Reverse lead? What am I doing wrong?

[dionysis]

Hi all,

I read with interest Wardi's thread, on the balance of sailboats. No real conclusion was reached there about how to design balance into a boat from first principles. Hmm, why is it so hard?

Let's start with the simplest case: imagine a cylinder with a pointy end for a hull, and put the upright centre of effort of the sailplan arbitrarily over the centre of lateral resistance; which for argument's sake is just aft of the longitudinal centre of the boat. Ignore the rudder for now.

Now set the boat in motion and heeled: the sails produce a forward thrust out to leeward creating a yaw moment = healing arm*cos(heel angle)*thrust, which has to be balanced either by helm action or moving the sailplan forward by an amount = lead*side force.

Moving the sailplan can't be right: you would end up with a neutral helm when heeled which is not good since the boat would not round up in a gust, and lee helm when the boat is upright.

Ok, so leave the sailplan alone and use the rudder instead. Then yaw moment = rudder arm*rudder lift force. All other things being equal this lift force would be adequate to counter the yaw moment.

So in this simple case there is no need for lead; in fact if you take into account the lateral area of the rudder you end up with reverse lead.

What am I doing wrong?

[gonzo]

You are not calculating the ratio of lateral resistance between the rudder and the rest of the hull. Also, the offset of the sails' CE changes with the angle of heel. It is not static. The CE of the resistance of the hull is offset opposite to the CE of the sails . It increases with the angle of heel too.

[dionysis]

You are not calculating the ratio of lateral resistance between the rudder and the rest of the hull.

Sorry gonzo; I don't know what you mean here. I thought that by applying rudder to counter the turning moment, I had included the rudder in the total lateral resitance. So while you don't have reverse lead, you still got no lead.

Also, the offset of the sails' CE changes with the angle of heel. It is not static.

CE changes with heel of course. As the boat heels you apply more rudder - you apply the maximum rudder at the maximum heel, and no rudder when the boat is upright. I am presuming that max rudder is 3 or 4 degrees, for argument's sake.

The CE of the resistance of the hull is offset opposite to the CE of the sails . It increases with the angle of heel too.

You are right there. I assumed that centre of resistance of hull, would be at or near the CLR, and would stay there with heel, because in this simplest case, the underwater shape is the same as the upright shape.

Thanks for the reply.

[sorenfdk]

The hydrodynamic center of lateral resistance (CLRhyd) is nowhere near the geometric center of the underwater hull in plan (CLRgeo) - it is in fact closer to 25% LWL aft of the forward end of the waterline!
Calculating the exact position of CLRhyd of the entire yacht is not possible, but if you go to HISWA's homepage (I don't remember the URL - google for HISWA), you can find a paper by Keuning that describes a way to get pretty close to perfect balance.

Søren Flening

[dionysis]

Thanks sorenfdk for the reference, I have found the article and am reading it with interest.

[sorenfdk]

It is indeed interesting, although the math is a bit involved... Nice, that they have put the HISWA-papers (or at least some of them) on the web. If only SNAME would do the same...

[gonzo]

The rudder is calculated as part of the plane of lateral resistance in its neutral position. When it moves to the side, it provides a turning moment. This is different from lead, or lack of, which changes the balance of the boat.

[dionysis]

Yes sorenfdk, the maths is a little involved, but from my first reading it looks as though you can do the necessary calculations by hand using the supplied coefficients. I agree - it would be nice if SNAME published some of their artcles too!

The rudder is calculated as part of the plane of lateral resistance in its neutral position. When it moves to the side, it provides a turning moment. This is different from lead, or lack of, which changes the balance of the boat.

You are right gonzo, you have to include the rudder otherwise you will not have the weatherhelm necessary to selfsteer. Good point. So now we are back to reverse lead, since the lateral sailforce is behind CLR.

My argument so far is that for this simple hull, you do not need lead to counter yaw due to heel, since the rudder is more that adequate to counter this moment.

[Chris Rapson]

If I might quote from bitter experience.
My 7 ton 32' hartley ferro was built with ferro decks and boiler punchings as ballast.
It had massive weather helm in a gust & always required heaps of rudder to keep it straight in any type of breeze(weather helm-wanted to round up into wind, made the boat very slow).
I saw the sail designer at a boat show and asked him about this and he said that the problem was the ballast. Too much weight high up in the boat. He recomended a block of lead on the bottom of the keel.
For my next boat, a Van der Stadt Zeemin I used solid lead blocks, right where the designer said to put them. That boat was faster than a heavy cat, and sailed beautifully!