If a gearless machine's drive sheave has a circumference of six feet, how many RPMs would be required to run the car at 800 fpm?

To determine the required revolutions per minute (RPM) for a gearless machine's drive sheave when the elevator car needs to travel at a speed of 800 feet per minute (fpm), we can use the relationship between the drive sheave's circumference and the travel speed of the elevator.

Here's how the calculation works:

1. The drive sheave has a circumference of six feet, which means that for each full revolution (one complete turn) of the sheave, the elevator car travels six feet vertically.

2. To find out how many revolutions are needed to achieve a speed of 800 fpm, we need to divide the desired speed by the distance traveled in one revolution of the drive sheave. This can be expressed mathematically as follows:

[

\text{Revolutions per minute} = \frac{\text{Desired speed (fpm)}}{\text{Circumference (ft)}} \cdot 60

]

By substituting in the values we have:

[

\text{RPM} = \frac{800 \text{ fpm}}{6 \text{ ft}} \cdot 60

]

3. First, calculate the number