Ackermann Linkage for Catamaran Rudders
Using Rhino Grasshopper, from an SA forum discussion, August, 2021 (ProaSailor)
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'.
Download
Grasshopper: Ackermann_2021_Aug9a.gh
And a simpler linkage model more suitable for beach cats: Ackermann_float_2021_Aug5a.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.
References:
- Ackermann Steering For Catamarans by Tom Speer
- On the Tiller Geometry of Cats by Martin Schöön, October 1998 (in English Feb. 2001)
(original: Efficient Steering of a Catamaran Using Ackermann Principles)