Sec. 62.6 



ESTIMATE OF ADDED LIQUID MASS 



437 



Remainino 



Essentially 

 Parallel to 

 its Mid- 



Position 



Fig. 62.M 



Modes op Motion of a Vibrating Screw 

 Propeller on a Ship 



for four modes of motion illustrated schematically 

 in Fig. 62.M: 



(1) Torsional or rotational, about the propeller- 

 shaft axis, as in diagram 1, assuming that the 

 latter remains essentially straight 



(2) Axial, parallel to or along that axis, indicated 

 in diagram 2 



(3) Lateral, corresponding to the sidewise motion 

 of a propeller shaft in a loose bearing next to the 

 propeller, as in diagram 3. This also includes a 

 motion due to sidewise bending of the propeller 

 shaft at the propeller, in which the propeller 

 moves only in a direction parallel to the normal 

 disc plane, without diametral rotation. 



(4) Diametral rotation, as in diagram 4, cor- 

 responding to angular motion of the propeller 

 out of the normal plane of its own disc, due to 

 bending or whirling of the propeller shaft about 

 some selected diametral axis in the propeller. 



There are indications that the depth of immer- 

 sion of a screw propeller is a factor in all four 

 modes, because of the "relieving" effect of a free 

 surface close to the vibrating blades. 



To determine the value of the added mass 

 moment of inertia for the torsional mode of (1) 

 preceding, a number of tests have been made with 

 model propellers, among them those of R. T. 

 McGoldrick, described in TMB Report 307 of 

 July 193L These tests comprised a set of tor- 



sional-vibration experiments on a group of brass 

 model propellers, 16 inches in diameter, conducted 

 in both air and water at the U. S. Experimental 

 Model Basin. The P/D values ranged from 0.60 

 to 2.00. However, these tests produced only the 

 general conclusions that: 



(a) For a fixed amplitude and frequency the 

 effect (on the polar moment of inertia ./) varies 

 directly with the blade-width ratio, and with the 

 pitch ratio. In other words, J increases as both 

 Cm/D and P/D increase. 



(b) For a given propeller the effect (on the polar 

 moment of inertia J) increases with frequency 

 and amplitude 



(c) In order to determine the per cent increase in 

 (polar) moment of inertia in any given case, the 

 amplitude and frequency of the propeller (vibra- 

 tion) must be approximately known. 



Some years later R. Brahmig made an analytic 

 study of the torsional-vibration problem of 

 screw propellers, listed as reference (29) of Sec. 

 62.8. He considered variations in frequency and 

 amplitude as affecting the added mass of the 

 entrained liquid, and gave a full statement of the 

 similitude conditions and scale effect involved 

 in the model experiment technique. Results are 

 quoted in his paper for torsional-vibration tests 

 on flat circular discs but none for model screw 

 propellers in the same mode. However, Table 2 

 of this reference lists rotational-amplitude and 

 frequency data for the propellers of three ships. 



As a rule, the amount of rotation amplitude 

 and the frequency in water are almost never 

 known with any reasonable certainty for a ship, 

 and the effect of the surrounding water oq the 

 polar moment of inertia varies widely as indicated 

 in TMB Report 307. It was therefore decided, 

 by those working in this field, that the only 

 practical interim answer was to accept a per- 

 centage increase in the polar moment of inertia 

 of the propeller mass in air, regardless of the 

 pitch ratio, the mean-width ratio, the ratio of 

 hub diameter to overall diameter, and all other 

 factors. For this mode of vibration, the effect of 

 an abnormally large or small hub is possibly less 

 pronoimced because of the small radii involved. 

 However, the sine of the geometric blade angle 

 is large at the radii near the hub. 



Based on these tests, an overall mean of 25 to 

 30 per cent increase in J, due to the added mass 

 of the entrained water, was used for many years; 

 this is the value given by J. R. Kane and R. T. 



