For a while now I've been pondering how the potential FPE an airgun can develop relates to the bore size (caliber) and to the port size between the valve and the barrel at the smallest point.... Everyone knows that as you restrict the transfer port the potential FPE of the gun decreases, but I haven't seen much hard data on how that relationship works.... I've done a few experiments myself, and have found that once the FPE begins to drop (which occurs when the TP is the point of restriction) that the relationship between FPE and diameter is pretty linear.... I began to explore this from a mathematical point of view by going back to basics and looking at the force at the base of the pellet for various pressures and calibers.... I calculated the bore area (caliber/2 squared times Pi) and then multplied by the pressure to obtain that force and then plotted it on the graph below....
As I pondered that graph, I began to wonder how that force relates to the potential FPE of the airgun.... I reasoned that since FPE is the energy in foot pounds (ft.lb) and that means the force over a distance, if I set the distance that force is applied as 1 foot, the force ends up being the potential FPE at 100% efficiency.... Here is a graph of that for the common airgun calibers....
I ran this data past Lloyd Sikes, who checked it with his spreadsheet and confirmed that if all the efficiency factors were set to 100% and a 12" barrel used, the results were consistent with my data, so I knew I was on the right track.... This doesn't mean that you can achieve this with a 12" barrel, however.... There would have to be an infinite air reservoir, no wasted volume between the valve and pellet, no resistance due to friction (air or pellet), and a 100% transfer of energy from the air to the kinetic energy of the pellet.... None of those factors are possible, but there is a way to overcome those losses by using a longer barrel and increasing the distance the force acts through....
I've done enough development on PCPs now to realize that you want to close the valve before the pellet reaches halfway down the barrel, otherwise efficiency suffers.... If you have a 24" barrel, and close the valve at 12", now you can achieve results pretty close to those on the graph.... As an example, my .257 Hayabusa, with wide open porting, achieved 160 FPE at 3000 psi.... almost right on the blue line on the graph.... using a 28" barrel.... I have numerous other examples of high performance PCPs that show results similar to those predicted above by using the 12" EFFECTIVE distance for the force.... What I am saying is that the expansion of the air in the extra barrel length makes up for the multitude of losses that occur in even a very efficient PCP....
In the next post, I'll explore the effect of a transfer port that restricts the flow below the full bore size, which is what the graphs in this post are about....
Bob
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Originally Posted by rsterne
