I don't know of any such formula. I think tthat for a newly designed hull
, one designed by a nautical architect using one of the several dedicated software
packages, the software
could produce figures for the boat in notional lightship condition.
For a boat with gear
, and crew on board, you could calculate some index of hobby horsing, but it would require a massive amount of data specifying the mass and 3D location of every bit of gear
, and crew members, plus an index of rigidity for the crew members etc.
I mentioned anchors in my earlier post, because an anchor
can be regarded simply as a point mass and its contribution to polar moment of inertia estimated easily knowing its distance from the pitch
point. An anchor
chain, extending over an area, would require integration of its mass distribution. But the point of mentioning them is that anchors and anchor chain are dense and can be moved easily.
There are easy ways to get a handle on tendency to hobby horsing and other measures of the time period of motion of a boat. And the easy ways also let you see if a different stowage scheme will reduce the tendency of hobby horsing, especially in the conditions you often experience.
The easy ways are:
(1) start with your boat in 'departure condition': fuel tanks
and water tanks
full, provisions loaded, crew aboard in their usual positions (e.g. one below, one or two in the cockpit
- whatever is your usual situation), but still at a dock
with loose docklines.
(2) start the boat pitching (by whatever means is at hand - pushing down on the bow, getting a crew member
to move to the bow), and then time 10 pitches of the bow, calculate the period of a pitch
cycle, and the frequency of pitching. Call that 'natural pitch period, departure condition' and 'natural pitch frequency, departure condition'.
(3) do the same with roll, resulting in 'natural roll period, departure condition' and 'natural roll frequency, departure condition'.
(4) repeat #3 and #4 when you've arrived back after coming close to exhausting provisions and stores.
(5) repeat #3 and #4 in lightship condition (if you're keen) or in different stowage schemes (especially one that follows of the rules of (a) keeping the ends of the ship as light as possible - including the mast
; (b) getting the anchor off the bow and moving anchor chain as close to the pitch point as possible; (c) stowing everything that is heavier than water as low and as close to the pitch point as possible; try also breaking each of those rules to see what happens).
(6) if you have discovered a way of starting a 'standard' pitch (such as getting the same person to jump onto your bow and then jump off) you can also count the number of discernible pitches before the movement decays and the hull
is at rest.
(7) in your local choppy conditions, measure wave period.
* avoid stowage systems that cause 'natural pitch period' in any load condition to be close to wave period; That leads to amplified pitching.
As several others on this thread have commented, usually the lighter the ship, the better; the lighter the ends, the better; and the longer the time before pitching decays the better (a surprise to some - you want the ends of the hull to respond to the waves; if pitching decays quickly, it usually means you have a barge, not a boat, or the ends are heavy).
For Led Myne, the natural pitch period in cruising trim is 2.5 seconds; natural roll period in cruising trim is 3.8 seconds (in design light ship trim, meaning the rare occasion the waterline is at the design waterline 3.9 seconds); roll acceleration (in design or lightship trim) 0.04397 g; and Ted Brewer's Comfort Factor (design lightship trim) 37.0.
As a fun thing to do, if you're at a boat show
with new boats in the water (or at a marina dock), you can choose a boat or three and start them pitching by rhythmically pushing the bow down and do the same measurements. Always good fun.