September 14, 191 1] 



NATURE 



355 



is reached is 8-25° without and 6-6° with bilge-keels, while 

 that due to uniform rolling is 4-35° without and 4-24° 

 with. We see, therefore, the important part that the near 

 approach to synchronism plays in creating large angles of 

 roll and the value of bilge-keels in reducing the rolling in 

 conditions approaching synchronism. When on waves of 

 smaller period, when small angles of roll may be expected, 

 the bilge-keels give but small advantage. The assumption 

 in these cases is that the vessel starts from rest in the 

 upright in the mid-height of the wave, and that the 

 rolling is caused by the assumed uniform swell. The vessel 

 will go through the cyclic change already described and 

 will reach a maximum inclination of not more than double 

 that which she reaches when uniform rolling has set in. 



A later investigator, Colonel Russo, of the Italian Navy, 

 found by experiment that by varying the assumption as to 

 starting condition of the ship, by letting the wave-action 

 begin to operate first when the vessel is upright and at 

 rest on the crest of the wave, the maximum angle before 

 uniform rolling sets in can be more than four times that 

 due to uniform rolling if the time of the ship is greater 

 than that of the swell. There is an infinite number of 

 solutions of rolling amongst waves because there is an 

 infinite number of initial circumstances, but, whatever 

 these may be, the rolling in a uniform swell will always 

 soon degenerate into a series of uniform forced oscillations 

 in the wave-period. 



From this discovery of Colonel Russo's, we see that the 

 region of investigation of possible causes of upsetting is 

 removed from that of uniform rolling even in a non- 

 synchronous sea. The following table shows for the 

 Revenge with bilge-keels the variation in maximum angle 

 of inclination before and during uniform rolling in terms 

 of the period and length of the swell : — 



Period of swell in seconds... 8 10 12 13*3 15 17 19 



Length of swell in feet ... 328 512 73S 910 1153 14S1 1850 

 Maximum angle in degrees 



before uniform rolling ... 63 S'o 147 2i'4 17-1 13x1 no 

 Maximum angle in degress 



during uniform rolling ... 2'5 4 - 2 I2'6 21'4 15*4 1 1 -o 87 



The period of free rolling of the Revenge through small 

 angles for a double roll was about 16 seconds. The fore- 

 going shows that the maximum rolling (which occurs at 

 synchronism) took place at a period of swell of 13-3 seconds. 

 The period of roll was less at large than small oscillations. 

 The above figures are for waves varying from r ? r ih to T ,' T th 

 of their length in height. The length of wave which 

 corresponds to maximum inclination is 910 feet and height 

 is about one-fiftieth. The maximum wave-slope for such 

 waves is 3-6°. We are in the habit of dealing with waves 

 of one-twentieth of their length in height for strength 

 calculations. Observers have recorded waves in the open 

 ocean of 600 to 800 feet in length and of 30 to 45 feet in 

 height, so that we know that the slope of the waves 

 assumed by Colonel Russo is much less than may be 

 encountered at sea. A wave the length of which is twentv 

 times its height has a maximum slope of 9 . Records of 

 waves having a ratio of height to length of as great as 

 one-thirteenth have been published. The maximum slope 

 of wave corresponding to these proportions is 14 . If it is 

 admissible to take much larger angles of wave-slope we 

 may expect to get much larger angles of maximum in- 

 clination both before uniform rolling sets in and when it 

 does. In a case given by Mr. Froude in which the 

 maximum inclination in the Revenge before uniform 

 rolling was 12-0°, he showed by calculation that the 

 corresponding maximum wave-slope must have been 5-09°. 

 For 20 maximum inclination the wave-slope was 10-3°. 

 Both these cases were for periods of ship and wave of 

 16 and 13 seconds respectively. For similar periods of 

 16 and 14-6 seconds the wave-slope to produce 20 maximum 

 before uniform rolling is only 7 . These figures give some 

 idea of the effect of the wave-slope on the maximum 

 inclination. It is to be remembered that these are the 

 maximum angles obtained by Mr. Froude ; but if we take 

 Colonel Russo's maximum angles, which in some cases 

 are double those obtained by Mr. Froude, it is easv to see 

 that large wave-slopes may produce very large angles of 

 roll. 



NO. 



2185, VOL. 87] 



Summarising, we see that : — 



(1) With wave-slopes of 3-6° the angles of maximum roll 

 obtained by them in the Revenge with bilge-keels may be 

 taken at 22 . 



(2) This roll takes place when synchronism exists between 

 the wave and the ship, when the wave is 910 feet long 

 and iSJ feet high and has a wave-slope of 3-6°. 



(3) Waves exist which are of this length, but which 

 may have a height of 50 feet, and possibly more, and a 

 wave-slope of io°. 



(4) In such steeper waves we should expect to get much 

 larger angles of roll. 



(5) Each ship has peculiarities of rolling due to its form 

 as well as to its lading and bilge-keels, &c. 



(6) These peculiarities and the effect they have upon 

 rolling, and the effect different waves will have upon the 

 rolling of the ship, can best be studied experimentally. 



It was my intention when you appointed me as your 

 President to have placed before you the results of an experi- 

 mental study made on lines somewhat similar to those 

 carried out by_ Colonel Russo, but extended to a wide range 

 of types of ship, waves, and resistance. 

 _ The machine for carrying out these experiments is prac- 

 tically complete, but having met with an accident at the 

 end of April last which incapacitated me for some time, I 

 was prevented from being able to do anything to this 

 subject since then. I am, therefore, obliged to ask you to 

 be content with the general risumi of the subject which 

 has been given. 



I think enough has been said to show what a field of 

 investigation is open to the experimenter. The little that 

 has been done and published by Colonel Russo is only for 

 three battleships of about the same size. For the great" 

 bulk of the ocean wayfarers nothing has been done. If Itr 

 is possible to determine the kind of rolling which is likely 

 to take place under stated conditions it seems to be' 

 desirable to do so. 



In all that has been said it will be seen that it is possible 

 to determine experimentally the kind of rolling which will 

 take place in a ship which is snug and seaworthy. But 

 it is also possible to study the effect of loose water in a 

 ship under the same set of conditions as to waves, lading, 

 and form of ship. This part of the subject has not 

 received any experimental treatment except in a very 

 limited number of full-sized ships. It is quite conceiv- 

 able that some conditions of loose water associated with 

 some conditions of sea may produce large angles of 

 inclination. 



The subject has been treated as one in which it is 

 probable that the kind of waves met with at sea will be 

 uniform in size and period. That this is not so is a fact 

 with which we are all more or less familiar. The effect 

 of a uniform system of waves is to rapidlv induce a con- 

 dition of uniform rolling. But any 'deviation from 

 uniformity of sea immediately introduces non-uniformity 

 of rolling, and generally greater extreme angles of roll. 

 Any experimental study of the action of waves upon a ship 

 must include a variation in the character of the waves. 

 The field of investigation is thereby widened and the 

 search for large angles of inclination made more laborious. 

 But the work is of a kind which can be done by many 

 people, and can be done fairly rapidlv, so that there seems 

 to be no insuperable objection to doing it. The details of 

 the apparatus need not be described, but the study of the 

 objects attained may be of interest. 



fi) Wave-motion is simulated bv the revolution about 

 parallel axes of two parallel cranks of different lengths. 

 The line joining the ends of the arms of the cranks is 

 always in the line of the norma! to the wave-surface, and 

 a line perpendicular to it is therefore parallel to the wave- 

 surface. 



(2) From the form of the ship are determined curves 

 which are the shape of rollers which roll on a straight 

 line parallel to the wave-surface. The form of these roliers 

 is such that the model of the ship in rolling maintains the 

 position in relation to the wave-surface (a) which cuts off 

 constant volume of displacement at any angle of inclina- 

 tion : (b) in which the perpendicular to the straight line 

 parallel^ to the wave-surface through the point of contact 

 is the line of the resultant of the water-pressures acting on 

 the vessel. 



