NATURE 



\July 13, 1882 



the Hydromotor may be compared with the Water-witch. 

 She gains upon the latter obviously in the avoidance of 

 much waste-work in the mechanism In the Ruthven 

 system there is necessarily more waste- work in the engines 

 which drive the turbines, and in the friction of the water 

 in the turbines and passages to the nozzles, than has to 

 be incurred in the Fleischer system. On the other hand, 

 in the latter system, there must be some loss from con- 

 densation of steam in the cylinders, and the high mean 

 velocity of ejection must be a disadvantage. The con- 

 siderable variations in the velocity of ejection at different 

 parts of the stroke must also be a disadvantage, as com- 

 pared with the uniform velocity of delivery from a tur- 

 bine. Respecting the condensation it is asserted, as the 

 result of experiment, that the losses are exceedingly small, 

 the cylinders being wood-lined, and a layer of hot water 

 being formed below the float. Experienced engineers 

 were scarcely prepared for this satisfactory result, antici- 

 pating that more serious losses would occur from the 

 alternate heating and cooling of the cylinders. Of course, 

 experience in such a matter is the true test ; but it is to 

 be observed that the Hydromotor appears to have very 

 ample boiler-power in relation to the indicated horse- 

 power assigned to her maximum speed. Losses from 

 condensation cannot be estimated from the statement of 

 indicated horse-power. The indicator diagrams which 

 have been published, show a very good performance. 



The varying rate of outflow through the nozzles must 

 be a source of disadvantage in the Fleischer system. 

 For the hydromotor it is stated that the mean velocity of 

 outflow was about 66 feet per second when the speed of 

 the vessel was about 15 feet per second. We are not 

 informed what was the maximum velocity of outflow ; the 

 minimum velocity is said to have exceeded the speed of 

 the vessel. This varying velocity, of course, carries with 

 it a varying thrust, and the hydromotor in this respect 

 must be less favourable to uniform motion of the ship 

 than the screw or paddle or Ruthven propeller, where 

 the thrust can be kept practically constant. With two 

 cylinders this might be more felt than with four or more 

 cylinders, but in all cases the drawback must exist. 



The high mean rate of outflow involved in the Fleischer 

 system is contrary to the generally accepted view as to 

 the condition most favourable- to efficiency. For a given 

 speed of ship, neglecting the augment of tow-rope 

 resistance which may be caused by the action of the 

 propeller, there must be a certain thrust developed, 

 which will overcome the resistance of the water to the 

 advance of the ship. This thrust in the jet-propeller is 

 measured by the sternward momentum generated in the 

 jet* No matter how the mechanism may be arranged, 

 what has to be done by it is to impart to water which has 

 entered the ship and acquired her forward velocity, a 

 sternward momentum which shall have a reaction equal 

 and opposite to the fluid resistance. Momentum, it need 

 hardly be explained, involves the consideration both of 

 the weight of the water acted upon and of the velocity 

 imparted to it in each unit of time. Nor is it possible 

 to create this momentum in the water expelled from the 

 nozzles without doing waste-work in overcoming fac- 

 tional and other resistances. The magnitude of this 

 waste work may vary greatly in different examples, and 

 it is difficult to estimate its value apart from experiment. 

 Hence in theoretical investigations, this waste-work is 

 usually neglected, although in practice it is of great 

 importance. . 



Leaving out of account for the moment this waste- 

 work, and the possible influence upon the efficiency of the 

 propeller exercised by the disturbance produced in the 

 surrounding water by the passage of the ship, it may be 

 well to explain briefly the accepted theory of the action 

 of jet-propellers. This is done in the following equa- 

 ls' v = the speed of outflow of the jets from the nozzles 



- . A. V.(V-v), 



in feet per second, v — the speed of advance of the ship, 

 A = the joint sectional area of the nozzles in square feet, 

 •w — weight in lbs. of a cubic foot of water. Then — 



Cubic feet of water acted upon per second =A . v. 



Sternward velocity of jets in relation to still ) 



> = V — V. 



water ) 



Thrust, or momentum created ) 

 per second j 



where g is the accelerating force of gravity — say 32 feet 

 per second. For sea-water 07 = 64 > so that w-i-g = 2 

 (nearly) Hence 



Thrust (in sea-water) = 2 A . v . (v — v). 

 Under the foregoing assumptions, we also have 

 U= Useful work of propeller (in \ = work done in pro- 

 unit of time) J pelling ship. 



= Thrust X speed of 



w=waste work in race 

 u4-w= total work of propeller 



ship. 

 = 2 a V (v - v) . v. 

 = i vis viva. 

 = av . {y-vf. 

 = 2 A.v(y—v)v 



+ A V (V - vf 

 = A V (V- - V-). 



Efficiency = — . — = — . 

 U+w v-\-v 



From the last of these equations it is seen that the more 

 nearly the velocity of outflow v approaches the speed of 

 the ship ?', the nearer will the efficiency approach its 

 maximum value, or unity. Moreover, for given values of 

 speed of ship and thrust, if the difference (v— v) between 

 the speeds of outflow and advance is diminished, the area 

 of the outlets must be correspondingly increased. That 

 is to say, if the value of v-v is diminished, the quantity 

 of water (A . v) operated upon must be increased. Now, 

 in general, it has been supposed that the inferior perform- 

 ance of jet-propelled vessels, as compared with screw 

 steamers was due to the small quantities of water acted 

 upon, In the IVaterwitch, for example, about 150 cubic 

 feet of water were expelled per second, whereas in the 

 rival twin-screw vessel Viper more than 2000 cubic feet 

 of water were operated upon per second. In the ll'a/er- 

 witch v = 30 feet per second, and z/= 157 feet per second ; 

 so that according to the foregoing formula 



Efficiency = 2X ' 57 =?iJ+=687 per cent. 

 157+30 457 

 In the Hydromotor v = 66 feet (mean velocity) v= xy2. 



Efficiency = ^iif=j^ = 37 '4 per cent. 

 152+66 8l"2 



Dr. Fleischer adopts the foregoing equations, so far 



as they relate to thrust and useful work, but for the total 



work he uses another formula, and it is here that we 



venture to think he goes wrong. According to his 



investigation — 



Total work = | vis viva of issuing streams. 



= JX Mass of water delivered per 



second X (speed of outflow),-'. 



■= \ X 2 A V X V 2 . 



Hence he writes — 



Useful work 2 A v (v - v) " 

 Total work 2AV X £v 2 



= 2 !(v-*). 



V 



In thus dealing with the total work, instead of using 

 the expression given above, Dr. Fleischer virtually 

 ignores the fact that the vessel is in motion ahead ; and 

 that the streams issuing from the nozzles have the velocity 

 v only relatively to her. It is upon this questionable 

 formula for the efficiency that his estimates above-men- 

 tioned are based. For example, in the hydromotor at 9 

 knots, according to Dr. Fleischer — 



Efficiency 



