How far will the sling bullet go?

Before rockets, guns, and cannons, humans had slings. Along with arrows and catapults, these ancient weapons allowed launching objects much farther — and harder — than a human was capable of unequipped.

A sling is made of two cords, a retention cord and a release cord, with a pouch in the middle to hold the thrown object, called a bullet. As a physicist and historian enthusiast, Mark Denny derived multiple equations to predict the launch speed of the launched bullet based on the parameters of the sling.

“The sling is a simple machine, but analyzing how a slinger launches a sling bullet is very complicated because of the movements made by the slinger during the launch phase,” said Denny.

In his first set of equations, Denny describes a thrower launching the sling bullet in a pirouette style similar to an Olympic hammer throw.

He also derives equations to determine the bullet spin and timing error in terms of target range.

In another set of equations, Denny considers the motion of a side-arm sling, which is performed with a single arm where the sling is rotated overhead. This equation determines the motion of the sling based on the average power transferred to the bullet by the slinger.

Together, these equations can help to characterize the ability of most sling designs.

“This research will be useful to, for example, archaeologists who dig up an ancient sling and wonder how well it performed,” Denny said.

It can also be used as a teaching model for students investigating the internal ballistics of the weapon.

Source: “Internal ballistics of the sling,” by Mark Denny, American Journal of Physics (2025). The article can be accessed at https://doi.org/10.1119/5.0226263 .