinate (Displacement/(LOA X BOA)) with the same lb/ft^2 or (Displacement/(LOA X BOA)) X (LOA/BOA)^3, again with the same dimensions of pressure. I believe that (Displacement/(LOA X BOA)) X (LOA/BOA)^0.5 versus LOA is significant as per the chart is an approximation to Ap/V^(2/3) when only the main dimensions (LOA, BOA and ship's weight) are know. The question is, how is this approximation mathematically obtained?

Hope I am not too digging into...

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### MorelgJunior Member

Oh, Ad Hoc, following your previous post, indeed Class rules provides bottom loading pressures for structural design (ABS is also nice to compute). This chart we are talking about is a guidline for performance (not structural design) and allows one to estimate how easy a boat will go into planning mode. Thus again I am returning to me not understanding the relation between Displacement/(LOA X BOA)) X (LOA/BOA)^0.5 and bottom loading

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Morelg

I am on my cell phone now so not able to provide a comprehensive reply nor type easily. Until i return home can you cite the paper title and authors. As i can then i provide a more in depth reply.

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### MorelgJunior Member

Hi,

The author is Donald Blount. The chart is presented in several of his papers, for example see "Achievements with Advanced Craft", Naval Engineers Journal, September 1994, see Appendix B of the above paper. It can be downloaded http://oa.upm.es/14340/2/Documentacion/3_Formas/SemiPlanPag6.pdf

Thank you for the help, I also emailed Don directly and I am sure he will provide an explenation.

Best Regards,

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Morelg

I don't have the original series 62 paper, since that is where he references the definition/term, in appendix B of your link. However, he does say that owing to the lack of hard data available, only the LOA's et al can be used in a simple quantitative form. However, until I can see where this is used and why he selected these parameters, in the original series 62 paper, I can't say for sure, why, other than it provides a nominal hull pressure v LOA. However, since you've emailed him directly...might as well get it from the horses mouth

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