Embodiments of this disclosure relate generally to computing information for aircraft, and more specifically to estimating aircraft weight based on aircraft parameters measured during flight.
In an embodiment, a method for aircraft weight estimation is provided. The method includes providing a dynamic pressure signal from a pitot-static subsystem; determining a calibrated angle of attack signal from an angle of attack indicator; determining a lift coefficient signal based on the calibrated angle of attack signal and a Mach number; providing a load factor signal from an accelerometer; and, determining a weight signal based on the dynamic pressure signal, the calibrated angle of attack signal, the lift coefficient signal, the load factor signal, and a wing surface area.
In another embodiment, a method for aircraft weight estimation is provided. The method includes measuring a horizontal control surface position with a sensor; providing a dynamic pressure from a pitot-static subsystem; determining a weight using historical flight data relating the horizontal control surface position to the dynamic pressure based on aircraft weight; and, repeating continuously during flight the steps of measuring the horizontal control surface position, providing the dynamic pressure, and determining the weight to provide a weight signal.
In yet another embodiment, a system for continuously estimating aircraft weight during flight is provided. The system includes a pitot-static subsystem for providing a dynamic pressure signal; an angle of attack indicator for providing a calibrated angle of attack signal; an accelerometer for providing a load factor signal; a controller configured to provide a weight signal based on an initial weight, the dynamic pressure signal, the calibrated angle of attack signal, and the load factor signal; and, a signal filter for filtering the weight signal to determine a stable aircraft weight.
Embodiments of the present disclosure provide methods 100, 200, and 300 of
In step 130, a lift coefficient is determined using Equation 1:
C
L
=C
L
α+CL
In Equation 1, CL is the lift coefficient, α is a calibrated aircraft angle of attack (AOA), CLα is a lift coefficient slope of the aircraft, and CLo is an aircraft lift coefficient for an AOA of zero degrees. The lift coefficient, CL, is a dimensionless coefficient that relates lift generated by a particular aircraft to air density and velocity for a given wing surface area. AOA is the angle between a wing and air flow. The calibrated aircraft AOA, α, includes a calibration factor to account for a difference in airflow angle at the wing compared to airflow angle at a vane used to measure AOA. Using Equation 1, CL, is determined from CLo plus CLα times α, provided in step 135. Generally, a larger a will provide more lift, up to a maximum α when the aircraft begins to stall.
Both CLα and GLo depend from for example airspeed (e.g., Mach number), flap position, and the lifting properties of a particular wing/aircraft and may be determined from lookup tables based on historical flight data (see for example step 230,
In an example of step 130, a first lookup table is used to determine, CLα, based on airspeed and flap position, and a second lookup table is used to determine, CLo, based on airspeed and flap position. In an embodiment, CLα may be constant, depending on the type of flap.
In step 135, the calibrated AOA, α, is provided. In an example of step 135, α is provided by an AOA indicator 535,
In step 175, the Mach number, M, of the aircraft is provided. In an example of step 175, M is provided by air data computer 550,
M=V/a Equation 2
In embodiment, air data computer 550 determines M by measuring dynamic pressure, Q, using one or more pitot tubes 542,
α=√{square root over (γRT)} Equation 3
In Equation 3, α is the speed of sound, γ is a ratio of the specific heat at constant pressure to the specific heat at constant volume (γ=1.4 for air), R is the gas constant, and T is a static air temperature. Substituting Equation 3 into Equation 2 provides Equation 4:
V may be determined from dynamic pressure, Q, and air density, ρ, using Equation 5:
Air density, ρ, may be determined using Equation 6:
In Equation 6, P is pressure, R is the gas constant, and T is static air temperature. P is measured using for example a pitot-static port of pitot tubes 542,
In step 128, dynamic pressure, Q, is measured using one or more pitot tubes. In an example of step 128, Q is measured using pitot tubes 542,
In step 148, the aircraft load factor, NZ, is provided, where NZ is vertical acceleration divided by the gravitational constant. An NZ indicator 548,
In step 149, the wing surface area, S, is provided.
In step 150, aircraft weight is determined using Equation 7.
In Equation 7, cos(α) is the cosine of the calibrated AOA, Q is the dynamic pressure, CL is the lift coefficient, S is the wing surface area, and NZ is the aircraft load factor.
Method 100 may be repeated continuously during flight to account for changing flight conditions that affect inputs of method 100 at varying rates and converge on a stable weight signal that varies with time. In order to smooth the weight signal, one or more signal filters may be employed. For example, during aircraft maneuvers, signals of continuously measured values, such as AOA, may vary rapidly causing transient spikes in estimated weight. By filtering the output weight signal, as in step 155 described below, a stable weight signal is determined and reported in step 160. In and embodiment, input signals of measured values may also be filtered, by time averaging for example, to reduce transient spikes.
In step 155, the weight value determined in step 150 is filtered. In an example of step 155, the weight value is filtered via signal filter 555,
In optional step 160, the weight value is reported. In an example of step 160, aircraft weight may be reported to a user via interface 556. Alternatively, aircraft weight is reported to air data computer 550 for subsequent calculations, such as synthetic airspeed determination.
In step 201, an initial weight is provided. The initial weight may be estimated from a known empty weight of the aircraft plus an estimated weight of cargo, fuel, passengers, etc.
In step 202, a switch determines which weight value to provide. During a first iteration of method 200, step 202 uses the initial weight provided in step 201. During subsequent iterations, step 202 switches to an updated weight from step 250, which is output from controller 220, described below.
In step 248, the aircraft load factor, NZ, is provided, where NZ is vertical acceleration divided by the gravitational constant. Step 248 is an example of step 148
In an optional step 249, NZ is limited between a maximum value and a minimum value. An example maximum NZ value is 1.5 and an example minimum NZ value is 0.9. In an embodiment, NZ limits are coordinated with AOA values due to non-linear effects at high AOA. In another embodiment, the gain provided in integral term 226 is set to zero when NZ is on the minimum or maximum limit.
In step 205, the product of W×NZ is determined, which provides an effective weight that accounts for vertical acceleration and deceleration. The effective weight, W×NZ, is provided to step 222.
In step 222, a difference is calculated between an effective lift, L×cos(α), from step 297 described below, and effective weight, W×NZ, from step 205. If any difference exists between effective lift and effective weight during flight, this difference is accounted for with an error value, ε, as shown in Equation 8.
(L×cos(α))−(W×Nz)=ε Equation 8
In Equation 8, L is the lift force exerted on the aircraft during flight. In controller 220, the error value, ε, is minimized in a first iteration of method 200 by updating weight, W.
In step 250, updated aircraft weight is provided. In an example of step 250, updated aircraft weight is provided for a next iteration of method 200, specifically to determine effective weight, W×NZ, in step 205 via switch 202. Updated weight is optionally reported in step 260, which is an example of step 160,
Controller 220 may include a feedback loop having a weighted sum of a proportional term 224 and an integral term 226, such that proportional term 224 adjusts W in proportion to the magnitude of ε, and integral term 226 adjusts W in proportion to both the magnitude and the duration of ε by integrating over time. The terms are weighted based on gains (e.g., coefficients), which may be tuned to provide a stable W value with a minimal ε. The proportional gain may be used to set a time constant of the feedback loop. In an embodiment, the integral gain provided in integral term 226 is set to zero when NZ, provided in step 249, is on the minimum or maximum limit. Controller 220 may be analog or digital without departing from the scope hereof Controller 520,
In step 290, lift, L, is determined using Equation 9:
L=QCLS Equation 9
In Equation 9, Q is the dynamic pressure provided in step 228, CL is the lift coefficient provided in step 230, and S is the wing surface area provided in step 249, which are described below.
In step 297, the product of L×cos(α) is determined to provide effective lift.
In step 228, dynamic pressure, Q, is measured using one or more pitot tubes. Step 228 is an example of step 128,
In step 230, which is an example of step 130,
In step 235, the calibrated AOA, α, is provided. Step 235 is an example of step 135,
In optional step 232, flap position is provided. Step 232 is an example of step 132,
In step 234, a first lookup table is used to determine, CLα, based on airspeed and optionally flap position. An example of the first lookup table is CLα lookup table 534,
In step 236, a second lookup table is used to determine, CLo, based on airspeed and optionally flap position. An example of the second lookup table is CLo, lookup table 536,
In step 275, Mach number, M, is provided. Step 275 is an example of step 175,
Method 200 may be iteratively repeated to minimize ε by updating W, thereby continuously providing an accurate and stable value for aircraft weight as aircraft and atmosphere parameters change during flight.
In step 310, a horizontal control surface position is provided. In an example of step 310, a control surface sensor 510,
In step 328, dynamic pressure, Q, is provided. Step 328 is an example of step 128,
In optional step 335, the calibrated AOA, α, is provided. Step 335 is an example of steps 135 and 235,
In step 375, Mach number, M, is provided. Step 375 is an example of steps 175 and 275,
In step 350, weight, W, is determined from a trim map of horizontal control surface position versus dynamic pressure, Q. The trim map is a series of curves from historical flight data relating Q with horizontal control surface position, such as a horizontal stabilizer angle for example, as a function of Mach number, M, and optionally the calibrated AOA, α. The trim map may optionally include horizontal control surface position as a function of CG.
In optional step 354, the aircraft center of gravity (CG) is determined using fuel burn curves provided in optional step 360. The fuel burn curves include plots relating weight and CG with decreasing fuel during flight based on historical flight data relating CG with weight for a given configuration (e.g., flap position and amounts of fuel, passengers and cargo onboard). In an embodiment, if a signal providing dynamic pressure, Q is lost due to malfunctioning pitot tubes for example, W may be estimated from the last known W based on the fuel burn curve and a fuel measurement.
Method 300 is repeated continuously during flight to determine weight as flight conditions change, for example as aircraft weight decreases during flight. Method 300 may be used cooperatively with an airspeed estimator, which depends on W. By providing a more accurate W using method 300, a more accurate airspeed estimate, V, may be determined from the airspeed estimator in the absence of a measured airspeed. In an embodiment, real-time CG may be determined from W and horizontal control surface angle and used to modify resistance of pilot controls for example.
The values plotted in trim map 400 may be grouped into two weight and CG conditions that bound potential stabilizer trim angles: 1) a light-aft condition 410, shown with squares, and 2) a heavy-forward condition 420, shown with triangles. For conditions 410, 420, the terms light and heavy refer to aircraft weight, while the terms aft and forward refer to CG position. Thus, light-aft condition 410 shows possible ranges of stabilizer angles for an aircraft flying in a light-weight mode, for example without passengers and cargo and with little fuel remaining. In the light-weight mode, the CG is in an aft position compared to heavier flight conditions. Heavy-forward condition 420 shows possible ranges of stabilizer angles for aircraft flying in a heavy-weight mode with a forward CG position, for example fully fueled with a maximum weight of passengers and cargo. Other dynamic pressures and stabilizer trim angles are of course possible, for example due to different flap positions.
Control surface sensor 510 may include one or more sensors configured to detect a position of a horizontal control surface for transmitting to air data computer 550. Example horizontal control surfaces include a horizontal stabilizer and an elevator. Control surface sensor 510 provides position information in for example step 310,
Controller 520 may be part of software 555 incorporated directly within air data computer 550. Alternatively, controller 520 may include a microcontroller, microprocessor, or programmable logic controller (PLC) in communication with, but separate from, air data computer 550, without departing from the scope hereof. Controller 520 may include a feedback mechanism for providing stable values from iterative numerical calculations, such as proportional-integral controller 220,
Flaps indicators 532 may include sensors located in the flaps of the aircraft wings for providing flap position information. For example, flap position indicators 532 provide flap position information in steps 132 and 232 of
CLα lookup table 534 is used to determine CLα, based on airspeed and flap position and used for example in step 234,
Angle of attack (AOA) indicator 535 is provided to indicate the aircraft's calibrated AOA, α, which is used to determine the lift coefficient, CL, as shown in Equation 1, for example. AOA indicator 535 is for example an AOA vane or a multi-port probe used to provide AOA information in steps 135 and 235,
Pitot tubes 542 may include one or more forward facing pitot tubes and one or more static ports. A forward facing pitot tube is for example a tube with a forward facing port. As the aircraft moves forward, air rams into the port generating pressure in the pitot tube known as pitot pressure. An increase in the aircraft's airspeed causes a corresponding increase in the pitot pressure. The static port measures static pressure, which is dependent on the aircraft's altitude. The static port is located for example on a side of an aircraft's fuselage, facing tangent to the forward direction, and therefore not exposed to pitot pressure. The aircraft's airspeed may be determined by air data computer 550 based on data from forward facing pitot tubes and static ports of pitot tubes 542. Dynamic pressure, Q, is determined in for example steps 128, 228 and 328,
Temperature sensing device 545 may include one or more of a thermometer, a thermocouple and/or a resistance temperature detector for determining temperature.
GPS unit 547 may provide aircraft position information based on the Global Positioning Satellite (GPS) system. GPS unit 547 may include a transceiver configured to determine three-dimensional position by transmitting signals to, and receiving signals from, a network of four or more Earth orbiting satellites. GPS unit 547 may be used to provide altitude information.
Load factor (NZ) indicator 548 may indicate vertical acceleration divided by the gravitational constant. NZ indicator 548 includes one or more accelerometers for example. Steps 148 and 248,
Signal filter 555 provides smooth signals without transient spikes. For example, as method 100 is repeated during flight to account for changing flight conditions, inputs of method 100 may be filtered using signal filter 555. For example, during aircraft maneuvers, signals of continuously measured values, such as AOA, may vary rapidly causing transient spikes in estimated weight. By filtering input signals of measured values, by time averaging for example, transient spikes are reduced. Similarly, the output weight signal is filtered using signal filter 555. Signal filter 555 may include electronic circuit filters and/or digital filters to provide one or more of low-pass filtering, high-pass filtering, band-pass filtering, notch filtering and time averaging without departing from the scope hereof
Many different arrangements of the various components depicted, as well as components not shown, are possible without departing from the spirit and scope of the present invention. Embodiments of the present invention have been described with the intent to be illustrative rather than restrictive. Alternative embodiments will become apparent to those skilled in the art that do not depart from its scope. A skilled artisan may develop alternative means of implementing the aforementioned improvements without departing from the scope of the present invention.
It will be understood that certain features and subcombinations are of utility and may be employed without reference to other features and subcombinations and are contemplated within the scope of the claims. Not all operations listed in the various figures need be carried out in the specific order described.
This application is a continuation-in-part of U.S. application Ser. No. 15/087,026, entitled “Airspeed Determination for Aircraft” and filed Mar. 31, 2016. The aforementioned application is incorporated by reference in its entirety.
Number | Date | Country | |
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Parent | 15087026 | Mar 2016 | US |
Child | 15407903 | US |