Angling dual outboards toe-in for docking

I own a small (30 foot) catamaran. Before I bought it, it had two diesel engines inboard. These were seized which didn't really bother me as I wanted to convert to electric anyway and did that using two electric outboards. As an electric the boat works beautifully (videos on youtube, Sailing Electra if you're curious), I can motor all day long at 4-5 knots without draining the battery or do 3 knots pretty much forever charging in the day and running on batteries at night.

I did have one major problem though. Because the outboards are only 1 meter apart compared to the diesel at 2.7 meters apart, docking was a real nightmare as I couldn't steer using "tank drive" with one motor forward and one in reverse. It was bad enough that I never wanted to go into a marina for fear of hitting something, and if it was windy catching a mooring ball was hell.

I've since rectified that by turning the motors toe-in around 25 degrees each when docking. This means that each motor now has a sideways thrust component and gives me the tank steer ability I wanted.

What I'm curious about now is how much it helps compared to the original motors. I'm fairly sure it can be calculated, but I don't know where to start. I've attached a few pictures here:

In the above image one you can see the electric outboards, the small grey squares in front of the rear solar panels. I've also drawn blue crosses where the old props would have been for the inboards, and in red I've shown where the sugar scoops are on the back of the boat is if it matters.

The outboards are rotated manually now for docking or motoring, and it works out to about 25 degrees each:

It makes a huge difference, I can now steer just on throttles, and because the throttles are wireless I can do it from any location on the boat, a huge benefit for docking or catching mooring balls.

Some boat specs:
Length - 9.65m
Width - 4.2m
Weight - 5 Tons

I'm wondering if someone can help me with the maths to see how much effect there is with angling the motors. I'd like to compare it to the original boat. It's purely an interest question, as I think it works well enough not to need any adjustment.

 

I take it steering those engines is a capability you're uninterested in adding? But if toeing them in turned the impossible into the possible that's some excellent empirical evidence right there.
Quantitative analysis instead of qualitative analysis is much harder, because you're trying to put numbers on your subjective experience.

 

That kind of maneuvering thrust vectors has been a fundamental enabler of twin waterjet vessel low-speed maneuvering for many years (more than 30..)..and more recently for independently controlled pod drives and even I/Os.

 

Just a friendly question.. are you sure the props are sized big enough?

Everything you are talking about suggests the possibility the props are undersized. Even at a meter apart; some amount of throttle steerage would be available.

 

What are the hp differences between the previous diesels and the current electric motors?

 

I would consider the possibility that the boat has some natural pivot point forward of the transom about which it will tend to rotate. If that is so, angling the motors 25° might increase the effective lever arm between the pivot point and the motor. Having no idea what your lateral plane looks like, I can't begin to estimate the effect. Of course, the same thing is true for me even if I did know, but I am speculating about a possibility for someone more versed in this to consider.

As an extreme example that may have little bearing on the behavior of a cat, I have a small skiff with a dagger board and no skeg. Without the rudder, it will rotate around the dagger board when one oar is pulled. Without the rudder, my skiff has very little directional stability with the board up and even less with the board down. With the board down and no rudder, at about 4-5 mph the boat will yaw out of control and spin around the board. All forward motion is lost by the time it has turned 90° but it will continue to rotate for several turns. Board up, it is only very hard to steer at that speed, but rowing that fast is difficult, so the lack of a skeg is tolerable. At rest, applying torque perpendicular to the transom with two hands two feet apart is slow to turn the boat with the board up and ridiculous with it down. Applying torque at an angle to the transom with the board down spins the boat easily. The dagger board only moves the center of rotation.

 

This is a very resonable explanaition.