Climb Performance Prediction Method for Flight Management System Based on the First Law

Abstract

The present invention discloses a climb performance prediction algorithm for a flight management system based on the first law, which calculates the true airspeed, equivalent airspeed, Mach number, total temperature, and total temperature ratio at the half climb altitude integration step of the aircraft; calculates the engine thrust, fuel flow rate, drag, and angle of attack required for the aircraft to climb to the N1 altitude; calculates the flight time, distance, and fuel consumption required for the aircraft to climb a single climb altitude integration step; calculates the next climb altitude integration step according to the altitude at the end point of the previous climb altitude integration and the target altitude. If the next climb altitude integration step is equal to zero, the climb performance prediction is terminated, and the flight time, distance, and fuel consumption of each climb altitude integration step are accumulated to obtain the flight time, fuel consumption, and distance required for the aircraft to climb to the given altitude. The present invention has the advantages of high prediction accuracy, good real-time performance, and a simple required performance database, and is applicable to the performance prediction function of a new generation of flight management systems.

Description

Technical Field

[0001] The present invention belongs to the technical field of flight management, and relates to a method for predicting the climb performance of a flight management system based on the first law, which has the advantages of high prediction accuracy and real-time performance, and can meet the performance prediction requirements of the flight management system. Background Art

[0002] Currently, most of the performance calculation modules installed in the active models are implemented by the interpolation calculation method based on the performance data table. The implementation method is as follows: 1) The performance data table calculated by the host computer is pre-stored in the performance database of the flight management system; 2) During flight, the flight management system searches and interpolates in the target data table based on the real-time flight state parameters to obtain the result, which may be the required performance data or support subsequent performance calculations.

[0003] The advantage of the performance calculation by the interpolation method is that the algorithm is relatively simple and the development efficiency is high. In addition, when the amount of data in the basic performance table is low, it has higher storage efficiency and calculation efficiency; the disadvantage is that when the amount of data in the basic table is very large, the storage efficiency and calculation efficiency are poor, which occurs in high-precision performance calculations or calculation tasks with more input parameters. The huge amount of data will also cause the efficiency of searching and interpolation to decrease exponentially, resulting in the loss of real-time performance of the calculation.

[0004] Since the International Civil Aviation Organization approved the FANS (Future Air Navigation System) system plan in 1992, the FANS system has developed rapidly and has now entered the implementation stage in developed countries. In order to conform to this development trend, after the mid-1990s, countries such as the United States and Europe have accelerated the pace of developing and equipping flight management systems for the CNS / ATM operating environment. The future air traffic operation mode based on four-dimensional flight tracks requires higher-precision flight track prediction. The basis of the prediction is high-precision performance calculation, and more parameters related to the aircraft itself and flight state need to be considered. In this regard, the existing interpolation-based performance calculation methods are difficult to balance high precision and high efficiency. In addition, the change of the state quantity during actual flight may exceed the upper and lower bounds of the parameter values in the data table. At this time, the performance calculation based on the interpolation method takes the boundary values in the table, which has an error from the actual value and further increases the calculation error. According to the analysis of relevant literature, during the takeoff and landing phases, the error caused by using the interpolation method for performance calculation will pose certain potential safety hazards.

[0005] The performance calculation technology based on the first law has an approximately constant calculation efficiency and theoretically the highest calculation accuracy, and has good research value and application prospects in airborne real-time performance calculation. The airborne real-time performance calculation based on the first law is the forefront direction and development trend in the field of flight management system research and development.

[0006] Currently, civil aircraft design manufacturers such as Boeing and Airbus adopt a performance calculation method based on the first law in the takeoff and landing performance calculation software provided for their customers. For example, Boeing's Onboard Performance Tool software and Airbus's OCTOPUS (Operational and Certified Takeoff and Landing Performance Software) software provide functions such as takeoff weight optimization, takeoff speed calculation, and takeoff thrust setting. In Airbus's OCTOPUS software, options for algorithms based on the first law and algorithms based on polynomial fitting are provided, and it is recommended in its documentation to use the calculation based on the first law to achieve weight optimization and give better takeoff weight suggestions with more accurate calculations.

[0007] Currently, the performance management function of domestic flight management system products is imperfect and the calculation accuracy needs to be improved. Summary of the Invention

[0008] To solve the problem of low prediction accuracy and real-time performance of the performance calculation method based on traditional interpolation in the flight management system, the object of the present invention is to provide a climb performance prediction method for a flight management system based on the first law. The present invention has the advantages of high prediction accuracy, good real-time performance, and a simple required performance database, and is applicable to the performance prediction function of a new generation of flight management systems.

[0009] The object of the present invention is achieved through the following technical solutions:

[0010] A climb performance prediction method for a flight management system based on the first law is as follows:

[0011] Step 1: Calculate the atmospheric state data related to the flight speed at the half climb height integration step of the aircraft, including the true airspeed V true , equivalent airspeed V e , Mach number M, total temperature T total , total temperature ratio θ total ;

[0012] Step 2: Look up the table according to the atmospheric state data obtained in Step 1 to obtain the engine thrust F N required for the aircraft to climb to N1 height and the fuel flow rate Q fuel ;

[0013] Step 3: Calculate the drag and angle of attack of the aircraft when climbing to N1 height:

[0014] Step 4: Calculate the flight time, distance, and fuel consumption required for the aircraft to climb a single climb height integration step according to the data in Steps 1 to 3;

[0015] Step 5: Determine whether to iterate the current climb height integration step length. If not satisfied, return to Step 3;

[0016] Step 6: According to the height h last at the end point of the previous climb height integration and the target height h end , calculate the next climb height integration step length Δh. If the next climb height integration step length Δh is greater than zero, return to execute Step 1; if the next climb height integration step length Δh is equal to zero, end the climb performance prediction, and accumulate the flight time, distance, and fuel consumption of each climb height integration step length to obtain the time, fuel consumption, and distance required for the aircraft to climb to the given height.

[0017] Preferably, Step 1 includes the following steps:

[0018] Step 11: According to the pressure altitude h p at half of the climb height integration step length and the static temperature T, calculate the temperature coefficient ratio θ and the pressure coefficient ratio δ:

[0019]

[0020] δ = [(288.15 - 0.001981×h p ) / 288.15] 5.25588 (2)

[0021] where T ISA is the static temperature corresponding to the pressure altitude h p under standard atmospheric conditions;

[0022] Step 12: According to the calibrated airspeed V c , the temperature coefficient ratio θ, and the pressure coefficient ratio δ, calculate the true airspeed V true corresponding to the calibrated airspeed, the equivalent airspeed V e corresponding to the calibrated airspeed, and the Mach number M corresponding to the calibrated airspeed:

[0023]

[0024]

[0025] Step 13: According to the static temperature T and the Mach number M, calculate the total temperature T total , the total temperature ratio θ total :

[0026] TAT = OAT * (1 + 0.2M 2 ) (6)

[0027] θ total = θ * (1 + 0.2M 2 ) (7).

[0028] Preferably, step two includes the following steps:

[0029] Step 21: According to the barometric altitude h p , total temperature T total , Mach number M and bleed air state B at the one-half climb height integral step, look up the engine climb N1 limit performance data table to obtain the engine limit value N1 at the climb N1 altitude;

[0030] Step 22: According to the barometric altitude h p , total temperature ratio θ total , the limit value N1 at climb N1 and Mach number M, look up the engine thrust performance data table to obtain the engine thrust F N ;

[0031] Step 23: According to the barometric altitude h p , static temperature T, bleed air state B, Mach number M and engine thrust F N , query the engine fuel flow performance data table to calculate the fuel flow Q fuel .

[0032] Preferably, step three includes the following steps:

[0033] Step 31: According to the climb path angle γ, aircraft angle of attack α and engine thrust F N , calculate the aircraft lift L at the one-half climb height integral step based on the motion equation during the climb process.

[0034] L = -F N sinα + Wgcosγ (9)

[0035] Where W is the total aircraft weight at the one-half climb height integral step;

[0036] The motion equation during the climb process is:

[0037]

[0038] Step 32: According to the aircraft lift L, wing area S and equivalent airspeed V e , calculate the lift coefficient C L as follows:

[0039]

[0040] Step 33: According to the flap landing gear configuration, aircraft center of gravity G, Mach number M and lift coefficient C L , obtain the drag coefficient C based on the lift-drag curve D ;

[0041] Step 34: Based on the flap landing gear configuration, Mach number M, aircraft center of gravity G, and lift coefficient C L , obtain the new angle of attack α from the angle of attack - lift coefficient performance data table.

[0042] Preferably, step four includes the following steps:

[0043] Step 41: Calculate the acceleration factor a based on the barometric altitude h p , static temperature T, and Mach number M at the half - climb - height integration step as follows: factor as follows:

[0044]

[0045] Step 42: Calculate the new climb path angle γ based on the engine thrust F N , total aircraft weight W, drag coefficient C D , equivalent airspeed V e , wing area S, and acceleration factor a as follows: factor as follows:

[0046]

[0047] Step 43: Calculate the climb rate V based on the true airspeed V true and the climb path angle γ as follows: RC as follows:

[0048] V RC = 101.268×V true sinγ (14);

[0049] Step 44: Calculate the required climb time Δt for the height integration step based on the given climb - height integration step Δh and climb rate V RC as follows:

[0050]

[0051] Step 45: Calculate the required climb distance Δd and climb fuel consumption ΔQ for one height integration step based on the true airspeed V true , climb path angle γ, wind speed V wind , fuel flow rate Q fuel and the climb time Δt for one height integration step as follows:

[0052] Δd=(V true +V wind )×Δt (16)

[0053] ΔQ = Q fuel ×Δt (17)

[0054] Preferably, Step Five includes the following steps:

[0055] Step 51: Update the total aircraft weight at the one-half climb height integration step.

[0056] Step 52: Determine whether the total aircraft weight at the one-half climb height integration step converges. If it does, execute Step Six; if not, return to execute Step Three.

[0057] The beneficial effects of the present invention are as follows:

[0058] The advantages of the climb performance prediction method for the flight management system based on the first law provided by the present invention are as follows:

[0059] ① The method proposed by the present invention calculates flight performance parameters in real time according to the current flight state, original model parameters, and dynamic equations. Compared with the interpolation method based on the performance database, it does not rely on historical experience data and can fully consider various parameters related to performance calculation, taking them as the inputs for calculation. Therefore, under the premise of accurate original model parameters, a high prediction accuracy can be achieved.

[0060] ② Since the method proposed by the present invention does not rely on data tables, it is not restricted by the upper and lower bounds of the table data either, and can ensure the accuracy of calculation under various flight conditions.

[0061] ③ The method proposed by the present invention has an approximately constant calculation efficiency and has good real-time performance in on-board real-time climb performance prediction. Description of the Drawings

[0062] Figure 1 A climb performance prediction method for a flight management system based on the first law as shown in the embodiments Detailed Embodiment

[0063] The present invention will be further described in detail below with reference to the drawings and embodiments. This embodiment is described by taking the climb from 1500 feet to 10000 feet and an initial climb height integration step of 5000 feet as an example.

[0064] Refer to Figure 1 As shown, a climb performance prediction method for a flight management system based on the first law as shown in this embodiment is as follows:

[0065] Step One: Calculate the atmospheric state data related to the flight speed at the one-half climb height integration step of the aircraft, including the true airspeed V true , equivalent airspeed V e , Mach number M, total temperature T total , total temperature ratio θ total , etc. The calculation process is as follows:

[0066] Step 11: Based on the initial climbing pressure altitude of 1500 feet and the climbing altitude integration step of 5000 feet, the pressure altitude at half of the climbing altitude integration step is 4000 feet. According to the pressure altitude of 4000 feet and the static temperature T at 4000 feet, calculate the temperature coefficient ratio θ and the pressure coefficient ratio δ.

[0067]

[0068] δ = [(288.15 - 0.001981×h p ) / 288.15] 5.25588 (2)

[0069] where T ISA is the static temperature corresponding to the pressure altitude h p under standard atmospheric conditions.

[0070] Step 12: According to the calibrated airspeed V c , the temperature coefficient ratio θ and the pressure coefficient ratio δ, calculate the true airspeed V true corresponding to the calibrated airspeed, the equivalent airspeed V e corresponding to the calibrated airspeed, and the Mach number M corresponding to the calibrated airspeed.

[0071]

[0072] Step 13: According to the static temperature T and the Mach number M at 4000 feet, calculate the total air temperature T total , the total air temperature ratio θ total and the total pressure ratio δ total .

[0073] TAT = OAT * (1 + 0.2M 2 ) (6)

[0074] θ total = θ * (1 + 0.2M 2 ) (7)

[0075] δ total = δ * (1 + 0.2M 2 ) 3.5 (8)

[0076] Step 2: Look up the table based on the atmospheric state data obtained in Step 1 to obtain the engine thrust F N required for the aircraft to climb to N1 altitude and the fuel flow rate Q fuel , and the process is as follows:

[0077] Step 21: According to the pressure altitude h p at half of the climbing altitude integration step, the total air temperature T total, Mach number M and bleed air state B, referring to the engine climb N1 limit performance data table, the engine limit value N1 at the climb N1 altitude can be obtained.

[0078] Step 22: According to the barometric altitude h at the half climb altitude integration step p , total temperature ratio θ total , the limit value N1 at climb N1 and Mach number M, referring to the engine thrust performance data table, the engine thrust F can be obtained. N .

[0079] Step 23: According to the barometric altitude h at the half climb altitude integration step p , static temperature T, bleed air state B, Mach number M and engine thrust F N , query the engine fuel flow performance data table to calculate the fuel flow Q fuel .

[0080] Step Three: Calculate the drag and angle of attack of the aircraft at the climb N1 altitude, the process is as follows:

[0081] Step 31: According to the climb path angle γ, aircraft angle of attack α and engine thrust F N , based on the motion equation during the climb process, the aircraft lift L at the half climb altitude integration step can be obtained.

[0082] L = -F N sinα + Wgcosγ (9)

[0083] Among them, W is the total weight of the aircraft at the half climb altitude integration step.

[0084] The motion equation during the climb process is:

[0085]

[0086] Including the thrust component in the calculation of lift can make the calculation more in line with the actual operating conditions and improve the calculation accuracy.

[0087] Step 32: According to the aircraft lift L, wing area S and equivalent airspeed V e , calculate the lift coefficient C L as follows:

[0088]

[0089] Step 33: According to the flap retraction / extension configuration, aircraft center of gravity G, Mach number M and the calculated lift coefficient C L , based on the lift-drag curve, the drag coefficient C can be obtained D .

[0090] Step 34: Based on the flap landing gear configuration, Mach number M, aircraft center of gravity G, and lift coefficient C L , a new angle of attack α can be obtained from the angle of attack - lift coefficient performance data table.

[0091] Step 4: Calculate the flight time, distance, and fuel consumption required for a single climb height integration step of the aircraft climb, the process is as follows:

[0092] Step 41: Based on the barometric altitude h p , static temperature T, and Mach number M at half of the climb height integration step, the acceleration factor a can be calculated as follows: factor As follows:

[0093]

[0094] When considering the speed change in the integration segment, it is calculated and considered through the acceleration factor, which can correct the influence of the speed change in the climb segment on the calculation accuracy, thereby improving the calculation accuracy.

[0095] Step 42: Based on the engine thrust F N , the total aircraft weight W, drag coefficient C D , equivalent airspeed V e , wing area S, and acceleration factor a at half of the climb height integration step, the new climb path angle γ can be calculated as follows: factor As follows:

[0096]

[0097] Step 43: Based on the true airspeed V true and the climb path angle γ, the climb rate V RC can be calculated as follows:

[0098] V RC = 101.268 × V true sinγ (14)

[0099] Step 44: Based on the given climb height integration step Δh 5000 feet and the climb rate V RC , the climb time Δt required for one height integration step can be calculated as follows:

[0100]

[0101] Step 45: Based on the true airspeed V true , climb path angle γ, wind speed V wind , fuel flow rate Q fuel , and the climb time Δt for one height integration step, the climb distance Δd and climb fuel consumption ΔQ required for one height integration step can be calculated respectively as follows:

[0102] Δd = (V true + V wind ) × Δt (16)

[0103] ΔQ = Q fuel × Δt (17)

[0104] When considering the influence of wind on distance, calculating the ground distance of the climbing flight based on the ground speed can avoid artificially introducing calculation errors.

[0105] Step Five: Determine whether to iterate the integration step of the current climbing altitude. If not satisfied, return to Step Three. The process is as follows:

[0106] Step 51: Update the total weight of the aircraft at half of the climbing altitude integration step.

[0107] Based on the total weight W0 of the aircraft at the start of the climbing altitude integration and the climbing fuel consumption ΔQ required for one climbing altitude integration step, the new total weight W of the aircraft at half of the climbing altitude integration step can be calculated as follows:

[0108]

[0109] Step 52: Determine whether the total weight of the aircraft at half of the climbing altitude integration step converges. Compare whether the difference between the updated total weight of the aircraft at half of the climbing altitude integration step and the original total weight of the aircraft at half of the climbing altitude integration step is less than 1 pound. If satisfied, execute Step Six; if not satisfied, return to execute Step Three.

[0110] Step Six: Calculate the next climbing altitude integration step Δh based on the height h last at the end point of the previous climbing altitude integration and the target height h end . For example, if the height at the end point of the previous climbing altitude integration is 6500 feet and the target height is 10000 feet, the next climbing altitude integration step is calculated as Δh = 3500 feet. If the next climbing altitude integration step Δh is greater than zero, return to execute Step One; if the next climbing altitude integration step Δh is equal to zero, end the climbing performance prediction, and the time, fuel consumption, and distance required for climbing between 1500 feet and 10000 feet are as follows:

[0111]

[0112] where N is the number of integrations from the starting height to the target height.

[0113] In summary, the present invention proposes a climb performance prediction method based on the first law. Starting from the established physical laws, using the aircraft original model parameter performance database and several given aircraft state variables, other aircraft state variables are solved, and then a climb performance prediction result with high accuracy and real-time performance is obtained. Calculating the average performance based on the half-height position of the integral segment can ensure the calculation accuracy while simplifying the calculation steps, thereby improving the calculation efficiency.

[0114] It can be understood that for those of ordinary skill in the art, equivalent substitutions or changes can be made according to the technical solution and inventive concept of the present invention, and all such changes or substitutions should fall within the protection scope of the appended claims of the present invention.

Claims

1. A method for predicting the climb performance of a flight management system based on the first law, characterized in that The process is as follows: Step 1: Calculate the atmospheric state data related to the flight speed at the half climb altitude integration step of the aircraft, including the true airspeed V true , equivalent airspeed V e , Mach number M, total temperature T total , total temperature ratio θ total ; Step 2: Look up a table based on the atmospheric state data obtained in Step 1 to obtain the engine thrust F required when the aircraft climbs to the N1 altitude N and the fuel flow rate Q fuel ; Step 3: Calculate the drag and angle of attack when the aircraft climbs to the N1 altitude: Step 4: Calculate the flight time, distance, and fuel consumption required for the aircraft to climb a single climb altitude integration step based on the data in Steps 1 to 3. The steps are as follows: Step 41: Calculate the acceleration factor a based on the barometric altitude h, static temperature T, and Mach number M at the one-half climb altitude integration step length p , as follows: factor as follows: Among them, T ISA is the static temperature corresponding to the barometric altitude h p under standard atmospheric conditions; Step 42: According to the engine thrust F N , the total aircraft weight W at half of the climb height integration step, the drag coefficient C D , the equivalent airspeed V e , the wing area S, and the acceleration factor a factor , calculate the new climb path angle γ as follows: Step 43: Calculate the climb rate V true according to the true airspeed V RC and the climb path angle γ as follows: V RC = 101.268 × V true sinγ (14); Step 44: According to the given climb height integration step size Δh and climb rate V RC , calculate the required climb time Δt for the height integration step size as follows: Step 45: According to the true airspeed V true , climb path angle γ, wind speed V wind , fuel flow rate Q fuel and a climb time Δt for a height integration step, calculate the climb distance Δd and climb fuel consumption ΔQ required for a height integration step as follows: Δd = (V true + V wind ) × Δt (16) ΔQ = Q fuel ×Δt (17) Step 5: Determine whether to iterate for the current climb altitude integration step. If not satisfied, return to Step 3; Step 6. According to the height h at the end point of the integration of the previous climbing height last and the target height h end , calculate the integration step size Δh of the next climbing height. If the integration step size Δh of the next climbing height is greater than zero, return to execute Step 1; if the integration step size Δh of the next climbing height is equal to zero, end the climbing performance prediction, and accumulate the flight time, distance, and fuel consumption of each climbing height integration step size to obtain the time, fuel consumption, and distance required for the aircraft to climb to the given height.

2. A method for predicting the climb performance of a flight management system based on the first law according to claim 1, characterized in that Step 1 includes the following steps: Step 11. Calculate the temperature coefficient ratio θ and the pressure coefficient ratio δ according to the barometric altitude h at the half-climb altitude integration step length p and the static temperature T: δ=[(288.15 - 0.001981×h p ) / 288.15] 5.25588 (2) Step 12: Calculate the true airspeed V c corresponding to the calibrated airspeed based on the calibration airspeed V true , the equivalent airspeed V e corresponding to the calibrated airspeed, and the Mach number M corresponding to the calibrated airspeed: Step 13: Calculate the total temperature T and the total temperature ratio θ according to the static temperature T and the Mach number M total and the total temperature ratio θ total : TAT = OAT * (1 + 0.2M 2 ) (6) θ total = θ * (1 + 0.2M 2 ) (7).

3. A method for predicting the climb performance of a flight management system based on the first law according to claim 1, characterized in that Step 2 includes the following steps: Step 21: According to the barometric altitude h at the half climb altitude integration step length p , total temperature T total , Mach number M and bleed air state B, look up the engine climb N1 limit performance data table to obtain the engine limit value N1 at the climb N1 altitude; Step 22: Based on the barometric altitude h at the half-climb altitude integration step length p , the total temperature ratio θ total , the limit value N1 and Mach number M during the climb of N1, and look up the engine thrust performance data table to obtain the engine thrust F N ; Step 23: Based on the barometric altitude h at the half-climb altitude integration step length p , static temperature T, bleed air state B, Mach number M, and engine thrust F N , query the engine fuel flow performance data table to calculate the fuel flow Q fuel .

4. A climb performance prediction method for a flight management system based on the first law according to claim 1, characterized in that Step 3 includes the following steps: Step 31: Based on the climb path angle γ, the aircraft angle of attack α, and the engine thrust F N , calculate the aircraft lift L at the half-climb height integration step based on the motion equation during the climb process: L = -F N sinα + Wgcosγ (9) Where W is the total weight of the aircraft at half of the climb altitude integration step; The motion equation during the climb is: Step 32: Calculate the lift coefficient C according to the aircraft lift L, wing area S, and equivalent airspeed V e , as follows: L as follows: Step 33: According to the flap landing gear configuration, the aircraft center of gravity G, the Mach number M, and the lift coefficient C L , obtain the drag coefficient C based on the lift-drag curve D ; Step 34: Based on the flap landing gear configuration, Mach number M, aircraft center of gravity G, and lift coefficient C L , obtain a new angle of attack α from the angle of attack - lift coefficient performance data table.

5. A method for predicting the climb performance of a flight management system based on the first law according to claim 1, characterized in that Step 5 includes the following steps: Step 51: Update the total weight of the aircraft at half of the climb altitude integration step; Step 52: Determine whether the total weight of the aircraft at half of the climb altitude integration step converges. If satisfied, execute Step 6; if not satisfied, return to execute Step 3.

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