Jefferson wrote:
Jim is a fx120i scale weighing to 2 hundredths of a grain accurate enough to weigh pellets?
To answer your question, let's take a look at the math, the pellet weight ranges, and also weighing environment:
0.02 grain maximum error MIGHT mean a total possible error range of 0.02 grains (i.e. + or - .01 grain) OR it might mean + or - 0.02 grain. It depends on how non-deceptive the manufacturer is with its specifications.
Let's assume the worst case of + or - 0.02 grains as the error range. This means a potential .02 + .02 = .04 grain total error range.
Now let's consider the range of possible pellet weights. That can range from about 5 grains in 177 caliber to at least 30 grains or more for large caliber pellets. 0.177 caliber is "the worst case", since the pellets are the lightest, so the scale's potential error range is a higher percentage of the pellet's weight. A higher percent error in pellet weight means a higher percent of variation in both pellet trajectory and wind resistance. (Yes, wind resistance is definitely affected by pellet weight).
So, for a 177 caliber pellet with "nominal" weight of 5 grains, the maximum potential 0.04 grain error is 0.04/5 grains = .008 of the pellet weight, or 0.8% of the pellet weight. Is this enough to change trajectory? Technically, yes, because while objects of different weights but equal air drag all fall at the same rate due to gravity, a weight change also means a change in muzzle velocity and flight time. The heavier pellet will be traveling slower and therefore spend more time in flight, and therefor give Gravity more time to accelerate it downward. But, will that tiny change in velocity be ENOUGH to SEE on a target?
Let's take a 50 yard example, which is "worst case" for many shooters (except fanatics like me).
Newton's laws say that vertical drop = ViT + 1/2aTT.
A 0.8% weight variance will likely translate to about a 0.8% muzzle velocity variance. Because of the above equation, the flight time effect of that 0.8% velocity variance will be magnified due to the "T-squared" in the 2nd half of the equation.
Let's say the pellet muzzle velocity of the fastest pellet (i.e. lightest pellet within the error range) is say 900 fps. To go 50 yards = 150 feet, that pellet will need 150/900 = 0.167 second.
The HEAVIEST pellet can be up to 0.8 % heavier and so 0.8% slower. So, its MV will be = 900*0.8/100 = 7.2 fps slower, or 892.8 fps. So, its flight time will be 150/892.8 = 0.168 second.
So, the difference in flight time 0.168-0.167 = 0.001 second, which is one thosuandth of a second.
Now technically, the difference ion flight time applies to both halves of that equation, but the second half is the one wioth the big impact because (a) it uses time SQUARED, and (b) the first half of the equation only applies to the VERTICAL component of the velocity which is tiny comapred to the horizontal component (even for an air riflewith a low MV).
Ignoring that vertical component, the flight drops for the lightest and heaviest pellets respectively calculate out to 0.449 foot and 0.454 feet. That's a difference of 0.005 foot = 0.06 inch or about 1/16 inch.
Is that small number large enough to be signfiicant? That depends. For shooting pests or knockdown Field Target targets, no it's not significant. For benchrest type compititon shooting, where the total 5-shot group size might be only half an inch, yes it is significant because it makes the group potentially 12.5% larger.
Now this assumes that the .02 grain scale error spec means + or - .02grain which is the worst case assumption, and it also assumes a 5 grain pellet that no one is likely to try to shoot at 50 yards.
At 50 yards, you are far more likely wanting to shoot a 15 to 30 grain pellet, which makes the potential flight variance due to pellet scale weight error pretty insignificant.
But wait, there's more . . . there is another important consideration.
Most very accurate scales are super sensitive in order to BE (Truly) super accurate. That means that the slightest air movement near them can and will affect the displayed weight. It also means that the lightest movement of the table they are sitting on, due to even just YOUR stepping on the floor near it, will affect its readings.
The precision scale I used at Honeywell's defence laboratory was FULLY ENCLOSED by a clear plastic box with a door in it. The box protected the scale from air movements, and the door allowed access to put in and then later remove the item being weighed. The scale was also on a CONCRETE table platform to ENSURE no vibration. The weighing process was:
- Turn the power on the scale "on" at least several minuted before use, to allow the electornics to thermally stabilize
- Check that the scale is properly "zeroed" before doing ANY weighing, by using provided known-to-be dead-accurate weights
- Open the door and insert the item to be weighed, using tweezers, being craeful to move slowly and not put excess pressure onto the weighing platform
- Close the door
- Wait several seconds for the air inside the clear box (which was moved by your opening the door, placing the item, and closing the door) to stop moving
- Note the stabilized weight reading and the number of decimal places displayed
Noting all of the above, how good is YOUR weighing environment?
Which leads back to more questions:
Just how much precision does YOUR shooting type require?
Are your skill sets good enough, or are you at least trying to make them good enough, to merit the rather extreme cost, complexity, and time associated with getting truly precise results?
Jim G