April 1, 1896.] 



KNOWLEDGE 



79 



observe and follow a particular wave crest in the rear of 

 the procession, we should see it advance throw/li the group, 

 and linally die out in front of the group. When a ship, 

 preferably a steamer, moves at a sutiicient speed through 

 smooth water, the group of waves is seen to have the form 

 shown in Fig. 1. Allowance must, of course, be made for 

 the fact that the vessel shown in the illustration is moving 

 in a curve. There are two sets of ship waves to be noticed, 

 the thwart-ship waves and the echelon waves. The former 

 are similar in appearance to a ground swell, with gently 

 rounded crest and trough ; they follow the ship at her own 

 speed (if that remain constant), and the length from crest 

 to crest is the length proper to a free wave travelling with 

 this velocity. Thus, if the vessel be going at six knots, 

 the wave-length is twenty feet ; at ten knots it is fifty-six 

 feet ; at twenty knots, two hundred and twenty-three feet ; 

 and at thirty knots, five hundred feet : the wave-length 

 being proportional to the square of the velocity. The 

 front of the advancing thwart waves is bent in a curve, of 

 which the radius increases as the waves travel on, the 

 crests flattening out as the curve expands. It will be 

 noticed that there is thus a great similarity between the 

 thwart waves and the waves which spring out from the 

 spot where a stone is thrown into a pond. If the motion 

 of the vessel were suddenly stopped, the thwart waves 

 would, of course, travel on ahead of the ship. 



The extremities of the thwart waves seem to rest, as it 

 were, upon the echelon waves. These are very difl'erent 

 in character from the thwart waves, being steep and 

 lumpy. They are the waves which form the lateral 

 boundaries of the group, and by which small craft are 

 often swamped. If we observe the echelon waves from 

 their origin at the bow of a vessel, we find that each 

 wave crest has no great extension from end to end, and 

 that they ai-e stepped back one behind the other. Each 

 crest tapers off somewhat from the middle towards the 

 ends, which overlap the next preceding and following crests. 

 Thus the echelon wave pattern does not, as a careless 

 observer might suppose, have a continuous front shaped 

 like a long fish-head. The falling behind of the energy 

 prevents this, the crest continually dying out in front and 

 a new crest forming behind. The distance between the 

 crests of the echelon waves is that proper to so much of 

 the ship's forward motion as is in the direction of advance 

 of the waves. This is a small fraction of her speed ; and 



Fio. 2. — Diagram showing the enclosing angle of a Ship's Track. 



the wave-length being proportional to the sijuare of velocity, 

 we find the crests of the echelon waves from steamers to 

 have generally a length of not more than, say, two feet 

 from crest to crest. 



The outline of the whole wave pattern is the same 

 whatever be the speed of the ship. Thus, let a circle be 

 drawn (Fig. 2), and a diameter A B be produced to a point 



C, such that the length B C is equal to the diameter A B. 

 From C let tangents be drawn to the circle. Then if C 

 be the bow of the ship, the whole pattern wLU be included 

 within the tangents drawn from C. 



Hitherto we have spoken only of the waves originating 

 from the bow of the ship, but at the stern also the 

 pressure of the water reaches a maximum ; there is a 

 hump of water near the stern as well as near the bow, and 

 from the stern there originates a wave pattern similar to 

 that from the bow. The two systems of echelon waves are 

 fairly easy to discriminate, but the two systems of thwart 

 waves are very often undistinguishable from one another. 

 Sometimes, however, if the ship have a long parallel-sided 

 middle body, the thwart waves due to the entrance or bow 

 part have flattened out so much before the run, or stern 

 part, of the ship is reached, that the series of thwart waves 

 due to the stern part can be separately distinguished. 



The steam-tugs which ply upon the Thames at London 

 give a fine display of ship waves, especially when going at 

 full speed without any barges in tow. At such times the 

 water rises almost to the level of the deck at bow and 

 stern, while amidships the sides are visible much below the 

 water line. Standing upon one of the bridges one may 

 look down upon the conspicuous echelon waves which form 

 a long track behind the vessels, and which sometimes are 

 of such height and power that they send a surf flying over 

 the landing piers. The thwart waves, with their greater 

 length and gentler slope, are less easy to observe at a 

 distance from the vessel. I have found the steamboat 

 pier near Westminster Bridge a good post for the observa- 

 tion of these waves. After a tug has passed under an arch 

 of the bridge the thwart waves may be seen in profile 

 against the sides of the arch, and their forward motion can 

 stiU be watched when the vessel has gone nearly a quarter 

 of a mile upon her course. Thwart waves may also be 

 well seen in profile against the side of a long steamer in 

 motion, as is shown in our illustration in the March 

 number of IVNOwLEnoE (page 54). 



If the length of a vessel be known, her speed may be 

 calculated from observation of the length between the 

 crests of the thwart waves as shown by her wave profile. 

 This follows from the connection between wave-length and 

 velocity, the length being proportional to the square of 

 the velocity. If at any particular velocity the wave-length 

 be such that the crest of the wave formed by the entrance 

 of the ship coincides with the crest of the wave formed by 

 the run, or stern part, this velocity is unfavourable to the 

 ship, owing to the great amount of the ship's power which 

 is expended in wave-making. On the other hand, a 

 velocity such that the crest of the wave due to the bow 

 coincides with the trough of a wave due to the stem is a 

 favourable velocity, since the two sets of waves tend to 

 annul each other, the wave-making resistance being thereby 

 diminished. For this reason a curve showing the total 

 resistance experienced by a vessel at different speeds has a 

 series of humps and hollows, depending upon the periodic 

 variation in the wave-making resistance. Again, if a ship 

 be designed for a certain speed, it is advisable that her 

 length should bo such that the crests of bow waves and 

 stern waves should not coincide. As far as the skin 

 resistance is concerned it is said to be best for a ship to be 

 all entrance and run, with no parallel-sided middle portion; 

 but the parallel middle body is an advantage where 

 increase of length is required to prevent coalescence of the 

 two wave systems. 



Ducks when swimming show the echelon waves beauti- 

 fully (Fig. ;i), and there are no better places to see " duck 

 waves " than the Serpentine and the water in St. -Tames's 

 Park. To got a good general view of the whole track of 



