What is the primary mechanical advantage gained by using a 2:1 roping configuration in a traction elevator?

The primary mechanical advantage of a 2:1 roping configuration in a traction elevator is that it halves the force required from the elevator machine (motor and drive system) to lift the elevator car and its rated load. A 2:1 roping configuration means that the hoisting ropes are arranged so that they pass over sheaves (pulleys) both at the top of the hoistway and underneath the elevator car. The rope is anchored at the top of the hoistway, runs down to a sheave on the car, then back up to another sheave at the top, and finally connects to the counterweight. Because the ropes support the car in two places, the tension in each rope is only half of the total weight of the car and its load. While the required force is halved, the distance the rope must travel to move the car a certain distance is doubled. For example, to lift the car one foot, the machine must pull two feet of rope. This trade-off between force and distance allows for the use of a smaller, less powerful, and therefore less expensive machine. The 2:1 roping configuration is commonly used in mid-rise buildings where the reduced machine size offers a significant cost benefit, and the doubled rope travel distance is not a major drawback. In contrast, a 1:1 roping configuration, where the ropes are directly attached to the car and the counterweight, requires the machine to exert the full force of the car and its load but provides a 1:1 relationship between rope travel and car movement. The 2:1 configuration is a trade-off to reduce the size of the required machine, at the expense of increased rope travel.