Describe the role of the diverting sheave in a roped hydraulic elevator system.

In a roped hydraulic elevator system, the diverting sheave plays a crucial role in redirecting the hoisting ropes to achieve a desired travel distance and mechanical advantage. Unlike direct-acting hydraulic elevators where the cylinder is directly connected to the elevator car, roped hydraulic elevators use a system of ropes and sheaves to multiply the travel distance. A diverting sheave is a pulley that changes the direction of a rope. In this system, the hydraulic cylinder moves a relatively short distance, and the ropes, running over the diverting sheave, translate that short movement into a longer movement of the elevator car. The diverting sheave is typically located at the top of the hoistway, and the hoisting ropes run from the elevator car, over the diverting sheave, and then down to the hydraulic cylinder. As the cylinder extends, it pulls on the ropes, causing the elevator car to rise. The amount of travel multiplication depends on the roping configuration. For example, a 2:1 roping configuration means that for every one foot the cylinder extends, the elevator car travels two feet. This is achieved by using a diverting sheave and anchoring one end of the rope to the top of the hoistway and the other end to the cylinder. The diverting sheave allows the elevator car to travel twice the distance of the cylinder's stroke. The diverting sheave also helps to reduce the required cylinder stroke length. Without the diverting sheave, the cylinder would need to be as long as the elevator's total travel distance, which would be impractical for taller buildings. The use of a diverting sheave allows for a shorter, more manageable cylinder length. Furthermore, the diverting sheave contributes to the mechanical advantage of the system. By using a roped system, the force required from the hydraulic cylinder is reduced, allowing for a smaller and less expensive hydraulic power unit.