The militia line, according to Lawrence Babits in A Devil of a Whipping consisted of four South Carolina militia regiments commanded by Brandon, Hayes, Roebuck, and Thomas. (I previously presented an alternative scheme). Babits noted (p. 36) that there were 5 battalions in these 4 regiments, and that each battalion had 120-250 men. This means, by extension, that the militia line had between 600 and 1,250 men. Elsewhere (p. 189, n. 11) he said that the 4 regiments had 150-200 men each, which means that the militia line had between 600 and 800 men.
In his maps depicting the militia line, each of the 4 regiments (including Brandon's two-battalion regiment) is shown as having a length of 190 feet. If there were 600 men in the 4 regiments, then each man in the ranks would have occupied 1.27 feet of frontage (190 feet / 150 men per regiment). If there were 800 men in the 4 regiments, then the number falls to .95 feet. These numbers do not make allowances for spacing between companies or the presence of trees.
I previously commented on open-order and closed-order formations and produced the estimate that soldiers standing in open order would occupy something like 42 inches, or 3.5 feet (see Modeling Notes). Soldiers standing in close order would occupy something like 33 inches, or 2.75 feet. However, this applies only to a single rank. If the soldiers were standing in two ranks, then each soldier occupies, in a sense, 1.75 feet in open order, and 1.38 feet in close order. Both values are well above the space allotment indicated by Babits' diagrams.
Two Versions of the American Deployment (click to enlarge). My interpretation appears on the left, and is as described above. Babits' interpretation appears on the right; the positioning of the units per his account is approximate. On the right, 1 = American Cavalry; 2 = Main Line; 3 = Militia Line; 4 = Skirmish Line. The two accounts also differ in terms of the location of the Green River Road. The road in my version follows Bearss and is shown in brown. Babits showed the Green River Road following a different course, which I have partially sketched out in black on the right panel.
In my order of battle, I have approximately 315 men on the American militia line (see Cowpens in Miniature 3). Babits not only placed many more men on the militia line, but he placed them in a smaller area. On his maps, the right end of the American line is bounded by a shallow "ravine." This feature does not appear on my topographic map, which is not a reason per se to discount its value as a military barrier. However, other writers well familiarized with the battlefield, namely John Moncure (map) and Edwin Bearss (map), did not indicate a barrier to troop movement in this area.
If Babits had ignored the ravine and gave more room for his large number of militia, then of course, the militia would not be so closely pressed together. However, even if Babits' militia line were spread out across the distance shown in my diagram or the distances covered in the Moncure and Bearss maps, the problem created by such hypothesized large numbers of militiamen might not be entirely eliminated. A moderately wider deployment might allow his numbers of militia to have been deployed in open-order, but it would still have been necessary for the militia to have been deployed in two ranks. Private William Neel of Virginia claimed that the Virginia militia were deployed in one rank (see transcribed statement on John Moncure's website). It's not unlikely that the South Carolinians were deployed in a comparable manner.
Related: Introduction, How Many Fought at Cowpens?, Morgan and Seymour