Useful notes and rules of thumb from various ACOUP posts.

New Acquisitions: How Fast Do Armies Move?

ACW brigade of 3,000 men…

  • Road 13ft wide
  • Column is 4,000 ft long
  • 1 mule per 6-8 men
  • 20 wagons per 1,000 men
  • 80 wagons per mile of road
  • Wagon train takes up 4,000 more ft
  • Total length 1.5 miles

Move 8-12 miles per day, rule of thumb. Avg 10 miles per day. Smaller armies are towards top end of this. Large armies low end or lower.

Mongols / horse nomads can manage long-distance horseback riding at 60 miles per day.

Collections: The Battle of Helm’s Deep, Part I: Bargaining for Goods at Helm’s Gate

Theoden manages 100 miles over 2 days in a forced ride with unencumbered cavalry and good roads. Bret notes this as reasonable.

Castles / fortresses with garrisoned cavalry deny enemy columns the opportunity to forage. Foot can only carry 10 days foot on their backs. Thus castles constrain the operational range of enemy armies.

Collections: The Preposterous Logistics of the Loot Train Battle (Game of Thrones, S7E4)

Rome needed to import 80 million kg of wheat per year for 200,000 households.

10 mile long columns are barely manageable. Preferably would be shorter. Needs to be shorter than the daily marching distance of 8-12 miles.

(Note: combining with above of 1.5 miles per 3,000 men, means that armies can operate in columns of 15,000 to 24,000 men max. Probably kept to 10,000 or less)

Wagon Train Rules of thumb:

  • Wagons hold 1,400 lb of food pulled by 2 horses.
  • 1 wagon and 2 horses per 20 soldiers –> means 50 wagons and 100 horses per 1,000 men. Close-ish to 20 per 1,000 above? I think ACW wagons were larger.
  • 3 lb of food per day per man.
  • 10 lb of food per day per horse (if grazing available)
  • 20 lb of food per day per horse (if not)
  • 1 soldier can carry 10 days food (30 lb)
  • 1 wagon needs 1 man (3 lb) and 2 horses (20 lb) to drive. Eat 23lb per day. Can carry 1,400 lb.

Wagons vs men endurance table is thus (in days):

men wagons        
  0 1 10 100 1000
0 0 61 61 61 61
1 10 55 60 61 61
10 10 32 55 60 61
20 10 24 50 60 61
50 10 17 41 58 61
100 10 14 32 55 60
1000 10 10 14 32 55
10000 10 10 10 14 32

Diminishing returns of adding wagons (or, the tyranny of the wagon equation).

Rules of thumb above from ACW and GoT examples give operational endurances of ~20 days (about double that of soldiers without wagon train).

Forage Rules of Thumb:

  • Sweep 5 miles in either direction of route = 80-120 sq mi per day.
  • Collect 10% of food production without triggering starvation (25 kg / 55 lb per farmer).

Those lead to this forage table:

historicity in medieval pop. density (farmers / sq mi) famers stolen from food foraged (lb) army size supported (assume 1 wagon & 2 horses / 20 men)
common 1 100 5500 1375
common 5 500 27500 6875
common 10 1000 55000 13750
common 15 1500 82500 20625
common 20 2000 110000 27500
plausible 30 3000 165000 41250
rare 40 4000 220000 55000
rare 50 5000 275000 68750
rare 60 6000 330000 82500

Collections: Logistics, How Did They Do It, Part II: Foraging

Year’s grain is gathered at harvest time in early summer or late spring. Village of 200 people has around 70,000 man-days of grain on hand.

Cavalry - forage 20 miles wide @ 10 miles / day = 200 sqmi per day

Foot - forage 10 miles wide @ 10 miles / day = 100 sqmi per day

Pre-industrial densities = 5,000 people / 200 sqmi = 25 people / sqmi

5,000 people have 1.35 million man-days of food on hand after harvest. Army of 20,000 soldiers, 4,000 noncombatants, 10,000 animals, needs ~67,500 person-days of food per day (5% of what is available in countryside). This jives with previously mentioned rule of thumb of an army able to deplete 5-15% of a rural countryside’s food via foraging.

By late fall, food available declines by half (so army in previous paragraph needs 10-30% of countryside’s food per day - this is unsustainable and army will starve).

Thus, campaigning season begins in late March or early April. Supplies from friendly territory carry the army until early summer harvest when forage becomes plentiful.

Army must keep moving. Remember, sample army of 20,000 depleted 5% of food in area per day. Will starve quickly if staying put for more than a few days.

Ancient army sizes were around 20,000. 40,000 big, occasional. More than 80,000 is unsustainable.

Collections: Logistics, How Did They Do It, Part III: On the Move

Armies generally had to move over roads. Especially with wagons.

Armies frequently carry 2 weeks supplies (note this lines up with 1 wagon per 50-100 men).

Rules of thumb:

  • army of 20,000 men + 4,000 noncombatants + 10,000 animals
  • needs minimum population density of 10 people per square mile in campaigning season
  • needs minimum population density of 15 people per square mile in fall season
  • needs 20-25 people per square mile to forage enough to winter in the field

Road spacing

  • Road fits 6 men abreast, or 4 horses
  • Infantry cohort of 480 men takes up 110m - 16,800 men takes up 2.4 miles
  • Cavalry squadron of 100 men takes up 75m- 2,400 cavalry takes up 1.1 miles
  • Baggage train - if 5,000 mules and 2,400 horses, takes up 3.1 miles. If 700 wagons, 5.2 miles long.
  • Total length, 6.6 miles with mules, call it 10 miles with wagons.

Marching speed

  • 2.5 to 3.0 miles / hr
  • Intermittent rests result in average speed ot 2.25 - 2.50 miles / hr
  • With rests and start/stop times to account for column length (6.6 mi), march for 6 or 7 hours. With 10 mile column, only get 5-6 hours per day.
  • Means 15.0-17.5 miles / day at 6.6 mile length, 11.1-15.0 miles /day.
  • If hot, slow end of 2.25 - 2.50 miles/hr range.
  • If double army size, double road length to 13.2 miles with mules = 3-4 hours marching time = 6.75-10.0 mi/day.
  • Rest one day per week.

A table to show the above.

Army Size 20,000 20,000 40,000 40,000
Noncombatants 4000 4000 8000 8000
Animals 9800 9800 19600 19600
Logistics 5,000 mules 700 wagons 10,000 mules 1,400 wagons
Soldier column length (mi) 3.5 3.5 7 7
Baggage train length (mi) 3.1 5.2 6.2 10.4
Total length (mi) 6.6 8.7 13.2 17.4
Marching time (hr) 6.5 5.5 3.5 2.75
Miles / day 15.4 13.1 8.3 6.5
Miles / wk 93 78 50 39
Forage area (sqmi / day) 309 261 166 131
Men food needs (lb/day) 72000 72000 144000 144000
Animal food needs (lb/day) 98000 98000 196000 196000
Food Needs (lb/day) 170000 170000 340000 340000
Farmers needed to be stolen from each day 3091 3091 6182 6182
Population density needed to sustain (people/sqmi) in summer 10 12 37 47
…in fall 15 18 56 71
…to winter in the field 20 24 74 95

Solutions to the tyranny of the wagon equation:

  1. Steal more. But this means peasants will flee, and take food with them.
  2. March faster. But this will impact morale and combat effectiveness.
  3. Divide the army. But this poses 2C concerns.
  4. Resupply by water. But this requires a bureaucracy and geography.

Enemy harrassment of foraging cuts foraged area by about half (meaning double the population density is required to feed army).

Conclusion: ancient / pre-modern generals have limited control & choices once battle is joined, but extensive control & choices in the operational landscape.