def mtow_plot(model):
model.cost = model["MTOW"]
fig, ax = plt.subplots()
x = np.linspace(1, 15, 500)
tol = 0.05
time = 0.0
nsolves = 0
ws = []
xs = []
for p in [85, 90, 95]:
wind = get_windspeed(38, p, 15000, 355)
cwind = get_windspeed(38, p, np.linspace(0, 15000, 11)[1:], 355)
for vk in model.varkeys["V_{wind}"]:
if "Climb" in vk.models:
model.substitutions.update({vk: cwind[vk.idx[0]]})
else:
model.substitutions.update({vk: wind})
model.substitutions.update({"MTOW": 1000})
model.cost = 1/model["t_Mission/Loiter"]
sol = model.solve("mosek")
time += sol["soltime"]
nsolves += 1
upper = sol("t_Mission/Loiter").magnitude
xmin_ = x[x < upper + 0.03]
xs.append(xmin_)
del model.substitutions["MTOW"]
model.cost = model["MTOW"]
bst = autosweep_1d(model, tol, model["t_Mission/Loiter"],
[1, xmin_[-1]], solver="mosek")
bsts = find_sols([bst])
sols = np.hstack([b.sols for b in bsts])
time += sum(np.unique([s["soltime"] for s in sols]))
nsolves += bst.nsols
ws.append(bst.sample_at(xmin_)["cost"])
print "%d solves in %.4f seconds" % (nsolves, time)
ax.fill_between(xs[0], ws[0],
np.append(ws[2], [1000]*(len(xs[0])-len(xs[2]))),
facecolor="r", edgecolor="None", alpha=0.3)
ax.plot(xs[0], ws[0], "r")
ax.plot(xs[1], ws[1], "r", lw=2)
ax.plot(xs[2], ws[2], "r")
for i, p in enumerate(["80%", "90%", "95%"]):
weight = ws[i].magnitude
we = 500 + min(abs(weight-500))
if we not in weight:
we = 500 - min(abs(weight-500))
end = xs[i][weight == we][0]
ax.annotate(p, xy=(end, we), xytext=(end+0.3, we+0.01),
arrowprops=dict(arrowstyle="-"), fontsize=12)
ax.grid()
ax.set_ylim([0, 1000])
ax.set_xlabel("Endurance [days]")
ax.set_ylabel("Max Take Off Weight [lbf]")
return fig, ax
def gas_lat(model, cost, subs=None):
plt.rcParams.update({'font.size': 15})
fig, ax = plt.subplots()
lat = np.arange(0, 60, 1)
model.substitutions.update(subs)
model.cost = model[cost]
for a in [80, 90, 95]:
mtow = []
wind = []
for l in lat:
wind.append(get_windspeed(l, a, 15000, 355))
maxwind = max(wind)
for v in model.varkeys["V_{wind}"]:
model.substitutions.update({v: maxwind})
try:
sol = model.solve("mosek")
mtow.append(sol(cost).magnitude)
except RuntimeWarning:
mtow.append(np.nan)
ax.plot(lat, mtow, lw=2)
ax.set_xlabel("Latitude [deg]")
labels = ["$\\pm$" + item.get_text() for item in ax.get_xticklabels()]
labels = ["$\\pm$%d" % l for l in np.linspace(20, 45, len(labels))]
ax.set_xticklabels(labels)
ax.legend(["%d Percentile Winds" % a for a in [80, 90, 95]],
loc=2,
fontsize=15)
return fig, ax
def fit_setup(altitude=(40000, 80000), latitude=45, day=355):
"""
Function that sets up the fit for altitude versus density. Density in
10^-1 kg/m^3
Inputs
------
altitude: tuple - two values for the upper and lower bound of altitude
range (ex. (40000, 80000)). Altitude in ft
latitude: int - latitude of earth in degrees
percentage: int - percentile wind speeds
Outputs
------
x: 1D array of x values for fit
y: 1D array of y values for fit
"""
N = 20
percentiles = range(75, 100, 5) + [99]
altitude = np.linspace(altitude[0], altitude[1], N)
df = pd.read_csv("usstd_atm.csv")
wind = []
ps = []
for p in percentiles:
wind.append(
np.array(get_windspeed(latitude, p, altitude, day)) / WIND_NORM)
ps.append([p / PERCT_NORM] * len(altitude))
hm = altitude * 0.3048
g = 9.80665 # m/s^2
R = 287.04 # m^2/K/s^2
T11 = 216.65 # K
p = 22632 * np.exp(-g / R / T11 * (hm - 11000))
density = p / R / T11 * RHO_NORM
u1 = np.hstack([density] * len(percentiles))
u2 = np.hstack(ps)
w = np.hstack(wind)
x = np.log([u1, u2])
y = np.log(w)
return x, y
def windalt_plot(latitude, sol1=None, sol2=None, p=0.90):
plt.rcParams.update({'font.size': 15})
alt = np.linspace(40000, 80000, 20)
fig, ax = plt.subplots()
if sol1:
p = sol1("p_{wind}").items()[0][1]
if sol2:
sols = [sol1, sol2]
else:
sols = [sol1]
for sol in sols:
altsol = altitude(min([sol(sv).magnitude for sv in sol("\\rho")]))
vsol = max([sol(sv).to("knots").magnitude for sv in sol("V")])
ax.plot(altsol / 1000, vsol, "o", markersize=10, mfc="c")
y = get_windspeed(latitude, np.round(p * 100), alt, 355)
f = interpolate.interp1d(alt, y, "cubic")
vwind = f(alt)
l = ax.plot(alt / 1000.0, vwind * 1.95384, linewidth=2)
ax.set_xlabel("Altitude [kft]")
ax.set_ylabel("90th Percentile Wind Speed [knots]")
ax.grid()
ax.set_ylim([0, 200])
return fig, ax
M = Mission()
M.cost = M["MTOW"]
M.substitutions.update({"W_{pay}": 10})
for e in M.varkeys["\\eta_{prop}"]:
M.substitutions.update({e: 0.75})
for cd in M.varkeys["CDA_0"]:
M.substitutions.update({cd: 0.01})
fig, ax = plt.subplots()
lower = 1
upper = 10
xmin_ = np.linspace(lower, upper, 100)
tol = 0.05
for p in [85, 90, 95]:
notpassing = True
while notpassing:
wind = get_windspeed(38, p, 15000, 355)
cwind = get_windspeed(38, p, np.linspace(0, 15000, 11)[1:], 355)
for vk in M.varkeys["V_{wind}"]:
if "Climb" in vk.models:
M.substitutions.update({vk: cwind[vk.idx[0]]})
else:
M.substitutions.update({vk: wind})
try:
bst = sweep_1d(M,
tol,
M["t_Mission/Loiter"], [lower, upper],
solver="mosek")
notpassing = False
except RuntimeWarning:
notpassing = True
upper -= 0.1
def ld_plot(model, num):
model.cost = 1/model["t_Mission/Loiter"]
for e in model.varkeys["\\eta_{prop}"]:
model.substitutions.update({e: 0.75})
fig, ax = plt.subplots()
wind = get_windspeed(38, 90, 15000, 355)
cwind = get_windspeed(38, 90, np.linspace(0, 15000, 11)[1:], 355)
for vk in model.varkeys["V_{wind}"]:
if "Climb" in vk.models:
model.substitutions.update({vk: cwind[vk.idx[0]]})
else:
model.substitutions.update({vk: wind})
model.substitutions.update({"MTOW": 200})
model.substitutions.update({"N_{max}_Mission/AircraftLoading/WingLoading/GustL": 0.1})
sol = model.solve("mosek")
re = sol("Re_Mission/Loiter/FlightSegment/AircraftPerf/WingAero")[-1]
if num == 1 or num == 2:
clm = sol("C_L_Mission/Loiter/FlightSegment/AircraftPerf/WingAero")
cdm = sol("c_{dp}_Mission/Loiter/FlightSegment/AircraftPerf/WingAero")
l = ax.plot(clm, cdm, "o", mfc="None", ms=7, mew=1.5,
label="With Wind Constraint")
ax.annotate("mission start", xy=(clm[0], cdm[0]), xytext=(0.87, 0.0062),
arrowprops=dict(arrowstyle="->"), fontsize=13)
ax.annotate("mission end", xy=(clm[-1], cdm[-1]), xytext=(0.42, 0.0072),
arrowprops=dict(arrowstyle="->"), fontsize=13)
cl = np.linspace(0.2, 1.5, 100)
cd = return_cd(cl, re)
cl15 = cl**1.5/cd
clmax = cl[cl15 == max(cl15)]
cdmax = cd[cl15 == max(cl15)]
for vk in model.varkeys["m_{fac}"]:
if "Loiter" in vk.descr["models"] and "FlightState" in vk.descr["models"]:
model.substitutions.update({vk:0.01})
sol = model.solve("mosek")
clw = sol("C_L_Mission/Loiter/FlightSegment/AircraftPerf/WingAero")
cdw = sol("c_{dp}_Mission/Loiter/FlightSegment/AircraftPerf/WingAero")
if num == 2:
l = ax.plot(clw, cdw, "s", mfc="None", ms=7, mew=1.5,
label="Without Wind Constraint")
ax.annotate("mission start", xy=(clw[0], cdw[0]), xytext=(1.2, 0.0087),
arrowprops=dict(arrowstyle="->"), fontsize=13)
ax.annotate("mission end", xy=(clw[-1], cdw[-1]), xytext=(0.9, 0.013),
arrowprops=dict(arrowstyle="->"), fontsize=13)
l = ax.plot(clmax, cdmax, "+", mec="#084081", mfc="None", ms=7, mew=1.5)
l = ax.plot(cl, cd, linewidth=2, label="Re=%3.fk" % (re/1000.),
c="#084081", zorder=1)
lines = [l[0]]
re = sol("Re_Mission/Loiter/FlightSegment/AircraftPerf/WingAero")
for i, r, col in zip(range(5), re, ["#0868ac","#0868ac","#0868ac", "#2b8cbe", "#2b8cbe"]):
cd = return_cd(cl, r)
cl15 = cl**1.5/cd
clmax = cl[cl15 == max(cl15)]
cdmax = cd[cl15 == max(cl15)]
if i == 2 or i == 4:
l = ax.plot(cl, cd, linewidth=2, label="Re=%3.fk" % (r/1000.),
c=col, zorder=1)
lines.append(l[0])
ax.plot(clmax, cdmax, "+", mec=col, mfc="None", ms=7, mew=1.5)
labelLines(lines, fontsize=12, zorder=[2.5]*3, align=False,
xvals=[1.05, 0.85, 0.7])
ax.set_xlabel("$C_L$")
ax.set_ylabel("$c_{d_p}$")
if num == 2:
ax.legend(["With Wind Constraint", "Without Wind Constraint"],
fontsize=15, loc=2)
if num == 1:
ax.legend(["With Wind Constraint"], fontsize=15, loc=2)
ax.grid()
for vk in model.varkeys["m_{fac}"]:
if "Loiter" in vk.descr["models"] and "FlightState" in vk.descr["models"]:
model.substitutions.update({vk:1})
return fig, ax
fig, ax = plt.subplots()
lat = np.arange(0, 60, 1)
M = Mission()
M.substitutions.update({"W_{pay}": 10})
for e in M.varkeys["\\eta_{prop}"]:
M.substitutions.update({e: 0.75})
for cd in M.varkeys["CDA_0"]:
M.substitutions.update({cd: 0.01})
M.substitutions.update({"t_Mission/Loiter": 7})
M.cost = M["MTOW"]
for a in [80, 90, 95]:
mtow = []
wind = []
for l in lat:
wind.append(get_windspeed(l, a, 15000, 355))
maxwind = max(wind)
for v in M.varkeys["V_{wind}"]:
M.substitutions.update({v: maxwind})
try:
sol = M.solve("mosek")
mtow.append(sol("MTOW").magnitude)
except RuntimeWarning:
mtow.append(np.nan)
ax.plot(lat, mtow)
ax.set_ylim([0, 1000])
ax.set_xlim([20, 50])
ax.grid()
labels = ["$\\pm$" + item.get_text() for item in ax.get_xticklabels()]
labels = ["$\\pm$%d" % l for l in np.linspace(20, 50, len(labels))]
def plot_lats():
fig, ax = plt.subplots()
lat = np.arange(20, 41, 1)
Mg = Mgas()
Mg.substitutions.update({"W_{pay}": 10})
Mg.substitutions.update({"t_Mission/Loiter": 7})
Mg.cost = Mg["MTOW"]
psolar = []
pgas = []
faillat = []
gtime = 0.0
gnsols = 0
stime = 0.0
snsols = 0.0
for a in [80, 90, 95]:
wg = []
ws = []
runagains = True
highestwind = 0
for l in lat:
if runagains:
Ms = Msolar(latitude=l)
Ms.substitutions.update({"W_{pay}": 10})
for vk in Ms.varkeys["p_{wind}"]:
Ms.substitutions.update({vk: a / 100.0})
Ms.cost = Ms["W_{total}"]
try:
sol = Ms.solve("mosek")
stime += sol["soltime"]
snsols += 1
ws.append(sol("W_{total}").magnitude)
except RuntimeWarning:
ws.append(np.nan)
faillat.append(l)
runagains = False
else:
ws.append(np.nan)
wind = get_windspeed(l, a, 15000, 355)
cwind = get_windspeed(l, a, np.linspace(0, 15000, 11)[1:], 355)
if wind > highestwind:
highestwind = wind
for vk in Mg.varkeys["V_{wind}"]:
if "Climb" in vk.models:
Mg.substitutions.update({vk: cwind[vk.idx[0]]})
else:
Mg.substitutions.update({vk: wind})
try:
sol = Mg.solve("mosek")
gtime += sol["soltime"]
gnsols += 1
wg.append(sol("MTOW").magnitude)
except RuntimeWarning:
wg.append(np.nan)
print "Fail, Lat: %d" % l
pgas.append(wg)
psolar.append(ws)
print "Solar: %d solves in %.4f seconds" % (snsols, stime)
print "Gas: %d solves in %.4f seconds" % (gnsols, gtime)
indl = psolar[0].index(max(psolar[0]))
indh = psolar[2].index(max(psolar[2]))
a = (psolar[2][indh] - psolar[0][indl]) / (lat[indh] - lat[indl])
b = psolar[0][indl] - a * lat[indl]
c = a * lat[indh + 1:indl + 1] + b
ax.fill_between(lat[0:indl + 1],
psolar[0][0:indl + 1],
np.append(np.array(psolar[-1][0:indh + 1]), c),
alpha=0.3,
facecolor="b",
edgecolor="None")
psolar[1][np.where(lat == 31)[0][0]] = np.nan
ax.plot(lat, psolar[1], "b", lw=2)
ax.plot(lat, pgas[1], "r", lw=2)
ax.plot(lat, psolar[0], "b")
ax.plot(lat, psolar[2], "b")
ax.fill_between(lat,
pgas[0],
pgas[2],
alpha=0.3,
facecolor="r",
edgecolor="None")
ax.plot(lat, pgas[0], "r")
ax.plot(lat, pgas[2], "r")
for i, p in enumerate(["80%", "90%", "95%"]):
ax.annotate(p,
xy=(36, pgas[i][np.where(lat == 36)[0][0]]),
xytext=(0.1, -20),
textcoords="offset points",
arrowprops=dict(arrowstyle="-"),
fontsize=12)
ax.annotate("80%",
xy=(30, psolar[0][np.where(lat == 30)[0][0]]),
xytext=(15, 15),
textcoords="offset points",
arrowprops=dict(arrowstyle="-"),
fontsize=12)
ax.annotate("90%",
xy=(28, psolar[1][np.where(lat == 28)[0][0]]),
xytext=(15, 15),
textcoords="offset points",
arrowprops=dict(arrowstyle="-"),
fontsize=12)
ax.annotate("95%",
xy=(27, psolar[2][np.where(lat == 27)[0][0]]),
xytext=(-30, 15),
textcoords="offset points",
arrowprops=dict(arrowstyle="-"),
fontsize=12)
ax.set_ylim([0, 350])
ax.set_xlim([20, 40])
ax.grid()
ax.set_xlabel("Latitude Requirement [deg]")
ax.set_ylabel("Max Take Off Weight [lbf]")
labels = ["$\\pm$" + item.get_text() for item in ax.get_xticklabels()]
labels = ["$\\pm$%d" % l for l in np.linspace(20, 40, len(labels))]
ax.set_xticklabels(labels)
ax.legend(["Solar-electric Powered", "Gas Powered"], fontsize=15, loc=2)
return fig, ax