The Dynamic Control Fixed Wing acceleration model provides a force and moment model for the Dynamic Control Procedure, which implements a simple Fixed Wing model with aero, propulsion and Flight Control systems. The Dynamic Control Fixed Wing performance model is comprised of four tabs - Basic, Aerodynamics, Propulsion, and Flight Control.
The Basic tab defines the turn rate behavior, climb/descent transitions, attitude transitions, and control authority information. The Aerodynamics and Propulsion tabs allow you to select and define strategies to model attitude and propulsion characteristics. The Flight Control tab allows you to set the control ranges (the underlying aero model uses normalized -1,1 ranges) and implements any autopilot modes.
Basic
The Basic tab is comprised of three sections - Level Turns, Climb and Descent Transitions, and Attitude Transitions - as described below.
Level Turns
The values specified for these parameters are the level turn values for the aircraft. STK's Aviator capability adheres to these values when possible, but in procedures where the turn is non-level the values may be adjusted to maintain the correct relationship between these interrelated parameters. Select one parameter to manually define; the other parameters are calculated relative to the parameter that you specified.
Table - Level Turns Parameters
Climb and Descent Transitions
The values specified for these parameters define the G force of transitions between climbing or descending and level flight.
Table - Climb and Descent Transitions Parameters
Accel Maneuver Mode Field
You can toggle if the aircraft turn or push/pull calculations use atmosphere density scaling. Alternatively, you can define specific parameters used in the turn calculation for more realistic results.
Table -Accel Maneuver Mode Options
Always Ignore Flight Path Angle Check Box
When you are working at the design limits of an aircraft model, you may commonly encounter problems with:
- pushing over at high path angles
- pulling up at low flight path angles
For example, an aircraft flying at high altitude and high speed may not have enough control authority to push over as a procedure requires. Or, the aircraft may need to violate another constraint such as the procedure ceiling.
In these situations, you can select the Always Ignore Flight Path Angle check box to ignore load factor limits. This option enables you to suspend these limits without needing to change to the aircraft model that you are using.
Attitude Transitions
Aircraft attitude is determined using a 123 Euler angle sequence of Bank, Angle of Attack The angle between the body X axis and the projection of the velocity vector onto the body XZ plane. The velocity vector is the velocity of the object as observed in the object's central body fixed coordinate system., and Sideslip, originating from a velocity aligned, nadir constrained set of axes. Attitude rates may be violated in the case of very short - or zero distance - procedures.
Table - Attitude Transitions Parameters
Required Control Authority (Omega Dots)
Similar to the Dynamics/Moments tab in the Basic Acceleration model, the Required Control Authority allows you to specify what angular rates are expected to safely control the vehicle. However, there is no need to define the surface area or moment arm length because the actuator is modeled in the aircraft. Therefore, these parameters were added to the "Basic" tab for this model.
Table - Required Control Authority Parameters
Aerodynamics and Propulsion Analysis
The Aerodynamics and Propulsion tabs of the Acceleration performance model function together as an analysis system that performs a trim calculation, as the aircraft flies, to compute lift, drag, thrust, throttle, and fuel consumption parameters at any given flight condition for the specified trajectory. The input to this system is the mission flight path while the outputs are the aerodynamics and propulsion data. The fuel flow is integrated into the weight of the aircraft, but these values do not directly influence the flight path.
The system will generate warnings when AOA limits are exceeded or when thrust deficits exist indicating the aircraft design is not capable of flying the path specified, but the path will still be flown as designed; this feature allows you to explore an aircraft design (perhaps based on high accuracy wind tunnel and engine test data) and its suitability to perform a desired mission.
Aerodynamics
The Aerodynamics tab is used to define the methods used to compute lift, drag, angle of attack, sideslip and intermediate / derived values. There are two aerodynamics strategies to choose from:
Fighter Aero
This model is a generalization of the F16 model from the Stevens book “Aircraft Control and Simulation.” It contains a variety of aerodynamic tables, which, for the F16 are derived from the wind tunnel.
This model version is generalized to allow you to supply different tables, however the form of the model is fixed. The idea is that this model is similar to other fighters not that different from an F16 model.
Force coefficients (body frame)
The body axis are a front, right, down (frd) system, labeled x, y, and z. All two dimensional tables in this section are described in fortran order (as in the Stevens model), i.e. C(a,b) means the columns are indexed by a, the rows by b. This is to help you understand the row/columns of the input table and how they relate to the concepts.
- CX = CX(alpha, elevator) – a full two dimensional table from alpha min to alpha max and -1 to 1 for the elevator.
- CY = CY(beta, aileron, rudder) = CY(1)*beta + CY(2)*aileron + CY(3)*rudder
- CZ = CZ(alpha,beta,elevator) = S*(1-beta^2)-ElevatorDZ*elevator (beta radians), S=S(alpha) a table lookup for the values of the CZ table. The values in the dialog are the S table.
The aerodynamic body forces are created by:
q = ½ rho * V^2, where rho = air density and V = wind velocity.
- QS=q*WingArea
- FX=QS*CX
- FY=QS*CY
- FZ=QS*CZ
Moment coefficients (body frame)
CL (roll moment coefficient) =CL(alpha, beta) is a table lookup on alpha and |beta|. The result is corrected based on the sign (+ or -) of beta. The range of the lookup on beta is between zero (0) and BetaMax.
CM (pitchmoment coefficient) =CM(alpha,elevator) is a table encoding the pitching moments. The effect of elevator is potentially nonlinear for this moment.
CN (yaw moment coefficient)=CN(alpha,beta) is the same lookup as CL, alpha and |beta| with the result corrected based on the sign (+ or -) of beta.
Control Effects on moment
The controls enter into CL and CN via a linear addition based on a set of tables which all have the same basic construction (just different values). Call the lookup of these tables DLD(T, alpha, beta). It uses the 2d values from T, and the lookups are on from AlphaMin to AlphaMax and -BetaMax to BetaMax. The corrections are as follows:
- CL += DLD(DLDA,alpha,beta)*aileron + DLD(DLDR,alpha,beta)*rudder
- CN += DLD(DNDA,alpha,beta)*aileron + DLD(DNDR,alpha,beta)*rudder
Aerodynamic damping
These values use the body rotation (P,Q,R) and a normalization related to the velocity to apply damping restoration forces. The damping table is a set of 1D tables (the second dimensions are unrelated).
The table itself is a function of the angle of attack.
DAMP = DAMP(alpha) this is a set of nine independent table lookups, resulting in nine nondimensional values.
Each row of the table is the i^th table lookup on alpha from AlphaMin to AlphaMax.
The resulting vector is (D{coefficient}D{input}):
| Parameter |
|---|
| DXDQ |
| DYDR |
| DYDP |
| DZDQ |
| DLDR |
| DLDP |
| DMDQ |
| DNDR |
| DNDP |
The corrections are applied as:
CX += Q*DAMP[0]
CY += B2V*(R* DAMP [1]+P* DAMP [2])
CZ += Q* DAMP [3]
CL += B2V*(R*DAMP[4] + P*DAMP[5])
CM += Q*DAMP[6]
CN += B2V*(R*DAMP[7] + P*DAMP[8])
CX += CQ*DAMP[0]
CZ += CQ* DAMP[3]
CM += CQ*DAMP[6]
Aerodynamic offset correction
With a value of AeroOffset = 0, the aerodynamic moment is at the CG and the non-dimensional coefficients are applied directly as computed above. The value of AeroOffset is a fraction of the chord distance, and a positive value implies a shift backward along the aircraft X axis. The moment transfer is applied to the coefficients directly. The transfer must take into account the fact that the moment coefficients are normalized by different values. It proceeds as follows:
CMT += CZ*AeroOffset
CNT += -CY*AeroOffset*MeanAeroChord/WingSpan
The aerodynamic body moments are created by:
MX = QS * WingSpan * CL
MY = QS * MeanAerochord * CM
MZ = QS * WingSpan * CN
Lift and Drag Factor
- Lift Factor is a scalar value applied to the aircraft's lift surface area for parametric analysis.
- Drag Factor is a scalar value applied to the aircraft's drag surface for parametric analysis.
Transport Aero
The Transport Aero model is based on the Research Civil Aircraft Model (RCAM), but the basic parameters of the model are configurable and suitable for a range of large transport aircraft.
The aerodynamic model is more highly parameterized than the Fighter model, and does not consist of aerodynamic tables. It is a more linear model and does not have the finer nonlinear elements of that model.
The normalization section contains two offset parameters- the aerodynamic center of this model can have both a longitudinal and a vertical offset.
The lift curve is the parameterization of a zero point (defining the alpha where the lift is zero), the critical point (where stall begins to onset), and a breakpoint where a cubic polynomial enters.
The first part of the curve (up to alphabreak) is a line with slope CLSlope that has X intercept at alphazero. At the point alphabreak a cubic polynomial takes over – the polynomial has the same slope as the linear section at this point, and has a maximum at alphacrit, where it begins to lessen and enter the stall region.
The lift curve has a cos(beta)*cos(beta) scaling (beta = sideslip), which models the reduction of direct wind (V_wind = cos(beta)V), so that the V^2 in the lift equation leaves this corresponding correction factor.
The tail adds a lift component as well as a moment, and is parameterized by the Elev Area.
Drag is a simple quadratic polynomial in CL, CD = CDZero + DragK*(CL-CLZero)^2.
As the airplane begins to sideslip, this drag coefficient is interpolated to a simple flat plate area (beta = 90), parameterized by SideFlatPlate.
The moments are computed with a term based on alpha/beta, a control component and a damping contribution which is applied to the body angular rates.
The Elev OffsetX is the lever arm from CG to elevator, and this modifies the longitudinal controllability. ControlFactor multiples the control effects and DampingFactor scales the moment damping.
Propulsion
The Propulsion tab is used to define the rate at which the aircraft will speed up or slow down and provides a method for computing the fuel flow; this involves computing the thrust requirements and the throttle setting for any given flight condition which in turn requires a full aerodynamics calculation.
The propulsion models provided with STK separate the acceleration and deceleration speed changes from the thrust available as computed by the models. This is done for ease of use and to allow for quick construction of flight paths without constraints imposed by the propulsion system. AGI recommends that you fine tune these separate parameters so that they result in a faithful representation of actual performance.
There are two propulsion strategies to choose from:
Each of the strategies are defined below.
Fighter Propulsion
The Fighter Propulsion model is closely modeled from the Stevens F16.
The thrust is primarily computed from a set of three tables, which are indexed by mach and altitude. Through the different models of operation, these tables are interpolated to arrive at the thrust.
The throttle ranges from 0 to 1, and the percent power output has an output breakpoint at MilThrottleFrac. For a MilPowerPct of 50 and a MilThrottleFrac of 0.77, the throttle to commanded power looks like the graph below:
Transport Propulsion
This model follows a similar paradigm to the Fighter model, however, it does not have the second mode, the burner mode. Thrust is a simple interpolation of thrust and mil tables, with a spooling time constant.
Duda, Holger et al. "Robust Flight Control Design Challenge - the Research Civil Aircraft Model (RCAM). A Model Following Control Approach." (1996).
Flight Control
The FixedWingFlightCtrl strategy stores the control ranges (the underlying aero model uses normalized -1,1 ranges). The strategy also implements any desired autopilot modes.
Controls
These are the actuators of the flight control. They represent pilot stick control, which for fixed wing are elevator, aileron, rudder, and throttle. The max deflections for the control surfaces are the max in the positive and negative directions.
VXF
This field represents autopilot mode. The CourseSnap option controls how aggressively the plane turns while in autopilot mode. The MaxBank value comes from the "Basic" tab bank angle.
Cutoff Values
The cutoff values are low pass cutoff frequencies for each of the controls coming out of VXF. This provides you a bit more tuning in case you run into oscillations.