How big was the bow and arrow formation on the ancient Chinese battlefield?

Most of the arrow formations in film and television works have extremely exaggerated effects. The Qin Army's arrow formation in "Heroes" looks very powerful. In fact, when the Qin Army fought the Changping War with Zhao Guo, how many people did the two countries have? One hundred thousand troops fought for more than a month. If the arrow array was really like what the movie says, Zhao's army would have been shot to death. How could they have fought for a month?

The most basic law that must be met as an arrow formation is that the range must exceed the length of the team, otherwise the arrows shot by the people behind will fall on the heads of the people in front. It is assumed that the range of ancient Chinese crossbows can reach the level of the British longbow. (The longbow has a maximum range of about 200 meters. It is the longest range single-person bow that can be verified.) If one person stands at 1.5 meters, the maximum is only 100. The person at the end of the row can shoot to 50 meters in front of the team. In this way, theoretically The arrow array can reach the scale of ten thousand people. In fact, the Chinese bow cannot reach the range of the long bow. The British and French successfully used the long bow in the Hundred Years' War. The most famous battle of Agincourt is that the British army brought 5,000 longbowmen to shoot arrows. After ten shots that consume arm strength, it is difficult to guarantee the shooting range. Taking into account the factor of maintaining physical strength by shooting in turns, the actual number of people shooting at the same time is usually a thousand people divided into multiple small formations and taking turns to attack is far more effective than a single large formation of 10,000 people.