How does a compound bow work

The principles of a compound bow are exactly the same as the recurve bow.  Force generated by your back and arm muscles is transferred into the bow by pulling back the bow string to distort (bend) the limbs of the bow.  This creates mechanical potential energy stored in the bow limbs.  When you let loose the bow string, under the principle of elasticity,  the bow limbs return to their original shape.  That mechanical potential energy is immediately converted into kinetic energy when the bow string is released.  The kinetic energy is transferred into the bow string which in turn transfers the kinetic energy into the arrow and accelerates the arrow forward.  Not all the kinetic energy is absorbed by the arrow with some of the kinetic energy being returned into the bow to be felt as vibration/oscillation, noise and heat.  All of this happens in a millisecond

A compound bow works by providing mechanical advantage to the user by using a block and tackle system to provide a mechanical advantage for the user so that the user has a decrease in the draw weight they have to pull and hold back at full draw. 

The compound bow achieves this mechanical advantage by the interplay between the bow string, cables, cams and the mod.

Bow string

A compound bow only has one bow string.  The bow string is what the arrow is knocked onto and what you hold on to draw backwards.  The bowstring rolls over it’s string cam and the bow string is attached to the inside of both cams of the top and bottom limbs.  Importantly, the bow string is only attached to the cams at either end of the bow.

Cables.

Each compound bow will have two separate cables separate from the bow string.  One cable end is attached to the axle of one limb and runs to the opposite limb running over the mod.  The second cable is attached to the bow similarly but mirrored to the first cable.  Both cables are the same length.  The cable and the bow string working together provide the mechanical advantage felt by the user as the “let off” effect.

Cams (also known as string cam)

The cams are the large wheels on the upper and lower limb which the bow string runs over. Think of them as pulleys.  Cams come in various shapes from perfectly round to elliptical (egg shaped).  Various elliptical shapes provide different advantages in term of how much let off can be achieved.  The cams have a grove all round which helps guide the bow string back into position each time the bow string is drawn and or released. 

Mods (also known as cable cams)

The mod is securely attached to the side of the cam at each limb end with the cable running over it to a secure point.  The mod can be unattached from the cam and its position re-adjusted to modify the bows draw length to suit the user, hence the name of “mod” as it can be modified.  Mods also have a grove to assist in aligning the cable travel.     

Interplay between bow string and cables

When you pull the bow string backwards you start to turn the cam.  As the cam is securely attached to the smaller circumference mod, the mod also starts to turn and “winds in” the cable over the mod making each cable shorter.  The more the mod rotates the shorter the cable will be.  This occurs at both limb ends simultaneously shortening both cables to distort (or bend) the limbs generating mechanical potential energy under the principal of elasticity in both limbs.  The mechanical advantage is obtained when the bow string is pulled backwards over the large cams which then turns the smaller mod to shorten both cables to apply huge distortion force to both limbs.   Effectively turning a large pulley (cam) to turn a small pulley (mod) to gain an exponential force benefit in distorting the bow limbs.  As the limbs distort this creates the draw weight of the bow.

So you can see that there are two systems in play at the same time.  The bow string over the cams creates rotation.  That rotation turns the mods shortening both cables to exert force to distort the limbs.

Let off

With a block and tackle system, there is a trade off between weight for distance.  Using multiple pulleys you can pull heavier loads but you must pull in more rope to move the load the same distance.  The goal of a compound bow is to control the amount of mechanical advantage gained as you pull the bow string back to full draw.  At the start of the draw you want a heavy draw weight to speed up the arrow where as at the end of the draw, (at proper draw length) you reach your proper draw length you want the mechanical advantage to kick in so that it is easier to hold the bow string at full draw.

Cams and mods are essentially a pulley system to provide mechanical advantage to the user when drawing back the bow string.  Unlike a recurve bow where you hold the full amount of the draw weight of the bow at full draw, a compound bow provides mechanical advantage so that you only hold a small portion, expressed as a percentage (%) of the bows draw weight at full draw.  So for example, when drawing a 60 pound recurve bow at full draw, your muscles will be holding 60 pounds.  But with a 60 pound compound bow,  as you draw the bow string backward to full draw, it will initially feel as if you are drawing the full 60 pounds, but as the cams and mods rotate as you start to move the bow string backwards,  the mechanical advantage of the pulley system comes into play, and the draw weight will significantly lessen as you draw back further until you reach the bow’s set draw length.  If the 60 pound compound bow has a 70% let off, at full draw you are only holding the residual 30% of the draw weight, a mere 18 pounds.