You would think that would be the worst possible case, because the barrel is the furthest from its position at rest.... but in fact it is pausing at that moment, because is it reversing direction.... In the second chart (a detailed view of the last peak in Chart 1), each dot represents the time the pellet arrives at the muzzle, with a dot every 10 fps from 800 to 1000 fps.... 900 fps is at the peak, because I chose the vibration frequency to make it so.... You will note that there is hardly any difference in the angle the pellet leaves the barrel for quite a large ES either side of 900 fps.... That intuitively might tell you that is the optimum velocity for a barrel vibrating at this frequency.... However, that is incorrect also....
The next chart shows the POI of the pellet (I chose a BC of 0.036 to get these numbers at the various velocities).... If the gun is sighted in at 100 yards when the velocity is 900 fps, then at 800 fps it hits about 6.5" low, and at 1000 fps about 4.2" high.... At 800 fps, a 20 fps ES changes the POI about 1.5".... At 900 fps, it makes about a 1.0" difference.... and at 1000 fps, that 2% ES changes the POI only about 0.7"....
When you combine the flatter trajectory of faster shots with the angle of the muzzle at the instant the pellet leaves the barrel.... you get an interesting result, as shown below (gun again sighted in at 900 fps at 100 yds.).... The slower pellets (eg. @ 800 fps), arriving after the peak of the barrel vibration, shoot lower on the target.... but the faster (1000 fps) pellets, arriving when the barrel is still travelling upwards, ALSO shoot lower on the target.... This increases the vertical dispersion for pellets travelling slower, and decreases it for pellets travelling faster.... Now, for that same 20 fps ES, pellets at 800 fps have vertical stringing of 2.1" (instead of 1.5").... those at 900 fps are still about 1.0".... but pellets at 1000 fps, with that same 2% ES, only have a vertical stringing of less than 0.3" (instead of 0.7")....
It is important that you do not interpret this to mean that faster is always better.... The concept I want you to understand is that by using a movable weight (or changing a weight) attached to the muzzle, you can change the frequency at which the barrel vibrates.... If you want to shoot at 900 fps, then you want the barrel to be on the upswing, but nearing the top of it's movement, when the slowest pellet arrives at the muzzle.... This adjustment is arrived at by trial and error, but can reduce the vertical dispersion of your groups once you find it....
Think about it this way.... The slowest pellet in your shot string arrives at the muzzle when the barrel is nearing the highest point on the swing, but still on the way up.... It is launched on a higher angle, but going slower, drops more.... Conversely, the fastest pellet arrives earlier in the vibration cycle, when the barrel isn't pointing quite as high, but going faster, drops less.... The combination of these factors can reduce the vertical stringing of the shots when they impact a target downrange.... I hope this explanation helps you understand the merits of tuning the harmonics of your barrel for the velocity you are using....
Bob
