Quan Tao: Balancing the Forces

King Wu asked Tai Gong:
"How many infantrymen can one chariot withstand in battle? How many infantry are needed to counter one chariot? When cavalry confront infantry, how many foot soldiers can one horseman defeat? How many infantry can resist one cavalryman? And when chariots face cavalry, how many horsemen can one chariot overpower? How many cavalry are needed to neutralize one chariot?"

Tai Gong replied:
"Chariots are the army's wings—their crushing force breaks enemy lines and cuts off retreats. Cavalry are the army's eyes—they scout, pursue fleeing foes, and raid supply lines. Yet if deployed poorly, one cavalryman may not equal a single infantryman.

Ratios of Force Effectiveness:

• On Flat Terrain:

  1. Chariot vs. Infantry: 1 chariot = 80 infantry | 80 infantry = 1 chariot.

  2. Cavalry vs. Infantry: 1 cavalry = 8 infantry | 8 infantry = 1 cavalry.

  3. Chariot vs. Cavalry: 1 chariot = 10 cavalry | 10 cavalry = 1 chariot.

• In Rugged Terrain:

  1. Chariot vs. Infantry: 1 chariot = 40 infantry | 40 infantry = 1 chariot.

  2. Cavalry vs. Infantry: 1 cavalry = 4 infantry | 4 infantry = 1 cavalry.

  3. Chariot vs. Cavalry: 1 chariot = 6 cavalry | 6 cavalry = 1 chariot.

In broad terms:

• 10 chariots can rout 1,000 enemies; 100 chariots crush 10,000.

• 10 cavalry can scatter 100 foes; 100 cavalry overwhelm 1,000."

King Wu asked:
"How should chariot and cavalry officers be organized, and what are their tactical formations?"

Tai Gong answered:
Chariot Units:

• Command Structure:
  5 chariots → 1 captain (长)
  10 chariots → 1 lieutenant (吏)
  50 chariots → 1 commander (卒)
  100 chariots → 1 general (将).

• Flat Terrain Formation:
  5 chariots per column.
  Column spacing: 40 paces front/rear, 10 paces left/right.
  Unit intervals: 60 paces between columns.

• Rugged Terrain Formation:
  Advance along paths.
  10 chariots → 1 cluster (聚); 20 chariots → 1 block (屯).
  Spacing: 20 paces front/rear, 6 paces left/right.
  Unit intervals: 36 paces.
  Activity radius: 2 li (≈1 km) in all directions.

Cavalry Units:

• Command Structure:
  5 cavalry → 1 captain
  10 cavalry → 1 lieutenant
  100 cavalry → 1 commander (率)
  200 cavalry → 1 general.

• Flat Terrain Formation:
  5 riders per column.
  Column spacing: 20 paces front/rear, 4 paces left/right.
  Unit intervals: 50 paces.

• Rugged Terrain Formation:
  Column spacing: 10 paces front/rear, 2 paces left/right.
  Unit intervals: 25 paces.
  30 cavalry → 1 cluster (屯); 60 cavalry → 1 wing (辈).
  Activity radius: 100 paces in all directions."

King Wu exclaimed:
"Superb!"