Volume Ten - Pre-Victorian to the present day - even more aspects - The Patent for the Penarth Slipway - 1881 . . .

The stress required for hauling up a vessel varies very much according to the efficiency of the ways. If everything was rigid it would be found by the following formula :
where S is the total pull on the links, w the weight, w1 that of the cradle, and w11 that of the links, all in tons, theta the angle made by the rails with the horizontal, r the radius of the rollers, r1 the radius of the roller-axle, f the coefficient of friction between the axle and its bearing, and f1, that between the links and the rails. The total pull to be provided in the haling cylinders, supporting the Author's gear to be used, would be this quantity S, added to the total pressure on the returning ram, and what is required to over come the friction of the hydraulic apparatus.

In practice the values of f and f1 are difficult to determine, and varying according to the state of lubrication, and as there is besides another unknown element in the shape of an extra pull to over come the effects produced by deflection of the ways, it is usual to estimate the hauling power in a much more empirical manner. The following rule, constructed from actual observations, is fairly accurate for ways of an inclination of about 1 in 20 :

s being the total pressure on the returning ram. For other inclinations some allowance must be made on one side or the other, but as the friction due to the weight of the vessel and cradle and of the hauling gear does not vary with change in gradient, the total pull is not as a rule subject to great alteration for a given size of vessel.

The time occupied in placing a vessel upon a cradle may be taken at about one hour, while the hauling up as a rule will occupy two hours, but this of course will vary according to the system employed, the length of way, and the engine power at disposal.