Pouring Dynamics of the Dendritics Weighing Pan

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(August 1995)

As a stone or stones are poured from the weighing pan it is desirable that they exit the pan in a smooth, controllable stream.  It is also desirable that the stone or stones are deposited (typically in a stone paper or small zip lock bag) with a minimum momentum to prevent it/them from bouncing off the surface on which they are intended to be deposited.  Although seemingly simple, the orientation of the surfaces on the top side of the pan must combine to form a system that precisely controls the direction and momentum of the pouring stones.

If the pan is full or close to being full (covering nearly all the flat area and nearly all the vertical area) the pouring process will begin with stones rolling over each other starting at the side of the pan which is raised (the up hill side).  As these stones fall downward across the diameter of the pan the momentum will reach equilibrium. The stones will lose energy impacting other stones on their way down at the same rate the stones gain energy by falling.  Thus the speed of these initial stones is controlled by the degree to which the pan is tipped.

However, as the flow continues, the down hill side of the nearly vertical area becomes covered by stones.  The stones then begin exiting the pan by flowing over the edge of the pan.  As the flow reaches its maximum, the width of the flow is primarily limited by the steepness of the nearly vertical section.

Once the stones have left most of the flat area the critical dynamics of the pouring begins.  With a pan with a recessed base, stones have a tendency to remain in the base until they can clear the angled area adjacent to the base.  It is important that the stones in the base leave the angled area before the last stone leaves the nearly vertical area as the stones remaining in the nearly vertical area act to damp the momentum of the last stones falling from the base. This damping effect is lost if the angled area is too close to vertical (stones remain in the base too long) or if the nearly vertical area is too far from vertical (stones leave it too soon).

If the total mass of stones being weighed is small they will cover the base area at the edge of the angled area.  As the pan is tipped nothing will happen until the tipped angle exceeds the slope of the angled area by a margin.  The stones then slip very quickly down the nearly flat area and land at the nearly vertical area.  The slope of the nearly vertical area is critical at this point.  If the slope is too close to the horizontal the momentum of the stones will merely be redirected as they fly off into space following the angle of the nearly vertical area.  If the slope is too close to vertical the pan needs to be tipped well past 90 degrees in order to empty the remaining stones.  This is an awkward movement for the hand as well as an uncontrolled momentum for the stones.

The height of the nearly vertical area also has its limits.  If the height is too low and there is no break to contain the stones as they are poured into the pan.  In addition, the momentum of the stones will not be broken as the stones are poured out.  If the height is too high, the pan will suffer from the defects exhibited by pans used by competing scales such as:

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Stones are lost from view as they sit on the bottom of the pan.

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The pan has to be tipped at an angle which exceeds the nearly vertical area and the stones accelerate downward and out into space.

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The higher the vertical section, the faster the stones leave the pan and hit their intended destination and bounce uncontrolled

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The overall vertical compactness of the pan and consequently the overall compactness of the scale suffers.

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