Jim wrote:
Another explanation is that the spin has two effects. First it concentrates the shot towards the outer edge of the pattern 'overkilling' those caught by the edge of the pattern and leaving few shot in the middle of the pattern. Second, is that the spin made the angle of divergence higher so that the shot spread out faster. It is important to remember that there were only 27 shot in a canister round in 1863. While the individual shot would carry to beyond 500 yards, at that range, the pattern was so wide that perhaps only a few shot would pass through the frontage occupied by marching soldiers.
I spent a lot of time doing numerical modeling of this issue and have the spreadsheets to prove it. The one missing item is hard data on the angle of divergence. I would pay cash for an artillery reenactor unit to fire an 1863 grade canister round at a large target at 200 yards from a 12 lb Napoleon and from a 3 in Ordnance rifle. This would provide the hard data needed to make the modeling really accurate.
-Jim
From John Gibbon's Artillery Manual
Grape and Canister shot leave the piece diverging from each other, in the form of a cone, the greater part of the balls being in the centre, and the extreme ones separating about one-tenth of the range. When fired at too short a distance, the balls occupy too small a space to produce the proper effect; and at too great a distance they diverge too much, and strike on too extended a surface. Good results can be obtained at from 300 to 600 yards, but the maximum effect is produced at from 300 to 450 yards. When firing at very short distances over hard, dry ground, a suitable dispersion of the balls may be produced by firing very low, and allowing the balls to ricochet.
The range and effect of grape-shot become greater, at ordinary distances, as the size of the balls is increased. For this reason, the grape from 12-pdr. guns and 32-pdr. howitzers, is more effective than that from 6-pdr. guns and 12 or 24-pdr. howitzers, and the 6-pdr. Grape is no longer used in the United States.*
* Grape-shot is now no longer used with any of our field-pieces.
If the balls ricochet over-hard, dry ground, grape-shot may be effective up to 800 yards, and the pointing is of but little importance; but with broken or soft ground, ricocheting cannot be depended on, and the angle of elevation should be regulated with care.
To ascertain the distance by the report of firearms, multiply the number of seconds which elapse between seeing the flash and hearing the report by 1,100; the product will be nearly the distance in feet.
http://www.usregulars.com/gibbons/gibbons_intro.htm