The Physics of War (7 page)

The English were beginning to weaken and break ranks behind the wall of shields. So William ordered another attack, and this time the Normans broke through and finished off Harold. Without a leader, many of the English began to desert and flee. Soon the fight was over and the English had a new king; William was crowned on Christmas day, 1066, at Westminster Abbey.

The main thing the battle demonstrated was the effectiveness of archers—the Norman army had taken the field with about eight thousand.

Disagreements between the English and the French continued for years. One of the major problems was that William, now the king of England, also remained duke of Normandy. Thus, English kings owed homage to the king of France. But in 1337 Edward III of England refused to pay homage to Philip VI of France, and this led to a series of wars that lasted for over one hundred years (from 1337 to 1453). Known as the Hundred Years' War, this period yielded one of the greatest advances in weaponry. It first appeared in the Battle of Crécy in 1346, and it was called the longbow.

The English army was led by Edward III, and the French army was led by Philip VI. The French army was about twice the size of the English army, which consisted of about 5,000 foot archers, 3,250 mounted archers, and 3,500 other troops. The French had about 6,000 crossbow men as well as a large infantry. The battle took place near the forest of Crécy.
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Philip placed his crossbow men in the front line, with the cavalry behind. Strangely, they left their wooden shields (their only defense) in carts at the rear of the formation. The battle began with a series of volleys from the French crossbow men, which proved to inflict little damage. The English had a new longbow, and while the crossbow men could only shoot at the rate of one to two shots per minute, the longbow men could fire five or six shots in the same time.
Furthermore, the longbows had a much greater range and a deadly penetrating power. To make things worse, the crossbow's strings had been weakened by a rainstorm just before the battle. The longbow men had unstrung their bows and protected them.

A longbow of the type used at Agincourt.

The hail of crossbow darts fell short, but the barrage of English arrows that followed didn't, and it was effective. The barrage continued, and, as a result, the crossbow men couldn't get close enough for their bows to be effective. Seeing their situation, many of the crossbow men began retreating through the lines of French knights behind them. Angered by the retreat, the knights began hacking at their own men, killing many of them. Then they decided it was time to charge. They forced their horses forward over the retreating crossbow men, trampling many of them. The English bowmen continued firing at the knights, and to the surprise of the French, many of the arrows penetrated their armor. As a result, many of them began to fall, and as more and more fell, they began blocking the men behind, and bodies began falling upon bodies.

When the battle was over the French had suffered tremendous casualties. According to one estimate, four thousand French knights were killed and as many as two thousand French archers. The English, on the other hand, suffered few casualties—most estimates were under three hundred. The decisive factor was the new longbow, and it would continue to play an important role for another hundred years or more.

The longbow was also decisive in the Battle of Agincourt in October 1415. By this time it had become even more effective. Again the English and the French were involved; this time the English army of about six thousand men was led by Henry V, and the French army numbered twenty-five thousand or more. The battle was fought on a narrow strip of open land near Agincourt.
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With a four or five to one advantage, the French were likely overconfident. They had eight thousand heavily armed men, but they would only be effective in hand-to-hand battle, so they had to get close. Furthermore, between the two armies was a recently plowed field, and it had rained heavily during the previous days. So it was muddy, much to the detriment of the French, many of whom were heavily armored. But on the English side, many of the troops were sick and exhausted from days of marching.

The English archers drove long, sharp stakes into the ground at an angle pointed toward the French line. This helped protect them from cavalry charges by the French knights. The French formed up in three lines, with the men-at-arms in the front and the archers and the crossbowman behind. The French were expecting the English to launch a frontal attack, but they didn't. Instead, the English longbow men opened up with a barrage of arrows. The well-trained longbow men could now fire up to fifteen arrows a minute, so within seconds there were thousands of arrows in the air. Furthermore, to the surprise of the French, the arrows easily penetrated their armor. Many of the arrows struck the horses on their backs and flanks, causing them to panic; as a result, wounded and panicked horses galloped through the advancing infantry, trampling them.
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The French men-at-arms tried to protect themselves as they moved forward. Because their helmets were the weakest part of their armor, most of them lowered their heads to avoid getting shot in the eye or through the breathing holes in the helmet. This restricted their vision. Along with this, they had to walk through knee-deep mud in places, and also over and around fallen comrades. And the barrage of arrows seemed to be unending. Soon the French ground troops were exhausted and disheartened; furthermore, they couldn't get close enough for hand-to-hand fighting.

To make things worse, the second and third line of French warriors didn't know what was happening up front, and they continued to forge forward, and soon they suffered the same fate. The battle lasted three hours, and in the end four thousand to ten thousand French were dead (according to various estimates), with English casualties as low as a few hundred. Many of the elite, including dukes, constables, royals, and so on, were killed. And again, it was the English longbow that was the decisive factor.

ORIGIN AND PHYSICS OF THE LONGBOW

The longbow was developed in several countries independently. In Great Britain it was first developed by the Welsh. And there's no doubt that they made
significant advances in its construction, not from understanding any of the science behind it, but mostly from trial and error.
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The English felt the effects of the Welsh longbow early on. It was used against them, mostly in ambushes and skirmishes at first, but eventually in larger battles, such as one in 1402 where the Welsh used it quite effectively against the English. This, of course, caused considerable concern for the English, and it also piqued their curiosity. They soon incorporated Welsh archers into their own army and learned their techniques.

The first English longbows were made of a single piece of wood—usually yew because it was particularly springy and sturdy. The major problem was that yew was not a common tree and was relatively rare in England. Because of this, they were sometimes made of elm or ash.

Staves were selected with great care and went through a relatively long production process. Oil and wax were applied to the stave to make it waterproof and help preserve it. It had to be relatively thin, and the length would be customized to the archer. The longest measured about six feet four inches, with shorter ones somewhat over five feet. Since there was a direct correlation between the bow length and the power it could generate, the longer the bow, the better. It was usually about two inches across at its thickest part. The force required to pull a longbow back to its maximum extension ranged from about eighty to one hundred twenty pounds. The draw length was from twenty-nine to thirty-two inches, and it was soon determined that it worked best when the bow was drawn back to the eye.

Arrows were made of a variety of woods. Aspen, poplar, elder, willow, and birch were all used, with the average length of an arrow being about three feet. It was determined early on that feathers along the side helped to stabilize the arrows in flight, and the feathers were usually seven to nine inches long, and glued to the shaft. The bowstring was usually made from hemp, but later on flax and silk were used.

One of the major problems with the longbow was the training required to master it. Because of the tremendous force required to pull it back, considerable practice was required to use it effectively, particularly in battle. As a result, English boys usually began their training by about age seven. They were trained extensively, and tournaments were held in all villages, with the best archers being selected for the military. And it was a great privilege to serve as a military archer, as the archers were considered to be members of an elite group.

The average trained English archer could fire at least twelve arrows a minute and hit targets at two hundred yards. Indeed, if you could fire at a rate of only ten arrows a minute you were considered a poor archer.

We looked at the physics of the bow and arrow briefly earlier, and much of what we said also applies to the longbow. We'll consider it in more detail, however. The physics involves both the mechanics of the bow and the flight of the arrow. As we saw, when the archer pulls back the bow he does work that is stored as potential energy. When the string is released this potential energy is converted to the kinetic energy of the arrow. Actually, some of the potential energy goes into the final motion of the bow (a slight vibration), but it is usually a small portion. It is important to note that the farther the string is pulled back for a given bow, the greater the potential energy. This is why the longbow was able to impart more kinetic energy to the arrow. It is longer and can therefore be drawn back farther.
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The range, or distance, the arrow travels, depends on the following things:

• Initial velocity
  
• Weight of the arrow
  
• Angle at which the arrow is shot
  
• Air resistance
  
• Effect of the wind
  

The arrow's initial velocity can be determined by equating the potential energy (F × d) of the bow (with the string pulled back) to the kinetic energy of the arrow (1/2 mv
²
, where m is the mass of the arrow). The angle at which the bow is pointed has a strong bearing on its flight path, or trajectory, and how far it will go. It's relatively easy to show that the greatest range is obtained an angle of forty-five degrees if air resistance and wind are not taken into consideration. But as we will see later, these variables are also important, and they do limit the range.

The path of the arrow is a parabola. This is the curve seen in the headlight of a car. But because of air resistance, it can be a slightly distorted parabola. Air resistance creates a force on the arrow that slows it down; this is the result of a transfer of some of the momentum of the arrow to the air. There are two types of drag on the arrow: sheer drag and form drag. Sheer drag occurs because the arrow drags the air adjacent to it along with it as it moves. Indeed, if you could closely examine the arrow in flight, you would see that there is a series of layers of air around it, with the layer closest to the arrow being dragged the most, the second layer being dragged to a lesser degree, and so on. Sheer drag is proportional to the velocity of the air moving past the arrow.
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Form drag occurs because sheer drag causes eddy currents behind it. These eddy currents form a turbulent wash behind the arrow in the same way that a speedboat creates a wash when it moves through water at high speed. And the
faster the arrow goes, the greater the turbulence and the greater the form drag. Mathematically, form drag is proportional to the square of the velocity (v
²
). It acts in a perpendicular direction, pushing the arrow to the side and creating frequency oscillations during its flight.

Furthermore, when an arrow is released, it creates a perpendicular kinetic energy. For a right-handed archer, when the arrow is released the string moves slightly to the left, causing the arrow to bend to the right. Then the string moves back to the right, causing the arrow to move left. All this happens in the brief time that the arrow is still attached to the string. But when the arrow leaves the bow, this slight right-left vibration continues through the flight. If the archer is left-handed, the vibration is opposite.

The amount of vibration depends on the stiffness of the arrow. If it is quite flexible it will vibrate excessively, which in turn will cut down on its speed and therefore its penetrating power. If it is too stiff, on the other hand, the arrow will not vibrate, and this affects its accuracy. So compromise is therefore needed.

The effective range of the longbow in the hands of early archers was generally about two hundred yards, and at that distance it could easily penetrate the chain mail armor used by most knights. Eventually, steel plates were placed over the chain for greater protection. But the longbow arrows could penetrate even the steel plates if the range was less than one hundred yards. The maximum range of the longbow was about four hundred yards. At the beginning of a battle, archers would usually shoot large numbers of arrows high in the air so that charging knights would encounter thousands of arrows falling from the sky. Later, as the charging knights got closer, the archers would select individual targets.