RUDDER TRIALS,1U. S. S. STERETT. 309 



The curves of twisting moment on speed may be expressed by an 

 equation of the form M=KV", where n varies with the speed-length ratio, 

 causing the hump in the curves (Fig. 10, Plate 120). The average value of n 

 for all the curves on steady turning (Fig. 10, Plate 120) was found to be 1.75. 



The curves of twisting moment plotted on helm-angles are, for angles 

 above 15°, straight lines which when produced do not all pass through the 

 origin. The equation for any line is therefore of the form, M=K{d — d), 

 in which 8 is the value of the intercept on the axis of abscissae. For speeds 

 above 20 knots, the average value of 5 is 4°. It seems not unlikely that the 

 helm-angle (6) should be diminished by some small angle which may be a 

 function of the drift angle. One of the conclusions drawn from Wellenkamp's 

 rudder trials* for the German Navy, reported by T. Schwartz, is that the 

 rudder angle is diminished by the angle of drift in turning. 



The equation for twisting moment may then be expressed in the form : — 



M=KV''' (d-d) 

 or in terms of the rudder constants, 



M=K'AXoV'''^ (6-4°) 

 in which A is the rudder area in square feet, and Xq is the distance in feet 

 from the center of area of the rudder to the rudder axis. The value of K' 

 in this equation was computed, from the curves of Fig. 10, Plate 120, to be 

 0.06, or — 



M=o.o6AXoV^''K6-4°)- 



With this formula, points were computed for new curves of twisting moment 

 on speeds between 12 and 28 knots. The resulting curves are shown by 

 broken line on Fig. 10, Plate 120. The greatest deviation of these new 

 curves from the original curves of twisting moment on steady turning is less 

 than 10 per cent, and the average deviation is less than 2 per cent of the 

 moment at 35° and 28 knots. 



The formula presented above is a simple mathematical form for the 

 results of the tests. It applies to the particular ship and rudder tested, 

 but cannot safely be assumed to apply, with the same constants, to ships 

 of very different form. However, the curves (Fig. 15, Plate 125) of coef- 

 ficient of reduction on Joessel's formula plotted on speed-length ratio —ly 



seem to show that ships of nearly the same type behave similarly in turning, 

 and that whatever formula is used in computing the twisting moment, the 

 same constants may be applied to ships of similar type. 



*See "Jahrbuch der Schiffbautechnischen Gesellschaft, 1910" "Uber Rudermomentmessungen, " 

 T. Schwartz, p. 714: "Die Derivationswinkel gestaltet den wirksamen Ruderwinkel kleiner, da die auf die 

 Ruderflaclie wirkenden Stromfaden in der Richtung der Kurve der Heckbahn verlaufen." 



