Prometheus - Western Engineering Rocketry Team 2022¶
Launched at Spaceport America Cup 2022 edition.
Western Engineering Rocketry Team is a rocket design team from Western University in London, Ontario (Canada).
Permission to use flight data given by Giorgio Chassikos, 2024.
Website: https://www.werocketry.com/
Team Information:¶
The Western Engineering Rocketry Team is a student-led engineering design team founded in 2016 at Western University in London, Ontario.
Comprised of engineering students from a variety of disciplines, the team's goal is to develop and launch rockets through the Intercollegiate Rocket Engineering Competition.
Flight Card Results:¶
- Launch Date: June 24th, 2022, 9:17am local time
- Last Simulated Apogee: 4190.05 m
- Official Recorded Apogee: 3898.37 m
If we calculate the simulation error and divide it by the actual apogee, we get a relative error of 7.48%.
In [1]:
%load_ext autoreload
%autoreload 2
In [2]:
from rocketpy import Function, Rocket, GenericMotor, Flight, Environment
from rocketpy.simulation.flight_data_importer import FlightDataImporter
import matplotlib.pyplot as plt
import numpy as np
plt.style.use("seaborn-v0_8-colorblind")
Define the Environment¶
In [3]:
env = Environment(
latitude=32.939377,
longitude=-106.911986,
elevation=1401,
)
env.set_date(date=(2023, 6, 24, 9), timezone="America/Denver")
env.set_atmospheric_model(
type="Reanalysis",
file="../../data/weather/spaceport_america_pressure_levels_2023_hourly.nc",
dictionary="ECMWF",
)
env.max_expected_height = 6000
In [4]:
env.info()
Gravity Details Acceleration of gravity at surface level: 9.7913 m/s² Acceleration of gravity at 6.000 km (ASL): 9.7771 m/s² Launch Site Details Launch Date: 2023-06-24 15:00:00 UTC | 2023-06-24 09:00:00 America/Denver Launch Site Latitude: 32.93938° Launch Site Longitude: -106.91199° Reference Datum: SIRGAS2000 Launch Site UTM coordinates: 321254.52 W 3646188.36 N Launch Site UTM zone: 13S Launch Site Surface Elevation: 1401.0 m Atmospheric Model Details Atmospheric Model Type: Reanalysis Reanalysis Maximum Height: 6.000 km Reanalysis Time Period: From 2023-06-19 00:00:00 to 2023-06-24 23:00:00 UTC Reanalysis Hour Interval: 1 hrs Reanalysis Latitude Range: From 36.75 ° To 29.0 ° Reanalysis Longitude Range: From -108.87999725341797 ° To -105.12999725341797 ° Surface Atmospheric Conditions Surface Wind Speed: 0.20 m/s Surface Wind Direction: 304.58° Surface Wind Heading: 124.58° Surface Pressure: 861.95 hPa Surface Temperature: 299.96 K Surface Air Density: 1.001 kg/m³ Surface Speed of Sound: 347.20 m/s Earth Model Details Earth Radius at Launch site: 6371.85 km Semi-major Axis: 6378.14 km Semi-minor Axis: 6356.75 km Flattening: 0.0034 Atmospheric Model Plots
Define the motor¶
In [5]:
motor_M1520 = GenericMotor(
# burn specs: https://www.thrustcurve.org/simfiles/5f4294d20002e900000006b1/
thrust_source="../../data/motors/cesaroni/Cesaroni_7579M1520-P.eng",
burn_time=4.897,
propellant_initial_mass=3.737,
dry_mass=2.981,
# casing specs: Pro98 3G Gen2 casing
chamber_radius=0.064,
chamber_height=0.548,
chamber_position=0.274,
nozzle_radius=0.027,
)
motor_M1520.info()
Motor Details Total Burning Time: 4.897 s Total Propellant Mass: 3.737 kg Average Propellant Exhaust Velocity: 2028.119 m/s Average Thrust: 1547.699 N Maximum Thrust: 1827.113 N at 1.652 s after ignition. Total Impulse: 7579.081 Ns
Define the Rocket¶
In [6]:
def prometheus_cd_at_ma(mach):
"""Gives the drag coefficient of the rocket at a given mach number."""
if mach <= 0.15:
return 0.422
elif mach <= 0.45:
return 0.422 + (mach - 0.15) * (0.38 - 0.422) / (0.45 - 0.15)
elif mach <= 0.77:
return 0.38 + (mach - 0.45) * (0.32 - 0.38) / (0.77 - 0.45)
elif mach <= 0.82:
return 0.32 + (mach - 0.77) * (0.3 - 0.32) / (0.82 - 0.77)
elif mach <= 0.88:
return 0.3 + (mach - 0.82) * (0.3 - 0.3) / (0.88 - 0.82)
elif mach <= 0.94:
return 0.3 + (mach - 0.88) * (0.32 - 0.3) / (0.94 - 0.88)
elif mach <= 0.99:
return 0.32 + (mach - 0.94) * (0.37 - 0.32) / (0.99 - 0.94)
elif mach <= 1.04:
return 0.37 + (mach - 0.99) * (0.44 - 0.37) / (1.04 - 0.99)
elif mach <= 1.24:
return 0.44 + (mach - 1.04) * (0.43 - 0.44) / (1.24 - 1.04)
elif mach <= 1.33:
return 0.43 + (mach - 1.24) * (0.42 - 0.43) / (1.33 - 1.24)
elif mach <= 1.49:
return 0.42 + (mach - 1.33) * (0.39 - 0.42) / (1.49 - 1.33)
else:
return 0.39
prometheus = Rocket(
radius=0.06985, # 5.5" diameter circle
mass=13.93,
inertia=(
4.87,
4.87,
0.05,
),
power_off_drag=prometheus_cd_at_ma,
power_on_drag=lambda x: prometheus_cd_at_ma(x) * 1.02, # 5% increase in drag
center_of_mass_without_motor=0.9549,
coordinate_system_orientation="tail_to_nose",
)
prometheus.set_rail_buttons(0.69, 0.21, 60)
prometheus.add_motor(motor=motor_M1520, position=0)
nose_cone = prometheus.add_nose(length=0.742, kind="Von Karman", position=2.229)
fin_set = prometheus.add_trapezoidal_fins(
n=3,
span=0.13,
root_chord=0.268,
tip_chord=0.136,
position=0.273,
sweep_length=0.066,
)
drogue = prometheus.add_parachute(
"Drogue",
cd_s=1.6 * np.pi * 0.3048**2, # Cd = 1.6, D_chute = 24 in
trigger="apogee",
)
main = prometheus.add_parachute(
"Main",
cd_s=2.2 * np.pi * 0.9144**2, # Cd = 2.2, D_chute = 72 in
trigger=457.2, # 1500 ft
)
In [7]:
prometheus.info()
prometheus.draw()
prometheus.plots.drag_curves()
Inertia Details Rocket Mass: 13.930 kg (without motor) Rocket Dry Mass: 16.911 kg (with unloaded motor) Rocket Loaded Mass: 20.648 kg (with loaded motor) Rocket Inertia (with unloaded motor) 11: 6.008 kg*m2 Rocket Inertia (with unloaded motor) 22: 6.008 kg*m2 Rocket Inertia (with unloaded motor) 33: 0.050 kg*m2 Rocket Inertia (with unloaded motor) 12: 0.000 kg*m2 Rocket Inertia (with unloaded motor) 13: 0.000 kg*m2 Rocket Inertia (with unloaded motor) 23: 0.000 kg*m2 Geometrical Parameters Rocket Maximum Radius: 0.06985 m Rocket Frontal Area: 0.015328 m2 Rocket Distances Rocket Center of Dry Mass - Center of Mass without Motor: 0.120 m Rocket Center of Dry Mass - Nozzle Exit: 0.835 m Rocket Center of Dry Mass - Center of Propellant Mass: 0.561 m Rocket Center of Mass - Rocket Loaded Center of Mass: 0.102 m Aerodynamics Lift Coefficient Derivatives Nose Cone Lift Coefficient Derivative: 2.000/rad Fins Lift Coefficient Derivative: 6.406/rad Center of Pressure Nose Cone Center of Pressure position: 1.858 m Fins Center of Pressure position: 0.191 m Stability Center of Mass position (time=0): 0.733 m Center of Pressure position (time=0): 0.588 m Initial Static Margin (mach=0, time=0): 1.042 c Final Static Margin (mach=0, time=burn_out): 1.768 c Rocket Center of Mass (time=0) - Center of Pressure (mach=0): 0.146 m Parachute Details Parachute Drogue with a cd_s of 0.4670 m2 Ejection signal trigger: At Apogee Ejection system refresh rate: 100.000 Hz Time between ejection signal is triggered and the parachute is fully opened: 0.0 s Parachute Details Parachute Main with a cd_s of 5.7789 m2 Ejection signal trigger: 457.2 m (AGL) Ejection system refresh rate: 100.000 Hz Time between ejection signal is triggered and the parachute is fully opened: 0.0 s
Simulate the Flight¶
In [8]:
test_flight = Flight(
rocket=prometheus,
environment=env,
inclination=80,
heading=75,
rail_length=5.18,
)
In [9]:
# test_flight.prints.initial_conditions()
# test_flight.prints.surface_wind_conditions()
# test_flight.prints.launch_rail_conditions()
test_flight.prints.out_of_rail_conditions()
test_flight.prints.burn_out_conditions()
test_flight.prints.apogee_conditions()
# test_flight.prints.events_registered()
# test_flight.prints.impact_conditions()
test_flight.prints.stability_margin()
test_flight.prints.maximum_values()
# test_flight.prints.numerical_integration_settings()
Rail Departure State Rail Departure Time: 0.385 s Rail Departure Velocity: 25.256 m/s Rail Departure Stability Margin: 1.090 c Rail Departure Angle of Attack: 0.455° Rail Departure Thrust-Weight Ratio: 8.326 Rail Departure Reynolds Number: 1.911e+05 Burn out State Burn out time: 4.897 s Altitude at burn out: 2271.761 m (ASL) | 870.761 m (AGL) Rocket speed at burn out: 328.201 m/s Freestream velocity at burn out: 326.875 m/s Mach Number at burn out: 0.950 Kinetic energy at burn out: 9.108e+05 J Apogee State Apogee Time: 29.113 s Apogee Altitude: 5591.386 m (ASL) | 4190.386 m (AGL) Apogee Freestream Speed: 35.967 m/s Apogee X position: 1524.285 m Apogee Y position: 427.117 m Apogee latitude: 32.9432166° Apogee longitude: -106.8956535° Stability Margin Initial Stability Margin: 1.042 c at 0.00 s Out of Rail Stability Margin: 1.090 c at 0.38 s Maximum Stability Margin: 1.886 c at 4.91 s Minimum Stability Margin: 1.042 c at 0.00 s Maximum Values Maximum Speed: 330.240 m/s at 4.71 s Maximum Mach Number: 0.955 Mach at 4.74 s Maximum Reynolds Number: 2.339e+06 at 4.66 s Maximum Dynamic Pressure: 5.021e+04 Pa at 4.69 s Maximum Acceleration During Motor Burn: 82.803 m/s² at 1.67 s Maximum Gs During Motor Burn: 8.444 g at 1.67 s Maximum Acceleration After Motor Burn: 11.737 m/s² at 17.59 s Maximum Gs After Motor Burn: 1.197 Gs at 17.59 s Maximum Stability Margin: 1.886 c at 4.91 s Maximum Upper Rail Button Normal Force: 0.191 N Maximum Upper Rail Button Shear Force: 0.060 N Maximum Lower Rail Button Normal Force: 0.119 N Maximum Lower Rail Button Shear Force: 0.038 N
Read the Telemetry Data¶
In [10]:
columns_map = {
"time": "time",
"altitude": "z",
"height": "altitude",
"acceleration": "acceleration",
"pressure": "pressure",
"accel_x": "ax",
"accel_y": "ay",
"accel_z": "az",
"latitude": "latitude",
"longitude": "longitude",
}
cots_altimeter_flight = FlightDataImporter(
name="Telemetry Mega",
paths="../../data/prometheus/2022-06-24-serial-5115-flight-0001-TeleMetrum.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', 'z', 'altitude', 'acceleration', 'pressure', 'latitude', 'longitude']
Compare Simulation and Telemetry Data¶
In [11]:
real_apogee = cots_altimeter_flight.altitude.max
rocketpy_apogee = test_flight.apogee - test_flight.env.elevation
a_error = abs(real_apogee - rocketpy_apogee)
r_error = a_error / real_apogee * 100
print(f"RocketPy apogee: {rocketpy_apogee:.2f} m")
print(f"Real apogee: {real_apogee:.2f} m")
print(f"Absolute error: {a_error:.2f} m")
print(f"Relative error: {r_error:.2f}%")
RocketPy apogee: 4190.39 m Real apogee: 3903.77 m Absolute error: 286.62 m Relative error: 7.34%
In [13]:
# Altitude comparison
Function.compare_plots(
[
(test_flight.altitude, "RocketPy"),
(cots_altimeter_flight.altitude, "Telemetry"),
],
title="Altitude Comparison",
xlabel="Time (s)",
ylabel="Altitude (m)",
lower=0,
# upper=30,
)
# Pressure comparison
Function.compare_plots(
[
(test_flight.pressure, "RocketPy"),
(cots_altimeter_flight.pressure, "Telemetry"),
],
title="Pressure Comparison",
xlabel="Time (s)",
ylabel="Pressure (Pa)",
lower=0,
# upper=30,
)
# Latitude comparison
# Function.compare_plots(
# [
# (test_flight.latitude, "RocketPy"),
# (cots_altimeter_flight.latitude, "Telemetry"),
# ],
# title="Latitude Comparison",
# xlabel="Time (s)",
# ylabel="Latitude (deg)",
# lower=0,
# # upper=30,
# )
# Longitude comparison
# Function.compare_plots(
# [
# (test_flight.longitude, "RocketPy"),
# (cots_altimeter_flight.longitude, "Telemetry"),
# ],
# title="Longitude Comparison",
# xlabel="Time (s)",
# ylabel="Longitude (deg)",
# lower=0,
# # upper=30,
# )
# Convert "deceleration" to "acceleration" for comparison
absolute_cots_acceleration = lambda x: abs(cots_altimeter_flight.acceleration(x))
# Acceleration comparison
Function.compare_plots(
[
(test_flight.acceleration, "RocketPy"),
(Function(absolute_cots_acceleration), "Telemetry"),
],
title="Acceleration Comparison",
xlabel="Time (s)",
ylabel="Acceleration (m/s^2)",
lower=0,
upper=30,
)
