# Logarithmic spiral used in rudder leverage

Discussion in 'Stability' started by Bahama, Jul 24, 2010.

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### BahamaJunior Member

I'm curious, has the logarithmic spiral been used to gradually increase leverage as the rudder angles further and further port or starboard?

If you've ever used those Nautilus weight machines then you'll know what I'm referring to right away. It seems like this would be a great idea for large boat that are right at that point where hydraulics would make life eaiser, but the owner doesn't want to lose the feel of the boat.

In this way, the wheel would get increased leverage gradually, logarithmically--so the pressure placed on the wheel could be made to stay the same throughout the entire turn if you like, or with less curve, the pressure would only seem to increase slightly... it would all be based upon the intensity of the curve used.

The pressure on the rudder is logarithmic, and so this is simply fighting back the same way. I think the simplest way would be to use 3 nautilus shells: the main one is used on the rudder arm itself, and the other two are placed on each side of the chain are are used to take up (or let out) slack in a mirrored relationship to the main rudder nautilus.

I'll try to draw something up later on--this will be a hard week for me, but I wanted to put this idea out now because I've been thinking about it for awhile and I wanted to get some input.

I'd though of something similar for hydralics, only there my idea was for a 3-speed system, that have a regular hydraulic cylinder, and then a 2X version, and then some controlling device (preferably mechanical) would use 1x for regular work, and if the load got too hard, would bump over to the 2X cylinder, and if things got REALLY hard (like a storm) it would use both cylinders for a 3X... it wouldn't turn as fast, but it would at least turn. What I liked about that idea was that you got fast speed when needed, and yet it had extra power when needed as well.

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### gonzoSenior Member

It would make steering kind of weird, because the speed of the rudder will not be in direct proportion to the speed of the wheel. A proper designed boat and steering system doesn't have a problem. I have not noticed the logarithmic increase on force you mention. Where are you getting the data from?

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### BahamaJunior Member

I've never seen what I'm describing, I'm just applying the laws of leverage to the idea. Longer lever, more leverage. So a person could decide just how much leverage they would want.

For example, let's say that your boat size is just on the boardline where it gets pretty tough to turn her manually, but you don't want to go with hydraulics. You could at that point go with some geared system that would provide the same gearing throughout the turns, but this means that you would need to turn the wheel more throughout the entire turn. Let' say that rather than 1:1 you now needed to go with some gearing of 1:0.9; so now it takes 10% more turning throughout the entire turn.

What I'm pondering, is why not spread this leverage out so that it's 1:1 in the center, and gradually would move toward 1:0.8 at the far extremes. In this way, you get to keep faster action in the steering for most of the turn, and then the true leverage doesn't kick in until you are turning toward the far extremes.

As I think of this, I think that it would become quite intuitive to the helmsman rather quickly and here's why:

Right now if you turn sharply the difficulting (the strain) increases as the rudder is turned more and more sharply (much more noticable on a big boat). So, now, with this new design, that difficulty would be far less, in fact you could design the leverage to exactly match the length of the rudder so that they strain level actually remained the same throughout the entire turn... or you could allow for some strain, but less than what a 1:1 leverage ratio would be.

I drew a quick picture of what I'm thinking of to show the concept. The angles are more dramatic than they would truly be, but it's easier to see the concept by exagerating the curve. The curves would be less because you are probably only needing an extra 10 or 20% leverage to make the steering go easier.

The tiller wheel would be round so each turn is the same; but the leverage on the rudder would change as it turned. The leverage would increase as the distance from the center point increased; the tension wheels just rotate to keep the tension stable on the chain.

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• ###### Logorythmic Steering.png
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### gonzoSenior Member

It is the opposite. As a boat turns, the resistance decreases.

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### daiquiriEngineering and Design

Hi Bahama,

The pressure on the rudder is transmitted to the rudder stock as a moment, and if you plot the Cm (moment coefficient) curve against angle of attack, you will see that it is more closely approximated by a parabolic function, not a logarithmic one.

I'm enclosing here an xls file with a calculation of a polar curve for a rectangular rudder 600 mm deep, with a chord of 400 mm (Ar = 1.5). The speed is 7.5 m/s (14.5 knots). The analysis was done with a 3D Vortex Lattice Method (just for your info, if you need it), because the aspect ratio is very low.

I've added an interpolation curve to every graph, so that you can see the governing equations.

You can change the value of X_stock (position of rudder stock, as a fraction of chord) to see how the Cm curve will vary.
Depending on the position of the rudder stock (compensation), you will have a different slope of Cm (moment coefficient) versus Alpha (angle of attack) curve. But it will generally be approximated by a parabolic (quadratic) function, as can be seen in the graph.
You can also change the X-axis setup of the Cm-Alpha graph, and select the "logarithmic" scale. You will see that the curve doesn't become linear, as it would if the Cm was a logarithmic function. So, if you wanted to

So, if your aim is to make the variation of Cm become less extreme between low and high angles of attack, some kind of a "square-root law" leverage would probably do better, imho.

Cheers.

#### Attached Files:

• ###### Rudder polars.xls
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### gonzoSenior Member

As the boat turns, the effort diminishes. Your formulas work if you are getting weather helm and trying to stay on course while the boat is rounding up. A well balanced design will not do that.

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### daiquiriEngineering and Design

Gonzo, I know what you mean. The polars are valid for the boat which is turning at a quasi-steady rate, and/or for a rudder whose tiller is being rotated at a quasi-steady rate too.

The angle of attack in the X axis is the aerodynamic angle of attack. It is an angle of attack relative to the inflow, and the rudder doesn't know what velocity components are there in the inflow. It's up to you (me, him) to account for the inflow inclination due to the rotation velocity component. For a fixed tiller angle, as the turn rate (rotation speed) increases, the tiller moment decreases, that's true. But it happens because the aerodynamic (or hydrodynamic, if you prefer) angle of attack becomes smaller, not because the curve is wrong or not valid. The Cm decreases along the that curve.

There will be an error when the turning radius becomes very small. The curvature of the apparent path of the incoming fluid will progressively make invalid the lift, drag and moment curves calculated for a steady rectilinear flow. But if one, for some reason, needs to account for that too, there are methods which can yield corrected coefficients.

Cheers

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### gonzoSenior Member

I think it is a lot of complication for no real advantage. Some things work well they way they are. We agree that in a very limited particular case, it could diminish the effort of steering. However, well designed boats never have a steering effort that is beyond the normal force that a helmsman can apply. I really can't see the point of making something so complex.

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### daiquiriEngineering and Design

I can only agree with that. I was really discussing the logarithmic-law claim.
A tiller force which increases with blade angle of attack is imho desireable for a good feeling of a rudder and for a tactile feedback of both the boat speed and the rudder deflection. It is beneficial for the safety, because it reduces the probability of an eccessive steering action by the helmsman.
I personally don't like the feeling of a tiller which steers "with a fingertip", though I often hear people praise and require that characteristics. A matter of personal preferences, I guess.

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### BahamaJunior Member

This is extremely helpful, thank you. The shape of the curve can emulate any logorymic (I could have also said exponential as well) and so it would be possible to simulate a square root using the curve. The math of the curve would be related to the rudder length and pivot point, and the amount of leverage that you would want to achive. I'll look at this more in depth once I get my head cleared up from the recent passing away of my favorite greatest dog ever, Sammie.

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### BahamaJunior Member

Thanks to both of you on the kind and insightful words. I want to make clear my original intention on this, which was related to a boat that was right on the boarderline where the boat was large enough to almost force you to need hydraulics, but the owner really didn't want to... so I was pondering if a very simple modification like what I proposed, would be a way to give yourself back that extra 10 or 20% leverage when you need it most, while letting you have something closer to 1:1 leverage for the easier work (which offers more speed and responsiveness).

I felt that this was a very simplistic idea to give a gradual increase/decrease in leverage. It would be easy to simply use gearing to offer the same gear ration throughout the entire turn, but this seemed like a hybrid way to provide nearly 1:1 ratio for much of the turn and then slight less ratio when the steering was starting to get to be more than you want to handle.

This seems far simpler and cheaper for someone who really didn't want to go with hydralics on their larger boat... large geing a relative term for the owner's strength and personal touch.

I added a shower and head to the owner's cabin of my boat and so it will now will be 15m LOA and so I don't anticipate that I'll need any leverage assistance, but I thought of the idea and wanted to put it out there for others to consider.

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### BahamaJunior Member

My head is starting to clear up from the recent death of my dog and I'm able to finally start to make some sense out of what you wrote. It was way over my head at the time, but now I believe that I get it. Let me repeat back what I believe to be true:

Good rudder design can counter act the strain on the rudder for even the largest of ships, by simply moving the pivot point aft a bit so that there is a forward leading edge that will help ease the strain of pressure placed on the aft section of the rudder.

This is called "Rudder Balance".

Much simpler than what I drew up! Thank you for the explaination, I get it.

Because I've stretch my boat 4' and increased the Sail Displacement Ratio from 16.04 to 17, I want to make sure that my rudder is sized correctly.

My LOA is 49', the LWL is 42', Beam is 14' 2", Draft is 6', and the Displacement will be 44,000 Lbs.

The original rudder design (for a 45' LOA, 39000 Lb. boat) was 63" tall and 30" wide without a leading edge.

I cannot go any deeper (the rudder's height) than the 63", other than I could safely provide a 4" triangle at the bottom of the rudder; so the rudder would be 67" tall (the height) on the aft edge, and the original 63" on the forward leading edge. Not much extra area, but some.

I can easily add up to 6" in the length of the rudder (fore to aft distance) without any real trouble. after that I have some room, but it gets harder. I can probably get 2" to 4" extra (so 8" to 10" extra in total), but then it gets harder still.

So, with this in mind, could you offer some advice that helps me to determine the length that I should choose? My concern is that with the increased sail area my rudder is too small.

Worst case scenareo, I can go with two rudders, where the inside is foiled like the airplain wing and the outside is flat; then only one rudder is in the water at one time.

If you can offer advice regarding where to place the pivot point on the rudder, that would be kind of you.

I am thinking that I'll go with a 10% maximum width (or thickness) on the rudder when compared to it's total length (it's cord length). Some people seem to go down to 8%, but I don't think that I'm gaining much efficiency on a large boat like this, and the risk is that it will stall easier. My question is, does this seem like a good ratio, or should I go with 12%? I see that some people go all the way up to 15% for an extremely forgiving design, but this has a lot of drag to it as well.

I also see that you can help delay the stall (and provide extra forgiveness) by placing this maximum width (or thickness) at the middle of the rudder's length (forward-to-aft); but you are allowed to design this maximum width to be further forward by as much as 15% (so then it would be 35% from the forward edge rather than the middle 50% location). From what I see, this can make the stall point occur slightly more quickly than if you have it at the 50% location... but is there any advantage to having it at 35%? If not, then I'll go with the middle to get maximum forgiveness on the stall point.

I hope that I didn't ask too many questions. This has helped, but I can see that rudder design is incredibly complex and I'm just starting to get my head on straight from my loss, so I'm still not 100% yet... it's amazing how a loss like this has goofed me all up for the past week.

OH! one other thing, for what it's worth, I just learned from Philip Bolger (Boats With an Open Mind) that a rudder can be made more efficient simply by adding a small vertical plate on the bottom edge of the rudder (this is also true by adding a horizontal plate like this on the bottom of the keel as well).

And I also learned that the best leading edge on a rudder is actually a blunt ellipse (blunt in relation to the maximum width) because it helps to eliminate the stall (because, remember that a thin rudder is more prone to stalling).

I also learned about how suction can occur on the portion of a rudder that sticks up above the water; it can cause the air to be sucked in and down along the rudder's low-pressure side. Very interesting. The only way to prevent this is to avoid (minimize) having the rudder stick up out of the water. I don't know how much is lost from this though, I just read about it.

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### daiquiriEngineering and Design

You're a quick learner.

Your sail area has increased by 15%, but in which direction? Is the sailplan uniformly scaled up, or have you increased it in some particular direction (more height, more jib, more main, etc.)? Did you change the mast position relative to the CLP or to the CoG? A combined effect of these details might have a big influence on trimming moments required from the rudder.

What hull type are we talking about? Modern canoe-like or a traditional full-keeled boat? A pic of the boat would be great.

Cheers!

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### Knut SandSenior Member

I'm not a sailboat guy, so I can only help with adding more questions...

You've lengthened the boat,; I'd assume that will be the area between keel/mast and rudder, that again will give the rudder an increased arm to work on; that may mean that the rudder area may not be increased as much as first considered.

The increased sail area; Is that for both main sail and genova? or just the genova 1/1 rig in contrary to 7/8 rig or something... (NOW i'm on thin ice...).
The times I've tried to "sail" I've used the genova as the main "engine", trimming the rudder position on the main sail, (more than 5° rudder angle= like driving with the hand brake applied..., quite normal for me...).

The start here about angle of rudder and torque; Don't think it'll be needed. but an easy way is a scotch yoke design, closer to 45° the arm of attack lengthens, giving increased torque.

http://en.wikipedia.org/wiki/Scotch_yoke

But to add another opinion; I think (as much I are capable of a evaluation on this issue); Gonzo and Diaquiri are spot on with their opinions.

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### Knut SandSenior Member

Doble posted...

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