Measuring Internal Ballistics

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ackuric

ackuric

Member
Mar 10, 2017
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Colorado, United States
I was inspired quite some time ago to attempt this, by someone who said it couldn't be done using basic math. After reviewing this article written by Domingo Tavella (you can google it if you'd like, its very well written) I felt compelled to give it a shot. My interpretation of whats happening in a pcp rifle is as follows and measures up with already established data in terms of basic math formulas to determine lift + dwell. eg: lift = hammer kinetic energy / closing force and dwell = 2x hammer momentum / closing force. That is with consideration of energy loss after lifting the valve off the seat which is pressure on the seat area * compression distance of poppet / 2. Closing force being (primarily) the cross sectional area of your poppet stem times the average pressure of the transfer plenum/port + spring.



Using my calculations and assuming the valve only remains open until the volumes are equal (volume released = volume between seat and pellet + barrel volume) allows me to calculate roughly how many inches the pellet travels until the valve closes by subtracting the volume between seat to pellet base prior to it moving from the volume released and taking the remaining volume and calculating that into barrel volume to determine barrel distance.. and calculating the speed of the valve stem after being hit by the hammer and using its velocity allows me to estimate how quickly the valve opens, as well as calculating how quickly it closes. There is quite a bit more depth but that is the basics of where I began.


From there I applied the basic law of pressure/volume p2=(p1+v1)/v2 to determine the pressure drop along the barrel and use the pressure + potential system losses to determine the velocity.



The following data is only ESTIMATED, but gives a GREAT representation of whats happening inside a PCP, especially at low power. I will likely do more data sets with other tunes in the future! This was done over the last 4 days! I've learned a lot and have way too much more to learn. But these figures represented here are VERY accurate.

(Click to enlarge)







-Matt
 
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I'm pretty sure that what happens is when the trigger is pulled it releases the hammer or striker being held under spring tension that flies forward and knocks a valve open, releasing a blast of air from a pressurized chamber that rushes into the barrel propelling a projectile down and out the barrel and down-range. But since I can't see through metal, I'm really just speculating!

On second thought, I'll take your word for it. 
 
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Its interesting to note certain key data, such as.



Valve open time, 2 MS! (estimated 2 different ways)

Air released 191 MG! (calculated based on air usage)

Equivalent port reduction fps = within 1% of actual calculated output AND real life output. (port reduction equivalence based on the lifts flow and a restricted port that would match it)

Valve closes (on this very detuned data set) by the time the pellets traveled only .37 inches down the barrel! 

Hammer lock time is 8x the valves lock time, and nearly 4x the pellets lock time. Total lock time on this set is only 11 ms from trigger pull to pellet exit, where as the valve is opening in 1/10th that speed!
 
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This is really interesting albeit the calculations are over my head. So the concept is that you are determining (estimating) fps velocity based on the air used and your particular airgun's internal physical dimensions/operation + physics laws applied? If I understand it correctly, the calculated velocity (655 fps) in your case came in very close to the actual measured (chrono used?) average velocity of 651.6 fps? This can be a huge thing, because could be applied to any airgun and calculate velocity for each pellet fairly accurately without any external devices. 

I am assuming that once a particular airgun is measured for all the internal ballistic parameters, you only have to do it once. So, if the airgun is not touched (lubricated, reg pressure the same, hammer spring the same, etc) these internal parameter numbers are constant and the only variables are the (1) starting pressure (2) temperature/humidity (3) pellet weight (4) pellet head size=> friction 

BUT.... my biggest question: how did you measure your internal volumes, dwell, etc??? The tolerances are extremely small and the measurement itself probably takes days? How would I go about measuring my own airgun and assured that the numbers would be accurate? 

Some other questions: what factor does pellet friction play in the accuracy? Should pellets be sized? Or overall the pellet-friction from pellet from pellet because of varying head size, etc is not a significant factor?.

If I understand the utility of this calculation correctly, this could be very useful for knowing velocities without a chrono.. 


 
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Updated the charts look, as well as corrected a calculation or two which didn't change valve performance. 



fe767,

Your assumption is correct in that the variables of every day life such as humidity, temp change, pressure change, , pellet variation + friction changes + hammer speed variations will all create what we know as an extreme spread. ...the calculations I made assumes an average of all and gives you a number close to what it thinks your average output will be based 100% upon your entered air usage (volume + pressure) per shot.

As I stated in the original post I cross verified my calculations for dwell + lift (internal mechanics) of the valve with known good starting points. Also if you can cross verify more times than one with multiple calculations then generally you're onto something or at least 'close enough'. As I said this is just a Data Model not a 100% representation.



You can a) assume air travels faster at your operating pressure than your average pellet shot. Which then means b) (if air mass accelerates and tops out much faster than pellet can move) pellets position relative to its closure = (barrel volume per inch - volume from valve seat to pellet base) * volume used. Calculate the time it takes air to reach the back of your pellet and then the time it takes to carry the pellet to the closure and you have dwell time. I may very well be wrong in my assumption but if the pellet can move faster then the air pushing it then it will have lost all potential energy and would just cruise along at the same speed much like it does generally later in the barrel or for example if you ran an extremely long barrel there is a point when pellet speed tends to overcome the average speed of the air left...all just IMO 



-Matt


 
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The lift / peak / close times are all calculated and the time it ROUGHLY takes the poppet to travel to the calculated lift and back, those aren't just divided among each other...


If the poppet is opening at 30 fps and has to accelerate (first accel = fast from collision/jerk) and then decelerate, then reverse its direction back towards the seat at again roughly 30 fps terminal speed, then its only accelerating back towards the seat and speeding up all the way until fully closed without any deceleration. I used the above speeds as examples but the speeds I use are calculated assuming the collision is elastic, and basing that on the hammer speed...which is again part of my calculation based on hammer weight + spring. That speed isn't assumed it uses Hookes Law. So if the hammer at 46 gr is held back by a 6.5 lb/in spring @ X distance you get Y velocity. If hammer hits a valve stem weighing 1.5 gr elastically you get Z velocity. Z velocity (velocity to lift - account for acceleration and deceleration phases) / distance = time. And that is an example of some of the math I used to cross verify other calculations such as dwell, if the speeds dont match up to get the poppet up to the calculated lift + back to the seat then somethings wrong! In my case I got it right or got lucky! 
 
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This is part of the hammer velocity equation I used. Here I calculate 

X = SpringRate(lb/in)*(Preload+Cocking distance) - DownForce from gravity

X is the force your spring imparts onto the hammer once the trigger is pulled, notice the DF from gravity? Well if you launch a ball/hammer on a spring straight in the air versus down into the ground, which one do you think will end up faster over the same distance? Which one do you think will go further? Of course our space is finite and neither up nor down so that number has to be estimated based on the direction of motion our hammer goes, then if you wanna go crazy you need a drag coefficient of your hammer, its center of mass, and lots of other data to really crunch down exactly whats happening...at some point you'd end up calculating down to the atomic/molecular level which is WAY beyond me!



-Matt
 
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Thanks for the details, Matt. I understand some parts of the project but some I would need to visualize with the airgun apart. I am actually waiting for a Huma reg and an upgraded valve seat for my FX Impact. Once those come in and I find time, I will rebuild the Impact and replace all the o-ring, etc. While I have everything apart at least I will get a better idea of the inner working of the airgun. I think the measurements are so precise and difficult to accomplish with layman tools...that it may be beyond my scope. 

An interesting thought about the Daystate Air Wolf...it has the adjustable power curve setting that varies the valve timing. Theoretically, once you set that curve for a particular pellet and measure the velocity, from that point on you should be able to set your velocity for that peller without needing any measurements. Do it for 4-5 pellet types and no need to use a chrono.


 
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Here is another chart for fun, I only added to the air use scale. so 7% more air use would mean I used 7% of 2100~ which = 147~ more psi used over same shot count (basically doubling the air used). I did this to see how it would scale and what do ya know, no other changes made it puts me at my max. Now believe it or not thats incidentally the neighborhood of my valves max shooting the 19.91 gr...1020-1040~



Notice the FPE Loss line on this graph compared to the last. Most that FPE lost is ADIABATIC and irretrievable! LOL. Also the Estimated MAX High shot count dropped due to avg pressure at the seat. dropping which is used in that calc...so less pressure at seat + less pressure in barrel = a few less fps :p

This graph is just a representation and not a data model nor are the scale settings finished. Just an example!

I blacked out quite a few things just because those measurements aren't currently set up to scale with this air use factor.




 
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The above chart is of a regulated rifle, with the Plenum volume being 53 cc and the main res being 190 cc. 



You can see in the very upper set of data I have a calculation that recommends a setpoint + volume within 5% for regulator at that fpe level that would work, which allows maximum head room space for HPA air + volume and shot count between fill pressure and set point.


It states I could reduce the plenum set point to 1250~ PSI with just a 7 CC plenum adding back 46 CC's of HPA and adding 780 more psi of space between fill and set point pressure on this very low 18.7 FPE tune. 

My 2000 psi set point has 106 lbs + spring force holding it shut

a 1250 psi setpoint would have only 66 lbs. Which also makes the valve much easier to open reducing the cocking force.



Of course I move my tune between 18-55 fpe so I won't be doing the above.



-Matt
 
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Here is a 25 FPE tune on the same 19.91 gr pellet...as you see its all set to scale and calculates more properly with more air usage for less fpe compared to the 40+ chart, which was just an example and NOT set to scale on all things, where as this one is according to my actual entered data. FPE / CI drops from 1.91 @ 18 fpe to 1.7 ~ @ 25 fpe. Considering this is a very light pellet you can't expect high efficiency numbers unless its at a very low power output. 

The recommended set point + cc volume for regulator on this tune is 1550 psi and 11cc +/- 5%

Also note the BC /Pellet Drop calculator is sync'd with my tune changes as the pellet drop went from around 12 inches on the 18 fpe tune down to 9~ at 25 fpe :)


Also the Thermal Efficiency and System Efficiency were swapped accordingly from last chart as I had them backwards. As you can see here there is 73%~ thermal efficiency which means 27% (roughly) of the potential energy was lost adiabatically. IMO. 



The system efficiency would measure approximate loses from energy out of the muzzle, energy lost in the transfer port. If I had no transfer channel from seat to pellet and a longer barrel this number could increase to 100%. again IMO. I wasn't too scientific about obtaining this number so thats why its very much an approximation.






 
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Here is where my spreadsheet currently is, still in development but I have only added features, haven't needed to tweak the arithmetic / calcs yet...I did however correct a few minor calcs that did not directly effect FPS/FPE or internal ballistic predictions...(For instance my 'ports max' Flow rate calcs were off by a measure of 6 due to a miscalculation. )Nonetheless here it is.

All data entered in was for my 56 FPE tune, from hammer weight/spring to air use and avg fps ect..This is what the spreadsheet calculated based on my inputs...







Quite fascinating...scaling from 18.5 to 56 fpe very well...this spreadsheet is still under development but has amazed me thus far with its progress and predictions. Some of which aren't predictions but just basic arithmetic.

-Matt
 
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Here is an example showing calculations that are empirical and ones that are complex or logical/predicted.

Yellow = Simple / empirical calculations

Orange = Complex (may be inaccurate yet to be 100% verified)

Blue = Predicted/Logical calculations (theoretical)







Here are the 'inputs' used to calculate all the above data..

Blue = For internal ballistics / efficiency / air usage ect (avg fps shot purely used for Efficiency not internal ballistic calcs directly)

Red = hammer energy data / valve lift + dwell predictions / estimated required hammer weight / spring ect..

The blacked out areas are features not implemented and top secret! Lol


 
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Ackuric, excellent work!, most of the math is beyond me...but understand most of the mechanics of the formula’s etc. I love full mechanical air guns but also believe electro-mechanical devices can be superior if quality components are used?,( I know everyone is thinking Daystate right now! ) there headed in right direction but QC of components not there yet compared to full mechanical systems like Thomas/RAW IMO. Also flow characteristics/pathways through valve & transfer port play a roll in efficiency eg. flow 90deg into barrel or straight inline with direction of pellet travel?, also I always liked the design & simplicity of Mac1 air rifles (which IMO is what the Thomas is patterned after!) just keep in mind (as I’m sure you can tell...) I’m no engineer, but have a decent Idea of what’s going on inside these wonderful devices!
 
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@nomojo65 I agree with a lot of what you said. The 180 degree turn most conventional valve setups use (minus air force) certainly effect performance/efficiency as well as distance from valve seat to pellet base and the many other variables I calculate such as pressure drop due to plenum size, valve open duration, ect. Electronic components can certainly produce very consistent results provided the board controlling them is programmed well, but in terms of efficiency or power I am afraid (IMO) they can only replicate a non electronically controlled valve. The main benefit to electronic valves is controlling valve dwell as the pressure drops allowing a much greater range of usable pressure opposed to conventional methods. Mac 1 is definitely a genius when it comes to air guns!
 
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Partial list of features so far.



***3 Different FPE/FPS prediction algorithms***

  • -Predict FPE/FPS based on pellet weight, air usage, and environmental factors + rifle specs (barrel, caliber, pressure, plenum, tp waste) (1% accuracy or better)
  • -Predict FPE/FPS based on hammer energy (lift and dwell modeled based on pressure holding valve closed + hammer energy, FPS/FPE predicted based on ports equivalent lift & caliber/port/pressure/barrel length(3~% accuracy or better)
  • -Predict valves HIGH FPE/FPS based on tried and true formula (same as above but no port reduction due to lift, accuracy 3~% or better)



***Analysis***

  • -Internal ballistics. Barrel pressure gradient, FPS, FPE, FPE Lost/left behind, FPE Potentially Recoverable (from less pressure drop while valve open + barrel length)
  • -Provide detailed analysis for hammer / spring / plenum / valve design / air flow / air usage / shots on/off reg / residual muzzle pressure / and much more
  • -Recommended spring/hammer combo range, as well as recommended plenum volume and regulated set point based on your desired power / caliber / barrel ect
  • -Lock times (From Hammer, to Valve, to Pellet)
  • -Shot string analyzer (not shown)
  • -3 Efficiency calculations (System, Thermal, Volumetric)
  • -Warning messages (For poor valve design(s), poor poppet material strength/sealing margin, high pressure drops during shot, poor hammer/spring combos)
  • -Compare gains going from Air to Helium or a mix of the two



***Additional features***

  • -Save/Store up to 5 Rifles and or tunes 
  • -Ballistic coefficient calculator (currently GA only)
  • -Change Barrel Length/Bore Size / Plenum Size / Air Density / Air Use / Pellet Weight / Port Size / Pellet Break Force / TP Waste / Friction while reviewing data
  • -Max potential shot count (based on current efficiency and max usable pressure range)



***Soon*** features I want to implement or that are partially working 

  • -Sequential Hammer Strike Detection (warning msg)
  • -Valve Over Dwell Detection (warning msg)
  • -Hammer weight & spring rate profiles (spreadsheet will calculate alternate combos that will equal the same hammer energy allowing one to easily make large shifts in weight/rating while maintaining energy levels, no guess work!)





I am always open to new ideas/suggestions to add. This spreadsheet is still in its infancy and I hope to continue growing it to help people understand whats going on internally inside our PCP's. 


Heres just a small peak into some back end calculations going on to make it all work..




 
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Ackuric this is all absolutely fascinating! If I ever win the lotto you and I are going into the airgun business together... I will gladly bank roll the project and put your keen mind to work on creating an air rifle that is as close to 100% percent efficiency as humanly possible to achieve. And thank you for stopping once in awhile to put your thoughts into more simplistic terms or for using a simple analogy to describe things so that I can grasp the concepts you are presenting. One of Albert Einsteins greatest accomplishments in physics was that he could explain even the most complicated concepts in simple terms that any layman could understand. He thought that even a brick layer or house painter would be interested in his theory's... and he was right! I thank you for taking the time and effort to type up such beautiful presentations. Keep up the good work! 

All the best, Chuck
 
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