[MHml] Ackermann for cats : pdf file

[Tom Speer]

Brian Southwood wrote:
> 
> Thanks Martin,
>     An interesting analysis. ...
> Tom Speer in particular may have some valuable comment on the hydrodynamics of
> the foils involved.


Thanks, Brian for drawing me in to this tar baby ;-)

My analysis can be found at
http://www.geocities.com/tspeer007/Ackermann.pdf.  

In a nutshell, here's what I found:
- When you include leeway (skidding), the geometry is basically
as Martin set it up, but the turning center is moved forward by
the amount of the leeway angle.  This effectively changes the
distance to the rudders.
- The large rudder deflection needed for tight turns gets to the
point where the linkage inverts itself - where the inside tiller
and the link line up and the outside rudder reaches its maximum
deflection.
- There's a tradeoff between balancing the two rudders with the
Ackermann angle and not having the linkage lock up too soon.  Low
Ackermann angles promote stall on the outside rudder, but allow
both rudders to deflect enough to match the turn radius.  Large
Ackermann angles could limit the rudder deflection and thus the
radius.  
- When I used the numbers for Martin's boat, plus some additional
parameters I only guessed at, it looks to me like the most
suitable Ackermann angle is much less than Martin derived - more
on the order of 10 to 15 degrees than his 35 degrees.  And the
corresponding turn radius (measured to the center of the boat)
was around 1 to 2 beam-widths.
- The turn radius is pretty much dictated by the stall angles of
the hull and rudders.
- It's better to drive the rudders from the inside tiller than
the link or the outside tiller because then you have full control
throughout the range of motion.  

I didn't get into the whole yaw moment balance, but that looked
to be the deciding factor on establishing the speed at which the
boat would turn best.  The more I got into it, the more I ended
up trying to analyze the whole boat.  The number of free
parameters was multiplying pretty fast!

Cheers,
-- 
Tom Speer
tspeer at gte.net
http://home1.gte.net/tspeer
fax: +1 206 878 5269