# Sectional area curve ?

Discussion in 'Boat Design' started by fcfc, Dec 7, 2004.

1. ### fcfcGuest

Is there any special shape to have for this curve in relation with design speed ?

For Fn near 0.4, I have been said that best was a parabolic curve (constant curvature = minimum curvature variation), so no shoulder effect.
But also heard that best was a sin fore + trochoidal aft curve.

NB: LCB and Cp are "shown" by this curve and both are related to design speed with least resistance, but that does not give indication for shape.

Thanks for any indication.

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### CDBarrySenior Member

Sine / trochoid is the old Colin Archer theory, and is based on an incorrect formulation of wave generation. It is definitely wrong, even Colin Archer dropped it.

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### maxhroomNew Member

sine plus Ln

I've come up with a sine curve plus Ln curve, attached is the spreadsheet. Change the values in the "factor" cell. It works for the range Cp 0.48 = factor 0.007, to Cp 0.75 = factor 0.96. You can move LCF by re-entering the linear values at columns A,B,F and K. keeping their end and mid values,
changing the steps.

I've translated the spreadsheet into code, which allows me to change sectional area, looping untill I get the desired DSP, Cp, LCF etc.

#### Attached Files:

• ###### Fn to Cp.xls
File size:
134 KB
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### sorenfdkYacht Designer

At the Sixth Chesapeake Sailing Yacht Symposium (1983), George Hazen and Steve Killing gave a speach on "Yacht Design with Computers". Here, they presented a function that enables the designer to come up with a curve of areas without loosing control over Cp and LCB. The function looks like this:

A = (1-(x+dx^)**2)**y

where "x" varies between -1 and 1 as position goes from the after to the forward end of the waterline. "dx" varies the position of the maximum sectional area station. "y" controls Cp in a complex, but quite predictable way.

"Optimum" values of LCB and Cp can be determined by using the resistance formulas given by Gerritsma et al. - see Larsson & Eliasson: "Principles of Yacht Design".

5. ### fcfcGuest

I was interested by the "hydrodynamic" view of this curve than a "mathematical" view.

For a given Fn, there is an optimal Cp and LCB. witch are characteristics of this curve.

NB really need a math editor, integral sign are diificult to show!

If the curve is [0,1] on LWL,
Cp = area of curve / max y value. =
Cp = (integral from 0 to 1 of f(x)) / max (f(x)) on [0,1]
LCB = x position of center of gravity of this area =
(integral from 0 to 1 of ((x-lcb) * f(x) ) ) = 0

if x = 1 bow and x = 0 transom
bow f(1) = 0
no transom = f(0) = 0

What I was wondering, is that are there any other known or accepted constraints from hydrodynamics on this curve ? except a "fair" aspect in the designer eyes.

such as avoid coke bottle effect = math traduction only one sign change for derivative.
Minimum change of curvature = math traduction second derivative continuous and most constant possible.
inflexion points, etc ...
---------> Is is here I am seeking ideas

What I would call the mathematical view would be tring to find a function f(x) such as it fits the above mathematical constraints, but thats not my immediate concerns.

Thanks for all ideas.

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### maxhroomNew Member

Optimum values

"Optimum" values of LCB and Cp can be determined by using the resistance formulas given by Gerritsma et al. - see Larsson & Eliasson: "Principles of Yacht Design".

The Delft series stops short at lwl/bwl 5, so in the design of multihulls lwl/bwl > 8, where would one find optimum values for LCB etc.? Is there a multihull bible?

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### ndiasJunior Member

Hi everybody...

Presenting myself... I'm a new one, an amateur boatbuilder, crazy about gaffrig boats.

A few thigs I wanted clarification, sorry if there are english gramatical errors...

Recently I bought a lifeboat hull, grp, 7,32 x 2,42 m, with 42 pax load capacity... I draw all the lines but unfortunatelly I lost all the calculations but the drawings, and have to start all again from zero!

so, Displacement calculations, I have to calculate, I have a planimeter stanley allbrit), underwater area of stations, use simpsons multiplicator and aply the formula A=s/3*Sum of products between area and simpson multiplicator.

For the water plane area, I'll do the same but aplying the beams on the waterline.

To find Momnt of inertia of water plane area, usefull to stability calculations, I have to use the half beam at waterline, cube them and use ItWP=2/3A, were A=1/3*s*Prod, s is the distance between stantions.

For CLR, can I do the underwater profile on cardboard and balance it and so finding the cg point?

For the VCG can I cut in cardboard the underwater sections, glue each of them and with the method os hanging them by two points find the equilibrium point, the so called VCG?

and for the CB?

I found in Sail Magazine an article about stability, can we trust so ?

best regards

ndias

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### terhohalmeBEng Boat Technology

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