These components can be deduced from the total hydrodynamic force as measured, say, by Sarpkaya 

 (12) and Mercier (13); or the components can be measured individually as discussed by Griffin and 

 Koopmann (4,6). This decomposition of the forces is carried one step further than one proposed by 

 Sarpkaya (1), who divides the total transverse force into "drag" and inertia terms. The "drag" term is 

 the negative of the lift as it is usually characterized. Both characterizations of the force components 

 have their merits depending upon the particular situation being studied and there is a direct correspon- 

 dence between them, as discussed in references 3 and 6, and in Appendix E. 



Some practical and useful comparisons can be made between the fluid forces measured when a 

 cylinder is forced to vibrate and the fluid forces measured when the cylinder is resonantly excited by 

 vortex shedding. The forced cylinder measurements discussed here were made in water by Sarpkaya 

 (1,12) and Mercier (13) and the self-excited cylinder measurements were made in air and in water by 

 Griffin and Koopmann, King and others as indicated in Table 2.3 (see references 3 and 6). 



Table 2.3. Hydrodynamic Forces on Circular 

 Cylinders; from Sarpkaya (12). 







Reduced Velocity, V^ = 5. 



Fluid Force C 



Dmponents, Equation (E1.10)| 





Inertia 



Drag 





Excitation, 



Damping, 



Inertia, 



Displacexnent, 



Coefficient/"^ 



Coefficient, 



Phase Angle, 



-Q/,C0S€ 



-C„„sine 



QftSine 



K= YID 



^mh 



Q/, 



0'=arctan[C,,/C„,] 









0.13 



0.4 



-0.2 



-26.6° 



0.18 



0.18 



0.089 



0.25 



0.4 



-0.35 



-41.2° 



0.26 



0.26 



0.23 



0.50 



1.0 to 2.2 



-0.9 



-42° to -22.3° 



0.67 to 0.83 



0.67 to 0.83 



0.67 to 0.83 



0.75 



1.0 to 2.2 



-0.6 



-28.8° to -11.9° 



0.48 to 0.54 



0.48 to 0.54 



0.26 to 0.11 



e = 13 + y and y = arc tan W, where W = r, a = - — . In addition IV = 0.05 is assumed (See 



1 - a oy„ 



Appendix E). 



The inertia coefficient is evaluated here in coordinates appropriate to a cylinder vibrating in a quiescent 

 fluid or, equivalently, a fluid in uniform, steady motion. 



Typical measurements reported by Sarpkaya appear in Figs. 2.3 through 2.6. The measured values 

 for the inertia coefficient C^i, are shown in Figs. 2.3 and 2.5 as a function of the reduced velocity F^, 

 for displacements from equilibrium of K = Y/ D = 0.5 and 0.75. Of particular note is the marked vari- 

 ation in Cf„h in the vicinity of V^ = 5. This effect corresponds to the large phase shift in the fluid force 

 relative to the vibratory displacement when the characteristic frequency of the flow is locked onto the 



10 



