If the crane is waiting on the hopper level to fall, then that is time the barge and tug boats have to wait. I want the level and VFD on the feeder to maintain a constant level in the hopper so the crane can continously unload barges.
When the radar level detector sees ANY increase in level (it doesn't matter how much - we know it will be about 16 yards), immediately jack the VFD to max speed (120 Hz on many drives, or whatever the belt can stand), run at max until a variable (XX%) hopper level, then reduce speed to about 10 Hz, or whatever minimum speed you can run without overheating the motor).
As an old TVA power engineer, for clamshell barge unloading, the real unloading time depends on many variables, so the average time is not very useful. Unloading cycle time depends on at least all of these things: (1)the skill and experience level of the crane operator; (2)how far into the barge the unloading has progressed (the horizontal distance from the crane to the part of the barge that is being unloaded); (3) the vertical distance from the barge to the unloading point (this varies from 0 to 40+ feet on the Mississippi River). It is not the "average unloading time" that is critical, but the shortest unloading time. When the operator first starts on a new barge, and the river is at high water level, and the operator is an old skilled hand, then the unloading time will be the shortest possible, and that is for what the drive speed switch point should FIRST be set. We want the operator to be able to unload rapidly when the crane cycle time is at the shortest path (the coal is closet to the crane). As the unload time becomes longer, the hopper will reach a lower level between dumps, but that is more efficent than having the crane operator wait on emptying the hopper. But at the same time, we do not want the hopper to empty out completely (to prevent overloading the belt on the next dump).
To prevent the hopper emptying completely as the cycle time increases, the VFD speed switch point from Max to Min must be a variable based on the present changing and MEASURED dump cycle time. This measured time will take into account all the above variables.
We have the radar detector that will allow starting a PLC timer that measures the time between dumps (time between max increase in hopper levels). As this time becomes longer, the VFD speed switch point should be moved to a higher hopper level. The scaling equation between dump cycle time and VFD speed switch point can be determined by trial-running the system with max and min hopper level speed switch points.
EDIT: Thinking back 30 years ago, most barge unloading systems could not reach the entire 80' barge. The operation had to halt while the barge was re-positioned using cable winches. In which case, the PLC will need a routine that detects a long pause between buckets and resets the VFD speed switch point to the default (beginning) level.