338 LOGARITHMIC SPEED-POWER DIAGRAM. 



lines to coincide. If the comparison is to be on the length basis, the shifting 

 lines and length lines are brought together. 



Each model should be adequately described on the sheet bearing its 

 power curve. In the illustrations are given the block coefficient, prismatic 

 coefficient, ratios of beam to draught and length to beam and the displace- 

 ment length coefficient, which may be described as the displacement in tons 

 of a model of the ship loo feet in length. Other means of describing the 

 model, such as a reproduction to some standardized scale of the curves of 

 immersed areas and water-line, may be used. 



It is to be noted, as shown in the appendix, that errors involved in this 

 method are small provided the ratio of reduction is not large. If the curve 

 is correct for a boat 200 feet long the curve may be used for boats from 50 to 

 800 feet in length with close approximation. Reduction directly, however, 

 from a model 15 feet long to a boat 600 feet in length would incur consider- 

 able error. It is then advisable to draw for the model the curve of residual 

 horse-power, using for a shifting line V, and reduce this to a full-sized boat; 

 and by separate calculation or curves to reduce the frictional power, then 

 add the two after reductions so as to construct the effective horse-power 

 curve of the full-sized ship. 



Once this curve is constructed for a large vessel, the error of conversion 

 from one size to another will be small. 



The screw propeller also yields readily to analysis by means of this 

 diagram, illustrated by Fig. 8, Plate 136. For this purpose the line marked 

 V^ on Fig. I, Plate 129, should be used as shifting line. Probably this is not 

 absolutely correct, but it is customary in propeller calculations to assume 

 that the power ratio of two similar propellers at equal slip is as the ratio of 

 the diameters with an exponent of ^ when the relative speeds of advance are 

 as the square root of the diameter. This would theoretically be exact if it 

 were not for friction, which, as in the case of the ship, does not follow the laws 

 of comparison. In this case, however, surface friction is a much smaller 

 fraction of the total power, and the assumption of the exact exponent prob- 

 ably is as well as can be done at the present time. 



On the power sheet for the propeller (Fig. 8, Plate 136), in addition to 

 the shifting line, are shown lines for diameter and pitch, which are read by 

 means of Fig. i, Plate 129, at the intersection of these lines respectively with 

 the length line, F^ of Fig. i, Plate 129. The projected area (or developed 

 area if known) is represented by another line which is read at its intersection 

 with the surface line, V^, of Fig. i, Plate 129. 



In the case of the propeller whose characteristics are represented on 

 Fig. 8, Plate 136, the experiments in the model tank (described in Professor 



