APPENDIX 

 ON THE LAW OF FORCE NORMAL TO A ROD AT VARIOUS ANGLES WITH A STREAM 



In problems involving the resistance of cables towed through water, physical 

 assumptions as to the law of force have been made. These assumptions, based on 

 experiments of Relf and Powell, have been reviewed in Report No. 418, Appendix I. 

 Since these experiments measured the forces on a cable in an air stream, it was 

 thought desirable to secure new experimental data for the force normal to a rod at 

 various angles to a stream of water. 



]$TES UNE_ 2: 



A diagram of the apparatus used is shown in Fig. 1 . The rod was free to 

 swing in a vertical plane about a pivot on the water surface, attached about 5" 

 forward of the bow of a 4-foot model. The pointer and quadrant shown are rigidly 

 connected to the rod and model respectively. 



The test was conducted in the eighty-foot model basin. The experimental 

 procedure consisted of reading the angle assumed by the rod (as indicated by the 

 position of the pointer along the quadrant) and measuring the model's speed through 

 the water by means of a chronograph. The rods tested were of 1/4" diameter and 

 ranged from 6.1" to 48.7" in length. 



The readings obtained are shown plotted as angle against speed in Fig. 2 for 

 a series of steel rods, and in Fig. 3 for a brass rod 4 ft. in length. The curves 

 were computed for a rod of infinite length on the assumption that the normal force 

 per unit length is given by R sin 8 <|>, where R is the force per unit length of rod 

 when normal to the stream. Let w be the weight per unit length of the rod when 

 submerged in water. Then the force per unit length normal to the rod is in equi- 

 librium with the component w cos <J> of the weight of the rod. Hence the computed 

 curves are determined by the equation 



w cos $ = R sin 2 4> 



