Abstract:
Apparatus and an associated method are described for an aircraft for providing an auto-changeover procedure from a calibrated airspeed control parameter to a Mach number control parameter when the aircraft is ascending; and, from a Mach number control parameter to a calibrated airspeed parameter when the aircraft is descending. The auto-changeover procedure is responsive to application of preselected calibrated airspeed and Mach number parameters. The data processing unit of the aircraft provides a continually updated prediction of the target parameter that would result should the aircraft execute the auto-changeover under the currently existing conditions. When the predicted value and the preselected value are equal, the changeover procedure is invoked, reducing the transients resulting from overshoot of the target parameter value. Provision is made for the circumstance wherein the changeover is determined by an altitude rather than a target parameter. Approximation equations for reducing the computational requirements are discussed.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     This invention relates generally to the flight control of an aircraft and, more particularly, to providing a smooth transition of an aircraft between aircraft flight operating in response to the calculated airspeed value and aircraft flight operating in response to the Mach number value. 
     2. Description of the Related Art 
     In the modern aircraft, low altitude control of an aircraft is performed in relationship to the calibrated airspeed (CAS) of the aircraft, while the high altitude control of aircraft is performed in relationship to the Mach number. When climbing to or descending from a high cruising altitude, it is necessary for the control apparatus of the aircraft to make the transition between response to the calibrated airspeed and the Mach number. Generally, a calibrated airspeed parameter or Mach number parameter is preselected by the flight deck of the aircraft, the preselected parameter being the parameter value for the aircraft after the transition. In the alternative, the flight deck of an aircraft can select an altitude (typically 26,000 feet) at which the transition is to take place. 
     However the transition of the control between the calibrated airspeed value and the Mach number value can involve overshoot of the preselected target aircraft speed. The calibrated airspeed and the Mach number are related by the true airspeed (TAS). When the aircraft is changing altitude while holding a selected calibrated air speed, the expression to convert the calibrated airspeed to the true airspeed is given by the expression: 
     
         TAS={7×G×R×T[{(P.sub.o /P)[{1+0.2(CAS/C.sub.o).sup.2 }.sup.3.5 -1]+1}.sup.(2/7) -1]}.sup.1/2                   1. 
    
     where: 
     T=ambient temperature ( o  K) 
     P o  =sea level air pressure (2116.2 lb/ft 2 ) 
     C o  =sea level speed of sound (661.45 knots) 
     R=ideal gas constant (96.03 ft/ o  K) 
     G=sea level acceleration of gravity (32.174 ft/sec 2 ) 
     P=static pressure (lb/ft 2 ) 
     From the foregoing equation, the true air speed increases as temperature increases and decreases as pressure increases. However, the changes in pressure are more important during a change in altitude. The result is a positive acceleration along the flight path during a climb and a negative acceleration during descent in the flight path, i.e., when the specific calibrated airspeed is maintained. 
     The corresponding expression for true airspeed in terms of the Mach number is: 
     
         TAS=(1.4×G×R×T).sup.1/2 (Mach number)    2. 
    
     where G, R, and T have been previously defined. 
     Referring to equation 2, when the Mach number is held constant, the true air speed increases with temperature. Because the temperature decreases with increasing altitude in the troposphere, a negative flight path acceleration results for the true air speed during an increase in altitude and positive flight path acceleration occurs for the true air speed during a negative change in altitude when the Mach number is held constant. (The derivation of the true air speed equations 1 and 2 can be found in Airplane Aerodynamics and Performance, Tau Edward Lan and Jan Roskam, Roskam Aviation, 1980, pages 15-25). 
     Because of the acceleration (positive or negative) of the true airspeed for a change in altitude, when the transition between the constant calibrated airspeed and the constant Mach number occurs, an overshoot in the target control parameter (i.e., the calibrated air speed or the Mach number) is experienced with the corresponding requirement to adjust the control parameter to the selected value. 
     In the prior art, transfer was made to the alternative parameter when the calibrated airspeed or the Mach number reached the preselected value of the alternate parameter. The preselected value of the alternative parameter was subject to overshoot, causing the aircraft to reverse the acceleration after transfer to the alternative parameter. 
     A need has therefore been felt for apparatus and an associated method to provide smooth transition from an aircraft operating in response to a constant calibrated airspeed parameter to a constant Mach number parameter or to provide a smooth transition when the control parameter of the aircraft changes from the calibrated airspeed to the Mach number at a preselected altitude. 
     FEATURES OF THE INVENTION 
     It is an object of the present invention to provide improved control of the flight of an aircraft. 
     It is a feature of the present invention to provide for a smooth transition between the flight of an aircraft controlled by a calibrated airspeed parameter and the flight of an aircraft controlled by Mach number parameter. 
     It is another feature of the present invention to provide improved operation for an aircraft for which the control of an aircraft changes from a calibrated airspeed parameter to a Mach number parameter. 
     It is yet another feature of the present invention to calculate a predicted target parameter value based on the present flight conditions and to change to the target parameter for control of the aircraft when the predicted target parameter value is equal to a preselected value of the target parameter. 
     It is a further feature of the present invention to provide approximation equations to reduce the processing requirements of the aircraft data processing system. 
     SUMMARY OF THE INVENTION 
     The aforementioned and other features are attained, according to the present invention, by providing an algorithm for use by the avionics apparatus and the apparatus controlling the flight of the aircraft that provides for an automatic and smooth transition between an aircraft controlled by a calibrated flight parameter and an aircraft controlled by a Mach number parameter. An algorithm is provided to predict, based on present flight conditions, the value of a target parameter. When the target parameter value is predicted, then the transition to the target parameter is implemented. Otherwise, the transition to the target parameter is executed at a predetermined altitude. The algorithm used to predict the value of the target parameter includes the flight path acceleration. Approximation equations for reducing the computational requirement of the algorithm are described. 
     These and other features of the invention will be understood upon reading of the following description along with the drawings. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a graph of the average temperature and the pressure ratio as a function of altitude. 
     FIG. 2 is a graph of the flight path acceleration for the calibrated airspeed parameter and for the Mach number for a constant vertical air speed. 
     FIG. 3 illustrates the true airspeed of an aircraft from sea level to 36,000 ft. for a given calibrated airspeed and for a given Mach number. 
     FIG. 4 illustrates the transition between the aircraft control parameters according to the prior art and according the present invention. 
     FIG. 5 is a flow diagram of the process for auto-changeover from the calibrated airspeed parameter to the Mach number parameter according to the present invention. 
     FIG. 6 is a flow diagram of the process for auto-changeover from a Mach number control of an aircraft to calibrated airspeed control of the aircraft. 
     FIG. 7 illustrates the auto-changeover from the calibrated airspeed aircraft control to the Mach number aircraft control. 
     FIG. 8 illustrates the flight path acceleration for the auto-changeover from the calibrated airspeed parameter to the Mach number parameter according to the present invention. 
     FIG. 9 illustrates the Mach number to calibrated airspeed auto-changeover according to the present invention. 
     FIG. 10 illustrates the flight path acceleration for the Mach number to calibrated airspeed auto changeover according to the present invention. 
     FIG. 11 illustrates the true airspeed of the aircraft during the auto-changeover from calibrated airspeed parameter control of the aircraft to Mach number parameter control of the aircraft. 
     FIG. 12 illustrates the true airspeed of the aircraft during the auto-changeover from Mach number control of the aircraft to calibrated airspeed control of the aircraft. 
     FIG. 13 is a block diagram of the apparatus used by the aircraft in the executing the auto-changeovers between the calibrated airspeed control parameter and the Mach number control parameter. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     Detailed Description of the Figures 
     Referring now to FIG. 1, the average temperature and pressure ratio are shown as a function of altitude. The temperature and pressure ratio can be calculated as a function of altitude by using the expressions: 
     
         T=T.sub.o [1-6.875×10(.sup.-6)×H]-273.15 (.sup.o C) 3. 
    
     
         PR=(1-6.875×10(.sup.-6)×H).sup.5.2541          4. 
    
     where: 
     T o  =288.15 o  K 
     H=altitude (ft), and 
     PR=P/P o   
     The change in the temperature and pressure is responsible for the flight path acceleration (or deceleration) when the flight of the aircraft is controlled by the calibrated airspeed or the Mach number. The derivation of equations 3 and 4 is given on pages 1-6 of Lan et al, cited above). 
     Referring now to FIG. 2, the flight path acceleration for a calibrated airspeed and for a Mach number with a vertical speed of 1500 ft/sec (a typical rate of vertical change at 30,000 ft) is shown. FIG. 2 is derived by calculating a digital derivative for the true airspeed equations. This acceleration is the origin of the overshoot problem. 
     Referring to FIG. 3, the true airspeed is shown for an aircraft for a calibrated airspeed of 300 knots and for a Mach number of 0.8 from sea level (0 ft) to 36,000 ft. In an actual flight plan according to the present invention, the aircraft would ascend on the calibrated airspeed curve until the intersection value with the Mach number curve is approached. Prior to actually reaching the intersection value, the auto-changeover to the new airspeed parameter is executed. The aircraft thereafter smoothly approaches the Mach number curve, but does not cross the line. On descent, the aircraft follows the Mach number curve until the cross-over value of the Mach number curve and the calibrated airspeed curve is approached. Prior to reaching the cross-over value, the aircraft control is transferred to the calibrated airspeed curve (i.e., the calibrated airspeed equal 300 knots) by means of auto-changeover procedure. The control of the aircraft is transferred to the calibrated airspeed parameter smoothly. (The curves of FIG. 3 are terminated at 36,000 ft because of the transition, at this altitude, to new atmospheric conditions). 
     Referring next to FIG. 4, the aircraft control parameter cross-over region for the calibrated airspeed curves and for the Mach number curves of FIG. 3 is shown with an expanded scale. Included in the FIG. 4 is the result of the auto-changeover between the calibrated airspeed parameter and the Mach number parameter on the true airspeed according to the prior art (undesired path) and according to the present invention (desired path). 
     Referring next to FIG. 5, the auto-changeover process for transferring control of the aircraft from the calibrated airspeed parameter to the Mach number parameter, according to the present invention, is shown. In step 501, a target Mach number is selected, i.e., by the aircraft flight deck, crew which will determine when the changeover is to occur. In step 502, the data processing apparatus, in response to parameters identified by the aircraft sensing apparatus, determines the current Mach number, the true airspeed, the flight path acceleration and the static pressure parameters of the aircraft. Based on the selected Mach number, the true airspeed, and the flight path acceleration, the data processing apparatus of the aircraft calculates a predicted Mach number which is required for a smooth transfer from the calibrated airspeed parameter control of the aircraft to the Mach number parameter control of the aircraft in step 503. In step 504, a determination is made as to whether a selected Mach number has been entered by the flight deck. When the flight deck has entered a selected Mach number, then a comparison is made to determine if the predicted Mach number is equal to, within prescribed tolerances, the present aircraft Mach number in step 505. When the present Mach number and predicted Mach number are not equal with in the prescribed tolerances, then the procedure is returned to step 502. When the present Mach number and the predicted Mach number are equal, then auto-changeover procedure by which the calibrated airspeed is replaced by the preselected Mach number. When a preselected Mach number has not been entered by the flight deck in step 504, then a determination is made as to whether the current altitude of the aircraft is greater than or equal to 26,000 ft. in step 507. When the aircraft is below 26,000 ft in 15 step 507, then the procedure is returned to step 501 where the option to preselect a target Mach number can be implemented. When, in step 507, the altitude is equal to, or above, 26,000 ft, then a determination is made as to whether a target (selected) calibrated airspeed is being maintained by the aircraft within preselected limits in step 508. The calibrated airspeed that has been selected will typically be maintained within specified limits unless, for example, a new calibrated airspeed has been selected for the aircraft and the aircraft is still in the process of adjusting to the newly selected target calibrated airspeed. When the calibrated airspeed is being maintained by the aircraft in step 508, then the predicted Mach number is selected as a new target in step 509. When the calibrated airspeed is not being maintained by the aircraft, then the target calibrated airspeed is converted to the equivalent Mach number. The Mach number from step 506, step 509, or from 510 is used provide the Mach number resulting from the changeover controlling the flight of the aircraft. 
     Referring next to FIG. 6, the procedure for auto-changeover from a Mach number control of an aircraft to calibrated airspeed control of the aircraft is shown. In step 601, the changeover (target) calibrated airspeed is entered in the data processing system by the flight deck. In step 602, the current calibrated airspeed, the true airspeed, the flight path acceleration, and the static pressure are determined. In step 603, the predicted calibrated airspeed is calculated. In step 604, a determination is made whether a preselected calibrated airspeed has been entered in the data processing system. When a preselected calibrated airspeed has been entered in the data processing system, then a determination is made whether the predicted calibrated airspeed is equal to the current airspeed in step 605. When the predicted calibrated airspeed is not equal to the current airspeed, then the procedure is returned to step 602. When the predicted calibrated airspeed is equal to the current airspeed, then in step 606, the preselected calibrated airspeed is the new target calibrated airspeed. When, in step 604, a preselected calibrated airspeed has not been entered in the data processing system, a determination is made whether the aircraft altitude is equal to or below 26,000 ft. When the altitude of the aircraft is not below 26,000 ft, the procedure is returned to step 601 where the option to preselect a target calibrated airspeed can be implemented. When the aircraft altitude is equal or below 26,000 ft, the determination is made whether aircraft is maintaining the selected (target) Mach number in step 608. Typically, the aircraft will maintain within specified limits the selected Mach number in the absence of a change resulting in a transient condition, such as a recent selection of a new selected (target) Mach number. When the selected Mach number is being maintained within specified limits, then the predicted calibrated airspeed value is selected as the target calibrated airspeed value in step 609. When the selected Mach number is not being maintained in step 608, then target calibrated airspeed is the equivalent calibrated airspeed resulting from the current Mach number in step 610. In step 611, transfer of control of the aircraft to the new calibrated airspeed is performed in response to step 606, step 609, or step 610. 
     Referring to FIG. 7, the auto-changeover from the control of an ascending aircraft by the calibrated airspeed parameter to control of the aircraft by the Mach number parameter. The transition point occurs at the time designated by the dotted line. The preselected Mach number is 0.8. Only minor overshoot is experienced in the transition. 
     Referring to FIG. 8, the flight path acceleration for the transition between the calibrated airspeed parameter and the Mach number parameter control of the aircraft according to the present invention, is shown. As in FIG. 7, the auto-changeover occurs at the dotted line. The acceleration changes from positive to negative. 
     Referring now to FIG. 9, the auto-changeover from aircraft Mach number parameter control to the calibrated airspeed parameter control according to the present invention is shown. The preselected calibrated airspeed is 300 knots (506.3 ft/sec). The changeover occurs at the dotted line. The overshoot resulting from the transition is minimal. 
     Referring now to FIG. 10, the flight path acceleration for the auto-changeover from the Mach number parameter control of the aircraft to the calibrated airspeed control of the aircraft according to the present invention is shown. The auto-changeover occurs at dotted line. Note that the flight path acceleration approaches a negative value greater in magnitude than the acceleration prior to changeover. 
     Referring to FIG. 11 and FIG. 12, the true airspeed for the auto-changeover from the calibrated airspeed parameter control of the aircraft to the Mach number control of the aircraft and from the Mach number control of the aircraft to the calibrated airspeed, respectively, according to the present invention is shown. The transitions occur between the 300 knot calibrated air speed and the 0.8 Mach number. 
     Referring to FIG. 13, the apparatus needed to implement the auto-changeover between the calibrated airspeed and the Mach number aircraft control parameters according to the present invention is illustrated. Flight control panel 130 receives operator selected parameters entered through parameter input device 130A. The parameters entered by the parameter input device 130A are applied to central processing unit 130B, the central processing unit 130B forming part of the flight control panel 130. The central processing unit 130B applies the calibrated airspeed target and the Mach number target to the longitudinal control processor 131B forming part of the flight control computer system 131. The longitudinal control processor 131B applies elevator control signals to the aircraft elevators 135 and thrust control signals to the aircraft engines 134 and the longitudinal control processor 131B receives elevator parameter feedback signals from the aircraft elevators 135 and receives engine parameter feedback signals from the aircraft engines 134. The longitudinal control processor 131B also receives signals from the feedback parameter estimation processor 131A, the feedback parameter estimation processor 131A forming part of the feedback control computer system. The feedback parameter estimation processor 131A applies signals (such as Mach number, static pressure, calibrated airspeed, flight path acceleration and true airspeed) to the central processing unit. The feedback parameter estimation processor 131A receives air data and inertial data signals from the inertial reference units and air data computer 133. The inertial reference units and air data computer 133 receive signals from the air and inertial data sensors 132 measuring parameters associated with the aircraft. Examples of air data sensors would be thermometers, pressure gauges, etc. for measuring parameters of the environment of the aircraft, while examples of inertial data sensors include accelerometers, gyroscopes, etc. for measuring parameters associated with the aircraft. 
     Operation of the Preferred Embodiment 
     The invention differs from the prior art in that the approach of a control parameter auto-changeover is predicted for preselected changeover values of the parameter. The prediction is based on the flight path acceleration, true air speed and known aircraft response to control commands. The parameter changeover is affected, based on the predicted parameter values, before the actual parameter changeover value is reached to prevent overshoot of the target control parameter. 
     The algorithm used to predict the changeover point between the calibrated airspeed parameter control and the Mach number control of the aircraft assumes that the change in flight path acceleration (FPACC) of the aircraft is exponential for small errors with a known time constant TAU. Currently, the flight path acceleration response of an aircraft lags a command by approximately 6 seconds. The change in the true airspeed is given by: ##EQU1## where FPACC d  is the difference between the initial flight path acceleration and the final flight path acceleration (the final flight path acceleration required to hold a specific calibrated airspeed or Mach number during a constant vertical speed maneuver, i.e., FPACC d  =FPACC i  -FPACC f ). 
     For the change in the Mach number, the relationship used includes: 
     
         Delta(TAS)/TAS=Delta(Mach)/Mach 
    
     Therefore, the change in the Mach number is: 
     
         Delta(Mach)=(FPACC.sub.d ×TAU)×Mach            6. 
    
     The predicted Mach, the Mach number that will be current after the changeover, is then Mach+Delta(Mach). When the preselected Mach number is within +/-0.0005 Mach (or 0.5 milliMach) of the predicted Mach number, then the auto-changeover takes place. 
     The expression is therefore: 
     
         Predicted Mach=[(FPACC.sub.d ×TAU/TAS)+1]Mach        7. 
    
     The changeover to the calibrated airspeed from the Mach number is determined by the approximation: 
     
         Delta (TAS)/TAS=Delta(CAS)/CAS 
    
     
         Predicted CAS=(FPACC.sub.d ×TAU/TAS+1)×CAS     8. 
    
     The final FPACC f  is approximated, in the preferred embodiment in the following manner. Because FPACC f  is the time derivative of the true airspeed (TAS), equation 1 can be used in the approximation. The intrinsic function performed on the calibrated airspeed (CAS) are a square, a 7/2 power, a 2/7 power, and a square root. To some degree of approximation, the true airspeed and, ultimately, FPACC f  is proportional to the calibrated airspeed (CAS). The true airspeed (TAS) and the final flight plan acceleration (FPACC f ) are approximately proportional to the square root of the pressure ratio. The temperature dependence is ignored, assumed to be accounted for in the vertical speed. Because the flight plan acceleration is a result of holding the calibrated airspeed at a constant vertical speed, VS, FPACC f  is proportional to the vertical speed. Therefore: 
     
         FPACC.sub.f =VS×CAS/[K1×(P/P.sub.o).sup.1/2 ]  11. 
    
     Using a similar procedure wherein the Mach number is held, the true airspeed, TAS, and, ultimately, the flight path acceleration, FPACC f  is proportional to the Mach number and to the vertical speed, VS. 
     Therefore: 
     
         FPACC.sub.f =VS×Mach/K2                              12. 
    
     The constants of proportionality are determined by computation of the complete equations for several conditions and providing the best fit for K1 and K2. Using this procedure, K1 is found to be approximately 70,000, while K2 is found to be approximately -257. When the selection is based on the altitude (e.g., 26,000 ft), then the changeover will occur at 26,000 ft altitude. Upon reaching or crossing the 26,000 ft altitude and when the calibrated airspeed of Mach number target has been captured, the changeover is forced at the current parameter levels. When the calibrated airspeed target or the Mach number target has not been captured and the 26,000 ft level has been crossed, then the target Mach number (TMach) and the target calibrated airspeed (TCAS) are given by the expressions: 
     
         TMach={5[{(P.sub.o /P)[{1+0.2(TCAS/C.sub.o).sup.2 }.sup.3.5 -5}+1}.sup.2/7 -1]}.sup.1/2                                              9. 
    
     
         TCAS=C.sub.o {5[{P/P.sub.o)[{(TMach.sup.2)/5+1}.sup.3.5 -1 +1}.sup.2/7 -1]}.sup.1/2                                              10. 
    
     The approximation equations for the FPACC f  are used to minimize the demands on the aircraft data processing apparatus. It will be clear that the complete equations can be used when sufficient computational capacity is available in the aircraft. 
     The present invention can provide for an auto-changeover at a predetermined altitude. Different auto-changeover modes are provided depending on whether the aircraft is currently maintaining a target aircraft speed parameter or is currently not maintaining a target aircraft speed (for example, when a new target airspeed has been recently entered). 
     In the preferred embodiment, the target airspeed or Mach number is determined in the central processing unit, the central processing unit receiving processed signals from environment and equipment sensors. It will be clear that a different arrangement of processing apparatus can perform the same functions. 
     The foregoing description is included to illustrate the operation of the preferred embodiment and is not meant to limit the scope of the invention. The scope of the invention is to be limited only by the following claims. From the foregoing description, many variations will be apparent to those skilled in the art that would yet be encompassed by the spirit and scope of the invention.