Replying to the thread in general...
A Yamato vs NJ contest would be highly predicated upon the weather conditions at the time. At night or in foggy weather, the NJ would have a clear advantage in fire control. However, people who haven't ever operated radar systems tend to credit them with being able to perform miracles. They could not. People also tend to confuse search radar and fire control radar abilities. For example, over-the-horizon capability (O-T-H being defined as a target that is totally below the horizon and out out of any visual detection capability). All WWII radars were line-of-sight. Search radars occasionally yielded detections over the horizon during WWII but that was normally a function of atmospherics not radar design. Fire control radar could not and did not ever provided an over-the-horizon detection. Their RF spectrum is much higher than search radars and far less prone to ducting.
Also when considering fire control systems, Yamato's optical system was a state-of-the-art system and provided very accurate information. Those 15 meter range finders were just as accurate as radar in good visibility conditions in determining range. Its main drawback was that it was a cumbersome system to operate (30+ people) and was visibillity limited. The main advantage of a radar control system is that it provides accurate ranges for gun layers much quicker and less prone to human error due to only about 15 people operating the system. But human error was still a possibility. An operator still had to interpret the radar scope, determine the correct target and then place the cursor on the center of the blip. Placing the cursor off center is probably the single biggest mistake an operator can make. For example, an operator who takes a reading off the bow of the target on one sweep and then off the stern a few sweeps later has induced a speed error into the calculation. The target displayed speed will be greater than acutal. Optical systems don't have this limitation as they commonly use mast height to determine range (assuming you know what the correct mast height is). One advanatge and optical system has over radar is that it can detect a course change much quicker. Radar has to wait for the target to actually move a ways down the new course before seeing whereas the optical operator will see the aspect change immediately. Also as stated in a previous post, radar systems were very prone to failure from vibration and shock. The shock of the main guns firing is quite likely to knock the radar offline for a period of time. The shock from an 18" shell impact can also have an adverse impact. Radar antennaes were delicate things and shrapnel tended to play hell with them so even splinters from anear miss could knock it out.
The Yamato was also a more stable gun platform due to her greater beam and weight. Yamato was also a drier ship. The Iowas were well known for being a wet ship at speed, especially in the area of B turret. The advantage though is highly dependent upon the sea state and is minimal.
Iowa had a greater rate of fire than did Yamato but Yamato's broadside weight was much greater. Yamato's armor was thicker than Iowa's but of slightly inferior quality. Post war testing of armor samples removed during Shinano's conversion revealed that Iowa would have a very hard time penetrating turret and belt armor. Yamato's deck armor was designed to resist a 2000lb armor piercing bomb hit from 10,000 feet. Nathan Okun is a recognized naval ordnance expert. His comments concerning Yamato armor follows:
CONCLUSIONS:
The U.S. Navy Ballistic Limit (complete penetration minimum velocity with this projectile at normal) estimated at 1839 feet/second (560.5 m/sec), plus or minus 3%, which gives it about a relative plate quality of 0.839 compared to U.S. Class "A" armor (estimated, as no such super-thick plate was ever made in the U.S.). This was about the same as the best WWI-era British KC-type armor, which was what the Japanese were trying for--they had not attempted to make improved face-hardened armor, as the U.S. Navy did during the 1930's, for actual ship installation.
The plate was excessively brittle internally, with too much "upper bainite" crystal structure due to too-slow cooling. This was due to using the same pre-WWI British Vickers KC-type armor-hardening techniques on plates over 17" (55.8cm) thick, for which they were never intended. This problem was solved during WWII, but no more VH was ever made except for some thin experimental plates. Brittleness did not seem to reduce resistance to penetration, though cracking might cause problems due to hits that ricocheted off.
Note that one of these experimental plates--7.21" (18.3cm) VH plate NPG #3133--was patterned on Krupp KC n/A (probably from data traded with Germany during WWII) and was tested by the U.S. Navy at the NPG using 335-pound 8" Mark 21 Mod 3 and Mod 5 (the latter with the super-hard AP cap, which turned out to be required to penetrate that plate intact) during this same test series. It was found to be THE BEST PLATE OF ITS THICKNESS RANGE (6-8" (15.2-20.3cm)) EVER TESTED BY THE U.S. NAVY, even though its steel was of the same rather poor quality as the other VH plates tested!!! This caused the U.S. test conductors to state that obviously they did not understand what it took to make a high-quality Class "A" plate, since the 7.21" VH plate should not have been so good from everything they thought they knew about face-hardened armor!!! Obviously the Japanese could make armor as good as anyone if the specifications had required it!
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FINAL COMMENTS:
At about 40,000 yards, the U.S. Navy 16"/50 firing a 16" Mark 8 Mod 6 AP projectile (the later Mod 7 and Mod 8 designs were post-WWII, so I usually do not count them and they were no better ballistically, to my knowledge) will hit at about 45° downward angle and 1607 feet/second (489.8 m/sec). Just as with a point blank hit at 2500 feet/second (762 m/sec) and 45° obliquity, this hit too will barely hole the plate as the projectile is hitting at 0° (normal) obliquity, though not completely penetrate it. Any slight barrel wear will lower the muzzle and striking velocities and no holing will occur at THESE OR ANY OTHER ranges, as mentioned. However, this is so far above any real fighting range (even with radar it is hard to see the target due to the earth's curvature interfering, especially in any kind of imperfect seeing conditions) that I do not even consider it in my computations, while putting the gun barrel up to almost touching the enemy turret is also a pipe dream in real life! Thus, no holing or complete penetrations, ever, though possibly some cracking of the plate and possible jamming of the turret if the crack-off plate piece is dislodged badly enough.
Therefore, these plates are the only warship armor plates that could not be completely penetrated by ANY gun ever put on a warship when installed leaning back at 45°, as they were in the actual turrets!!! Even to completely hole the plate all the way through at that inclination requires a brand new 16"/50 Mark 7 or German 38cm SK C/34 gun at point-blank range firing the latest versions of their respective AP projectiles; it might be cracked at a lower striking velocity, but no hole put entirely through it!
The armor tested was from the Shinano's original 18" gun turret face. Obviously Yamato's armor wasn't as thick in all places but it certainly was capable of doing its job as good or better than many other battleships.
One other aspect to think of. The Japanese 18" AP shells were designed with a different philosophy than were ours. One of their design philosophies was that of an amor penetrating UNDERWATER hit! They believed that shells should be aimed to strike the water a little short of the target and that these shells would follow a parabolic trajectory. In effect, they would become torpedoes and strike the ship at or below the belt armor. As there were no engagements at ranges where this was possbile, we have no data proving its value. But it is an interesting thought.
But who would win between the two? The winner goes to the one who scores the first telling hit that reduces the fighting efficiency of the enemy. Be it through destroying the fire control system, reducing the target's firepower or slowing it down. If you had to pin me down I would say thay Iowa had a slight advantage at longer ranges as long as she had her radar systems online. Without radar, I think the nod goes to Yamato, especially if the ranges are under 15000 yards. The weight of Yamato's shells will penetrate nearly every part of Iowa's armor at that range. Iowa could only penetrate Yamato's deck and tower armor (and a penetrating deck hit is highly unlikely given the angle). Iowa must remain at 20000+ yards to achieve the right angle for deck penetration.
Personally, I would hate be on either one of them. Neither is going to be very battleworthy after such an action and neither may even be seaworthy. Still, it makes for an interesting discussion.
Chez