Roll Period Test... Waterline Beam or Total Beam?

I am planning on doing a roll period test tomorrow. I will use slow mo video to measure roll period in seconds. I have 540 lbs of removeable ballast on the boat now.

See this gallery:

New Keel, Who Dis? | Boat Design Net

I know that the roll period should be between 1 an 1.1 times the "beam in meters". But is that waterline beam or total beam? Why?

 

The formula I know for the approximate value of the roll period T is as follows :

T = f * B/sqr(GM0)​

where :

T is the time of a complete roll period in seconds
f is a factor that varies between 0.6 and 0.9
B is the vessel's beam, meters
GM0 is the initial value of the GM, meters.​

 

In both cases, your rule of thumb and TANSL's formula, Beam is the waterline beam because both are based upon the "wall sided" assumption of a typical ship hull. For a slack bilged vessel like a submarine, f can be as low as 0.36.

A more accurate formula slack bilged sailing vessels could be T = 2*pi*k/sqrt(gravity*GMo) or T= 1.108*k/sqrt (GMo) where k is the mass radius of gyration. But again, this really doesn't take into account the damping action of the fin keel.

The above data was pulled from PNA, I haven't drug out my copy of Principles of Yacht Design by Lars Larsson (Author), Rolf Eliasson (Author) which might have a different formula.

 

If you do not like doing sums, this table might be easier to use?

In the table the beam is the maximum beam at deck level - note that it takes freeboard into account as well.

 

LOL, we used to sally aircraft carriers. Getting 1000+ grumpy sailors run accross the flight deck in the morning pierside was difficult until they actually found out they could make it roll.

 

Hull beam.
Neither the waterline beam nor the total beam: the hull beam, measured amidship in the side/main deck intersection.

 

Roll period is 2.0 seconds. Hull beam is 8.5 feet, or 2.6 meters. Plenty of stability. When I add a large canopy with solar panels up high I will retest.

She is floating several inches above the painted waterline and clearly floats higher than a stock pearson 26.

Sadly this means I *really* need a 25” shaft outboard.

 

Roll tested without mast and rigging?

 

I believe so yes...and with the removal of the fin keel and the fitting of a "ballast" keel and the addition of internal ballast.

Not really sure from his posts.... Project Log - New Keel, Who Dis? (Pearson 26 to Electric Cruiser) https://www.boatdesign.net/threads/project-log-new-keel-who-dis-pearson-26-to-electric-cruiser.65430/

 

Correct. No mast, no 2200 lb cast iron keel.

Replaced keel with a 150 “skeg keel” ll feet long but only 4” high. Added another 560 lbs of brick ballast.

 

Interesting.

So am I concluding correctly that you will have no mast/rigging/sails of any kind? (pardon my naivety)

I’ve always thought of sails as the greenest propulsion. The idea of removing them perplexes me.
(Though I have lived offgrid w/ solar for 6 years now I’m pragmatic, not thunburgesque or any other kind of patronizing superhero)

 

Sailing is definitely greener.

But - I don’t want to sail. I don’t want to put up a mast or wrangle ropes or tack. I want to putter along quietly wind or no wind.

This hull may not have been the best choice for this project, but I think I will love the result.

 

That hull, without the mast or rigging, which are weights placed very high, without the sails, which produce an enormous heeling moment, has to be very stable, perhaps a little too stable. You'd have to run the numbers to get a real idea of how it behaves.

 

Tests beat calculations. Every time.

The boat is in the water and has a roll period of 2 seconds and a beam of 8.5 feet. By the numbers it is a bit “too stable” but the motion feels fine to me.

When I add 100 lbs of solar panels 7 feet over the cockpit floor I will test again.

 

Being a little "too stable" would only be a problem if it bothered you or the passengers. So there's no need to worry.