Marching - Is either in slow time, quick time, or double-quick time. In slow or quick time, the length of the step or pace is thirty inches, except in stepping out, when it is increased to thirty three inches, and in stepping short, when it is reduced to ten inches. In double-quick time, the step or pace is thirty-six inches. In slow time, seventy-five steps or paces are taken in a minute; in quick time, one hundred and eight, and in double-quick time, one hundred and fifty. The side or closing step, which is taken when it is necessary to move a small distance to either flank, is ten inches, and is always taken in quick time; but when taken to clear or cover another soldier, it is twenty-one inches. In stepping back, the step or pace is thirty inches.

--  http://vermontcivilwar.org/research/mno.php

( Such would mean that the pace in double quick time is 150 per minute, 36 inches per step, 5.1 miles per hour, 11.8 minutes per mile)

In 1834, Scott translated and adapted the latest French manual, the Ordonnances of 1831. The following year Scott’s three-volume Infantry Tactics was adopted as the drill for American infantry, a position that it held for over twenty years. In general, the tactics were slow-moving and relied on the massing of troops as opposed to rapid movements and firepower. Scott’s Infantry Tactics stressed close-ordered lines of either two or three ranks (Scott assumed that the three-rank formation would be the most common, but it was suspended by the War Department in 1835). Scott’s Infantry Tactics was more concerned with maintaining order than with creating élan. He did not want attackers to make a rapid advance. Men advanced with a “direct step” of 28 inches at a “common time” rate of 90 steps per minute. He also allowed the “quick time” rate of 110 steps per minute. Scott discouraged the use of any step-rate faster than quick time. He believed that the “double-quick time” and the run were unnecessary for line infantry in ordinary circumstances.

Hardee introduced a “double-quick time” step of 165 paces per minute, and the run. Henceforth all foot drill movements could be executed at the double-quick. Modern American soldiers would recognize the double-quick as the “airborne shuffle.” The troops were trained by regulations to cover five miles in one hour in full marching order with rifle and knapsack to condition them to react promptly in combat and to deploy and maneuver quickly.

 ...I perceived at once, however, that Hardee’s tactics – a mere translation from the French with Hardee’s name attached – was nothing more than common sense and the progress of the age applied to Scott’s system...

-- http://www.cwreenactors.com/~sykes/instruction/DrillBooksAndRifles_Pt1.html

Cadence and length of step;

Hardee defines three cadences each of which has its own length of step, plus "the run":

1. Common time: Common time is 90 steps per minute, length 28 inches. This covers 70 yards a minute.

Common time is to be used only for recruit training "Common time will be employed only in the first and second parts of the School of the Soldier." (and, customarily, for funerals). Common time WAS the fighting cadence once upon a time, in the 18th century and before, which is why Rev War or English Civil War reenactors look like they are marching in slow motion. But by the time of the American Civil War, trained troops were expected to be able to move faster and still keep their formation.

2. Quick time: This is the ordinary maneuvering pace of Civil War armies. Quick time is 110 steps a minute, each 28 inches long. Quick time covers 85.55 yards a minute. So it is a little slower and shorter than the modern U.S. military marching step (120 x 30") which covers 100 yards a minute.

3. Double quick time: This is not a run, but is a jog. It is ordinarily 165 steps a minute, each 33 inches long. This covers 151 yards a minute. It can be sped up to 180 per minute, "At this rate a distance of four thousand yards would be passed over in about twenty-five minutes." (Hardee, 114) Units double timing do keep their dress and cover, so double timing is not a command to straggle, and we should make every effort to keep our formation. Hardee tells drill instructors to practice the soldiers in wheeling and changing direction at the double time. [Hardee, 323] Well trained skirmishers in the presence of the enemy should take intervals, assemble, and rally at the double; but we may not be so well trained. Charges are done at the double.

-- http://www.6thtx.org/Maneuver%20of%20the%20Month_forward.htm

94. The length of the direct step, or pace in common time, will be twenty-eight inches, reckoning from heel to heel, and, in swiftness, at the rate of ninety in a minute.

101. Common time will be employed only in the first and second parts of the School of the Soldier. As soon as the recruit has acquired steadiness, has become established in the pi. , of shouldered arms and it) the mechanism, length and swiftness of the stop in common time, he will be practiced only in quick time, the double quick time, and the run.

104. The length of the double quick stop is thirty-three inches, and its swiftness at the rate of one hundred and sixty-five steps per minute.

114. The double quick step may be executed with different degrees of swiftness. Under urgent circumstances the, cadence of this step may be increased to one hundred and eighty per minute. At this rate a distance of four thousand yards would be passed over in about twenty-five minutes.

117. It is recommended in marching at double quick time, Or the run, that the men should breathe as much as possible through the nose, keeping the mouth closed. Experience has proved that, by conforming to this principle, a man can. pass over at much longer distance and with less fatigue. 

-- http://www.usregulars.com/Hardeess02.html#LESSON%20III.-%20PRINCIPLES%20OF%20THE%20DIRECT%20STEP.  ( Lesson IV. - Principles of the double quick step )

Hardee drew extensively on his knowledge of the French military and their 1841 drill manual, as well as his own experiences on the Texas Frontier (1849-41) and the Mexican War, to accomplish his task. His brief was to thoroughly modernise the U.S. infantry into a faster, lighter force, capable of taking advantage of the new rifle. Hardee's Tactics was finished in 1854; it was tested, approved, then published in June 1855. This new manual thoroughly modernised the U.S. infantry into a faster, lighter force, capable of taking advantage of the new rifle, where quick time (110 steps per minute) was the norm, and double quick time (165 steps per minute) was common.

-- http://www.acws.co.uk/archives/reenact/gilhams.htm

13.—The length of the common step is 2 feet 4 inches, measured from heel to heel its quickness is at the rate of 90 per minute.

33.—The length of the quick step is the same as that of the common step, and its quickness is at the rate of 110 per minute.

DOUBLE QUICK STEP. 

27.—The squad marching in common or quick time, to change to double quick time, the instructor commands: 

1. Double quick.   2. MARCH. At the command MARCH, the men increase the length of step to 33 inches, and its rapidity to 166 steps in a minute. In this march the carriage of the body is different, being nearer that of running The body is more advanced, the knees more bent, the arms with their natural motion.

-- http://www.usregulars.com/Cooke_files/cooke_04.htm

This then, was Hardee's "Tactics:" a modernization of American infantry drill at the company and battalion level, aimed at incorporating several important features of light infantry tactics into the normal field functioning of infantry. The most important tactical improvements, which took into account the long-range capabilities of the rifle, were an increased tempo where quick time (110 steps per minute) was the norm, and double quick time (165 steps per minute) was common, along with simplified instructions to deploy a column into line at the double quick, without first halting. To be sure, many of these innovations could be found in other manuals of the 1850s, but Hardee's became the official manual for the U.S. Army. (See note 5)

-- http://216.247.222.222/vpp/ccg/manualarms_1.htm