Where does A/C abbreviation for aircraft come from?
Solution 1:
There are a couple of possible sources, and it may well be influenced by more than one:
You get it most often with two-letter abbreviations, where it serves to make the pair of letters stand out as an abbreviation where they might instead look like a word, at least on first glance; the idea being that one will see A/C and immediately think something abbreviated with A and C rather than what does AC spell?
(w/ is by analogy to w/o, and in some other such abbreviations the slash really does represent a slash in the full form, or separates components that are themselves abbreviations).
Now, this form was popular around the beginning to the middle of the century. They were not as heavily abbreviated as we are in our era of TLAs, but they certainly did like to save paper and ink. They also though wanted to make the abbreviation clearly an abbreviation.
At that time, Britain and some other English-speaking countries had a currency of "old pounds" which would be written abbreviated as e.g. £2 3/11 for "two pounds 3 shillings and eleven pence", but omitting parts that weren't needed so 3/11 for 3 shillings and eleven pence and 3/- or 3/ for 3 shillings.
As such, it was a common way of separating two components that one wanted to demonstrate were separate, rather than one running on from the other.
I don't know if A/C was being used for aircraft at the time, but it certainly was for aircraftman since around the first world war. Since the A and the C weren't next to each other in the full form the abbreviation sought to convey this and so you would get A/C (and sometimes even A./C. in which having both periods and a solidus seems redundant).
It's conjecture to suggest that the use for shilling was an origin, but as it was so commonly used to separate components in that use, the conjecture is at least reasonable.
/ for shillings in turn comes from ſ, a long-s standing for solidus (with £ being a mutated L standing for libra and the d that would be used for pence on their own standing for denarius).
Another source is the virgule, which could be either / or | and was originally a mediaeval mark to indicate a pause, whether to mark meter or as we would now use a comma. This survived into several uses to mark a separation (the slash of and/or comes from this).
These two sources give a precedent for / being used where one wants to point out a separation between two things, like people wanted to do with two-letter abbreviations.
Solution 2:
The first theory seems likely, although not completely satisfactory in view of the fact that the second mark cited as a forward slash is, strictly speaking, a solidus.