Measuring Internal Ballistics

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Appreciate the kind words Chuck. What appears simple on the surface can get very complex the more you dig into it.



I already added nearly all the features I had listed to be added earlier, and then some. Here is a simple comparison of a hammer preload adjustment side by side, highlighted are all the calculations taking that into effect. 







Still have LOTS of work cut out for me on this spreadsheet in the future and its not on my top list of things to do (as one can tell I took a few weeks hiatus). Some of the very technical nitty gritty work can be very dreadful and stays on the back burner longer than it should. I am sure others can relate. The spreadsheet has taken a life of its own though.



-Matt
 
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Let me make it clear that the FPE Lost in the graph represents a loss that cannot be obtained (theoretically at least), where as the FPE Potential is the max combined FPE if one were to have less pressure drop (larger plenum) and more barrel length, it is not in addition to the already obtained FPE. Just to be clear. So with my current configuration, with a longer barrel and a much bigger plenum, I would see 74~ FPE on this same amount of air used, opposed to the current 56.55. That "in theory' would be with a 27" barrel and 100~ CC's of plenum.

And to cross verify I ran the calculation with another formula, only changing my barrel length from 19.5" to 27.5" I get the following

1546497608_16741453855c2dae48ea1de6.64449491_hammerplcomparison.jpg


-Matt
 
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Sweet! Many of the factors involved in airgun tuning were explained to me by a kind gentleman in New Zealand that I believe is a mentor to Brian at Edgun West also. He gave me to understand that one of his main goals in tuning is to achieve the velocity being sought after with the lowest regulator pressure possible. And that the larger the plenum size the better up to the point of diminishing returns. I believe this is why Brian is able to get 60+ fpe out of an R5M using just a reg pressure of 120-125 bar if I remember correctly.
 
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You are absolutely correct. The greater the pressure drop across the valve seat and behind the pellet during valve opening the higher you need to set your regulator pressure to compensate for the pressure drop. 



Having lower pressure drop also helps reduce sequential hammer strikes re-opening or keeping the valve open longer than desired (after Elvis has left the building). If your pressure drop is too high (20-30%) that leaves upwards of 20-30% less force holding the valve shut until the regulator refills, which is designed to happen fairly slowly, the hammer can bounce back with its reduced energy and strike the valve stem upwards of 3-4 times and if there isn't enough force to resist whatever energy remains in the hammer, extra sips of air go bye bye.



My favorite approach to reducing/eliminating hammer bounce is a large plenum with low pressure drop, combined with a free flight gap (.04"~ / 1mm) for the hammer (has to travel that distance twice between bounces = more time for reg to refill and valve to close properly) works best.



-Matt


 
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Comparison of 4 current tunes, 20, 22 fpe, 41 fpe, 56 fpe. Shows the progression of more inherent losses both systematically and thermally as you push more air down the barrel. Interesting that the 25.4 gr is calculated at a faster lock time than the 33.95, even with less terminal velocity...due to its weight and increased acceleration / avg velocity. You can note the progression of residual muzzle pressure which of course results in more sound report. The mass of air on the 20 fpe shots were just 250~ grams where as the 56 fpe shot was just shy of 800..Each tune has its 'ideal set point / plenum size' calculated for maximum shot count @ that power. 























The trend with % of energy obtained from the air mass ejected is really similar across the scales, essentially boiling down to only 30%~ of the available K.E making it to the pellet, which can translate to a lot of air use with a lot of energy. 10 fpe with 20 fpe loss isn't shabby, but 100 fpe with 200 fpe loss seems like a lot, and 1000 with 2000 fpe losss even more so...the thermal efficiency of an airgun is inherently poor, even when shot at very low/reduced power levels.




P.S. FWIW My spreadsheet currently is using 0 Correction factors or 'fudge factors'...or mixing of adiabatic / isothermal ect...its just straight forward calculations taking into account any possible losses along the way with adiabatic conditions.
 
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"Adiabatic free expansion of a gas[edit]

See also: Free expansion

For an adiabatic free expansion of an ideal gas, the gas is contained in an insulated container and then allowed to expand in a vacuum. Because there is no external pressure for the gas to expand against, the work done by or on the system is zero. Since this process does not involve any heat transfer or work, the first law of thermodynamics then implies that the net internal energy change of the system is zero. For an ideal gas, the temperature remains constant because the internal energy only depends on temperature in that case. Since at constant temperature, the entropy is proportional to the volume, the entropy increases in this case, therefore this process is irreversible."

"En·tro·py


  1. 1.PHYSICS

    a thermodynamic quantity representing the unavailability of a system's thermal energy for conversion into mechanical work, often interpreted as the degree of disorder or randomness in the system.

    [/LIST=1]

    ... which all leads me to say that I am really flabbergasted at the proportion of the energy lost compared to the energy converted to the work of getting the pellet down the barrel. Using a burst of compressed air to propel an object is a terribly inefficient means of doing so. Its hard to believe that only 30% of the energy is being used to accomplish any work while 70% of the energy is lost. So then it should be the goal of some enterprising physicist and some mechanical engineer to come up with a more efficient system that turns that energy transfer equation upside down so that 70% of the energy is being used for work with only a 30% loss.

    Just sayin...

    Chuck







 
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While I may be able to calculate and articulate the losses inherent in pcp's, far more brilliant minded people than myself have pondered that same thought. I think the losses are what they are, entropy and just what we must accept, although I don't oppose out of the box thinking...my best thought to obtain more power out of a pcp is a secondary transfer port half way down the barrel that is timed, ideally by something detecting projectile movement that provides a perfectly sequenced secondary burst of air..as complex as the design sounds it would provide maximum energy output in a given barrel length/distance...and would be loud as heck....imo. :)




 
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:) I am thrilled and fascinated and amused all at the same time at the thought of a secondary transfer port at some point further down the barrel! That thought is a stroke of genius! :)

Now let me add a couple thoughts to that one. I am sure you are well acquainted with the Venturi effect where air or fluids speed up as they pass through a constriction and the subsequent drop in pressure. So could the Venturi effect be used somehow to increase the pellets' velocity while also using the accompanying drop in pressure to our benefit. What if just beyond the second transfer port there is a constricted or choked portion of the barrel that acts as a Venturi causing the gases to speed up so as to increase the velocity of the projectile with no cost in mechanical energy? You know that in many respects compressed air acts more like a liquid than a gas... so can that attribute be used advantageously in a Venturi as the compressed air is in the process of becoming uncompressed? 

"In fluid dynamics, an incompressible fluid's velocity must increase as it passes through a constriction in accord with the principle of mass continuity, while its static pressure must decrease in accord with the principle of conservation of mechanical energy. Thus any gain in kinetic energy a fluid may accrue due to its increased velocity through a constriction is balanced by a drop in pressure."

I guess my question is can we somehow use low pressure compressed air through a Venturi or choked barrel to increase our pellets' velocity with no cost in mechanical energy? And would this allow us to use a very low regulator setting resulting in the velocity we seek and yet rewarding us with a much higher shot count?

Just wondering...Chuck
 
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I think the Venturi effect concept is possible, but ideally employed in the valve by going over bore porting up to the base of pellet. In theory the gases would hit the choke @ the barrel and speed up right at the base of the pellet, provided you aren't looking for increased thermal or volumetric efficiency but rather increased system efficiency. I am not sure at which point the wasted volume would be more detrimental than than the benefit from the increased airways to create such an effect, but I don't doubt going over bore size porting would help, however I don't think enough testing has been done to know how much, as even just going bore size itself can be a doozy and over bore sized would be quite a task.



I think the dual transfer port idea is novel but would ideally be done electronically and with nano second precision. Would be a herculean task.




















 
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So I took my Internal ballistic measurements a step further, and now I measure internally @ the valve with certain figures...this was to develop and perfect, a tunable balanced valve, which was a success. Lots of hours have gone into this, and many calculations are approximations but as comparable as one can get to reality. 



I am not displaying balanced valve data here, but that part of the sheet has been tested, and confirmed working. I can calculate valve closure down to 100~ microseconds, which helps make a bell curve possible for balanced valves that open really easy, and then quickly return to conventional. The sheet reveals enough to a deep thinker that they can grasp exactly how I accomplished this task and replicate it.



The above is a development with how PCP valves tick, not many knew before, and many still don't...and others refuse to accept my formulations, and thats fine. As I said these are approximations and as close as I've seen anyone get. The Balanced Valve's mystery is absolutely no more! There will be plenty of valves that use my knowledge pertaining to the internals of a pcp valve coming out, you can bet your money on it..many valves coming out in the next year + will be applying my findings into their valve tech...good times ahead!



Added features:

*Port size losses (losses due to port restriction, of course more air would flow and air usage go up but I decided to include this..)

*Balanced valve calculations for both Hammer energy/spring energy requirements, to operation / dwell time control of a balanced valve, provides optimizations if required...

*Light/Med/Hammer weight+spring rating recommendations compared next to current

*Recommendations on port size, barrel length, plenum, and pressure if any condition is detecting as lacking for the power you are @ or are seeking...

*Graphical representation of any singular change to the rifle and what power would be available if such were done.







-Matt
 
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