Sec. X1.2 



SYMBOLS AND THEIR TITLES 



909 



w — Weight density, or weight per unit volume, 

 = W/V = pg 



Wf — Wake fraction, Froude, = (F — Va)/Va 



Wq — Wake fraction, determined from torque 

 identity 



Wt — Wake fraction, determined from thrust 

 identity 



W — Weight in general; displacement weight; 

 weight or gravity force; scale weight of a body 

 or ship, where W = mg 



W — Wind velocity 



Wn — Weber number, relating to surface tension, 

 = C7'L/k (kappa) = C/'i)/ k; see NOTE under C^, 



W B — Wind velocity, relative to ship 



Wt — Wind velocity, true, over the earth's 

 surface; sometimes called the natural-wind veloc- 

 ity 



W s A — Wind velocity, still-air, caused solely by 

 the motion of a ship in still air 



X — Longitudinal body axis, positive forward 



x' — Radius ratio, 0-diml, of a screw propeller, 

 = R/Rm^^ 



Xo — Motion axis, reckoned usually in an ahead 

 direction, tangent to the sea surface 



X — Component of hydrodynamic force on a 

 body or ship along its longitudinal or a;-axis 



y — Normal distance, perpendicular to the 

 surface, to any point in the boundary layer of a 

 viscous liquid 



y — Transverse body axis, positive to starboard 



2/0 — Motion axis, reckoned usually to starboard 

 or to the right of the a;o-axis 



Y — Component of hydrodynamic force on a 

 body or ship along its transverse or y-axis 



z — Vertical body axis, positive from deck to keel 



Zc — Shaft convergence, expressed as an angle 

 or slope with reference to the centerplane, after 

 projection on the baseplane 



Zd — Shaft declivity, expressed as an angle or 

 slope with reference to the baseplane, after pro- 

 jection on the centerplane 



2o — Motion axis 



Az — Sinkage of a body or ship when moving on 

 the surface of a Uquid 



Z — Component of hydrodynamic force on a 

 body or ship along its keelward or z-axis 



Z — Number of blades in a propulsion device 



a (alpha) — Acceleration, angular 



a — Angle of attack of a hydrofoil, geometric 



a — Angle of encounter of waves, between the 



direction of wave travel and the direction of ship 

 motion. For a head sea, a = 180 deg. 



a — Designed waterplane coefficient; alternative 

 symbol C w 



a — Ratio, linear or scale, full-size body or ship 

 to model, greater than unity; alternative symbol 

 X (lambda) 



ua — Nominal angle of incidence on a control 

 surface 



(1/2)q:b — Angle of entrance, half, neglecting 

 local shape at the stem; alternative symbol is 



oti — Angle of attack of a hydrofoil, hydrody- 

 namic, measured from the attitude or position of 

 zero hft to the direction of the resultant velocity, 

 taking induced velocity into account 



ai^ — Angle, neutral, between the zero-hft posi- 

 tion of a control surface and the body or ship axes 



ao — Angle of attack of a hydrofoil, zero-lift; 

 alternative symbol a^ 



as — Angle of attack of a hydrofoil, stalhng 



ttz — Angle of attack of a hydrofoil, zero-lift; 

 alternative symbol ao 



acR — Angle of attack of a hydrofoil, critical 



;S(beta) — Advance angle for a propeller-blade 

 element, = tan"' [VA/{2irnR)] for the radius R 



fi — Angle of bossing termination, extreme after 

 edge, with reference to the baseplane; slope of 

 floor if or "deadrise" in a planing craft; angle of 

 obliquity for a flat surface impacting a Uquid 



— Angle of drift in turning 



/3 — Coefficient, midlength section; alternative 

 symbol Cm 



fii — Hydrodynamic pitch angle of a screw-pro- 

 peller blade section at any radius R, taking 

 induced velocity into account 



7 (gamma) — Projected angle of roll 



7 — Dihedral angle, measured from the axis of a 

 hydrofoil to a normal erected on the plane of 

 symmetry 



r (gamma, capital) — Circulation, strength of, 

 around a hydrofoil or body 



S (delta) — Angular displacement of a control 



surface from its neutral position 



5 — Coeflacient, block; alternative symbol Cb 

 5 — Thickness of a boundary layer in viscous flow 

 5 — Advance ratio of D. W. Taylor, = nD/V a . 



When n is expressed in rpm, D in ft, and Va in kt, 



as was done by Taylor, this ratio is dimensional 



and equal to 101.33/7 



bs — Angle, bow plane, with reference to ship 



axis 



