Lehman and Kaplan 



references cited above, which are also included in the present paper. However, 

 comparison of trends and indicated behavior can be made and will be described. 



The influence of propeller thickness on both the axial and transverse induced 

 forces acting on an appendage is shown by the experimental results described 

 earlier in this paper, and is illustrated by results such as those in Figs. 13 and 

 16. The theoretical verification of the lack of blade- rate axial forces for odd- 

 bladed propellers, and the similar lack of transverse forces for even-bladed 

 propellers, is shown in the experimental results cited earlier for the case of a 

 symmetrically disposed appendage. Since the present theory is two-dimensional, 

 the total force of a symmetrical appendage is proportional to the span of the ap- 

 pendage for a fixed propeller diameter. As a result the induced forces will vary 

 linearly with the appendage span for a particular separation distance, and this 

 behavior is verified, in a limited sense, by the data in Ref. 10. Thus, the agree- 

 ment indicated for these particular characteristics supports the qualitative pre- 

 dictions of the theory. --^ „_ ' .; 



The exponential decay with distance for the induced forces is indicated by the 

 experimental results with the exception of data at large separations, where very 

 small force magnitudes (with possible errors in measurement, noise effects, 

 etc.) occur. Thus the exponential variation appears to be a plausible represen- 

 tation for the decay with increasing separation distance. Since no dependence on 

 the advance ratio is indicated by this exponential form, the variation should be 

 the same for all values of J and depend only on the number of blades. Although 

 only limited data are available and precise comparison cannot be made, it ap- 

 pears that this result is plausible, as illustrated by the data in Figs. 24 and 28 

 for the range of significant thrust values. 



The data in Ref. 10 consider the variation in axial force brought about by 

 changing the appendage thickness, and it is shown there that the axial force is not 

 linearly proportional to thickness. The present theory predicts proportional 

 values, and a possible explanation for this disagreement is the influence of the 

 wake of the appendage through which the propeller must operate. However no 

 evaluation of this particular hypothetical influence can be obtained from the 

 present theory, since wake effects and any interaction of the appendage in alter- 

 ing the propeller thrust characteristics have been neglected in the theoretical 

 development. Further experimental and/or theoretical work will be necessary 

 to determine the influence of this primarily viscous effect. 



The theory shows that the ratios of the induced axial and transverse forces 

 to the propeller thrust have only a small dependence on the advance ratio, as in- 

 dicated by Fig. 50. Experimental results in Ref. 16, as illustrated in Fig. 51, 

 indicate this lack of significant dependence of the force ratios upon the propeller 

 loading, thereby supporting the theoretical contention. The data in Fig. 51 indi- 

 cate this agreement in the range where significant thrust values occur; depar- 

 ture from this behavior occurs only in the range of higher j values. 



While precise comparisons cannot be made because of the particular se- 

 lected conditions for computation, it can be seen that the general magnitudes of 

 the induced forces inferred by the theory are of the same order as the actual 

 values experienced in the experiments. The spacing distance is defined in the 



226 



