210 LAUNCHING OF SHIPS IN RESTRICTED WATERS. 



obtained from a set of runs with the model. To facilitate the transfer of all data 

 from the model record to these curves, a set of nomographs has been prepared, giv- 

 ing rapid solutions of about six of the principal equations. The velocity-distance 

 curve. Run No. 119, and the velocity-distance curve. Run No. 121, are drawn di- 

 rectly from the chronograph record. The time-distance curve. Run No. 1 19, has 

 been plotted as a convenience in checking from the curves of the Cuyama. The 

 curve of brake pull. Run No. 119, is taken directly from the diagram on the record 

 sheet, and the traces of bow and stern pencils from the vertical board shown in the 

 photographs. The contour of bow and stern have been added to make the diagram 

 more complete. 



In the figures presented by Mr. Hiley in his paper on the launching brake, the 

 water resistance is assumed to absorb about 20 per cent of the total energy of the 

 vessel. This figure is necessarily quite approximate, for reasons stated at the be- 

 ginning of this paper, and an attempt has been made at this point to arrive at a 

 more definite value of this quantity. As is well known, the water resistance of the 

 vessel during launching can be represented by the equation i?w = K2V^, provided 

 the cradle and other fittings are of such shape as to produce wave-making resist- 

 ance only. This is not exactly the case, however, as the skin friction resistance is 

 a considerable portion of the whole ; the water resistance is best represented, there- 

 fore, by a simple equation of the form Rv = K^V^. Although this equation, as it 

 stands, does not conform exactly to the theory of mechanical similitude, it is used 

 here as a means of simplifying the work. To translate model resistances into ship 

 resistances would require an excessive amount of work, if this operation were to 

 be carried out exactly as is done at the Model Basin. 



By substitution and integration of the equation i?w = K^V^, we find that the 



velocity-distance curve is represented by the following equation, V — — —^ 



Where V is the velocity and vS" the distance run, measured from a certain origin, 

 Ki and Kz are constants. The value of K2 for this hyperbolic curve may be found 

 by solving two simultaneous equations representing two points on the velocity curve 

 where the vessel is clear of the ways and running freely. 



The curve of velocity thus obtained is only approximate, but it agrees closely 

 with the curve as actually recorded, and it forms a very convenient means of com- 

 puting the water resistance during the period when the ship is being brought to 

 rest by the brakes. For instance, two points on the curve of Run No. 121 are taken 

 at 19 feet per second and 14 feet per second; the two equations are then VS = 

 K, = 13,085, and i?w = K2V' = 81.64 V\ 



The first equation indicates that the ship, leaving the ways as on Run No. 121, 

 and neglecting the effects of wind and tide, would still have a velocity of i foot 

 per second at a distance of 2j4 miles. 



The second equation enables us to plot the curve of water resistance as shown 

 on the plan, taking values of velocity, of course, from the curve of Run No. 119. 

 When integrated, the curves give the following results : — 



