uniquely characterized only as the field of a sink disk plus a perturbation potential 

 field grad </>*. This results as a steady solution of Oseen's equations in the first approxi- 

 mation, which contains a continuous (never discrete) ring vortex distribution over 

 the slipstream. No other distribution is compatible with the motion equations, and a 

 discrete distribution is not an approximation. For a steady flow theory it is not neces- 

 sary to consider more than a general simple layer distribution over the propeller circle. 

 For a non-steady theory it is at least necessary to compute a field compatible with the 

 existence of a finite number of helical rotating free vortex sheets. 



The great importance of the theory and formulae mentioned by Dr. Lerbs and 

 here commented, lies in its broad applicability, especially the results and general 

 formulae of ref. [3]. 



A solution for general ellipsoids is at present in development as extension of 

 the above results [3, 12]. 



I think that the extension of the theory, formulae, and method of calculus for 

 submerged hull with two propellers is immediate, with the appropriate "interaction 

 potential" for the total field. 



The interaction theory of "thrust deduction" for the surface ship is in develop- 

 ment [11, 12], considering the free surface of water. The "interaction field" has a 

 quite different form. The velocity field for the hull-propeller combination is charac- 

 terized as boundary value problem with a linear boundary condition on the free 

 surface. The perturbation potential is a modified Michell's potential that includes an 

 interaction term due to the propellers inflow [12]. The essential result is that the 

 "Potential thrust deduction" appears as an augmentation of the wave resistance. 



REFERENCES 



1. Lerbs, H. W., Lecture, Symposium on Naval Hydrodynamics, Washington, D. C, Sep- 



tember 26, 1956. 



2. Hunziker, R. R., Discussion, Symposium on Naval Hydrodynamics, Washington, D. C, 



September 26, 1956. 



3. Hunziker, R. R., Final Report III on Effective Wake and Thrust Deduction, Id. August 



30, 1956. 



4. Helmbold, H. B., Schraubensog und Nachstrom. Werft-Reederei-Hafen, Bd. 19 (1938) 



p. 35. 



5. Dickmann, J. E., Schiffkorpersog, Wellenwiderstand eines Propellers und Wechselwirkung 



mit Schiffswellen. Ingenieur-Archiv. 1948. 



6. Lagally, M., Berechnung der Krafte und Momente, die stromenden Flussigkeiten auf ihre 



Begrenzung ausiiben. ZAMM. December 1922. 



7. Korvin-Kroukowsky, B. G., International Shipbulding Progress. Vol 3, No. 17, pp. 3-24 



(1956). 



8. Basin, A. M., Teoriia Vzaimodeiistviia Dvijiteliia s'Korpusom Soudna v'Bezgranichnoii, 



Idealnoii Tidkosty, Izvestiia Akademii Nauk, S.S.S.R., 1946, No. 12. 



9. Burgers, J. M., On the Application of Oseen's Hydrodynamical Equations to the Prob- 



lem of the Slipstream from an Ideal Propeller. Kon. Ak. Wetenshapen, Amsterdam 32, 

 p. 1278, 1929. 



10. Lerbs, H. W., Marine Propulsion, Applied Mech. Reviews Vol. 9, No. 7, July 1956, 



pp. 281-282. 



11. Hunziker, R. R., Internal Working Papers, December 1955, and January 1956, Research 



Division, Reed Research Inc., Washington, D. C. 



12. Hunziker, R. R., and Florio, J. S., Reed Research Internal Report, September 1956. 



/. Martinek and G.C.K. Yeh 



We wish to congratulate Dr. Lerbs for his fine and comprehensive presentation 

 of a subject to which he has contributed so much in the past and in which he has 



174 



