Flute acoustics: measurement, modelling and design - School of ...

332 APPENDIX B. PROGRAM LISTINGS
/* calculate complex end corrections */
d_flanged = divz(arctanz(divz(Z_flanged, multz(j, Z0))),real(k));
d_cyl = subz(d_flanged, real(0.47 * a * pow(a / b, 0.8)));
/* add empirical correction */
d_cyl = addz(d_cyl, real(CORR_OPEN_FINGER_HOLE_LENGTH * a));
Z = multz(j, multz(Z0, tanz(multz(real(k), d_cyl))));
return Z;
}
complex openKeyedHoleLoadZ(double f, Hole hole) {
double a, d, q, h, e, w;
double d_corr, d_e_on_a, k;
complex Z_circ, Z0, d_circ, d_disk, Z, R;
Key key = hole->key;
a = hole->radius;
d = key->radius;
q = key->holeRadius;
h = key->height;
e = key->thickness;
w = key->wallThickness;
/* hack for classical flutes since the keyed holes have no
chimneys */
if (key->chimneyHeight == 0) w = DBL_MAX;
k = (2*M_PI*f)/hole->c;
/* calculate the characteristic impedance */
Z0 = charZ(hole->c, hole->rho, a);
/* Dalmont et al. (2001) Radiation impedance of tubes with different
flanges: Numerical and experimental investigations, Journal of
Sound and Vibration 244(3), 505--534, eqs. (48, 51, 52) */
d_corr = a / (3.5 * pow(h/a, 0.8) * pow(h/a + 3 * w/a, -0.4) + 30
* pow(h/d, 2.6));
/* add empirical length correction */
d_corr = d_corr + CORR_OPEN_KEYED_HOLE_LENGTH * a;
if (q > 0) {
d_e_on_a = 1.64*a/q - 0.15*a/d - 1.1 + e*a/(q*q);
d_corr = d_corr / (1 + 5*pow(d_e_on_a, -1.35)*pow(h/a, -0.2));
}
Z_circ = radiationZ(f, hole->c, hole->rho, a, w/a);
/* calculate complex end corrections */
d_circ = divz(arctanz(divz(Z_circ, multz(j, Z0))),real(k));
d_disk = addz(d_circ, real(d_corr));
Z = multz(j, multz(Z0, tanz(multz(real(k), d_disk))));
/* add empirical resistance */
R = multz(Z0, real(0.4 * pow(k * a, 2)));
Z = addz(Z, R);