Calculating drag force on a rotating body

[Massimo]

TL;DR Summary

I want to know how to calculate the drag force acting against the rotational motion of a specific body, and if/how it affects simultaneous linear drag.

For context, I'm developing a submarine simulator with a heavy focus on realism, especially on the physics side of things. I've already implemented a fairly accurate linear drag model for forward/backward and rise/dive movements, but I'm not sure where to start with calculating the rotational drag against my submarine when it's turning from side to side (yaw movement); also, I have some questions about if/how rotational and linear drag affect each other in simultaneous rotational and linear movements, e.g. a submarine turning to the right while moving forward. Does anyone have any ideas?

 

[Baluncore]

... also, I have some questions about if/how rotational and linear drag affect each other in simultaneous rotational and linear movements, e.g. a submarine turning to the right while moving forward. Does anyone have any ideas?

When turning, the section of the hull across the flow, is greatly increased because of the length of the hull. The drag coefficient is that for a circular section, not an elongated hull.
The highest drag on a road transport vehicle, is when there is a strong crosswind. The vector sum of ground speed, and the crosswind, becomes expensive in lost energy.

 

[Lnewqban]

... I'm not sure where to start with calculating the rotational drag against my submarine when it's turning from side to side (yaw movement); also, I have some questions about if/how rotational and linear drag affect each other in simultaneous rotational and linear movements, e.g. a submarine turning to the right while moving forward. Does anyone have any ideas?

These articles may help you:
https://www.mdpi.com/2077-1312/9/12/1451

https://www.mdpi.com/2077-1312/10/10/1417

https://www.mdpi.com/2077-1312/11/11/2091

As you analyze the total velocity, and subsequent drag, acting on several cross-sections of the hull, you will see that those have a maximum value around the bow and the stern, as well as a minimum value around the center of mass of the ship (through which the yaw vertical axis passes).

Although the forward component of that total velocity is the same for all the sections, the tangential component is different in magnitude and direction for each section.

The main function of the rudder is to make the values of drag very different for each, the port and the starboard sides.
That induces a yaw moment, which must overcome the huge yaw moment of inertia during the beginning of the turn.

Once the rate of turn is stablished, that yaw moment fights the additional rotational drag that the turn itself is inducing.
That drag comes in the form of friction and form drag (less hydrodynamic surfaces and cross-sections shape facing the flow), plus certain amount of profile drag due to port and the starboard fins going through different types of flows.

Besides the rudder, other control surfaces may need to consume extra kinetic energy or forward moment of the ship, only to compensate for coupled not desired pitch and roll movements induced by the changes in the distribution of the dynamic forces during the turn, as well as for reducing drifting or skid by leaning the hull (similar to what boats and airplanes do).

Consider that the extra energy that turning requires must come from the engine(s), and that unless additional thrust is available, the forward velocity will get reduced; more as the turn is sharper.

 

[Lnewqban]