LAUNCHING OF SHIPS IN RESTRICTED WATERS. 209 



reduce and regulate this velocity to correspond with what may be reasonably ex- 

 pected on the day of the launch. A short length of cord is attached to the model 

 and drawn through an improvised friction brake, the length of cord being varied 

 to suit the final launching velocity required. As the effect of this retardation is 

 only to reduce the initial velocity, and as this action ceases long before the brakes 

 are applied, it need not be considered except when determining the shape of the 

 entire velocity curve. The final speed (when entering the water) may be varied in 

 this way from 12 feet to 24 feet per second. 



The chronograph is so proportioned that each of the intervals between record 

 marks represents about 19.2 feet travel of the vessel. A specimen record is shown 

 on Plate 92. For the sake of convenience, all units, unless otherwise noted, will here- 

 after be expressed in proper terms for the full-sized vessel. All calculations and 

 curves have been worked up on this basis, as the work is then more easily followed 

 by all concerned. 



The length ratio, L, as noted above, is 96. 



The displacement ratio is therefore U = 884,736. For a weight of ship and 

 cradle of 16,000 tons, this corresponds to a model weight of 40.52 pounds. 



The ratio of cable pull on the model and brake pull on the ship is also L^ or 

 884,736. (From the theory of mechanical similitude, where / X -J = 3^ m^/^) 



A pull of 500,000 pounds on the ship is equivalent to a pull on the model cable 

 of 9.042 ounces, which, in turn, is represented by an ordinate of 0.81 inch on the 

 recording paper. The model brake is capable of exerting a total relative pull of 

 about 900,000 pounds, or some 400 tons. 



The brake mechanism has been calibrated with extreme care, using a specially 

 constructed and calibrated spring to exert a tension upon the cable in its normal di- 

 rection, with the brakes set and the recording mechanism in operation. After re- 

 peated measurements of the resistance, due to the rotation of the drum, the rota- 

 tion of the idler pulley and the friction of the pencils on the trimming masts, it has 

 been assumed that this resistance may be neglected, as being within the limits of 

 accuracy of the observations as a whole. 



In order that the traces of the bow and stern may be correct in shape, it is 

 necessary that the moment of inertia of the model about a transverse horizontal 

 axis through its center of gravity should bear the proper relation to that of the large 

 vessel; that is, K, the radius of gyration, should vary as L. To this end, the model 

 is suspended by two cords of known length equidistant from the center of gravity, 

 and K determined in the usual manner. The inside lead ballast weights are then 

 placed in such position as to fulfil the required conditions. It is understood, of 

 course, that K for the large vessel must be found by more or less approximate 

 methods. The pivoting point, the drop of the bow, the clearance of bow and stern, 

 the final trim afloat and the position of the model when it comes to rest are easily 

 obtained from the record of the trimming masts. The time and point of application 

 of the brakes are indicated on the recording strip as shown on the plan. 



For purposes of illustration, there is shown a complete set of curves and data 



