Compound bow is a very intelligent design based on the system of pulleys to maximize performance and minimize struggle. There can be two answers to how does a compound bow work, first I will answer simply like when you pull the bow string, the design of pulleys pull together the limbs storing energy and then at a point called let off effect it will drop a lot of draw weight needed to keep holding the bow drawn.
The second type of answer lies in the upcoming sections where I have discussed every detail of the working of compound bow. In the end we will also look at the draw curves of two compound bows and the advantages of compound bows.
Understanding the Anatomy of a Compound Bow
To comprehend how a compound bow functions, we need to dissect its anatomy. A typical compound bow consists of several key components, each playing a crucial role in its operation:
The riser is the central part of the bow, often made of aluminum or carbon. It serves as the foundation, connecting the limbs, grip, and other accessories. The riser’s design significantly impacts the bow’s stability, balance, and overall performance.
The limbs are attached to the riser and come in various shapes and materials, such as fiberglass or carbon. When drawn, the limbs store energy, which is then transferred to the arrow upon release.
Cams and Wheels
One of the most defining features of a compound bow is its cams or wheels. These are located at the ends of the limbs and are responsible for the bow’s let-off, a critical advantage that reduces the holding weight when fully drawn.
Bowstring and Cables
The bowstring connects the cams, and when drawn, it stores the potential energy that propels the arrow forward. Cables, on the other hand, play a vital role in synchronizing the movement of the cams and controlling the bow’s performance.
Sight, Arrow Rest, and Stabilizers
Accessories like sights aid in aiming, arrow rests provide a platform for the arrow, and stabilizers improve balance and reduce vibrations during the shot.
The Secret Behind Compound Bows
I will divide the main story into two sections:
The first section is how energy is stored in the limbs of compound bow that I will explain with the help of block and tackle system. The second section will be about working of cams and let off.
Compound bows and Block and tackle system
A compound bow basically follows the block and tackle system. In a block and tackle system there are two pulleys connected to an axle, when force is applied on larger pulley the smaller moves along with it. In this way both pulleys move with same energy but there is a catch, the distance moved by both pulleys is not the same. The smaller pulley moves a shorter distance, but energy is the same as on the larger pulley then according to the formula of work that is force times distance equals energy, we can say the smaller pulley applies more force to the load.
Comparing the System with parts of compound bow
Now lets compare it with the parts of compound bow. The pulley can be referred as a cam (two inner and outer wheels attached to the axle), the larger wheel is attached to the bow string and the inner wheel is attached with the cables. Mirror this configuration and we have a compound bow. The cables are connected to the inner wheels of both cams in a way that one side is connected to the center of the first cam and other rolls around the inner wheel. But when this cable goes down to the second cam, the cable that was connected to the center of the first cam is rolled around the inner wheel of second cam. I have added images to make you understand.
Now is the part to make everything work, When you draw the bow string back, both large wheels rotate and so do the inner wheels, as the inner wheels rotate a shorter distance applying greater force on the cables putting them in tension. The cables pull both the upper and lower cam axis together and thus bending the limbs with much greater the force that you apply
This system allows compound bow to multiply your force and store more energy in the limbs than you actually apply. But there is a bit more to it that is the magic of compound bows, let off effect.
The Cam System and Let-off
The cam system is the heart of a compound bow, and its design significantly impacts the draw cycle. There are different types of cam systems that include single cam, hybrid cam, and binary cam systems.
As the bow is drawn, the cams rotate, which causes the bow’s draw weight to increase until it reaches its peak weight (usually around 70-80% of the bow’s maximum draw weight). At this point, the let-off occurs, meaning the cams’ shape allows the archer to hold a reduced amount of weight at full draw. This let-off enables archers to aim more steadily and execute precise shots, making it easier to hold the bow in a drawn position for an extended period.
The Role of Cam Design in Compound Bows
Cam design is a crucial aspect of compound bows, significantly influencing their draw cycle, performance, and overall shooting experience. Unlike traditional bows, which have a linear increase in draw weight as the bowstring is drawn back, compound bows utilize a cam system to achieve a more efficient and user-friendly draw force curve.
Upper and Lower Cam Design:
The cam system in single cam compound bows consists of two cams: the power cam and idler wheel. These cams are connected by the bow’s limbs and bowstring and cables, forming the foundation of the bow’s mechanical advantage.
The lower cam, also known as the power cam, is usually larger in diameter and asymmetrical in shape is directly connected to the bow’s limbs. The upper cam, also called the idler cam, is typically smaller and connected to the opposite limb through the bowstring. This configuration creates an asymmetrical cam shape, which plays a crucial role in generating the unique draw force curve of a compound bow.
The Working Principle:
The cam system operates as the archer draws the bowstring back. As the archer initiates the draw, the cams begin to rotate, causing the bow’s limbs to flex and store potential energy. During the early stages of the draw, the larger power cam provides a higher mechanical advantage, making it easier for the archer to pull the bowstring.
As the draw continues, the idler cam gradually rotates, contributing to the increase in draw weight. This progressive increase in draw weight is a notable advantage of compound bows compared to traditional bows, as it allows archers to reach higher draw weights with less effort.
Relation Between Radii and Gear Ratio:
During the draw, the larger and inner wheels of the cam system due to the elliptical shape of larger wheel have different radii. Initially the radius of larger wheel is small and at this point, most force is required to draw the string. This is because cam is in an awkward shape and its hard to rotate it and also a stretched arm can exert more force than a bent arm.
Then as the radius increases the draw weight moves towards the peak weight and a time comes when it changes its shape, this point is called let off. After the let off, draw weight reduces drastically
You can see in the picture, its hard to pull the bowstring with a smaller radius of large wheel, but after the rotation (change of shape) it seems relatively easier to hold the draw weight
The ratio of the radii from center where bowstring and cable makes contact with the larger and inner wheel respectively is called gear ratio. At the end of draw cycle gear ratio is maximum.
The Peak Weight:
As the archer continues to draw the string, the limbs continue to bend, storing more and more elastic potential energy. This continues until the archer reaches the full draw length of the bow, at which point the limbs are maximally bent, and the bow is at its peak weight.
The design of the cams comes into play at this moment. Just when it might seem challenging for the archer to hold the full draw weight, the cams reach a point where they “roll over.” This is commonly referred to as the “let-off” point. At this stage, the shape of the cams allows the archer to hold the bow with significantly less force. Check out the complete guide about let off
The let-off percentage refers to the reduction in draw weight at full draw compared to the peak weight. Most compound bows have a let-off percentage ranging from 70% to 80%. For instance, if a bow has a peak draw weight of 70 pounds and a let-off of 80%, the archer would only need to hold approximately 14 pounds at full draw. This let-off advantage enables archers to aim more steadily and execute precise shots.
Now comes the moment of release! When the archer releases the bowstring, the stored elastic potential energy in the limbs is unleashed rapidly. As the limbs revert to their original position, they push the bowstring forward. This rapid movement of the bowstring transfers the stored energy to the arrow, propelling it forward at high speed.
The transferred energy, now in the form of kinetic energy, propels the arrow forward with incredible velocity and power. It is this kinetic energy that allows the arrow to travel long distances and penetrate targets effectively.
Shot Execution and Follow-Through
During the shot execution, it is crucial for the archer to maintain proper form and follow through. A consistent and smooth release, along with a steady grip, helps optimize the energy transfer from the bow to the arrow.
Force X Distance:
In physics, work is defined as the application of force to an object, causing it to move a certain distance in the direction of the force.
We pull the bow string with some force to draw it to a distance in order to shoot it. The amount of energy required to pull the bowstring is called draw weight and the distance the string travels is called the draw length.
To calculate the work done in drawing the bow, we use the work formula mentioned earlier:
Work (W) = Force (F) × Distance (d) × cos(θ)
In the context of a compound bow, θ is typically considered to be 0 degrees since the force applied is in the same direction as the distance moved. As a result, the cosine of 0 degrees is 1, simplifying the equation to:
Work (W) = Force (F) × Distance (d)
In this case, the work done is directly proportional to both the applied force (draw weight) and the distance the bowstring is drawn (draw length). As the archer exerts more force and draws the bowstring back a greater distance, more work is done in storing potential energy in the bow.
So basically what I wanted to teach you is that the draw force curve of compound bow will have draw weight in the y-axis and draw length in the x-axis. We will see it in the next section.
Compound bow draw force curve:
The curve shows that the archer when starts to draw the string the draw weight increases but after the peak draw weight there comes the let off point. Here the magic starts, due to the working of cams as discussed the shape of the cams allows the archer to hold more weight with less force.
The area under the curve is the energy stored in the limbs. This area differs for different compound bows for example:
We can see that bow 1 (orange) is hard and it is much more difficult to reach the peak draw weight it also has less let off as compared to bow 2 (yellow) which is soft. Therefore the graph of bow 1 is greater as compared to bow 2 meaning that there is more energy stored in the limbs of bow 2.
How Does a Compound Bow Shoot Fast
The draw cycle of a compound bow follows a unique pattern, unlike that of a traditional bow. As the archer pulls the string back, there’s a noticeable peak in effort partway through the process, but towards the end, there’s a significant let-off. This design allows the archer to hold only a fraction of the bow’s peak weight at full draw, reducing strain and providing more time for precise aiming, resulting in a steadier shot.
The compound bow cam consists of two pulleys connected at the axle, ensuring that when one pulley moves, the other moves in sync. When you exert force on the larger pulley, the smaller pulley moves as well but over a shorter distance. Since energy is the product of force and distance, moving something a shorter distance with the same energy input translates to greater force applied. It would create a lot of energy. Also, there are two of these cams
Top Speed of Latest Compound Bow
The top speed of the latest compound bows can exceed 300 feet per second (fps) or even reach 350 fps in some high-performance models. This incredible speed is achieved through advanced cam designs and materials.
Advantages of Using a Compound Bow
The compound bow’s design offers several advantages over traditional recurve or longbows:
Reduced Holding Strain
As mentioned earlier, the let-off feature reduces the holding weight of a fully drawn compound bow, making it less taxing on the archer’s muscles. This advantage is particularly crucial during hunting situations or competitions where a steady aim is essential.
The combination of the cam system and stabilizers significantly improves shooting accuracy. The reduced recoil and minimized hand torque lead to more consistent and precise shots.
Versatility and Adjustability
Compound bows are highly adjustable, allowing archers to modify draw length and draw weight according to their preferences. This versatility makes them suitable for archers of all ages and skill levels.
Maintenance and Care
To ensure the longevity and optimal performance of your compound bow, regular maintenance is essential:
The compound bow’s draw cycle, draw weight, and draw length are intricately linked and significantly impact its performance. The cam system, coupled with the let-off advantage, allows for faster arrow speeds and improved accuracy, making the compound bow a favorite among archers of all levels. Understanding the physics behind force, distance, and energy in a compound bow empowers archers to optimize their shooting experience and unleash the full potential of this marvel of modern archery technology.