September 16, 2010

Sailplans and heeling

EVERY NOW AND THEN I come across a comment in the yachting literature that puzzles me. One that pops up quite regularly is this: a long, low sailplan causes less heeling than a tall, narrow sailplan.

I don’t buy it. I can see where it starts, though. It’s all about leverage. It’s quite obvious that the taller the mast, the longer the lever, and the easier it is to make the boat heel over.

But something deep down inside me keeps saying that’s not all there is to it.

I readily confess that I lack the mathematical and engineering skills to work this out logically. Hell, if I was that clever I’d have a decent job instead of being a writer. But listen up for a moment, will you?

To make a boat heel to a certain angle there must surely be a certain fixed sideways force. It is the combined sum of all the sideways forces experienced by the sails at different levels all the way up the mast. Now I can’t see why it matters whether those sideways forces are generated higher up, as in the case of a high-aspect-ratio racing mainsail, or lower down, as in a gaff-rigged yawl with a long bowsprit.

I’ve tried to see why it matters but I have failed. It’s the force that’s generated that matters, not whether it’s generated high up or low down. So I am still very suspicious of any statement that claims a low sailplan leads to less heeling. If, in practice, it does, it can only mean that there isn’t enough sail area in the low sailplan. I think this whole thing belongs in the category of marine urban legend and I wish people would stop repeating it and spreading a misleading myth that makes me mad to think about. Well, not mad, but it does irritate the hell out of me.

I will grant you that a long, low sailplan makes it easier to balance the boat for weather helm. I will grant you that the gaff rig is powerful off the wind and well suited to many offshore cruising hulls. But I don’t want to hear any more about its causing less heeling, if you don’t mind.

The willful perpetrators of this myth presumably think that heeling is bad for a sailboat’s performance, otherwise they wouldn’t bother to crow so loudly about the benefits of a long, low rig. But that’s not altogether true, either. If a boat has long overhangs, heeling helps raise the potential hull speed by lengthening the waterline. On the other hand, as dinghy sailors know full well, heeling spills wind from the sails and robs a boat of some of its motive force.

That’s the trouble with sailing. You never know what to do for the best until someone comes sailing past you with a big smirk on his face. Only then do you know that what you are doing is wrong. But by then it’s too late.

Today’s Thought
We hold rumour
From what we fear, yet know not what we fear.
But float upon a wild and violent sea
Each way and move.
— Shakespeare, Macbeth

Boaters’ Rules of Thumb, #95
Galley stove gimbals. If your gimbaled galley stove has only one pivoting axis, it should swing sideways, that is from port to starboard. If you install it so that it swings fore and aft, it will incline as the boat heels and everything will slide off. Single-burner stoves gimbaled in both directions don’t have this problem.

Newspapers do all they can to protect the public. They print warnings of storms, floods, tsunamis, twisters, droughts, and epidemics of swine flu. They even print the TV programs in advance.

(Drop by every Monday, Wednesday, Friday, for a new Mainly about Boats column.)


Todd Bates said...

Ever use a teeter totter. If the children using it are different weights then you can change the length of each side until it balances. More length, more torque. With a sail its more torque, more heal. The thing is that a tall sail is more efficient and gives the same performance with less sail. The performance is so much better that the sail is small enough that there is less torque for a given performance. Notice that the really high performance boats have tall narrow rigs. Thats to give them the best performance/ballast ratio. So if the performance is the constant then the tall rig will heal less.

j2jenkins said...

John, I just started reading your blog last month and am really enjoying your writing.

The key bit of physics that you are ignoring is the "moment arm." The moment is calculated by multiplying the (Force) x (the distance from the axis of rotation.)

The larger the distance from the axis the larger "moment" is experienced.

If two sail plans create identical horizontal forces, the one that is centered higher will have a larger moment and cause the boat to heel more.

This is why you can create more force on a wrench by adding an extension.

Aaron Headly said...

I'll try this one on a saltier tack.

Ask yourself which sails a square-rigger strikes when a blow is coming, the big old courses and mains, or the little (but higher up) topsails and royals?

Was it Archimedes who said "Give me a long enough lever, and I'll move the world"?

Unknown said...

John, I'm a lubber (vs. marine) engineer , but let me give it a try. Imagine a "center of rotation" for the hull -- a line through the hull around which the boat would turn in a rollover. Also consider that the force of the wind on a sail can be resolved into a fore/aft component and a lateral port/stbd component acting through the center of effort (centroid) of the sail. Then, the heeling moment of a sail in foot-pounds is the lateral wind force in pounds multiplied by the distance from the center of rotation in feet. In a triangular sail, this point is located at 1/3 of the hoist. In the case of multiple sails, the heeling moments simply add together.
I know you were comparing gaff rig to bermudan, but the geometry of vertical right triangles makes the comparison of tall and skinny vs. short and long easier. Let's compare a bermudan sloop to a ketch carrying comparable sail area spread over two sails equally, like a Sea Pearl. For simplicity, neither boat is flying a jib. With the assumption that wind force (F) acting on a sail is proportional to it's area, then the sloop sees F while a ketch with an equally split sail plan would be F/2 + F/2. The total lateral wind force is the same, as you suspected. In the over-simplified case where the boom length is constant for all sails, then the ketch main and mizzen masts (M/2 ft) are half as tall as the sloop (M ft). If the height of the boom above the center of rotation of the hull is the same for the sloop and ketch and small compared to mast height M, the effect can be disregarded. So, the heeling moment for the sloop is (F)(M/3) = h, while the heeling moment for the ketch is (F/2)(M/2)/3 +(F/2)(M/2)/3 = (F)(M)/6 = h/2. The ketch has HALF the heeling moment as the sloop for equal total sail area given my assumptions.

Ken said...

As my Trade High School education is the limit of my technical ability (other than a few thousand offshore miles in the North Atlantic)to decipher these kinds of discussions I'll have to go with Aaron and the simple saltier tack.

Good stuff John!