NUMERICAL RESULTS 



In this section we will calculate the forces and moments acting on a submer- 

 sible moving under the free surface or under ice. Numerical results based on 

 the present method will be compared with results obtained from earlier theoreti- 

 cal methods and experiments. First, forces acting independently on the bare 

 hull and control plane will be compared; then, results for the combined hull and 

 plane will be compared. i 



Figure 9 shows the forces and moments on a Rankine ovoid having a length of 

 4 ft (1.22rc). The ratio of length to diameter (D) is 10.5. The Rankine ovoid 

 is created by distributing sources and sinks along a line which is assumed to be 

 in a uniform stream In an unbounded fluid (see Reference 12). The computed ver- 

 tical forces (F') are generally somewhat larger than the experimental data for 

 z 



smaller submergence (h) and smaller for larger submergence. The computed 

 moments (M*) are generally smaller than the experimental data for all sub- 



y 



mergences when the Froude number Is larger than 0.5. However, the overall trend 

 of the computed results is similar to that of the measurements. Results calcu- 

 lated by the present method are In good agreement with values obtained from pre- 

 vious analytical methods. Figure 10 shows the same results plotted as a 

 function of submergence. As the submergence becomes larger than three times the 

 diameter, the force and moments decrease rapidly for all Froude numbers. 



Figures 11, 12 and 13 show similar data for a spheroid whose ratio of length 

 to diameter is 7. The findings here are somewhat different from those discussed 

 previously for the Rankine ovoid (see Figure 9). When pitch angle is zero (see 

 Figure 11) the experimental data for the spheroid extracted from Reference 13 

 are larger than the computed values at Froude numbers less than 0.5. The 

 agreement between computation and experiment is generally good when the 

 submergence is equal to or larger than the dianeter: when the ratio of 

 submergence to diameter is 0.7 5, there is substantial difference. When the 



2 3 



