Keel : Rudder Length

[Alixander Beck]

What is the reason for the Keel being longer than the rudder on a boat?

What would happen if the rudder was longer than the keel? would this produce adverse effects?

Practically speaking I have a dinghy that draws 32" of draft from the centreboard. What would happen if the rudder also had a depth of 32"

I would think that this would be alright as they would both produce some good CLR and make the boat track well and possible head to windward better.

[Seafarer24]

Rudder size is determined by how much you need in order to turn the boat. It really doesn't take much, and if you have too big a rudder you're causing undue drag and could have a very twitchy helm.

Check out the Dotan Marine website. Their Sampson series should have a great rudder for your dingy.

[Skippy]

The rudder is also weaker than the keel, so you want the keel to be deeper than the rudder just in case you bash into some rocks. That way the rudder is protected and hopefully the keel will survive.

[yokebutt]

Some boats do, but you get a fairly high aspect ratio, and that can be tricky to reattach flow to if you stall it. Another thing is that most boats have some degree of rocker, wich leads to the top of the keel being deeper than the top of the rudder. Also, as previously said, the keel being deeper helps protect the rudder from unanticipated load conditions.

Yoke

[Alixander Beck]

So aside from occasional grounding there is no performance reason to not have a rudder at equal depth with the keel?

The Dotan Series Rudder 20 is similar to my design but with more area for the same given boat length, So I think mine should work out fine.

I notice that all the Dotan rudders and to a large degree many rudders are unbalanced.

What difference in performance could be expected from a balanced rudder over an un-balanced one? with say the leading edge being 1" forward of the pivots.

[Seafarer24]

The Dotan rudders are not exactly unbalanced. There is an adjustment in the way the rudder pivots so that the blade can be raked further forwards for more balance. You have to tune the rudders to your boat, mast rake, etc.

[Alixander Beck]

thanks Seafarer,

I guess you could consider forward rake to be "balanced" .
I am using the term "balance" to explain the position forward of the pivot of the leading edge of the rudder on a plumb vertical to the transom.

While the Dotan ones look versatile and adjustable - it would defeat the exercise of building one myself and exacting the beauty of fine woods being used.

[Doug Lord]

CBTF boats use a fwd foil and aft foil of equal size to develop lateral resistance and turn the boat.
The ARC 21 catamaran uses a concept called "shared lift" where the daggerboard is forward of the cross beam and the rudder is the same size or slightly bigger than the board.
On most dinghy's the rudder is somewhere near 50% of the area of the board; if you just arbitrarily made the rudder larger w/o also moving the daggerboard forward the boat would probably develop lee helm because, in effect,you have moved the center of lift of the foils(sometimes called CLR-center of lateral resistance) aft keeping the CE(center of effort of the sails ) in the same place.
Having 15-19% of the rudder area forward of the pivot point simply reduces the load you feel on the end of the tiller-while still allowing you to "feel" weather helm(or lee helm!); raking the rudder blade fore and aft allows an adjustable amount of area for doing the exact same thing.

[Alixander Beck]

I guess there is no mathematical way to calculate whether the new rudder will produce lee helm without actually getting it on the water?

while both foils will pull equal draft. the rudder will be ~60% area of the Board with ~190 insq and ~320 insq respectively.

Having used roughly the same area as the original rudder but in a higher aspect design I hope that there will be a slight decrease in weather helm, but that more can be added if neccessary by raking the rig.

I will post a picture of the pre-epoxied rudder if anyone is interested.

[yokebutt]

Alixander,

No, you won't get any lee helm from merely inreasing the area of the rudder, the balance of forces doesn't change. The only real downside of a larger rudder (within reason) is skin friction.

Yoke.

[Doug Lord]

Bad advice, Yoke. If you increase the rudder area on a previously well balanced boat you are moving the effective CLR of the boat aft in relationship to the sails. You will- at the very least- substantially decrease weather helm and could ,in fact, create lee helm. To be damn sure of my 45 plus years of experience I double checked by calling Eric Sponberg, a friend and a naval architect. He concurred with my previous advice.(Thanks Eric!)
You can visualize this by considering the balance of the Arc 21 previously described: by manipulation of the areas of the rudder foil and daggerboard Bill Roberts was able to place the daggerboard in a position that with a "normal" rudder would have caused unacceptably high weather helm. His concept proves rather emphatically that changing rudder AREA can have a profound effect on BALANCE. By visualizing a CBTF boat with the twin equal size foils it may also make it clearer: if you keep those two foils the same distance apart and move them forward relative to the rig the boat will have excessive weather helm; if you move them aft the boat will have lee helm. The point is that the "Center" of lateral resistance lies between the two foils.
Another way to look at it is to visualize a"normal" well balanced(I pressume) boat such as yours with the rudder held at zero degrees(parallel to the cl of the boat). Assume that the daggerboard is twice the size of the rudder. With the rudder held on the cl upwind the boat should want to turn into the wind and would begin to do so slowly. If you then doubled the rudder area the tendency of the boat to turn into the wind would be significantly reduced and could result in neutral or lee helm. That is all true because we know the boat is developing leeway and so it is obvious(I hope) that with the rudder held on the centerline both the daggerboard and rudder are developing lateral resistance proportional to their areas. If the weather helm was correct BEFORE the area change it will be less positive with the area change even ,possibly ,to the point of being neutral or lee helm.
If you not only change the area but change the efficiency of the area(aspect ratio) from what you previously had the effect could be magnified.

[yokebutt]

Okay, thought experiment here. Sail along in a boat, sails trimmed to give zero weather-helm. Now, increase area of rudder, do we get weather-helm all of a sudden with that?

I'd argue that the boat doesn't know how big the rudder is, but then again, few boats have 45 years of experience.

Yoke.

[Skippy]

Lorsail: Bad advice, Yoke. ... my 45 plus years of experience ... Eric Sponberg, a friend and a naval architect. ....(Thanks Eric!)

That's wonderful Doug.

Lorsail: You can visualize this by considering the balance of the Arc 21 previously described: by manipulation of the areas of the rudder foil and daggerboard Bill Roberts was able to place the daggerboard in a position that with a "normal" rudder would have caused unacceptably high weather helm. His concept proves rather emphatically that changing rudder AREA can have a profound effect on BALANCE."

Doug, that proves nothing without a description and explanation. It sounds like the larger rudder made it easier to compensate for a greater weather helm. That would be profoundly unremarkable.

By visualizing a CBTF boat with the twin equal size foils it may also make it clearer: if you keep those two foils the same distance apart and move them forward relative to the rig the boat will have excessive weather helm; if you move them aft the boat will have lee helm. The point is that the "Center" of lateral resistance lies between the two foils.

By visualizing the tiller or wheel left unattended, one can quickly determine that freely rotating foils have no effect on helm balance at all.

Another way to look at it is to visualize a"normal" well balanced(I pressume) boat such as yours with the rudder held at zero degrees(parallel to the cl of the boat).

If you're holding the rudder in any position, even straight ahead, I would not call that the boat's natural tendency. The helm balance is what the boat does when the rudder is free.

I seem to recall people including half the rudder area in finding the CLR. This must be a compromise between the boat's natural behavior unattended and its response to the tiller being held to weather under normal sailing conditions. Sounds reasonable from a practical point of view. Doug, why don't you ask Eric what he thinks about that?

[Alixander Beck]

Lorsail, good explanation.

In this particular case it is not that I am increasing the area a great deal from the original rudder. The original rudder was a disgusting piece of iron bolted to a rough stock with a tiller. There was absolutely no shape to the rudder what-so-ever, just a flat board of iron.

I have taken the original area of 160 in2 up to 192 in2 roughly adding 17% more area and put it on a higher aspect balanced (16%) design. My original questions regarding helm force and balanced were answered and the previous discussions have explained a lot (albeit, a lot that I already know) but good explanations regardless.

I would have to agree with Lorsail on what Skippy has just questioned him on:

Another way to look at it is to visualize a"normal" well balanced(I pressume) boat such as yours with the rudder held at zero degrees(parallel to the cl of the boat).

If you're holding the rudder in any position, even straight ahead, I would not call that the boat's natural tendency. The helm balance is what the boat does when the rudder is free.

I would argue that holding the rudder at 0 degree is the same as a "free" rudder. either way you slice it, the boat will reveal its helm balance with the new rudder if the foil is held at CL.

incidentally I think I will be ok with the helm balance as the old rudder could produce a lot of weather and pull at speed and frequently went totally dead when surfing down waves. (I am not 100% sure why still)

but if there are any educated opinions as to why......

[Doug Lord]

Yoke,in your thought experiment if you suddenly increased the rudder area you would definitely not increase weather helm but you might create lee helm since you are moving the area of the underwater lift AFT as compared to the CE(center of lift) of the sails.You set up the conditions as the boat having zero weather helm. So the rudder is on the centerline. Now we know that the boat is developing lateral resistance and it should be clear that both the rudder and daggerboard would be contributing lateral resistance roughly in proportion to their areas,right? Then if you all of a sudden double the rudder area the boat would have to "know" that it had more rudder area -45years of experience or not, right?
-------
Skippy,regarding the Arc 21 I thought I had given a description but I'll try to be clearer. Roberts moved the daggerboard forward and, as compared with "normal" cats, both decreased the daggerboard size and increased the rudder size. As best I can tell he did this to improve the boats' handling to weather particularly tacking since with the "shared lift" system the boat now has a longer moment arm between the foils.Both foils develop lateral resistance("shared lift") and because the rudder is larger and further away from the "new" daggerboard the turning force is also bound to be improved as compared to a "normal" set up.
The illustration of the boat with the rudder held on the centerline was an attempt to illustrate the fact that both foils develop lateral resistance and that substantially changing the rudder area of an already well balanced boat would be very likely to change the balance of the boat.
Many designers, including Eric, consider the whole rudder area in looking at both lateral resistance and balance particularly in small light boats where the hull plays less of a role in both.
PS-Yoke and Skippy- I apologize for sounding like a boorish jackass but I was trying to get Alixander the most accurate information possible....

[Alixander Beck]

Concerning Lift.

If the board has a flat profile and the rudder a NACA 0012 profile then is the board only producing lateral resistance and the rudder producing both lateral resistance and Lift?

In that case would all lift be generated by the rudder and how would this affect windward performance?

[Doug Lord]

Alixander, both foils are producing lift in the course of developing lateral resistance. The flat profile won't be as efficient in doing so as the properly shaped foil.I'm not 100% sure but the more efficient section on the rudder MAY have an effect similar to increasing it's area as compared to the flat profiled daggerboard.
Were both original foils flat? And by flat do you also mean squared off edges?

[Skippy]

Alixander Beck: I would argue that holding the rudder at 0 degree is the same as a "free" rudder. either way you slice it, the boat will reveal its helm balance with the new rudder if the foil is held at CL.

Careful Alixander, as far as the air and water are concerned, a geometrical line on the hull is irrelevant to how the boat behaves. Even Lorsail agrees that the rudder will exert a force on the boat when held firm on the centerline:

Lorsail: You set up the conditions as the boat having zero weather helm. So the rudder is on the centerline. Now we know that the boat is developing lateral resistance and it should be clear that both the rudder and daggerboard would be contributing lateral resistance roughly in proportion to their areas,right? Then if you all of a sudden double the rudder area the boat would have to "know" that it had more rudder area -45years of experience or not, right?

Lorsail: The illustration of the boat with the rudder held on the centerline was an attempt to illustrate the fact that both foils develop lateral resistance ...

Since we seem to be agreed that the boat will make some leeway, the CL is definately NOT parallel to the boat's true direction of motion, so even on the CL, the tiller is in fact being actively held to weather. The CL is not equivalent to a free tiller, as you will quickly find out if you ever fall overboard when you're singlehanding. If the boat has a weather helm without the rudder, it will round up when the tiller is released, regardless of how big the rudder is.

The only other possibility I can think of is if the the rudder is fairly heavy, so that its weight actually affects the helm. But I really don't think that's common. Other than that, it sounds like we're using different definitions of the word "balance". I would argue that including a helmsman's force on the tiller to define a quality of the boat, is not necessarily the best place to start. Maybe the best argument for including the helmsman's force is that it's more conservative: It will encourage designs that have even more weatherhelm and therefore will round up even more quickly when the tiller is released. But for a large keelboat or a racer, that might be considered either impractical or unnecessary, as I'm sure Eric knows, and would never make the mistake of ignoring. :cool: Let's all follow Eric's example, get our definitions straight, and make sure we know whether the helmsman is on the boat or not! :p

[Doug Lord]

The key point is that if the rudder area were changed substantially the balance(weather, neutral or lee helm) would CHANGE.It is the understanding that BOTH foils contribute to lateral resistance(achieved via the foils operating at an angle of attack to the water) that is key to understanding the effect of a substantial change in rudder area in the previous examples and to understanding the effect of reconfiguring the foil areas in the Arc 21 case or in any case for that matter.
---------------------
Speaking of definitions and clarity: "....so even on the CL the tiller is in fact actively being held to weather". Isn't it mutually exclusive to say that a tiller held on the CL is also "actively being held to weather"?
---------------------
edit:If the tiller on a boat with weather helm is held on the centerline of the boat the boat will turn into the wind just as it would if the tiller was let go-only slower....

[Skippy]

Lorsail: The key point is that if the rudder area were changed substantially the balance(weather, neutral or lee helm) would CHANGE. It is the understanding that BOTH foils contribute to lateral resistance(achieved via the foils operating at an angle of attack to the water) that is key to understanding the effect of a substantial change in rudder area in the previous examples and to understanding the effect of reconfiguring the foil areas in the Arc 21 case or in any case for that matter.

The key point, Doug, is that the whole question depends on how you define the word "balance", and that if you define it as the natural behavior of the boat with the helm free, then the rudder does NOT affect the "balance", only ONE foil (the keel) produces lateral resistance in that case, and the key to understanding the issue is to read other people's posts better instead of just rephrasing your original point.

Skippy: Since we seem to be agreed that the boat will make some leeway, the CL is definately NOT parallel to the boat's true direction of motion, so even on the CL, the tiller is in fact being actively held to weather.

Lorsail: Speaking of definitions and clarity: "....so even on the CL the tiller is in fact actively being held to weather". Isn't it mutually exclusive to say that a tiller held on the CL is also "actively being held to weather"?

Considering the fact that the CL, which defines the apparent heading, points to windward of the true course, and the tiller is held along the CL, no it is not mutually exclusive to say that the CL-oriented tiller is being held to weather of the true course, which is the direction that affects the rudder's lift and is therefore relevant to the boat's behavior.

[Alixander Beck]

Here is a picture of the original rudder and the new one (not yet glassed)

[yokebutt]

Doug, with a larger rudder you might not need quite as much angle of attack, but the amount of force required from the rudder remains the same, otherwise you'd be sailing in circles. An irate attitude doesn't justify fuzzy thinking.

Yoke.

[Eric Sponberg]

Gentlemen,

My presence has been requested.

When a boat is in perfect balance, and there is neither lee helm or weather helm, the Center of Effort (CE) of the sailplan is some distance forward of the Center of the Lateral Plane (CLP). If the CE moves forward from this position, the boat will tend to have lee helm, and when left on her own (nothing holding the tiller) the boat will tend to bear away from the wind. Keep in mind that the rudder is still causing some drag, and perhaps sporadic lift, even though no one is holding onto it. Similarly, if the CE moves aft of its perfect balance position, the boat will tend to have weather helm, and left on her own the boat will tend to round up into the wind. The same applies if you consider moving the CLP in relation to the CE. Moving the CLP forward creates a tendency toward weather helm, and moving the CLP aft creates a tendency towards lee helm. Changing the position of CLP can be done by moving areas themselves (daggerboard or rudder, as we are discussing) or by changing the areas of those items.

When sailing, that is, when someone is actively holding onto the tiller and trying to sail a consistent course, if the tiller must be held to leeward of the boat's centerline, she has lee helm. If the tiller must be held to windward of the boat's centerline, she has weather helm. The angle of the tiller to the boat's centerline is the "degree of helm", i.e. so many degrees of lee helm or weather helm. In boat design, one always strives for about 2-3 degrees of weather helm. This gives the most natural feel for sailing and gives positive control for steering. You do not want any more weather helm, like 4 or 5 degrees or more, because then the drag created by the rudder actually slows the boat down. And you never want lee helm because steering just feels unnatural, particularly when you are sitting on the weather side of the boat.

In past generations of yacht design, when sailboats had much larger keel areas in relation to the size of the rudder, designers tended to ignore the rudder area altogether in order to compare different boat designs. Gradually, as keels became smaller, rudders did not necessarily become any bigger, but rudders did become more important to the overall balance. Therefore, rudder area started being accounted for in the evaluation of underwater profile area and balance. These days, we always include rudder area in the calculation of CLP, but we correspondingly have had to change our rules of thumb to assess where best to put the rudder and keel (or daggerboard). In the end, however, the definition remains the same: The degree angle of the tiller off the boat's centerline, to windward or leeward, gives the degree of weather or lee helm. Again, we strive for 2-3 degrees of weather helm in modern designs.

If you have a nicely balanced sailboat with such a slight weather helm, and you double or triple the size of the rudder, the degree of weather helm will become smaller, to the point that it may disappear or switch to lee helm--you will be generating more lift at smaller angles of attack (smaller tiller angle) than what you required before. But by the same token, you will also be creating more drag. And the CLP will move correspondingly aft in relation to the CE, and therefore, there is a tendency toward lee helm.

That is how we assess the problem in sailing yacht design.

Eric

[Skippy]

Uh oh, one of the Big Guns wades into the water! :eek: Thanks for participating Eric. :)

This was the original exchange:

Alixander: I guess there is no mathematical way to calculate whether the new rudder will produce lee helm without actually getting it on the water?
Yoke: No, you won't get any lee helm from merely inreasing the area of the rudder, the balance of forces doesn't change.
Doug: Bad advice, Yoke. ...

I seriously doubt Alixander really cares exactly what the angle of the tiller has to be. It sounds like he's just worried that with the big rudder maybe the boat will suddenly start veering to leeward, which we certainly would not want to happen. I would agree with Yoke that Alix does not have to worry about that, that increasing the size of the rudder will not significantly affect how much force Alix will have to apply to the tiller, which way he will have to push it, or what will happen whenever he releases it. I don't see anything bad about Yoke's advice at all.

Eric: The degree angle of the tiller off the boat's centerline, to windward or leeward, gives the degree of weather or lee helm.

Based on the difference between apparent heading and true course, I would argue that this definition is slightly misleading. With a large enough rudder, the tiller could actually require a force to windward even to hold it a degree or so to leeward of the centerline, since it's still pointing slightly to weather of the boat's line of motion.

Eric: If you have a nicely balanced sailboat with such a slight weather helm, and you double or triple the size of the rudder, the degree of weather helm will become smaller, to the point that it may disappear or switch to lee helm

To the extent that this is true within the narrow, technical context of the definition above, I would argue that it's irrelevant and doesn't warrant discussion. It seems to suggest that a large rudder can actually require a force to leeward on the tiller to keep the same boat on course that required a force to windward with a smaller rudder. I would find that exceedingly hard to believe, and would very much like to see an explanation if it's true.

Eric: When a boat is in perfect balance, and there is neither lee helm or weather helm, ... If the CE moves forward from this position, the boat will tend to have lee helm, and when left on her own (nothing holding the tiller) the boat will tend to bear away from the wind.

Based on the definition above of helm balance, I would have to say that, technically speaking, this is not always true given a large enough rudder. Getting back to the definition again, I would say that it's not an accurate measure of what I would consider "perfect balance". I still agree with Yoke's basic point that there's no such thing as the size of the rudder changing the direction of the force on the tiller required to hold the boat on course.

[Alixander Beck]

So essentially if I am to cut through all the theoretical banter, what you are saying is that there will be little difference in Helm Balance with this new rudder and hopefully there will be a great decrease in drag and chatter.

That is what I expected, and I have thoroughly enjoyed being a "fly on the wall" to this academic pissing contest. ;) and appreciate your experience and opinions.

Perhaps I could introduce a new topic of which to flex your minds around?

Why did the rudder go 'dead' running down wind ? It was a pretty hairy day and the dinghy was overpowered and pushing hull speed. I caught a wave, the Helm got massively heavy and the rudder produced no turning force which lead into a subsequent capsize. I cannot figure out why this had happened and feel that in some way it relates to not having the Jib up (CE being to far aft = increased weather helm?)

[Eric Sponberg]

Skippy said: "Based on the difference between apparent heading and true course, I would argue that this definition is slightly misleading. With a large enough rudder, the tiller could actually require a force to windward even to hold it a degree or so to leeward of the centerline, since it's still pointing slightly to weather of the boat's line of motion."

The difference between the boat's course and its hull centerline does not really enter into the discussion of balance. That difference is called "leeway" and has little to do with lee helm or weather helm. The vast majority of boats have leeway, only a very few specialized boats are capable of "windway", in which the course line is to windward of the boat's hull centerline.

Skippy: It seems to suggest that a large rudder can actually require a force to leeward on the tiller to keep the same boat on course that required a force to windward with a smaller rudder. I would find that exceedingly hard to believe, and would very much like to see an explanation if it's true.

You have to remember that there is drag associated with lift, and there is form drag--that is, the drag just due to the frontal area and volume of the appendage. Taken to the extreme, form drag in a very large rudder can upset the balance of the whole boat to the point that a large rudder could require some lee helm to keep a boat on course. Because of the size of the rudder, that lee helm angle might be quite small. And remember, in most boats, that course we be to leeward of the boat's centerline.

Alixander:Why did the rudder go 'dead' running down wind ? It was a pretty hairy day and the dinghy was overpowered and pushing hull speed. I caught a wave, the Helm got massively heavy and the rudder produced no turning force which lead into a subsequent capsize. I cannot figure out why this had happened and feel that in some way it relates to not having the Jib up (CE being to far aft = increased weather helm?)

Most likely, your flat plate rudder stalled. The massively heavy helm was your reaction to hold lift (and drag) at a very high angle of attack because you had just the main up, and therefore, very bad weather helm. To sustain balance, you needed a large force on the rudder, and you could only get that with a high angle of attack. Unfortunately, it was too close to the stall angle. Suddenly, the rudder stalled--the flow separated off the leading edge of the rudder and it lost all lift. With no lift, you lost control. It takes some moments for lift to catch again after a stall, and you probably crashed before lift could be generated again.

This is exactly analagous to a plane stalling and going into a spin. It loses all lift suddenly, and then teh plane starts plummeting nose-first into the ground. If you are up high enough, you might be able to get the lift back on the wings again, but you are going to fall a few thousand feet before you succeed. This is why in stall/spin training in an airplane, you should start at least 3,000 feet above the ground, and if you're a student pilot, you should start 5,000 feet above the ground. Make sure you have a CFI in the right seat to catch you if you screw up! So in your case, you lost lift on the rudder in a stall and did not have time to get lift re-established again.

Eric
(Licensed Private Pilot)

[Skippy]

Eric: The difference between the boat's course and its hull centerline does not really enter into the discussion of balance. That difference is called "leeway" and has little to do with lee helm or weather helm.

That's exactly my point Eric:

Doug: You set up the conditions as the boat having zero weather helm. So the rudder is on the centerline. Now we know that the boat is developing lateral resistance and it should be clear that both the rudder and daggerboard would be contributing lateral resistance roughly in proportion to their areas,right?

Alixander: I would argue that holding the rudder at 0 degree is the same as a "free" rudder. either way you slice it, the boat will reveal its helm balance with the new rudder if the foil is held at CL.

Skippy: Careful Alixander, as far as the air and water are concerned, a geometrical line on the hull is irrelevant to how the boat behaves. Even Lorsail agrees that the rudder will exert a force on the boat when held firm on the centerline...

The boat's course relative to the orientation of the foils is very relevant to the lift they produce. The centerline, on the other hand, is just a geometrical feature of the boat. It does not affect the behavior of an unrestrained rudder, and is related to the keel only because the keel is connected to the hull.

But your definition of helm balance is stated clearly in terms of the centerline:

Eric:
When sailing, that is, when someone is actively holding onto the tiller and trying to sail a consistent course, if the tiller must be held to leeward of the boat's centerline, she has lee helm. If the tiller must be held to windward of the boat's centerline, she has weather helm. The angle of the tiller to the boat's centerline is the "degree of helm", ...
...
In the end, however, the definition remains the same: The degree angle of the tiller off the boat's centerline, to windward or leeward, gives the degree of weather or lee helm.

And you use this definition to predict the boat's behavior in the water:

Eric: When a boat is in perfect balance, and there is neither lee helm or weather helm, ... If the CE moves forward from this position, the boat will tend to have lee helm, and when left on her own (nothing holding the tiller) the boat will tend to bear away from the wind.

I just don't see how that's consistent.

------------------------------------------------------------------

Skippy: It seems to suggest that a large rudder can actually require a force to leeward on the tiller to keep the same boat on course that required a force to windward with a smaller rudder. I would find that exceedingly hard to believe, and would very much like to see an explanation if it's true.

Eric: You have to remember that there is drag associated with lift, and there is form drag--that is, the drag just due to the frontal area and volume of the appendage. Taken to the extreme, form drag in a very large rudder can upset the balance of the whole boat to the point that a large rudder could require some lee helm to keep a boat on course. Because of the size of the rudder, that lee helm angle might be quite small. And remember, in most boats, that course we be to leeward of the boat's centerline.

Okay, that's fine. Rudder drag combined with leeway generates some amount of lee helm. But the drag will be much smaller than the lift the rudder is capable of generating at normal operating angles. So including rudder area in CLP with a 100% weighting still seems like a gross overestimate of drag effects, especially since the larger rudder will spend more time in its low-drag bucket if it has one. That's the main point of contention, how can you treat an adjustable rudder in the same way as a fixed keel? Even 50% sounds like a lot based on drag alone.

[cyclops]

Mr. Beck. Boat is at a fast speed and the water passing along side the hull is becoming turbulant. Same or even more so on the bottom section. All the jumbled water converges in front of the rudder. Add a wave which creates even more turbulance. The rudder is operating in a swirling mass. It has " stalled ". The shape and area of rudder are useless till the waters around it are less turbulant.----------Old power boats suffer from the same effect when speeds are raised and small, simple,slab of wood rudder is left on the boat.

[Eric Sponberg]

Yes, the boat and its foils produce lift and induced drag because of the leeway angle (angle between the boat's centerline and its course line).

When you are on the boat holding a course, your frame of reference is always the boat's centerline, not its course line. You judge the amount of weather helm or lee helm in relation to the boat's centerline.

Let's say that you are on the boat sailing and have very bad lee helm. Your boat is a shallow draft design like the old Cal 21 which has a keel/centerboard and a narrow, deep rudder. You have just the jib up, and not the main. The center of effort of the sail is way forward, and the bow of the boat persists in falling off the wind. (You can probably tell I am speaking from personal experience!). In order to hold the bow of the boat into the wind, you have to put the tiller way over to the lee side, and the angle of attack on the rudder will be opposite to what you normally want. The boat still has a course to leeward. But the balance of forces on the sails, keel and rudder demand that the rudder be pushed to leeward to hold course.

All we have established in our definition of balance--weather helm and lee helm--is the position of the tiller in relation to the boat's centerline and what is necessary to hold a stable course. Trying to determine the direction of the boat's course, the amount of leeway angle, and the boat's overall performance are completely separate problems that require different analysis.

Skippy: Rudder drag combined with leeway generates some amount of lee helm.[I]

That is not where lee helm comes from. Lee helm or weather helm comes from the balance required between the overall turning moment of the sails in relation to the overall turning moment in the opposite direction from the underwater profile area. Some portion of that underwater area (the rudder) can be used to alter the balance of forces to cause the boat to assume a certain steady and consistent course. That course, in the vast majority of boats, will always be to leeward. The leeway angle is actually the sum of the total aerodynamic drag angle and the hydrodynamic drag angle. (Read C.A. Marchaj's "Aero-Hydrodynamics of Sailing" for a complete description.)

[I]Skippy: But the drag will be much smaller than the lift the rudder is capable of generating at normal operating angles.[I]

You are describing only the induced drag, that is, the drag that is inescapably and by definition the result of creating lift. In most keel and rudder analysis, we temporarily ignore the effects of form drag and friction drag, they being generally small and in proportion to the profile areas and volumes of the appendages. But if you all of a sudden change a normally sized rudder to a very big rudder 2 or 3 times larger, your form and friction drag go way up to the point that they cannot be ignored, and they have a very big influence on balance, even before you start talking about lift and induced drag.

[I]Skippy: So including rudder area in CLP with a 100% weighting still seems like a gross overestimate of drag effects, especially since the larger rudder will spend more time in its low-drag bucket if it has one. That's the main point of contention, how can you treat an adjustable rudder in the same way as a fixed keel? Even 50% sounds like a lot based on drag alone.

In many modern boats, the hull itself under the water has shrunk away to almost nothing, and the only areas left under water are the rudder and keel. So in modern boats, we tend to treat the rudder at 100% of area in order to determine the overall profile area. But then of course, our definitions as to the proper amount of lead, or the positions of the CE and the CLP have to change. We cannot use the old definitions that applied to conventionally designed boats where the hull itself contributes a lot to overall drag, and the rudder is small in proportion to the rest of the boat. Back then, we either ignored the rudder or we treated it at 50% of its area.

In modern boats, we have to treat the rudder at 100% of its area just to be smart, but at the same time, we must change our definition of proper balance. Where should the CE go in relation to the CLP? The effects are going to be the same: CE well forward will create lee helm, and CE well aft will create weather helm. But how much is the lead, and is the lead positive or negative (CE ahead or behind, respectively, of the CLP). Many designers have found (myself included) that in such shallow-hulled boats, the CE should be positioned over the leading edge of the keel. Comparing the Centers, the lead is still positive. This produces acceptable balance with a slight weather helm.

Eric

[Skippy]

Eric: When you are on the boat holding a course, your frame of reference is always the boat's centerline, not its course line. You judge the amount of weather helm or lee helm in relation to the boat's centerline.

Eric, people including myself may from time to time find it convenient to discuss specific problems in other reference frames as the situation demands. I hope that's not too inconvenient for you. I will always make it very clear whenever I do so.

Eric: Let's say that you are on the boat sailing and have very bad lee helm. Your boat is a shallow draft design like the old Cal 21 ... the balance of forces on the sails, keel and rudder demand that the rudder be pushed to leeward to hold course.

That's a nice story Eric. I'm not sure what it has to do with the topic at hand, but yes, it is an example of lee helm.

Eric: All we have established in our definition of balance--weather helm and lee helm--is the position of the tiller in relation to the boat's centerline and what is necessary to hold a stable course. Trying to determine the direction of the boat's course, the amount of leeway angle, and the boat's overall performance are completely separate problems that require different analysis.

Eric, I am well aware that defining a technical term and analyzing a boat's dynamics are two different things. Which again is exactly my point. You took your definition one step farther, applying it to the boat's motion, even though it's defined only in terms of the centerline:

Eric: When a boat is in perfect balance, and there is neither lee helm or weather helm, ... If the CE moves forward from this position, the boat will tend to have lee helm, and when left on her own (nothing holding the tiller) the boat will tend to bear away from the wind.

And while we're on the topic of definitions,

Eric: The difference between the boat's course and its hull centerline does not really enter into the discussion of balance. That difference is called "leeway" and has little to do with lee helm or weather helm. The vast majority of boats have leeway

I am also familiar with the meaning of the term "leeway" and the fact that it is quite common. I suspect many other people on this forum know about it as well.

Skippy: Rudder drag combined with leeway generates some amount of lee helm.

Eric: That is not where lee helm comes from.

Then why did you just say in your previous post that rudder drag DOES tend to increase lee helm???

Eric: Taken to the extreme, form drag in a very large rudder can upset the balance of the whole boat to the point that a large rudder could require some lee helm to keep a boat on course.

Leeway should only increase that effect, since the stern will be somewhat farther leeward than it would be with no leeway. So I don't understand those comments at all.

Eric: Lee helm or weather helm comes from the balance required between the overall turning moment of the sails in relation to the overall turning moment in the opposite direction from the underwater profile area. ...

In that case, you still have not explained why rudder area should be part of CLP in predicting the boat's behavior with a free helm.

Skippy: But the drag will be much smaller than the lift the rudder is capable of generating at normal operating angles.

Eric: You are describing only the induced drag, that is, the drag that is inescapably and by definition the result of creating lift. In most keel and rudder analysis, we temporarily ignore the effects of form drag and friction drag, they being generally small and in proportion to the profile areas and volumes of the appendages. But if you all of a sudden change a normally sized rudder to a very big rudder 2 or 3 times larger, your form and friction drag go way up to the point that they cannot be ignored, and they have a very big influence on balance, even before you start talking about lift and induced drag.

No Eric, I am not describing only induced drag. I am referring to the form drag of an unrestrained rudder. Regardless of whether it does or does not induce lee helm, which your posts seem to be unclear on, my point is that I would like to know why it warrants including rudder area in CLP.

Skippy: So including rudder area in CLP with a 100% weighting still seems like a gross overestimate of drag effects, especially since the larger rudder will spend more time in its low-drag bucket if it has one. That's the main point of contention, how can you treat an adjustable rudder in the same way as a fixed keel? Even 50% sounds like a lot based on drag alone.

Eric:
In many modern boats, the hull itself under the water has shrunk away to almost nothing, and the only areas left under water are the rudder and keel. So in modern boats, we tend to treat the rudder at 100% of area in order to determine the overall profile area. ... Back then, we either ignored the rudder or we treated it at 50% of its area.

In modern boats, we have to treat the rudder at 100% of its area just to be smart, ...

With all due respect Eric, do you really think I or most people on this forum need to be lectured on what is or is not "smart"? You say that since the lateral area of the hull is smaller, the rudder area must be weighted more heavily. That doesn't make sense to me. When the rudder area is small, giving it the same 100% weight shouldn't make much difference anyway, and I don't see why the basic dynamics of the rudder itself would be significantly affected by the details of the hull shape. What I do see is the phrase "treat the rudder at 100%" mentioned twice with little or no explanation that makes any sense to me.

[Alixander Beck]

Skippy,

What I see, is you continuously trying to 'prove' your intellectual power by using over-complicated explanations and reasonings with little proof, re-iterations, and non-relevant examples in an argumentative manner which does not lead to productive conversation.

and I for one am getting sick of it.

Lorsail and Eric your comments have been helpful and your agruments well proven. Thank you.

I think this thread has run its course.

[Eric Sponberg]

Skippy,

Please, I am not lecturing. By being "smart", I am not saying that some of us are smart and others not, I am merely stating that designers try to make knowledgeable decisions about their work, to figure out what works in their analyses. When it comes to the current crop of boat design styles, there is little reason to ignore the rudder in the calculation of the lateral plane. You can use whatever criteria you want, just so long as you are consistent in your analysis.

Skippy: you still have not explained why rudder area should be part of CLP in predicting the boat's behavior with a free helm.

The calculation of CLP and CE and the balance between the two are used to determine the balance of the boat when the helm is restrained and the boat is sailing properly.

We do not, in general, use the design guidelines of CE, CLP, and balance to predict the behavior of the boat with a free helm. The free helm problem is a secondary consideration. Generally, we have found that boats with weather helm when sailing (helm restrained) tend to round up into the wind if the helm is left free. With lee helm, the opposite happens--with the helm free, the boat will fall away. That's as far as we need to go.

The helm is restrained the vast majority of the time, so that is when balance is important. And with shallow draft hulls, the rudder is simply a very influential element of the underwater profile by virtue of its relative size. Therefore, it makes sense to include it wholly in the calculation of underwater area and the calculation of CLP for analysis of the boat sailing when the helm is restrained.

This analysis as I have described works, and if it works, why fix it? I grant you that there may be a few boats, designed with 100% of the rudder in the CLP, which for some reason or another, do not work as expected--that is, the boat may have nice weather helm but behave unpredictably when left unattended. But if I had to guess about the numbers of such designs, I would say that those examples are very few. If a designer finds such an example in his work, he will likely endeavor to find out the reasons why the boat behaves that way, and alter his analysis accordingly. I have never found such a boat so far in my work.

Eric

[tspeer]

There are very good physical reasons for not counting the rudder at 100% of its area.

The first is that rudders are typically of lower aspect ratio than the keel. The lift curve slope (lift per unit of angle of attack) is lower for low aspect ratio surfaces than high aspect ratio surfaces. Both the keel and the rudder see the same leeway angle, so if the lift curve slope is less it means the same area is less effective at the same angle of attack. The formula for this effect is:

a = a0 / (1 + 57.3*a0/(pi * AR))

where a0 is the two-dimensional section lift coefficient slope, per degree. a0 is just about universally 0.1 per degree for all sections operating in their linear lift range. a is the 3-dimensional lift curve slope of the planform, and AR is the aspect ratio.

So the effective area of the rudder needs to be reduced by the ratio of the lift curve slope of the keel vs rudder, or

effective area ratio = (1 + 5.73/(pi * AR_keel)) / (1 + 5.73/(pi * AR_rudder)

The second reason for discounting rudder area is the sidewash from the keel. The keel produces lift by deflecting water to leeward. When this wake its the rudder it reduces then angle of attack on the rudder. The amount of this reduced angle of attack is proportional to the lift on the keel, which is proportional to the leeway angle. So as the leeway angle increases, the local leeway angle at the keel is increasing at less than 100% of the leeway angle at the keel. This, again, makes it look as though the rudder area is not as effective as the keel area.

This effect is well known in aircraft design, and it results in an apparent reduction in stability that requires a larger tail to compensate for it. The downwash angle at the tail (analogous to the reduction in leeway at the rudder) is typically given the symbol epsilon, and the effective tail area is reduced by a factor of (1 - d_epsilon / d_alpha), where d_epsilon / d_alpha is the derivative of the change in downwash angle per change in angle of attack. Wind tunnel tests are typically performed with the tail on and off the model to quanitfy the downwash effects.

How much the rudder is influenced by the wake depends on where the rudder is located relative to the wake. This is why you see T-tails on STOL aircraft like the deHaviland Buffalo and Dash-7. The downwash from the wing is very strong when flying slowly, and it would cause both a reduction in stability and a large change in the elevator deflection required to trim the pitching moments. Symmetry doesn't allow the boat designer to move the rudder out of the way of the wake like the T-tail on an aircraft.

There are charts of d_epsilon/d_alpha, such as NACA TR 648 (http://naca.larc.nasa.gov/digidoc/report/tr/48/NACA-TR-648.PDF) and NACA TN 3346 (http://naca.larc.nasa.gov/reports/1955/naca-tn-3346/naca-tn-3346.pdf), from which one can estimate the downwash effects. The free surface will affect the resuls somewhat, but these should be good for a start if you want to be more precise than the current rules of thumb.

Note, too, that the change in leeway angle at the rudder means that the tiller has to be deflected to weather just to produce the same lift that the rudder would if the keel were not present.

[Skippy]

Okay, let's talk attitude.

First of all, thanks to Tom, not for agreeing with me, but for actually supporting what he says with explanations. I don't even care if someone proves everything I say to be wrong, as long as they give valid reasons.

Eric, from most of what I have seen in this forum, I am convinced that you are a very competent professional, and generally a considerate, respectable guy. You have an excellent reputation, and I have always welcomed your comments on any subject.

As far as I'm concerned, Yokebutt was right and Doug was wrong. Not only that, but Doug was self-promoting and needlessly critical. Furthermore, he persisted in repeating his original point without providing explanation. If you look back in the thread, you will find that I provided at least some justification for everything I said. You will also find that a lot of what I said was very friendly and evenhanded. I have very little patience for thoughtless, unhelpful nonsense, and I am not going to apologize for responding to it appropriately.

Eric, there is no law that says you had to involve yourself in this thread, so just for the record, it is irrelevant whether your presence was "requested". There is no law that says you had to take the position you did, which I consider to be either incorrect or not relevant to the topic. If you go back and reread your original post (http://boatdesign.net/forums/showpost.php?p=61244&postcount=23), I think you will find that it is exactly in the form of a lecture. I for one do not need to be reminded of what the word "leeway" means, be told what reference frame I should think in, have people read my mind as to whether I'm thinking about one kind of drag or another, or be informed like a child as to what is or is not "smart". To be perfectly honest, I do not detect a tremendous amount of effort on your part to determine the actual question at hand, or the knowledge and understanding of the people you address. I will always question or disagree with any claims that I consider incorrect or unproven, and otherwise respond as I consider appropriate under the circumstances. Even if you're Nathaniel Herreshoff. :)

I agree that this has turned into a really stupid thread, and to the extent that your motives were positive Eric, thank you for trying. You certainly appear to be trying to contribute in a positive, helpful way. Now please feel free to respond (or not) as you see fit. :)

[yipster]

"this has turned into a really stupid thread"
not to me Skip, knew some things but i'm still learning

[Skippy]

Skippy: this has turned into a really stupid thread
yipster: not to me Skip, knew some things but i'm still learning

From whom? :D

On a more positive note,

Skippy: you still have not explained why rudder area should be part of CLP in predicting the boat's behavior with a free helm.

Eric: The calculation of CLP and CE and the balance between the two are used to determine the balance of the boat when the helm is restrained and the boat is sailing properly. We do not, in general, use the design guidelines of CE, CLP, and balance to predict the behavior of the boat with a free helm.

Thank you, that makes a lot more sense. In fact, while we were caught up in all this quibbling, I formed a theory about the 100% rudder-area formula, which I would welcome anyone to confirm or deny:

I think there is a reason to include the rudder area in CLP with a 100% weighting. In order to maximize the efficiency of the foils, you want to avoid overstressing either/any of them. The simplest approach I can think of would be to design for all the foils to operate under typical conditions with the same average pressure as each other. In that case, the 100% weighting comes out naturally, since the force from each foil is just proportional to its area. This would apply regardless of the rudder size, including older designs that were originally conceived with a different formula. With a large rudder, there would be problems caused by the large total force required of the rudder. It would require either a long tiller, lots of purchase in a wheel steering system, a strong helmsman, or a balanced rudder. Each of these solutions, of course, introduces its own issues.

Other than performance, safety is not an issue, since the boat will always develop even more weather helm whenever the tiller breaks loose.

My main criticism at this point would be that the formula is not relevant to the discussion, because it doesn't address the original question. It suggests an answer that to me seems absurd and obviously incorrect. It assumes a specified amount of pressure on the rudder, and is therefore appropriate only for new design work. As for increasing the size of a rudder on an existing boat, which is the topic of this thread, Yokebutt correctly points out that the helmsman will exert basicly the same amount of force as he did with the old rudder, the main difference being that the pressure on the new rudder will be less. The angle of attack will also be lower, and the drag may or may not be less, depending on the details. But the boat certainly will not start veering to leeward any time the tiller is released just because of a larger rudder, which I got the impression was the initial concern.

[Eric Sponberg]

Skippy,
I do not question your knowledge, but since this is a public forum, simplified discussion is sometimes beneficial to everyone else's understanding, as I am certain you are aware. My discussions are never intended to be insulting or condescending, and if any reader got that impression, I am truly sorry.

I was indeed requested by telephone to say something specifically with respect to balance between CE and CLP as they related to weather and lee helm by one of the other participants. Since my name had been mentioned a few times, I felt justified in doing so. If not for that request, I would not have entered the discussion. In general, it had been discussed many times before.

I do not have anything more to say.

Eric

[Skippy]

tspeer: There are very good physical reasons for not counting the rudder at 100% of its area. The first is that rudders are typically of lower aspect ratio than the keel.

This of course would apply more to a racer or dinghy than a full-keel cruiser. It sounds like you might actually want to weight the rudder more than 100% with a full keel, or just have a better formula that takes more applications into account.

[tspeer]

I think the right way to combine the spade rudder and keel areas in the total lateral plane is to add in the effective rudder area:

Effective Rudder Area = Planform Area * (1 + 5.73/(pi * AR_keel)) / (1 + 5.73/(pi * AR_rudder) * (1 - d_epsilon/d_lambda)

where AR_keel and AR_rudder are the aspect ratios of the keel and spade rudder, epsilon is the sidewash angle at the rudder, and lambda is the leeway angle.

For a keel mounted rudder, the chord of keel+rudder is large. The common practice seems to be to take the centrer of lateral resistance at the centroid of the lateral area, but the pressure distribution is really centered more on the quarter-chord. So if you consider keel and rudder together, you're off by a quarter of the chord. By not taking the rudder into consideration, you've moved the center of area forward, reducing the mismatch between the true center of lateral resistance and the centroid of the lateral area.

[SuperPiper]

I'm an amateur. So, I have had to create models in my mind just to follow this thread. And, I think that I have stumbled across the one point that may clarify the situation. I just pray that I can explain it in a manner that everyone will understand.

The discussion has been about relative areas. But what you are really discussing is the proportion of LIFT created by a keel and a rudder. The keel produces a fixed amount of lift and the rudder produces a variable amount of lift depending on where the tiller is pointed.

If the amount of sail area remains the same, the amount of total lift will remain the same. But if the rudder is made bigger, then how does the skipper keep the amount of lift the same? He adjusts the helm.

Calculating areas is just a rule of thumb for design purposes. Skippy is right, the bigger rudder is not going to change the way the boat sails. It may change how the skipper points the tiller.

[tspeer]

You are absolutely right with respect to trim yawing moment.

The question then becomes, "What happens when the yacht is disturbed from trim?" This is where the helm-fixed vs helm-free issue comes in, and how much workload is required to maintain course.

If the rudder is sized so that the change in yawing moment per change in leeway from both the keel and the rudder is equal and opposite to the yawing moment caused by the increased pressure on the sail rig that caused the leeway angle to increase in the first place, then the yacht will track straight without any operator change to the helm angle. This will give the impression of a well-balanced boat.

If the rudder is larger than this balanced size, when a gust hits and the leeway angle increases, the yacht will want to turn down and the helm has to be moved to leeward to compensate. If the rudder is smaller than the balanced size, then the helm has to be moved to windward to produce the lift necessary to compensate for the change in yawing moment from the sail rig. In both cases, the yacht will be brought back into equilibrium by the pilot. But the workload to do so will be increased, and the yacht's handling qualities will be perceived as degraded compared to the balanced yacht.

[Skippy]

Wow, that's interesting. Any unbalanced rudder (I mean rotationally -- center of lift behind the rudder post) will tend to do that on its own by trying to yank the tiller out of the helmsman's hand, won't it?

[yokebutt]

Tom,

I am not sure my redneck brain fully understands. Let us say that in both cases (large and small rudder) the tiller is the same length and the distance between the CE and axis of rotation of the rudder is also the same, would the force the driver feels in the tiller change? I fully understand that if the rudder is big enough to have its own flag and a seat in the UN, the dynamics would change a bit, so lets assume twice the area.

Yoke.

[cyclops]

Weird. I actually understand all of TSPEER. It is logical and makes sense.

[tspeer]

Let us say that in both cases (large and small rudder) the tiller is the same length and the distance between the CE and axis of rotation of the rudder is also the same, would the force the driver feels in the tiller change? ...

When you talk about the force on the tiller, now you're getting into more than just the yaw trim and stability of the boat, you need to consider the hinge moments about the rudder's axis of rotation. The two are related, but not the same.

Hinge moment is the tendency of the rudder to want to feather itself into the flow. Most rudders have the hinge line well forward on the rudder or in front of the rudder leading edge. A transom-mounted rudder is a good example. The hydrodynamic center of the rudder is behind the hinge line, so it causes a moment about the hinge that has to be resisted by a force on the tiller. This is moment is stabilizing because an increase in lift on the rudder will cause a change in the hinge moment in the direction of reducing the angle of attack of the rudder.

If you move the hinge line back on the rudder, the hinge moment is reduced and the force on the tiller is less. The rudder will still produce the same lift at the same angle of attack, but you won't feel it as much. When the hinge line gets back to the hydrodynamic center (approximately a quarter of the way from the leading edge of a spade rudder), there will be no change in moment as the rudder's angle of attack changes, and there will be no tiller force required to hold the rudder at a given position. If you move the hinge line farther back than that, you get an over-balanced rudder, in which you have to actually hold the tiller back from wanting to increase the rudder angle. When you put in a little rudder, it will seem to want to snatch it out of your hands and run away, so you are constantly fighting it.

If you have a kick-up rudder that moves back even a little bit, you will notice a large change in the force on the tiller. The rudder hasn't necessarily changed its effectiveness, but the hinge moment has been significantly increased. A designer may intentionally sweep the rudder back in order to provide a more definite feel to the helm, especially in light winds.

A designer of a high-speed craft like a trimaran will typically opt for a fairly balanced rudder so the force on the tiller does not become excessive at high speed, since the hinge moments at a given angle increase with the square of the speed.

The hinge moment is a function of the leeway angle and a function of the rudder deflection. An increase in either will increase the tiller force in much the same way for an unbalanced rudder. If you hold a constant force on the tiller, an increase in leeway will result in a decrease in rudder deflection to maintain that balance, making the boat want to round up.

In my previous post, I mentioned a boat that had a rudder that was bigger than the size necessary to balance the change in yawing moment when the leeway angle increased. In that boat, the tiller had to be moved to leeward to keep the boat on track. But it didn't necessarily mean that the force on the tiller was any less. Even though the rudder deflection may have been less, the increased leeway resulted in an increase in lift on the rudder, an increase in hinge moment, and an increase in tiller force. So when the pilot let the tiller down, it was more of a matter of not opposing the full force than it was of having to push the tiller away.

If the rudder is large and unbalanced, the pilot will perceive a heavy weather helm, even if it doesn't take a large deflection of the tiller to trim the yacht. Conversely, you can put an undersized, balanced rudder on a yacht, and even though the pilots have to pull it to their navels to maintain course, there won't be much feel to the helm. That's why you need to note the tiller angle if you are interested in tuning for performance, but you vary the rudder planform if you want to correct the feel.

So tuning the hinge moment of the rudder to the yaw balance of the boat is important for achieving good handling qualities. A somewhat over-sized, somewhat under-balanced rudder is probably a good combination. It allows the boat to round up if the tiller is unattended, and it gives the pilot a feel of what's happening with the boat. By holding the tiller nearly stationary and going slightly with the feel on the tiller (as though one's arm were a spring holding the tiller to windward), the boat will track straight through gusts with little conscious action on the part of the pilot.

The importance of the design and balance of a yacht's rudder is probably under-appreciated. It's the same way with aircraft. I used to think that if you made an aircraft reasonably stable so it would basically fly itself that it would have good handling qualities, and the actual mechanization of the controls didn't matter all that much. Then I had the chance to fly on a variable-stability testbed, in which one could twiddle the knobs on a feedback control system to vary its characteristics in flight, and I found out how wrong I was. You could have two configurations with identical stability and even the same force on the controls, but if you varied how much the controls moved in response to the force, it would seem like a completely different aircraft. I've no doubt it's the same with boats.

[yokebutt]

Thanks Tom, that makes sense.

Furthermore, I do have a confession to make. I realized a while back that the reason for all this acrimony is that we all have our own ideas of how to define weather helm. And of course, without having a precise definition in common of what it is, we are all just talking past each other.

But then again, I didnt see any harm in letting Dougs stomach acids eat away at his esophagus for a while.

Yoke.

[Doug Lord]

Well, I'll be damned-will wonders never cease...

[Skippy]

Yoke: ... we all have our own ideas of how to define weather helm. And of course, without having a precise definition in common of what it is, we are all just talking past each other.

Absolutely, that's an excellent thing for anyone to remember. I think a lot of disputes just about everywhere boil down to that, people just talking about different things. Every participant in any conversation is responsible for trying to understand what other people mean by what they say. On a technical forum like this one, novices sometimes use terms with imprecise, colloquial meanings, or ideas that may be based on common misperceptions. I like having both experts and beginners here, and I would expect to see this issue to crop up again in the future.

[yokebutt]

Dear Doug,

I truly have no issue with most of your ideas, in fact, I think they are frequently quite brilliant. However, I do get the impression that you are not particularly inclined towards objectively evaluating matters at hand, but would rather prefer to push your own point of wiew without further consderation. I'd strongly recommend that you read a couple books by Dr. Feynman, perhaps you'll find a wider way of wiewing of the world.

Yoke.

[RHough]

You are absolutely right with respect to trim yawing moment.

The question then becomes, "What happens when the yacht is disturbed from trim?" This is where the helm-fixed vs helm-free issue comes in, and how much workload is required to maintain course.

If the rudder is sized so that the change in yawing moment per change in leeway from both the keel and the rudder is equal and opposite to the yawing moment caused by the increased pressure on the sail rig that caused the leeway angle to increase in the first place, then the yacht will track straight without any operator change to the helm angle. This will give the impression of a well-balanced boat.

If the rudder is larger than this balanced size, when a gust hits and the leeway angle increases, the yacht will want to turn down and the helm has to be moved to leeward to compensate. If the rudder is smaller than the balanced size, then the helm has to be moved to windward to produce the lift necessary to compensate for the change in yawing moment from the sail rig. In both cases, the yacht will be brought back into equilibrium by the pilot. But the workload to do so will be increased, and the yacht's handling qualities will be perceived as degraded compared to the balanced yacht.

In aircraft design I'd think of this as positive or negative dynamic stability. I'm working out keel and rudder areas for a design and have decided to consider the foils in relation to each other independent of the hull.

The problem I run into (based on self-learned glider theory) is that the tailplane (rudder) has to generate a pitch down moment to cancel a pitch up disturbance. The easy way to get this balance in an airframe is to have the CG at or forward of the 1/4 cord point of the wing. The wing has a higher AOA than the tailplane and in steady state the tailplane's lift is opposite the wing.

A sailboat going to weather needs to have the lift of both foils acting in the same direction. In a glider that means moving the CG aft of the 1/4 chord point so the tailplane load is positive. Can positive dynamic stability be achieved with symmetrical foils when both are positively loaded?

[tspeer]

...
The problem I run into (based on self-learned glider theory) is that the tailplane (rudder) has to generate a pitch down moment to cancel a pitch up disturbance. The easy way to get this balance in an airframe is to have the CG at or forward of the 1/4 cord point of the wing. The wing has a higher AOA than the tailplane and in steady state the tailplane's lift is opposite the wing.

This is only partially correct. For static stability (the tendency to return to trim), the center of gravity has to be ahead of the neutral point, not the quarter chord of the wing. Only a flying wing or canard configuration would have the c.g. ahead of the quarter chord - aircraft with aft tails have the c.g. well aft of the quarter chord. The reason is you have to consider the pitching moment from the fuselage and tail/canard as well as the wing.

It's possible to have a stable aircraft with a lifting tail, too. Many freeflight models are set up this way - it's not unusual to see c.g. locations near 100% chord for gas-powered models. It requires a large tail, though, on the order of 25% of the wing area. But the tail will be more lightly loaded than the wing. They go this route to avoid excessive speed stability, because they need to climb at high speed and glide at low speed.

A sailboat going to weather needs to have the lift of both foils acting in the same direction. In a glider that means moving the CG aft of the 1/4 chord point so the tailplane load is positive. Can positive dynamic stability be achieved with symmetrical foils when both are positively loaded?

Yes, it's done every day! The vast majority of sailboats are designed this way.

[RHough]

This is only partially correct. For static stability (the tendency to return to trim), the center of gravity has to be ahead of the neutral point, not the quarter chord of the wing.

Leave it to you to point out the difference between the neutral point of the aircraft and 1/4 chord of the wing. :)

The FF model has to operate in two very distinct modes. High speed near zero lift and low speed minimum sink. During during the launch phase the thrust vector provides stability, in glide phase min sink requires an aft cg to load the tailplane. If the airframe fails to make the transition from high speed climb to low speed glide they tend to tuck and "re-kit" themselves.

What I overlooked in my train of thought is that a glider's speed changes with AOA where the foils of a sailboat operate at the same speed when AOA is changed.

I'll have to spend some more time thinking about how the load on the foils changes with changes in yaw moment while the speed remains constant.

Sailboats and math R hard ... :)

[tspeer]

Yaw stability is generally not that much of an issue with sailboats. Most of the problems we've been talking about have to do with yaw trim and its effect on performance, not yaw stability.

[RHough]

Yaw stability is generally not that much of an issue with sailboats. Most of the problems we've been talking about have to do with yaw trim and its effect on performance, not yaw stability.

OK.

Doesn't yaw stability effect performance? In that reducing the number and amplitude of yaw corrections needed would make the boat both easier to sail and faster?

Greater yaw stability should mean that the optimum yaw trim is attained a higher percentage of the time.

[tspeer]

OK.

Doesn't yaw stability effect performance? In that reducing the number and amplitude of yaw corrections needed would make the boat both easier to sail and faster?

Greater yaw stability should mean that the optimum yaw trim is attained a higher percentage of the time.


Yes, I suppose so. I guess for the boats with which I'm acquainted, when you get enough rudder area for low-speed maneuvering, etc., there's enough area for stability.