Yoyo Drum Cable Payout
Notes & Use
Calculates the payout (in feet), and total number of wraps for a yoyo drum, with the following considerations…
- the yoyo drum must have a single line per groove,
- the calculation is a simplified method that divides the area of the usuable wraps by the cable diameter. This method is not exact, but is more than adequate for the purposes of stage machines; it estimates the area of the cable pack, and divides that quantity by the cable diameter. This method does not take into account any cable elongation.
Figure
Terms
$D_{id}$ = Smallest diameter of drum wrap (tread diameter), typically when the yoyo drum is empty. Does not include safety wraps, *inches*
$D_{od}$ = Outer diameter of drum, typically the diameter when the yoyo drum is full, *inches*
$d_{cable}$ = Cable diameter, *inches*
$w_{inner}$ = number of safety wraps on the Tread Diameter
$w_{outer}$ = number of safety wraps on the Outer Diameter. This ensures the cable will not over-fill the drum and spill over the cheekplates
$L = payout, the length of usable cable that will fit on the yoyo drum, feet
$w_{usable}$ = number of usable wraps, does not include safety wraps
Equations
Calculate the smallest diameter of the yoyo drum when the safety wraps are included…
$$ D_{Isafe} = D_{id} + 2 w_{inner} d_{cable} $$
Calculate the largest diameter of the yoyo drum when the safety wraps are included…
$$ D_{Osafe} = D_{od} - 2 w_{outer} d_{cable} $$
Return the payout… $$ L = \frac { \pi \left( \frac{ D_{Osafe}} {2} \right)^2 - \pi \left( \frac{ D_{Isafe}} {2} \right)^2 } {12 d_{cable}} $$
Return the number of wraps: $$ w_{usable} = \frac {D_{Osafe} - D_{Isafe}} {2 d_{cable}} $$