September 14, 191 1] 



NATURE 



353 



SECTION G. 



ENGINEERING. 



Opening Address by Prof. J. H. Biles, LL.D., D.Sc, 

 M.Inst.C.E., President of the Section. 



It has happened during recent years that accidents have 

 happened to ships and they have mysteriously disappeared. 

 The complete disappearance without leaving any trace has 

 led to the assumption that the vessel has capsized. The 

 circumstances of such cases obviously preclude the exist- 

 ence of any direct evidence. The only subjects of investiga- 

 tion can be (i) the condition of the ship prior to the 

 accident, and (2) the probability that such a condition 

 could be one which in any known possible circumstances 

 could lead to disaster. The first is determinable by 

 evidence in any particular case. The second involves a 

 consideration of the whole question of the behaviour of 

 ships at sea. What is the effect upon any given ship of a 

 known series of waves? What waves is a ship likely to 

 meet? 



This subject has occupied the attention of scientific 

 engineers, and it may be said to have been considered a 

 solved problem. We have thought that if a ship has a 

 certain metacentric height and a certain range of positive 

 stability she is quite safe from the action of a series of 

 waves of any kind which we know to exist. If, however, 

 a known ship (and perhaps more than one) has these 

 safety-ensuring qualities and mysteriously disappears, it 

 may be desirable to review the grounds of our belief to see 

 whether any known possible combination of circumstances 

 may cause disaster. 



Let us then first briefly review the grounds of our belief. 

 Fifty years ago Mr. Wm. Froude showed that the large 

 angles occasionally reached in rolling are not due to a 

 single wave-impulse, but are the cumulative effect of the 

 operation of successive waves. The period T of a small 

 oscillation of a ship in water free from wave disturbance 



and resistance is ir K /— % where k is the radius of gyration 



•\ gh 

 and h is the metacentric height (i.e., the height of the 

 metacentre above the centre of gravity). The period T of 



a wave is »/ — , where I is the length of the wave and g 



is the acceleration due to gravity. The line of action of 

 the resultant of the supporting pressures acting on a ship 

 in undisturbed water is the vertical through the centre of 

 gravity of the volume of the water displaced by the ship. 

 In wave-water it is in the normal to the effective wave- 

 slope (which is approximately the wave-surface). The 

 oscillation of this normal as the waves pass causes a 

 varying couple tending to incline the vessel. If the vessel 

 is very quickly inclined by this couple she will place herself 

 in or near the normal and the inclining couple will be of 

 zero value. If, however, her movements are very slow, the 

 normal may make one or more oscillations before any 

 appreciable effect is produced on the vessel. The tendency 

 to incline in one direction caused by the normal acting on 

 one side of the vertical is checked by the rapid oscillation 

 of the normal to the other side of the vertical. It is, 

 therefore, evident that the relation between the period of 

 the ship and that of the wave normal is a dominating 

 feature in the resulting movement of the ship. Mr. W. 

 Froude 's mathematical solution of this relation is the basis 

 of our belief that we understand the behaviour of a ship in 

 the uniform system of waves when the vessel is placed 

 broadside on to the waves. To obtain this solution he 

 assumed that within the limits considered, the moment of 

 stability varied as the angle of inclination. In the curve 

 of righting levers of a ship, usually known as a curve of 

 stability, this condition holds generally for angles up to 

 about io°. The curve usually reaches a maximum value 

 at about 30° to 40 and vanishes at 60° to 8o°, so that for 

 large angles of roll the assumption does not hold. On this 

 assumption, however, he showed that the motion of a ship 

 amongst such a system of waves is the same as for still 

 water plus a motion composed of two sine terms. The 

 amplitude of this latter motion depends upon the maximum 



T 

 slope of the waves and the ratio -^ (the period of the ship 



in undisturbed water to the period of the wave). If the 



NO. 2185, VOL. 87] 



ship starts from rest in the upright, is the maximum 

 angle of inclination of the ship and 0, the maximum wave- 

 slope ; then 



of the equation cf 



-1 T , 



He considered several solutions 

 motion : — 



(1) T=T, ; this is synchronism and the angle cf inclina- 

 tion gradually increases. Each wave-impulse adds some- 

 thing to the ship's inclination and without any resistance 

 to rolling the vessel would capsize. 

 T 



( z ) ^r =0 ; this is the case of the ship's period being very 



small compared with that of the wave. will then 

 be positive and equal to r In other words, the ship will 

 place herself normally to the wave-slope. The maximum 

 amplitude will onlv be the maximum wave-slope. 

 T 



T"^ 1, 1" tm s case the wave-period is greater than 



(3) 



that of the ship and is always positive and greater Than 

 0,. The vessel alwavs inclines away from the wave-slope. 

 If 



that of the ship, and is always negative. The vessel 

 inclines towards the wave-slope. 



T 

 If - =11, then = -476 0, ; 

 Ti 



= 1-26, then = 



= 20, then = -0, : 



= 2-235, then = J «,. 



M 



This shows the advantage of having T greater than T,. 

 He showed that the ship goes through a cycle of changes 



T 

 and considered the effect of variations of ,-77- upon these 



'J'l 



cycles. He showed that 



T _4 



better than =^-=-. 

 li 5 



T = 5 



Tj 4 

 that it is better to lengthen T rather than to shorten it. 



T 

 Similar results for .=-=2 and 3 respectively gave better 



results by lengthening than shortening T. In each of the 



cases =5 and = =- the results show baulked oscilla- 



1 1 9 l] 5 



tions in which, while the vessel swings towards the 

 vertical, she does not reach it but swings back again. The 

 lengthened value of T here also gave better results than 

 for shortening it. The results given above are greater 

 than would be obtained in practice, because resistance has 

 been neglected. Later he determined the effect of resist- 

 ance upon rolling in still water free from waves. He 

 determined the law of resistance and found it to vary 

 partly as the angular velocity and partly as the square of 

 it. He rolled a ship, and after she was allowed to roll 

 free from disturbance he measured the angle of inclination 

 at the end of each roll. These showed the rate of extinc- 

 tion of the rolling due to the resistance. The loss of 

 extreme angle of roll between one roll and the next repre- 

 sented the work done by the ship in rolling. It is possible 

 to calculate the work done in inclining the vessel to any 

 angle, and the difference between the amount of work thus 

 done in two different angles represents the difference in 

 work necessary, and therefore work done in resistance to 

 bring the ship to these angles of inclination. Hence the 

 work done by resistance between the two consecutive rolls 

 can be actually measured by measuring the extreme angle 

 of inclination in successive rolls. 



Having determined the resistance in terms of angles of 



