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According to what I've read, during the Warring States period and also later during the Three Kingdoms period there were armies of the magnitude of (a few) hundred thousands.
How could they coordinate such an immense mass of people? How could they provide the logistics? These armies had to be separated into smaller armies I suppose. Then how could the different battalions work together despite the distance?
In Ancient China, the primary method of coordinating units were to use flags, drums and gongs. Beating drums was a signal to advance, whereas ringing gongs was an order to retreat. The use of flags instructed units on the battlefield to move in specific directions.
《吳子‧應變》 凡戰之法，晝以旌旗旛麾為節，夜以金鼓笳笛為節。麾左而左，麾右而右。鼓之則進，金之則止。
(Wuzi, chapter "Reaction") The method of war is always to command with flags during day, and with gongs and drums at night. Move left when the flag points left, and right when the flag points right. Advance at the sound of drums, and stop at the sound of gongs.
Such commands could be issued and carried out because these armies were not masses of random strangers thrown together. In fact, Chinese armies possessed a full hierarchy of units during the Warring States period. Generally speaking, an army had a fighting strength of 12,500, evenly divided into five divisions of 2,500 each. Each division in turn consisted of five 500-strong brigades. Below the brigade level, there were smaller units of 100, 50, 25 and 5 men.
In a battle, therefore, more specific orders or intel could passed down through the ranks via the chain of command, usually by dedicated messengers. This complements the use of flags, drums and gongs for broad coordination to realise effective command in a battle.
Logistics were primarily reliant on having stockpiles of supplies. Ancient Chinese states were agrarian societies, and governments taxed their peasants in kind. Surplus rice would thus be stockpiled for military use. Consequently, these states generally did their best to improve agricultural productivity, and reforms were major factors in improving a state's military performance.
When war breaks out, although an army would march into the field with whatever supplies it could carry, this would have been only good for a few days.
《荀子‧議兵》 魏氏之武卒，以度取之，衣三屬之甲，操十二石之弩，負服矢五十個，置戈其上，冠冑帶劍，贏三日之糧，日中而趨百里
(Xunzi or Hsun-tzu, chapter "On War") The elite soldiers of Wei wear three layers; wield crossbows of 12 stones with 50 arrows; are equipped with halberds and swords; and they can carry three days supply of food.
Thus, the primary means of keeping an army fed were supply trains. Every war involved numerous wagons responsible for replenishing an army in the field with supplies from the state's central stockpiles.
《孫子兵法‧作戰》 凡用兵之法，馳車千駟，革車千乘，帶甲十萬，千里饋糧
(The Art of War, chapter "Waging War") Wars are fought with a thousand chariots, a thousand supply wagons, a hundred thousand soldiers, and food is delivered across a thousand miles.
Occasionally armies would harvest the farmlands of their enemies as well as forage, but for the larger armies of the late Warring States era, supply wagons were a necessity.
There were no armies several hundred thousand strong during the Three Kingdoms period. However, the largest engagement of the era, the Battle of Red Cliff, did involve over 200,000 troops under Cao Cao (Tsao Tsao). In that example, his forces were divided into two main prongs as well as six smaller groups, which were either held in reserve or advancing towards other targets. Within each army, individual generals commanded smaller units of perhaps 5,000 soldiers each.
Therefore, not all 200,000+ soldiers were physically present at Wulin, where the famous burning of the ships took place. Note that some have argued that Cao Cao's forces totaled ~220,000 overall, i.e. some were left in the north to guard his homeland. In this interpretation, perhaps no more than 100,000 actually took part in the battle.
Those are a lot of questions! Referenced quotes at the bottom.
How could they coordinate such an immense mass of people?
Divide up the command.
How could they provide the logistics?
They brought everything with them and hoped either to resupply from the enemy or not at all (win quickly).
These armies had to be separated into smaller armies I suppose.
Could not find any such evidence for supply reasons (tactics is another but very risky one).
Then how could the different battalions work together despite the distance?
Distance was the battlefield only, and signals and signs were used.
The Art of War by Sun Tzu states: (http://www.gutenberg.org/files/132/132.txt)
1 Sun Tzu said: The control of a large force is the same principle as the control of a few men: it is merely a question of dividing up their numbers.
That is, cutting up the army into regiments, companies, etc., with subordinate officers in command of each. Tu Mu reminds us of Han Hsin's famous reply to the first Han Emperor, who once said to him: "How large an army do you think I could lead?" "Not more than 100,000 men, your Majesty." "And you?" asked the Emperor. "Oh!" he answered, "the more the better."]
2 Fighting with a large army under your command is nowise different from fighting with a small one: it is merely a question of instituting signs and signals.
23 The Book of Army Management says: On the field of battle, the spoken word does not carry far enough: hence the institution of gongs and drums. Nor can ordinary objects be seen clearly enough: hence the institution of banners and flags.
26 In night-fighting, then, make much use of signal-fires and drums, and in fighting by day, of flags and banners, as a means of influencing the ears and eyes of your army.
1 Sun Tzu said: In the operations of war, where there are in the field a thousand swift chariots, as many heavy chariots, and a hundred thousand mail-clad soldiers, with provisions enough to carry them a thousand LI,the expenditure at home and at the front, including entertainment of guests, small items such as glue and paint, and sums spent on chariots and armor, will reach the total of a thousand ounces of silver per day. Such is the cost of raising an army of 100,000 men.
