Looking at a close-up of the Moskva class helo carrier, it appears she also has the exact same VDS as the Krivak I (considering the years of construction, that doesn't come as a surprise).
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An interesting note I found while researching other ships that may have the same VDS as the Slava, The Kara class apparently do not have conical indentation under its stern that is seen on Slava, Udaloy and Kirov classes, despite having VDS. So that indentation is not perfectly correlated with the need to deploy a sonar towed body while underway. So either the Russians haven’t discovered the merit of the indentation yet while they were designing the Kara, or the indentation actually serves a different purpose then smoothing water flow for the VDS
There following observation suggest to me the indentation indeed serves a different purpose than help water flow for VDS. . Unlike most ship’s boats, which has a V shaped bottom or a flat bottom, The small powered speed boat like boat carried on most larger Russian surface ships also has a similar indentation on the bottom near the stern.
Valid point. I also recently noticed the same "indentation" on the stern of merchant ships, notably a container ship and a RoRo vessel. Although I do not know what was their configuration below the waterline, it might actually have to do with the single rudder configuration, which also most Soviet ships seemed to have. It doesn't explain why Kirovs have it though... It also starts behind the rudder rather than having the rudder in the indentation.
Not sure when they actually introduced it. The shape of the indentation is also rather special, in some cases rather smooth and wide, in others, like Neustrashimiy, very sharp/deep, flanked by the twin rudders, while in case of Kirov the rudders are still some distance away from the indentation.
What it might have to do with is either course stability (instead of a skeg between the props) or to avoid slamming in rough seas, where wide flat aft ships tend to get punched pretty hard.
For now I can confirm:
Ships that don't have it:
-Grisha
-Nanuchka
-Kanin
-Krivak I to III
-Sovremenny
-Moskva
-Kapusta
-Nedelin
Ships that have it:
- Neustrashimy
- Udaloy
- Slava
- Kirov