Salvesen 



body representation cannot be used for a second-order theory. For a submer- 

 gence of 1.25 feet the use of this body representation for speeds up to about 4.5 

 feet per second, and higher speeds for deeper submergences, seems justified, 

 as can be seen from Fig. 7. 



It is interesting to note that the body can be made closed simply by applying 

 a small angle of attack and hence without introducing any new singularities. In 

 other words, a closed body can be obtained by an appropriate rotation of the line 

 on which the 11 sources are located. The amount of rotation necessary to close 

 the body will obviously depend on the velocity and the submergence of the 

 cylinder. 



EXPERIMENTAL RESULTS 



An experiment was conducted to see how well this second-order theory can 

 predict wave elevations and wave resistance for submerged two-dimensional 

 foil-shaped bodies. The experiment was performed at the University of Michi- 

 gan model tank (360 ft by 20 ft by 9 ft) on an 11-ft two-dimensional strut seen in 

 Fig. 8. The model's cross-sectional offsets are given in Fig. 1. The instru- 

 mentation for measuring horizontal drag force and wave elevation is schemati- 

 cally shown in Fig. 9. The horizontal drag force was measured on the middle, 

 2-foot section of the model by waterproofed strain gages mounted on two small 

 cantilever beams (Fig. 10). The wave elevation was measured by a 0.0016-in. 

 capacitance wire attached to a small carriage which could move on a 10-ft rail 

 as shown in Fig. 11. The change in capacitance of this wire as caused by 

 changes in water elevation was registered by a highly sensitive capacitance 

 bridge (Wayne Kerr B541) from which results were traced on an x-y recorder. 

 The X coordinate was used for the position of the carriage, and the y coordinate 

 was used for wave elevation. With this capacitance wire we were able to obtain 

 the wave profile to a good accuracy, about ±0.03 in. for speeds up to 4.5 ft/sec. 



Fig. 8 - Foil with supports 

 610 



