Newman 



On the other hand for a flat low aspect-ratio wing of rectangular planform and 

 span 2T we obtain the well known results* 



Y = 7rpV2/3T2 



N = -j-rrpV^ /3T^L . 



The practical application of these simple formulae is somewhat limited by 

 the occurrence of separation. However if attention is focused upon the side 

 force acting only upon the forebody, these results will be expected to furnish 

 more realistic predictions. This situation is illustrated by the experiments and 

 theoretical calculations of Norrbin (1965a), which are summarized in Table 1. 

 Measurements were made on both the total force and the force on the forebody 

 of a double -body model of a cargo ship. Experimental data are shown for the 

 side force acting on the forebody alone, on the total hull without rudder, and on 

 the total hull with rudder. Theoretical predictions are given for the forebody 

 based upon slender -body theory as well as upon the low aspect -ratio flat plate 

 theory which, since the draft is constant along the length, is applicable either to 

 the forebody or to the entire hull. For the forebody alone both theories are in 

 fair agreement with the experiments, the slender-body theory being within 5% 

 and the low aspect-ratio wing theory within 10% of the measured force. As 

 might be expected the comparison is less satisfactory for the entire hull. In 

 this case the low aspect-ratio wing result is very close to the measured value 

 for the bare hull but differs substantially from the measured value with the rud- 

 der fitted. Since the presence of the rudder may be expected to improve the 

 validity of the theory, in the sense of providing a more substantial trailing edge, 

 the good agreement in the case of the bare hull should be regarded with caution. 



Table 1 

 Comparison of Theoretical and Experimental 

 Side Force Coefficients Y/QApV^ fiLT) Obtained 

 by Norrbin (1965a) 



Low aspect -ratio theory 



Slender -body theory, forebody 



Forebody, experiment 



Total hull, experiment (no rudder) 



Total hull, experiment (with rudder) 



0.184 

 0.193 

 0.203 

 0.172 

 0.232 



Unsteady effects associated with non-zero yaw velocity also can be analyzed 

 within the framework of low aspect-ratio wing theory or slender-body theory. 

 Lighthill (1960) has shown that the two-dimensional unsteady side force is sim- 

 ply given by the expression 



*The formal extension of the slender-body theory results to this case is per- 

 nnissible for the lateral force and monnent in spite of the fact that the leading 

 edge violates the pointed-bow requirement (Ward, 1955). 



216 



