Aircraft Nonlinear Dynamic Instability Warning System

Abstract

A system and method for predicting aircraft nonlinear instability includes the steps of: (1) a pre-built aircraft state parameters for all possible flight conditions, (2) real time measuring flight parameters to determine aircraft state, (3) calculating the inertial coupling frequencies and periods as well as the nonlinear instability threshold based on the nonlinear instability theory recently developed by the inventor, (4) providing a first warning signal if the threshold is approached, (5) providing a second warning signal if the threshold has been exceeded.

Claims

1. A method of predicting aircraft nonlinear pitch dynamic instability including: a. pre-obtained aircraft state parameter and coefficient data for all possible flight states; b. measuring current flight parameters to determine the aircraft state; c. calculating the inertial coupling frequencies and periods as
.sub.1st=.sub.10+.sub.30 and T.sub.1st=2/.sub.1st,
.sub.2nd=|.sub.10.sub.30| and T.sub.2nd=2/.sub.2nd; d. displaying the 1.sup.st and 2.sup.nd inertial coupling frequencies and periods; e. calculating the pitch instability threshold as $A_T=\max .Math.\left\{\frac{2}{{}_{1.Math.\mathrm{st}}}.Math.\sqrt{\frac{b_1.Math.b_3}{\left(I_z-I_y\right).Math.\left(I_y-I_x\right)}}-{}_m,{}_m\right\};$ f. calculating the pitch response around the preset equilibrium flight state as
A.sub.R|=.sub.0.sub.T|; g. providing a first warning signal under the following condition:
A.sub.T<A.sub.R<A.sub.T; h. providing a second warning signal under the following condition:
A.sub.RA.sub.T.

2. The method of claim 1, wherein the pre-obtained aircraft state parameter and coefficient data are obtained in advance by measurements and analyses during test flights of an aircraft.

3. The method of claim 1, wherein the pre-obtained aircraft state parameter and coefficient data are obtained in advance by empirical formulas and aerodynamic derivatives based on wind tunnel tests.

4. The method of claim 1, wherein the minimum threshold .sub.m is in the range of (0.0018, 0.09) radian, i.e. (0.1, 5) and depending on aircraft type and size.

5. The method of claim 1, wherein the safety factor is in the range of (0.5, 0.99) and depending on individual aircraft type and size.

6. A method of predicting aircraft nonlinear roll dynamic instability including: a. pre-obtained aircraft state parameter and coefficient data for all possible flight states; b. measuring current flight parameters to determine the aircraft state; c. Calculating the inertial coupling frequencies and periods as
.sub.1st=.sub.20+.sub.30 and t.sub.1st=2/.sub.1st,
.sub.2nd=|.sub.20.sub.30| and T.sub.2nd=2/.sub.2nd, d. displaying the 1.sup.st and 2.sup.nd inertial coupling frequencies and periods; e. calculating the roll instability threshold as $A_T=\max .Math.\left\{\frac{2}{{}_{1.Math..Math.\mathrm{st}}}.Math.\sqrt{\frac{b_2.Math.b_3}{\left(I_z-I_z\right).Math.\left(I_x-I_y\right)}}-{}_m,{}_m\right\};$ f. calculating the roll response around the preset equilibrium flight state as
A.sub.R=|.sub.0|; g. providing a first warning signal under the following condition:
A.sub.T<A.sub.R<A.sub.T; h. providing a second warning signal under the following condition:
A.sub.RA.sub.T.

7. The method of claim 6, wherein the pre-obtained aircraft state parameter and coefficient data are obtained in advance by measurements and analyses during test flights of an aircraft.

8. The method of claim 6, wherein the pre-obtained aircraft state parameter and coefficient data are obtained in advance by empirical formulas and aerodynamic derivatives based on wind tunnel tests.

9. The method of claim 6, wherein the minimum threshold .sub.m is in the range of (0.0018, 0.18) radian, i.e. (01., 10) and depending on individual aircraft type and size.

10. The method of claim 6, wherein the safety factor A is in the range of (0.5, 0.99) and depending on individual aircraft type and size.

11. A method of predicting aircraft nonlinear yaw dynamic instability including: a. pre-obtained aircraft state parameter and coefficient data for all possible flight states; b. measuring current flight parameters to determine the aircraft state; c. calculating the inertial coupling frequencies as
.sub.1st=.sub.10+.sub.20 and T.sub.1st=2/.sub.1st,
.sub.2nd=|.sub.10.sub.20| and T.sub.2nd=2/.sub.2nd; d. displaying the 1.sup.st and 2.sup.nd inertial coupling frequencies and periods; e. calculating the yaw instability threshold as $A_T=\max .Math.\left\{\frac{2}{{}_{1.Math..Math.\mathrm{st}}}.Math.\sqrt{\frac{b_1.Math.b_2}{\left(I_y-I_z\right).Math.\left(I_z-I_x\right)}}-{}_m,{}_m\right\};$ f. calculating the yaw response around the preset equilibrium flight state as
A.sub.R=.sub.0|; g. providing a first warning signal under the following condition:
A.sub.T<A.sub.R<A.sub.T; h. providing a second warning signal under the following condition
A.sub.RA.sub.T.

12. The method of claim 11, wherein the pre-obtained aircraft state parameter and coefficient data are obtained in advance by measurements and analyses during test flights of an aircraft.

13. The method of claim 11, wherein the pre-obtained aircraft state parameter and coefficient data are obtained in advance by empirical formulas and aerodynamic derivatives based on wind tunnel tests.

14. The method of claim 11, wherein the minimum threshold .sub.m is in the range of (0.0018, 0.35) radian, i.e. (0.1, 20) and depending on individual aircraft type and size.

15. The method of claim 11, wherein the safety factor A is in the range of (0.5, 0.99) and depending on individual aircraft type and size.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0031] FIG. 1 is 1 schematic diagram of an aircraft nonlinear instability warning system in accordance with the disclosure.

[0032] FIG. 2 is a diagram of aircraft flight parameters in accordance with the disclosure.

[0033] FIG. 3 is a flow chart for pre-measured values of restoring coefficients and damping coefficients in accordance with the disclosure.

[0034] FIG. 4 is a diagram of aircraft with body axes.

[0035] FIG. 5a and FIG. 5b are diagrams of parameter definitions for a pitch up flight mode in accordance with the disclosure.

[0036] FIG. 6a and FIG. 6b are diagrams of parameter definitions for a pitch down flight mode in accordance with the disclosure.

[0037] FIG. 7 is a flow chart for calculating an unstable axis and associated frequencies in accordance with the disclosure.

[0038] FIG. 8 is a flow chart for calculating inertial coupling frequencies and periods in accordance with the disclosure.

[0039] FIG. 9 is a flow chart for calculating a nonlinear instability threshold in accordance with the disclosure.

[0040] FIG. 10 is a flow chart for calculating a potential unstable response in accordance with the disclosure.

DESCRIPTION

[0041] The following text and figures set forth a detailed description of specific examples of the invention to teach those skilled in the art how to make and utilize the best mode of the invention.

[0042] Referring to FIG. 1, an aircraft nonlinear instability warning system 100 is part of or associated with the flight management computer (FMC) 200. The FMC 200 provides the system 100 with the necessary current flight parameters to feed into a module 101. The module 101 identifies the current flight state using the real time flight parameters and passes the information to a module 102 which communicates with a pre-determined aircraft flight coefficients 103 to identify the aircraft flight coefficients, such as the damping coefficients of roll, pitch, and yaw as well as the restoring coefficients of roll, pitch, and yaw. A module 104 determines the nonlinear instability axis and the associated frequencies using the coefficients from the module 102 and then passes the results to a module 105 which indicates the 1.sup.st and 2.sup.nd inertial coupling frequencies and periods. A module 106 uses the flight coefficients to calculate the nonlinear instability threshold A.sub.T. A module 107 is to determine whether an allowable nonlinear instability threshold AA.sub.T is larger than a minimum threshold .sub.m or not, where A is a safety factor less than 1, for example 0.9 or other number depending on aircraft size and type, and .sub.m is a pre-determined small positive number, for example, 0.0175 radian (1) or other small number depending on aircraft size and type. This minimum threshold .sub.m is chosen to prevent the threshold from going to zero. This minimum threshold is a safety margin which needs to be determined during flight tests of every aircraft for light turbulence which is assumed to occur on every flight and causes slight, erratic changes in attitude of roll, pitch, and yaw. If the allowable threshold A.sub.T is larger than .sub.m, the A.sub.T will be the dominant threshold and the system 100 goes to a module 109. If the allowable threshold A.sub.T is smaller than .sub.m, .sub.m becomes the dominant threshold and the aircraft current flight state is considered to be in a nonlinear unstable mode and the system 100 goes to a module 113. A module 108 identifies and calculates a potential nonlinear unstable response A.sub.R. The module 109 is to determine whether the response A.sub.R is smaller than the allowable threshold A.sub.T. If the response A.sub.R is less than A.sub.T, the current flight state is considered to be in a stable mode and the system 100 goes to a module 110 to turn audible alert and visual alert off if they are on. If the response A.sub.R is larger than A.sub.T, the current flight state is either in an approaching to unstable mode or already in an unstable mode. Then the system 100 goes to a module 111 for a further check. If A.sub.R is larger than A.sub.T but still smaller than A.sub.T, the current flight state is in an approaching to unstable mode and the system 100 goes to a module 112 to generate and turn on audible and visual alerts for Approaching Unstable mode, maybe with a yellow light for example. If A.sub.R is larger than A.sub.T, the current flight state is considered in an unstable mode and the system 100 goes to a module 113l to generate and turn on audible and visual alarms to warn the flight crew for the Unstable mode, maybe with a red light for example. The system 100 continues run during an entire flight.

[0043] Referring to FIG. 2, the module 101 collects flight parameters and determines the current flight state. The flight parameters include the aircraft gross weight and the center of gravity location 101-1, the aircraft moments of inertia at this state 101-2, the aircraft altitude 101-3, the wind information 101-4, the load factors 101-5, the angle of attack (AOA) 101-6, the icing state and the outside air temperature 101-7, the pitch trimmed angle of attack (AOA) .sub.T 101-8, the current flight path angle 101-9, the preset flight path angle .sub.0 101-10, the aircraft configuration 101-11, the true airspeed or Mach number (TAS) 101-12, preset roll trim 101-13, and preset yaw trim 101-14. The aircraft configuration includes positions of flaps, gears, slats, and airbrakes as well as the settings of thrust, sideslip, horizontal stabilizer, rudder, and ailerons.

[0044] The current flight state information is then passed to the module 102 which communicates with the flight state parameter module 103 as shown in FIG. 1 to identify the flight dynamic coefficients for the current flight state. The module 103 is stored in a hard drive of the FMC 200 and contains pre-determined flight parameters. As shown in FIG. 3, the module 103 includes aircraft gross weight and center of gravity location of flight state 103-1, aircraft moments of inertia 103-2, aircraft configuration 103-3, aircraft altitude 103-4, true airspeed or Mach number (TAS) 103-5, icing condition and outside atmosphere temperature (OAT) 103-6, pitch trimmed angle of attack (AOA, .sub.T) 103-7, preset flight path angle (.sub.o) 103-8, load factors 103-9, wind information 103-10, preset roll trim 103-11, preset yaw trim 103-12, flight path angle () 103-13, and angle of attack (AOA, ) 103-14. The module 103 also includes roll damping coefficients b.sub.1, pitch damping coefficients b.sub.2, yaw damping coefficients b.sub.3 for every possible flight state. In addition, the module 103 also includes roll restoring coefficients k.sub.1, pitch restoring coefficient k.sub.2, yaw restoring coefficient k.sub.3 for every possible flight state. These coefficients are to be determined by using free decay tests for roll, pitch, and yaw, respectively during flight tests for every possible flight state of an aircraft. In general, aircrafts have static stability in normal flight. By this means the aircraft can be trimmed to be in a stable equilibrium. The free decay tests are to be performed around a trimmed equilibrium condition. The trimmed equilibrium is a condition at which the aircraft continues to fly when the pilot releases the controls. Each flight state in the module 103 is determined first by the flight gross weight, the center of gravity, and the moments of inertia I.sub.x, I.sub.y, I.sub.z which are the moments of inertia of roll, pitch, and yaw about the principal axes of inertia X, Y, Z, respectively. These principal axes of inertia can be approximated by the body axes as shown in FIG. 4. Each flight state is further determined by two conditions to be tested. The first condition is a base case condition which corresponds to a trimmed equilibrium flight condition represented by a preset flight path angle (.sub.0) 103-8 and a pitch trimmed angle of attack (.sub.T) 103-7 in addition to other necessary parameter settings for flight. In this case, the aircraft is in a stable equilibrium and no pilot control is needed. The free decay tests are to be performed by a sharp and recognizable roll, pitch, and yaw input, respectively. The time histories of these aircraft responses from these tests are to be recorded and analyzed to determine the natural oscillation frequencies .sub.10, .sub.20, and .sub.30 for roll, pitch, and yaw motions at that flight state, respectively. From these natural frequencies, the restoring coefficients for roll, pitch, and yaw can be calculated as:

k.sub.1=I.sub.x.sub.10.sup.2, k.sub.2=I.sub.y.sub.20.sup.2, k.sub.3=I.sub.z.sub.30.sup.2. Math. 11

Next for the same preset flight state with the same pitch trimmed AOA, .sub.T and the same preset flight path .sub.0 as above, pilot applies control inputs to modify the flight path angle to a new value and the angle of attack to a new value . In general, is different with .sub.0 and is different with .sub.T. The new and represent a flight state deviating from the preset state. In this condition, free decay tests are to be performed again. The time histories of the aircraft responses to a sharp and recognizable roll, pitch, and yaw inputs are to be recorded and analyzed to determine roll damping coefficient b.sub.1, pitch damping coefficient b.sub.2, and yaw damping coefficient b.sub.3, respectively. In summary, the restoring coefficients k.sub.1, k.sub.2, k.sub.3 are related to 103-1, 103-2, 103-3, 103-4, 103-5, 103-6, 103-7, 103-8, 103-9, 103-10, 103-11, and 103-12 as shown in FIG. 3. The damping coefficients b.sub.1, b.sub.2, b.sub.3 are related to 103-1, 103-2, 103-3, 103-4, 103-5, 103-6, 103-7, 103-8, 103-9, 103-10, 103-11, 103-12, 103-13, and 103-14 as shown in FIG. 3.

[0045] The relation of the preset flight path and the pitch trimmed angle of attack for a pitch up flight mode is illustrated in FIG. 5a with a deviated flight path at a pitch angle of . The current flight path angle and angle of attack which may be deviated from the preset flight state defined by a preset flight path angle .sub.0 and a pitch trimmed angle of attack .sub.T are illustrated in FIG. 5b for a pitch up flight mode. The relation of the preset flight path and the pitch trimmed angle of attack for a pitch down flight mode is illustrated in FIG. 6a with a deviated flight path at a pitch angle of . The current flight path angle and angle of attack which may be deviated from the preset flight state defined by a preset flight path angle .sub.0 and a pitch trimmed angle of attack .sub.T are illustrated in FIG. 6b for a pitch down flight mode.

[0046] The above damping coefficients and restoring coefficients may be provided as a function of flight parameters under a tabulated form, under empirical formulas, or some other appropriate forms which can be stored in a standalone computer or the flight management computer and can be accessed and used by the standalone computer or the flight management computer. If a current flight parameter falls in between two parameters in the pre-determined values, an interpolation may be used.

[0047] By comparing moments of inertia, the module 104 determines the nonlinear unstable axis which has the intermediate moment of inertia. Then the associated frequencies for that unstable axis are calculated using the restoring coefficients and the moments of inertia about the other two axes, respectively. For example, if the pitch moment of inertia is the intermediate then the nonlinear unstable axis is the pitch axis and the associated frequencies for unstable pitch axis are the roll and yaw natural frequencies which are calculated as .sub.10={square root over (k.sub.1/I.sub.x)} and .sub.30={square root over (k.sub.3/I.sub.z)}, respectively. In general, commercial passenger aircrafts have a pitch nonlinear unstable mode, such as Boeing 737, Airbus 300, and etc. For some military transportation aircrafts such as B-52, the nonlinear unstable axis is roll axis because the intermediate moment of inertia of these aircrafts is roll axis instead of pitch axis. In this case, the associated frequencies are pitch and yaw natural frequencies which are calculated as .sub.20={square root over (k.sub.2/I.sub.y)} and .sub.30={square root over (k.sub.3/I.sub.z)}, respectively. It is also possible to design an aircraft which has intermediate moment of inertia about yaw axis. Then for such case the associated frequencies become roll and pitch natural frequencies which are calculated in a similar way as above as shown in FIG. 7.

[0048] The module 105 calculates the first and second inertial coupling frequencies and the corresponding periods. For example, for pitch nonlinear unstable mode, the first inertia coupling frequency and period are calculated as .sub.1st=.sub.10+.sub.30 and T.sub.1st=2/.sub.1st, respectively and the second inertial coupling frequency and period are calculated as .sub.2nd=|.sub.10.sub.3051 and T.sub.2nd=2/.sub.2nd, respectively. For roll and yaw unstable cases, the corresponding frequencies and periods are calculated in a similar way as shown in FIG. 8. The module 105 also displays these results through the flight deck similar to displays of many other parameters by an analog scale and pointer and/or digital representation.

[0049] The module 106 calculates the nonlinear instability threshold as shown in FIG. 9. For example for pitch nonlinear unstable case, the nonlinear instability threshold is calculated as

[00002]$\begin{array}{cc}{A}_T=\max .Math.\left\{\frac{2}{{}_{1.Math..Math.\mathrm{st}}}.Math.\sqrt{\frac{b_1.Math.b_3}{\left(I_z-I_y\right).Math.\left(I_y-I_x\right)}}-{}_m,{}_m\right\},& \mathrm{Math}..Math.12\end{array}$

where .sub.m is a pre-determined small positive number, for example, 0.0175 radian (1) or other small number depending on aircraft size and type. This minimum threshold .sub.m is chosen to prevent the threshold from going to zero. This minimum threshold is a safety margin which needs to be determined during flight tests of every aircraft for light turbulence which is assumed to occur on every flight and causes slight, erratic changes in attitude of roll, pitch, and yaw. For roll and yaw unstable cases, the minimum thresholds may be different from the above case of pitch instability and depending on aircraft size and type, but the fundamental mechanisms are same, i.e. it is needed to account for light turbulence in roll or yaw directions, respectively. The minimum thresholds for roll and yaw are also to be determined during flight tests.

[0050] During a flight, a flight state may deviate from a preset flight state and oscillate around the preset flight state. The motion response amplitude along the nonlinear unstable axis is calculated as shown in FIG. 10. For a potential pitch unstable case A.sub.R=|.sub.0.sub.T| where the definitions of , .sub.0, .sub.T are shown in FIG. 5a and FIG. 5b for pitch up flight mode and in FIG. 6a and FIG. 6b for pitch down flight mode. For a potential roll unstable case A.sub.R=|.sub.0|, where is the current flight roll angle and .sub.0 is a preset roll trim angle if there is any. For a potential yaw unstable case A.sub.R=|.sub.0|, where is the current flight yaw angle and .sub.0 is a preset yaw trim angle if there is any.

[0051] It should be understood that the above descriptions may be implemented to many types of aircrafts, for example, such as a commercial aircraft, a military aircraft, an unmanned aerial vehicle (UAV), or some other appropriate type of aircraft. It should also be understood that the detailed descriptions and specific examples, while indicating the preferred embodiment, are intended for purposes of illustration only and it should be understood that it may be embodied in a large variety of forms different from the one specifically shown and described without departing from the scope and spirit of the invention. It should be also understood that the invention is not limited to the specific features shown, but that the means and construction herein disclosed comprise a preferred form of putting the invention into effect, and the invention therefore claimed in any of its forms of modifications within the legitimate and valid scope of the appended claims.