GTA
All Springer/NP/PCP Air Gun Discussion General => "Bob and Lloyds Workshop" => Topic started by: DomingoT on August 12, 2018, 04:57:50 PM
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This issue may be of interest to folks who sort pellets by weight and applies to CG or any other calculator. I also felt this is the most appropriate gate given the nature of the topic.
"DISCLAIMER: I personally don't think it is worthwhile worrying about pellet weight variation as long as it isn't huge - that said, I might worry about this issue if I were a better shooter. Regardless, this is an interesting issue worth examining."
If you have pellets of unequal weight, it is interesting to know how much of an effect the weight variability has on the POI, especially at longer distances.
If you change the weight of a pellet, and don't change the muzzle velocity (nor the BC), the POI doesn't change. In order to compute the POI change due to weight variability, you need a criterion to change the muzzle velocity when the pellet weight changes. (You could also bring in the BC into the picture, which conceivably changes when the weight changes, but let's concentrate on the effect of the weight on the muzzle velocity.)
When you change the pellet weight, ChairGun tries to be helpful by allowing you to change the exit velocity such that the pellet energy is preserved. This criterion, however, leads CG to overestimate the negative effect of weight variability on POI. Here is why.
Of two pellets of the same caliber and same BC, the heavier one will exit with lower velocity and, in general, with higher energy. That the heavier pellet leaves with lower velocity is intuitively obvious, but it is not obvious that it also leaves with higher energy. You can prove this curious fact using elementary calculus. Figuring out the precise drop in velocity and increase in energy, however, isn't straightforward.
Example:
Per CG, a 8.44 grain pellet with BC = 0.021, with a zero at 35 y, and exit velocity 909.44 ft/s (15.497 fpe) has a POI at -2.36 in at 55 y.
What will be the POI of an 9.00 grain pellet, same BC? Using the preservation of energy criterion, you reset the velocity to 880.65 (CG does it for you), and run the calculation again. This time the POI is at -2.54.
According to CG, the change in POI due to a weight change of 9 - 8.44 = 0.56 gr is -2.54 + 2.36 = -0.18 in.
The 0.18 in value is exaggerated because of the assumption that the energy remains constant. If you calculate the "actual" velocity loss and energy gain (using a theory like the one I recently posted on the internet), you get the following values (for a rifle with a barrel 300mm long).
For a 9 gr pellet: Muzzle velocity = 888.46 ft/s, energy = 15.77 fpe (notice the energy "gain" of about 0.28 fpe)
If you now run CG with this velocity, you get a POI at -2.49 in at 55 y (compared with -2.54).
In summary, the effect on POI at 55 y due to pellet weight variability of 0.56 grains:
a) According to constant energy assumption in ChairGun: 0.18 in additional vertical drop
b) Accounting for actual energy gain: 0.13 in additional vertical drop
Difference is about 30% (for this particular gun and pellet)
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Subscribed!
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...Of two pellets of the same caliber and same BC, the heavier one will exit with lower velocity and, in general, with higher energy....
With piston guns, it is common to get lower velocity AND lower energy when using heavier pellets.
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You are correct, for practical values of pellet mass, this observation mostly applies to PCPs. The energy inequality as stated strictly holds for "sufficiently light" pellets. In the case of a simulated 0.177 springer (about 18 fpe), I found that pellets heavier than about 7 grains lose speed as well as energy when their weight goes slightly up (computed values).
The reversal should also happen for some combination of parameters in PCPs, but I haven't found any yet.
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I know you ignored the effect of the BC in your calculations.... but since the BC = SD / FF (Sectional Density divided by Form Factor)…. if the FF is the same (a reasonable assumption if the shape is unchanged)…. since the SD is directly proportional to the weight, the heavier pellet will also have a higher SD.... and therefore a higher BC.... If you assume that BC is proportional to weight (given the same weight and caliber)…. then you can use that higher BC in ChairGun to refine the drop even further.... This effect will bring pellets of varying weights even closer to the same POI downrange when fired from the same gun....
Bob
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Bob, if the weight anomaly were due to the thickness of the skirt, for example, the form factor would be unchanged and what you say would apply verbatim. If it were due to a variation in the external dimensions, preserving the pellet shape, the form factor would also remain constant.
Assuming the form factor doesn't change, the increment in BC cancels most of the effect of the weight anomaly. In the example above the net effect at 55 y would be 0.06 in, hardly something to worry about, I suppose.
Probably the best way to use this calculation is for establishing upper and lower bounds: the effect of 0.56 gr on the POI at 55 y is greater than 0.06 in and less than 0.13 in.
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" In the example above the net effect at 55 y would be 0.06 in, hardly something to worry about, I suppose."
You've got that right. When you can show me a gun, or person, that can shoot 0.06" center to center groups at 55 yds, then you can start to think about things like this.
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I have always said that sorting pellets by weight is a waste of time.... Head diameter, maybe....
Also, if the weight did make a difference to the POI.... then you should resight your gun between the sorted batches.... ::)
Now if you are shooting at 1000 yd. like Carl.... maybe a different story.... ;)
Bob
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Hi Domingo for the most part I do tend to agree... in a perfect or very good rifle there is a good chance there will not be a difference worth worrying about...
But...
I did sort some of the old Remmy domed 9.8 which had good head size consistency... what they did not have was a consistent weight... they varied in weight from 9.3g to 10.2g over several tins... Though the internal vs external ballistic thing will tend to even things out there was still some vertical stringing going on... why..? It was Harmonics most likely... leaving the barrel at slightly different times... in that case the stringing was vertical... could have been more towards diagonal or horizontal stringing also...
I do suppose the slightly differing balances could also cause one to have less stable/different flight characteristics than the other also...
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Wow, that was deep! One more article in my collection to help me become a better shooter.
I like you guys' thinking, calculating, not guessing, fly-by-the-seat-of-your-pants.
Or rather, shoot-by-the-seat-of-your-pants...! ;D