be of interest to study the interaction under that adverse condition and the effect on 

 separation phenomena due to the propeller action. 



S. F. Hoerner 



It has been mentioned here this morning several times that there is a lack of 

 understanding and contact between "mathematicians" and the naval architects. Now, 

 as one who has been on the inside of aviation as well as naval architecture, I would 

 like to tell you that that situation prevails in the field of aviation just the same. 



There are highly skilled mathematicians working on theory, and there is the 

 engineer who tries to apply the results. Usually, the engineer is lost. He does not 

 fully understand the language of theory. 



Since the advent of modern computers there is also the idea that those com- 

 puters would solve all problems. This is not so at all. The computer is a "perfect" 

 idiot; the scientific term is "idiot-savant." Now, the man who handles the computer 

 must provide the brains to put the right information into it, and to give an adequate 

 interpretation of what is coming out of it. 



In the field of propellers, this is also true to a certain extent, and this has been 

 realized in aviation for some time (for some twenty-five years). To help the engineer, 

 methods have been evolved known as "polar methods," replacing the propeller blades by 

 "equivalent" wings. The characteristics of the propeller are then reduced to those of 

 wings. 



Such an interpretation is much more understandable to the engineer. 



I would suggest that for the benefit of the engineer, we would revive these 

 methods a little bit. This does not mean, however, that I would critize the efforts of 

 men such as Dr. Lerbs. He is in his perfect right to develop an accurate theory. 



R. R. Hunziker 



I would like to comment on the subject of "thrust deduction" and interaction 

 phenomena of propeller and hull in deeply submerged submarines, a subject which was 

 a part of the extensive and sound lecture of Dr. Lerbs [1]. Dr. Lerbs started from the 

 general propeller theory and considered later the hull-propeller system, pointing out 

 the interaction character of the hydrodynamic phenomena. He mentioned the use of 

 Lagally's theorem [2], as starting point of the theory, and the introduction of a sink-disk 

 as a "first approximation" for the propeller. I would refer to my recent theoretical 

 work investigating the interaction phenomena of the hull-propeller system. 



Details may be found in my last paper [3] (30 August 1956) which supersedes 

 my earlier paper cited by Dr. Lerbs. 



First, I have dealt with the construction of the hull-propeller velocity field that 

 satisfies the hydrodynamic equations in the form of Oseen [4], as an extension of 

 Burger's [5] analysis for the open water propeller. 



Departing from the Oseen equations, I have proved that in the steady flow 

 hypothesis (used also by Burgers), the velocity field in the first approximation contains 

 a system of helical vortices shed by a propeller of an infinite number of blades. 



In the exterior of the slipstream and around the body, the field has zero 

 tangential component, and is given by the superposition of the flow for the body alone, 

 plus the axial and radial fields of a circular sink-disk over the propeller circle, plus 

 an interaction harmonic field with which the hydrodynamic boundary condition remains 

 satisfied over the body. This idea of the interaction field, characterizing the effective 

 wake over the propeller circle, was introduced by Helmbold in 1938 [Ref. 6 p. 354 Eq. 

 5a]. In the interior of the slipstream the flow is rotational and at infinity has a net 

 augmentation of the axial asymptotic velocity U, which is equal to the strength c of 

 the simple layer over the disk. It is not too much to observe that the constructed 

 velocity field which is singular over the propeller disk, implies a removal of the 

 D'Alembert paradox for the body. 



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