To admit since when was the J-15 designed from day one with catapult in mind !?? Do we have any credible source that confirms this ?? I wonder a bit why You repeatedly say this again and again without any prof.
From what we know, the J-15 is plain and simple a Chinese Su-33 modified with similar modifications (structure, avionics, ...) to the J-11B-standard and even if surely planned from the beginning like
@SinoSoldier already explained, the current J-15s are not able to catapult-take-off while the prototype J-15T or A (whatever You call it) is to do.
Even more the changes from the J-15 to J-15T/A are more than a mediocre batch-update, especially the front gear is very much different with most likely modified - aka strengthened - structure to cope the catapult-forces during take-off, so that IMO a new letter is more than justified.
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Again IMO the current J-15 is a Chinese J-11B-equivalent to the Russian Su-33 with J-11B-derived avionics, maybe a higher composite percentage on its fuselage but it is not able to take off from a catapult.
The current J-15T/A is therefore so far only a prototype incorporating the strengthened fuselage & the new catapult-capable front-gear and WS-10H but otherwise there's no need for it to act also as an avionics-testbed with a new radar. If testing is done these structural changes will be incorporated in a dedicated catapult-capable version.
This newly reported radar however is planned to be used in that version.
As such maybe - pending how long it will take to mature either the catapult or AESA - there will be an interim version based on the standard J-15 but already featuring that AESA, which then will be called J-15A, while the final version would then be the J-15B.
Deino
Pardon, but that's exactly where You miss the facts or at least a proof esp. for Your point 1 !!
Point 2 is also quite sure, but why does an AESA-equipped updated version then should not get a new letter ??? IMO the changes from a J-11A to B are dramatically minor - in fact only a new avionics + WS-10A - in contrast to these changes from the J-15 to J-15A.
Point 3 is also interesting: so far there is only one confirmed J-15A/T ... ? Or do You know more?
And finally point 4: Yes, therefore they are batches similar to the J-11B batch 01 to Batch 07 or now the J-15 Batch 01 and current Batch 02, but that new catapult-capable version is so much different that it surely deserves a new letter. Otherwise please explain why You deem these structural changes NOT important enough to warrant a new designation ??
Deino