I’m finding your images a bit hard to make sense of - do you have an ROV with four layers of thrusters? From what I can tell your first image shows 8 thrusters pointing forwards/backwards, and another 4 pointed 45 degrees, between vertical and lateral - is that correct?
It can be helpful to think of thrusters in terms of the pressure change they induce in the water around them. In pushing water from in front to behind it, a thruster creates low pressure in front, and high pressure behind. If there’s no obstruction to the flow in or out, then there’s a net force away from the direction of water movement, which pushes and pulls the thruster in the direction of motion, like below
If you put two thrusters in series, such that the outflow of one goes into the inflow of the other, the water between them is already moving, so if they’re going the same way then you basically just lose some of the differential, which results in slightly lower net force than two operating independently (but still more than one)
If you have them rotating in opposite directions however, the thruster behind basically gets extra bite into the water from the thruster in front, which helps to effectively focus the outflow, and results in more of the energy going into the desired motion. This effect is nicely displayed in the following image from a computer fan manufacturer, which I found in this relevant quora answer
It’s worth noting that what you put around and between the thrusters can also have a significant effect on the dynamics. If you’ve got something attached right behind a thruster then the outflow ends up going sideways, and can even end up going slightly forwards which causes a slight backwards force, partially offsetting the forwards force from the low pressure region in front
Accordingly, having one set of your ‘lateral’ thrusters in between the top forwards ones will likely reduce the forward efficiency because
- they block the water flow between the forward thrusters, which removes some of the desired force, and
- if they’re on at the same time as the forward ones, they basically create a wall of water, which makes that blocking effect more pronounced.
It’s perhaps also worth noting that to go directly in either lateral direction may not be possible with this setup, partly depending on where the center of mass and buoyancy are. As an example considering each side together, if you want to go left, the lateral thrusters on the right have to push down+right, which moves the ROV left but also up, and causes roll. To counter the roll the lateral thrusters on the left can push down+left, but then that reduces the force to the left and increases the force upwards. If they push the other way (up+right) to counter the upwards motion then they increase the left force, but also increase the roll so the ROV would start spinning. There are similar issues if you consider the diagonals together instead, but with yaw instead of roll.
Hope this is a helpful explanation