Any cone of objects following a ballistic trajectory, including a cone of objects of uniform weight and shape, will strike the ground in an oval pattern.
Assume the cone of objects follows a path parallel to the ground. Also assume that the bottom edge of the cone intersects the ground at some distance from the point of origin. Also assume that the gound is perfectly flat.
The cone itself will be deformed over time by the force of gravity acting on the objects and by friction of the air reducing forward velocity. In other words, all objects will fall to the ground sooner or later.
Now consider a vertical slice through the cone at the centre of the cone. The bottom of this slice will include the objects that will strike the ground first since their trajectory is already tending down and is doing so at a steeper slope than any other objects in the cone. The top of the slice would be the trajectory of the objects with the greatest vertical component in their vector - if there was no gravity and no friction from air. These objects will travel the furthest. The distance between first and last strike is a function of the standard ballistic equations, with initial angle of departure being the critical factor. The distance from first strike to last strike would be substantial at ranges considered appropriate for cannister. So that establishes the length of the beaten zone.
The width of the beaten zone can be determined by establishing the spread of the cone of objects. The maximum width is at the distance at which the widest horizontal slice of the cone intersects the ground. This point can be calculated using standard ballistic calculations and should be approximated by using the elevation of the piece as the angle of departure. After that distance, there are fewer and fewer objects still in the air, and they are the ones on the uppermost portion of the cone, so they are close to the middle of the cone and at the top.
You can simulate the beaten zone with a flashlight to a certain extent. If you aim it at a vertical surface like a wall, you see a circular pattern where the light hits. If you hold it parallel with a flat surface, you will see light deposited as a long streak. that continues to expand until it is so disipated that you can no longer see it. Light is not affected by gravity in such short distances, and consequently the light hitting the surface is an expanding cone. Now try a hose with a spray nozzle. Gravity does work on the water and you will see an oval pattern if the force aplied to the water is significantly greater than the force of gravity. You may need to use a fire hose for that.
Remember that the beaten zone is the pattern of deposition on the ground. If you were to set up a vertical target, the area impacted would be more circular until the target was beyond first strike. At ranges beyond that, the area would look like the setting sun as the range is increased.
I think a lot of the experiments of the day were on single targets that were vertical, simulating infantry standing in line. For a linear target, the beaten zone is irrelevant. However, if the target were a column or square, the beaten zone is of great interest. I am not at all sure that these concepts would be recognized by soldiers of the day. They are critical to the efficient use of many weapons today, but much of the theory was driven by learning how to use the machine gun to full effect.
Can anyone identify any experiments that assessed the effectiveness of cannister through the depth of a target? Or, are all the experiments only looking at impact in the vertical plane at the front face of the target.