Lever arm comparison on a boat with toe-in motors

[patrickza]

TL;DR

Have a catamaran, old motors were 2.7m apart, new ones are 1m apart but I angle them 25 degrees toe-in for docking. They are 4.2m behind the centerpoint of the boat. How does this new setup compare to the old in relation to turning with differential thrust?

I have a small catamaran that used to have two motor under the hulls spaced 2.7m apart. I've replaced those motors with outboards which are spaced 1m apart, and placed about 4.2m behind the centerline of the boat. Initially it was impossible to use differential thrust to turn the boat, but since then I have made it possible to angle both motors "toe-in" 25 degrees for docking. This has made a remarkable difference, and it's now very easy to turn the boat using the motors, what I'm trying to figure is how to compare the new effectiveness with the old.

Below you can see the outboard motors, they're the small grey rectangles (electric outboards). The Blue X is more or less where the old motors had their props, and the red is the back of the boat. To give some scale the boat is just under 10m long, and according to my measurements the new motors are about 4.2m behind the center point.

And below is how I use the motors for docking:

Now I haven't done physics since high school, but I'm looking to try and understand what the difference would be when comparing the original 2.7m apart setup with the new 1m apart, but 25 degree toe in setup? I don't know what it was like before, because the motors were dead when I got the boat, so I changed them straight away.

Thanks for the help.

 

[Baluncore]

Welcome to PF.

I would begin by considering the circle of water flow that is tangential to the two motors. The old system was centred on the point between the motors. The new system circle is centred forward of the motors.