enk dC

where —- is the slope at a=0 in lift coefficient curves, and CDC is the drag coefficient of da cross current which depends on tip shape and rake ratio (e.g. Quadrate tip: CDC =0.8. Smooth tip: CDC =0.4). Cd0 is the airfoil profile drag coefficient (viscous drag). For the profile section NACA0015, Cd0 =0.0065. A is the sweptback angle at 1/4 chord of the fin. k is the aspect ratio. a is the angle of attack (degree).

In order to get CL and CD, we should know the real effective angle of atttack. As the fin located at some offset from the origin of the AUV coordinate system, it experiences the following effective velocities

where x^n, y , and zfin are the body-fixed coordinates of the fin posts. The effective fin angles of attack 5se and 5re are given by

where 5r and 5s are the fin angles referenced to the vehicle hull, pre and pse are the effective angles of attack of the fin zero plane, as shown in Fig.4. pre and are given by

P = ^ = v + xfinr - ZfinP p = f = w + yfin - Xfin<l (2Q)

" Ufin U+Z fin - yfinr " U fin U+ Zfin - yfiJ

Based on the above analysis, equation (1) could be rewritten into more detailed form

(Mrb + M A )V = t G + t prop + tr + D( V)V - (CSB(V) + C A (V))V (21)

(b) Effective stern plane angle of attack

(a) Effective rudder angle of attack Fig. 4. Effective angle of attack scheme

(b) Effective stern plane angle of attack

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