if the bare main contact conductors a a hoist are 21 meters long and do not have intermediate supports , the smallest copper wire that may be used for the conductors is

To determine the smallest copper wire that can be used for the conductors of a hoist, we need to consider the electrical current-carrying capacity, mechanical strength, and voltage drop requirements.

First, we need to determine the current-carrying capacity of the wire. This depends on the expected maximum current that will flow through the conductors. The current-carrying capacity of a wire is usually specified in terms of its ampacity. You can consult the National Electrical Code (NEC) or other relevant standards to find the ampacity for copper wires of different sizes.

Next, we need to consider the mechanical strength of the wire. Since the conductors are 21 meters long and do not have intermediate supports, the wire should be able to withstand the weight of its own length without sagging excessively. This is important to ensure the integrity and safety of the hoist system. You can refer to wire manufacturer specifications or engineering handbooks to determine the mechanical strength of different wire sizes.

Lastly, we need to consider voltage drop requirements. In electrical systems, the voltage drop along the conductors should be within acceptable limits to ensure proper operation of the equipment. The voltage drop depends on the current, length of the conductor, and the electrical resistance of the wire. Higher current and longer conductor lengths result in larger voltage drops. The acceptable voltage drop for a specific application can be obtained from engineering guidelines or equipment manufacturer recommendations.

Once you have the ampacity, mechanical strength, and acceptable voltage drop requirements, you can compare them to the specifications of different wire sizes. Choose the smallest copper wire size that meets all the criteria mentioned above. It is recommended to consult with a qualified electrical engineer or an expert familiar with hoist systems to determine the appropriate wire size for your specific application.