Neglecting the impact of fleet angle on the length of the rope, the minimum length, in m, of new winding rope is _____ (round off up to 2 decimals).

Steps to Solve

1. Calculate the Effective Distance From the Pulley to Bottom Landing

The total vertical distance is calculated by adding the height from the pulley to the bottom landing (215 m) and the distance from the drum to the pulley (which is half the drum diameter, i.e., $0.6 , m$):

[ \text{Height to bottom landing} = 215 , m + 0.6 , m = 215.6 , m ]

2. Account for Rope Length Needs During Operation

The maximum life allows for 2 full wraps of rope on the drum plus the height of the anchorage rope (1 m). Thus, the required rope length would be calculated as follows:

The rope wraps around the drum, and the total length removed due to recapping is included.

[ \text{Total rope length} = \text{Height to bottom landing} + \text{windings} \times \text{circumference of the drum} ]

The circumference of the drum is given by:

[ \text{Circumference} = \pi \cdot \text{diameter} = \pi \cdot 1.2 , m \approx 3.7699 , m ]

The total wraps needed is 2 wraps:

[ \text{Total length for wraps} = 2 \times 3.7699 , m \approx 7.5399 , m ]

3. Combine All Lengths for the Final Calculation

Now, sum the height to bottom landing with the added length for winding:

[ \text{Total rope length required} = 215.6 , m + 7.5399 , m + 1 , m ]

Calculating this gives:

[ \text{Total rope length required} \approx 224.1399 , m ]

4. Round to Two Decimal Places

Finally, we round the total length calculated:

[ \text{Rounded length} = 224.14 , m ]