Instant BM

Hello,

Found one day a very simple equation for metacentric radius in modern sail boat:

BM = 0.1 B^2 / T, where B is the waterline width and T is the draught of canoe body.

This formula looks to be right in a few percent.


How did I get there?

Displacement volume D = L * B * T * Cb

Second moment of the water plane I = L * B^3 / 12 * k

k is a constant and depens on waterplane shape, approximation k = Cw^2

Just using algebra:

Metacentric radius BM = I / D = B^2 / (12 T) * Cw^2 / Cb

(found later, this was statet by Mc Cloghrie)

Approximation: In modern sailboat hull Cw is about 0.7 and Cb about 0.4, so Cw^2 / Cb is about 1.2 . Put this in BM equation, we have after reduce:

BM = 0.1 B^2 / T

Example a boat with B = 3.0 m and T = 0.6 m have BM = 0.1 * 3.0^2 / 0.6 = 1.5 m

This very simplistic, but tells quite clear what geometric factors influence on instant stability.

Any comments? Seen this before?

 

But.. but.. then just anybody can calculate BM

 

Well, anybody can calculate his/her money balance:

Property = Earnigs - Expencies

Still, only some are rich.

 

I got another approximation as:
(See: http://www.boatdesign.net/forums/stability/what-bm-t-b-2-a-20642.html)

(BM*T)/B^2 = 0.08*Cwp^2/Cp

Asuming Cwp = Cp ^ 2/3 (Schneekluth)

we come to (BM*T)/B^2 = 0.08*Cp^1/3
and so BM = 0.08*Cp^1/3*(B^2/T)

For an efficient motoring hull Cp = 0,63

so roughly BM = 0.07 B^2/T

Another approximate formula is:

BM = (0.008 +0.0745 * Cwl^2) * B^2/(Cb*T),

As we can estimate also the vertical centre of buoyancy using:

Munro-Smith: KB = T*Cwl/(Cb+Cwl), or
Normand-Morrish: KB = T*[5/6 - Cb/(3*Cw)]

(The M-S formula usually gives a value about 0.01*T lower than the N-M)


we can, as KM = KB + BM, get KM and then performing a weights/centers calculation estimate KG and so GM.


Note: L = length, B = beam, T = draft, Cb = block coefficient, Cwl = waterplane area coefficient

Cheers.

 

This is true only if Cm = 1 then Cp = Cb*Cm = Cb

 

Hello,

Would anyone know Terho Halme's email contact details as the email quoted on his website keeps rebounding?

Cheers

 

My website is outdated history... just foating somewhere in cyperspace and no controllable anymore

Just pick my name and send me an email.

Terho

 

Hi Terho,

Tried to email you without success.
Could you email me on: janie.50@bigpond.com
I would just like to canvass your opinion on designs.

Cheers

Chris