I'm sure you will correct me if I'm wrong. I use latitude difference only.Starting from an estimated position of the wreckage for 11:20am and working the drift of current backward toward the wreck site for about 2½ hours, we find that the wreckage at the time Carpathia departed would be close to 41° 37’ N, 50° 00’ W. After leaving the scene of the wreckage, Carpathia briefly headed southward for a couple of miles and then southeastward to parallel the eastern edge of the pack ice. Eventually they would turn southward and then southwestward to get around the southern extent of the pack before heading due west. In that wireless message to Haddock, Rostron said that the pack ice extended as far south as 41° 16’ N, and that bergs and floe ice could be expected as far eastward as 49° 30’ W.
From the derived location of the wreckage for 9am, Carpathia would have had to go 20 miles to the south in latitude to reach the southern extent of the ice. Notice that this distance happens to match the “20 miles of field ice with bergs amongst” mentioned by Captain Rostron in his wireless message to Cunard’s New York office. But the pack ice was trended southeastward from the area of wreckage as far as the eye could see according to Rostron. That means Carpathia had to first go southeastward before she could turn southwestward and then westward. Eventually, Carpathia was able to get around the ice to reach a latitude of 41°15’N, one mile south of the southernmost point of the heavy pack. At 2:30pm NYT, a little over 7½ hours after departing the wreckage, Carpathia was reported at 41° 15’ N, 51° 45’ W, where she was put on a course of 267° True direct for the Nantucket Shoals light vessel. We know this from another message from Rostron to Hddock: "Captain Olympic: 7.30 G.M.T. [2:30pm NYT] Lat. 41.15 north, long. 51.45 west. Am steering south 87 west, true. Returning to New York with Titanic’s passengers. Rostron." In addition to this, we have the position, 41° 15’ N, 50° 20’ W, given to IMM’s vice president Franklin by the Cunard Line. This position is exactly 64 nautical miles due east of the 2:30pm NYT position for Carpathia sent in the message from Rostron to Haddock. At her normal fullahead speed of 14 knots, Carpathia would have covered that distance in 4 hours 35 minutes. That means that Carpathia would have passed 41° 15’ N, 50° 20’ W at 9:55am NYT, about three hours after Carpathia departed the area of wreckage. On Carpathia, it would have been less than half an hour before local apparent noon which came at 10:22am NYT on that date and location.
The departure course for Carpathia begins at the derived location of the wreckage for 6:55am NYT at 41° 37’ N, 50° 00’ W. It then follows a path down along the eastern edge of the pack ice southeastward, then south and around southwestward, and then westward to 41° 15’ N, 50° 20’ W, the location given to IMM’s Philip Franklin, for 9:55am NYT. The distance along the route shown to that point is 42 nautical miles, a distance that Carpathia would have traveled in 3 hours at 14 knots, Carpathia’s normal full-ahead service speed. From there, Carpathia would head due west (270° True) for another 64 nautical miles reaching 41° 15’ N, 51° 45’ W at 2:30pm NYT, where a slight course change to 267° True would put her on a direct heading for the Nantucket Shoals light vessel.
According to James Bisset, Carpathia did not reach open water until sometime after they took sights of the sun at local apparent noon where they would have obtained their precise latitude. At local apparent noon April 15, 1912, Carpathia would have been crossing 50° 28’ W longitude at 10:22am NYT, about 3½ hours after departing the wreckage. According to Captain Rostron, Carpathia was traveling about 4 hours, a distance of 56 miles at 14 knots, before reaching open water. This means that they did not reach completely open water until passing longitude 50° 40’ W in latitude 41° 15’ N. According to a Hydrographic office report submitted by Californian’s Captain Lord, Californian did not reach completely open water after resuming her voyage to Boston until she reached longitude 50° 42’ W in latitude 41° 33’ N. Clearly, the sea was spotted with lots of icebergs and patches of ice floes over a very large area extending well to the west of that major field of pack ice that we have been so involved with.
If the wreckage was at 41-33 north at 11-20 am, then by your reckoning, it was at 41-37 North at 9 am, This is a drift/leeway rate of 1. 74 nautical miles every hour. If this was the case . then we can estimate where the wreckage and survivors were, five (5) hours earlier, at 4 am when Carpathia found them...41-45.7'North?
Leaving out the leeway due to wind and using a south-setting current of 1.1 for the period 11-45 pm until 4 am, we then add another 4.7' to the 4 am latitude and arrive at a latitude of 41-50.4/North for the place where Titanic finally came to a halt.
We can also forget about leeway and simply add 1.1 minute of latitude to the latitude of the wreck site to obtain the latitude when Titanic finally stopped. That gives us a stop latitude of 41-47'North (rounded-up).
I note that none of the "maps" show Lord's search area which must have been at least 45 square miles of the area to the south and east of Carpathia's position at 9 pm.
You keep mixing up Pack Ice with Filed Ice.
The former is part of the latter.
Carpathia entered the Ice Field at 2-45 am and was in it from then until he cleared the westward side on the afternoon of April 15.
If you care to plot the ice reports, you will discover that the main Field extended from the north to south then tapered southeastward to about 41-28'North where Carpathia first encountered it. It had a central "spine" of pack ice interspersed with bergs and had bergs and small stuff tapering southwestward to latitude 41-15 North.
The plot of ice reports between April 11 and April 18 suggest that the bergs were being entrained in the northern margin of the North Atlantic Current...Not the Gulf Stream. The latter ends at about 60 West.
If as you suggest, Carpathia headed in a SE direction when 2 miles south of her starting point at 9 am, then she would simply have retraced her journey between 2-45 am and 4 am and been in bergs all the way. We know for sure that there were many bergs in that direction. This from Captain Lord:
" Q I will ask you whether you saw any icebergs while you were making that circle?
A: I was surrounded by icebergs.
Q: How large were they?
A: The ones way to the southeast were much larger than the ones to the westward."
Now why would captain Rostron take the route you suggest if his declared intent was not to aggravate the suffering of the survivors by prolonging their time in sight of ice bergs?