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special notes:
Ships equipped with CXAM Radar as of December 7 (and with the Pacific Fleet)
BB California, West Virginia, Pennsylvania
CV Lexington, Yorktown, Enterprise
CA Pensacola, Northhampton, Chester, Chicago
seaplane tender Curtis

All US destroyers have sonar, none yet have radar

CXAM has a search range of 50 to 100 miles (depends who you ask), but the Lexington picked up a Japanese strike at 65 miles at the Battle of Coral Sea so I am going with that (but assuming 50-60 miles factoring in decision time frames)

No Japanese ships have radar (and will not for some time to come), Japanese destroyers, even the best equipped, only carry 12-20 depth charges and these are set too shallow (for now)


Air Search
The Japanese use float planes from their cruisers (which are in trouble from just about anything else that flies and has guns), and Kates if they are really serious and know American carriers are about. In this timeline they are looking for American CVs, so usually 12 Kates provide additional coverage to the seaplanes aboard the Tone and Chikuma. The BB float planes generally are used for antisubmarine patrols

The Americans use the Dauntless, indeed one squadron is a Scouting Squadron, so up to 18 per carrier is typical. These search aircraft carry bombs (usually a 500 pound bomb as the 1,000 pound bomb reduces their air search time). The float planes are not used for search and indeed spent a lot of time simply being fire hazards (after Savo Island they were flown off right away if a surface action was expected). They did good work in the search and rescue missions.

The Americans still have the overwhelming majority of the PBY force at Oahu (about 65) and Midway (12 or so, plus a couple that were on their way to the Dutch that were kept on December 7). These have an effective search range of 500-600 miles. However it is a big ocean, and while that sounds like a lot of search aircraft, they still miss things.

There are two American submarines off Midway on December 7, and both will remain on station, the Argonaut) whose captain hid below the surface when two Japanese destroyers from the Pearl Harbor attack force shelled that island that evening in OTL) and the Trout, which was on the opposite side of the atoll and thus out of position that evening.

The Japanese submarines are all clustered around Oahu, however a few are heading toward Midway.. However their speed is 22 knots at most, but as they are a long way from home a more conservative 18 knots (high end of cruise) is called for, and they can only do that safely during night time hours. They are thus out of position until around December 9 at the very least (this is a departure from historical in terms of where the submarines went after Pearl Harbor)

The American S boats and fleet boats from the Picket Force have pretty much been left behind. The three submarines at Pearl Harbor that are available will not be able to sortie until December 9 as they were undergoing maintenance at the time of the attack.

MidwayIsland
The AAA batteries and 5 inch batteries are present, and like Wake Island, they are still under manned and there is no radar yet at Midway (its on its way). The airfield is completed, and there are stores, including bombs, present for the VMSB 231 and its Vindicators which were supposed to be flown off on December 7.

There are stores and fuel for the PBYs present (and plenty for any other aircraft). If necessary the PBYs can rebase to French Frigate Shoals, especially as the Curtis is en route there to provide support to PBYs from Oahu that are about to be sent there.

Japanese land based aircraft in the Mandates are busy attacking Wake Island at the moment and are well out of range in any event