To move a cage and skip up and down by 500 m, the number of cable turns on the drum depends on the drum’s diameter.

1. Core idea and formula

Each turn of cable is one full wrap around the drum, so the length of cable per turn is the circumference of the drum:

length per turn=π×D\text{length per turn}=\pi \times Dlength per turn=π×D

where DDD is the drum diameter (in metres). Then:

number of turns=required cable lengthlength per turn=LπD\text{number of turns}=\frac{\text{required cable length}}{\text{length per turn}}=\frac{L}{\pi D}number of turns=length per turnrequired cable length​=πDL​

Here L=500L=500L=500 m (the vertical distance).

2. Step‑by‑step method

  1. Convert drum diameter to metres (if given in mm, divide by 1000).
  2. Calculate circumference: C=πDC=\pi DC=πD.
  3. Divide 500 m by that circumference.
  4. Round up to the next whole turn (you cannot have a fraction of a wrap in practice).

3. Worked examples for typical drum sizes

Below, “Turns for 500 m” is rounded up.

html

<table>
  <tr>
    <th>Drum diameter D (m)</th>
    <th>Circumference πD (m)</th>
    <th>Turns for 500 m</th>
  </tr>
  <tr>
    <td>1.0</td>
    <td>≈ 3.14</td>
    <td>≈ 159 turns</td>
  </tr>
  <tr>
    <td>2.0</td>
    <td>≈ 6.28</td>
    <td>≈ 80 turns</td>
  </tr>
  <tr>
    <td>3.0</td>
    <td>≈ 9.42</td>
    <td>≈ 54 turns</td>
  </tr>
</table>

If, for example, your drum diameter is 6 m (a number used in some textbook problems), then:

  • Circumference ≈ 3.14×6≈18.843.14\times 6\approx 18.843.14×6≈18.84 m
  • Turns ≈ 500/18.84≈26.5500/18.84\approx 26.5500/18.84≈26.5, so you would need 27 turns.

4. Practical notes (for a “cage and skip” in a shaft)

  • This calculation assumes all 500 m is wound on the drum barrel at a constant diameter.
  • In reality, additional safety length is added (for anchoring, terminations, and travel beyond nominal 500 m), and the effective diameter increases as cable builds up in layers.
  • For basic exam or classroom questions, they usually expect you to:
    • Use the bare drum diameter given in the problem statement.
    • Apply N=500/(πD)N=500/(\pi D)N=500/(πD).
    • Round up to the next whole number of turns.

If you share the exact drum diameter from your question, I can plug it in and give you the specific number of turns for that case.