ElectricThruster

Mathematical Models

The ElectricThruster model supports several models for computation of thrust and and mass flow rate and the model used is set by the ThrustModel field. When ThrustModel is set to ThrustMassPolynomial, the following polynomials are used to compute thrust and mass flow rate

where P is the power provided to the thruster which is computed using the power logic defined on the FiniteBurn resource, f_d is duty cycle, f_s is thrust scale factor, R_iT is the rotation matrix from the thrust coordinate system to the inertial system, and T_hat is the thrust unit vector. By industry convention, the mass flow rate and thrust polynomial equations are in mg/s and milli-Newtons respectively. GMAT internally converts the units to be consistent with the equations of motion.

When ThrustModel is set to ConstantThrustAndIsp, the following polynomials are used to compute thrust and mass flow rate

where C_t1 is set using the ConstantThrust field, Isp is set using the Isp field, f_d is duty cycle, f_s is thrust scale factor, R_iT is the rotation matrix from the thrust coordinate system to the inertial system, and T_hat is the thrust unit vector. Note, by industry convention, the mass flow rate and thrust polynomial equations are in mg/s and milli-Newtons respectively. GMAT internally converts the units to be consistent with the equations of motion.

When ThrustModel is set to FixedEfficiency, the following polynomials are used to compute thrust and mass flow rate

where P is the power provided to the thruster which is computed from the power logic defined on the FiniteBurn Resource. "Eta" is the FixedEfficiency setting, f_d is duty cycle, f_s is thrust scale factor, R_iT is the rotation matrix from the thrust coordinate system to the inertial system, and T_hat is the thrust unit vector.

Use of Thruster Resource in Conjunction With Maneuvers

An ElectricThruster resource is used only in association with finite maneuvers. To implement a finite maneuver, you must first create both an ElectricTank and a FiniteBurn resource. You must also associate an ElectricTank with the ElectricThruster resource and you must associate an ElectricThruster with the FiniteBurn resource. The actual finite maneuver is implemented using the BeginFiniteBurn/EndFiniteBurn commands.

For a complete descripton of how to configure all Resources required for electric propulsion modelling, see the Tutorial named Chapter 12, Electric Propulsion

Local Coordinate Systems

Here, a Local coordinate system is defined as one that we configure "locally" using the ElectricThruster resource interface as opposed to defining a coordinate system using the Coordinate Systems folder in the Resources Tree.

To configure a local coordinate system, you must specify the coordinate system of the input thrust acceleration direction vector, ThrustDirection1-3. If you choose a local coordinate system, the four choices available, as given by the Axes sub-field, are VNB, LVLH, MJ2000Eq, and SpacecraftBody. VNB or Velocity-Normal-Binormal is a non-inertial coordinate system based upon the motion of the spacecraft with respect to the Origin sub-field. For example, if the Origin is chosen as Earth, then the X-axis of this coordinate system is the along the velocity of the spacecraft with respect to the Earth, the Y-axis is along the instantaneous orbit normal (with respect to the Earth) of the spacecraft, and the Z-axis completes the right-handed set.

Similarly, Local Vertical Local Horizontal or LVLH is also a non-inertial coordinate system based upon the motion of the spacecraft with respect to the Origin sub-field. Again, if we choose Earth as the origin, then the X-axis of this coordinate system is the position of the spacecraft with respect to the Earth, the Z-axis is the instantaneous orbit normal (with respect to the Earth) of the spacecraft, and the Y-axis completes the right-handed set.

MJ2000Eq is the J2000-based Earth-centered Earth mean equator inertial coordinate system. Note that the Origin sub-field is not needed to define this coordinate system.

SpacecraftBody is the attitude system of the spacecraft. Since the thrust is applied in this system, GMAT uses the attitude of the spacecraft, a spacecraft attribute, to determine the inertial thrust direction. Note that the Origin sub-field is not needed to define this coordinate system.

Caution Regarding Force Model Discontinuties

Note that when modellign shadows on a SolarPowerSystem Resource, it is possible that there is not enough power available to power an ElectricThruster. This occurs when the power available from the SolarPowerSystem, or the power distributed to the thruster, is less than MinimumUsablePower. When this occurs, the thruster model turns off thrust and this can cause a discontinuity in the force model. To avoid this, you must propagate to the boundary and switch propagators, or configure the Propagator to continue propagating if a poor step occurs.

Create a default ElectricTank and an ElectricThruster that allows for fuel depletion, assign the ElectricThruster the default ElectricTank, and attach both to a Spacecraft.

%  Create an ElectricTank Resource
Create ElectricTank anElectricTank

%  Create an Electric Thruster Resource
Create ElectricThruster anElectricThruster
anElectricThruster.CoordinateSystem = Local
anElectricThruster.Origin = Earth
anElectricThruster.Axes = VNB
anElectricThruster.ThrustDirection1 = 1
anElectricThruster.ThrustDirection2 = 0
anElectricThruster.ThrustDirection3 = 0
anElectricThruster.DutyCycle = 1
anElectricThruster.ThrustScaleFactor = 1
anElectricThruster.DecrementMass = true
anElectricThruster.Tank = {anElectricTank}
anElectricThruster.GravitationalAccel = 9.810000000000001
anElectricThruster.ThrustModel = ThrustMassPolynomial
anElectricThruster.MaximumUsablePower = 7.266
anElectricThruster.MinimumUsablePower = 0.638
anElectricThruster.ThrustCoeff1 = -5.19082
anElectricThruster.ThrustCoeff2 = 2.96519
anElectricThruster.ThrustCoeff3 = -14.4789
anElectricThruster.ThrustCoeff4 = 54.05382
anElectricThruster.ThrustCoeff5 = -0.00100092
anElectricThruster.MassFlowCoeff1 = -0.004776
anElectricThruster.MassFlowCoeff2 = 0.05717
anElectricThruster.MassFlowCoeff3 = -0.09956
anElectricThruster.MassFlowCoeff4 = 0.03211
anElectricThruster.MassFlowCoeff5 = 2.13781
anElectricThruster.FixedEfficiency = 0.7
anElectricThruster.Isp = 4200
anElectricThruster.ConstantThrust = 0.237

%  Create a SolarPowerSystem Resource
Create SolarPowerSystem aSolarPowerSystem

%  Create a Spacecraft Resource and attach hardware
Create Spacecraft DefaultSC
DefaultSC.Tanks = {anElectricTank}
DefaultSC.Thrusters = {anElectricThruster}
DefaultSC.PowerSystem = aSolarPowerSystem

BeginMissionSequence