The "I"s would decide the range, and it's clear that they would chose to fight at the closer, the better (as was seen with the german ACs at the Falklands). And that is the trump card for the british ships: not only bigger guns, but also a higher top speed to decide the range of the fight. Blucher could have a good armor for her size and class, but still would be quite hard pressed to stop 12'' shells (faulty caps or not), her best range would be a non-factor given that she couldn't decide the range of the fight, and her main guns weren't exactly adequate to deal even with the very lacking armor setup of the I's.
For me there's no real contest between both ships, even while it might be a much closer matchup than what it might look at a first glance.
Top speed isn´t really that different here. INVINCIBLE´s top speed in peacetime trial conditions was 26.61 kts forced (INFLEXIBLE= 26.41 kts & INDOMITABLE= 26.11 kts) while SMS BLÜCHER logged in an average of 25.82kts in her 6 hour trials. Depending on which ship You relate this to, this makes for a difference of +0.29 kts to + 0.79 kts. The combat speeds would be less for many reasons, BLÜCHER was designed to sustain 24.5 kts while the INVINCIBLE design speed was 26 kts, which they were hard pressed to match.
BLÜCHER on the other hand would have been derated under german wartime trial rules and not able to achieve even 25 kts of her fastest run.
Dictating the range of the engagement is practically impossible with a mere kts speed difference. The GF considered in period sources a difference of at least 3, preferably 4 kts sufficiant to be of any tactical benefit.
Dictating the range is further impossible when You are heavily outranged by Your opponent. Remember, BLÜCHER´s 8.2in gun´s were able to engage out to 20,900 yards while INVINCIBLE´s 12in mk X with 2crh AP were only able to reach to 16,450 yards with new guns.
It takes about two hours at both ships max sustainable speed to bridge this 4,500 yards gap in a stern chase in which INVINCIBLE cannot respond to BLÜCHER´s fire. This is more than enough time to completely deplete BLÜCHER´s 85 rounds per gun containing main magazines for the stern and after wing turrets if shooting at a slow average of 1rpm (max possible: 4-5 rpm) in such a long timeframe.
I attempted to make a comparison for each others protection relying on Nathan Okuns facehd and M79 APCLC programs. Note that an long range engagement exposes the armour decks of the INVINCIBLE.
Presumably this analysis applies to the 1914/15 time frame when both types are somewhat obsolescent. At time of launch she would presumably be firing crappy 8” shells which would struggle to penetrate much over 4” of armour at medium range which needs to be considered in a balanced assessment of her design capabilities.
I think you mentioned in a previous post that these ships were designed to fight at close range and this seems to confirm it.
That´s true. Originally and to 1912, the BLÜCHER alike other ships were intended to engage enemy AC (bot not PDN´s, BC´s or DN´s) at very close range. This is also the reason for the 50mm KNC slope behind the 180mm armour backed by a coal bunker and another protected bulkhead. Enough to defeat 9in main calibre guns from even short range. They were given a large main gun elevation mainly in an attempt to create long range reach against shore targets for coastal raids not to faciliate long range naval gunnery.
But by the summer trials in 1911 and 1912 they conducted long range naval gunnery and found it feasable. BLÜCHER owing to the large gun elevation became the HSF´s main long range gunnery exercising cruiser and was the first eqiupped tripod and centralised firecontroll. It also stood in an ever lasting contest with ACR SCHARNHORST and GNEISENAU for winning the annual gunnery award. BLÜCHER on the prize in 1911 for beeing the best shooting ship of the entire HSF in that yaers manuever period. It pioneered the usage of gyrostabilization elements in gun mountings during 1912 and in 1913 received increased elevation spotting top with Siemens stabilized mountings and Zeiss stereoscopic rangefinder for long range cetral director shooting.
Originally, at long range only HE base fused or HE nose fused would be fired in order to derate the exposed equipments and unprotected ship ends. It was not before Krupp replaced it´s lyddite filler (Gr.f. 88 in german terminology) with wood plugged, block cast TNT and introduced hard armour piercing caps at about the same timeframe that AP long range fire became a viable option.
By the time of Doggerbank the ACR has changed to become a long range thread, it´s armour still sufficiant at this range unless very heavy calibre guns are fired at it (13.5in, 14in and 15in) and it´s guns, the firecontroll suite and the training level of the crew optimised for long range action.
At short range action (say, 8000 yards or less) BLÜCHER may still overpower an I-class by volume of fire of it´s 8.2in main and 5.9in sec. gns but unless it can claim a critical hit in a magazine, turret or barbette, I would still give the advantage to INVINCIBLE owing to the larger guns and larger size (size helps absorbing damage).
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edit: SMS BLÜCHER´s turret faces are not 7.1" but 9.8" thick, so take the figure of CT alike instead