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Who should build them? AFAIR they had only two docks large enough for these kind of ships.
The main guns would be a completely new type which would most likely not be ready befor 40/41, even the 38cm gun of Bismarck as an evolution of a WW1 gun wasn't ready for SH/GN.
Diesel engines were not really feasible for big warships in this time.
Instead of SH/GN, BS/TP and all five Hipper Class (Hipper, Bluecher, Prinz Eugen, Lützow and Seydlitz/90% ready 1941) plus Graf Zeppelin,
6 x 35-36000ts general purpose german BB (more near SH/GN as BS/TP) plus one more Deutschland Class.
SH/GN were 31550ts standard deplacement at their introduction.
My plan is a BB with 3 x 2 x 40,6cm SK 34, mixed power unit ( 8x 12 MZ12 42/58 on the outer propeller, plus 8 x Wagner boilers with 2 x turbines to the inline propeller = 4x propeller)
To my calculations a 245m, 33m, 10m, vessel, with 320mm outline belt, 105mm slopes, 145mm upper belt, 50mm weather deck and 80mm main deck (over magazine 100 + 80mm), spaced array armour, 73000 WPS Diesel + 100000 WPS oil fired gear turbine, would be at 365000-37000ts.
This is to my opinion the optimal german BB since 1935 and should be built 6 times instead of all other units.
And they should go to missions only as SISTERS, just like the Twins! This is my personal six gunner program!
Something like 6 x very tough german Renowns on steroids!
Why not just rearm the SC GN with 15in as soon as the guns were available, and take it from there?
It is a possibility!
To my opinion SH/GN had three design flaws.
1. The 45mm upper belt was much to thin for sure decapping and reduction of shell power (as protective shield for the main armour deck), the 145mm upper belt of the BS class was much better and balanced for the german armour sheme and cost only 600ts more.
2. The high pressure steam turbinis were not reliably and the fuel consumption at cruising speed (18-24kn) was much to high.
3. They were wet ships, because they had not enough buoyancy through their "smal" beam.
If you put 16 or 15 inch guns to such a ship is debatable, my proposal of 16 inch guns was a compromise to have only 6 guns.
The hit performance of the Deutschland Class as 6 gunners was equal to the BS SH and Hipper Class and Renown as six gunner was the best RN artillery ship (best hit performance) for several years.
Instead of SH/GN, BS/TP and all five Hipper Class (Hipper, Bluecher, Prinz Eugen, Lützow and Seydlitz/90% ready 1941) plus Graf Zeppelin,
6 x 35-36000ts general purpose german BB (more near SH/GN as BS/TP) plus one more Deutschland Class.
SH/GN were 31550ts standard deplacement at their introduction.
My plan is a BB with 3 x 2 x 40,6cm SK 34, mixed power unit ( 8x 12 MZ12 42/58 on the outer propeller, plus 8 x Wagner boilers with 2 x turbines to the inline propeller = 4x propeller)
To my calculations a 245m, 33m, 10m, vessel, with 320mm outline belt, 105mm slopes, 145mm upper belt, 50mm weather deck and 80mm main deck (over magazine 100 + 80mm), spaced array armour, 73000 WPS Diesel + 100000 WPS oil fired gear turbine, would be at 365000-37000ts.
This is to my opinion the optimal german BB since 1935 and should be built 6 times instead of all other units.
And they should go to missions only as SISTERS, just like the Twins! This is my personal six gunner program!
Something like 6 x very tough german Renowns on steroids!
Six guns is too few for good salvo fire for a line BB, and 35-36k tons is not enough for a balanced German BB with 38cm or 40.6com guns. Whose definition are you using for standard displacement (each country interpreted it differently)?
IMO, your best bet is a Scharnhorst with the extended (Gneisenau rebuilt) bow with 9x35cm (Krupp proposal for the Bismarck class and would have been the most powerful 35cm afloat - but make them lightweight guns like the 14" originally proposed for the North Carolinas), dump the single 15cm pedestal mounts, shave the main belt to 30cm, shave the conning tower armor to 15-20cm, increase the upper belt to about 70cm, give them a transom stern, and use a Turco Electric drive with the Brown-Boveri steam plant used by Gneisenau (G didn't seem to have the problems with her plant that S did with her Deschimag kit).
You'll also need to develop an automatic 3.7cm AA gun or use the 4cm bofors.
Dump the single 2cm - mount only 2cm Vierlings.
Consider using 8.8cm flak instead of the 10.5 cm if there are significant weight savings.
With the armor shaving, deletion of the pedestals, and transom stern you should save some weight.
The 35cm guns make her a danger to any other BB afloat at normal gun ranges, and the belt/slope combination is still proof against BB-caliber guns at normal ranges.
STE drive will improve range OR lower fuel requirements for the same range, remove the single-reduction gear box, and remove the need for a multi-stage turbine. I'd also consider deleting the diesel generators and running all power off the main plant. It will also help response to the helm. As well, you can have shorter shat runs (motors closer to the screws) which will reduce power losses versus the longer shafts needed for a typical steam turbine plant. You can also cross-connect power to the motors in event of battle damage.
The extended bow will improve weatherkeeping.
You'll need to keep the aircraft on-board for search purposes.
Did you account for the extra horizontal armor weight required by broadening the beam 2m?
The problem with the S&G wasn't their standard weight, it was their war load weight. You've got to add fuel, ammunition, manpower, stores, etc. B&T went from 42k tons to 51k tons standard to war load.
Check out the program at SpringSharp.com.