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. 9
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 Ã 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. 10
Form drag occurs because
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. 9
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 Ã 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. 10
Form drag occurs because
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