Patent Publication Number: US-10768201-B2

Title: System for estimating airspeed of an aircraft based on a drag model

Description:
FIELD 
     The disclosed system and method relate to a system for estimating airspeed of an aircraft and, more particularly, to a system that includes a model for estimating airspeed, especially at high speed conditions of the aircraft. 
     BACKGROUND 
     A pitot tube or probe is typically mounted on a vehicle and measures the velocity of a vehicle relative to a fluid in which the vehicle is moving. In one application, a pitot probe is mounted upon an aircraft and measures the velocity of the aircraft relative to the air mass during flight. Pitot probes generally include a hollow tube that defines an open end pointing in the direction of fluid flow or vehicle movement. The hollow tube of the pitot probe contains a fluid, such as air in the case of an aircraft. The pressure within the pitot probe provides a stagnation pressure measurement, which is also called total pressure. The total pressure is combined with a static pressure, which is typically measured at a different location on the aircraft fuselage, or on the side of the pitot probe in the case of a combined pitot-static probe, in order to determine an impact pressure. The impact pressure is used to determine the airspeed of the aircraft. 
     Sometimes pitot probe based airspeed systems may produce incorrect airspeed readings. The incorrect reading may be caused by issues such as probe contamination, damage to the probe, or maintenance issues. Some examples of probe contamination include, but are not limited to, ice, volcanic ash, and insect invasion. Systems that estimate airspeed based on a model of an aircraft currently exist, however these systems may not be able to robustly calculate an accurate airspeed during some types of operating conditions. More specifically, these systems may not be able to calculate accurate airspeeds during high speed flight regimes, especially at transonic Mach numbers. Also, the airspeed calculated by the system may be susceptible to variations of a sensed angle of attack of the aircraft. Finally, the airspeed may also be susceptible to any discrepancies of a lift model, even in regimes where it is possible to calculate accurate airspeeds. 
     SUMMARY 
     The disclosure is directed to an improved system for estimating the airspeed of an aircraft, especially during high speed operating conditions. The aircraft operates at high speed conditions when flaps of the aircraft are retracted and the aircraft travels at about 0.4 Mach or higher. 
     In one example, a system for estimating a plurality of airspeed parameters of an aircraft is disclosed. The system comprises one or more processors and a memory coupled to the processor. The memory storing data comprises a database and program code that, when executed by the one or more processors, causes the system to receive a plurality of operating parameters that each represent an operating condition of the aircraft. The system is further caused to determine a stability-axis drag coefficient based on the plurality of operating parameters. The stability-axis drag coefficient quantifies a stability-axis drag of the aircraft created during high speed conditions. The system is caused to determine a body-axis lift coefficient based on the plurality of operating parameters. The body-axis lift coefficient corresponds to a lift of the aircraft along a vertical body-axis created during low speed conditions. The system is also caused to determine a dynamic pressure based on one of the stability-axis drag coefficient and the body-axis lift coefficient. The system is also caused to estimate the plurality of airspeed parameters based on the dynamic pressure. 
     In another example, a method of estimating a plurality of airspeed parameters of an aircraft is disclosed. The method includes receiving, by a computer, a plurality of operating parameters that each represent an operating condition of the aircraft. The method also includes determining, by the computer, a stability-axis drag coefficient based on the plurality of operating parameters. The stability-axis drag coefficient quantifies a stability-axis drag of the aircraft created during high speed conditions. The method also includes determining a body-axis lift coefficient based on the plurality of operating parameters, the body-axis lift coefficient corresponding to a lift of the aircraft along a vertical body-axis created during low speed conditions. The method includes determining a dynamic pressure based on one of the stability-axis drag coefficient and the body-axis lift coefficient. Finally, the method includes estimating the plurality of airspeed parameters based on the dynamic pressure. 
     Other objects and advantages of the disclosed method and system will be apparent from the following description, the accompanying drawings and the appended claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is an exemplary schematic block diagram of the disclosed airspeed calculation system of an aircraft; 
         FIG. 2  is a perspective view of an exterior of the aircraft shown in  FIG. 1 , where a stability-axis drag based on the aircraft operating at high speed conditions is illustrated; 
         FIG. 3  is an illustration of a computer system used by the airspeed calculation system of  FIG. 1 ; 
         FIG. 4  is an exemplary block diagram of a dynamic pressure module of the airspeed calculation system shown in  FIG. 1 , where the dynamic pressure module includes a drag submodule and a lift submodule; 
         FIG. 5  is an exemplary block diagram of the drag submodule shown in  FIG. 4 , wherein the drag submodule includes a drag model, a thrust model, and a force calculation block; 
         FIG. 6  is a detailed view of the drag model shown in  FIG. 5 ; 
         FIG. 7  is a detailed view of the thrust model illustrated in  FIG. 5 ; 
         FIG. 8  is a perspective view of an exterior of the aircraft shown in  FIG. 1 , where a body-axis lift based on the aircraft operating at low speed conditions is illustrated; 
         FIG. 9  is an exemplary block diagram of the lift submodule shown in  FIG. 4 ; and 
         FIG. 10  is an exemplary block diagram of the logic submodule shown in  FIG. 4 . 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1  is an exemplary schematic block diagram of the disclosed airspeed system  10 . The airspeed system  10  estimates airspeed parameters of an aircraft  18  constantly, without relying upon traditional pitot probe measurements. The airspeed system  10  receives as input a plurality of operating parameters  20 , which are each described in greater detail below. The operating parameters  20  are each representative of a particular operating condition of the aircraft  18 . The airspeed system  10  includes a dynamic pressure module  22  and an airspeed parameter estimation module  24 . The dynamic pressure module  22  receives as input the operating parameters  20 , and estimates a dynamic pressure Qbar value based on the input. The airspeed parameter estimation module  24  receives as input from the dynamic pressure module  22  the dynamic pressure Qbar, and estimates at least one airspeed parameter based on the dynamic pressure Qbar. Specifically, as explained in greater detail below, the airspeed parameters include a Mach number M MDL , an equivalent airspeed Veas MDL , an impact pressure Qc MDL , a calibrated airspeed Vcas MDL , and a true airspeed Vt MDL  of the aircraft  18 . The airspeed parameters are used to constantly calculate the airspeed of the aircraft  18 . 
     The operating parameters  20  that are input into the airspeed system  10  include an angle of attack α, an angle of sideslip β, a plurality of control surface positions, a stabilizer surface position, a flap position, a landing gear position, static pressure ps, engine speed N1, total air temperature T TOT , aircraft weight W, and acceleration or load factor. In one embodiment, a pressure altitude hp may be used instead of the static pressure ps, and an engine pressure ratio EPR may be used instead of the engine speed N1. Control surfaces of the aircraft  18  include, without limitation, ailerons, flaperons, rudders, spoilers, elevators, trim devices, and flaps. The control surface positions represent the position of moveable flight control surfaces of the aircraft  18 . In the embodiments as described the control surface position may refer to the various positions of a plurality spoilers  8  ( FIG. 2 ) and a rudder  6  ( FIG. 2 ) of the aircraft  18 . 
     Referring now to  FIG. 2 , the stabilizer surface position is a measure of an incidence angle of the horizontal stabilizer  14  relative to a body  12  of the aircraft  18 , as seen in a side view. The flap position is indicative of position of a plurality of trailing edge flaps  28  ( FIG. 2 ) of the wings  16 . More specifically, the flap position indicates whether the trailing edge flaps  28  are in a retracted position. In one embodiment, the aircraft  18  includes a three-position landing gear lever, where the three positions are DOWN, UP, and OFF. The landing gear position would be DOWN, UP, or some value in-between if the gears are in transit. The total air temperature T TOT  may also be referred to as the stagnation temperature, and is measured by a total air temperature probe (not illustrated) mounted on the aircraft  18 . 
     The load factor is the ratio of total aerodynamic and propulsive force generated by the aircraft  18  to the total weight of the aircraft  18 . For example, during straight and level flight of the aircraft  18 , the total lift is equal to the total weight. Accordingly, the load factor is one gravity. The acceleration or load factor is determined by one or more accelerometers. However, many types of accelerometers actually measure the load factor. If the accelerometers do truly measure accelerations, then the corresponding load factor is calculated by subtracting the acceleration due to gravity along each axis. 
       FIG. 2  is an illustration of a stability-axis drag model, which is created as the aircraft  18  operates at high speed conditions. The high speed conditions are described in greater detail below. As seen in  FIG. 2 , the parameters X B , Y B , and Z B  represent the x, y, and z body axes of the aircraft  18  respectively, and CG represents the center of gravity for the aircraft  18 . The angle of attack α is measured between a body-axis X B  of the aircraft  18  and a vector X S , which represents a forward stability-axis of the aircraft  18 . The forward stability-axis X S  is a projection of an airspeed direction X W  of the aircraft  18  onto a plane defined by the x and z axes. The angle of sideslip β is measured between the forward stability-axis X S  and the airspeed direction X W  of the aircraft  18 . 
     Turning back to  FIG. 1 , all of the operating parameters  20  may be available as inputs from sensors. However, sometimes the angle of attack α, the angle of sideslip β, and the static pressure ps may be calculated or estimated values instead of sensed values. Specifically, the static pressure ps may be measured by a reliable static source such as a static port or, in another embodiment the static pressure ps is calculated based on the geometric altitude of the aircraft  18 . In one non-limiting embodiment, the geometric altitude may be obtained from a global positioning system (GPS). In one embodiment, the angle of attack α may be derived from inertial measurements of the aircraft  18 . However, in another approach, the angle of attack α may also be provided by angle of attack sensors. The angle of sideslip β may be measured by a sensor, or estimated based on aerodynamic side force model of the aircraft  18 . In another embodiment, the angle of sideslip β is derived from inertial measurements. 
     Continuing to refer to  FIG. 1 , in one embodiment the airspeed system  10  may be used as a primary source to determine the airspeed of the aircraft  18 . In another approach, the airspeed system  10  may be used as an independent source of airspeed, and is used to monitor another source of airspeed such as, for example, a pitot tube. Specifically, the airspeed system  10  may be used to determine the accuracy of a pitot tube (not illustrated). In still another embodiment, the airspeed system  10  may be used as only one of multiple airspeed sources. 
     Referring now to  FIG. 3 , the airspeed system  10  is implemented on one or more computer devices or systems, such as exemplary computer system  30 . The computer system  30  includes a processor  32 , a memory  34 , a mass storage memory device  36 , an input/output (I/O) interface  38 , and a Human Machine Interface (HMI)  40 . The computer system  30  is operatively coupled to one or more external resources  42  via the network  26  or I/O interface  38 . External resources may include, but are not limited to, servers, databases, mass storage devices, peripheral devices, cloud-based network services, or any other suitable computer resource that may be used by the computer system  30 . 
     The processor  32  includes one or more devices selected from microprocessors, micro-controllers, digital signal processors, microcomputers, central processing units, field programmable gate arrays, programmable logic devices, state machines, logic circuits, analog circuits, digital circuits, or any other devices that manipulate signals (analog or digital) based on operational instructions that are stored in the memory  34 . Memory  34  includes a single memory device or a plurality of memory devices including, but not limited to, read-only memory (ROM), random access memory (RAM), volatile memory, non-volatile memory, static random access memory (SRAM), dynamic random access memory (DRAM), flash memory, cache memory, or any other device capable of storing information. The mass storage memory device  36  includes data storage devices such as a hard drive, optical drive, tape drive, volatile or non-volatile solid state device, or any other device capable of storing information. 
     The processor  32  operates under the control of an operating system  46  that resides in memory  34 . The operating system  46  manages computer resources so that computer program code embodied as one or more computer software applications, such as an application  48  residing in memory  34 , may have instructions executed by the processor  32 . In an alternative embodiment, the processor  32  may execute the application  48  directly, in which case the operating system  46  may be omitted. One or more data structures  49  also reside in memory  34 , and may be used by the processor  32 , operating system  46 , or application  48  to store or manipulate data. 
     The I/O interface  38  provides a machine interface that operatively couples the processor  32  to other devices and systems, such as the network  26  or external resource  42 . The application  48  thereby works cooperatively with the network  26  or external resource  42  by communicating via the I/O interface  38  to provide the various features, functions, applications, processes, or modules comprising embodiments of the invention. The application  48  also includes program code that is executed by one or more external resources  42 , or otherwise rely on functions or signals provided by other system or network components external to the computer system  30 . Indeed, given the nearly endless hardware and software configurations possible, persons having ordinary skill in the art will understand that embodiments of the invention may include applications that are located externally to the computer system  30 , distributed among multiple computers or other external resources  42 , or provided by computing resources (hardware and software) that are provided as a service over the network  26 , such as a cloud computing service. 
     The HMI  40  is operatively coupled to the processor  32  of computer system  30  in a known manner to allow a user to interact directly with the computer system  30 . The HMI  40  may include video or alphanumeric displays, a touch screen, a speaker, and any other suitable audio and visual indicators capable of providing data to the user. The HMI  40  also includes input devices and controls such as an alphanumeric keyboard, a pointing device, keypads, pushbuttons, control knobs, microphones, etc., capable of accepting commands or input from the user and transmitting the entered input to the processor  32 . 
     A database  44  may reside on the mass storage memory device  36 , and may be used to collect and organize data used by the various systems and modules described herein. The database  44  may include data and supporting data structures that store and organize the data. In particular, the database  44  may be arranged with any database organization or structure including, but not limited to, a relational database, a hierarchical database, a network database, or combinations thereof. A database management system in the form of a computer software application executing as instructions on the processor  32  may be used to access the information or data stored in records of the database  44  in response to a query, where a query may be dynamically determined and executed by the operating system  46 , other applications  48 , or one or more modules. 
       FIG. 4  is a block diagram illustrating the dynamic pressure module  22  and the airspeed parameter estimation module  24  in  FIG. 1 . The dynamic pressure module  22  includes submodules  50 ,  52 ,  54 . The submodules  50 ,  52 ,  54  are shown as distinct components, which may indicate the use of modular programming techniques. However, the software design may decrease the extent to which the submodules  50 ,  52 ,  54  are distinct by combining at least some program functions of multiple modules into a single module. Moreover, the functions attributed to the submodules  50 ,  52 ,  54  may be distributed in other ways, or on other systems than those depicted. Thus, embodiments of the invention are not limited to the specific arrangement of systems or modules shown in  FIG. 4 . 
     The submodule  50  is a drag submodule  50  that estimates a drag based dynamic pressure Qbar drag , which is based on a drag model of the aircraft  18  ( FIG. 1 ). The drag based dynamic pressure Qbar drag  is used to determine the dynamic pressure Qbar unless the aircraft  18  operates at low speed conditions. The airspeed system  10  determines that the aircraft  18  operates at high speed conditions in response to determining that the flaps  28  of the aircraft  18  ( FIG. 2 ) are retracted, and in response to receiving an estimated Mach number M MDL  having a value greater than about 0.4 from the airspeed parameter estimation module  24 . The airspeed system  10  determines that the aircraft  18  operates at low speed conditions in response to determining that the flaps of the aircraft  18  are not retracted or, alternatively, in response to receiving an estimated Mach number M MDL  having a value equal to or less than about 0.4 from the airspeed parameter estimation module  24 . 
     The submodule  52  is a lift submodule  52  that determines a low speed dynamic pressure Qbar lift  assuming the aircraft  18  operates at low speed conditions. The logic submodule  54  is a speed logic switch. As explained below and seen in  FIG. 10 , the logic submodule  54  receives as input a high speed dynamic pressure Qbar drag  determined by the drag submodule  50  and the dynamic pressure Qbar lift  determined by the lift submodule  52 , and determines an estimated dynamic pressure Qbar based on the operating conditions of the aircraft  18  ( FIG. 1 ). When the airspeed system  10  transitions between the high speed conditions and the low speed conditions, the logic submodule  54  of the airspeed system  10  employs a hysteresis logic and a transition smoothing algorithm  94  to determine the estimated dynamic pressure Qbar. The hysteresis logic and the transition smoothing algorithm  94  are described in greater detail below. 
     The airspeed parameter estimation module  24  receives as input the dynamic pressure Qbar from the dynamic pressure module  22  as well as the static pressure ps or the pressure altitude hp. As explained below, the airspeed parameter estimation module  24  determines the estimated Mach number M MDL , the equivalent airspeed Veas MDL , the impact pressure Qc MDL , the calibrated airspeed Vcas MDL , and the true airspeed of the aircraft Vt MDL  based on the inputs. As seen in  FIG. 4 , the estimated Mach number M MDL  is returned to the submodules  50 ,  52  of the dynamic pressure module  22  as feedback input. 
     Calculation of the dynamic pressure Qbar drag  determined by the drag submodule  50  will now be discussed.  FIG. 2  illustrates a stability-axis drag D of the aircraft  18 , which is created during high speed operating conditions. As seen in  FIG. 2 , the forward stability-axis X S  is directed along the project of the direction of flight of the aircraft  18  onto X B Z B  plane. In other words, the forward stability-axis X S  is not associated with a fixed direction of the aircraft  18 .  FIG. 2  also illustrates the stability-axis drag D in dashed or phantom line, which is directed in a direction that opposes the forward stability-axis X S . 
       FIG. 5  is a more detailed block diagram of the drag submodule  50 . Referring now to both  FIGS. 2 and 5 , the drag submodule  50  includes a non-linear stability-axis drag model  60 , a stability-axis thrust model  62 , and a force calculation block  64  that determines the dynamic pressure Qbar drag .  FIG. 6  is a detailed block diagram of the drag model  60  of the drag submodule  50 . Referring to both  FIGS. 5 and 6 , the drag model  60  receives as input the operating parameters  20 , which each represent an operating condition of the aircraft  18 , and determines a stability-axis drag coefficient C D  based on the operating parameters  20 . More specifically, the drag model  60  receives as input the angle of attack α, the angle of sideslip β, the control surface positions, the stabilizer surface position, the flap position, the landing gear position, and the estimated Mach number M MDL  (from the airspeed parameter estimation module  24  seen in  FIG. 4 ). As explained in greater detail below, the drag model  60  determines the stability-axis drag coefficient C D  based on the inputs and a plurality of components C D1 -C D6 . The stability-axis drag coefficient C D  quantifies the stability-axis drag D of the aircraft  18  illustrated in  FIG. 2 , where a lower stability-axis drag coefficient C D  indicates less drag. 
     The components C D1 -C D6  are tabular functions of the inputs (i.e., the angle of attack α, the angle of sideslip β, the control surface positions, the stabilizer surface position, the flap position, the landing gear position, and the estimated Mach number M MDL ). As seen in  FIG. 6 , the stability-axis drag coefficient C D  is determined by Equation 1 as:
 
 C   D   =C   D1 (α, M   MDL )+ C   D2 (Flap, M   MDL )+ C   D3 (Gear, M   MDL )+ C   D4 (Spoiler,α, M   MDL )+ C   D5 (stabilizer,α, M   MDL )+ C   D6 (rudder,β, M   MDL )  Equation 1
 
where Flap represents the flap position indicative of the position of trailing edge flaps  28  ( FIG. 2 ) of the wings  16 , Gear represents the landing gear position, Spoiler represents the various positions of the spoilers  8  ( FIG. 2 ), Stabilizer represents the stabilizer surface position, and rudder represents the position of the rudder  6  of the aircraft  18  ( FIG. 2 ). The components C D1 -C D6  are each determined based on respective lookup tables saved in memory  34  of the airspeed system  10  ( FIG. 3 ). For example, the component C D1  is determined by taking the specific values of the angle of attack α and the estimated Mach number M MDL , finding these values on one of the lookup tables, and then determining the component C D1  based on the specific values of the angle of attack α and the estimated Mach number M MDL . Moreover, the components C D4 -C D6  are each determined based on a three-dimensional lookup table. In an alternative embodiment, the components C D1 -C D6  are determined based on mathematical functions, such as polynomials.
 
     Continuing to refer to  FIG. 6 , it is to be appreciated that the stability-axis drag coefficient C D  increases in value as the Mach number of the aircraft  18  enters a transonic region (i.e., between 0.8 to 1.0). Accordingly, Equation 1 provides a relatively accurate estimate (i.e., up to about 5%) of the stability-axis drag coefficient C D  even at transonic Mach numbers. Furthermore, the stability-axis drag coefficient C D  is relatively insensitive to the angle of attack α, especially at smaller values. Therefore, the resulting airspeed that is eventually calculated by the airspeed system  10  is not overly sensitive to small errors in measuring or determining the angle of attack. Specifically, assuming error in parameters used in the calculation of drag and thrust, the airspeed may be accurate by about 5%. 
     The value of the stability-axis drag coefficient C D  does not go to zero, or become negligible. Therefore, the model shown in  FIG. 6  may estimate the airspeed accurately, even during conditions where the normal load factor reaches zero g-force. Finally, the stability coefficient C D  of many aircraft current available is not significantly affected by aeroelasticity or by unsteady aerodynamics. Accordingly, Equation 1 does not include factors for these effects. However, in an embodiment additional terms may be introduced to Equation 1 in order to account for aeroelasticity or unsteady aerodynamics, which may improve the accuracy of the stability-axis drag coefficient C D . 
       FIG. 7  is a detailed view of the thrust model  62  illustrated in  FIG. 5 . As seen in  FIG. 7 , the thrust model  62  includes an engine gross thrust model block  70 , an engine ram drag model  72 , and a stability-axis thrust block  74  that determines a forward stability-axis thrust component T XS . The thrust model  62  receives as input the engine speed N1 or engine pressure ratio EPR, the static pressure ps or altitude, the total air temperature T TOT , the Mach estimate M MDL , the angle of attack α, and the angle of sideslip β. Additionally, the thrust model  62  also receives as input a factor of engine incidence angle x FCT , which is with respect to the body-axis X B  ( FIG. 2 ) and a factor of engine incidence angle z FCT , which is with respect to the axis Z B  ( FIG. 2 ). Both the factors of engine incidence angles x FCT , z FCT  are geometric constants, and are fixed values based on the specific installation of a turbojet engine of the aircraft  18  (not illustrated). 
     The gross thrust of the aircraft turbojet engine (not illustrated in the figures) is the thrust produced by the outlet flow of an aircraft turbojet engine. The engine gross thrust model block  70  receives the input and determines two gross thrust components, G XB  and G ZB . The gross thrust component G XB  is the gross thrust with respect to the body-axis X B  ( FIG. 2 ), and the gross thrust component G ZB  is the gross thrust with respect to the axis Z B  ( FIG. 2 ). The gross thrust component G XB  is determined based on Equation 2, and the gross thrust component G ZB  is determined based on Equation 3. Equations 2 and 3 are listed below as:
 
 G   XB   =T 1( N 1 ,ps,M   MDL   ,T   TOT ) x   XFCT   Equation 2
 
 G   ZB   =T 1( N 1 ,ps,M   MDL   ,T   TOT ) z   XFCT   Equation 3
 
where T1 is a tabular function of the engine speed N1, the static pressure ps, the estimated Mach number M MDL , and the total air temperature T TOT .
 
     Continuing to refer to  FIG. 7 , the engine ram drag model  72  determines a ram drag R D . The ram drag represents the drag caused by the momentum of incoming air into the turbojet engine of the aircraft  18  (not illustrated). The ram drag R D  is determined by Equation 4, which is:
 
 R   D   =T 2( N 1 ,ps,M   MDL   ,T   TOT )  Equation 4
 
where T2 is a tabular function of the engine speed N1, the static pressure ps, the estimated Mach number M MDL , and the total air temperature T TOT .
 
     The stability-axis thrust block  74  of the system  10  determines the forward stability-axis thrust component T XS  by subtracting the ram drag from the engine gross thrust. The ram drag is the drag caused by the momentum of incoming air into the turbojet engine of the aircraft  18 , while the engine gross thrust is the total thrust produced by the aircraft turbojet engine. More specifically, the forward stability-axis thrust component T XS  is determined by Equation 5, which is:
 
 T   XS   =G   XB  cos α+ G   ZB  sin α− R   D  cos β  Equation 5
 
     Turning back to  FIG. 5 , the stability-axis drag coefficient C D  and the forward stability-axis thrust component T XS  are both received as input by the force calculation block  64 . The force calculation block  64  also receives as input the aircraft weight W, the acceleration/load factors Nx, Nz, the angle of attack α, and a reference area S ref . The reference area S ref  represents a wing planform area. The force calculation block  64  then determines the dynamic pressure Qbar drag  created as the aircraft  18  operates at high speed conditions. The dynamic pressure Qbar drag  is based on the force along the stability-axis N XS . Equation 6 determines the force along the stability-axis N XS , and Equation 7 determines the dynamic pressure Qbar drag  created at high speed conditions.
 
 N   XS   =N   X  cos α− N   Z  sin α  Equation 6
 
 Q bar drag =( T   XS   −N   XS   W )/( C   D   S   ref )  Equation 7
 
     Calculation of the dynamic pressure Qbar lift  determined by the lift submodule  52  will now be discussed.  FIG. 8  is an illustration of a body-axis lift model as the aircraft  18  operates at low speed conditions. As seen in  FIG. 8 , a body-axis lift L of the aircraft  18  is created in a direction that substantially opposes the axis Z B . The body-axis lift L represents a force that generally opposes the weight of the aircraft  18  during level flight. It should be appreciated that force along the axis Z B  is fixed with respect to the body  12  of the aircraft  18 . Conventionally, the lift vector of an aircraft is expressed along a direction that is perpendicular to the direction of flight. 
       FIG. 9  is an illustration of the lift submodule  52 . Referring now to both  FIGS. 8 and 9 , the lift submodule  52  includes a non-linear body-axis aerodynamic lift module  80 , a body-axis thrust model  82 , and a force calculation block  84 . As explained below, the aerodynamic lift module  80  determines a body-axis lift coefficient C L , which corresponds to a lift L ( FIG. 8 ) along the vertical body-axis Z B  created during low speed operation of the aircraft  18 . 
     Referring now to  FIG. 9 , the non-linear body-axis aerodynamic lift module  80  determines the body-axis lift coefficient C L  based on the angle of attack α, the angle of sideslip β, the control surface positions, the stabilizer surface position, the flap position, the landing gear position, and the estimated Mach number M MDL  (from the airspeed parameter estimation module  24  as seen in  FIG. 4 ). Similar to the stability-axis drag coefficient C D , the body-axis lift coefficient C L  is determined based on a plurality of components C L1 -C L6 . The components C L1 -C L6  are tabular functions of the inputs (the angle of attack α, the angle of sideslip β, the control surface positions, the stabilizer surface position, the flap position, the landing gear position, and the estimated Mach number M MDL ) and the body-axis lift coefficient C L  is determined based on Equation 8 as:
 
 C   L   =C   L1 (α, M   MDL )+ C   L2 (Flap, M   MDL )+ C   L3 (Gear, M   MDL )+ C   L4 (Spoiler,α, M   MDL )+ C   L5 (stabilizer,α, M   MDL )  Equation 8
 
     The body-axis thrust model  82  determines a body-axis propulsive lift, which is referred to as T ZB  based on Equation 9 as:
 
 T   ZB   =G   ZB   −R   D  sin α cos β  Equation 9
 
The body-axis lift coefficient C L  and the body-axis propulsive lift T ZB  are both received as input by the force calculation block  84 . The force calculation block  84  also receives as input the aircraft weight W, the acceleration/load factor Nz, and the reference area S ref . The force calculation block  84  then determines the dynamic pressure Qbar lift  created as the aircraft  18  operates at low speed conditions. The dynamic pressure Qbar lift  is based on the force along the body-axis Z B . Equation 10 determines the dynamic pressure Qbar lift  as:
 
 Q bar lift =( N   Z   W+T   ZB )/( C   L   S   ref )  Equation 10
 
     Turning back to  FIG. 4 , the dynamic pressure Qbar drag  from the drag submodule  50  and the dynamic pressure Qbar lift  from the lift submodule  52  are both received by the logic submodule  54 . As explained below, the logic submodule  54  estimates the dynamic pressure Qbar based on either the dynamic pressure Qbar drag  or the dynamic pressure Qbar lift . In other words, the dynamic pressure Qbar is based on either the stability-axis drag coefficient C D  or the body-axis lift coefficient C L .  FIG. 10  is an illustration of the logic submodule  54 . As seen in  FIG. 10 , the logic submodule  54  includes a selection switch  90 , which is used to select the dynamic pressure Qbar drag  or the dynamic pressure Qbar lift . It is to be appreciated that  FIG. 10  is merely an exemplary embodiment of the logic submodule  54 . Indeed, the logic submodule  54  may be implemented by a variety of approaches for selecting the source of dynamic pressure Qbar. For example, in another embodiment a blending function based on a weighted average of two source values over a specified transition range of the Mach number M MDL  and flap position may be used as well. 
     Continuing to refer to  FIG. 10 , the logic submodule  54  receives as input the dynamic pressure Qbar drag  from the drag submodule  50 , the estimated Mach number M MDL , a signal indicative of the position of trailing edge flaps  28  ( FIG. 2 ) of the wings  16 , and the dynamic pressure Qbar lift . The input is sent to a selection block  92 . The selection block  92  generates a logical signal indicating true in response to the estimated Mach number M MDL  having a value that is greater than about 0.4 and the flaps  28  being in a retracted position. The true signal indicates the aircraft  18  operating at the high speed condition. In response to the logical signal indicating that the aircraft  18  ( FIG. 1 ) is operating at the high speed condition, the switch  90  selects the dynamic pressure Qbar drag  from the drag submodule  50  as the estimated dynamic pressure Qbar. 
     At all other conditions the aircraft  18  is determined to be operating at the low speed condition, and the selection block  92  sets the logical signal to false. More specifically, the selection block  92  generates a logical signal indicating false in response to the estimated Mach number M MDL  having a value less than or equal to about 0.4, or in response to the flaps  28  not being retracted (i.e., deployed). The false signal indicates the aircraft  18  is operating at the low speed condition. In response to the logical signal indicating that the aircraft  18  is operating at the low speed condition, the switch  90  selects the dynamic pressure Qbar lift  from the lift submodule  52  as the estimated dynamic pressure Qbar. 
     The selection block  92  also includes a hysteresis logic. The hysteresis logic may substantially prevent continuous toggling between two sources if the Mach number M MDL  is near the 0.4 threshold. Specifically, in response to the estimated Mach number M MDL  increasing from a value below about 0.4 to a value that is greater than about 0.4 by a margin of about 0.02, and in response to the flaps  28  ( FIG. 2 ) being retracted, the hysteresis logic changes the logical signal created by the selection block  92  from false to true. Accordingly, the hysteresis logic determines that the aircraft  18  is switching from the low speed conditions to the high speed conditions. The hysteresis logic is used to determine that the Mach number changes in value from below about 0.4 to a value that is substantially above 0.4, which in turn substantially prevents continuous toggling. Similarly, in response to estimated Mach number M MDL  subsequently decreasing to value less than or equal to about 0.4 by a margin of about 0.02, the hysteresis logic changes the logical signal created by the selection block  92  from true to false. Accordingly, the hysteresis logic determines that the aircraft  18  is switching from the high speed conditions to the low speed conditions. 
     Continuing to refer to  FIG. 10 , the switch  90  also includes the transition smoothing algorithm  94 . The transition smoothing algorithm  94  provides a smooth transition as the estimated dynamic pressure Qbar switches from one source value to another. Specifically, a value of the estimated dynamic pressure Qbar is switched between the dynamic pressure Qbar drag  and the dynamic pressure Qbar lift  based on the transition smoothing algorithm  94 , where the transition smoothing algorithm  94  gradually changes the value of the estimated dynamic pressure Qbar over a period of time. The period of time to transition between the dynamic pressure values Qbar drag , Qbar lift  is about several seconds. The transition smoothing algorithm  94  may be based on any number of different approaches such as, but not limited to, a transient-free switch. 
     Referring back to  FIG. 4 , the estimated dynamic pressure Qbar is then sent to the airspeed parameter estimation module  24 . The airspeed parameter estimation module  24  then determines the airspeed parameters, which include the estimated Mach number M MDL , the equivalent airspeed Veas MDL , the impact pressure Qc MDL , the calibrated airspeed Vcas MDL , and the true airspeed Vt MDL  of the aircraft  18 . The airspeed parameters are used to constantly calculate the airspeed of the aircraft  18 . The true airspeed Vt MDL  represents the aircraft  18  velocity relative to a free air stream, and the equivalent airspeed Veas MDL  is the true airspeed corrected by the local air density. The calibrated airspeed Vcas MDL  is computed based on impact pressure Qc MDL . The estimated Mach number M MDL  is determined based on Equation 11, the equivalent airspeed Veas MDL  is based on Equation 12, the impact pressure Qc MDL  is based on Equation 13, the calibrated airspeed Vcas MDL  is based on Equation 14, and the true airspeed Vt MDL  is based on Equation 15:
 
 M   MDL =1.195√{square root over ( Q bar/ ps )}  Equation 11
 
 Veas   MDL =√{square root over (295.374  Q bar)}  Equation 12
 
 Qc   MDL =[(1+0.2 M   MDL   2 ) 7/2 −1] ps   Equation 13
 
 Vcas   MDL =661.5√{square root over (5[( Qc   MDL   /p   0 +1) 2/7 −1])}  Equation 14
 
 Vt   MDL =38.97 M   MDL √{square root over ( T   TOT /(1+0.2 M   MDL   2 )}  Equation 15
 
where the equivalent airspeed Veas MDL , the calibrated airspeed Vcas MDL , and the true airspeed Vt MDL  are all measured in knots, the dynamic pressure Qbar, and the impact pressure Qc MDL  are both in pounds per square foot, p 0  represents standard day pressure at sea level, and the total air temperature T TOT  is expressed in Kelvin.
 
     Referring generally to the figures, the disclosed airspeed system provides a reliable approach for estimating the airspeed, without the need to depend upon traditional pitot probe measurements. As explained above, the airspeed system includes a drag model that may be used to estimate various airspeed parameters during high speed regimes of the aircraft. Accordingly, the airspeed system provides a relatively accurate estimate of the airspeed parameters throughout the transonic flight envelope. In contrast, a system based solely on a lift model may not be able to calculate accurate airspeeds during high speed flight regimes, especially at transonic Mach numbers. Additionally, the airspeed calculated by a system based solely on a lift model may be susceptible to variations of a sensed angle of attack of the aircraft at high speeds, or when the aircraft is at a relatively low weight. The disclosed airspeed system also includes decreased sensitivity to variations in the angle of attack when compared to the lift-based systems that are currently available. 
     While the forms of apparatus and methods herein described constitute preferred examples of this invention, it is to be understood that the invention is not limited to these precise forms of apparatus and methods, and the changes may be made therein without departing from the scope of the invention.