Keel : Rudder Length

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.

 

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

 

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 and NACA TN 3346, 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.

 

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, 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.

 

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

 

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

From whom?

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.

 

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

 

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.

 

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.

 

Lift NOT Area

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.

 

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.

 

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?

 

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.

 

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

 

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.