KC-135. The receivers cannot switch. AF is configured for the boom and the Navy is configured for the basket. The AF tankers can be configured for either. Navy tankers only have the hose and basket.
Away from the boat, the Navy uses the AF tankers. The tactical jets the Navy uses for tanking will usually only pass around 2k at a time.
And to further muddy the waters, KC-10 is (at least in my experience) always dual configured, i.e. can drop the boom for AF, or string the hose for USN/USMC/NATO. They have to administratively reel in/raise the current fueling device, and do some stuff internally with their pumps/settings which takes a few mins, but they can effectively switch type of receiver real time in the air.
KC-135 comes in two configurations......one is MPRS, which are the little buddy stores on either/both outboard wing stations, that serve probe/drogue, and allow the jet to retain a boom that can fuel AF jets as well. Other, somewhat more common configuration is just the boom, with an adapter hose and basket that extends from the end of the boom. In this configuration, the jet is unable to service USAF style aircraft until it lands and they take the hose/basket off. This particular appendage is called the "Iron Maiden" by USN/USMC aviators, as it is a comparatively "hard" basket (pretty much all metal), and moreso because it is at the end of a very very short hose, and you have very very little slop in terms of drifting out of position, or alternately when first plugging. It will snap a refueling probe in a heartbeat, or in my case when I was first learning, completely destroy an AoA probe and damage the nosecone/radome, causing multiple FCS degrades and requiring an emergency divert. It isn't hard most of the time once you get the hang of it, but if you get lazy or complacent, it will bite you.
KC-130 is always probe/drogue configured, with wingtip buddy stations, much like MPRS KC-135, though it flies about 60-70 knots slower, and is therefore slightly more uncomfortable to receive from, at least from a jet/tacair perspective.
Lastly, there are a bunch of older NATO aircraft that are a mixed bag, mainly along the lines of the KC-10 config. Also, OMEGA operates KC-707's (and I think one KC-10), which are all USN/USMC configured, since we are the only customer. OMEGA doesn't participate in combat ops, but they provide gas for a lot of workup/training exercises. Nice soft basket, like the -10, MPRS, or -130 (or F/A-18E/F for that matter)
Sorry, end thread jack
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