def q2():
lm = np.linspace(Ma[0], Ma[1])
n = len(lm)
for i, ms_i in enumerate(ms):
for j, km_i in enumerate(km):
PLANE.set_mass_and_static_margin(km_i, ms_i)
F0 = np.zeros(n)
F1 = np.zeros(n)
for k, m_i in enumerate(lm):
va0 = dynamic.va_of_mach(m_i, h[0])
va1 = dynamic.va_of_mach(m_i, h[1])
X0, U0 = dynamic.trim(PLANE, {'va': va0, 'h': h[0]})
X1, U1 = dynamic.trim(PLANE, {'va': va1, 'h': h[1]})
F0[k] = dynamic.propulsion_model(X0, U0, PLANE)
F1[k] = dynamic.propulsion_model(X1, U1, PLANE)
plt.subplot(2, 2, i + 2 * j + 1)
plt.plot(lm, F0, label="$h={}$".format(h[0]))
plt.plot(lm, F1, label="$h={}$".format(h[1]))
plt.legend()
plt.title("$m_s={}, k_m={}$".format(ms_i, km_i))
plt.xlabel("$M_a$")
plt.ylabel("$F$")
plt.tight_layout(.5)
plt.savefig(file + "q2" + format)
plt.show()
def plot_trims(aircraft, gamma=0., saturate=True):
'''
Affichage de trims sous forme de surfaces colorées
'''
vs = np.linspace(60, 350, 21, endpoint=True)
hs = np.linspace(1000, 14000, 21, endpoint=True)
trims = np.zeros((len(hs), len(vs), 2))
for i,v in enumerate(vs):
for j,h in enumerate(hs):
Xe, Ue = dyn.trim(aircraft, args = {'va': v, 'h': h, 'gamma': gamma})
trims[j, i] = Xe[dyn.s_a], tons_of_newton(dyn.propulsion_model([0, h, v, 0, 0, 0], [0, Ue[dyn.i_dth], 0, 0], aircraft))
if saturate:
alpha_c, T_c = trims[j,i][0], trims[j,i,1]
alpha_max = ut.rad_of_deg(15)
if alpha_c > alpha_max:
trims[j,i][0] = 1e16
trims[j,i][1] = 1e16
Tmax = tons_of_newton(dyn.propulsion_model([0, h, v, 0, 0, 0], [0, 1, 0, 0], aircraft))
if T_c > Tmax:
trims[j,i, 0] = 1e16
trims[j,i, 1] = 1e16
fig = plt.figure(figsize=(0.75*20.48, 0.5*10.24))
ax = plt.subplot(1,2,1)
thetas_deg = ut.deg_of_rad(trims[:, :, 0])
v = np.linspace(0, 15, 16, endpoint=True)
plt.contour(vs, hs, thetas_deg, v, linewidths=0.5, colors='k')
plt.contourf(vs, hs, thetas_deg, v, cmap=plt.cm.jet)
ax.set_title(u'$\\alpha$ (degrés)')
ax.xaxis.set_label_text('vitesse (m/s)')
ax.yaxis.set_label_text('altitude (m)')
plt.colorbar(ticks=v)
ax = plt.subplot(1,2,2)
T_tons = trims[:, :, 1] #/9.81/1000.
v = np.linspace(2, 10, 17, endpoint=True)
plt.contour(vs, hs, T_tons, v, linewidths=0.5, colors='k')
plt.contourf(vs, hs, T_tons, v, cmap=plt.cm.jet)
ax.set_title('thrust (tons)')
ax.xaxis.set_label_text('vitesse (m/s)')
ax.yaxis.set_label_text('altitude (m)')
plt.colorbar(ticks=v)
def plot_thrust(P, filename=None):
figure = ut.prepare_fig(None, u'Poussée {}'.format(P.name))
hs = np.linspace(3000, 11000, 5)
for h in hs:
Machs = np.linspace(0.5, 0.8, 30)
thrusts = np.zeros(len(Machs))
for i in range(0, len(Machs)):
thrusts[i] = dyn.propulsion_model([0, h, dyn.va_of_mach(Machs[i], h), 0, 0, 0], [0, 1., 0, 0], P)
plt.plot(Machs, thrusts)
ut.decorate(plt.gca(), u'Poussée maximum {}'.format(P.name), r'Mach', '$N$',
['{} m'.format(h) for h in hs])
if filename<> None: plt.savefig(filename, dpi=160)
return figure
def evol_poussee(P):
U = [0, 1, 0, 0]
hs = np.linspace(3000, 11000, 5)
machs = np.linspace(0.5, 0.8, 30)
for h in hs:
Poussee = [
dyn.propulsion_model([0, h, dyn.va_of_mach(mach, h), 0, 0, 0], U,
P) for mach in machs
]
plt.plot(machs, Poussee)
ut.decorate(plt.gca(),
title='Poussée maximale en fonction du Mach',
xlab='Mach',
ylab='Poussee (N)',
legend=['{} m'.format(h) for h in hs])
plt.show()
'gamm': 0.,
'h': l
})
alphatrim[ib, jb, kb, lb] = X[3]
dphrtrim[ib, jb, kb, lb] = U[0]
dthtrim[ib, jb, kb, lb] = U[1]
for kbb, k in enumerate(Ma1):
for lbb, l in enumerate(h):
va_h0b = dynamic.va_of_mach(k, l, k=1.4, Rs=287.05)
Xb, Ub = dynamic.trim(avion, {
'va': va_h0b,
'gamm': 0.,
'h': l
})
prop[ib, jb, kbb,
lbb] = dynamic.propulsion_model(Xb, Ub, avion)
affiche()
'''''' '''''' ''''''
# question 3
valeur_trim = alphatrim[0, 0, 0, 0], dphrtrim[0, 0, 0, 0], dthtrim[0, 0, 0,
0]
point_trim = [3000.0, 0.4, -0.2, 0.1]
h_trim, Ma_trim, ms_trim, km_trim = point_trim
p_trim, rho_trim, T_trim = utils.isa(h_trim)
avion.set_mass_and_static_margin(km_trim, ms_trim)
va_trim = dynamic.va_of_mach(Ma_trim, h_trim, k=1.4, Rs=287.05)
# calcul de va en m/s
va = dy.va_of_mach(mac, h)
# calcul de rho
rho = ut.isa(h)[1]
args = {}
args['h'] = h
args['va'] = dy.va_of_mach(mac, h) # conv mach en m/s
X, U = dy.trim(P, args)
alpha16 = X[3] # alpha en radians
dphr16 = U[0] # delta PHR en radians
dth16 = U[1] # thrust de 0 à 1
# calcul de la poussée pour le point de trim 16
F16 = dy.propulsion_model(X, U, P)
# calcul de CL16, la val du CL au point de trim16
CL16 = 2 * (P.m * P.g - math.sin(alpha16)) / ((rho * np.power(va, 2) * P.S))
print("valeurs obtenues via la fonction trim.")
print("alpha16 = ", alpha16, " rad")
print("angle réglage PHR dphr16 = ", dphr16, " rad")
print("Gaz ou thrust dth16 = ", dth16)
print("CL16 = ", CL16)
# 4.2.2.4 Conclure quant à la technique de réglage de la vitesse de l’avion.
# >>>> pour augmenter la vitesse, il faut diminuer CL donc alphae donc augmenter algébriquement
# l'angle du PHR pour augmenter la portance ou diminuer la déportance.
alphatrim = np.zeros((len(h), len(Ma), len(ms), len(km)))
dphrtrim = np.zeros((len(h), len(Ma), len(ms), len(km)))
dthtrim = np.zeros((len(h), len(Ma), len(ms), len(km)))
prop = np.zeros((len(h), len(Ma), len(ms), len(km)))
for ib, i in enumerate(ms):
for jb, j in enumerate(km):
avion.set_mass_and_static_margin(j, i)
for kb, k in enumerate(Ma):
for lb, l in enumerate(h):
va_h0 = dynamic.va_of_mach(k, l, k=1.4, Rs=287.05)
X, U = dynamic.trim(avion, {'va': va_h0, 'gamm': 0., 'h': l})
alphatrim[ib, jb, kb, lb] = X[3]
dphrtrim[ib, jb, kb, lb] = U[0]
dthtrim[ib, jb, kb, lb] = U[1]
prop[ib, jb, kb, lb] = dynamic.propulsion_model(X, U, avion)
def affiche():
for i in range(len(ms)):
for j in range(len(km)):
for k in range(len(Ma)):
plt.suptitle('ms=' + str(ms[i]) + ', km=' + str((km[j])))
plt.subplot(1, 4, 1)
plt.title("alpha")
plt.plot(h,
utils.deg_of_rad(alphatrim[i, j, k, :]),
label="Mach = " + str(Ma[k]) + "")
plt.ylabel('alpha en degre')
plt.xlabel('altitude')
plt.legend()
def question_1():
trims = get_all_trims(aircraft, hs, Mas, sms, kms)
plot_trims(aircraft)
trim_select = trims[0]
plot_traj_trim(aircraft,trim_select[0][1], Mas[1], sms[1], kms[1])
print(dyn.propulsion_model(trim_select[0],trim_select[1],aircraft))