Implement wind angle representation of six-degrees-of-freedom equations of motion of simple variable mass
For a description of the coordinate system employed and the translational dynamics, see the block description for the Simple Variable Mass 6DOF (Quaternion) block.
The relationship between the wind angles, T, can be determined by resolving the wind rates into the wind-fixed coordinate frame.
Inverting J then gives the required relationship to determine the wind rate vector.
The body-fixed angular rates are related to the wind-fixed angular rate by the following equation.
Using this relationship in the wind rate vector equations, gives the relationship between the wind rate vector and the body-fixed angular rates.
Specifies the input and output units:
|Metric (MKS)||Newton||Newton meter||Meters per second squared||Meters per second||Meters||Kilogram||Kilogram meter squared|
|English (Velocity in ft/s)||Pound||Foot pound||Feet per second squared||Feet per second||Feet||Slug||Slug foot squared|
|English (Velocity in kts)||Pound||Foot pound||Feet per second squared||Knots||Feet||Slug||Slug foot squared|
Select the type of mass to use:
Mass is constant throughout the simulation.
Mass and inertia vary linearly as a function of mass rate.
Mass and inertia variations are customizable.
The Simple Variable selection conforms to the previously described equations of motion.
Select the representation to use:
Use wind angles within equations of motion.
Use quaternions within equations of motion.
The Wind Angles selection conforms to the previously described equations of motion.
The three-element vector for the initial location of the body in the flat Earth reference frame.
The three-element vector containing the initial airspeed, initial sideslip angle and initial angle of attack.
The three-element vector containing the initial wind angles [bank, flight path, and heading], in radians.
The three-element vector for the initial body-fixed angular rates, in radians per second.
The initial mass of the rigid body.
A scalar value for the empty mass of the body.
A scalar value for the full mass of the body.
A 3-by-3 inertia tensor matrix for the empty inertia of the body, in body-fixed axes.
A 3-by-3 inertia tensor matrix for the full inertia of the body, in body-fixed axes.
Select this check box to add a mass flow relative velocity port. This is the relative velocity at which the mass is accreted or ablated.
|Vector||Contains the three applied forces in wind-fixed axes.|
|Vector||Contains the three applied moments in body-fixed axes.|
|Scalar or vector||Contains one or more rates of change of mass. This value is positive if the mass is added (accreted) to the body in wind axes. It is negative if the mass is ejected (ablated) from the body in wind axes.|
|Three-element vector||Contains one or more relative velocities at which the mass is accreted to or ablated from the body in wind axes.|
|Three-element vector||Contains the velocity in the fixed Earth reference frame.|
|Three-element vector||Contains the position in the flat Earth reference frame.|
|Three-element vector||Contains the wind rotation angles [bank, flight path, heading], in radians.|
|3-by-3 matrix||Applies to the coordinate transformation from flat Earth axes to wind-fixed axes.|
|Three-element vector||Contains the velocity in the wind-fixed frame.|
|Two-element vector||Contains the angle of attack and sideslip angle, in radians.|
|Two-element vector||Contains the rate of change of angle of attack and rate of change of sideslip angle, in radians per second.|
|Three-element vector||Contains the angular rates in body-fixed axes, in radians per second.|
|Three-element vector||Contain the angular accelerations in body-fixed axes, in radians per second squared.|
|Three-element vector||Contains the accelerations in body-fixed axes.|
|Scalar element||Contains a flag for fuel tank status:|
The block assumes that the applied forces are acting at the center of gravity of the body.
Mangiacasale, L., Flight Mechanics of a μ-Airplane with a MATLAB Simulink Helper, Edizioni Libreria CLUP, Milan, 1998.
Stevens, B. L., and F. L. Lewis, Aircraft Control and Simulation, John Wiley & Sons, New York, 1992.