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CAT RUDDER CROSS CONNECTIONS


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Have a client with a 13m Stealth cat. Rudder connection system sucks. Two wheels, each each push/pulls line that connects to a crank arm. Carbon rod also connects to crank & runs aft to arm coming off rudder cassette. This  (half) part works well - it's the system connecting the two hulls that is poor.

    The crank arm axle is a  carbon tube that goes to center of boat, where it connects to a Lewmar bevel drive. Other hull same set up. Bevel drive reverses rotation (which is necessary)

In use, if you turn the one wheel, that side  rudder turns instantly with large deflection. The other rudder, however, lags in response & only turns 1/2 the angle (or less) of the other side. So if you're steering into a turn to helmsman's side, inside rudder turns a lot & outside rudder hardly at all. Completely opposite of 'Ackerman' steering.

The carbon tubes run thru a couple of tight holes, so they must be removed to try any other system, and must be cut into pieces to remove.

At present I'm thinking of using vectran or wire to cross hulls, but would like to hear any thoughts on this as changes are final.

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My cat had a wheel with a wooden rope drum, and under bridgedeck criss-cross rope steering (1/4" dacron) to the external tillers. A bit stretchy but it was very responsive. You could feel the load on the rudders. Would have been better with a non stretch rope I think - but I'm not sure if the length doesn't change as the tillers move. I do know if it was tensioned too much it would tend to feel like it was binding. My tillers were toed in to provide Ackerman angles. Dirt simple. Only moving parts were some pulleys and a piece of rope. Could be fixed in any 3rd world hardware store at a pinch.

I really need a diagram/sketch to visualize your client's system. I can sketch up my system.

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For Ackerman steering the inside rudder should turn more than the outside rudder as the turn radius is smaller, so as you describe it is correct. However, if the rudder on the side with the wheel turn more regardless of direction, then it is not correct.

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7 hours ago, random. said:

Except that toe-in is not Ackerman, it's just toe in for stability in a straight line.

Ackerman is delivered by the tiller arms on each rudder being angled in at a calculated angle, even it the rudders had no toe-in.

Correct. That's what I said. The rudders were not toed in. The tillers were. The tillers and rudders were not in-line with each other.

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10 hours ago, hump101 said:

. However, if the rudder on the side with the wheel turn more regardless of direction, then it is not correct.

This is the current operation. The amount of rotation of the cross connecting tubes is controlled by the length of the crank arm (about 9") Rudder cassettes are partially inset into the transoms, so are limited to about 75 deg total travel. max rotation of cross tubes during turning is about 20 deg total

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On 8/2/2021 at 3:07 AM, Zonker said:

Correct. That's what I said. The rudders were not toed in. The tillers were. The tillers and rudders were not in-line with each other.

I'm going to making some new rudders for my boat soon. How much ackerman is a good thing?

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1 hour ago, jmurph said:

How much ackerman is a good thing?

Depends on the distance between rudders and turning radius of the boat.

 

Same thread, from @pwormwood:

Quote

The easiest way to do it that I know of is on a sheet of paper. Draw a top view of the boat to scale - you don't need a complete drawing, just the length and distance between hull centerlines, and the pivot points of the rudders. If you know how tight an actual turning radius your boat has, you will be more accurate. If not, make a reasonable guess. Draw a circle that goes through the center of your boat's pivot point (somewhere between the daggerboards, in the middle of the boat); with its center off to the side of the boat, at the center of the turning radius. Once you locate that center point, draw two more circles with the same center point through the pivot points of the rudders. Then draw lines tangent to those circles through the rudder pivot points. The angle between those two lines is your Akerman angle. On a catamaran, each of the tillers are angled in half of this angle; and then connected with a shorter tiller connector tube. The result is that the rudders both run straight when the helm is on center; and the inner rudder turns tighter when the helm is put over...

 

From Tom Speer at boatdesign.net:

Quote

Look up "Ackermann steering geometry" for cars. It's essentially the same problem for catamarans.

The easiest way to achieve it is to use tillers to control the two rudders, linked together with a bar connecting the ends of the tillers. If you angle the tillers toward the centerline, the inside rudder will be turned more than the outside rudder.

How much to angle the tillers depends on what you are trying to achieve. The tighter the turning radius, the more Ackermann angle to use. As a quick approximation, draw lines perpendicular to the keels/boards at their center of lateral resistance (say, the quarter chord) and perpendicular to the plane of each rudder and board. You want all three lines to meet at the center of the turning radius. This sets the amount of differential deflection of the rudders.

I've done a more complete analysis of the effects of Ackermann geometry on the turning of catamarans, including the effect of the leeway angle on boards and rudders. If you're really into the math, I can dig it up.

I think most owners have found 10 - 15 degrees of toe-in to the tillers to be adequate.

 

http://hem.bredband.net/b262106/doc/TSpeer_acker.pdf

Ackermann_tspeer.png.060d00deae36c715cbfef8b8cb61bdc0.png

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4 hours ago, jmurph said:

How much ackerman is a good thing?

I just created a Rhino Grasshopper model for Ackermann Angle that depends on three parameters:

  1. Distance between rudders
     
  2. Turn Radius (which in a sense corresponds to rudder angle)
     
  3. Distance between CLR and rudder pivots (or is that boat length?)

Anyone who has Rhino is welcome to try it and let me know if it makes sense and is accurate?
As noted in the code (and by @pwormwood above), "Use half of Ackermann Angle for each tiller's toe-in angle."

This diagram shows an Ackermann Angle of 12.53 degrees, the difference between the two rudder angles, so each tiller will be toed-in half of that.

GIVEN:

  1. Distance between rudders = 8
  2. Turn Radius =15.23
  3. Distance between CLR and rudder pivots = 12

Ackermann_2021_Aug3a2.thumb.png.ef02bd6d553cb6f4a766cbccb91a0ee6.png

Ackermann_2021_Aug3a3.thumb.png.e4d24e4e649cce65dbf2a809c942f9b0.png

Ackermann_2021_Aug3a.thumb.png.f01045446d40523ef84c193c1cc9ca40.png

Ackermann_2021_Aug3a.gh

P.S.  If tiller lengths (actually distance between rudder and cross bar pivot points) were added to this model, the cross bar length (actually distance between cross bar pivot points) could be computed.

P.P.S.  Another resource:

Efficient Steering of a Catamaran Using Ackermann Principles
http://www.swingcat.co.uk/how/bridgedeck/ackermann_steering.pdf

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On 7/31/2021 at 10:09 PM, longy said:

Rudder connection system sucks. Two wheels, each each push/pulls line that connects to a crank arm. Carbon rod also connects to crank & runs aft to arm coming off rudder cassette. This  (half) part works well - it's the system connecting the two hulls that is poor.

    The crank arm axle is a  carbon tube that goes to center of boat, where it connects to a Lewmar bevel drive. Other hull same set up. Bevel drive reverses rotation (which is necessary)

In use, if you turn the one wheel, that side  rudder turns instantly with large deflection. The other rudder, however, lags in response & only turns 1/2 the angle (or less) of the other side.

What a nightmare!  Clearly very wrong.  Both wheels should always remain synchronized, which can be done with quadrants and cables.  What happens after that, including the Ackermann issue, should also be symmetrical on both sides.

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8 minutes ago, Rasputin22 said:

I wonder how many readers here will take the effort to download your .gh to see just how that works? You know I will, thanks!

Please let us know if it's accurate and matches real world examples.

The 'FoilExpCrv' component is a remnant of the Keel/bulb Replacement thread, which explains the 'exp1' and 'exp2' inputs.

NACA-00xx_2021_Aug_3a.gh

Keel/bulb Replacement on Beneteau First 235
http://www.islandcad.com/marine/keel_replacement/

 

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On 8/1/2021 at 1:25 AM, hump101 said:

For Ackerman steering the inside rudder should turn more than the outside rudder as the turn radius is smaller, so as you describe it is correct. However, if the rudder on the side with the wheel turn more regardless of direction, then it is not correct.

Bingo!  That sounds exactly right to me.

1 hour ago, ProaSailor said:

2. Turn Radius (which in a sense corresponds to rudder angle)

It is evident from the Grasshopper model that for any given boat (Distance between rudders and Distance between CLR and rudder pivots), Ackermann Angle increases as Turn Radius goes down, which corresponds to inside rudder angle going up.  In other words, Ackermann Angle is valid only for a specific rudder angle.  Either rudder, inside or outside the turn.

For example, using the same parameter values as before (1. = 8, 3. = 12), when the inside rudder is at 30 degrees, the outside rudder is at 18 degrees so Ackermann Angle = 12 degrees.  When the inside rudder is at 45 degrees, the outside rudder is at 23.2 degrees so Ackermann Angle = 21.8 degrees.

That means that toed-in tillers are optimized for just one inside rudder angle!
In this case, six degrees each (1/2 of Ackermann) for inside rudder angle of 30 degrees.

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Our set up:

tillers are connected using 2 carbon tubes running to a traveler car mounted in the centre of the boat. Wheel rope then connects to the traveler car as well.(same as what you have I think) This system is positive, light and has the added benefit that if one wheel fails brakes etc you have another independent system.

I would not worry about the Ackerman thing, it is not a beach cat.

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2 hours ago, bushsailor said:

I would not worry about the Ackerman thing, it is not a beach cat.

Granted, big boats may rarely do sharp turns, but think of it this way for a large cat (55 feet, guesses based on photos):

  1. Distance between rudders = 20 feet  (beam between hull centerlines)
  2. Turn Radius =30 feet
  3. Distance between CLR (daggerboards) and rudder pivots = 21 feet

The GH model I posted says that inside rudder angle will be 30 degrees, outside rudder angle should be 15.4 degrees, so Ackermann Angle is 14.6 degrees.  That means without Ackermann, the outside rudder (also at 30 degrees) will be 14.6 degrees away from optimal, creating drag on the "outside" of the turn.

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Thank you proasailor for the awesome info! Greatly appreciated. I have some homework to do now!

1 hour ago, ProaSailor said:

Granted, big boats may rarely do sharp turns, but think of it this way for a large cat (55 feet, guesses based on photos):

  1. Distance between rudders = 20 feet  (beam between hull centerlines)
  2. Turn Radius =30 feet
  3. Distance between CLR (daggerboards) and rudder pivots = 21 feet

The GH model I posted says that inside rudder angle will be 30 degrees, outside rudder angle should be 15.4 degrees, so Ackermann Angle is 14.6 degrees.  That means without Ackermann, the outside rudder (also at 30 degrees) will be 14.6 degrees away from optimal, creating drag on the "outside" of the turn.

 

Or maybe more to the point, the outside rudder will be doing all the work while the inside is just coasting along at much smaller AOA.

Edited by jmurph
I fucked it up
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Remember that when calculating Ackerman angle you need to account for all the geometric components, as the difference in angle between the rudders also depends on the angle applied to the helm, since the response is non-linear due to the sin component of the tiller offset. This is what makes the Ackerman tiller setup work not just at one angle, but if suitable sized, across a range of angles.

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Yes, Asia catamarans. Very well concieved/built boats (expect for this one issue).  Most have a fair bit of owner customization. They don't use this cross system any more (may have been just this boat) I'd buy on for myself.

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11 hours ago, hump101 said:

Remember that when calculating Ackerman angle you need to account for all the geometric components, as the difference in angle between the rudders also depends on the angle applied to the helm, since the response is non-linear due to the sin component of the tiller offset. This is what makes the Ackerman tiller setup work not just at one angle, but if suitable sized, across a range of angles.

Ah yes, the linkage system connecting the toed-in tillers...  I built another model inside the one I posted yesterday to explore this and wow!  I'm confused.  Reluctant to post the model or even discuss it because I don't understand it well enough yet to make it right.  Many details affect the outcome!

The simplest possible linkage is a direct connection between two tillers, like a Hobie cat.  It floats without constraint except for the two end points.  A loop of low stretch Dyneema could be attached at the mid-point to pull it side to side.  I didn't model that.

What I did instead is the more typical arrangement on big cats with a linkage from each tiller to a sliding mid-point on a traveler, or to the end points of a third linkage in the middle (shown in white below) that slides side to side.

Ackermann_2021_Aug4b.thumb.png.b092d56a533d1c772a5ff13e5131f243.png

In this model, the length of the white connecting linkage can be adjusted or set to zero so the two blue linkages meet at a point.  Just for grins, the traveler can also be offset forward.

As you can see the results aren't even close to the optimal outside rudder angle from yesterday!!?  I've been messing with this on and off all day and don't get it.  Every parameter affects the result, like tiller length, length of the white linkage, percent of Ackermann Angle for toe-in, etc., etc,  :unsure:

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3 hours ago, ProaSailor said:

Ah yes, the linkage system connecting the toed-in tillers...  I built another model inside the one I posted yesterday to explore this and wow!  I'm confused.  Reluctant to post the model or even discuss it because I don't understand it well enough yet to make it right.  Many details affect the outcome!

The simplest possible linkage is a direct connection between two tillers, like a Hobie cat.  It floats without constraint except for the two end points.  A loop of low stretch Dyneema could be attached at the mid-point to pull it side to side.  I didn't model that.

What I did instead is the more typical arrangement on big cats with a linkage from each tiller to a sliding mid-point on a traveler, or to the end points of a third linkage in the middle (shown in white below) that slides side to side.

Ackermann_2021_Aug4b.thumb.png.b092d56a533d1c772a5ff13e5131f243.png

In this model, the length of the white connecting linkage can be adjusted or set to zero so the two blue linkages meet at a point.  Just for grins, the traveler can also be offset forward.

As you can see the results aren't even close to the optimal outside rudder angle from yesterday!!?  I've been messing with this on and off all day and don't get it.  Every parameter affects the result, like tiller length, length of the white linkage, percent of Ackermann Angle for toe-in, etc., etc,  :unsure:

Double the turn radius ( the radius you are using for a large catamaran is unrealistic) and increase the tiller offset inboard to 12% and it will get closer 

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53 minutes ago, bushsailor said:

Double the turn radius ( the radius you are using for a large catamaran is unrealistic) and increase the tiller offset inboard to 12% and it will get closer 

The tiller linkage model I discussed today wasn't using the large cat numbers but I will try them.  What do you mean by "increase the tiller offset inboard to 12%"?  12% of what?  Or do you mean 12 degrees?  It's been too long since I drove a large catamaran, or even a 35 footer, so I don't remember.  60 feet is a large radius.

I'm reasonably confident about the optimal rudder angles from yesterday (the GH model I posted), though am not certain about the 'CLR_Rudder' distance value?  For this model, maybe that should be closer to boat length?  With rudders 20 feet apart, using a value of 21 feet between rudder and CLR (daggerboards) and a turning radius of 60 feet, the inside rudder angle is only 12 degrees!?  Changing the 'CLR_Rudder' distance from 21 to 51 feet (near full boat length) makes the inside rudder angle 30 degrees, which sounds more reasonable.

I set aside the tiller linkage model I made this morning and implemented a Hobie-style "free floating" tiller bar that directly connects the tillers.  It's interesting but not a significant improvement in reaching optimal difference in rudder angles.  I'm discouraged, dreaming of fly-by-wire technology that would turn each rudder separately to get optimum inside and outside rudder angles...  But it can't be that complicated?

P.S.  This image shows rudders 20 feet apart connected by a Hobie-style "free floating" tiller bar with each tiller toed-in by 20 degrees(!), yet still not enough difference in rudder angles.

Ackermann_float_2021_Aug4a.png.ce437d349976cbb9586e5dd629a88c88.png

With each tiller toed-in 30 degrees (a far cry from half), the difference in rudder angles finally gets to something reasonable.

Ackermann_float_2021_Aug4a2.png.77f95f5ada2451e90e78a7acc60c1828.png

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The geometrical Ackerman model showing a boat turning with the hull(s) tangent to circular path and aligned with velocity vector is wrong !

To turn the hulls need a centripetal force which is created by the lift of the hulls and appendages, and they need an angle of attack to the flow.

Only model right is Tom Speer's one which take's into account the lift of hulls and appendages !

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14 minutes ago, patzefran said:

The geometrical Ackerman model showing a boat turning with the hull(s) tangent to circular path and aligned with velocity vector is wrong !

To turn the hulls need a centripetal force which is created by the lift of the hulls and appendages, and they need an angle of attack to the flow.

Only model right is Tom Speer's one which take's into account the lift of hulls and appendages !

depending on design the rudders might or might not be adding lift from leeway

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48 minutes ago, Sailabout said:

depending on design the rudders might or might not be adding lift from leeway

Agree, so you have to take into account leeway and refined dynamic model of boat's motion to assess Ackerman utility, if any !

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6 hours ago, patzefran said:

The geometrical Ackerman model showing a boat turning with the hull(s) tangent to circular path and aligned with velocity vector is wrong !

To turn the hulls need a centripetal force which is created by the lift of the hulls and appendages, and they need an angle of attack to the flow.

Only model right is Tom Speer's one which take's into account the lift of hulls and appendages !

I have always admired and respected Tom Speer's analytical abilities but frankly, my eyes glaze over looking at pages like this:

Ackermann_Speer_2021_Aug5a.thumb.png.e6ddd3a046f5434efd99bdfafe514863.png

Still, I am re-reading his Ackermann PDF and noticed this line: "This is actually very close to the result obtained by Martin Schoon's geometric analysis", for which I have two comments:

  1. My Grasshopper models are geometric constructions where most of the math is hidden.  The diagrams I posted referring to "CLR" are the same as most diagrams explaining Ackermann for wheeled vehicles (where the concept was first developed).  I find the diagram useful, though have since adopted the term "Wheelbase" instead of "Distance between CLR and rudder pivots".  It's a convenient abstraction since it determines the angle of the transom (the line between rudder pivot points) with respect to the turning track.
     
  2. I remember Martin Schoon from the old Multihull Mailing List and met him when he visited San Francisco.  Would be great to reconnect.

So far, I have failed to make the connection between the difference in rudder angles indicated by that diagram and the toe-in angle of the tillers?

If you have a working Ackermann model, please share it?

I doubt there are many implementations that consider all the variables that Tom Speer does:

Ackermann_Speer_2021_Aug5a2.png.ee507cc49b10a843f0fb327bab3d48e5.png

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I believe my linkage model is accurate and interesting enough to publish as is:

Ackermann_2021_Aug6a.thumb.png.caf6c706ce3a058ca60f42552707c19d.png

Ackermann_2021_Aug6a.gh

The so-called "Ackermann Angle" is arbitrary so a 'Manual Ackermann' slider is available to set it.  A 'Pct Ackermann' slider determines how much effect it has and should probably be removed.  It was added for experimental purposes since the meaning of Ackermann Angle differs among the experts:

  • Peter Wormwood says "The angle between those two lines is your Akerman angle [the optimal difference between inside and outside rudder angles]. On a catamaran, each of the tillers are angled in half of this angle"...
     
  • Tom Speer says "The tillers of the two rudders are offset from the rudder centerline by the Ackermann angle" [not half the angle]

Arbitrary Ackermann Angle?!  I'm afraid so, since it depends on several factors such as speed and turning radius which my "Wheelbase Model" (included) doesn't account for, even though it illustrates the issue rather well.  In one sense, an undersized turning radius in the 'WB Model' can be considered to emulate the effect of leeway that affects actual turning radius, which is partly a function of boat speed.  Since tiller toe-in angle is fixed, not adjusted for speed, the Ackermann Angle is an arbitrary compromise anyway.

For what it's worth, I'll post the Hobie-style "free floating" tiller bar linkage model as well:

Ackermann_float_2021_Aug5a.gh

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It's a 3D world...  The 'Linkage Model' I posted has a 'Fwd Offset' slider to address the issue of the linkage traveler being forward of the tiller ends but forgot to include a 'Z Offset' slider to model a traveler that is some distance vertically above the tiller ends.  I just added that now and so far, it looks like the only effect is to lengthen the two blue linkages with no change to rudder angles.  But I want to be sure about this so will sleep on it for a day or two to make sure.

Just mentioning it now in case anyone tries to use this for a real boat?  Another assumption is that the rudder pivots are vertical; if they are not, the model needs to be modified further.  It may be hard to see in a 2D image but this shows the yellow "traveler" and white "Mid Bar" being 1.5 units (18 inches) above the tiller ends.

Ackermann_2021_Aug7a.png.679394d03a702f21ec66e48165498532.png

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This Rhino Grasshopper 'Linkage Model' uses eight primary parameters to create an interactive model for exploring rudder angle differences on a catamaran:

  • 'CB' - Centerline Beam (distance between rudders)
  • 'Ackermann Angle' - Tiller toe-in angle
  • 'Tiller Length' - Horizontal distance between rudder axis and linkage pivot
  • 'Mid Bar' - Length of middle linkage (white line) as a fraction (0 to 1) of 'CB'
  • 'V Offset' - Vertical offset of traveler midpoint above tiller ends
  • 'Fwd Offset' - Distance of traveler midpoint forward of tiller ends
  • 'Rudder Stop' - Half of the linkage midpoint travel distance
  • 'Steering' - Rotation of both rudders, -1 to 1 (applied to 'Rudder Stop' distance)

The 'Wheelbase Model' (included) is a visualization tool that uses two additional parameters, 'Turn_R' (Turn Radius) and 'WB' ("Wheelbase" forward of rudder pivots). The result is an Ackermann Angle that may be used in the 'Linkage Model', though has proven to be of little value and can be overridden by setting 'Manual Ackermann'.

Ackermann_2021_Aug8a2.thumb.png.122b6318a9e5b62ca8d2dd6c2e029398.png

Ackermann_2021_Aug8a3.thumb.png.fbb621d4f722271aeef1769438376526.png

Ackermann_2021_Aug8a.thumb.png.b8171fa0f99d1df13b532b17f0bb355d.png

Ackermann_2021_Aug7a.gh

NOTES:
To my surprise, there is no definitive model for Ackermann Angle since it depends on several factors that are not constant such as how far the "inside rudder" is rotated, boat speed and leeway. Therefore, getting the right toe-in angle for the tillers is largely a matter of judgement and experimentation. This suggests that tiller toe-in angle should be adjustable, along with the length of the connecting linkages, at least until satisfactory results are demonstrated by testing.

This reminds me of sailing with Mike Reppy on the Shuttleworth trimaran "N'aia" when rudders were added to the amas. We wanted to figure out why steering was different on port and starboard tacks so disconnected one of the rudder linkages, allowing that rudder to trail at whatever angle it wanted. Very interesting!

The 'Mid Bar' length on this model (white line) can be set to zero so the two blue linkages meet in the middle.  When the length is not zero, the yellow "Travel" indicator would not be the appropriate location for the traveler. Instead, two travelers would be positioned so both ends of the white bar slide horizontally. When the 'Mid Bar' is long, it can add ~two degrees to the difference in rudder angles, in this case.

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