def gammag(lK, Rg, beta, delta, omegat):
alpha = 0.5 * np.pi - beta
cb = np.cos(beta)
sb = np.sin(beta)
cot = np.cos(np.radians(omegat))
sot = np.sin(np.radians(omegat))
cotd = np.cos(np.radians(omegat) + delta)
sotd = np.sin(np.radians(omegat) + delta)
ltx = np.cos(alpha) * cotd + cb * lK - cot * Rg
lty = sotd - sot * Rg
ltz = -np.sin(alpha) * cotd + sb * lK
Rwx = cot * Rg
Rwy = sot * Rg
Rwz = 0
lt = np.sqrt(ltx * ltx + lty * lty + ltz * ltz)
return np.degrees(np.arccos((Rwx * lty - Rwy * ltx) / (lt * Rg)))
def gammak2(lK, Rg, beta, delta, omegat):
alpha = 0.5 * np.pi - beta
cb = np.cos(beta)
sb = np.sin(beta)
cot = np.cos(np.radians(omegat))
sot = np.sin(np.radians(omegat))
cotd = np.cos(np.radians(omegat) + delta)
sotd = np.sin(np.radians(omegat) + delta)
cotdt = np.cos(np.radians(omegat + 90) + delta)
sotdt = np.sin(np.radians(omegat + 90) + delta)
ltx = np.cos(alpha) * cotd + cb * lK - cot * Rg
lty = sotd - sot * Rg
ltz = -np.sin(alpha) * cotd + sb * lK
eyrx = np.cos(alpha) * cotdt
eyry = sotdt
eyrz = -np.sin(alpha) * cotdt
lt = np.sqrt(ltx * ltx + lty * lty + ltz * ltz)
return np.degrees(np.arccos((eyrx * ltx + eyry * lty + eyrz * ltz) / lt))
def gammak(lK, Rg, beta, delta, omegat):
alpha = 0.5 * np.pi - beta
cb = np.cos(beta)
sb = np.sin(beta)
ca = np.cos(alpha)
sa = np.sin(alpha)
cot = np.cos(np.radians(omegat))
sot = np.sin(np.radians(omegat))
cotd = np.cos(np.radians(omegat) + delta)
sotd = np.sin(np.radians(omegat) + delta)
Rax = ca * cotd
Ray = sotd
Raz = -sa * cotd
ltx = Rax + cb * lK - cot * Rg
lty = Ray - sot * Rg
ltz = Raz + sb * lK
lt = np.sqrt(ltx * ltx + lty * lty + ltz * ltz)
return np.degrees(
np.arccos((sa * (Ray * ltz - Raz * lty) + ca *
(Rax * lty - Ray * ltx)) / lt))
vMarzmean = np.vectorize(Marzmean) vMarzmean0 = np.vectorize(Marzmean0) f, (ax1, ax2) = plt.subplots(1, 2) alpha = np.radians(60) # 90 - beta | 62.3608549873 betas = np.radians(0) # 4.38381787735 lK = 2 Rg = 1 N = 4 delta = np.arange(0, 181, 1) beta = np.radians(30) a, b, Ma, Mg = vMarzmean(lK, Rg, alpha, betas, beta, np.radians(delta)) ax1.plot(delta, np.degrees(a), 'r', label=r"\$\alpha\$") ax1.plot(delta, np.degrees(b), 'b', label=r"\$\betas\$") ax2.plot(delta, Ma, 'r', label=r"\$\Mamean/(\Rk\Fakz)\$") #ax2.plot(delta, vMarzmean0(lK, Rg, alpha, betas, beta, np.radians(delta)), 'b--') beta = np.radians(45) a, b, Ma, Mg = vMarzmean(lK, Rg, alpha, betas, beta, np.radians(delta)) ax1.plot(delta, np.degrees(a), 'r') ax1.plot(delta, np.degrees(b), 'b--') ax2.plot(delta, Ma, 'r') #ax2.plot(delta, vMarzmean0(lK, Rg, alpha, betas, beta, np.radians(delta)), 'b--') beta = np.radians(60) a, b, Ma, Mg = vMarzmean(lK, Rg, alpha, betas, beta, np.radians(delta)) ax1.plot(delta, np.degrees(a), 'r') ax1.plot(delta, np.degrees(b), 'b--')
marker='o',
s=80,
linewidth=1.2,
edgecolor='k',
facecolor='w')
plt.xlim(1.0, 5.0)
plt.ylim(0.0, 3.0)
plt.xticks(np.arange(1.0, 5.01, 1.0))
plt.yticks(np.arange(0.0, 3.01, 1.0))
minorLocator = MultipleLocator(0.5)
ax.xaxis.set_minor_locator(minorLocator)
ax.yaxis.set_minor_locator(minorLocator)
plt.xlabel(r"Relative distance between rotor centers \$\lK/\Rk\, [-]\$",
labelpad=10)
plt.ylabel(r"Rotor size ratio \$\Rg/\Rk\, [-]\$", labelpad=10)
# Test to compare with Fig. 17
a, Ma, f = vMarzmean(5.0, 1.25, alpha, betas, beta, delta)
print "Ma = ", Ma, " alpha = ", np.degrees(a), " betas = ", np.degrees(
betas), "Rko/Rk = ", lK * np.sin(beta) / np.sin(a)
# Save as SVG file
plt.subplots_adjust(left=0.07,
bottom=None,
right=0.93,
top=None,
wspace=None,
hspace=None)
plt.savefig("fig18_diagram.svg")
plt.show()
vMarzmean = np.vectorize(Marzmean)
f, (ax1, ax2) = plt.subplots(1, 2)
alpha = np.radians(60)
betas = np.radians(0)
beta = np.radians(30)
delta = np.radians(45)
#lK = 1./np.tan(beta)
lK = 2.6
Rg = np.arange(2.6, 3.0, 0.01)
N = 4
a, b, Ma, Mg, Ftau = vMarzmean(lK, Rg, alpha, betas, beta, delta)
Mam = np.ma.masked_where(Ftau > 10., Ma)
ax1.plot(Rg, np.degrees(a), 'r')
ax1.plot(Rg, np.degrees(b), 'b')
ax1.plot([0.0, 3.0], [60.0, 60.0], 'k', label="positive ground clearance")
ax2.plot(Rg, Mam, 'r')
ax2.plot(Rg, Ftau, 'g')
print "lK = ", lK, " Rg = ", Rg[np.argmax(Ftau > 10.) -
1], " Mam = ", Mam[np.argmax(Ftau > 10.) - 1]
ax1.set_xlim(0.0, 3.0)
ax1.set_ylim(0.0, 90.0)
ax2.set_xlim(0.0, 3.0)
ax2.set_ylim(0.0, 2.0)
ax2.yaxis.tick_right()
ax2.yaxis.set_ticks_position('both')
return fmin(fopt(Ftrminmax, lK, Rg, alpha, betas, beta, delta, omegat, pos), guess, xtol=0.00001, ftol=0.00001, maxiter=100)
f, (ax1, ax2) = plt.subplots(1, 2)
beta = np.radians(30)
alpha = np.radians(60) # 90 - beta | 62.3608549873
betas = np.radians(0) # 4.38381787735
delta = np.radians(30) # 30
lK = 2
Rg = 1
N = 4
pos = np.array([ 0, 0.5*np.pi, np.pi, 1.5*np.pi ])
omegat = np.arange(0, 360, 1)
a, b = orientation(lK, Rg, alpha, betas, beta, delta, omegat, pos)
print "alpha = ", np.degrees(a), " betas = ",np.degrees(b)
alpha = a
betas = b
ax1.plot(omegat, Ftrxsum(lK, Rg, alpha, betas, beta, delta, omegat, pos), 'r', label=r"\$\Fakx/\Fakz\$")
ax1.plot(omegat, Ftrysum(lK, Rg, alpha, betas, beta, delta, omegat, pos), 'b', label=r"\$\Faky/\Fakz\$")
ax1.plot(omegat, Marxsum(lK, Rg, alpha, betas, beta, delta, omegat, pos), 'k')
ax1.plot(omegat, Marysum(lK, Rg, alpha, betas, beta, delta, omegat, pos), 'r--')
ax1.set_xlim(0,360)
ax1.set_ylim(-0.01,0.01)
ax1.set_xticks(np.arange(0,361,90))
#ax1.set_yticks(np.arange(-1,1.1,0.5))
ax2.plot(omegat, Marzsum(lK, Rg, alpha, betas, beta, delta, omegat, pos), 'r', label=r"\$\Ma/(\Rk\Fakz)\$")
ax2.plot(omegat, Mgrzsum(lK, Rg, alpha, betas, beta, delta, omegat, pos), 'b', label=r"\$\Mgz/(\Rk\Fakz)\$")
omegat = np.arange(0, 360, 1)
return np.amax(lt(lK, Rg, beta, delta, omegat))
vltfreemin = np.vectorize(ltfreemin)
vltfreemax = np.vectorize(ltfreemax)
vltmin = np.vectorize(ltmin)
vltmax = np.vectorize(ltmax)
f, (ax1, ax2) = plt.subplots(1, 2)
lK = 2
Rg = 1
beta = np.radians(np.arange(0, 91, 1))
delta = np.radians(0)
ax1.plot(np.degrees(beta), vltmax(lK, Rg, beta, delta), 'r')
ax1.plot(np.degrees(beta), vltmin(lK, Rg, beta, delta), 'b')
#print 'ltmin & ltmax ', ltmin(lK, Rg, np.radians(30), delta), ltmax(lK, Rg, np.radians(30), delta)
delta = np.radians(30)
ax1.plot(np.degrees(beta), vltmax(lK, Rg, beta, delta), 'r')
ax1.plot(np.degrees(beta), vltmin(lK, Rg, beta, delta), 'b')
delta = np.radians(60)
ax1.plot(np.degrees(beta), vltmax(lK, Rg, beta, delta), 'r')
ax1.plot(np.degrees(beta), vltmin(lK, Rg, beta, delta), 'b')
delta = np.radians(90)
ax1.plot(np.degrees(beta), vltmax(lK, Rg, beta, delta), 'r')
ax1.plot(np.degrees(beta), vltmin(lK, Rg, beta, delta), 'b')
delta = np.radians(120)
#ax1.plot(np.degrees(beta), vltmax(lK, Rg, beta, delta), 'r')
#ax1.plot(np.degrees(beta), vltmin(lK, Rg, beta, delta), 'b')
delta = np.radians(150)
CM = 2 * Ma / (rho * Rko * S * vw * vw) Cp = lam * CM aeff = np.arccos(cb * ca) Ftrxam = Ftrxminmax(lKRk, RgRk, alpha, betas, beta, delta) Ftryam = Ftryminmax(lKRk, RgRk, alpha, betas, beta, delta) h = np.sin(beta) * lK - sa * Rko print "Pnom : ", Pnom print "lK/Rk : ", lKRk print "Rg/Rk : ", RgRk print "vtip : ", vtip print "lambda: ", lam print "Ma : ", Ma print "S : ", S print "alpha : ", np.degrees(alpha) print "betas : ", np.degrees(betas) print "MaRF : ", MaRF print "Fakz : ", Fakz print "Ftiz : ", Fakz / N print "test : ", Ma / (Rk * Fakz) print "L : ", L print "D : ", D print "LoD : ", LoD print "CL : ", CL print "CD : ", CD print "CM : ", CM print "Cp : ", Cp print "aeff : ", np.degrees(aeff) print "Ftrx : ", Ftrxam print "Ftry : ", Ftryam
# vector base rotating reference frame
e = le * eb(ot0)
ebx = e[:, 0]
ax.plot([0, ebx[0]], [0, ebx[1]], [0, ebx[2]], linewidth=3, color='b')
eby = e[:, 1]
ax.plot([0, eby[0]], [0, eby[1]], [0, eby[2]], linewidth=3, color='b')
ebz = e[:, 2]
#ax.plot([0, ebz[0]], [0, ebz[1]], [0, ebz[2]], linewidth=2, color='b')
# elevation angle
r0 = np.array([0, 0, 0])
R = 32
e = ewx
n = -ewy
r = arc(r0, R, e, n, np.degrees(beta), omegat)
ax.plot(r[0, :], r[1, :], r[2, :], zorder=20, linewidth=2, color='r')
# rotor spinning
R = 20
e = ewx
n = ewz
r = arc(r0, R, e, n, ot0, omegat)
ax.plot(r[0, :], r[1, :], r[2, :], zorder=20, linewidth=2, color='r')
# Flying rotor
r = rA(lK, Rk, alpha, betas, beta, delta, omegat)
ax.plot(r[0], r[1], r[2], zorder=-10, linewidth=1.2, color='#00ff00')
r = rA(lK, Rk, alpha, betas, beta, delta, ot0 + ot[0])
ax.scatter(r[0],
r[1],
