Tendency to broach during beat or close reach

Water Addict--everything you say, I agree with. My point about negative lift is that normally when sailing to windward, the lift on the keel not only pulls you to windward, but it also acts to increase heel. The center of lift is below the center of buoyancy and the LCF, which causes a rotation that tends to heel the boat more. With lift on the leeward side of the keel, yes, the boat will have more leeway, but it will also tend to be pulled back upright because the lift is causing the boat to rotate in the opposite direction.

Eric

 

here's a good round-up shot with the rudder barely in the water. Love the driver sitting in the bottom of the cockpit.

 

The fact is that this is an argument which alone could fill up an entire book on sailing aero/hydrodynamics.
To explain it in a more rigorous way, one needs to take into account at least all these things and then mix them all together:

Aerodynamic influence of wind gusts:
- the apparent wind is a sum of two components: true wind and airflow due to boat velocity. When a wind gust arrives, the true wind speed component increases, thus inreasing the aerodynamic angle of attack (A.A.) of the sail.
The same happens when the wind changes the direction, rotating in the sense of increasing A.A.
- the center of effort (C.E.) of the sails move aft with the increase of the A.A. To give an idea of this, increasing the A.A. from 10° to 20° will shift the C.E. from the initial 30% to about 40% of the mean sail chord.
It means that for a, say, 42 yacht with a sail having some 14 feet mean chord, the C.E. will travel by more than 1 feet for 10° of change in A.A.
- A wind gust increases the pressure on sails, thus increasing the heel angle.
So you have more pressure, acting through a point located more aft than the equilibrium situation prior to the wind gust. If the helmsman doesn't correct the rudder angle to compensates for this, a heeling and yawing rotation (i.e. a broach) of the boat starts off.

2) Aerodynamic influence of heel
Now, the influence of the heel is a hard to analyse, because of the strong coupling between heel, pitch and yaw angles. This is principally due to hull form and weight distributions.
If the pitch and yaw angles remain unchanged (a sort of ideal canoe-body hull) the effect of heel is a diminishing A.A. seen by the sail, because the component of the wind speed perpendicular to the sail plan will be smaller. The result of this is that the pressure forces acting on the sail become smaller with increasing heel.
But if the hull form is of wide-transom type, there will be a strong coupling between the heel and the pitch/yaw angles. Both pitch and yaw will increase, leading to an increase in A.A. compared to the previous situation.
So, when you sum the negative variation of the A.A. due to the heel and the positive variation due to pitch/yaw, the final result might be an equal, bigger or smaller A.A. (and the relative pressure force), depending on hull form. If the A.A. increases than the pressure on sails will increase (relative to a situation with no heel/pitch/yaw coupling), the C.E. will move aft and will contribute to the broaching moment.
Thet's a real pain to analyse, indeed.

3) Hydrodynamic influence of heel:
Same story below the water surface. Let's consider the heel first. By applying the same reasoning seen before, we arrive to the conclusion that the A.A. of the keel will become smaller due to heel. That's because the component of the water velocity perpendicular to the keel plane becomes smaller. Thus, the keel will produce less lift and, in order to re-establish the equilibrium of forces, the boat's leeway angle will increase.
If the hull is of canoe-type, the heel angle will not have other influences on the keel because the C.E. of the keel varies little with the A.A.
But, if the hull has a wide transom, we will once more have to take into account the coupling between heel, pitch and yaw angles, and the final result will be an even more pronounced decrease in A.A. seen by the keel. And that's not all. An increase in pitch due to heel means that the boat will be navigating head-down, thus shifting it's center of lateral resistance (C.L.R.) forward.
So at the end there will be an increase in lever arms (C.E. of the sails move aft, C.L.R. moves fwd) of the opposite-acting aero and hydrodynamic forces which will have to be kept in equilibrium by the rudder.
But the same effects seen by the keel will be seen by the rudder too, with the aggravating influence of the ventilation. If the boat has a head-down attitude due to heel, the rudder will tend to work closer to the surface and could suffer a loss of lift due to ventilation. Since the rudder is what keeps all the forces and moments in equilibrium it is easy to understand that when it's efficiency decreases too much due to the effects seen above, nothing remains to prevent broaching (due to increased lever arms, as seen before).

There is also an influence of waves. When a boat is navigating in following seas with breaking waves, the movement of the water close to the surface will be such that it will tend to drift the bow towards the incoming wave, while pushing the stern away from it. So the boat will tend to rotate towards the wave, and that will have to be counteracted by the rudder. Now, since it is due to the nature of waves and is not related to a particular design feature of a boat hull, I'll not get any deeper into this.

So the conclusions of all this are: the rudder(s) need to be abundantly dimensioned and placed in a position which will assure that it is always immersed in the water and in the proper working conditions. A hull should have a form which will not produce an excessive coupling of the heel, pitch and yaw. The C.E. of the sails should be analysed in all conditions, knowing that it can travel back and forth as much as 15-20% of the mean chord length. And the rudder (again) has to be able to equilibrate the moments arising from these extreme lever arms without stalling.
It may sound like something obvious, but making all these things fit together is not a banality.

 

One of my discoveries in researching my paper was that the schooner yacht America came out perfectly balanced when subjected to the Turner analysis. This evidently was no accident, as this quote from the Lawson History of the America's Cup (1902):

"Captain A.J.Kenealy of New York, one of the best-informed writers on yachting on either side of the water, an old sea-dog, and English by birth, thus summarizes the reasons for America's success:

'The model of America was designed with a special regard to stability. She was a sea-going craft, as well as a fast yacht, and with her long and somewhat hollow bow she had a cleanness of after-body which is, even at this day, worth copying ... George Steers in his design of America took care to produce a model in which the centre of buoyancy was not at a ridiculous angle with the centre of the load water-line. He had hosts of imitators in England, and the result was that those who thought they had copied him were completely at sea when they tried to balance their ships — that is, to give them such a lateral plane as would bring the centre into the proper relation with the fixed point already determined. This could not be done, and the rig put on them had to be shifted back and forth until the required equilibrium was attained. There was, therefore, in several of the imitations of America, one force acting against the other, the evil effect of which became especially manifest when they were subject to heavy pressure, while in the America the harder it blew the faster she sailed. The chief defects in the English boats referred to, such as Gloriana, built by Ratsey in 1852, and Aqualine, built by Harvey in the same year, were that they were all bow, leaving nothing for the after-body, and moreover, especially short-bodied under water. Their sea-going qualities were not, therefore, the kind that a naval architect could be proud of.'"

America's upright waterplane was nearly symmetric fore and aft, and so the center of the LWL would be very close to with the LCF. Working through his Edwardian prose I get the following understanding:

The copiers didn't understand hull balance, and didn't put the LCF in proper relation to the LCB. They then attempted to compensate for the "heel causes yaw" phenomenon of an unbalanced hull by playing with sail balance, that is, moving the CE of the rig to compensate. This only works (as I have learned with free-sailing models) for a limited range of wind speeds, whereas a balanced hull tracks properly (and therefore maintains sail balance) over a wide range of wind speeds. Or at least, that's what I *think* he's saying

Cheers,

Earl

 

@Daiquiri

I have not found any reference regarding this broaching phenomenon and its calculation. What is the size and type of boat which can be expected to broach. I ask this question because of the following two videos in which those two phenomena are termed as broaching. Is it right?

https://www.youtube.com/watch?v=utmJGpfgMEk

https://www.youtube.com/watch?v=Wt1j7wiS5Zk

Is there some formula to predict this for any hull?

 

There is this video with some explanations:
https://www.youtube.com/watch?v=p1m13bJKsDM

Also the MSC Circular 707:
http://www.sjofartsverket.se/upload/7156/707.pdf

Interesting info.

 

https://www.youtube.com/watch?v=NKusg6Jyc9Y
the vastly superior coursekeeping abilities of a long keel...

 

Among radio yachts, the EC12 class (5 ft long, 6 ft mast, 24 lbs, full keel) is notorious for entering a "death roll" on the run, in which the boat starts oscillating with increasing period until it broaches. The EC12 hull is based on a tow tank model for a 12m.

Here's a good picture of one right on the hairy edge. Note how the rudder is starting to ventilate.

Cheers,

Earl

 

She veers around 30 or 40 degrees at times, doesn't she? I've always thought that vid looked very uncomfortable, as you'd expect of a boat designed for inshore racing.

 

...at >21m she is not exactly an "inshore only racer"...