def alfaV(self, v0):
"""Retourne le alfa tel que V(alfa) = v0. Ne correspond pas à l'équilibre."""
# return newton(lambda alfa : self.V(alfa)-v0, radians(6.0), full_output=True, disp=False)
# except RuntimeError as msg : return nan
alfa, res = newton(lambda alfa: self.V(alfa) - v0,
radians(6.0),
tol=self.EPS,
full_output=True,
disp=False)
if res.converged:
return alfa % π
else:
alfa = res.root
res = dict(root=fmt(degrees(res.root)),
iterations=res.iterations,
function_calls=res.function_calls,
converged=res.converged,
cause=res.flag)
rn = norm(self.resultante(self.normalise(alfa)))
r = norm(self.resultante(alfa))
cm = fmt(self.CmT(alfa))
debug('alfaV : non CV')
print("alfa_normalisé = %s," % fmt(degrees(alfa % π)),
'resultante = (%s,%s),' % fmt((rn, r)), 'CmT =', cm)
print('résultats newton = ', fmt(res))
print()
if abs(r) < self.EPS:
return alfa % π
def equilibre(self, **kargs):
"""
:param kargs: les variables à modifier, parmi self.VARIABLES
:return:float, l'incidence alfa° telle que CmT(alfa)=0
>>> P = Parapente('diamir')
>>> eq = Equilibriste(P)
>>> alfa = eq.equilibre(c=29.0, mp=100.0, S=28.0, d=10.0)
# alfa sera l'incidence d'équilibre pour le parapente P,
# avec un calage c, un pilote de masse mp, une surface S, et 10% de freins
"""
objectif = self.CmT
def objectif(alfa):
"""
La fonction à annuler pour trouver l'équilibre
Peut être que return self.CmT(alfa) suffit...
"""
alfa = alfa % π
fx, fz = self.resultante(alfa)
return self.CmT(alfa)**2 + fx**2 + fz**2
return fx**2 + fz**2
if kargs: self.load(kargs)
#disp=False pour que newton ne lève pas une exception
alfa, res = newton(objectif,
radians(6.0),
tol=self.EPS,
full_output=True,
disp=False)
if res.converged:
return alfa % π
else:
alfa = res.root
res = dict(root=fmt(degrees(res.root)),
iterations=res.iterations,
function_calls=res.function_calls,
converged=res.converged,
cause=res.flag)
rn = norm(self.resultante(self.normalise(alfa)))
r = norm(self.resultante(alfa))
cm = self.CmT(alfa)
debug('Non CV', resultante=(rn, r), CmT=cm, res=res)
if abs(r) < self.EPS:
return alfa % π
# debug('Non CV', resultante=(fmt(rn,6), fmt(r,6)))
return nan
def write(self, filename=None, **kargs):
"""
:param freins:tuple, les % de freins pour lesquels on calcule l'équilibre, ∈[0.0, 100.0]
:type filename: fichier ou str
"""
if not kargs:
kargs = readPyData(Path(DATA_DIR) / 'preferences' / 'aero2d.dict')
if filename is None:
fout = open(self.P.compfile, 'w')
# filename=self.P.aerodir/"%s.comportement.txt"%self.session
elif isinstance(filename, str):
fout = open(filename, 'w')
else: #fichier ouvert. p. ex. sys.stdout
fout = filename
dump = fmt(self.toDump())
print(sapero(), maintenant(), "\n\n", file=fout)
with fout:
titre = sursouligne(" Lexique et valeurs des paramètres ", "=")
print(titre, file=fout)
for key in sorted(self.VARIABLES):
print("%5s = %-6s = %s" %
(key, dump[key], self.VARIABLES[key]),
file=fout)
print(
"\nN.B. la valeur 'nan' (Not A Number), pour signifier que le calcul n\'a pas abouti (plantage, non convergence..)",
file=fout)
print(
"""\nN.B. suivant la valeur de l'incidence, le vol peut être d'un des types suivants (dans les 2 ou 3 derniers cas... à utiliser avec circonspection !):
. > vol normal,
* > vol marche arrière,
** > vol dos,
*** > vol dos + marche arrière.""",
file=fout)
self._writeEquilibre(fout)
for key, values in kargs.items():
if key == 'mp':
self._writeVariationMassePilote(values, fout)
if key == 'c':
# rdebug(values)
self._writeVariationCalage(values, fout)
def _writeVariationMassePilote(self, Ms, fout):
eldump0 = self.toDump(
) #On le sauve car je crois qu'on le modifie un peu
eldump0['mp'] = '***'
print("\n\n", file=fout)
titre = sursouligne(" Variation masse pilote ", "=")
print(titre, file=fout)
if 0: print("paramètres :\n", fmt(eldump0), file=fout)
eldump0 = self.toDump(
) #On le sauve car je crois qu'on le modifie un peu
CZs, CXVs, CMVs, REs, Vs, VZs, CPs, FINs, CMTs = [], [], [], [], [], [], [], [], []
THETAs, ALPHAs, vols = [], [], []
for c in Ms:
try:
alfa = self.alfaEq(mp=c)
except RuntimeError as msg:
debug(msg, calage=c)
alfa = nan
idx, _ = self.typeDeVol(alfa)
vols.append('.' if idx == 0 else idx * "*")
ALPHAs.append(alfa * 180 / π)
FINs.append(self.finesse(alfa))
Vs.append(self.V(alfa) * 3.6)
VZs.append(self.Vz(alfa))
CPs.append(100 * self.CP(alfa))
THETAs.append(self.θ(alfa) * 180 / π)
r = self.resultante(alfa)
REs.append(abs(r[0]) + abs(r[1]) + abs(self.CmT(alfa)))
CMTs.append(self.CmT(alfa))
CZs.append(self.Cz(alfa))
CXVs.append(self.Cxv(alfa))
CMVs.append(self.Cmv(alfa))
rdebug(vols)
print("---------------------|" + "-".join([7 * '-' for c in Ms]),
file=fout)
print(" masse pilote (kg) |",
" ".join(['%-7.2f' % c for c in Ms]),
file=fout)
print("---------------------|" + "-".join([7 * '-' for c in Ms]),
file=fout)
# if not any(vols) :
print(" Type de vol |",
" ".join(['%-7.2s' % c for c in vols]),
file=fout)
print(" Incidence (°) |",
" ".join(['%-7.2f' % c for c in ALPHAs]),
file=fout)
print(" Vitesse (km/h) |",
" ".join(['%-7.2f' % c for c in Vs]),
file=fout)
print(" Vz (m/s) |",
" ".join(['%-7.2f' % c for c in VZs]),
file=fout)
print(" Finesse |",
" ".join(['%-7.2f' % c for c in FINs]),
file=fout)
print(" Assiette (°) |",
" ".join(['%-7.2f' % c for c in THETAs]),
file=fout)
print(" Centre poussee (%) |",
" ".join(['%-7.2f' % c for c in CPs]),
file=fout)
print("---------------------|" + "-".join([7 * '-' for c in CPs]),
file=fout)
print(" Cz |",
" ".join(['%-7.2f' % c for c in CZs]),
file=fout)
print(" Cx voile |",
" ".join(['%-7.2f' % c for c in CXVs]),
file=fout)
print(" Cm voile |",
" ".join(['%-7.2f' % c for c in CMVs]),
file=fout)
print("---------------------|" + "-".join([7 * '-' for c in CPs]),
file=fout)
print(" Resultante(=0 ?) |",
" ".join(['%-7.0g' % c for c in REs]),
file=fout)
print(" Moment(=0 ?) |",
" ".join(['%-7.0g' % c for c in CMTs]),
file=fout)
print("---------------------|" + "-".join([7 * '-' for c in Ms]),
file=fout)
self.load(eldump0)
def _writeEquilibre(self, fout):
eldump0 = self.toDump(
) #On le sauve car je crois qu'on le modifie un peu
titre = sursouligne(' Equilibre ', "=")
print('\n\n', file=fout)
print(titre, file=fout)
if 0: print("Paramètres:\n%s" % fmt(self.toDump()), file=fout)
CZs, CXVs, CMVs, REs, Vs, VZs, CPs, FINs, CMTs = [], [], [], [], [], [], [], [], []
DELTAs, THETAs, ALPHAs = [], [], []
alfa = self.equilibre()
ALPHAs.append(alfa * 180 / π)
FINs.append(self.finesse(alfa))
Vs.append(self.V(alfa) * 3.6)
VZs.append(self.Vz(alfa))
CPs.append(100 * self.CP(alfa))
THETAs.append(self.θ(alfa) * 180 / π)
r = self.resultante(alfa)
REs.append(abs(r[0]) + abs(r[1]) + abs(self.CmT(alfa)))
CMTs.append(self.CmT(alfa))
CZs.append(self.Cz(alfa))
CXVs.append(self.Cxv(alfa))
CMVs.append(self.Cmv(alfa))
# debug(titre="Je ne sais plus d'ou vient la formule pour simuler les freins !!")
print(" Frein (%) |",
" ".join(['%-7.1f' % c for c in DELTAs]),
file=fout)
print("---------------------|" + "-".join([7 * '-' for c in CPs]),
file=fout)
print(" Incidence (°) |",
" ".join(['%-7.2f' % c for c in ALPHAs]),
file=fout)
print(" Vitesse (km/h) |",
" ".join(['%-7.2f' % c for c in Vs]),
file=fout)
print(" Vz (m/s) |",
" ".join(['%-7.2f' % c for c in VZs]),
file=fout)
print(" Finesse |",
" ".join(['%-7.2f' % c for c in FINs]),
file=fout)
print(" Assiette (°) |",
" ".join(['%-7.2f' % c for c in THETAs]),
file=fout)
print(" Centre poussee (%) |",
" ".join(['%-7.2f' % c for c in CPs]),
file=fout)
print("---------------------|" + "-".join([7 * '-' for c in CPs]),
file=fout)
print(" Cz |",
" ".join(['%-7.2f' % c for c in CZs]),
file=fout)
print(" Cx voile |",
" ".join(['%-7.2f' % c for c in CXVs]),
file=fout)
print(" Cm voile |",
" ".join(['%-7.2f' % c for c in CMVs]),
file=fout)
print("---------------------|" + "-".join([7 * '-' for c in CPs]),
file=fout)
print(" Resultante(=0 ?) |",
" ".join(['%-7.0g' % c for c in REs]),
file=fout)
print(" Moment(=0 ?) |",
" ".join(['%-7.0g' % c for c in CMTs]),
file=fout)
self.load(eldump0)
def plot(self, **kargs):
"""TODO : tracés pour variation calage, longueur cône suspentage, CxV, Cxs, Cxp,..."""
# csfont = {'fontname':'Comic Sans MS'}
hfont = {'fontname': 'Liberation Serif'}
if not kargs:
kargs = readPyData(Path(DATA_DIR) / 'preferences' / 'aero2d.dict')
if 'mp' in kargs:
Vs, VZs, CPs, FINs, ALPHAs = [], [], [], [], []
Mp = kargs['mp']
for m in Mp:
alfa = self.alfaEq(mp=m)
if alfa < 0:
# alfa = self.normalise(alfa)
debug('Fermeture, vol impossible; alfa=%s' %
fmt(degrees(alfa)))
alfa = nan
alfa = alfa % π
# idx, _ = self.typeDeVol(alfa)
# typevols.append(' .' if idx==0 else ' '+idx*"*")
ALPHAs.append(alfa * 180 / π)
FINs.append(self.finesse(alfa))
Vs.append(self.V(alfa) * 3.6)
VZs.append(self.Vz(alfa))
CPs.append(100 * self.CP(alfa))
r = self.resultante(alfa)
# REs.append(abs(r[0]) + abs(r[1]) + abs(self.CmT(alfa)))
# CMTs.append(self.CmT(alfa))
# CZs.append(self.Cz(alfa))
# CXVs.append(self.Cxv(alfa))
# CMVs.append(self.Cmv(alfa))
# adeg = linspace(min(self.alfadegs), max(self.alfadegs), 100)
# arad = linspace(min(self.alfas), max(self.alfas), 100)
# Cxs, Czs = self.Cx(arad), self.Cz(arad)
debug(finesses=fmt(FINs))
debug(Vz=fmt(VZs))
fig = plt.figure()
ax1 = fig.add_subplot(221)
ax2 = fig.add_subplot(222, sharex=ax1)
ax3 = fig.add_subplot(223, sharex=ax1)
ax4 = fig.add_subplot(224, sharex=ax1)
# ax4.set_xlim(left=0.0, right=max(Cxs))
# ax4.set_ylim(bottom=0.0, top=max(Czs))
ax1.plot(Mp, FINs, 'b.-') #, label='$ \\phi $')
# ax1.plot(self.alfadegs, self.Czs, 'b.', label='data')
# ax1.legend()
ax1.set_xlabel('$ m_p (kg) $')
ax1.set_ylabel('$ \\phi $')
ax1.set_title('Finesses', **hfont)
ax2.plot(Mp, Vs, 'b.-') #, label='$V$')
ax2.set_xlabel('$ m_p (kg) $ ')
ax2.set_ylabel('$ V (km/h) $')
ax2.set_title('Vitesse sur trajectoire (km/h)', **hfont)
# ax2.legend()
ax3.plot(Mp, VZs, 'b.-') #, label='data')
ax3.set_ylabel('$ V_z (m/s) $')
ax3.set_title('Taux de chute (m/s)', **hfont)
if 0:
ax4.plot(Mp, ALPHAs, 'b.-') #, label='data')
ax4.set_ylabel('$ \\alpha (°) $')
ax4.set_title('Incidences', **hfont)
if 1:
ax4.plot(Mp, CPs, 'b.-') #, label='data')
ax4.set_ylabel('$ CP $ ')
ax4.set_title('Centre de poussée % de corde', **hfont)
fig.suptitle(
'Session %s : variation de la masse pilote $m_p$\n' % AC.SESSION,
**hfont)
plt.tight_layout()
plt.show()
def _writeVariationCalage(self, Cs, fout):
eldump0 = self.toDump()
eldump0['c'] = '###'
titre = sursouligne(" Variation calage ", "=")
print("\n\n", file=fout)
print(titre, file=fout)
if 0: print("paramètres:\n", fmt(eldump0), file=fout)
eldump0 = self.toDump()
CZs, CXVs, CMVs, REs, Vs, VZs, CPs, FINs, CMTs = [], [], [], [], [], [], [], [], []
THETAs, ALPHAs, typevols = [], [], []
for c in Cs:
try:
alfa = self.alfaEq(c=c)
except RuntimeError as msg:
debug(msg, calage=c)
alfa = nan
# continue
if alfa < 0:
alfa = nan
alfa = alfa % π
debug('Fermeture, vol impossible')
idx, _ = self.typeDeVol(alfa)
typevols.append(' .' if idx == 0 else ' ' + idx * "*")
ALPHAs.append(alfa * 180 / π)
FINs.append(self.finesse(alfa))
Vs.append(self.V(alfa) * 3.6)
VZs.append(self.Vz(alfa))
CPs.append(100 * self.CP(alfa))
THETAs.append(self.θ(alfa) * 180 / π)
r = self.resultante(alfa)
REs.append(abs(r[0]) + abs(r[1]) + abs(self.CmT(alfa)))
CMTs.append(self.CmT(alfa))
CZs.append(self.Cz(alfa))
CXVs.append(self.Cxv(alfa))
CMVs.append(self.Cmv(alfa))
print("---------------------|" + "-".join([7 * '-' for c in CPs]),
file=fout)
print(" Calage (% de corde) |",
" ".join(['%-7.1f' % (100 * c) for c in Cs]),
file=fout)
print(" Type de vol |" +
" ".join(['%-7s' % c for c in typevols]),
file=fout)
print("---------------------|" + "-".join([7 * '-' for c in CPs]),
file=fout)
print(" Incidence (°) |",
" ".join(['%-7.2f' % c for c in ALPHAs]),
file=fout)
print(" Vitesse (km/h) |",
" ".join(['%-7.2f' % c for c in Vs]),
file=fout)
print(" Vz (m/s) |",
" ".join(['%-7.2f' % c for c in VZs]),
file=fout)
print(" Finesse |",
" ".join(['%-7.2f' % c for c in FINs]),
file=fout)
print(" Assiette (°) |",
" ".join(['%-7.2f' % c for c in THETAs]),
file=fout)
print(" Centre poussee (%) |",
" ".join(['%-7.2f' % c for c in CPs]),
file=fout)
print("---------------------|" + "-".join([7 * '-' for c in CPs]),
file=fout)
print(" Cz |",
" ".join(['%-7.2f' % c for c in CZs]),
file=fout)
print(" Cx voile |",
" ".join(['%-7.2f' % c for c in CXVs]),
file=fout)
print(" Cm voile |",
" ".join(['%-7.2f' % c for c in CMVs]),
file=fout)
print("---------------------|" + "-".join([7 * '-' for c in CPs]),
file=fout)
print(" Resultante(=0 ?) |",
" ".join(['%-7.0g' % c for c in REs]),
file=fout)
print(" Moment(=0 ?) |",
" ".join(['%-7.0g' % c for c in CMTs]),
file=fout)
print("---------------------|" + "-".join([7 * '-' for c in CPs]),
file=fout)
#On rétablit dans sa config originale
self.load(eldump0)
def __str__(self):
return "(" + str(fmt(self.x)) + ", " + str(fmt(self.y)) + ", " + str(
fmt(self.z)) + ")"
print(souligne('Pour B = (x,y,z) on doit trouver T(B) = (z,1,1-x)'))
for B in (Point(1, 0, 0), Point(0, 0, 1), Point(0, 1,
0), Point(1, 1, 0),
Point(0, 1, 1), Point(1, 0, 1), Point(1, 1,
1), Point(1, 2, 3),
Point(random(), random(), random())):
print('B = %s' % B, '=> T(B) = %s' % T(B))
print('T = %r' % T)
if 0:
debug(paragraphe="l'invariant est-il invariant ?")
T1 = Torseur(A=Point(random(), random(), random()),
R=Vecteur(random(), random(), random()),
M=Vecteur(random(), random(), random()))
for i in range(10):
P = Point(random(), random(), random())
print("T1.invariant(P)", fmt(T1.invariant(P), 10))
#################################################################
## VECTEUR TEST, NE PAS MODIFIER
T1 = Torseur(Point(1, 1, 1), Vecteur(1, 2, -1), Vecteur(-1, 1, -2))
#################################################################
## VECTEUR TEST, NE PAS MODIFIER
if 0:
debug(titre='somme de Torseurs T+=T1')
print('T = %r' % (T), 'invariant=%s' % fmt(T.invariant()))
print('T1 = %r' % (T1), 'invariant=%s' % fmt(T1.invariant()))
T += T1
print('T += T1') # =>\nT = %r'%(T))
print('T après : %r' % T,
'invariant=%s' % fmt(T.invariant())) # =>\nT = %r'%(T))
print('T1 après : %r' % T1,
'invariant=%s' % fmt(T1.invariant())) # =>\nT = %r'%(T))