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Joined: Nov 2005
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Sidelock
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Sidelock
Joined: Nov 2005
Posts: 4,598 |
Don, If there was no wad, I would agree with your math. But the pellets exit together. If you look at the photography, They do not begin to separate until nearly 6" from the muzzle. At 12" the column is deformed. Add in the fact that some pellets are compressed, thus deforming them and changing their co-efficient. The wad, hardness of the shot and any buffering material all play a role. Given that, I believe that a mathematically pristine Rayleigh distribution is impacted. The theory at least assumes all components of the distribution to be equal. In practice an allowance is always made for reality. The pellets do not impact the plane of the target simultaneously. Not just because of the length of the column, but also because of minor variations in velocity and ballistic co-efficient. This becomes obvious to the shotgunner at the patterning board.  Pete
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Joined: Feb 2003
Posts: 4,035 Likes: 47
Sidelock
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Sidelock
Joined: Feb 2003
Posts: 4,035 Likes: 47 |
It's less. He used 'worst case'.
"The price of good shotgunnery is constant practice" - Fred Kimble
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Joined: Feb 2003
Posts: 4,035 Likes: 47
Sidelock
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Sidelock
Joined: Feb 2003
Posts: 4,035 Likes: 47 |
Pete, you've restated the reason for the shotstring having appreciable length in the first place. Other than choke effect, the factors you name cause the string to lengthen and thus cause difference in time of flight of the individual pellets. Explain how that changes the statistical distibution.
"The price of good shotgunnery is constant practice" - Fred Kimble
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Joined: Jan 2006
Posts: 15,456 Likes: 86
Sidelock
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Sidelock
Joined: Jan 2006
Posts: 15,456 Likes: 86 |
Rocketman - your calcs were run at ten yds. The angular displacement of the target at 50yds at the same speed is not the same.
HTH
Dr.WtS Not much string'n going on at the muzzle or 10 yards.
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Joined: Jan 2002
Posts: 5,954 Likes: 12
Sidelock
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Sidelock
Joined: Jan 2002
Posts: 5,954 Likes: 12 |
Wonker - righteio, old chap, it isn't. Isn't 'tall. So, lets us do 'z mathematikz. Circumference of 50 yard radius = 2 pi X 150 feet = 943 feet. 943 feet / 100 feet per second = 9.43 seconds. 360 degrees / 9.43 seconds = 38 degrees per second. 38 degrees per second X 0.00007 seconds = 0.0027 degrees = 0.16 Minutes Of Angle (MOA). So, the shot string would be bent by 0.08 inches at 50 yards.
Fast and close is worst case for angular velocity of the shotgun and high angular velocity is what is required to bend the shot string.
Questions?
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Joined: Jan 2006
Posts: 15,456 Likes: 86
Sidelock
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Sidelock
Joined: Jan 2006
Posts: 15,456 Likes: 86 |
So what yer saying is....the longer the shot column is in a loaded shell the longer the shot string'n effect is at longer distances.
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Joined: Jan 2002
Posts: 5,954 Likes: 12
Sidelock
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Sidelock
Joined: Jan 2002
Posts: 5,954 Likes: 12 |
Don, If there was no wad, I would agree with your math. But the pellets exit together. The Rayleigh distribution is not dependent on separate exit. It has been proven to describe single exit (rifle, artillery, arrows, etc.) and multiple exit (sticks of bombs, shotguns, etc.) equally well.If you look at the photography, They do not begin to separate until nearly 6" from the muzzle. At 12" the column is deformed. The centers of impact relative to the aiming point of multiple patterns will be described by a Rayleigh distribution. The distribution of shot, assuming the pellets separate, relative to the center of impact of each pattern will also be described by a Rayleigh distribution in the radial direction.Add in the fact that some pellets are compressed, thus deforming them and changing their co-efficient. The wad, hardness of the shot and any buffering material all play a role. Given that, I believe that a mathematically pristine Rayleigh distribution is impacted. The theory at least assumes all components of the distribution to be equal. In practice an allowance is always made for reality. Disagree. The Rayleigh distribution assumes that there are differences and tells you how, on average, those differences will influence the point of impact relative to center of impact. This is the same principle as describing the tallness of humans via a normal distribution.The pellets do not impact the plane of the target simultaneously. Not just because of the length of the column, but also because of minor variations in velocity and ballistic co-efficient. This becomes obvious to the shotgunner at the patterning board. True, and, along with the exacting pressures on the pellet at time of separation which determine the pellets initial departure velocity and direction, determine where, relative to the other pellets the individual pellet will impact.On average, the radial direction distribution of pellets will approximate a Rayleigh distribution and the circumferential distribution should be even (same number of pellets per segment of a "washer").Pete
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Joined: Feb 2003
Posts: 4,035 Likes: 47
Sidelock
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Sidelock
Joined: Feb 2003
Posts: 4,035 Likes: 47 |
That's not what Rocket is investigating. He's putting math to the concept of latteral dispersion caused by angular motion of the gun ("swing"). This is to explain the reason it's not a factor in shotstringing rather than just shouting down people as idiots for even mentioning it. Seems he's done that, and the issue is certainly settled now.
"The price of good shotgunnery is constant practice" - Fred Kimble
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Joined: Apr 2010
Posts: 41
Sidelock
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Sidelock
Joined: Apr 2010
Posts: 41 |
If you take a tripod photo (single vector) of a moving car with a very slow shutter speed and look at the result, you're left with the impression that the moving object (car or shot string on a towed patterning board a la Brister) is "longer" than it really is. The 12 foot long imprint on the moving board is an artifact of a combination of lateral travel of the board and variations in arrival time among the different pellets. So you get what appears to be a "sling effect", even though all of the pellets are exiting the rt. barrel of the 1892 H & H along essentially the same vector because of the fantastically small elapsed time interval?
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Joined: Feb 2003
Posts: 4,035 Likes: 47
Sidelock
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Sidelock
Joined: Feb 2003
Posts: 4,035 Likes: 47 |
The observed elongated pattern is not caused by gun movement.
It's caused by the fact that during the passage of the shot cloud (it has length as well as width) the target moves.
Think of Brister's elongated patterns as a photo from the target's perspective.
"The price of good shotgunnery is constant practice" - Fred Kimble
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