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The limbs of a compound bow are much stiffer than those of a recurve bow or longbow. This limb stiffness makes the compound bow more energy-efficient than other bows, in conjunction with the pulley/cams. The compound bow has its string applied to pulleys (cams), and one or both of the pulleys have one or more cables attached to the opposite limb. When the string is drawn back, the string causes the pulleys to turn. When the draw commences, the archer has reduced mechanical advantage, but during the draw, as the pulley cams rotate, the (limb plus cam radius) distance gets longer, and the archer gains mechanical advantage over the bending limbs, and less force is needed to bend the limbs more, in comparison to other bows.
The use of this levering system gives the compound bow a characteristic draw-force curve which rises to a peak weight and then "lets off" to a lower holding weight, allowing the shooter to hold the string at full draw for much longer when compared to recurve bows. This is because recurves don't "let off", meaning that the full weight (force) of the draw is in your hand. A compound bow moves a lot of the weight away from the draw string (hand), allowing for longer, more accurate and far less strenuous aiming, especially when shooting several times in a row.
The compound bow is little affected by changes in temperature and humidity and this gives it superior accuracy, velocity, and distance compared to other bows. The compound bow was first developed in 1966 by Holless Wilbur Allen in Missouri, and a US patent was granted in 1969. The compound bow has become increasingly popular. In the United States, the compound is the dominant form of bow.
A bow's central mount for other components such as the limbs, sights, stabilizers and quivers is called the riser. Risers are designed to be as rigid as possible. The central riser of a compound bow is usually made of aluminium, magnesium alloy, or carbon fiber and many are made of the aircraft-grade 7075 aluminium alloy.
Limbs are made of composite materials and are capable of taking high tensile and compressive forces. The limbs store all the energy of the bow – no energy is stored in the pulleys and cables. A draw weight generally falls between 10 and 100 pounds enabling arrow speeds of 150 to 370 feet per second (46 to 113 m/s)
In the most common configuration, there is a cam or wheel at the end of each limb. The shape of the cam may vary somewhat between different bow designs. There are several different concepts of using the cams to store energy in the limbs, and these all fall under a category called bow eccentrics. The four most common types of bow eccentrics are Single Cam, Hybrid Cam, Dual Cam and Binary Cam. However, there are also other less common designs, like the Quad Cam and Hinged. The "let off" is a term that describes what happens as the cam rolls all the way over. This can be seen in the close-up picture. As the bow is drawn, the draw weight increases to a peak and then "lets off" a certain percentage of the peak draw weight before a stop (known as "the wall") prevents the bow from being drawn further. The let-off is commonly between 65% and 80% of the peak weight for recently designed compound bows, although some older compound bows provided a let-off of only 50% and some of the most recent designs achieve let offs in excess of 90%.
The photo on the right shows the axle attaching the limb to cam is mounted at the edge of the cam as opposed to the center. As the string is drawn the cam turns and imparts force to compress the limb. Initially, the archer has the 'short' side of the cam, with the leverage being a mechanical disadvantage. High energy input is therefore required. When near full draw is reached, the cam has turned to its full extent, the archer has gained mechanical advantage, and the least amount of force needs to be applied to the string to keep the limbs bent. This is known as "let off". The lower holding weight enables the archer to maintain the bow fully drawn and take more time to aim. This let-off enables the archer to accurately shoot a compound bow with a much higher peak draw weight than other bows (see below).
However, there are quite a few youth-oriented compound bows with low draw weights that feature no let-off and have a maximum draw length deliberately set farther than the majority of young shooters would reach. This effectively makes the bow function very similar to a recurve, with the draw length determined by the shooter's preferred anchor point. This feature removes the necessity to adjust the bow draw length or use a different bow for different shooters (or to change bows as the shooter gets older). This type of bow is required for use in the U.S. National Archery in the Schools Program.
At the other extreme, one manufacturer, Concept Archery, is known for producing a compound bow with 99% let-off. Although it is quite unsafe to do so, such a bow can be drawn and pointed at the ground, and the mere weight of the bow will keep it drawn even if the grip is released and the bow is hung by the string (although extreme caution must be exercised when the bow is drawn to avoid accidentally disturbing the bow out of the let-off zone without first establishing a firm grip on the string and the foregrip).
Compound bow strings and cables are normally made of high-modulus polyethylene and are designed to have great tensile strength and minimal stretchability, so that the bow transfers its energy to the arrow as efficiently and durably as possible. In earlier models of compound bows, the cables were often made of plastic-coated steel.
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AMO standard draw length is the distance from the string at full draw to the lowest point on the grip plus 1.75 inches / 4.45 cm. Because the draw force may increase more or less rapidly, and again drop off more or less rapidly when approaching peak draw, bows of the same peak draw force can store different amounts of energy. Norbert Mullaney has defined the ratio of stored energy to peak draw force (S.E./P.D.F.). This is usually around one foot-pound-force per pound / 3 joules per kilogram but can reach 1.4 ft·lbf/lbf / 4.2 J/kgf.
Efficiency of the bows also varies. Normally between 70-85% of the stored energy is transferred to the arrow. This stored energy is referred to as potential energy. When transferred to the arrow it is referred to as kinetic energy. The product of S.E./P.D.F. and efficiency can be called power factor. There are two measurement standards of this quantity, AMO and IBO speed. AMO is defined as the initial velocity of a 35 g / 540 grain arrow when shot from a bow with a peak draw weight of 270 N / 60 lbf and draw length 76 cm / 30 inches. IBO speed is defined as the initial velocity of a 22.7 g / 350 grain arrow shot from a bow with a peak draw weight of 300 N / 70 lbf and a draw length of 76 cm / 30 inches.
Brace height is the distance from the pivot point of the grip to the string at rest. Typically a shorter brace height will result in an increased power stroke, but comes at the price of a bow that's less forgiving to shooter error and having harsher string slap.
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Arrows used with compound bows do not differ significantly from arrows used with recurve bows, being typically either aluminium alloy, carbon fiber, or often a composite of the two materials. The only notable difference is that the spine of the arrow, which is a measure of its stiffness, is not as great for a compound bow as it would be for a recurve bow of the same draw weight (power). This is due to the fact that a compound bow will accelerate an arrow more gently and linearly as the cam unwinds so flexing the arrow less, as compared to the explosive acceleration of an arrow from a recurve bow where the full power of the limbs is applied to the arrow as soon as the string is released.
Wooden arrows are not recommended for use with compound bows due to the higher overall forces that are applied to the arrow being more likely to break the arrow, possibly driving parts of the broken arrow shaft into an archer's arm.
Manufacturers produce arrow shafts with different weights (mass), different spines (stiffness), and different lengths in the same model of shaft to accommodate different draw weights and lengths, matched to archers' different styles, preferences and physical attributes.
Arrow stiffness (spine) is an important parameter in finding arrows that will shoot accurately from any particular bow (see Archer's paradox), the spine varying with both the construction and length of the arrow.
Another important consideration is that the IBO (International Bowhunter Organization) recommends at least 5 grains of total arrow weight per pound of draw weight, this means a bow that draws 60 lb would need at least a 300 grain finished-with-tip arrow.