Measure The Speed Of A Speeding Bullet

In the study of ballistics, you can do very little without knowing the velocity of a projectile. Whether you need to hit a target at over a mile, check if a paintball gun is safe for opposing players, or photograph high-velocity objects, you need a way to measure that velocity. [td0g] enjoys the challenge of photographing bullets impacts, and has created an open-source ballistic chronograph to help achieve this.

A rifle bullet punching through a wine glass, captured with the help of the chronograph

[td0g]’s design makes use of two light gates spaced some distance apart, and the time that an object takes to travel between the two is measured and used to calculate velocity. Most commercial ballistic chronographs also work in this way. [td0g] created the light gates using pairs of infrared photodiodes and LEDs. When there is a sudden dip in the amount of light received by the photodiode, the Arduino control circuit knows that an object has passed between the photodiode and LEDs and triggers the timer. An LCD shield on the Arduino is used to control the software and display velocity. As you probably guessed, clock accuracy is very important for such time measurements, and [td0g] demonstrates a simple technique using a smartphone metronome app to manually calibrate the clock to acceptable accuracy for his purposes.

This is the second such chronograph that [td0g] has built, and he changed the frame to be mostly 3D printed for easier construction, and upgraded the sensor boards to custom PCBs instead of the perfboard. If you want to build your own, all the design files are up on Github, and the light gate sensors should be for sale on Tindie soon. He has successfully used the rig to measure various projectiles ranging from 100m/s (paintball) to 875 m/s (rifle bullet). With a high power rifle, the chronograph needs to be at least 2 m from the muzzle to avoid damage or false readings from the muzzle blast, which also means the careful aim is required to put the bullet through the sensing area, without killing the chronograph in the process.

Getting the shutter to trigger at just the right moment is probably the biggest challenge of high speed photography. We’ve a number of different triggers, including for water balloon photography, and a laser for droplets.

52 thoughts on “Measure The Speed Of A Speeding Bullet

      1. FYI, legal maximum for airsoft pellet in my country is 0.9J with 90m/s or 395fps in muzzle velocity. Restrictions vary by country but that bullet in the board can no way be an airsoft.

        1. “Air gun” in the United States is not “air soft.” I have an air gun that fires .177 caliber lead pellets at the same muzzle velocity as a .22 caliber rifle. “Air soft” is a kids toy that would have gotten you laughed at when I was a kid. The kids I grew up with owned air guns, and could hunt squirrels and birds with them.

          1. I doubt that. A .22 LR goes 370 – 500 m/s unless you fire subsonic loads, whereas an air gun cannot exceed the speed of sound (340 m/s) and in practice won’t even come close. The best air rifles peak at around 280-300 m/s.

          2. LOL
            In Australia both, “air gun” and “air soft” are considered FIREARMS needing a firearm license to purchase and only to be used in approved shooting ranges or private land.

            Please stop laughing …

          3. From what I’ve observed the purpose of air guns and air soft guns is very different. I’ve seen some videos of air soft combat on youtube and it seems to require a lot of skill. I can’t imagine a squirrel putting up much of a fight.

          4. Airsoft can be fun, but it’s mostly people polluting the place up with the little plastic pellets, and the scene seems to be full of people who stroke their guns a little too much…

          5. Luke: 22LR with the 30gr bullets are 520 meters per second o 1700fps. Close enough to 500 to fit your variation. But “22 caliber” as so many say, is a property of the barrel’s bore and the bullet diameter. A 22-250 with a 35gr bullet will produce around 4500fps or 1360m/s (Mach 4). It is still a 22. [And many others. 218 Bee, 219 Zipper, 22 Hornet, 223/5.56, 221 Fireball, etc.

            I guess a nice chrono will cover from around 200 fps (arrows and such) to 5000 fps.

  1. Years ago I worked in the film business, and we had to shoot a close-up shot of a bullet coming out of a revolver.

    We played with all kind of neat cameras that had spinning prisms instead of shutters and could crank at 10,000 fps. It was cool, but the short exposures, slow optical systems and high grain of the 16mm stock needed for the fastest cameras didn’t give us the image we wanted.

    Then someone realized that we could remove the powder from the cartridge, turn down the bullet for a looser fit in the barrel, and fire the gun using just the primer.

    The muzzle velocity dropped from 900+ FPS to something probably around 50 or so, and that allowed us to shoot with a conventional 35mm high speed camera. On the second try we added a bit of flash powder for effect. Looked great, especially with the burning gas leaking past the undersized bullet, and nobody could figure how we got such crisp, clear images of such a fast event.

    1. For anyone trying this, be careful. He just described a squib load, and those are famous for lodging the bullet in the barrel. Fire another round behind the stuck bullet, and your barrel undergoes a Rapid Unplanned Disassembly.

      That said, that’s a brilliant trick for getting a difficult shot.

      1. Good point. We were particularly careful about that and, as is usual on a film shoot using actual firearms, had an assigned “armorer” on set whose only function is to carefully attend to the weapon while everyone’s attention is elsewhere.

        I should have mentioned that caveat in my post.

      2. Not quite a squib, more like a training round. There’s a variety of ammunition available with light bullets and just the primer.
        The original comment stated that they turned the bullet down for a looser fit as well.
        A squib is the term used when the bullet doesn’t have sufficient propellant behind it to even leave the barrel.

        1. I don’t know if it’s called a squib, but it’s possible to “underload” the cartridge such that the powder doesn’t burn in a controlled fashion any longer. Some of it burns while the rest breaks down into CO gas, which then detonates and blows the breech up in your face.

      3. There are parlor guns that do exactly that by design. They have a short .22 cartridge with only the primer for propulsion, and they’re meant for indoor shooting.

  2. Couldn’t you use a modified scale attached to a target to measure the impact force and then, using the known weight of the bullet, calculate the impact velocity? You know use the force? (Check the date.)

    1. Perhaps but I’d expect bullets with differing constructions to have a different impact vs time curve. A frangible bullet might be very different from a conventional hollow point vs a simple lead wadcutter in how much force you measure. Short of another calibration method I don’t know how to come up with a proper compensation factor.

      If you want to measure velocity downrange then a technique similar to the chrono above can be used. You just need to swap out the sensors. Some people have used microphones for supersonic rounds. I’ve used aluminum foil. Two sheets separated by a thin foam insulator makes an (open switch) target. As the bullet (conductive) passes through it, the sheets are shorted together, ie – a closed switch. Put 2 such sensors a known distance apart and you’ve got a big fat downrange chrono. You will have to replace the sensors on a regular basis though.

      Extra credit if you use a 555 timer ! :)

      1. Momentum is always conserved. One could check the absolute accuracy by making a ballistic pendulum and you basically make a target on a swing and measure how high it goes when absorbing a bullet. You need an accurate weight of the target and a way to tell how high it went. Mass(of target + bullet) x g x height change = mgh = increase in potential energy. Set it equal to kinetic energy when the two masses first colide and solve for v of the combined mass. Then (v.bullet)(mass of bullet) = (v.pendulum)(m. bullet + m.pendulum). Wallah!

        Well, it is harder than it looks to get precise. And the angle depends on the cosine of the momentum so you need to pick a pendulum mass that gets you around 90 degrees deg of swing, where cosine is changing the fastest. Recording a laser dot on the wall that is reflected from a mirror on the rotation point of the pendulum could be pretty accurate.

        Dang! Now I want to try it!

      1. I find it interesting that the formulas in the ballistic pendulum write-up don’t seem to give much consideration to the energy dissipated by the act of catching the bullet. Some energy has to get dissipated in deforming lead, moving sand, splintering wood, etc.

        I guess you can make the argument that you’re measuring momentum, not energy, and as long as you capture all the initial material, that’s what matters, but it still seems like there has to be some accounting of the material that gets shoved sideways or otherwise bounced around, into the walls of the catch tube and dissipated as heat, and doesn’t contribute to the linear momentum of the tube.

        1. Variations in amount of gun powder, weights, mechanical differences etc. can all contribute in variation between shots. You can only account for so many things between lab results and real life.

          As for the material shoved sideways, you could consider the X and Y displacement and account it as a vector.

        2. A tungsten block with a cup that matches the shape of the bullet should help with capturing the full energy. You would really only be able to do this very close to the muzzle since any travel through the air could deform the bullet. The cup would be able to capture the bullet and preserve the forward momentum without losing any energy to deformation of the bullet that would happen if if hitting a flat surface. A cone shape could work too but you may lose more energy as the bullet deforms into the tip of the cone. Add some known friction to the rotation of the pendulum so the air leaving the barrel in front of the bullet cannot push the block off center.

        3. Momentum is always conserved. Energy can change form. You can ignore the kinetic energy that goes into heat. The Wiki explanation is ot quite correct or at least not clear enough. What the calculation really does is look at the speed of the pendulum IF IT FELL from the maximum height it achieved. That is why they can use the kinetic energy to get, v by going in reverse. You are right. You can’t rely on kinetic energy in the collision. Heat transfer is not deterministic, but momentum in collisions is. That means you can run the clock backwards and it all works.

    2. You just described the principal of the ballistic pendulum. Search it. It’s how ballistics were done before electronics existed.

      In summary they would essentially take a log tie with a rope and suspend it. Knowing the mass of the bullet and the log and the length of the rope they only had to measure how far back the log swung after it absorbed the bullet and you can use the laws of conservation of momentum.

  3. Thick catalogues make great bullet absorbers. Or a years worth of National Geographic Magazines stacked together.. As with plywood, or 2X4’s, it’s important to move the target after every shot. A bullet chasing the same hole can bounce back out. For Supersonic projectiles (.22LR is in that class), there is a really neat trick, that avoids calculating timing. All supersonic projectiles are preceded by a bow shock. A piezo element can be placed to capture the bow shock and use that to trigger a strobe.

    1. There is also the two layers of foil separated by paper trick to trigger a strobe. Or the “cutting the wire with the bullet trick”. Neither of those have a velocity requirement of supersonic to work.

    1. i have a commercial chrono but they are finicky and unreliable unless you go for something more serious than a 80$ unit.
      they do not have active illumination, but use the shadow of the bullet passing on top of two sensors. hence, any nearby fluorescent or led light which are typical of indoor ranges will render them useless.
      i have tried fitting some leds with a linear regulator but for some reason it doesnt work very well.
      outdoors they work a little better, but when testing rifle loads you will quicky overtake the price of the cheap chrono having to shoot 4 or 5 times every load before getting a reliable measurement
      this device uses dedicated IR illumination so could be much better (if it ignores ambient light)
      there are other types of chrono: doppler radar (very expensive) and a system where a sensor close to the muzzle will magnetically measure the passing bullet speed. very cool for rifles but useless for handguns.

  4. The energy dissipated is irrelevant, since the ballistic pendulum relies on conservation of impulse.

    Actually, to be able to make use of that, you rely on as much energy to be dissipated that, at the end, the bullet is at rest wrt the pendulum’s body. So you can calculate the energy dissipated in the event.

    Ah… physics :-)

    1. “at the end, the bullet is at rest wrt the pendulum’s body.” My concern is that the quoted isn’t always true. Anyone who’s shot steel targets has felt lead splatter on their face. Not all of the bullet ends up at rest wrt the pendulum. Any fragment not just dropping due to gravity (or stuck on the pendulum) is momentum not accounted for, KE not measured.

        1. The maximum transfer of impulse would happen if the pendulum was already swinging away from the bullet at half its speed. Compare the case to a Pelton Wheel turbine. If the pendulum doesn’t move, the bullet just bounces/splatters off.

          1. The max transfer of momentum is if the bullet is captured in any way. Bullet trap that makes it into dust, ballistic gel, it doesn’t matter. Just don’t send bits of it flying outside the problem.

  5. Hackaday authors, you have failed in your trailing links! Why build a janky light gate that needs alignment when you could build a radar system. Link to the cheap radar modules! The commercial solution is, of course, the labradar https://mylabradar.com/ I own one, and it works quite well…..except when shooting suppressed for some reason. I’d love to see an open source version…..If only I had time :D

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