How Compound Bows Work

It’s no longer enough to aim a bow towards the sky and fire an arrow into the distance. Thanks to compound bow technology, you can now direct your arrow at your target and really strike it. Let’s have a look at how they operate.

The purpose of every bow is to take the work—or energy—that an archer put into it and transmit it to the arrow. The energy you expend when you pull back the bow is stored in the bent limbs. When you let go of the bowstring, the limbs return to a neutral position, exchanging potential energy for kinetic energy that is used to propel the arrow.

There are losses in all mechanical systems: the amount of energy exerted on the arrow is less than the amount of energy applied to the bow by the archer. The purpose of bow design is to reduce these losses as much as possible. The more energy you put into the arrow, the quicker it will go, and the faster it travels, the flatter its arc will become. A flatter arc also ensures more precision.

Mathews Archery’s bows, according to Jeff Ozanne, are 87 to 89 percent efficient in transferring the archer’s input energy to the arrow. That’s surprising since the current vehicle, for example, only converts combustion into motive power at a 25 to 35 percent efficiency.

Distance x Force

Work (energy) is a function of force times distance, as you learnt in high school. In a draw-force curve, that’s what you’re looking at. The horizontal x-axis represents the length of a bow, while the vertical y-axis represents the weight necessary to pull the bow to that length. The area under the curve represents the total amount of labour (or potential energy) you put into a bow (shaded blue).

Let’s start with a standard longbow’s draw-force curve. The distance you draw them back and the effort you put in to do so have a linear connection. It’s worth noting that the amount of energy needed to hold a drawn longbow is proportional to how far it’s pulled back. We will explain.

Compound Bows: How Do They Shoot Faster?

A longbow’s arrows move at a speed of less than 200 feet per second. The fastest compound bows on the market today can shoot arrows at speeds of up to 370 feet per second. What are their methods for doing this? In a nutshell, with increased efficiency.

A compound bow’s draw cycle is not linear: when you pull the string back, the effort needed peaks halfway through and then drops down at the conclusion. This means the archer only has to carry a portion of the bow’s peak weight at full draw, which means she’ll be less stressed as she prepares to release the arrow, giving her more time to aim and a steadier shot.

A compound bow functions in the same way as a simple block and tackle does, multiplying input energy across a longer distance. Let’s take a look at how that block and tackle works first. At the axle, two pulleys are linked so that as one moves, the other moves as well. When you pull down on the huge pulley, the inner pulley moves with the same amount of energy as the large pulley, but it pulls the rope a shorter distance. Because energy equals force multiplied by distance, moving anything a shorter distance for the same amount of energy requires greater force.

Why Are Compound Bows Easier to Use?

Compound bows employ noncircular wheels, or cams, to create variable draw weight. As the archer completes the draw cycle, the force needed of the archer changes.

Two distinct draw-force curves for two different compound bows are shown here. Both have the same peak draw weight, but the blue one achieves its peak necessary effort faster, maintains it for longer, and has less let-off at the end. It would be more difficult to draw and hold than the friendly cycle of the green bow.

Remember that the area under the curve represents the amount of energy stored in the flexed limbs, and we can see that the more aggressive blue bow has more potential energy than the more friendly green bow. This is why compound bows with similar draw weights may shoot arrows at varying speeds.

“Some draw-force profiles are meant to conserve as much energy as possible, while others are designed to enhance comfort,” Ozanne explains. He goes on to say that the purpose of the bows he builds for Mathews is to achieve the ideal middle ground—speed and comfort.

However, no composite bow is completely efficient. A composite bow’s let-down stroke (which propels the arrow) differs from the draw curve. We can see that some energy is wasted due to friction and noise in the diagram above. As a consequence, the arrow receives less energy than the archer’s potential energy stored in the flexed limbs of the bow.

The Effects of Cams on the Draw Cycle

On a compound bow, at least the outside cam has an oval form, and the bow designers often make the inner cam oval as well. At every point during the draw cycle, the ratio between the two radii is measured where the cable and string make contact with the cams (shown here with white arrows). Designers may change the gear ratio by adjusting the radii.

When you initially draw the bow and the cam starts spinning, the outer cam radius is rather tiny, which makes it the most difficult to draw and needs the greatest effort. This is because, as a human, you can draw more weight with an extended arm than with one that is retracted. At full draw, an archer’s pulling arm is entirely retracted.

The radius of the outer cam is substantially bigger than the radius of the inner cam, resulting in a high gear ratio. The cam’s gear ratio boosts the amount your force is multiplied at the conclusion of the draw cycle, making it more than the energy stored in the limbs. This is what allows you to breathe easier.

Compound bows feature a “back wall” at full draw that prevents the bow from being pulled any farther. A mechanical stop or a severe dip in the cams’ draw-force curve that surpasses the amount of force you can apply, stopping you from drawing the string any farther, may be used to accomplish this.

Putting Everything Together

You can see the confluence of all of these forces in the field. You’ll immediately feel the full weight of the bow you’ve chosen if you clip your release on the D-loop, press on the riser with one hand, and draw the string back with the other. The cams quadruple our input energy, storing more potential energy in the flexed limbs than we’re expending, even though we’re drawing 70 pounds on our bows.

When your draw reaches its maximum length, the weight will abruptly release, enabling you to stably hold the bow while waiting for a target to appear. For example, the Mathews Halon 5 that I shoot has a 75 percent let-off. So, although I need to pull 70 pounds at first, I’m only holding approximately 18 pounds by the time the rope reaches my ear.

When you let go of the string, the limbs spring forward, dragging the string ahead and propelling the arrow onward. Because noise equals lost energy, this occurs in near quiet. The Halon launches its arrows in a fairly flat arc at 353 feet per second, maximizing the relative precision of our shots.

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