# Estimate of AVS formula

Discussion in 'Sailboats' started by Alby1714, Sep 18, 2021.

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### Alby1714Junior Member

Hi all,
I have been given the following formula to derive an estimate of the AVS for a given boat:
AVS=110+400/(SSV-10)
where SSV= Beam**2/(Ballast Ratio x Draft of Canoe Body x (Total Weight/1025)**1/3)

clearly for any given boat the AVS can be increased by decreasing SSV which in turn can be decreased by increasing the total weight by increasing the ballast. However the formula does not take into account where one would place the additional ballast. One could place it under the floor boards , could make the keel deeper or could place it on top of the mast, the estimated AVS would always increase and would be the same for all cases.
Does anyone have a formula for the AVS which takes into account the weight distribution/location ?
Thank you.

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### TANSLSenior Member

Nice formula, really. Do you mean that any boat, whatever its type and shape, that has no ballast, has an AVS = 110? By the way, in what units are the results of this formula expressed.
I do not know if there is the formula you are asking for but I can tell you that any procedure to calculate the AVS takes into account the total weight of the boat, in the condition in which the study is made, and its CoG (or the weight distribution, if you prefer it)

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### jehardimanSenior Member

Well it's obvious that the formula is metric. (Total Weight/1025)**1/3 is just the length of a side of a cube that represents the displaced volume. And Ballast Ratio x Draft of Canoe Body just scales this cube to assume that all that ballast volume is placed at the bottom of the canoe hull. I'd need to do some cyphering, but I'm pretty sure this formula comes from a set of rules where 110 represents the minimum required AVS and/or downflooding angle and the SSV term is related to the use of BM to adjust that angle.

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### TANSLSenior Member

@jehardiman, this is what I've asked :

This does not mean anything and, above all, it does not indicate in which units its results are obtained because 110 exagesimal degrees, for any ship without ballast it seems nonsense to me. Out of discretion and respect for you, I will not continue commenting on your post.

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### jehardimanSenior Member

Apparently, as found in this thread, the formula comes from K. Adlard Coles and Peter Bruce (eds.) Adlard Coles’ Heavy Weather Sailing, revised 3rd edition, chapter 2: ‘Stability of Yachts in large breaking waves’, pp11-23, International Marine, Camden, Maine 1980.

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### sharpii2Senior Member

This is very confusing. I can't even figure out what the terms are. Does "Beam 2" mean Beam times 2? Or does it meam Beam squared? And what'with the double apostrophe? Does that mean squared?

This is the danger of using formulae when one doesn't understand how they work.

This also underscores the danger of not knowing how stability works.

Since most sailboats have a Vertical Center of Gravity (VCG) that is above their Vertical Center of Buoyancy (VCB), the Horizontle Center of Buoyancy (HCB) must move further to the low side than the Horizontle Center of Gravity (HCG), when the boat heels.

Vanishing stability occurs when the HCG is directly above the HCB. At this point, if the boat heels any further, it is almost certain to flip.

So, what really matters is the vertical distance between the VCG and the boat's Vertical Center of Volume (VCV) , divided by the boat's average Beam. The larger this fraction is, the greater the boat's AVS is.

There are three ways to increase this fraction:

1.) increase the distance between the VCV and the VCG by simply adding more ballast. This is an ancient approach. This is why a lot of sea-going work boats with low sides tended to have deep hulls and were heavy. This is probably the most reliable method. Boats using this method often had long keels that tended to dampen snap rolls. They were notoriously hard to flip.

2.) extend the ballast deep beneath the hull, while adding as little buoyance there as possible. This is the modern approach. This way, it is possible to have a boat that is relatively light for its Beam, yet still have a high AVS. But this method does not necessarily guarantee the boat will be unstable when upside down. There was once an Open 60 racer that got capsized in the Southern Ocean. It lost its rig but kept its bulb-keel. It floated in that condition for months on end, despite almost certain encounters with huge breaking waves. The flair of its low sides and the shortness of its deep keel gave little area for the waves to work with. Also, the heavy bulb, held about 20 feet into the air, provided a lot of inertia against any snap roll breaking waves might cause.

3.) raise the sides of the hull, as well as the deck, while keeping the average Beam the same. This method harms performance by raising the Center of Effort of the sails relative to the Beam. This also moves the weight of the spars higher above the WL. For this reason, this method is rarely used. It, more than the other two, trades initial stability for a higher AVS.

I suppose this formula tries to take these three methods into account.

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### jehardimanSenior Member

So I actually haven't seen the relevant quote in print, only from the dead post; but I'm pretty sure like Alby (the OP of this thread) it is beam squared. "**" is FORTRAN for exponential, just like "^" is for BASIC. That makes sense as the quote text talks about knockdown AVS (a function of RM from BM) so BM ( in BASIC) = (1/12 *K* L* B^3 )/Cp *L*B*T >> canceling B and L >> {1/12*K/Cp}*B^2/T. So there is some method behind the madness...Just what it is will take some time to tease out.

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### The QSenior Member

Having wandered around the net looking at the formula ** is ^ is "raised to the power of"

Anyway it's not a formula I'd tried before, so I did for my small boat,.
It came out as 113 for the boat empty, 120 with me on board.
This is good since my boat is purely for inland waterways.

From this site which gives a good explanation of the formula.
Angle of Vanishing Stability - www.yachtdatabase.com https://www.yachtdatabase.com/en/encyclavs.jsp

0 - 80 This indicates a boat suitable for calm water only.
80 - 100 This indicates a boat for inland water only.
100 - 120 This indicates a boat for offshore sailing.
120 - 140 Boats with this angle will usually be left floating upside down once capsized.
140 - + Boats with this angle will usually right themselves.

Sharpii2s comments reinforce ideas that were for design of the boat , the lead is on the bottom of the keel, the sides of the hull are high enough so 90degree knock down shouldn't allow water on board.

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