there is quite literally not a singular instance in history as far as i know where battlecruisers were in the same division as battleships prior to the engagements
Prince of Wales and
Hood;
Prince of Wales and
Repulse as Force Z;
Renown,
Valiant, and
Queen Elizabeth as the First Battle Squadron in late 1943 and 1944;
Queen Elizabeth,
Valiant,
Richelieu, and eventually
Renown during Operations Cockpit and Transom (yes,
Richelieu's generally considered a battleship, but it's also about eight knots faster than
Queen Elizabeth and
Valiant)
wall of text so tldr
half of those examples are forces and the ships mentioned were not in the same division but rather the same force
hood and Richelieu are the only 2 of that not happening but both had SEVERE engine problems and thus speed was reduced close to their accompanying ships
repulse after her refit was only 2.5 knots faster than POW in force Z and we dont know whether she had her own division or was part of POWs
ok lets first establish something
a force is larger than a divsion as shown by in game screenshot at the bottom
a Squadron is larger than a division
a fleet is larger than division
picture in game which shows how divisions and forces are split up
notice the word
FORCE-Z
a force is the INTIRE FORCE not a singular division
also you forgot to mention Force Zs compliment of destroyers which themselves would be the escort division while the renown and POW mostly likely were in seperate divisions unless they wished to limit renowns speed (which would only be limited by 3 knots)
also worth noting that repulse after her 1926 refit would only do 30.5 knots compared to POW which would punch out 28 which made for a grand total of 2.5 knot speed difference while not small it wasent major either
depending on how Force Z was set up i might have been wrong regard the battleship/battle cruiser thing but as far as i can see its only this singular instance and my statement still holds true for literally all other cases
during 1916 at jutland the first battle squadron was made up of DIVISIONS and so was the 1943 and 1944 battle squadron which had also received carriers which were part of a totally different division and destroyers which again were part of a different division (escorts)
as shown in the second picture the 1916 composition
hood by the battle of the denmark strait was not in optimal shape and was due for a refit a short time after the battle (which she obviously never got) and her speed was limited to less than 30 knots which might have effected the division to put her in the same division as the prince of wales which at the time was totally new and could make max speed
also worth noting that hood never got a complete boiler overhaul even after 2 world cruises and had not been replaced in some 25 years
she likely could still do 30-31 knots if she wanted to in a pinch although with permanent damage to engines maintained speed was probably some 29 knots
according to a friend who owns "the mighty hood" book she could make a max of 29.4 maintained
she had also stripped an intire turbine during mers el kebir and was only given very basic repairs in anticipation for a full refit which never happend
the maximum speed achieved by them at the battle was 28 knots (also max speed of prince of wales)
"The carriers were accompanied by a
two task forces of 20 other warships, not counting the carriers.
Force 69 was commanded by British Eastern Fleet commander Admiral Sir James Somerville and was consisted of the battleships Queen Elizabeth, Valiant, and Richelieu, supported by an array of other ships;
Force 70 contained battlecruiser Renown, carriers Saratoga and Illustrious, and other ships."the only oddity here is the Richelieu combined with the older dreadnoughts but on the other hand Richelieu had just finished repairs in USA and had been handed over to the british for a short while and they decided to use her in this operation
according to Wikipedia she did in fact have boiler problems
(it does have a source attached)
she was most likely limited in speed and thus was sent as part of the battleship division of force 69 instead of the battlecruiser division which was part of force 70
conclusion ?
only cases where battleships SIGNIFICANTLY faster than other battleships operated together was when they had boiler problems or old machinery in need of refit or repairs
battleships and battlecruisers did not operate under the same division though they did operate under the same force
(unless you wanna call hood a battleship which she really is not same with the Richelieu they are both fast battleships)
generally speaking though ships with a few knots diffrence often were in the same division but a large speed difference such as found between a ww1 battlecruiser and dreadnought would be a bit too extreme
for example the hood could probably sail with the KGV even with perfect engines due to "only" a speed difference of 3 knots which while still major was not extreme
on the other hand the valiant and Richelieu (assuming both in perfect machinery conditions) had a solid 6 knot speed difference
or an extreme example american dreadnoughts with 22 knot speed vs the iowa class at some 34-35 on a good day
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