Brain teaser of the day -- measuring the speed of a bullet

[blasto9000]

I figured my esteemed EEVBlog colleagues would be the best group of gents to bounce this question off of.

A friend and I are characterizing several aspects of bullet flight.  We can closely estimate bullet impact  using aerodynamic data provided by bullet manufacturers, local atmospheric conditions, off-the-shelf ballistics calculators, and visual observation of the bullet's behavior "downrange."  (Distances 1,000 to 2,000 meters.)

Right now we're estimating bullet velocity by entering a (guessed) baseline velocity into the ballistic calculator and then observing the impact point downrange.  If the impact elevation doesn't match what the ballistic calculator says, we adjust the muzzle velocity data in the calculator until the calculator's prediction matches the bullet impact.

Using this method, we have been able to tune the ballistic calculator to an accuracy of ±30 seconds of angle out to approximately 2,200 meters.  However, I find that an experienced shooter can exceed this precision with several practice shots.

So, I would like to try boosting the precision of our ballistics calculation by directly measuring the bullet's velocity just as it exits the barrel of the firearm.

There are off-the-shelf chronographs for this; they are low-cost but their accuracy and precision are very rough.  This type of chronograph is usually a rectangular box with two vee-shaped sensors sticking out of it, and the user is to fire the bullet through the vees.  So there must be some type of sensor in the vees and the box must somehow take the time-of-flight between the vees and turn it into a human-readable velocity figure.

The bullet velocities we seek to measure would be in the range of 850 to 4,500 feet per second (260 to 1350 m/s).

Should easily be captured by a DSO, and I can easily design/build an optical sensor, but I suppose there is a better way?

How would YOU do it on a non-governmental budget?

BTW, the bullet is 0.30 inches in diameter, 1.1 inch in length.  (7.62 mm x 28 mm), mass = 11 grams +0.2 gram.

[SeanB]

IR emitter and photodiode in the V sections, aimed up and looking for a reflection from the shiny metal bullet as it passes. Needs either an IR laser diode of 5mW or a IR led on a good heatsink ( no difference really there between them) and a photodiode with an IR blocking filter and a high gain amplifier to get a high signal level then a comparator, preferably one with a sliding reference ( triggers on sudden change in light intensity) that starts a high resolution timer with a high speed clock. Space start and stop 1m apart and clock at 10MHz and you get a resolution of 100 nanosecond for time of flight. Will give you 700 counts on the fastest bullet, 3000 on the slowest. You read with a counter with a 5 digit display or use a binary counter to count and read it with a micro to do the math.

[Rufus]

There are off-the-shelf chronographs for this; they are low-cost but their accuracy and precision are very rough.

It is trivially easy to measure the time between two signals with high precision so if the accuracy and precision really is very rough as you claim the problem is coming up with a practical and accurate sensor to produce the signals.

Your claim of being able to easily design/build an optical sensor is likely very optimistic.

Oehler is the only place I found any specification and they claim around 0.1% accuracy with 8 feet sensor spacing. 1/10th of an inch error in that 8 feet is 0.1% Can you make a practical sensor where the position at which a bullet is sensed is accurate and repeatable to better than 1/10th inch?

It sounds like your gun is held in a jig of some sort so a sensor with a much smaller aperture might be practical in your case. If you can reliably shoot through two beams from laser pointers for example accuracy becomes much easier.

[ee851]

Modern microprocessors are, I think, fast enough to execute tens of millions of instructions per second.        How fast can a modern microprocessor service two consecutive hardware interrupts?    I don't know, but I suspect the answer would be in the tens of microseconds.    So it ought be possible to trigger two consecutive interrupts, each using an IR photodetector to detect the leading edge of the projectile.    Use the microprocessor to measure the elapsed time between the two consecutive interrupts.     The only variable would be the distance between the two IR photodetectors.    Set that distance so that it is easy for you to measure the speed of the fastest projectile and to measure a speed that is 5 percent higher or lower than this value.

The hard part might be--and this is just speculation--rigging the IR photodetectors to the muzzle of the rifle so that they don't interfere with the rifleman's ability to aim and shoot the rifle.

[ddavidebor]

You should not use hardware interrupt. You should use timers.

You can configure a internal timer to start and stop on the rising or falling edge of a signal

[robrenz]

I suggest using the tail of the bullet for your measurements since the back of the bullet provides a more accurate positional reference since it is flat and almost the diameter of the bullet (probably boat tail but still better than the tip). You will onlly have to be within .1" of being on the axis of the bullet using the tail. The triggering on the somewhat parabolic pointed end of the bullet will have huge variation from the beam not being perfectly centered on the axis of the bullet.

Ignore all this microprocessor talk and use your DSO like you said in your first post.

[ddavidebor]

Good idea

[ConKbot]

Since this if for a work application, and time is money, I'd get 2 commercial units and accurize them.  Bolt 2 sky screens together and attach them to a solid, repeatable mounting frame, and put the other 2 at your known distance and measure between them.  If you have access to someone with a CMM you could put the finished thing on the CMM and measure between each sensor with extreme accuracy. If not I'd check with a few different tape measures.

Hook the 4 sky-screens up your recording device (DSO, counters, whatever you like) so that youre measuring twice, and that should hopefully come out to the exact same velocity to a few significant figures. If not, then you know you can work on your calibration.

Just for clarity, youd have them arranged:
1,2______________________3,4, and youd be using 1 an 3 for the first measurement, and 2 and 4 for the 2nd. 

[ejeffrey]

Ignore all this microprocessor talk and use your DSO like you said in your first post.

This.  The timing measurement itself is trivial.  The actual accuracy will probably be dominated by other factors -- trigger jitter caused by the finite rise-time of the detector pulse, variations in pulse amplitude, the shape of the bullet, and deviations of the trajectory from straight down the detector axis.  An oscilloscope will show you the analog waveform and help you figure out what is going on.  Once you can do sufficiently accurate measurements with the scope you can think about using an MCU for convenience.

As a guess, the detector circuit in the commercial devices is just a comparator fed into a microprocessor trigger.  The problem is that as the pulse height varies, you are detecting at different points on the waveform.  This is a classic problem from particle detectors, and the solution is a vonstant fraction discriminator which accurately detects the arrival time of pulses with the same shape but varying amplitude in a way that is insensitive to the pulse amplitude.

[smashedProton]

Out of curiosity, what is your application?  Why would you want to get anything more accurate than 30 seconds?  30 seconds is about a half inch at 100 yards

[grumpydoc]

Out of curiosity, what is your application?  Why would you want to get anything more accurate than 30 seconds?  30 seconds is about a half inch at 100 yards

To be fair blasto9000 did say "Distances 1,000 to 2,000 meters" and at 2km, 30 seconds of arc is just under 30cm (I was tempted to say "a foot" to thoroughly confuse the units of measurement).

Mind you I also note that he said "an experienced shooter can exceed this precision with several practice shots" which I'm having fun with conceptually. Mind you I've never shot the sort of weapon that you'd need for this so it's way out of my experience.

[TorqueRanger]

Out of curiosity, what is your application?  Why would you want to get anything more accurate than 30 seconds?  30 seconds is about a half inch at 100 yards

To be fair blasto9000 did say "Distances 1,000 to 2,000 meters" and at 2km, 30 seconds of arc is just under 30cm (I was tempted to say "a foot" to thoroughly confuse the units of measurement).

Mind you I also note that he said "an experienced shooter can exceed this precision with several practice shots" which I'm having fun with conceptually. Mind you I've never shot the sort of weapon that you'd need for this so it's way out of my experience.

What kind of gun are you using and caliber ?
In reality your first shot is the most important because it's what they call a cold bore shot ...The more shots you put down range  without allowing the barrel to cool down causing the barrel to heat up and to move around affecting the shot ... Also at that range you have to compensate for the rotation and the gravitational pull of the earth because of the extend flight of the bullet... I don't see you really getting that accurate at 2000 yrds  because there is too many factors that can't be figure out ....Like the whether the bullet is factory made or homemade ,What kind of powered ,Cast bullet or turned bullet for percision,depth of round in the casing ,rest shot or free stance shooting,bull barrel or tapered barrel ,what kind of stock and is it glass bedded ,and what kind of crown is on the barrel and is it free of burs or nicks ..

[mikes]

What kind of gun are you using and caliber ?

Well, obviously a .50 BMG or smaller (maybe 416 Barrett?), or else "do it on a non-governmental budget" wouldn't be a concern.

But, yeah, it takes a well tuned rifle to shoot under .5 MOA consistently, and even a High Master very rarely hits within 1 MOA (X ring) every time, and at much shorter range (albeit with worse ballistics). So the "30 seconds" experienced shooter claim is very much a stretch.

Commercial chronos are mostly within .25%, if more accuracy is needed, then a radar Doppler unit is called for. But then you're back to the whole "governmental budget" thing.

[mzzj]

What kind of gun are you using and caliber ?

Well, obviously a .50 BMG or smaller (maybe 416 Barrett?), or else "do it on a non-governmental budget" wouldn't be a concern.

But, yeah, it takes a well tuned rifle to shoot under .5 MOA consistently, and even a High Master very rarely hits within 1 MOA (X ring) every time, and at much shorter range (albeit with worse ballistics). So the "30 seconds" experienced shooter claim is very much a stretch.

Commercial chronos are mostly within .25%, if more accuracy is needed, then a radar Doppler unit is called for. But then you're back to the whole "governmental budget" thing.

Bench rest competition rifles are the most accurate short-to-medium range rifles and  competition shooters can do most of the time better than 0.2 MOA (or 12 arc seconds) at 100 meters with optimal enviromental conditions. Things get more difficult at 600 meters and keeping your shots under 1 MOA is pretty hard.

[kfitch42]

You don't work for TrackingPoint, do you?

http://arstechnica.com/gadgets/2013/01/17000-linux-powered-rifle-brings-auto-aim-to-the-real-world/

P.S. Your avatar seems a just a bit incongruous next to your post.

[SeanB]

Most range for me is 300m with a generic gotten from store R2, but after a few minutes of practice I was doing the best part of shooting training - take the tip of the pointer off.  R5 was better, probably as it had less than a million rounds through it. I worked with a few pro shooters though, and I was often given a pile of pistols to strip, clean and oil for them. Those had to be clean enough to eat off afterwards, and polished to a gloss. The benefit of being the slave labour/apprentice.

Learnt how to paint there, along with assorted other things, like building, paving and keeping warm in winter without falling asleep at the gate. Tried golf, sucked at it, lost many balls into the swamp. Learnt that you do not try to pump the ocean out of the hardstand drains at high tide, phone first and ask the tower when it would be low tide and then it would be dry. Never was suckered into KP, just was a waiter at a few formal dinners, and was the unfortunate victim of a few as well.

So wanted to go out with the heli gunship though, all I was doing was helping epoxy the seats and gun mounts back in the floor every time, along with change lamps that had died from the shock. We were using Araldite in 20l cans for that, until the new floor panels arrived, then it became a shell with broom sticks holding things up. Worst was cleaning the chopper after a dagga ops, leaves and twigs everywhere, and tons of it, all soaked in JetA or Paraquat, and having to almost strip the panels off to clean it out of the controls, you would think they were mowing it with the blades instead of the chainsaws they took with, but it grows here to higher than the chopper so is trimmed vigorously during landing.

[ftransform]

eww bullets

were you in the army seanb?
is a dagga op = creating a landing zone?

[SeanB]

Nope, in the flying circus. Air Force. Helped make precisely located holes in the ground, and hopefully not on our own guys either.

The growers do not make a convenient place to land, you sort of choose a level spot and drop down into it. Easy to see from the air, go in the dry season and look for the blue green rectangles, land, spray, chop down, pile in heap and burn. Cops stand downwind, we and the pilots upwind, we wanted to get home in one piece. Sample taken for the court case, generally a half ton, and the farmers get a ride along too. We always had volunteers at base to unload though, though one or two of the known smokers would leave looking like the Michelin man.

[glatocha]

What resolution of the measurement do you want.
1m/s, 0.1m/s,  lower?

I am thinking. If you know where the gun is aiming (some laser or something) and knows where the bullet hit the target. You know it falls xx mm on the distance of yy m. Maybe you calc can assume the speed.