Waypoint Constraints¶
This example constrains Amsterdam Schiphol (EHAM) to Rome Fiumicino (LIRF) through named fixes from OpenAP's packaged navigation database. The fixes intentionally create a one-sided convex detour away from the direct route, and the optimizer is constrained to pass within 2 km of each fix.
In [1]:
import warnings
import matplotlib.pyplot as plt
import openap
from cartopy import crs as ccrs
from cartopy.feature import BORDERS, LAND, OCEAN
import opentop as top
warnings.filterwarnings("ignore")
In [2]:
actype = "A320"
origin = "EHAM"
destination = "LIRF"
m0 = 0.85
fix_names = ("SIGEN", "FUSSE", "ROKIB")
waypoint_tolerance_m = 2_000
waypoints = []
for fix_name in fix_names:
lat, lon, _ = openap.nav.fix(fix_name)
waypoints.append((float(lat), float(lon)))
list(zip(fix_names, waypoints))
Out[2]:
[('SIGEN', (50.846111, 8.279444)),
('FUSSE', (47.574289, 10.429847)),
('ROKIB', (45.935556, 11.692222))]
In [3]:
cruise_optimizer = top.Cruise(actype, origin, destination, m0)
cruise_optimizer.setup()
cruise_flight = cruise_optimizer.trajectory(
objective="fuel",
waypoints=waypoints,
waypoint_tolerance_m=waypoint_tolerance_m,
)
complete_optimizer = top.CompleteFlight(actype, origin, destination, m0)
complete_optimizer.setup()
complete_flight = complete_optimizer.trajectory(
objective="fuel",
waypoints=waypoints,
waypoint_tolerance_m=waypoint_tolerance_m,
)
In [4]:
def closest_distances(flight, waypoints):
distances = []
for waypoint in waypoints:
fix_distances = [
openap.aero.distance(lat, lon, waypoint[0], waypoint[1])
for lat, lon in zip(flight.latitude, flight.longitude)
]
distances.append(min(fix_distances))
return distances
print("Route: " + origin + " -> " + " -> ".join(fix_names) + " -> " + destination)
for label, optimizer, flight in (
("Cruise", cruise_optimizer, cruise_flight),
("CompleteFlight", complete_optimizer, complete_flight),
):
fuel_burn = flight.mass.iloc[0] - flight.mass.iloc[-1]
elapsed_time = flight.ts.iloc[-1] / 60
print(f"\n{label}")
print(f" success: {optimizer.success}")
print(f" fuel burn: {fuel_burn:.1f} kg")
print(f" elapsed time: {elapsed_time:.1f} min")
for fix_name, distance in zip(fix_names, closest_distances(flight, waypoints)):
print(f" {fix_name}: closest trajectory point {distance / 1000:.1f} km")
Route: EHAM -> SIGEN -> FUSSE -> ROKIB -> LIRF Cruise success: True fuel burn: 4385.2 kg elapsed time: 97.2 min SIGEN: closest trajectory point 2.0 km FUSSE: closest trajectory point 2.0 km ROKIB: closest trajectory point 2.0 km CompleteFlight success: True fuel burn: 4820.2 kg elapsed time: 108.7 min SIGEN: closest trajectory point 2.0 km FUSSE: closest trajectory point 2.0 km ROKIB: closest trajectory point 2.0 km
In [5]:
origin_info = openap.nav.airport(origin)
destination_info = openap.nav.airport(destination)
airport_points = [
(origin, float(origin_info["lat"]), float(origin_info["lon"])),
(destination, float(destination_info["lat"]), float(destination_info["lon"])),
]
all_lons = [*cruise_flight.longitude, *complete_flight.longitude]
all_lats = [*cruise_flight.latitude, *complete_flight.latitude]
all_lons.extend(lon for _, lon in waypoints)
all_lats.extend(lat for lat, _ in waypoints)
all_lons.extend(lon for _, _, lon in airport_points)
all_lats.extend(lat for _, lat, _ in airport_points)
map_extent = [
min(all_lons) - 1.0,
max(all_lons) + 1.0,
min(all_lats) - 0.8,
max(all_lats) + 0.8,
]
def plot_route_map(flight, title, color):
projection = ccrs.TransverseMercator(
central_longitude=9,
central_latitude=47,
)
_fig, ax = plt.subplots(
figsize=(8, 7),
subplot_kw={"projection": projection},
)
ax.set_extent(map_extent, crs=ccrs.PlateCarree())
ax.add_feature(LAND, facecolor="#f3f0e8", edgecolor="none")
ax.add_feature(OCEAN, facecolor="#d9ecf2", edgecolor="none")
ax.add_feature(BORDERS, lw=0.5, color="0.45")
ax.coastlines(resolution="50m", lw=0.5, color="0.45")
ax.gridlines(draw_labels=True, color="0.6", alpha=0.5, ls="--")
ax.plot(
[airport_points[0][2], airport_points[1][2]],
[airport_points[0][1], airport_points[1][1]],
color="tab:gray",
lw=1.0,
ls="--",
label="Direct airport line",
transform=ccrs.PlateCarree(),
zorder=1,
)
ax.plot(
flight.longitude,
flight.latitude,
marker="o",
color=color,
lw=1.5,
ms=4,
label="Optimized trajectory",
transform=ccrs.PlateCarree(),
zorder=3,
)
ax.scatter(
[lon for _, lon in waypoints],
[lat for lat, _ in waypoints],
marker="x",
s=90,
color="tab:red",
label="Fixes",
transform=ccrs.PlateCarree(),
zorder=6,
)
ax.scatter(
[lon for _, _, lon in airport_points],
[lat for _, lat, _ in airport_points],
marker="^",
s=80,
color="tab:gray",
label="Airports",
transform=ccrs.PlateCarree(),
zorder=7,
)
for fix_name, (lat, lon) in zip(fix_names, waypoints):
ax.text(
lon + 0.08,
lat + 0.05,
fix_name,
fontsize=9,
transform=ccrs.PlateCarree(),
zorder=8,
)
for airport, lat, lon in airport_points:
ax.text(
lon + 0.08,
lat + 0.05,
airport,
fontsize=9,
transform=ccrs.PlateCarree(),
zorder=8,
)
ax.set_title(title)
ax.legend(loc="lower left")
plt.tight_layout()
plt.show()
In [6]:
plot_route_map(
cruise_flight,
"Cruise waypoint detour from Amsterdam to Rome",
"tab:blue",
)
In [7]:
plot_route_map(
complete_flight,
"CompleteFlight waypoint detour from Amsterdam to Rome",
"tab:green",
)
In [8]:
time_min = complete_flight.ts / 60
fig, axes = plt.subplots(2, 1, figsize=(8, 6), sharex=True)
axes[0].plot(
time_min,
complete_flight.altitude,
marker="o",
ms=4,
color="tab:green",
)
axes[0].set_ylabel("Altitude [ft]")
axes[0].set_title("CompleteFlight vertical profile")
axes[0].grid(True, alpha=0.3)
axes[1].plot(time_min, complete_flight.tas, marker="o", ms=4, color="tab:green")
axes[1].set_xlabel("Elapsed time [min]")
axes[1].set_ylabel("TAS [kt]")
axes[1].set_title("CompleteFlight speed profile")
axes[1].grid(True, alpha=0.3)
plt.tight_layout()
plt.show()
