Where does the expression “at a crack” come from?

The phrase at a crack is sometimes used to mean at one time. For example §§:

Companies that have had generations of employees growing up under a no-layoff policy are now dumping 10,000 people onto the street at a crack.

What's the history of at a crack?

I suspect that "at a crack" is closely connected to the idiomatic phrase "have a crack at," so let's start with that phrase.

The idiom 'have a crack at'

From Christine Ammer, American Heritage Dictionary of Idioms (1996):

have a crack at Also, get or have a go or shot or whack at; take a crack at. Make an attempt or have a turn at doing something. For example, Let me have a crack at assembling it, or I had a shot at it but failed, or Dad thinks he can—let him have a go at it, or Dave had a whack at changing the tire, or Jane wants to take a crack at it. The oldest of these colloquialisms is have a shot at, alluding to firing a gun and first recorded in 1756; crack and go date from the 1830s, and whack from the late 1800s.

Likewise, Harold Wentworth & Stuart Flexner, Dictionary of American Slang (1960) has this:

crack ... n. ... 3 A try at some undertaking whether large or small. 1934: "...To take a crack at something bigger." Cain, Postman, 29.

The Cambridge International Dictionary of Idioms (1998) includes entries for both "have/take a crack at" and "get a crack at"—the latter entry without a definition. Here is the former entry:

have/take a crack at sth

to try to do something although you are not certain that you will succeed [example omitted]

And John Ayto, Oxford Dictionary of English Idioms, third edition (2009) has this:

have a crack at make an attempt at doing, achieving or winning (something).

The complementary phrase "at one crack" or "at a crack" would therefore mean "in a single shot or attempt or turn," and by extension "at one time."

The idiom 'at one crack'

The first instance of "at one crack" in a Google Books search dates back to 1872. From Lyman Abbot, Laicus: Or, The Experiences of a Layman in a Country Parish (1872):

There are a few treaties that are worth reading and re-reading ; but they are exceptional. Generally the student gets the gist of a book in one reading, as a squirrel the kernel of a nut at one crack. What remains on his shelves thereafter is only a shell.

From The Nickel Library (1877[?] [snippet]):

"Well, kurnel," said the red-bearded man, turning to Dan, "I had an idea, and an alfired strong one you kin make sartin. I've heard o' you boys often, and when the time came that I needed help, my mind went right to ye, and I swore I'd hev no others. Fack is. boys, the time has arrived wen ye kin make yer fortunes all at one crack.

From "Hard Luck!" in The Mechanical Engineer (September 30, 1882):

Allow m to thank the writer of "The Professor in the Machine Shop" article for his warning against partners, his able and manly language generally., and especially his objection to mortgages in starting a new shop. My experience tallies exactly with his danger signal. If he had only written these articles about six years ago I should have been $6,000 better off, and six years time, for I lost that amount of tools slick and clean at one crack, just like a lightning stroke, and have been struggling to get over it ever since.

Also of note, from "First Session of the Council," in National Liberal Federation, Proceedings at the Annual Meeting of the Council of the National Liberal Federation (January 17, 1895) [Mr. Lloyd-George, M.P., being quoted]:

In 1892 a majority of the people of Ireland, Wales, and Scotland, and something not far short of one-half of the people of England, declared that justice required the concession of Home Rule to Ireland as the first step of the incoming Government. That was only two years ago, and now they were told that they had dropped that policy and that they had gone back upon it, simply, it appeared, because an obstacle had been interposed in the shape of a ricketty old institution known as the House of Lords. The House of Lords had thrown Home Rule out, and at once three millions of people had dropped it in consequence. Three nations and a-half cowered at one crack of a lordly whip. What a picture of British pluck!

And from A. Leamy, "A Day's Fox Hunting Vermont," in Hunter-Trader-Trapper (July 1912):

I had waited perhaps twenty minutes when I saw him [the fox] coming with great leaps about a rod long. Now, the thought arose, will he come in the same place or won't he? He finally decided he would and when about eight rods off I let drive, dropping him at one crack.

Aside from the purely metaphorical uses of "at one crack" in these early examples, we have four instances where the crack is treated as part a simile or as an actual sound: the cracking of a nut (by a squirrel), the crack of a lightning bolt, the cracking of a whip, and the crack of a gunshot. The originator of "at one crack" might have had any of these ideas in mind.

"At a crack" is probably from "take/have a crack at".

"I never felt such a desire to have a crack at any thing in all my life." A Narrative of the Life of David Crockett, Written by Himself," Philadelphia, 1834

I have used the phrase "at a crack" myself, and have heard it often in Pennsylvania. The meaning is clearly "attempt", and more precisely "successful attempt."

The explanation for "take/have a crack at" meaning "attempt" or "try" refers to the crack of a gun shooting, which could make it a variant of the popular "take a shot at". See crack.

The crack of a bat hitting a baseball evokes the same sense of "attempt", suggesting a possible variation of the popular "take a swing at".

Regardless, the source of "at a crack", which is clearly relatively new, seems to be from that usage "take a crack at", with "attempt" transforming slightly into "successful attempt".

The Online Etymology Dictionary has this explanation for 'crack' as a noun: Adjectival meaning "top-notch, superior" (as in a crack shot) is slang from 1793, perhaps from earlier verbal sense of "do any thing with quickness or smartness" (Johnson).

Also, there's the expression 'at the crack of dawn' where 'crack' also suggests a certain immediacy.

On the other hand, I am more prone to understand the meaning of 'at a crack' via the collocation 'a crack of thunder' which suggests fastness, speed and unexpectedness.

This is a very common idiom in US English. Have no idea as to the origin, but the meaning, in the above context, is simply "in one single action", usually with the implication that other similar actions occur.

One might say "He's spending $500 a crack for fancy ties and he doesn't have enough money to pay his rent." Or maybe "The garbage grinder chews up 2000 pounds of garbage at a crack, and then comes back for more.

(Sorry for the lousy examples, but the best I can do right now.)