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What is a Ballistic Pendulum?

Mary McMahon
Updated May 21, 2024
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A ballistic pendulum is a device which is used to arrive at the kinetic energy and velocity of a bullet. The development of the ballistic pendulum was a significant event in the history of ballistics, allowing this field of study to advance significantly. Today, other devices are used to study the movement of bullets, but the ballistic pendulum lives on in physics classrooms around the world, where it is used to provide a simple introduction to concepts like momentum. In classrooms, a springloaded “gun” is usually used to fire a mock bullet, for safety reasons.

The design of a ballistic pendulum is fairly simple. The device consists of a weight attached to an arm. The weight has a wooden block attached which is designed to catch a bullet when it is fired at the block. Knowing the properties of the pendulum and the properties of the bullet, someone can fire a bullet at the pendulum, take note of how far it travels, and use this information as the basis of several equations to determine velocity and collect other information about the bullet's movement.

This device appears to have been developed in England in 1700s. Benjamin Robins, a British mathematician and ballistics expert, is often credited with the development of the ballistic pendulum. His 1742 book New Principles In Gunnery introduced the ballistic pendulum and explained how it could be used. Robins noted that one could also use the device by attaching a gun to the pendulum, firing it, and noting the movement of the pendulum in the wake of the explosion.

With the 1800s came the development of ballistics devices which could directly measure velocity, making for more accurate and easy measurements. However, the basic principles behind the ballistic pendulum are still sound, and such devices can be used with a variety of projectiles, not just bullets. Historically, ballistic pendulums were used to measure the momentum of everything from bullets to cannon balls, providing a great deal of information which had not been available before to members of the ballistics community.

In physics classes, students are sometimes shown a ballistic pendulum demonstration or film to learn about conservation of momentum and conservation of energy. Students may be asked about what kinds of calculations they can use to gather information about the movement of the bullet, and they may be asked about the physics behind the movement of the bullet and the pendulum.

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Mary McMahon
By Mary McMahon

Ever since she began contributing to the site several years ago, Mary has embraced the exciting challenge of being a All The Science researcher and writer. Mary has a liberal arts degree from Goddard College and spends her free time reading, cooking, and exploring the great outdoors.

Discussion Comments
By Izzy78 — On Aug 23, 2011

Once you have done a ballistic pendulum trial, what is the information useful for? It sounds like you would be able to tell the speed of the bullet and how much force the gun applied, but why is this important.

I don't know anything really about guns, but I would guess that the amount of gun power in a bullet directly affects its speed. Also, I know a lot of newer guns use compressed air. I assume you could use to information to tweak those guns to get optimal performance. Maybe someone who knows more about guns can help.

By kentuckycat — On Aug 22, 2011

@matthewc23 - What jmc88 described is what is used in most lab settings today. I have seen videos, though, of people who have made their own ballistic pendulums to test personal firearms. They look a lot like what you described.

I did a little bit of reading about Benjamin Robins' first ballistic pendulum, and his technique for measuring the swing of the pendulum was very ingenuousness. Now, I'm sure they probably use cameras, but instead, he tied a piece of ribbon to the pendulum arm, and was able to measure the length of the swing by measuring how far the ribbon was pulled.

I think it would have been very hard to do these experiments back in the 1700s. For one, the muskets used were very inaccurate. Also, I'm sure measuring cannons was a huge undertaking.

By jmc88 — On Aug 22, 2011

@matthewc23 - I couldn't tell you what the first ones of these devices looked like, but I can tell you what the basic ballistic pendulum apparatus looks like that is used in physics labs.

It is a small desktop device. It is about a foot and a half long and I assume made of something heavy like iron. On one end is something that looks like a gun, but instead pushed out a metal rod with a certain amount of force. The rod hits the pendulum, and it swings back. Somewhere on the apparatus is a gauge that measures the maximum angle of the swing. From this, you can use certain equations to figure out the force that was put on the pendulum.

I would be interested to know what the first ones of these looked like, though. Especially one that caught real bullets.

By matthewc23 — On Aug 21, 2011

I am having a hard time imagining what one of these would look like or how exactly it would work.

I am thinking of something like a piece of wood hanging from the ceiling. Then someone fires a gun at it, and they somehow measure the force of the bullet based on how far back the pendulum goes. The problem I'm having is how they measure the pendulum motion. Now, we could just use a slow motion camera to tell the exact spot where the pendulum went back the farthest. If one of these was first invented in the 1700s, though, that definitely wasn't how it was done.

What exactly does one of these look like, and how does it work. I have a feeling I'm not imagining what it really looks like.

Mary McMahon
Mary McMahon

Ever since she began contributing to the site several years ago, Mary has embraced the exciting challenge of being a...

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