Indefinitely Wild

How Compound Bows Work

An aerospace engineer explains the mechanics behind higher arrow speeds, improved accuracy, and easier shooting

Archers compete in the CenterShot National Championship in Louisville, Kentucky. The contest is open to shooters from third grade and up. The sport is experiencing a boom in popularity, particularly among young women. Thank Katniss Everdeen for that. (Mathews Archery)

Firing a bow is no longer a case of pointing it into the sky and lobbing an arrow into the distance. Now you can point your arrow at your target and actually hit it, thanks to the technology behind compound bows. Let’s break down how they work.

The goal of any type of bow is to take the force an archer puts into it and transfer that work—or energy—to the arrow. As you draw the bow back, the energy you exert is stored in the bent limbs. When you release the bowstring, the limbs spring back to their neutral state, exchanging their potential energy for kinetic energy that’s applied to the arrow.

As with all mechanical systems, there are losses: the amount of energy exerted on the arrow is less than the amount of energy the archer applies to the bow. The goal of bow design is to minimize these losses. The more energy applied to the arrow, the faster it will go, and the faster it goes, the flatter its arc. And a flatter arc means better accuracy.

Jeff Ozanne, a bow designer for Mathews Archery, tells us his bows are 87 to 89 percent efficient at transferring the archer’s input energy to the arrow. That’s remarkable—the modern automobile, for instance, is only 25 to 35 percent efficient at turning combustion into motive force.

Force x Distance

Back in high school, you learned that work (energy) is a function of force times distance. That’s what you’re looking at in a draw-force curve. The horizontal x-axis is the distance a bow is drawn, while the vertical y-axis is the weight required to draw the bow to the corresponding distance. The cumulative work (or potential energy) that you put into a bow is the area under the curve (shaded blue).

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Traditional bow draw-force curve. (Corey Hass)

Let’s first look at the draw-force curve of a traditional longbow. These have a linear relationship between the distance you pull them back and the effort you apply to do so. It’s important to note that the energy required to hold a drawn longbow directly corresponds to how far it’s drawn back. We explain.

How Compound Bows Shoot Faster

Arrows fired by a longbow typically travel at less than 200 feet per second. Today’s fastest production compound bows propel arrows at up to 370 feet per second. How do they do that? In short, with better efficiencies.

The draw cycle of a compound bow is not linear: as you pull the string back, the effort required peaks part of the way along, and then lets off at the end. This means the archer is left holding a fraction of the bow’s peak weight at full draw, leaving her less strained as she prepares to release the arrow—allowing more time to aim and facilitating a more stable shot.

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With a simple block and tackle, a user applies force to the outer wheel, which moves over a longer distance than the inner wheel, multiplying the force of that inner wheel. (Corey Hass)

A compound bow works like a simple block and tackle, multiplying input energy over distance. To get started, let’s look at how that block and tackle works. Two pulleys are connected at the axle so that when one moves, the other moves with it. If you pull down on the large pulley, the inner pulley moves with equal energy but pulls its rope a shorter distance. Because energy equals force times distance, moving something a shorter distance for the same energy means more force is applied.

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A compound bow looks a lot like a paired block and tackle. When the archer pulls on the string, it rotates the wheels, causing the two to be drawn closer together. Drawing on the larger wheels multiplies the force applied by the smaller ones. (Corey Hass)

Now, let’s double this setup, connecting the two ropes that pass around the larger radii as a single string and replacing the ropes that go around the smaller radii with cables. The result looks like a compound bow with cams on both ends, right?

Each cable attached to the inner wheels is directly connected to the center of the opposite wheel. The bowstring connects the two outside wheels. As you pull back on the bowstring, both outer wheels rotate, multiplying the force applied to the cables on the inner wheels. Because that cable pulls on the the axis of both wheels, they are drawn together with more force than the archer applies to the string. This is what bends the bow limbs.

In short, working like a block and tackle enables a compound bow to multiply an archer’s input force, storing more potential energy in the flexed limbs than would be possible with a traditional bow of equivalent draw weight.

But this doesn’t explain how compounds achieve that let-off at the end of their draw cycle. Stay with us.

Why Compound Bows Are Easier to Shoot

To achieve a variable draw weight, compound bows use noncircular wheels, or cams, that change the force required of the archer as they complete the draw cycle.

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Draw-force curves for two fictional compound bows. The blue curve is an aggressive bow, while the green is friendlier to shoot. (Corey Hass)

Here are two different draw-force curves for two different compound bows. As you see, both have the same peak draw weight, but the blue one reaches its peak required effort much quicker, holds it there for longer, and has less let-off at the end. It’d be more difficult to pull and more difficult to hold than the green bow’s friendlier cycle.

Remember that the area under the curve corresponds to the amount of energy stored in the flexed limbs, and we can clearly see that the more-aggressive blue bow holds more potential energy than the friendlier green one. This is why compound bows of equivalent draw weights may achieve different arrow speeds.

“Some draw-force profiles are designed to store the maximum amount of energy, where others are designed to maximize comfort,” says Ozanne. He goes on to explain that achieving the perfect middle ground—speed and comfort—is the goal of the bows he designs for Mathews.

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A fictional compound bow's draw cycle (gray) versus its let-down cycle (blue). (Corey Hass)

But no compound bow is 100 percent efficient. The let-down stroke (which drives the arrow) of a compound bow is different than the draw curve. Above, we can see that some energy is lost to friction and noise. As a result, the amount of energy imparted on the arrow is less than the potential energy stored by the archer in a bow’s flexed limbs.

How Cams Alter the Draw Cycle

Typically, at least the outer cam on a compound bow has an oval shape, and very often, the bow designers make this inner cam oval. The ratio between the two radii is measured where the cable and string are making contact with the cams at any point in the draw cycle (shown here with white arrows). By changing the radii, designers can alter the gear ratio.

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A compound bow cam at rest, providing a low gear ratio. (Corey Hass)

As you first draw the bow and the cam begins rotating, the outer cam radius starts out relatively small, which is when it is hardest to draw and requires you to exert the most energy. This is because you, as a human, are capable of pulling more weight with an extended arm than a retracted one. An archer at full draw is fully retracting his pulling arm.

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A compound bow cam at full draw, providing a high gear ratio. (Corey Hass)

Above, you can see that the radius of the outside cam is much larger than the inner cam, providing a high gear ratio. At the end of the draw cycle, the cam’s gear ratio maximizes the amount your force is multiplied, making it so great that it’s more than the energy stored in the limbs. This is what provides the let-off.

At full draw, compound bows have a “back wall” that stops the bow from being drawn farther. This can be achieved either through a mechanical stop or a sharp valley in the cams’ draw-force curve that exceeds the amount of force you’re able to apply, preventing you from pulling the string any farther.

Putting It All Together

In the field, you witness the culmination of all these factors. Clip your release on the D-loop, push against the riser with one hand, and pull the string back with the other, and you’ll initially feel the full weight of the bow you’ve selected. Even though we’re pulling 70 pounds on our bows, the cams are multiplying our input energy, thereby storing more potential energy in the flexed limbs than we’re exerting.

As your draw reaches its maximum length, the weight will suddenly let off, allowing you to hold the bow steadily as you wait for a target to present itself. The Mathews Halon 5 that I shoot has a 75 percent let-off, for instance. So, while I need to pull 70 pounds at the beginning, by the time the string is at my ear, I’m left holding only about 18 pounds.

Release the string, and the limbs spring outward, pulling the string forward and driving the arrow. This happens in near silence, as noise equates to wasted energy. At 353 feet per second, the Halon fires its arrows through a very flat arc, maximizing the relative accuracy of our shots.

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