please explain in public for the benefit of all, how an aircraft carrier under a replenishment operation with a tanker at such a close range and at great speed, are not just bumping into each other?
Known as an underway vertical replenishment maneuver as you well know. And as you are well aware, there are many factors that come into effect here, including the sizes of vessels, lateral and longitudinal separation between them, their wetted hull shapes, the depth of water. Forces of sway and yaw change during the approach, to a more or less steady state during the replenishment, and change quite a bit again during the separation maneuver. This has been studied extensively. One such example for a given sea and wind state is shown below for the benefit of the public as you requested.
Ship A is the approach ship, which comes up from behind and has to match the speed and course of the guide ship B. After the replenishment phase (about 33 minutes here) is completed, ship A has to increase its speed and move carefully away from the guide ship B. The guide ship's role is to maintain course and speed throughout. Rudder control on both vessels is quite critical to prevent the two from coming together (see upper right of the diagram below).
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If they would inadvertently bump against each other, how could the angle of collision be at 67°?
They (the carrier and tanker) can't inadvertently bump into each other at any large angle during the replenishment phase because of the relatively close transverse distance between vessels.
This is not the same situation as Olympic and Hawke. As to having a reluctance to change my mind because of a book already publish, I can assure you that I am more than willing to revise what's in the book based on new information and interpretation that can be cited. (By the way, nothing better for an author than to have a new version of a book on the market.) What I'm not convinced of is that the Hawke's helmsman turned the wheel the wrong way. However, I could see him distracted by this massive vessel passing on his left and loosing site of the fort that he was supposed to be steadying on, as well as others who were there, until someone (Blunt?) noticed too late that things weren't going according to plan. As I said, you have me going over the available primary evidence, which I thank you for, and I'm trying to do so with an open mind.
 
Hi Samuel. Einstein stated; «Pure logical thought cannot give us any knowledge of the empirical world; all knowledge of reality starts from experience and ends with it. Information is not knowledge; the only source of knowledge is experience».

You said; «What I'm not convinced of is that the Hawke's helmsman turned the wheel the wrong way». I gave you two factual cases based on experience where a wheelsman turned the wheel the wrong way. How many examples would you need to be convinced that a wheel turned the wrong way is a frequent occurrence under pilotage? I also relate from my own experience that when you meet a passenger vessel in a narrow channel, everyone gets excited thus distracted to the point that no one apart from the pilot is watching anything else except the love boat.

You said: «According to the testimony of Hawke eyewitnesses, Olympic came within about 100 yards (1/2 cable) of Hawke by the time she completed that hard turn around the W. Bramble». #854

Then; «Anyway, FYI, Hawke's tactical diameter was 1764 ft. To turn about 67° and then strike, the separation between vessels would be about 580 ft, or close to 1 cable». #23

Next: «They (the carrier and tanker) can't inadvertently bump into each other at any large angle during the replenishment phase because of the relatively close transverse distance between vessels». #858

I am optimistic that if you read back assiduously your own statements, you will find the answers to your questions! ;)

«This is not the same situation as Olympic and Hawke». What is so different; you have two ships steaming at close range and great velocity performing dangerous fuel replenishment. Ships’ interaction should therefore be tremendous; how could they hold their position then? From your vessels approach sketches, you deduce that the long and rather narrow Olympic, built with a razor blade plumb stem, would have pushed Hawke port quarter so powerfully that she would swerve sharply and slice open the liner at 67°? I stand with Laing; «Theory is one thing, practice is another»!

Again, I confidently disbelieve that ships’ interaction within a natural channel where the water depth was between 60-65 feet deep, bounded by gentle slopes coasts, could have generated such tremendous forces that would have caused an overtaken vessel to sheer up to 67° and collide forcefully with an overtaking vessel separated by a cable off. Captain Blunt shouted; «What are you doing with your helm? Port, Hard-a-Port !!!» for the reason that Hawke was turning so «rapidly and sharply» toward the Olympic that the only reason captain Blunt could come up with, was that her Edgar-class protected cruiser was responding to a wheel turned in the wrong direction. The severe vessel turning inertia to port could just not be overcome by a mere rudder jammed at 15° to starboard. On the other hand, I would be the least surprised that Blunt sought to race the largest ocean liner in the world. Since he probably didn’t have to keep a tight schedule as the liner, he should have act as a gentlemen by cutting down her speed to let the faster liner go by as good seamanship would advise, so to abide by the spirit of article 27; «In obeying and construing these Rules, due regard shall be had to all dangers of navigation and collision, and to any special circumstances which may render a departure from the Rules in order to avoid an immediate danger».

Conclusively, if ships’ interaction was problematic in that area, you would easily find MAIB reports on such occurrences since thousands of overtaking manoeuvres took place in that district during the past hundred years. And believe me; they were not all that easy!

There she goes «Hard-a-Starboard»!

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If these two navy vessels would be proceeding into a narrow channel, they would collide bodily on the spot. In open waters, matters are different since the hydraulic interaction adverse effect has all the space to dissipate, but there still limits.

I suppose they hold some kind of tables or software to calculate the safe distance off they have to maintain. As a rule of thumb example, if the carrier is 30m wide and the tanker 20m then; [(30 + 20)/2] x 1.5 = 38m, and 38m equates 0.2 cables safe distance off. We are well inside ½ to 1 cable off from the Hawke affair. In our pilotage district we keep 60m off, the overtaking vessel to proceed at 10k max while the overtaken at 6k. And nowadays, the manoeuvre is doubly recorded by the ship’s VDR and by the Coast Guard VST. They seem not to trust testimonies any more, I wonder why?

Note: to maintain the vessels parallel and at constant distance, the easiest is to use a 3cm Radar VRM, an extended COG vector, and a sober steersman on direct steering and order system.
 
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