This installs pyfme to be run in this online notebook
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!pip install git+https://github.com/AeroPython/PyFME.git
In order to perform a simulation, the first thing we need is an aircraft:
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from pyfme.aircrafts import Cessna172
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aircraft = Cessna172()
Aircraft will provide the simulator the forces, moments and inertial properties in order to perform the integration of the dynamic system equations:
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print(f"Aircraft mass: {aircraft.mass} kg")
print(f"Aircraft inertia tensor: \n {aircraft.inertia} kg/m²")
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print(f"forces: {aircraft.total_forces} N")
print(f"moments: {aircraft.total_moments} N·m")
For the aircraft, in order to calculate its forces and moments it is necessary to set the controls values within the limits:
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print(aircraft.controls)
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print(aircraft.control_limits)
but also to provide and environment (ie. atmosphere, winds, gravity) and the aircraft state, which will also determine the aerodynamic contribution.
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from pyfme.environment.atmosphere import ISA1976
from pyfme.environment.wind import NoWind
from pyfme.environment.gravity import VerticalConstant
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atmosphere = ISA1976()
gravity = VerticalConstant()
wind = NoWind()
The atmosphere, wind and gravity model make up the environment:
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from pyfme.environment import Environment
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environment = Environment(atmosphere, gravity, wind)
The environment has an update method which given the state (ie. position, altitude...) updates the environment variables (ie. density, wind magnitude, gravity force...)
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help(environment.update)
Even if the state can be set manually by giving the position, attitude, velocity, angular velocities... Most of the times, the user will want to trim the aircraft in a stationary condition. The aircraft controls to flight in that condition will be also provided by the trimmer.
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from pyfme.utils.trimmer import steady_state_trim
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help(steady_state_trim)
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from pyfme.models.state.position import EarthPosition
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pos = EarthPosition(x=0, y=0, height=1000)
psi = 0.5 # rad
TAS = 45 # m/s
controls0 = {'delta_elevator': 0, 'delta_aileron': 0, 'delta_rudder': 0, 'delta_t': 0.5}
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trimmed_state, trimmed_controls = steady_state_trim(
aircraft,
environment,
pos,
psi,
TAS,
controls0
)
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trimmed_state
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trimmed_controls
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Now, all the necessary elements in order to calculate forces and moments are available
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# Environment conditions for the current state:
environment.update(trimmed_state)
# Forces and moments calculation:
forces, moments = aircraft.calculate_forces_and_moments(trimmed_state, environment, controls0)
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forces, moments
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The aircraft is trimmed indeed: the total forces and moments (aerodynamics + gravity + thrust) are zero
In order to simulate the dynamics of the aircraft under certain inputs in an environment, the user can set up a simulation using a dynamic system:
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from pyfme.models import EulerFlatEarth
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system = EulerFlatEarth(t0=0, full_state=trimmed_state)
Let's set the controls for the aircraft during the simulation. As a first step we will set them constant and equal to the trimmed values.
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from pyfme.utils.input_generator import Constant
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controls = controls = {
'delta_elevator': Constant(trimmed_controls['delta_elevator']),
'delta_aileron': Constant(trimmed_controls['delta_aileron']),
'delta_rudder': Constant(trimmed_controls['delta_rudder']),
'delta_t': Constant(trimmed_controls['delta_t'])
}
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from pyfme.simulator import Simulation
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sim = Simulation(aircraft, system, environment, controls)
Once the simulation is set, the propagation can be performed:
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results = sim.propagate(10)
The results are returned in a DataFrame:
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results
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%matplotlib inline
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kwargs = {'marker': '.',
'subplots': True,
'sharex': True,
'figsize': (12, 6)}
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results.plot(y=['x_earth', 'y_earth', 'height'], **kwargs);
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results.plot(y=['psi', 'theta', 'phi'], **kwargs);
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results.plot(y=['v_north', 'v_east', 'v_down'], **kwargs);
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results.plot(y=['p', 'q', 'r'], **kwargs);
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results.plot(y=['alpha', 'beta', 'TAS'], **kwargs);
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results.plot(y=['Fx', 'Fy', 'Fz'], **kwargs);
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results.plot(y=['Mx', 'My', 'Mz'], **kwargs);
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results.plot(y=['elevator', 'aileron', 'rudder', 'thrust'], **kwargs);
Let's set the controls for the aircraft during the simulation. As a first step we will set them constant and equal to the trimmed values.
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from pyfme.utils.input_generator import Doublet
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de0 = trimmed_controls['delta_elevator']
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controls = controls = {
'delta_elevator': Doublet(t_init=2, T=1, A=0.1, offset=de0),
'delta_aileron': Constant(trimmed_controls['delta_aileron']),
'delta_rudder': Constant(trimmed_controls['delta_rudder']),
'delta_t': Constant(trimmed_controls['delta_t'])
}
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sim = Simulation(aircraft, system, environment, controls)
Once the simulation is set, the propagation can be performed:
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results = sim.propagate(90)
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results.plot(y=['x_earth', 'y_earth', 'height'], **kwargs);
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results.plot(y=['psi', 'theta', 'phi'], **kwargs);
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results.plot(y=['v_north', 'v_east', 'v_down'], **kwargs);
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results.plot(y=['p', 'q', 'r'], **kwargs);
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results.plot(y=['alpha', 'beta', 'TAS'], **kwargs);
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results.plot(y=['Fx', 'Fy', 'Fz'], **kwargs);
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results.plot(y=['Mx', 'My', 'Mz'], **kwargs);
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results.plot(y=['elevator', 'aileron', 'rudder', 'thrust'], **kwargs);
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dt = 0.05 # seconds
sim = Simulation(aircraft, system, environment, controls, dt)
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results = sim.propagate(0.5)
results
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We can propagate for one time step even once the simulation has been propagated before:
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results = sim.propagate(sim.time+dt)
results
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Notice that results will include the previous timesteps as well as the last one. To get just the last one one can use pandas loc or iloc:
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results.iloc[-1] # last time step
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results.loc[sim.time] # results for current simulation time
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