aerosandbox.library.propulsion_electric#
Module Contents#
Functions#
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A function for predicting the performance of an electric motor. |
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Performs a propulsion analysis for an electric propeller-driven aircraft. |
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Estimates the internal resistance of a motor from its no_load_current. Gates quotes R^2=0.93 for this model. |
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Estimates the mass of an ESC. |
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Estimates the mass of a lithium-polymer battery. |
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Estimates the mass of a brushless DC electric motor. |
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Estimates the mass of wires used for power transmission. |
Attributes#
- aerosandbox.library.propulsion_electric.motor_electric_performance(voltage=None, current=None, rpm=None, torque=None, kv=1000.0, resistance=0.1, no_load_current=0.4)[source]#
A function for predicting the performance of an electric motor.
Performance equations based on Mark Drela’s First Order Motor Model: http://web.mit.edu/drela/Public/web/qprop/motor1_theory.pdf
Instructions: Input EXACTLY TWO of the following parameters: voltage, current, rpm, torque.
Exception: You cannot supply the combination of current and torque - this makes for an ill-posed problem.
Note that this function is fully vectorized, so arrays can be supplied to any of the inputs.
- Parameters:
voltage (Union[float, aerosandbox.numpy.ndarray]) – Voltage across motor terminals [Volts]
current (Union[float, aerosandbox.numpy.ndarray]) – Current through motor [Amps]
rpm (Union[float, aerosandbox.numpy.ndarray]) – Motor rotation speed [rpm]
torque (Union[float, aerosandbox.numpy.ndarray]) – Motor torque [N m]
kv (float) – voltage constant, in rpm/volt
resistance (float) – resistance, in ohms
no_load_current (float) – no-load current, in amps
- Returns:
- “voltage”,
”current”, “rpm”, “torque”, “shaft power”, “electrical power”, “efficiency” “waste heat”
And values are corresponding quantities in SI units.
Note that “efficiency” is just (shaft power) / (electrical power), and hence implicitly assumes that the motor is operating as a motor (electrical -> shaft power), and not a generator (shaft power -> electrical). If you want to know the efficiency of the motor as a generator, you can simply calculate it as (electrical power) / (shaft power).
- Return type:
A dictionary where keys are
- aerosandbox.library.propulsion_electric.electric_propeller_propulsion_analysis(total_thrust, n_engines, propeller_diameter, op_point, motor_kv, motor_no_load_current, motor_resistance, wire_resistance, battery_voltage, propeller_tip_mach=0.5, gearbox_ratio=1, gearbox_efficiency=1, esc_efficiency=0.98, battery_discharge_efficiency=0.985)[source]#
Performs a propulsion analysis for an electric propeller-driven aircraft.
May be used for single-engine or multi-engine aircraft, so long as all engines / propellers are identical.
- Parameters:
total_thrust (float) – Total thrust force produced by all engines at the cruise operating point [N].
n_engines (int) – Number of engines on the aircraft.
propeller_diameter (float) – Diameter of each of the propellers [m].
op_point (aerosandbox.performance.operating_point.OperatingPoint) – The cruise operating point. Must be an AeroSandbox OperatingPoint object.
motor_kv (float) – Motor voltage constant [rpm/volt].
motor_no_load_current (float) – Motor no-load current [amps].
motor_resistance (float) – Motor resistance [ohms].
wire_resistance (float) – Round-trip resistance of the wires connecting the ESC to the battery [ohms].
battery_voltage (float) – Battery voltage [volts].
propeller_tip_mach (float) – Mach number at the propeller tip. Defaults to 0.50. From a propulsive efficiency perspective, you want this to be as high as possible while still keeping the tip speed (hypotenuse of the velocity triangle) below the critical Mach number of the propeller blade airfoil. This is because motor efficiency and specific power tend to be better at high-speed low-torque conditions, and also the propeller aerodynamics tend to be better at low solidity. But there may be reasons to lower this, such as propeller structural considerations or noise considerations (with noise being a strong function of tip Mach).
gearbox_ratio (float) – Gearbox reduction ratio. Defaults to 1 (no gearbox). For example, a gearbox_ratio of 5 is a 5:1 reduction, meaning that the propeller turns 5 times slower than the motor.
gearbox_efficiency (float) – Gearbox efficiency. Defaults to 1, only because the gearbox_ratio defaults to 1 (no gearbox), and so this represents no losses. If you have a gearbox, you should probably use a value of 0.98 or so.
esc_efficiency (float) – Efficiency of the electronic speed controller (ESC), sometimes called the inverter. Defaults to 0.98, which is a reasonable value for a high-quality ESC at a large (>5 kW) scale. Small components will lower efficiencies than this.
battery_discharge_efficiency (float) – Coulobmic efficiency of the battery in discharge only (i.e., not round-trip). Defaults to 0.985, which is a reasonable value for a high-quality lithium-polymer battery. Other battery chemistries will have different values.
- Return type:
Dict[str, float]
Returns: A dictionary of various parameters of the propulsion analysis. Of particular note are the following keys:
“air_power”: The power delivered to the air (thrust * velocity) [W]
“shaft_power”: The power at the propeller shaft (after the gearbox; rotational speed * torque) [W]
“motor_electrical_power”: The electrical power input to the motor [W]
“esc_electrical_power”: The electrical power input to the ESC [W]
“battery_power”: The power draw from the battery [W].
“propeller_efficiency”: The propulsive efficiency of the propeller, defined as (air_power / shaft_power).
“motor_efficiency”: The efficiency of the motor, defined as (shaft_power / motor_electrical_power).
“overall_efficiency”: The overall efficiency of the propulsion system, defined as (air_power / battery_power).
- aerosandbox.library.propulsion_electric.motor_resistance_from_no_load_current(no_load_current)[source]#
Estimates the internal resistance of a motor from its no_load_current. Gates quotes R^2=0.93 for this model.
- Source: Gates, et. al., “Combined Trajectory, Propulsion, and Battery Mass Optimization for Solar-Regen…”
https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=3932&context=facpub
- Parameters:
no_load_current – No-load current [amps]
- Returns:
motor internal resistance [ohms]
- aerosandbox.library.propulsion_electric.mass_ESC(max_power)[source]#
Estimates the mass of an ESC.
Informal correlation I did to Hobbyking ESCs in the 8S LiPo, 100A range
- Parameters:
max_power – maximum power [W]
- Returns:
estimated ESC mass [kg]
- aerosandbox.library.propulsion_electric.mass_battery_pack(battery_capacity_Wh, battery_cell_specific_energy_Wh_kg=240, battery_pack_cell_fraction=0.7)[source]#
Estimates the mass of a lithium-polymer battery.
- Parameters:
battery_capacity_Wh – Battery capacity, in Watt-hours [W*h]
battery_cell_specific_energy – Specific energy of the battery at the CELL level [W*h/kg]
battery_pack_cell_fraction –
Fraction of the battery pack that is cells, by weight.
Note: Ed Lovelace, a battery engineer for Aurora Flight Sciences, gives this figure as 0.70 in a Feb.
2020 presentation for MIT 16.82
- Returns:
Estimated battery mass [kg]
- aerosandbox.library.propulsion_electric.mass_motor_electric(max_power, kv_rpm_volt=1000, voltage=20, method='hobbyking')[source]#
Estimates the mass of a brushless DC electric motor. Curve fit to scraped Hobbyking BLDC motor data as of 2/24/2020. Estimated range of validity: 50 < max_power < 10000
- Parameters:
max_power (float) – maximum power [W]
kv_rpm_volt (float) – Voltage constant of the motor, measured in rpm/volt, not rads/sec/volt! [rpm/volt]
voltage (float) – Operating voltage of the motor [V]
method (str) –
method to use. “burton”, “hobbyking”, or “astroflight” (increasing level of detail).
Burton source: https://dspace.mit.edu/handle/1721.1/112414
Hobbyking source: C:ProjectsGitHubMotorScraper,
Astroflight source: Gates, et. al., “Combined Trajectory, Propulsion, and Battery Mass Optimization for
Solar-Regen…” https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=3932&context=facpub
Validity claimed from 1.5 kW to 15 kW, kv from 32 to 1355.
- Returns:
Estimated motor mass [kg]
- aerosandbox.library.propulsion_electric.mass_wires(wire_length, max_current, allowable_voltage_drop, material='aluminum', insulated=True, max_voltage=600, wire_packing_factor=1, insulator_density=1700, insulator_dielectric_strength=12000000.0, insulator_min_thickness=0.0002, return_dict=False)[source]#
Estimates the mass of wires used for power transmission.
- Materials data from: https://en.wikipedia.org/wiki/Electrical_resistivity_and_conductivity#Resistivity-density_product
All data measured at STP; beware, as this data (especially resistivity) can be a strong function of temperature.
- Parameters:
wire_length (float) – Length of the wire [m]
max_current (float) – Max current of the wire [Amps]
allowable_voltage_drop (float) – How much is the voltage allowed to drop along the wire?
material (str) –
Conductive material of the wire (“aluminum”). Determines density and resistivity. One of:
”sodium”
”lithium”
”calcium”
”potassium”
”beryllium”
”aluminum”
”magnesium”
”copper”
”silver”
”gold”
”iron”
insulated (bool) – Should we add the mass of the wire’s insulator coating? Usually you’ll want to leave this True.
max_voltage (float) – Maximum allowable voltage (used for sizing insulator). 600 is a common off-the-shelf rating.
wire_packing_factor (float) – What fraction of the enclosed cross section is conductor? This is 1 for solid wire, and less for stranded wire.
insulator_density (float) – Density of the insulator [kg/m^3]
insulator_dielectric_strength (float) – Dielectric strength of the insulator [V/m]. The default value of 12e6 corresponds
rubber. (to) –
insulator_min_thickness (float) – Minimum thickness of the insulator [m]. This is essentially a gauge limit.
mm. (The default value is 0.2) –
return_dict (bool) – If True, returns a dictionary of all local variables. If False, just returns the wire
False. (mass as a float. Defaults to) –
Returns: If return_dict is False (default), returns the wire mass as a single number. If return_dict is True, returns a dictionary of all local variables.