A method for determining constant indicated airspeed and mach number climb performance of a flight management system

Abstract

The application provides a kind of equal speed and Mach number climb performance determination method of flight management system, belong to aircraft management system technical field. Including: based on performance database initialization aerodynamic and engine data;Based on the initial parameters of each item input by aircraft climb state;Based on the corresponding true airspeed of CAS and Mach of climb strategy equal to calculate climb conversion height hpc;By comparing climb conversion height hpc, climb end height hpf and step midpoint height hpsemi to judge subsequent equal CAS climb calculation or equal Mach climb calculation;Calculate the step number n of climb process, the step midpoint height hpsemi of i step;hpsemi is used as input parameter respectively to call corresponding function;Calculate new step hpstepx, and it is used as new step, and corresponding function is called again respectively;Output corresponding step calculation result, and store in output result matrix Outputm.The performance parameter obtained by the application is more accurate.

Description

TECHNICAL FIELD

[0001] The application provides a method for determining the constant indicated airspeed and Mach number climb performance of a flight management system, and belongs to the technical field of aircraft management. BACKGROUND

[0002] The performance management function of a flight management system (FMS) is an indispensable part of an avionics system, which provides important support for the flight efficiency and economy of an aircraft. Constant indicated airspeed / Mach number climb refers to a planned speed combination in which the aircraft climbs at a corrected airspeed at low altitudes and at a Mach number at high altitudes. During the constant indicated airspeed / Mach number climb, the calculation of key performance parameters based on the flight management system is extremely important for the actual flight of the aircraft.

[0003] The en route climb performance calculation requires the calculation of the full-power climb performance of the aircraft under different configurations, weight and center of gravity, buffet margin, thrust state, bleed air state, wind direction and speed, temperature, and the output of relevant physical parameters in the climb.

[0004] The traditional table lookup method based on the onboard performance database mainly processes performance data through reading, indexing, querying, and interpolation. It is only suitable for the processing of light data, has a simple algorithm, and has low precision. For the constant indicated airspeed / Mach number climb task that pursues higher accuracy, we can achieve it by constructing a performance model. The algorithm and formula are used to accurately calculate the performance parameters and fuel consumption during flight. This method not only significantly reduces the required data volume, but also flexibly meets various complex flight profile calculation requirements. SUMMARY

[0005] The technical problem solved by the application is to efficiently and accurately solve the key performance parameters during the constant indicated airspeed / Mach number climb phase of the aircraft to meet the safety, economy, and efficiency needs of flight.

[0006] The application provides a method for determining the constant indicated airspeed and Mach number climb performance of a flight management system, and the performance parameters at least include: step fuel consumption Fuelstep, step time Timestep, step distance Diststep, true airspeed Vt, indicated airspeed Vc, Mach number Mach, climb angle γ, climb rate R / C, %N1, fuel flow FF, total aircraft thrust , lift coefficient , drag coefficient , temperature coefficient ratio θ, and pressure coefficient ratio δ. The algorithm can complete the performance parameter calculation of the entire flight constant indicated airspeed / Mach number climb phase, and has larger data processing capacity, higher precision, and faster efficiency, which improves the economy and safety of flight.

[0007] The technical scheme of the present application:

[0008] A method for determining the constant-airspeed and Mach-number climb performance of a flight management system, comprising the following steps:

[0009] S1, initializing aerodynamic and engine data based on a performance database; the aerodynamic data at least includes: Mach number Mach, lift coefficient and drag coefficient ; the engine data at least includes: %N1, engine thrust FN / δ and fuel flow FF;

[0010] S2, inputting initial parameters based on the climb state of the aircraft, at least including: climb start height hpi, climb end height hpf, height step hpstep, climb start weight Minitial, climb strategy CAS / Mach, ISA deviation deltaISA;

[0011] S3, calculating the climb conversion height hpc based on the corresponding true airspeed of the CAS and Mach of the climb strategy;

[0012] S4, judging whether to make subsequent constant-CAS climb calculation or constant-Mach climb calculation by comparing the climb conversion height hpc, the climb end height hpf and the step midpoint height hpsemi; specifically, if the climb conversion height hpc> the climb end height hpf, it means that only constant-CAS climb is made from the climb initial height hpi to the climb end height hpf; if the climb conversion height hpc< the climb end height hpf and the step midpoint height hpsemi< the climb conversion height hpc, it means that constant-CAS climb is made from the climb initial height hpi to the climb conversion height hpc; if the climb conversion height hpc< the climb end height hpf and the step midpoint height hpsemi> the climb conversion height hpc, it means that constant-Mach climb is made from the climb conversion height hpc to the climb end height hpf;

[0013] S5, calculating the step number n in the climb process and the step midpoint height hpsemi of the i-th step;

[0014] S6, taking hpsemi as an input parameter to call corresponding functions respectively; if it is constant-CAS climb calculation, GetFuelstep_Vc function is called; if it is constant-Mach climb calculation, GetFuelstep_Mach function is called;

[0015] S7, calculate new step hpstepx, and call corresponding function again as new step, call GetFuelstep_Vc function if equal CAS climb calculation, call GetFuelstep_Mach function if equal Mach climb calculation;

[0016] S8, output corresponding step calculation result, and store in output result matrix Outputm.

[0017] Wherein, S6 is specifically:

[0018] S61, if hpc> hpf, calculate step number , the midpoint height of the i-th step step is ; if hpc< hpf and hpsemi< hpc, calculate step number , the midpoint height of the i-th step step is ; if hpc< hpf and hpsemi> hpc, calculate step number , the midpoint height of the i-th step step is .

[0019] Wherein, S7 is specifically:

[0020] Equal CAS climb calculation calls GetFuelstep_Vc function, equal Mach climb calculation calls GetFuelstep_Mach function, the main difference between the two is that the acceleration factor is different.

[0021] S71, input initial parameters: height step hpstep, the midpoint height of the i-th step step hpsemi, temperature deltaISA, etc.

[0022] S72, if hpsemi< 36089, use formula (1) and (2) to calculate temperature coefficient ratio θ and pressure coefficient ratio δ ; if hpsemi> 36089, use formula (3) and (4) to calculate temperature coefficient ratio θ and pressure coefficient ratio δ ;

[0023] (1)

[0024] (2)

[0025] If hpsemi> 36089:

[0026] (3)

[0027] (4)

[0028] wherein is the pressure altitude, is the ISA deviation.

[0029] S73, based on the temperature coefficient ratio θ , the pressure coefficient ratio δ and the climb corrected airspeed V c , the equivalent airspeed V e , the climb true airspeed V t and the Mach number Mach are calculated using equations (5), (6), (7)

[0030] (5)

[0031] (6)

[0032] (7)

[0033] S74, through the engine database, the N1, engine thrust FN / and fuel flow FF are found, and the total aircraft thrust δ is calculated; ;

[0034] S75, the lift coefficient is calculated using equation (8), wherein is the lift, is the wing reference area;

[0035] (8)

[0036] S76, according to the lift coefficient , the Mach number Mach, the aerodynamic database is queried to find the drag coefficient ;

[0037] S77, the acceleration factor is calculated according to equations (9)-(12); the difference between the GetFuelstep_Vc function for the constant CAS climb and the GetFuelstep_Mach function for the constant Mach climb lies in the acceleration factor, wherein is the standard temperature, is the actual temperature;

[0038] (9)

[0039] Constant CAS climb above the troposphere:

[0040] (10)

[0041] wherein, ,

[0042] Mach climb below tropopause:

[0043] (11)

[0044] Mach climb above tropopause:

[0045] (12)

[0046] S78, calculate the climb angle γ according to formula (13), and calculate the climb rate R / C according to formula (14), wherein is the total machine thrust, is the weight;

[0047] (13)

[0048] (14)

[0049] S79, calculate the step time Timestep of each step according to the known climb rate R / C and the height step hpstep; based on the step time Timestep, the distance Diststep and the fuel consumption Fuelstep passed in each step are obtained by multiplying the fuel flow and the ground speed by the step time; and based on the step fuel consumption Fuelstep, the step midpoint weight and the step end weight are calculated;

[0050] S710, calculate the new lift coefficient using the weight corrected by the climb angle;

[0051] S711, repeat the iteration of steps S75-S79 until the step midpoint lift of the i+1 step and the step midpoint lift of the i step differ by less than 0.0001. Finally output the result parameters, including at least: step fuel consumption Fuelstep, step time Timestep, step distance Diststep, true airspeed V t , indicated airspeed V c , Mach number Mach, climb angle γ , climb rate R / C, %N1, fuel flow FF, total machine thrust , lift coefficient , drag coefficient , temperature coefficient ratio θ , and pressure coefficient ratio δ .

[0052] Compared with the prior art, the present application has the following beneficial effects:

[0053] Different from the traditional table lookup method, the performance parameters in the process of the equal CAS / Mach number climb are calculated by using the algorithm and the formula, so that the data capacity can be greatly reduced, and the more flexible flight profile calculation can be coped with. The whole process of the climb is subdivided into several steps according to the height by using the obtained input data, so that the climbing time, distance, fuel consumption, speed, height and other information corresponding to each step are obtained, and finally the data of each step are summarized to obtain the time, distance, fuel consumption and other information corresponding to the whole climbing stage. The performance parameters obtained by the algorithm are more accurate, and are of great significance to the economy and safety of the actual flight. BRIEF DESCRIPTION OF DRAWINGS

[0054] Figure 1 the equal CAS / Mach number climb main function flow chart of the application;

[0055] Figure 2 the equal CAS climb GetFuelstep_Vc function flow chart of the application. DETAILED DESCRIPTION

[0056] The technical solutions of the application will be described in detail below with reference to the drawings. Obviously, the described embodiments are only some of the embodiments of the application, but not all the embodiments.

[0057] Reference Figure 1 the equal CAS / Mach number climb main function flow chart, which is used for the equal CAS / Mach number climb performance algorithm of the flight management system, and the method comprises the following steps of:

[0058] S1. initializing the aerodynamic and engine data based on the performance database; the aerodynamic data at least comprises: Mach number Mach, lift coefficient and drag coefficient ; the engine data at least comprises: %N1, engine thrust FN / δ and fuel flow FF;

[0059] S2. inputting initial parameters based on the aircraft climb state, at least comprising: climb starting height hpi, climb ending height hpf, height step hpstep, climb starting weight Minitial, climb strategy CAS / Mach, ISA deviation deltaISA;

[0060] S3. calculating the climb conversion height hpc based on the equal CAS and Mach corresponding to the true airspeed of the climb strategy;

[0061] S4. Determine whether to calculate the next step as a constant CAS climb or a constant Mach climb by comparing the climb transition height hpc, the climb end height hpf, and the step midpoint height hpsemi;

[0062] S41. If hpc> hpf, it means that only constant CAS climb is needed from the initial climb height hpi to the end climb height hpf.

[0063] S42. If hpc< hpf and hpsemi< hpc, it means that constant CAS climb is needed from the initial climb height hpi to the transition climb height hpc.

[0064] S43. If hpc< hpf and hpsemi> hpc, it means that constant Mach climb is needed from the transition climb height hpc to the end climb height hpf.

[0065] S5. Calculate the step number n and the step midpoint height hpsemi.

[0066] S6. Call the corresponding function with hpsemi as the input parameter. If it is a constant CAS climb, call the GetFuelstep_Vc function; if it is a constant Mach climb, call the GetFuelstep_Mach function.

[0067] S61. If hpc> hpf, calculate the step number , and the step midpoint height .

[0068] S62. If hpc< hpf and hpsemi< hpc, calculate the step number , and the step midpoint height .

[0069] S63. If hpc< hpf and hpsemi> hpc, calculate the step number , and the step midpoint height .

[0070] S7. Calculate the new step height hpstepx, and use it as the new step to call the corresponding function again. Refer to the constant CAS climb GetFuelstep_Vc function flowchart, if it is a constant CAS climb, call the GetFuelstep_Vc function; if it is a constant Mach climb, call the GetFuelstep_Mach function. Figure 2

[0071] ​The CAS climb calculation calls the GetFuelstep_Vc function, and the Mach climb calculation calls the GetFuelstep_Mach function. The main difference between the two is the acceleration factor.

[0072] S71. Input initial parameters: height step hpstep, ith step midpoint height hpsemi, temperature deltaISA, etc.

[0073] S72. If hpsemi < 36089, use Equations (1) and (2) to calculate the temperature coefficient ratio θ and the pressure coefficient ratio δ ; if hpsemi > 36089, use Equations (3) and (4) to calculate the temperature coefficient ratio θ and the pressure coefficient ratio δ .

[0074] If hpsemi < 36089:

[0075] (1)

[0076] (2)

[0077] If hpsemi > 36089:

[0078] (3)

[0079] (4)

[0080] where is the barometric height, is the ISA deviation.

[0081] S73. Based on the temperature coefficient ratio θ , the pressure coefficient ratio δ , and the climb corrected airspeed V c from S72 in S7, use Equations (5), (6), and (7) to calculate the equivalent airspeed V e , the climb true airspeed V t , and the Mach number Mach.

[0082] (5)

[0083] (6)

[0084] (7)

[0085] S74. By checking the engine database, find %N1 and engine thrust FN / δ And fuel flow rate FF, and calculate the total thrust of the engine. ;

[0086] S75. Calculate the lift coefficient using formula (8) ,in For lift, This refers to the wing reference area.

[0087] (8)

[0088] S76. Based on the lift coefficient Use the Mach number (Mach) to find the drag coefficient in an aerodynamic database. ;

[0089] S77. Calculate the acceleration factor according to formulas (9)-(12). The difference between the GetFuelstep_Vc function for CAS climb and the GetFuelstep_Mach function for Mach climb calculation lies in the acceleration factor. Standard temperature This refers to the actual temperature.

[0090] (9)

[0091] CAS rise above the troposphere:

[0092] (10)

[0093] in, ,

[0094] Mach climbs below the troposphere:

[0095] (11)

[0096] Mach climbs above the troposphere:

[0097] (12)

[0098] S78. Calculate the climb angle according to formula (13). γ Formula (14) is used to calculate the climb rate R / C, where For the total thrust of the engine, Weight;

[0099] (13)

[0100] (14)

[0101] S79. Calculate the step time Timestep of each step based on the known climb rate R / C and the height step hpstep; based on the step time Timestep, calculate the distance Diststep and the fuel consumption Fuelstep of each step by multiplying the fuel flow and the ground speed by the step time; and based on the step fuel consumption Fuelstep, calculate the step midpoint weight and the step end weight;

[0102] S710. Calculate the new lift coefficient using the climb angle corrected weight

[0103] S711. Repeat the iteration S75-S79 until the step midpoint lift of the i+1 step and the step midpoint lift of the i step differ less than 0.0001. Finally output the result parameters, including at least: the step fuel consumption Fuelstep, the step time Timestep, the step distance Diststep, the true airspeed V t , the indicated airspeed V c 、 the Mach number Mach, the climb angle γ , the climb rate R / C, the %N1, the fuel flow FF, the total aircraft thrust , the lift coefficient , the drag coefficient , the temperature coefficient ratio θ , and the pressure coefficient ratio δ ;

[0104] S8. Output the corresponding step calculation results and store them in the output result matrix Outputm;

[0105] The above embodiments are only specific implementations of the present application and are not intended to limit the protection scope of the present application. Although the foregoing embodiments further illustrate the purpose, technical process and benefits of the present application, those skilled in the art can still modify, improve and replace, etc. within the spirit and scope of the present application. The above operations should be within the protection scope of the present application.​

Claims

1. A method of determining the constant-airspeed and Mach-number climb performance of a flight management system, characterized by, The method comprises the following steps: S1, initialize aerodynamic data and engine data based on performance database; the aerodynamic data includes: Mach number Mach, lift coefficient and drag coefficient ; the engine data includes: %N1, engine thrust FN / δ and fuel flow FF; S2, input initial parameters based on aircraft climbing state, including: climbing start height hpi, climbing end height hpf, initial height step hpstep, climbing start weight Minitial, climbing strategy CAS / Mach, ISA deviation deltaISA; S3, calculate climbing conversion height hpc based on the corresponding true airspeed of CAS and Mach of climbing strategy; S4, judge whether to make equal CAS climbing calculation or equal Mach climbing calculation by comparing climbing conversion height hpc, climbing end height hpf and step midpoint height hpsemi; specifically, if climbing conversion height hpc≥climbing end height hpf, it is indicated that only equal CAS climbing is made from climbing initial height hpi to climbing end height hpf; if climbing conversion height hpc<climbing end height hpf and the step midpoint height hpsemi≤climbing conversion height hpc, it is indicated that equal CAS climbing is made from climbing initial height hpi to climbing conversion height hpc; if climbing conversion height hpc<climbing end height hpf and the step midpoint height hpsemi>climbing conversion height hpc, it is indicated that equal Mach climbing is made from climbing conversion height hpc to climbing end height hpf; S5, calculate climbing process step number n and the i-th step midpoint height hpsemi; S6, call corresponding functions respectively by taking hpsemi as an input parameter; if it is equal CAS climbing calculation, call GetFuelstep_Vc function; if it is equal Mach climbing calculation, call GetFuelstep_Mach function; S7, calculate new step hpstepx and take it as a new step, and call corresponding functions again respectively; if it is equal CAS climbing calculation, call GetFuelstep_Vc function; if it is equal Mach climbing calculation, call GetFuelstep_Mach function; S8, output corresponding step calculation result and store it in output result matrix Outputm.

2. The method of determining the constant-airspeed and Mach number climb performance of a flight management system according to claim 1, wherein, S6 specifically comprises the following sub-steps: S61, if hpc ≥ hpf, calculate the number of steps , the height at the midpoint of the step length of the i-th step is ; if hpc < hpf and hpsemi ≤ hpc, calculate the number of steps , the height at the midpoint of the step length of the i-th step is ; if hpc < hpf and hpsemi > hpc, calculate the number of steps , the height at the midpoint of the step length of the i-th step is .

3. The method of determining the constant-airspeed and Mach number climb performance of a flight management system according to claim 1, wherein, In S7, equal CAS climbing calculation calls GetFuelstep_Vc function and equal Mach climbing calculation calls GetFuelstep_Mach function, and the difference between them lies in different acceleration factors; Specifically, the following sub-steps are included: S71, input initial parameters: height step hpstep, i-th step midpoint height hpsemi and temperature deltaISA; S72, if hpsemi < 36089 use equations (1) and (2) to calculate temperature coefficient ratio θ and pressure coefficient ratio δ ; If hpsemi > 36089, the temperature coefficient ratio is calculated using equations (3) and (4) θ and the pressure coefficient ratio δ ; If hpsemi≤36089: （1） （2） If hpsemi>36089: （3） （4） wherein is the barometric height, is the ISA deviation; S73, the temperature coefficient ratio based on the temperature coefficient ratio obtained in S72 θ , the pressure coefficient ratio δ , and the climb corrected airspeed , the equivalent airspeed is calculated using equations (5), (6), (7) , the climb true airspeed , and the Mach number Mach; （5） （6） （7） S74, by the engine database, find Nl, engine thrust FN δ and fuel flow FF, and calculate the total aircraft thrust ; S75, calculate the lift coefficient using equation (8) where is the lift, is the wing reference area; （8） S76, look up lift coefficient , Mach number Mach, look up drag coefficient ; S77, calculate the acceleration factor according to formulas (9)-(12) The difference between the GetFuelstep_Vc function for constant speed climb and the GetFuelstep_Mach function for constant Mach climb is the acceleration factor, where is the standard temperature, is the actual temperature; （9） Equal CAS climbing above the troposphere: （10） wherein , Equal Mach climbing below the troposphere: （11） Equal Mach climbing above the troposphere: （12） S78, calculate the climb angle γ according to formula (13) and the climb rate R / C according to formula (14), where is the total machine thrust, is the weight; （13） （14） S79, calculate the step time Timestep for each sub-step according to the known climb rate R / C and the height step hpstep; based on the step time Timestep, obtain the distance Diststep and the fuel consumption Fuelstep for each step by multiplying the fuel flow and the ground speed by the step time; and further based on the step fuel consumption Fuelstep, calculate the step intermediate weight and the step end weight; S710, using the climb angle corrected weight calculate a new lift coefficient; S711, repeat iteration S75-S79 step, until the step midpoint lift of the i+1 step and the step midpoint lift of the i step difference is less than 0.0001; the final output results parameters, including: step fuel consumption Fuelstep, step time Timestep, step distance Diststep, true airspeed V t , true airspeed V c , Mach number Mach, climb angle γ , climb rate R / C, %N1, fuel flow FF, total aircraft thrust , lift coefficient , drag coefficient , temperature coefficient ratio θ and pressure coefficient ratio δ .

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