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sect6_5.py
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sect6_5.py
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import matplotlib as mpl
import matplotlib.pyplot as plt
from pylab import np
from scipy.optimize import fmin
#
# Figure size
mpl.rcParams['figure.figsize'] = 11, 5.625
# Text and numbers are substituded by Inkscape's PDF+Latex export option.
# By varying the sizes we can adjust the positioning
# http://stackoverflow.com/questions/30201310/use-of-hyphen-or-minus-sign-in-matplotlib-versus-compatibility-with-latex
mpl.rcParams['axes.unicode_minus'] = False
mpl.rcParams.update({'font.size': 15})
mpl.rc('xtick', labelsize=20)
mpl.rc('ytick', labelsize=20)
#
# This is important for font substitution
mpl.rcParams['svg.fonttype'] = 'none'
def Ftrx(lK, Rg, alpha, betas, beta, delta, omegat, ot):
cb = np.cos(beta)
sb = np.sin(beta)
ca = np.cos(alpha)
sa = np.sin(alpha)
cbs = np.cos(betas)
sbs = np.sin(betas)
cot = np.cos(np.radians(omegat)+ot)
sot = np.sin(np.radians(omegat)+ot)
cotd = np.cos(np.radians(omegat)+ot+delta)
sotd = np.sin(np.radians(omegat)+ot+delta)
#
ekxx = ca*cbs
ekxy = ca*sbs
ekxz = -sa
#
ekyx = -sbs
ekyy = cbs
ekyz = 0
#
ekzx = sa*cbs
ekzy = sa*sbs
ekzz = ca
#
ltx = ekxx*cotd + ekyx*sotd + cb*lK - cot*Rg
lty = ekxy*cotd + ekyy*sotd - sot*Rg
ltz = ekxz*cotd + sb*lK
#
return (ltx*ekxx+lty*ekxy+ltz*ekxz)/(ltx*ekzx+lty*ekzy+ltz*ekzz)
def Ftrxsum(lK, Rg, alpha, betas, beta, delta, omegat, pos):
return (Ftrx(lK, Rg, alpha, betas, beta, delta, omegat, pos[0]) +
Ftrx(lK, Rg, alpha, betas, beta, delta, omegat, pos[1]) +
Ftrx(lK, Rg, alpha, betas, beta, delta, omegat, pos[2]) +
Ftrx(lK, Rg, alpha, betas, beta, delta, omegat, pos[3]))/4
def Ftry(lK, Rg, alpha, betas, beta, delta, omegat, ot):
cb = np.cos(beta)
sb = np.sin(beta)
ca = np.cos(alpha)
sa = np.sin(alpha)
cbs = np.cos(betas)
sbs = np.sin(betas)
cot = np.cos(np.radians(omegat)+ot)
sot = np.sin(np.radians(omegat)+ot)
cotd = np.cos(np.radians(omegat)+ot+delta)
sotd = np.sin(np.radians(omegat)+ot+delta)
#
ekxx = ca*cbs
ekxy = ca*sbs
ekxz = -sa
#
ekyx = -sbs
ekyy = cbs
ekyz = 0
#
ekzx = sa*cbs
ekzy = sa*sbs
ekzz = ca
#
ltx = ekxx*cotd + ekyx*sotd + cb*lK - cot*Rg
lty = ekxy*cotd + ekyy*sotd - sot*Rg
ltz = ekxz*cotd + sb*lK
#
return (ltx*ekyx+lty*ekyy+ltz*ekyz)/(ltx*ekzx+lty*ekzy+ltz*ekzz)
def Ftrysum(lK, Rg, alpha, betas, beta, delta, omegat, pos):
return (Ftry(lK, Rg, alpha, betas, beta, delta, omegat, pos[0]) +
Ftry(lK, Rg, alpha, betas, beta, delta, omegat, pos[1]) +
Ftry(lK, Rg, alpha, betas, beta, delta, omegat, pos[2]) +
Ftry(lK, Rg, alpha, betas, beta, delta, omegat, pos[3]))/4
def Marx(lK, Rg, alpha, betas, beta, delta, omegat, ot):
cb = np.cos(beta)
sb = np.sin(beta)
ca = np.cos(alpha)
sa = np.sin(alpha)
cbs = np.cos(betas)
sbs = np.sin(betas)
cot = np.cos(np.radians(omegat)+ot)
sot = np.sin(np.radians(omegat)+ot)
cotd = np.cos(np.radians(omegat)+ot+delta)
sotd = np.sin(np.radians(omegat)+ot+delta)
#
ekxx = ca*cbs
ekxy = ca*sbs
ekxz = -sa
#
ekyx = -sbs
ekyy = cbs
ekyz = 0
#
ekzx = sa*cbs
ekzy = sa*sbs
ekzz = ca
#
eaxx = ekxx*cotd + ekyx*sotd
eaxy = ekxy*cotd + ekyy*sotd
eaxz = ekxz*cotd
#
ltx = eaxx + cb*lK - cot*Rg
lty = eaxy - sot*Rg
ltz = eaxz + sb*lK
#
vcx = eaxy*ltz - eaxz*lty
vcy = eaxz*ltx - eaxx*ltz
vcz = eaxx*lty - eaxy*ltx
#
return (vcx*ekxx+vcy*ekxy+vcz*ekxz)/(ltx*ekzx+lty*ekzy+ltz*ekzz)
def Marxsum(lK, Rg, alpha, betas, beta, delta, omegat, pos):
return (Marx(lK, Rg, alpha, betas, beta, delta, omegat, pos[0]) +
Marx(lK, Rg, alpha, betas, beta, delta, omegat, pos[1]) +
Marx(lK, Rg, alpha, betas, beta, delta, omegat, pos[2]) +
Marx(lK, Rg, alpha, betas, beta, delta, omegat, pos[3]))/4
def Mary(lK, Rg, alpha, betas, beta, delta, omegat, ot):
cb = np.cos(beta)
sb = np.sin(beta)
ca = np.cos(alpha)
sa = np.sin(alpha)
cbs = np.cos(betas)
sbs = np.sin(betas)
cot = np.cos(np.radians(omegat)+ot)
sot = np.sin(np.radians(omegat)+ot)
cotd = np.cos(np.radians(omegat)+ot+delta)
sotd = np.sin(np.radians(omegat)+ot+delta)
#
ekxx = ca*cbs
ekxy = ca*sbs
ekxz = -sa
#
ekyx = -sbs
ekyy = cbs
ekyz = 0
#
ekzx = sa*cbs
ekzy = sa*sbs
ekzz = ca
#
eaxx = ekxx*cotd + ekyx*sotd
eaxy = ekxy*cotd + ekyy*sotd
eaxz = ekxz*cotd
#
ltx = eaxx + cb*lK - cot*Rg
lty = eaxy - sot*Rg
ltz = eaxz + sb*lK
#
vcx = eaxy*ltz - eaxz*lty
vcy = eaxz*ltx - eaxx*ltz
vcz = eaxx*lty - eaxy*ltx
#
return (vcx*ekyx+vcy*ekyy+vcz*ekyz)/(ltx*ekzx+lty*ekzy+ltz*ekzz)
def Marysum(lK, Rg, alpha, betas, beta, delta, omegat, pos):
return (Mary(lK, Rg, alpha, betas, beta, delta, omegat, pos[0]) +
Mary(lK, Rg, alpha, betas, beta, delta, omegat, pos[1]) +
Mary(lK, Rg, alpha, betas, beta, delta, omegat, pos[2]) +
Mary(lK, Rg, alpha, betas, beta, delta, omegat, pos[3]))/4
def Marz(lK, Rg, alpha, betas, beta, delta, omegat, ot):
cb = np.cos(beta)
sb = np.sin(beta)
ca = np.cos(alpha)
sa = np.sin(alpha)
cbs = np.cos(betas)
sbs = np.sin(betas)
cot = np.cos(np.radians(omegat)+ot)
sot = np.sin(np.radians(omegat)+ot)
cotd = np.cos(np.radians(omegat)+ot+delta)
sotd = np.sin(np.radians(omegat)+ot+delta)
#
ekxx = ca*cbs
ekxy = ca*sbs
ekxz = -sa
#
ekyx = -sbs
ekyy = cbs
ekyz = 0
#
ekzx = sa*cbs
ekzy = sa*sbs
ekzz = ca
#
eaxx = ekxx*cotd + ekyx*sotd
eaxy = ekxy*cotd + ekyy*sotd
eaxz = ekxz*cotd
#
ltx = eaxx + cb*lK - cot*Rg
lty = eaxy - sot*Rg
ltz = eaxz + sb*lK
#
vcx = eaxy*ltz - eaxz*lty
vcy = eaxz*ltx - eaxx*ltz
vcz = eaxx*lty - eaxy*ltx
#
return (vcx*ekzx+vcy*ekzy+vcz*ekzz)/(ltx*ekzx+lty*ekzy+ltz*ekzz)
def Marzsum(lK, Rg, alpha, betas, beta, delta, omegat, pos):
return (Marz(lK, Rg, alpha, betas, beta, delta, omegat, pos[0]) +
Marz(lK, Rg, alpha, betas, beta, delta, omegat, pos[1]) +
Marz(lK, Rg, alpha, betas, beta, delta, omegat, pos[2]) +
Marz(lK, Rg, alpha, betas, beta, delta, omegat, pos[3]))/4
def Mgrz(lK, Rg, alpha, betas, beta, delta, omegat, ot):
cb = np.cos(beta)
sb = np.sin(beta)
ca = np.cos(alpha)
sa = np.sin(alpha)
cbs = np.cos(betas)
sbs = np.sin(betas)
cot = np.cos(np.radians(omegat)+ot)
sot = np.sin(np.radians(omegat)+ot)
cotd = np.cos(np.radians(omegat)+ot+delta)
sotd = np.sin(np.radians(omegat)+ot+delta)
#
ekxx = ca*cbs
ekxy = ca*sbs
ekxz = -sa
#
ekyx = -sbs
ekyy = cbs
ekyz = 0
#
ekzx = sa*cbs
ekzy = sa*sbs
ekzz = ca
#
eaxx = ekxx*cotd + ekyx*sotd
eaxy = ekxy*cotd + ekyy*sotd
eaxz = ekxz*cotd
#
ltx = eaxx + cb*lK - cot*Rg
lty = eaxy - sot*Rg
ltz = eaxz + sb*lK
#
vcz = cot*lty - sot*ltx
#
return vcz/(ltx*ekzx+lty*ekzy+ltz*ekzz)
def Mgrzsum(lK, Rg, alpha, betas, beta, delta, omegat, pos):
return (Mgrz(lK, Rg, alpha, betas, beta, delta, omegat, pos[0]) +
Mgrz(lK, Rg, alpha, betas, beta, delta, omegat, pos[1]) +
Mgrz(lK, Rg, alpha, betas, beta, delta, omegat, pos[2]) +
Mgrz(lK, Rg, alpha, betas, beta, delta, omegat, pos[3]))/4
def Ftrminmax(lK, Rg, alpha, betas, beta, delta, omegat, pos):
a = np.amin(Ftrxsum(lK, Rg, alpha, betas, beta, delta, omegat, pos))
b = np.amax(Ftrxsum(lK, Rg, alpha, betas, beta, delta, omegat, pos))
c = np.amin(Ftrysum(lK, Rg, alpha, betas, beta, delta, omegat, pos))
d = np.amax(Ftrysum(lK, Rg, alpha, betas, beta, delta, omegat, pos))
# print np.abs(a+b)+np.abs(c+d)
return (np.abs(a+b)+np.abs(c+d))
def Ftrxminmax(lK, Rg, alpha, betas, beta, delta):
pos = np.array([ 0, 0.5*np.pi, np.pi, 1.5*np.pi ])
omegat = np.arange(0, 360, 1)
a = np.amin(Ftrxsum(lK, Rg, alpha, betas, beta, delta, omegat, pos))
b = np.amax(Ftrxsum(lK, Rg, alpha, betas, beta, delta, omegat, pos))
return (np.abs(b-a))
def Ftryminmax(lK, Rg, alpha, betas, beta, delta):
pos = np.array([ 0, 0.5*np.pi, np.pi, 1.5*np.pi ])
omegat = np.arange(0, 360, 1)
c = np.amin(Ftrysum(lK, Rg, alpha, betas, beta, delta, omegat, pos))
d = np.amax(Ftrysum(lK, Rg, alpha, betas, beta, delta, omegat, pos))
return (np.abs(d-c))
def fopt(f, lK, Rg, alpha, betas, beta, delta, omegat, pos):
def foptfixed(p):
return f(lK, Rg, p[0], p[1], beta, delta, omegat, pos)
return foptfixed
def orientation(lK, Rg, alpha, betas, beta, delta, omegat, pos):
guess = [ alpha, betas ] # can be improved by passing proving
return fmin(fopt(Ftrminmax, lK, Rg, alpha, betas, beta, delta, omegat, pos), guess, xtol=0.00000001, ftol=0.00000001, maxiter=1000)
# mean aerodynamic moment over one cycle
def Marzmean(lK, Rg, alpha, betas, beta, delta):
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)
alpha = a
betas = b
Ma = np.mean(Marzsum(lK, Rg, a, b, beta, delta, omegat, pos))
Mg = np.mean(Marzsum(lK, Rg, a, b, beta, delta, omegat, pos))
return alpha, betas, Ma, Mg
def Marzmean0(lK, Rg, alpha, betas, beta, delta):
pos = np.array([ 0, 0.5*np.pi, np.pi, 1.5*np.pi ])
omegat = np.arange(0, 360, 1)
return np.mean(Marzsum(lK, Rg, alpha, betas, beta, delta, omegat, pos))
vw = 12.
Rg = 25.
Rk = 20.
Rko = 35.
N = 4
lK = 100.
beta = np.radians(30)
omega = 2.05
delta = np.radians(45)
Pnom = 1.4e6
rho = 1.225
lKRk = lK/Rk
RgRk = Rg/Rk
vtip = omega*Rko
lam = omega*Rko/vw
Ma = Pnom/omega
S = np.pi*(Rko*Rko-Rk*Rk)
alpha = np.radians(60) # Initial value
betas = np.radians(0) # Initial value
a, b, c, d = Marzmean(lKRk, RgRk, alpha, betas, beta, delta)
alpha = a
betas = b
MaRF = c
MgRF = d
Fakz = Ma/(MaRF*Rk)
sa = np.sin(alpha)
ca = np.cos(alpha)
sb = np.sin(betas)
cb = np.cos(betas)
L = Fakz*np.sqrt(sb*sb*sa*sa+ca*ca)
D = Fakz*cb*sa
LoD = L/D
CL = 2*L/(rho*S*vw*vw)
CD = 2*D/(rho*S*vw*vw)
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
print "h : ", h