Originally Posted by msponer
My eyes are not glazing! I'm interested in this since our new boat has a hydraulic lift keel. I have almost zero experience with this boat and have been curious if we'd ever experiment
with lifting the keel in any situation that is not wanting to reduce the draft
while making landfall.
Would you mind explaining this?
My undergraduate degree is in physics, which I am only mentioning since that means I have a surface familiarity with the types of thought a domain expert would use to figure this out, but none of the details.
Anyways, my non-domain-expert intuition is that raising the ballast will decrease the roll inertia and make it much easier to roll the boat. So I am guessing that part of your thought is that raising the keel decreases other inputs -- reduces 'tripping' if the boat is hit by a wave sideways, or etc?
Is there any math or other thought that makes this idea come up the clear winner?
Yay ! Someone who won't go "meh...", or "whatever... !" , the moment things get difficult !
( I suppose I should read you your rights ... you are allowed to switch allegiance to the "eyes glazing over" camp after the first thousand words!)
Without knowing more about your boat I'd have to guess there will be some ballast in the keel, and some internal ballast in the boat (either 'formal' dedicated ballast, or informal, such as a chain locker or machinery space situated low and amidships)
When you raise such a keel, the overall centre of mass does indeed rise somewhat (realistically we're probably talking less than 150mm, possibly much less).
However the radius of gyration of the whole system (and hence the rotational mass moment of inertia, or "roll inertia") does not change much.
One way of looking at this: because the mast
is so much further from the CoM, and its mass is so spread out, it makes a considerable contribution to the combined gyRadius.
Moving the CoM of the hull and keel slightly closer to the CoM of the rig is not going to exert much influence on the combined gyRadius, and hence the "roll inertia"
Whereas losing the rig has a huge influence, and it's sometimes a major problem after a dismasting
in high seas: even though the CoM is (slightly) lower with no rig, the "roll inertia" is so much reduced that the boat can have a perceptibly increased risk of wave action capsize
In one other respect, it can be a good thing that the CoM is raised with the keel.
I say this because the most inexorable mechanism for a wave-action capsize
is generally held to go something like this (although I've fleshed it out with some detail to do with orbital action, which I haven't quantified so it may be controversial):
Assume the boat is beam-on.
Assume further that the wave we're focussing on is at the point of reaching a certain critical steepness, which will result in the crest (consisting of aerated water) becoming detached from the body of the wave. This body of water
will continue to act like a semi-solid ramp
, advancing at up to forty knots in highly exceptional circumstances, but not taking the water with it (in fact the opposite is true as the boat starts up the face - see below).
The crest will avalanche under the influence of gravity down this ramp
which is in turn moving towards the boat, consequently it may reach truly dangerous speed by the time it impacts the topsides.
(Consolation: This mechanism almost NEVER happens in deep water: what most people call "breakers" are actually spilling the majority of water harmlessly down the back, if you look closely)
I'll focus first on the approach of the boat up the flank, before the crest topples forward.
As the hull is lifted up the solid flank of the approaching wave, it has a tendency to conform to the 'new normal' waterplane, which progressively tilts increasingly steeply, causing the boat to roll the windward topsides up out of the water.
If you have a narrow waterline beam and a deep ballast keel (particularly a thin strut and a heavy bulb) this won't happen to any great degree, and in this case raising the keel might be a bad idea.
However with a typical swing keel, which has a reasonable amount of planform area but often is only ballasted towards the tip, leaving it down might do more harm than good in this phase, even with a relatively narrow waterline beam (rare in modern designs).
I say this because there's something else happening here which is insidious and not widely recognised:
(I'll assume anyone who doesn't know about the orbital motion of a notional water particle will look this up on the internet)
Viewed side on to the direction of advance of the wavetrain, individual particles of water are moving contrary to the direction of advance, during the bottom semicircle of their circular orbit.
The radius of the orbit is increased in direct proportion to wave height. If the period is short in relation to height (eg, steep waves on the point of breaking), this speed can be substantial for high or very high waves.
This means the surface water is trying to carry the boat sideways towards and then up the face of the wave by means of the underbody, including (if it's down) the keel. The conservation of linear momentum means the boat's mass resists this lateral acceleration. Because the combined centre of mass is well above the centre of lateral resistance (more so with a lifting keel fully down), this resistance creates a roll moment, again rolling the windward topsides out of the water.
This I think is a bit of a worry, because if you track the change in direction of the water particle vector, as the boat travels up the wave and the keel swings towards the horizontal, the vector is simultaneously swinging towards the vertical (travelling vertically up, carrying the mass of the boat with it against gravity and inertia).
If I'm right about this, the force, at least in theory, could 'follow' the keel around, still tending to increase the roll. If I'm not, most of my explanation (and my conclusions) will, I believe, still apply.
Remember that a typical modern hull form, with plenty of "form stability" (wide waterline beam) is already likely to be at a considerable roll angle as it tries to conform to the local waterplane, which could be approaching 60 degrees to the horizontal in extreme cases.
The problem with all this is that the crest of the wave is about to impact the hull, and we very much don't want to be presenting a broad expanse of topsides, and a high gunwhale, to that crest.
It's the impact of the detached crest against this area (remember, that crest is travelling ABOVE the local waterplane, which is what floats the boat) which is generally believed to be the main motive force for a knockdown.
So rolling away from the oncoming wave creates several problems: it presents more area of hull to the crest, it presents it higher off the water, and it presents it more perpendicularly (angle of incidence closer to 90 deg)
So we have this very large force vector acting on the exposed topsides, acting substantially parallel to the local waterplane, but raised above it by about half the height of the gunwhale on that side.
We now have to think about the reaction force to this imposed, external force vector.
There are two: one is due to F=m.a, or the conservation of linear momentum.
So, (counterintuitively), we actually want the Centre of Mass as high as possible, ideally approaching the midheight of the exposed topsides, so it lies on or close to the force vector.
I think this addresses the reasonable question you raised, which reflects good common sense and conventional wisdom.
After all, we grow up thinking of ballasted keels as conferring security
from capsize: that's their primary purpose, certainly in classical recreational sailing mythology. (Which is a fancy way of saying, that's what we tell our womenfolk!)
The other reaction force might be thought of as the "tripping" lever arm, which you referred to. It's obvious that the deeper and larger the keel, the longer this lever arm, and consequently the greater the tendency of the boat to be knocked down. (Dinghy sailors who have to cross a bar regularly will be familiar with this effect). The problem is that the keel is down in green water, which furthermore is unhelpfully travelling in the opposite direction to the toppling crest.
I've only been in this situation once in an offshore
sailboat, in seas of serious proportions, so I can't pretend to have plenty of experience.
We had our keel swung way aft, and almost retracted. The rudder was large and deep. Hence the centre of lateral resistance was only moderately deep, but well aft. We were doing maybe fourteen knots at the time of impact, so we had hydrodynamic lift up the wazoo. We were beam reaching whenever we could, (and at the time of our knockdown) because that took us in the direction of our only safe exit.
When I replay the memory tape, I have a sense of the boat turning her bow slightly away from the impact, so that although we were knocked down with the mast
well below the horizontal, we surfed down the wave in that attitude without tripping*. We didn't have enough keel down to trip us, and I think it was our residual forward speed, skewed in a more favourable, down-wave direction by the reaction vector aft, which prevented us tripping over our leeward gunwhale. (The problem here is that the boat is thrown down into the trough, where the 'local waterplane' is relatively level, so the lee gunwhale becomes a real tripping danger)
*Our direction of travel during this surf was a compromise between following the mast and following the bow, but mainly the former. I think the lee bow back to the master section must have been providing lots of hydrodynamic lift, otherwise we might well have done a diagonal pitchpole.