The Physics of Crossbows

Crossbows started to disappear from military use when reliable firearms became widely available. However, they remained popular for hunting in Europe in the 15th and 16th centuries. Hunters and target shooters still use them today, although modern crossbows often appear far more sophisticated than their early counterparts. They're usually made from exceptionally strong, lightweight metals, and they can incorporate scopes, adjustable stocks and other gadgets. But no matter how sophisticated a crossbow is, at its heart it's basically a bow. Similarly, a bow is basically a spring.

You've probably seen firsthand how a spring responds to force. If you press down on a spring, it expands to its original shape when you let go. The same thing happens if you pull its ends in opposite directions. This is because of the spring's elastic potential energy -- the energy it stores because of a change in its shape. When you pull one end of a spring, it stores elastic potential energy until you let go. Its potential energy then becomes kinetic energy, the energy of movement, allowing the spring to resume its normal shape and sometimes to bounce around. You can read more about kinetic and potential energy in How Force, Power, Torque and Energy Work.

This is exactly what happens when you draw a bow. Unlike with many toy bows, you aren't pulling on a stretchy string. Instead, as you pull the string toward your ear, you pull the tips of the bow's limbs toward you and closer together -- your strength changes the bow's shape. When you let go, the bow springs back to its original shape and the bowstring moves back to its original position. The movement and energy propel the arrow from the bow at high speed

Two factors determine the amount of energy a bow can hold. Its draw weight is the amount of force required to draw the bow. A bow's draw weight increases the farther back you pull the string. Its draw length is the distance between the bowstring's position at rest and its position when drawn. The total amount of energy that a bow can hold is approximately equal to its draw weight times its draw length, divided by two. In other words, a bow's overall strength depends on how hard it is for you to pull the string and how far back you are able to pull it. Bow manufacturers express this strength in terms of:

  • The bow's energy, measured in foot-pounds or joules
  • The arrow's velocity, measured in feet or meters per second

A recurve crossbow with a draw weight of 150 pounds and a telescopic sight.

Image courtesy Liam Skoda

Several factors can affect a bow's draw weight and length, changing the velocity at which an arrow will travel:

  • Its size: Simple longbows are much more powerful than simple short bows.
  • Its shape: The first bows were simple curves of wood. Recurve bows, used today in Olympic archery events, curve away from the user at the end of each limb. These curves shorten the bracing height, the distance between the string and the bow at rest. This means that the string travels farther before coming to a stop and releasing the arrow, which can give the arrow a little extra momentum. The shape of the bow also causes it to apply additional spring force to the string.
  • Its composition: A bow's density and tensile strength determine how much energy it can hold and how well it can return to its original shape when shot. English longbows were often made from yew wood because it was strong and elastic. Many modern bows are composite bows, which use different materials in different parts of the bow, making some parts more flexible and others more rigid.

All of the physics concepts that apply to bows apply to crossbows as well. Larger crossbows that a person aims from the shoulder are more powerful than smaller, handheld crossbows. Most modern crossbows have fiberglass limbs, which are strong but flexible, and older crossbows used steel limbs. Nearly all use recurve or compound bow designs, although some have two separate bow limbs rather than one continuous bow.

Regardless of which bow design they use or what they're made from, most have the same basic loading, firing and safety procedures. We'll look at those next.