Camões - Rocket Experiment Division

Launched at EUROC’23, achieved the target apogee of 3000 meters, with a flawless ascent phase, featuring effective air brake operation throughout. The recovery phase had only the actuation of a drogue parachute.

Permission to use flight data given by Gonçalo Machado, 2024.

These results were extracted out of the flight card:

1. Team number: 20

2. Launch date: October 14th, 2023. 14h local time

3. Simulated apogee: 3003 m

4. Official recorded apogee: 3015 m

The relative error of altitude apogee is only 0.39%!

%load_ext autoreload
%autoreload 2

The autoreload extension is already loaded. To reload it, use:
  %reload_ext autoreload

from rocketpy import Function, Environment, Flight, Rocket, SolidMotor
from rocketpy import AirBrakes, _Controller
from rocketpy.motors import CylindricalTank, SolidMotor
from rocketpy.motors.tank import MassFlowRateBasedTank

import matplotlib.pyplot as plt

plt.style.use("seaborn-v0_8-colorblind")

Environment

env = Environment(
    gravity=9.80665,
    date=(2023, 10, 14, 14),
    latitude=39.3900032043457,
    longitude=-8.2895383834838,
    elevation=107,
    datum="WGS84",
    timezone="Portugal",
)

env.set_atmospheric_model(
    type="Reanalysis",
    file="../../data/weather/euroc_2023_all_windows.nc",
    dictionary="ECMWF",
)
env.max_expected_height = 4000
env.info()

Gravity Details

Acceleration of gravity at surface level:    9.8066 m/s²
Acceleration of gravity at   4.000 km (ASL): 9.8066 m/s²


Launch Site Details

Launch Date: 2023-10-14 13:00:00 UTC | 2023-10-14 14:00:00 Portugal
Launch Site Latitude: 39.39000°
Launch Site Longitude: -8.28954°
Reference Datum: WGS84
Launch Site UTM coordinates: 44367.90 W    4373424.89 N
Launch Site UTM zone: 30S
Launch Site Surface Elevation: 107.0 m


Atmospheric Model Details

Atmospheric Model Type: Reanalysis
Reanalysis Maximum Height: 4.000 km
Reanalysis Time Period: from 2023-10-12 08:00:00 to 2023-10-15 18:00:00 utc
Reanalysis Hour Interval: 1 hrs
Reanalysis Latitude Range: From 40.0° to 39.0°
Reanalysis Longitude Range: From -9.0° to -7.0°

Surface Atmospheric Conditions

Surface Wind Speed: 207.00 m/s
Surface Wind Direction: 27.00°
Surface Wind Heading: 0.90°
Surface Pressure: 1000.00 hPa
Surface Temperature: 295.59 K
Surface Air Density: 1.179 kg/m³
Surface Speed of Sound: 344.66 m/s


Earth Model Details

Earth Radius at Launch site: 6369.57 km
Semi-major Axis: 6378.14 km
Semi-minor Axis: 6356.75 km
Flattening: 0.0034


Atmospheric Model Plots

Motor

Mariachi = SolidMotor(
    thrust_source="../../data/rockets/camoes/thrust_source.csv",
    burn_time=3.72,
    grain_number=6,
    grain_density=1637,
    grain_initial_inner_radius=0.015,
    grain_outer_radius=0.045,
    grain_initial_height=0.15,
    nozzle_radius=0.034,
    throat_radius=0.0135,
    grain_separation=0.005,
    grains_center_of_mass_position=-0.7566,
    dry_inertia=(0, 0, 0),
    center_of_dry_mass_position=0,
    dry_mass=0,
    nozzle_position=-1.3346,
)

Mariachi.info()

Nozzle Details
Nozzle Radius: 0.034 m
Nozzle Throat Radius: 0.0135 m

Grain Details
Number of Grains: 6
Grain Spacing: 0.005 m
Grain Density: 1637 kg/m3
Grain Outer Radius: 0.045 m
Grain Inner Radius: 0.015 m
Grain Height: 0.15 m
Grain Volume: 0.001 m3
Grain Mass: 1.389 kg

Motor Details
Total Burning Time: 3.72 s
Total Propellant Mass: 8.331 kg
Structural Mass Ratio: 0.000
Average Propellant Exhaust Velocity: 1320.764 m/s
Average Thrust: 2957.984 N
Maximum Thrust: 4145.791 N at 1.65 s after ignition.
Total Impulse: 11003.702 Ns

Rocket and Aerodynamic surfaces

For comparison purposes, no parachute will be added to the simulation

CAMOES = Rocket(
    radius=0.0715,
    mass=22.8,
    inertia=(16.2, 16.2, 0.066),
    center_of_mass_without_motor=0,
    power_off_drag="../../data/rockets/camoes/drag_coefficient_power_off.csv",
    power_on_drag="../../data/rockets/camoes/drag_coefficient_power_on.csv",
    coordinate_system_orientation="tail_to_nose",
)

CAMOES.set_rail_buttons(0.5, 0.2)

CAMOES.add_motor(Mariachi, position=0)

NoseCone = CAMOES.add_nose(
    length=0.455,
    kind="vonKarman",
    position=1.1884,
)

FinSet = CAMOES.add_trapezoidal_fins(
    n=4,
    span=0.155,
    root_chord=0.185,
    tip_chord=0.15,
    position=-1.0866,
)

Tail = CAMOES.add_tail(
    top_radius=0.0715, bottom_radius=0.037, length=0.048, position=-1.2866
)

def drogue_trigger(p, h, y):
    return True if y[5] < 5 and y[2] > 300 else False


Drogue = CAMOES.add_parachute(
    "Drogue", cd_s=0.33, sampling_rate=400, lag=1.5, trigger=drogue_trigger
)

CAMOES.draw()

Air Brakes - Active Control Systems

For privacy reasons, the controller function is not the one developed and used by the team.

The controller function just describes the actuation with time of the algorithm developed by the team.

import numpy as np


def controller_function(
    time, sampling_rate, state, state_history, observed_variables, air_brakes
):
    new_deployment_level = 0

    if time <= 11.4:
        new_deployment_level = 1
    else:
        new_deployment_level = (
            -0.002906 * np.power(time, 3)
            + 0.1497 * np.power(time, 2)
            + -2.563 * time
            + 14.96
        )

    if time > 19.6:
        new_deployment_level = 0

    if time < 3.8:
        new_deployment_level = 0

    air_brakes.deployment_level = new_deployment_level

    return time, air_brakes.deployment_level

air_brakes = CAMOES.add_air_brakes(
    drag_coefficient_curve=[
        # Mach 0.1
        [0, 0.1, 0.7692],
        [10 / 100, 0.1, 0.7663],
        [20 / 100, 0.1, 0.7762],
        [30 / 100, 0.1, 0.7847],
        [40 / 100, 0.1, 0.7999],
        [50 / 100, 0.1, 0.8246],
        [60 / 100, 0.1, 0.8310],
        [70 / 100, 0.1, 0.8499],
        [80 / 100, 0.1, 0.8738],
        [90 / 100, 0.1, 0.8945],
        [100 / 100, 0.1, 1.1018],
        # Mach 0.2
        [0, 0.2, 0.7508],
        [10 / 100, 0.2, 0.7513],
        [20 / 100, 0.2, 0.7670],
        [30 / 100, 0.2, 0.7782],
        [40 / 100, 0.2, 0.7943],
        [50 / 100, 0.2, 0.8063],
        [60 / 100, 0.2, 0.8243],
        [70 / 100, 0.2, 0.8493],
        [80 / 100, 0.2, 0.8781],
        [90 / 100, 0.2, 0.8925],
        [100 / 100, 0.2, 0.9851],
        # Mach 0.3
        [0, 0.3, 0.7445],
        [10 / 100, 0.3, 0.7571],
        [20 / 100, 0.3, 0.7699],
        [30 / 100, 0.3, 0.7828],
        [40 / 100, 0.3, 0.7985],
        [50 / 100, 0.3, 0.8114],
        [60 / 100, 0.3, 0.8379],
        [70 / 100, 0.3, 0.8634],
        [80 / 100, 0.3, 0.8834],
        [90 / 100, 0.3, 0.8947],
        [100 / 100, 0.3, 0.9782],
        # Mach 0.4
        [0, 0.4, 0.7492],
        [10 / 100, 0.4, 0.7566],
        [20 / 100, 0.4, 0.7698],
        [30 / 100, 0.4, 0.7840],
        [40 / 100, 0.4, 0.7994],
        [50 / 100, 0.4, 0.8136],
        [60 / 100, 0.4, 0.8399],
        [70 / 100, 0.4, 0.8665],
        [80 / 100, 0.4, 0.8834],
        [90 / 100, 0.4, 0.8969],
        [100 / 100, 0.4, 0.9659],
        # Mach 0.5
        [0, 0.5, 0.7454],
        [10 / 100, 0.5, 0.7537],
        [20 / 100, 0.5, 0.7651],
        [30 / 100, 0.5, 0.7811],
        [40 / 100, 0.5, 0.7987],
        [50 / 100, 0.5, 0.8163],
        [60 / 100, 0.5, 0.8404],
        [70 / 100, 0.5, 0.8631],
        [80 / 100, 0.5, 0.8788],
        [90 / 100, 0.5, 0.8951],
        [100 / 100, 0.5, 0.9416],
        # Mach 0.6
        [0, 0.6, 0.7036],
        [10 / 100, 0.6, 0.7237],
        [20 / 100, 0.6, 0.7359],
        [30 / 100, 0.6, 0.7496],
        [40 / 100, 0.6, 0.7684],
        [50 / 100, 0.6, 0.7899],
        [60 / 100, 0.6, 0.8153],
        [70 / 100, 0.6, 0.8406],
        [80 / 100, 0.6, 0.8539],
        [90 / 100, 0.6, 0.8712],
        [100 / 100, 0.6, 0.9286],
        # Mach 0.7
        [0, 0.7, 0.6810],
        [10 / 100, 0.7, 0.6948],
        [20 / 100, 0.7, 0.7076],
        [30 / 100, 0.7, 0.7233],
        [40 / 100, 0.7, 0.7427],
        [50 / 100, 0.7, 0.7629],
        [60 / 100, 0.7, 0.7876],
        [70 / 100, 0.7, 0.8073],
        [80 / 100, 0.7, 0.8272],
        [90 / 100, 0.7, 0.8453],
        [100 / 100, 0.7, 0.8960],
        # Mach 0.8
        [0, 0.8, 0.6578],
        [10 / 100, 0.8, 0.6739],
        [20 / 100, 0.8, 0.6870],
        [30 / 100, 0.8, 0.7036],
        [40 / 100, 0.8, 0.7240],
        [50 / 100, 0.8, 0.7457],
        [60 / 100, 0.8, 0.7676],
        [70 / 100, 0.8, 0.7880],
        [80 / 100, 0.8, 0.8098],
        [90 / 100, 0.8, 0.8278],
        [100 / 100, 0.8, 0.8799],
        # Mach 0.9
        [0, 0.9, 0.6574],
        [10 / 100, 0.9, 0.6634],
        [20 / 100, 0.9, 0.6794],
        [30 / 100, 0.9, 0.6958],
        [40 / 100, 0.9, 0.7201],
        [50 / 100, 0.9, 0.7395],
        [60 / 100, 0.9, 0.7618],
        [70 / 100, 0.9, 0.7844],
        [80 / 100, 0.9, 0.8057],
        [90 / 100, 0.9, 0.8278],
        [100 / 100, 0.9, 0.8628],
        # Mach 1.0
        [0, 1.0, 0.8350],
        [10 / 100, 1.0, 0.8241],
        [20 / 100, 1.0, 0.8403],
        [30 / 100, 1.0, 0.8593],
        [40 / 100, 1.0, 0.8832],
        [50 / 100, 1.0, 0.9070],
        [60 / 100, 1.0, 0.9358],
        [70 / 100, 1.0, 0.9639],
        [80 / 100, 1.0, 0.9881],
        [90 / 100, 1.0, 1.0093],
        [100 / 100, 1.0, 1.0347],
        # Mach 1.1
        [0, 1.1, 0.8610],
        [10 / 100, 1.1, 0.8447],
        [20 / 100, 1.1, 0.8617],
        [30 / 100, 1.1, 0.8800],
        [40 / 100, 1.1, 0.9027],
        [50 / 100, 1.1, 0.9244],
        [60 / 100, 1.1, 0.9515],
        [70 / 100, 1.1, 0.9810],
        [80 / 100, 1.1, 1.0069],
        [90 / 100, 1.1, 1.0253],
        [100 / 100, 1.1, 1.0560],
    ],
    controller_function=controller_function,
    sampling_rate=10,
    reference_area=None,
    clamp=True,
    initial_observed_variables=(0, 0),
    override_rocket_drag=True,
    name="Air Brakes",
)

air_brakes.all_info()

Flight Simulation Data

test_flight = Flight(
    rocket=CAMOES, environment=env, inclination=84, heading=133, rail_length=12
)

R:\RocketPy\rocketpy\simulation\flight.py:1201: UserWarning: time_overshoot has been set to False due to the presence of controllers or sensors.
  warnings.warn(

test_flight.prints.apogee_conditions()
test_flight.plots.trajectory_3d()

Apogee State

Apogee Time: 23.034 s
Apogee Altitude: 3110.284 m (ASL) | 3003.284 m (AGL)
Apogee Freestream Speed: 16.887 m/s
Apogee X position: 399.259 m
Apogee Y position: -457.173 m
Apogee latitude: 39.3858907°
Apogee longitude: -8.2848916°

Airbrakes actuation analysis

import matplotlib.pyplot as plt

time_list, deployment_level_list = [], []

obs_vars = test_flight.get_controller_observed_variables()

for time, deployment_level in obs_vars:
    time_list.append(time)
    deployment_level_list.append(deployment_level)

# Plot deployment level by time
plt.plot(time_list, deployment_level_list)
plt.xlabel("Time (s)")
plt.ylabel("Deployment Level")
plt.title("Deployment Level by Time")
plt.grid()
plt.show()

Data analysis

from rocketpy.simulation.flight_data_importer import FlightDataImporter

columns_map = {
    "ts": "time",
    "filtered_altitude_AGL": "altitude",
    "filtered_acceleration": "az",
}

cots_altimeter_flight = FlightDataImporter(
    name="COTS Altimeter Flight",
    paths="../../data/rockets/camoes/flight_data.csv",
    columns_map=columns_map,
    units=None,
    interpolation="linear",
    extrapolation="zero",
    delimiter=",",
    encoding="utf-8",
)

The following attributes were create and are now available to be used:  ['time', 'altitude', 'az']

Function.compare_plots(
    [
        (test_flight.altitude, "RocketPy"),
        (cots_altimeter_flight.altitude, "COTS Altimeter"),
    ],
    title="Altitude Comparison",
    xlabel="Time (s)",
    ylabel="Altitude (m)",
)

columns_map = {
    "ts": "time",
    "latitude": "latitude",
    "longitude": "longitude",
}

cots_gnss_flight = FlightDataImporter(
    name="COTS GNSS Flight",
    paths="../../data/rockets/camoes/gnss_flight.csv",
    columns_map=columns_map,
    units=None,
    interpolation="linear",
    extrapolation="zero",
    delimiter=",",
    encoding="utf-8",
)

The following attributes were create and are now available to be used:  ['time', 'latitude', 'longitude']

Function.compare_plots(
    [(test_flight.latitude, "RocketPy"), (cots_gnss_flight.latitude, "Actual - GNSS")],
    title="Latitude Comparison",
    xlabel="Time (s)",
    ylabel="Latitude (deg)",
)
Function.compare_plots(
    [
        (test_flight.longitude, "RocketPy"),
        (cots_gnss_flight.longitude, "Actual - GNSS"),
    ],
    title="Longitude Comparison",
    xlabel="Time (s)",
    ylabel="Longitude (deg)",
)