I understand that the Soyuz 2.1v launcher will switch from using the NK33 engine to the new RD-193 when stocks of the former are finished.
Does anyone know how many launches, beyond the two so far, are planned using the NK33 type?
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According to now almost three years old news article (in Russian, Google Translate version) from April 2013 that quotes Energomash CEO Vladimir L. Solntsev, there were at the time in total of about 20 NK-33 engines left in the warehouse, which would be enough for about 10 launches.
It is a bit difficult to predict how long the NK-33 supplies will last. Launch vehicle is now awaiting return to flight after the partial failure with Kosmos 2511 (Kanopus-ST) failing to separate from the upper stage in December 2015, and it is also unclear when we'll see the first Soyuz-2-1v launch from Vostochny. First Soyuz-2.1a is currently scheduled to launch from there on April 25, but I haven't seen any announcement of Soyuz-2-1v launch from Vostochny yet. So far, only three Soyuz-2-1v launches from Plesetsk are expected till 2018 according to Spaceflight 101, and usually well informed Gunter Dirk Krebs currently only lists one planned launch.
According to Anatoly Zak, the new Soyuz-2-1v (previously referred to as Soyuz-1) configuration with RD-193 engines will be called Soyuz-2-1d, but searching the web by that moniker didn't yield any more information, I'm afraid.
If I had to guess, then my bet is that Baikonur will never see a Soyuz-2-1v launch at all (because of the nature of its typical payloads and target orbital inclinations, and because Baikonur isn't in Russia), and we'll see inaugural RD-193 on Soyuz-2-1v (Soyuz-2-1d?) launch from Vostochny, likely before Plesetsk runs out of NK-33 engines, somewhere around 2020. Sooner, if they decide they'll only supply Vostochny with RD-193's and keep all NK-33's at Plesetsk.