17. If the moment of the load against the engine at the beginning of the hoist is to equal that at the end of the hoist, it is possible to determine what relative diameters of drum will produce such an effect, as follows:
| Let | Wₘ | = | weight of material hoisted; |
| Wₖ | = | weight of cage and car; | |
| Wᵣ | = | weight of rope; | |
| R | = | large radius of drum; | |
| r | = | small radius of drum. |
The load moment may be calculated by including friction as ⅒ of the total weight hoisted, except the weight of the rope, as shown in [Art. 14]; or the friction may be disregarded without serious error. Then, under the conditions shown in [Fig. 9 (a)], and disregarding friction,
Load moment = (Wₘ + Wₖ + Wᵣ)r - WₖR (1)
and under the conditions shown in [Fig. 9(b)],
Load moment = (Wₘ + Wₖ)R - (Wₖ + Wᵣ)r (2)
Placing formula 1 = formula 2,
(Wₘ + Wₖ)R - (Wₖ + Wᵣ)r
= (Wₘ + Wₖ + Wᵣ)r - WₖR,
and
| (Wₘ + 2Wₖ + 2Wᵣ) | ||
| R = | r ———————— | (3) |
| (Wₘ + 2Wₖ) |