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Saw the Scharnhorst armour scheme: the main belt (350mm) is penetrated from Alaska only under 16 km, but for real damage the projectile need pass almost also a 30 mm deck...
average rate of fire of 2.4-3 rounds per minute and could throw an 1140 pound AP projectile 38573 yards at an elevation of 45 degrees.
much longer and heavier reach with guns
She was armored against 12 inch shell fire barely
Assuming a much more practical max range of 25,000-30,000yds which ship had the better chance of penetrating it's oppenents deck?
Main belt is a mighty small target compared to the deck at these ranges.
Not so sure about this if we are comparing fire control for the same time period. U.S.S. Alaska was not worked up until December 1944. If Scharnhorst survives that long it will have late war German fire control improvements.
The longest ranged set developed by the germans was the FuMO 34, which had had a peak power of 125 kw and a reported theoretical range of 40-50000 metres. With a pulse width of 4 milliseconds, this was still not a short wavelength set, and did not provide surface fire control radar capability.
It does not compare very well to the equivalent USN fire control radars, of which the Mk 34 was typical. The power output of this set was 1500-2000kw, the range similar at 45000 m (before the advent of AEW this was about the limit of surface radars), Pulse width, 0.5 ms, . This setwas very accurate 15 metre error at 40000 yards. It was also capable producing very reliable range data, something even the latest naval radars in Germany could not do.
A Scharnhorst fighting an Alaska in 1945 will be fighting at a severe disadvantage due to its poor radar fits. Ship borne radar was one area in technolgy where the allies achieved a massive superiority by wars end....