Kicking and dropping cars are names for switching maneuvers where railroad cars are cut off from the train while in motion to make spotting cars more efficient for the crew. There were significant safety concerns about both practices, though to be honest more concern about dropping than kicking) back in the days when switch crews consisted of four or five men, most of whom had year of prior on the job training, and they are (in my opinion) entirely unsafe with a two or three man crew, though they might still be used in certain yard switching operations.
Kicking cars occurs when a locomotive has several cars to switch into several tracks; the cars being switched have neither air- nor handbrakes applied. A member of the crew out near the switch is ready to throw the switch, another member of the crew will pull the pin. Upon the signal from the foreman, the engineer will accelerate to about 4 or 5 miles per hour, pushing towards the desired siding. The member of the crew that is to pull the pin, uncoupling the cars as they go by, and the engineer immediately applies the brakes. This allows the uncoupled cars to roll on along into the siding, coming to a stop at some point, perhaps near any cars already in the siding. If there are no cars in the siding, nor a skate to stop the movement, sometimes a crew member will ride the cars, and apply the handbrakes as they roll bringing the car to a stop. The engineer then reverses, pulling back and the process is repeated to put the next car or cars into a different track. There are safety concerns with this maneuver; a crewmember riding a car can fall off; the brakes may not be working properly so the cars roll out the other end, the man throwing the switch may not get it at quite the right time, and the man pulling the pin may miss, or slip and fall.
This is a much more hazardous maneuver out in the field, where if cars are kicked into a siding too hard, they may roll off the end of the track and derail, or even roll into the street and cause a major traffic hazard. And if the car does not stop at the right place in a spur, the locomotive has to go into the siding to respot it. Finally, the maneuver is impossible to execute without three crew members plus the engineer.
Dropping cars, like kicking them, is also a maneuver where a car is cut off on the fly, except in this case the car is to be spotted into a facing point spur. Again, the car is coupled to the locomotive, there is a member on the ground to throw the switch, another to pull the pin (usually riding on the locomotive, and a member to ride the car. The locomotive pulling the car starts from down the track a distance pulling the car to be dropped, and accelerates. At the desired point, the member pulling the pin will uncouple the locomotive from the car, at which point the locomotive will accelerate away from the car. After the locomotive crosses the switch, the member making the switch will throw it to divert the care into the siding, while the member on the car sets the handbrakes. hopefully stopping the car at the desired location for unloading. Dropping a car is a potentially much more dangerous maneuver than kicking, and has long been officially against the operating rules of every railroad whose operating rules or special instructions I have examined. In practice, though, it was tolerated if the crew managed to get the car to the right spot without incident. Again, due to the number of crew members required to perform the maneuver, it has been years since I have seen a railroad with enough people on a switch crew to execute the maneuver. Another thing to keep in mind about dropping and kicking cars: these maneuvers were standard (if discouraged) practice in years when the average weight of a loaded car was significantly less than it is today. It's easier for a crew member to apply brakes effectively on a loaded car that weighs 80,000 pounds (in total), than one which weighs 283,000 pounds.
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