A real-time calculation method for transport aircraft climb performance data

Abstract

The present application provides a method for real-time calculation of climb performance data of transport aircraft, including: obtaining input data, the input data including basic aircraft layout parameters, aircraft longitudinal aerodynamic characteristics data and engine power data; determining the climb speed range of the transport aircraft and the corresponding aerodynamic characteristics data according to the input data, fitting the aircraft longitudinal aerodynamic characteristics data required for climb performance into a linear function or polynomial form, fitting the engine power data into a polynomial form, and forming a smooth curve; approximating the lift curve model and climb rate model of the aircraft climbing state, and calculating the climb rate, rapid ascent speed and the corresponding climb rate and ceiling. The method of the present application can calculate the relevant parameters of the climb performance in real time, without the need to establish a climb performance database with huge data, reducing the workload of aircraft designers and improving work efficiency.

Description

Technical Field

[0001] The present application belongs to the technical field of aircraft performance design, and in particular relates to a real-time calculation method for climb performance data of transport aircraft. Background Art

[0002] In the flight management system, it is necessary to display the climbing performance data of the aircraft in the current configuration, temperature, and weight state in real time, such as the rapid ascent speed, steep ascent speed, ceiling, etc. At the same time, under given climbing conditions, the climbing time, distance, and fuel consumption of climbing to the target altitude are estimated based on the climb rate. In the aircraft's mission planning system, it is also necessary to predict the aircraft's climbing performance. At present, in these airborne or ground support systems, the prediction of climbing performance data is based on the overall parameters, aerodynamic characteristics, and power characteristics of the aircraft, and the climbing performance data under various conditions are pre-calculated to establish the aircraft's climbing performance database within the flight envelope. In the airborne or ground support system, the climb performance data is obtained by interpolating the pre-stored climb performance data. However, this method requires aircraft designers to perform a large amount of performance calculations so that the climb performance data chart can cover the range of the aircraft's use envelope. This is very computationally intensive for designers, especially when the aircraft's aerodynamic or power data changes and the aircraft's performance data needs to be updated, it takes a lot of time to recalculate and update the database.

[0003] With the rapid improvement of the computing power of flight management computers and related support equipment, it has become possible to calculate the climb performance data in real time. Therefore, it is necessary to provide a method for real-time calculation based on the aerodynamic characteristics and power data of the aircraft. This method needs to have fast calculation speed and good convergence, and can reduce the workload of designers while ensuring the correctness of the calculation results. Summary of the invention

[0004] The purpose of the present application is to provide a real-time calculation method for climb performance data of a transport aircraft to solve or alleviate at least one problem in the background technology.

[0005] The technical solution of the present application is: a real-time calculation method for climb performance data of a transport aircraft, the method comprising:

[0006] Acquiring input data, wherein the input data includes basic aircraft layout parameters, aircraft longitudinal aerodynamic characteristics data, and engine power data;

[0007] Determine the climbing speed range of the transport aircraft and the corresponding aerodynamic characteristic data according to the input data, fit the longitudinal aerodynamic characteristic data of the aircraft required for climbing performance into a linear function or a polynomial form, fit the engine power data into a polynomial form, and form a smoothing curve;

[0008] The lift curve model and climb rate model of the aircraft climbing state are approximated, and the climb rate, rapid ascent speed and the corresponding climb rate and ceiling are calculated.

[0009] Furthermore, the process of fitting the aircraft longitudinal aerodynamic characteristic data required for the climb performance into a linear function or a polynomial form includes:

[0010] Step 1: First, express the lift curve of the aircraft cruise configuration as a linear function of the angle of attack. The calculation model is as follows:

[0011] CL=f(Ma,ɑ)=K Ma ×ɑ+B Ma

[0012] Among them, K Ma is the slope of the lift curve corresponding to the Mach number Ma, B Ma is the intercept of the lift curve corresponding to the Mach number Ma, ɑ is the angle of attack, and CL is the lift coefficient.

[0013] Step 2: Express the drag coefficient CD as a quadratic function of the lift coefficient CL. The calculation model is as follows:

[0014] CD=f(Ma,CL)=+K1 Ma CL 2 +K2 Ma CL+CD0 Ma

[0015] Among them, CD0 Ma K1 is the drag coefficient when the lift coefficient CL is zero at the corresponding Mach number Ma, Ma , K2 Ma , CD0 Ma is a constant value;

[0016] Step 3, interpolating the known lift coefficient curve to obtain the lift coefficient curve corresponding to any Mach number;

[0017] Similarly, the known drag coefficient curve is interpolated to obtain the drag coefficient curve corresponding to any Mach number;

[0018] At any climbing flight Mach number Ma x ,(Ma n-1 <Ma x ≤Ma n ) is the lift coefficient CL Ma_x It is approximately expressed as:

[0019] CL Ma_x =K Ma_x ×ɑ+B Ma_x

[0020] K Ma_x=K Ma_n-1 +(Ma x -Ma n-1 ) / (Ma n -Ma n-1 )×(K Ma_n -K Ma_n-1 )

[0021] B Ma_x =B Ma_n-1 +(Ma x -Ma n-1 ) / (Ma n -Ma n-1 )×(B Ma_n -B Ma_n-1 )

[0022] At a certain flight speed Ma x ,(Ma n-1 <Ma x ≤Ma n ) is expressed as:

[0023] CD=f(Ma x , CL)=+K1 x CL 2 +K2 x CL+CD0 x

[0024] K1 x =K1 Ma_n-1 +(Ma x -Ma n-1 ) / (Ma n -Ma n-1 )×(K1 Ma_n -K1 Ma_n-1 )

[0025] K2 x =K2 Ma_n-1 +(Ma x -Ma n-1 ) / (Ma n -Ma n-1 )×(K2 Ma_n -K2 Ma_n-1 )

[0026] CD0 x =CD0 Ma_n-1 +(Ma x -Ma n-1 ) / (Ma n -Ma n-1 )×(CD0 Ma_n -CD0 Ma_n-1 ).

[0027] Furthermore, the process of fitting the engine thrust data into a polynomial form includes:

[0028] Step 1: Fit the thrust of the aircraft in the climbing state at different temperatures into a speed polynomial. The calculation model is as follows:

[0029] P T1 =f(h,Ma)=A3 T1 ×V 3 +A2 T1 ×V 2 +A1 T1 ×V+A0 T1

[0030] …

[0031] P Tn =f(h,Ma)=A3 Tn ×V 3 +A2 Tn ×V 2 +A1 Tn ×V+A0 Tn

[0032] Among them, P represents thrust, T1-~Tn represent different temperatures, h is height, A3, A2, A1, A0 are coefficients, A3 Tn 、A2 Tn 、A2 Tn 、A1 Tn is a linear function of height h:

[0033] A3 Tn =KA3 Tn ×h+BA3 Tn

[0034] A2 Tn =KA2 Tn ×h+BA2 Tn

[0035] A1 Tn =KA1 Tn ×h+BA1 Tn

[0036] A0 Tn =KA0 Tn ×h+BA0 Tn

[0037] Among them, KA3 Tn KA2 Tn KA1 Tn KA0 Tn BA3 Tn BA2 Tn BA1 TnBA0 Tn is a constant;

[0038] Step 2: interpolate the thrust curves of the climbing state at different altitudes and temperatures to obtain the climbing thrust curve at any altitude hx and temperature Tx. The interpolation process is as follows:

[0039] When it is necessary to obtain the climbing thrust at a certain flight speed V, at an altitude hx, and at a temperature Tx (Ti-1≤Tx≤Ti), the calculation model is as follows:

[0040] P(Tx, hx, V) = P Ti-1 +(T x -T i-1 ) / (Ti-Ti-1)×(P Ti -P Ti-1 )

[0041] P(Tx, hx, V) = A3 Tx ×Ma 3 +A2 Tx ×Ma 2 +A1 Tx ×Ma+A0 Tx

[0042] Among them: A3 Tx =[KA3 Ti-1 +(Tx-T i-1 ) / (Ti-Ti-1)×(KA3 Ti -KA3 Ti-1 )]×h+BA3 Ti-1 +(Tx-T i-1 ) / (Ti-Ti-1)×(BA3 Ti -BA3 Ti-1 )

[0043] Similarly, we get A2 Tx 、A1 Tx 、A0 Tx expression.

[0044] Furthermore, it is characterized in that the process of calculating the climb rate includes:

[0045] The longitudinal force balance equation of the aircraft during climbing is:

[0046]

[0047] When the aircraft is climbing, the flight path angle is very small, cosθ≈1, then the expression of the lift coefficient CL is as follows:

[0048]

[0049] Among them, L is lift, W is gravity, θ is the aircraft's flight path angle, P is the engine thrust, and ɑ is the fuselage angle of attack. is the engine installation angle (known quantity), S is the wing reference area;

[0050] The angle of attack ɑ can be obtained from the above formula;

[0051] The expressions for climb rate ROC and climb gradient sinθ are as follows:

[0052]

[0053] sinθ=ROC / V

[0054] Where D is the resistance: D = 1 / 2ρV 2 S×CD.

[0055] Furthermore, the process of calculating the rapid rise speed includes:

[0056] Step 1: The climb rate of an aircraft at altitude H, weight m (gravity W), and climb speed V is expressed as:

[0057] dH / dt=Vsinγ=(Pav-D)V / W

[0058] Where H is the height, t is the time, is the available thrust. Under normal circumstances, the installation angle of the engine is generally zero or very small. For transport aircraft, the angle of attack of the aircraft is small within the climbing speed range. When solving the speed corresponding to the maximum climb rate, let Pav≈P, P is the engine thrust, and D is the drag;

[0059] Step 2: At the position corresponding to the maximum climb rate, the derivative of the climb rate with respect to the speed is equal to zero, and the following expression is given:

[0060]

[0061]

[0062] Step 3: From step 2, according to the calculation model of engine thrust P and drag D, we have:

[0063] 1 / W×(4×A3 Tx ×V 3 +3×A2 Tx ×V 2 +2×A1 Tx ×V+A0 Tx +4×K2×W / (ρSV 3 )-2×K1×W-ρS×CD0×V)=0

[0064] Step 4: According to the chord intercept method, at altitude H, the climb speed is calculated within the range of the aircraft's minimum operating speed V a ~Maximum operating speed V MO / Maximum operating Mach number M MO , solve the maximum climb rate ROCmax and the corresponding climb speed Vx within this speed range, the process includes:

[0065] 1) Under a given altitude H, temperature T, and flight weight W, let V1 = Va, V2 = Vmax according to the aircraft's speed range and its minimum operating speed Va and maximum operating speed VMO;

[0066] 2) Solve for the speeds V1 and V2 calculate

[0067] 3) Judgment Then the speed corresponding to the maximum climb rate at the height H is Vx=V1, calculate the climb rate ROCmax at the speed V1, and output the calculation result;

[0068] 4) If The chord intercept method is used to iteratively calculate the speed point Vx corresponding to the maximum climb rate. The steps are as follows:

[0069] 5) Order Calculate the Vx like (ε is a very small value), then Vx at this time is the speed value corresponding to the maximum climb rate under given conditions, calculate the climb rate ROCmax at this time, and output the calculation result; otherwise, continue the calculation according to the following steps:

[0070] 6) If calculate like Then let V1 = Vx, otherwise let V2 = Vx, and return to execute steps 2) to 5) until The maximum climb rate ROCmax and the corresponding climb speed Vx under given flight conditions can be obtained.

[0071] Furthermore, the process of calculating the ceiling includes:

[0072] Step 1: Input flight conditions: flight weight W, temperature t, and maximum operating altitude Hmax of the aircraft;

[0073] Step 2: Let the ceiling Hcrmax be equal to the maximum flight altitude: Hcrmax = Hmax. Calculate the maximum rate of climb ROCmax_Hmax at altitude Hmax according to the maximum rate of climb at the given altitude, temperature, and weight. Compare the relationship between ROCmax_Hmax and the required rate of climb ROC0 for the aircraft ceiling. If ROCmax_Hmax ≥ ROC0, then take the aircraft ceiling as the maximum operating altitude, i.e., Hcrmax = Hmax, and the calculation ends.

[0074] Step 3: If ROCmax_Hmax < ROC0, calculate the ceiling according to the following steps:

[0075] Step 4: Let H1 = 0 and H2 = Hmax. Obtain ROCmax_H1 and ROCmax_H2 according to the calculation function of the maximum rate of climb. Let Hcrmax = H1 + (ROC0 - ROCmax_H1) / (ROCmax_H2 - ROCmax_H1) × (H2 - H1), and calculate the maximum rate of climb ROCmax_Hcrmax at altitude Hcrmax.

[0076] Step 5: Compare the ROCmax_Hcrmax obtained in Step 4 with the required rate of climb ROC0 for the ceiling. If |ROCmax_Hcrmax - ROC0| < ε, where ε is a threshold, then Hcrmax is the ceiling of the aircraft under the given conditions. Output the ceiling value Hcrmax and the speed Vmax corresponding to the maximum rate of climb, and the calculation result; otherwise, continue the calculation according to the following steps:

[0077] Step 6: If |ROCmax_Hcrmax - ROC0| ≥ ε in Step 5, then if ROCmax_H1 ≥ 0 and ROCmax_Hcrmax ≥ ROC0, let H1 = Hcrmax (obtained in Step 4); if ROCmax_H1 ≥ 0 and ROCmax_Hcrmax < ROC0, let H1 = Hcrmax.

[0078] Return to perform the operations in Step 4 and Step 5 until |ROCmax_Hcrmax - ROC0| < ε.

[0079] Step 7: If |ROCmax_Hcrmax - ROC0| ≥ ε in Step 5, and if ROCmax_H1 < 0, then let H2 = H1 + (ROC0 - ROC1) / × (ROC2 - ROC1) × (H2 - H1), and return to repeat the operations in Step 4 and Step 5 until |ROCmax_Hcrmax - ROC0| < ε.

[0080] The method of the present application can calculate the relevant parameters of the climb performance in real time in the flight management system or ground mission planning system of the transport aircraft, without the need to establish a huge climb performance database, which reduces the workload of aircraft designers. In particular, when the climb performance of the aircraft changes due to some reason and the climb performance data of the aircraft needs to be updated, the repetitive work of the aircraft designers can be greatly reduced, and the work efficiency can be improved. In the present application, the flight speed range characteristics of the transport aircraft during the climb are fully considered, and the lift curve is processed into the form of a linear function, and the polar curve is processed into the form of a binomial; the engine thrust data is fitted into a polynomial to keep the input original data smooth, ensure the smoothness of the calculation process and the convergence of the calculation results; the present application fully considers the flight characteristics of the transport aircraft during the climb phase, and reasonably approximates the real-time calculation model of the climb parameters to meet the calculation efficiency requirements of the real-time calculation, while ensuring that the calculation results meet the engineering accuracy requirements; the method of the present application can be implemented in the programming of the real-time calculation of the climb performance data of the transport aircraft. When the parameters are iteratively solved, reasonable initial values ​​are given to the parameters, which effectively reduces the number of iterations and improves the convergence speed and calculation efficiency of the real-time calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] In order to more clearly illustrate the technical solution provided by the present application, the following is a brief introduction to the accompanying drawings. Obviously, the accompanying drawings described below are only some embodiments of the present application.

[0082] Figure 1 This is a flow chart of the real-time calculation method of climb performance data for transport aircraft in this application.

[0083] Figure 2 A schematic diagram of a lift curve for a transport aircraft according to an embodiment of the present application.

[0084] Figure 3 A schematic diagram of a polar curve of a transport aircraft according to an embodiment of the present application.

[0085] Figure 4 A schematic diagram of the climbing thrust of a transport aircraft according to an embodiment of the present application. DETAILED DESCRIPTION

[0086] In order to make the purpose, technical solutions and advantages of the implementation of this application clearer, the technical solutions in the embodiments of this application will be described in more detail below in conjunction with the drawings in the embodiments of this application.

[0087] In order to solve the above problems, the present application proposes a real-time calculation method for the climb performance data of transport aircraft, which includes a processing method for the original data of the calculation input - aerodynamic characteristic data and power characteristic data, and a real-time calculation model and computer implementation method for basic climb performance parameters: climb rate, rapid ascent speed, and ceiling.

[0088] The real-time calculation method for realizing the rapid ascent speed, maximum climb rate, and cruising ceiling (maximum climb rate is 1.5m / s) of a transport aircraft at various altitudes under the conditions of flight weight m (gravity W) and temperature Tx in the ground mission planning system is as follows:

[0089] 1. Obtain input data, wherein the input data includes basic aircraft layout parameters, aircraft longitudinal aerodynamic characteristics data and engine power data.

[0090] 2. Determine the climbing speed range of the transport aircraft and the corresponding aerodynamic characteristic data based on the input data, fit the aircraft longitudinal aerodynamic characteristic data required for climbing performance into a linear function or polynomial form, and fit the engine power data into a polynomial form.

[0091] 2.1. Pre-processing of aerodynamic data required for climb performance calculation

[0092] 2.1.1. First, according to the characteristics of the speed range of transport aircraft during climb, its minimum route climb speed must have a certain margin with the stall speed (relevant specifications, such as CCAR25: route climb speed is not less than 1.18Vs). At this time, the lift coefficient range corresponding to the climb speed is shown in Figure 2 The solid line part of the lift curve shows a linear relationship between the lift coefficient and the angle of attack within the lift coefficient range. Therefore, the lift coefficient curve of the aircraft cruise configuration is processed and expressed as a linear function or polynomial form of the angle of attack and stored in the aerodynamic database. The lift coefficient curves at different Mach numbers are expressed as follows:

[0093] CL=f(Ma,ɑ)=K Ma ×ɑ+B Ma

[0094] In the formula, K Ma is the slope of the lift curve corresponding to the Mach number Ma, B Ma is the intercept of the lift curve corresponding to the Mach number Ma;

[0095] K can be obtained at each Mach number Ma Ma and B Ma The value of .

[0096] 2.1.2, according to the aircraft climbing speed range, the extreme curve range used is as follows: Figure 3 In the solid line part, the drag coefficient CD can be approximately expressed as a quadratic function of the lift coefficient CL within the range of this extreme curve. Therefore, the extreme curve model of the aircraft during climbing is expressed as a quadratic function of the drag coefficient CD to the lift coefficient CL as follows:

[0097] CD=f(Ma,CL)=+K1Ma CL 2 +K2 Ma CL+CD0 Ma

[0098] Among them, CD0 Ma is the drag coefficient when the lift coefficient CL is zero at the corresponding Mach number Ma;

[0099] K1 can be obtained at each Mach number Ma Ma , K2 Ma and CD0 Ma The value of .

[0100] 2.1.3, During flight x ,(Ma n-1 <Ma x ≤Ma n ) when the lift coefficient CL Ma_x , can be calculated by the following formula:

[0101] CL Ma_x =K Ma_x ×ɑ+B Ma_x

[0102] Among them, K Ma_x =K Ma_n-1 +(Ma x -Ma n-1 ) / (Ma n -Ma n-1 )×(K Ma_n -K Ma_n-1 )

[0103] B Ma_x =B Ma_n-1 +(Ma x -Ma n-1 ) / (Ma n -Ma n-1 )×(B Ma_n -B Ma_n-1 )

[0104] At a certain flight speed Ma x ,(Ma n-1 <Ma x ≤Ma n The drag coefficient under the condition of ) can be calculated by the following formula:

[0105] CD=f(Ma x , CL)=+K1 x CL 2 +K2 x CL+CD0 x

[0106] Among them, K1x =K1 Ma_n-1 +(Ma x -Ma n-1 ) / (Ma n -Ma n-1 )×(K1 Ma_n -K1 Ma_n-1 )K2 x =K2 Ma_n-1 +(Ma x -Ma n-1 ) / (Ma n -Ma n-1 )×(K2 Ma_n -K2 Ma_n-1 )

[0107] CD0 x =CD0 Ma_n-1 +(Ma x -Ma n-1 ) / (Ma n -Ma n-1 )×(CD0 Ma_n -CD0 Ma_n-1 )

[0108] 2.2. According to the thrust curve of the transport aircraft engine in climbing state, see Figure 4 As shown in the figure, the power data required for climbing performance data calculation is processed, including the following contents:

[0109] Step 1: Fit the thrust of the aircraft in the climbing state at different temperatures into a speed polynomial. The calculation model is as follows:

[0110] P T0 =f(h,Ma)=A3 T0 ×V 3 +A2 T0 ×V 2 +A1 T0 ×V+A0 T0

[0111] …

[0112] P Tn =f(h,Ma)=A3 Tn ×V 3 +A2 Tn ×V 2 +A1 Tn ×V+A0 Tn

[0113] In the formula, A3Tn 、A2 Tn 、A2 Tn 、A1 Tnis a linear function of height h:

[0114] A3 Tn = KA3Tn ×h+BA3 Tn

[0115] A2 Tn =KA2 Tn ×h+BA2 Tn

[0116] A1 Tn =KA1 Tn ×h+BA1 Tn

[0117] A0 Tn =KA0 Tn ×h+BA0 Tn

[0118] in, KA3Tn KA2 Tn KA1 Tn KA0 Tn BA3 Tn BA2 Tn BA1 Tn BA0 Tn is a constant.

[0119] Step 2: When a certain flight speed V is required, the climbing thrust calculation model at the altitude hx and temperature Tx (Ti-1≤Tx≤Ti) is as follows:

[0120] P(Tx, hx, V) = P Ti-1 +(Tx-T i-1 ) / (Ti-Ti-1)×(P Ti -P Ti-1 )

[0121] P(Tx, hx, V) = A3 Tx ×Ma 3 +A2 Tx ×Ma 2 +A1 Tx ×Ma+A0 Tx

[0122] Among them: A3 Tx =[KA3 Ti-1 +(T x -T i-1 ) / (T i -T i-1 )×(KA3 Ti -KA3 Ti-1 )]×h+BA3 Ti-1 +(Tx-Ti-1 ) / (Ti-Ti-1)×(BA3 Ti -BA3 Ti-1 )

[0123] Similarly, we can get A2 Tx 、A1 Tx 、A0 Tx expression.

[0124] 3. Approximate the lift curve model and climb rate model of the aircraft climbing state, and calculate the climb rate, rapid ascent speed and the corresponding climb rate and ceiling.

[0125] 3.1. When determining the aircraft's climb performance, the climb rate is a key parameter of the climb performance. The real-time calculation method and implementation process of the climb rate are as follows:

[0126] The longitudinal force balance equation of the aircraft during climbing is:

[0127]

[0128] For transport aircraft, the flight path angle is very small when climbing, and cosθ≈1 can be approximated. The expression of the lift coefficient CL is as follows:

[0129]

[0130] Among them, L is lift, W is gravity, P is engine thrust, ɑ is the fuselage angle of attack, is the engine installation angle (known quantity), S is the wing reference area;

[0131] The angle of attack ɑ can be obtained from the above formula;

[0132] The expressions for climb rate and climb gradient are as follows:

[0133]

[0134] sinθ=ROC / V

[0135] Among them, the climbing thrust P is obtained by the calculation model in 3, and D is the resistance: D = 1 / 2ρV 2 S×CD, the drag coefficient CD is obtained by the calculation model in 2.

[0136] 3.2. The calculation method and specific steps of the aircraft's rapid ascent speed and corresponding maximum climb rate at a certain flight altitude are as follows:

[0137] Step 1: The climb rate of an aircraft at altitude H, weight m (gravity W), and climb speed V is expressed as:

[0138] dH / dt=V sinγ=(Pav-D)V / W

[0139] Where H is the time, t is the time, is the available thrust. For transport aircraft, when solving the speed corresponding to the maximum climb rate, take Pav≈P, where P is the engine thrust and D is the drag.

[0140] Step 2: At the position corresponding to the maximum climb rate, the derivative of the climb rate with respect to the speed is equal to zero, and the following expression is given:

[0141]

[0142]

[0143] Step 3: From step 2, according to the calculation model of P and D in 2 and 3, we can get:

[0144] 1 / W×(4×A3 Tx ×V 3 +3×A2 Tx ×V 2 +2×A1 Tx ×V+A0 Tx +4×K2×W / (ρSV 3 )-2×K1×W-ρS×CD0×V)=0

[0145] Step 4: According to the chord intercept method, at the height H, the climbing speed calculation range is V A ~V MO / M MO , solve the maximum climb rate ROCmax and the corresponding climb speed Vx within this speed range, the solution method is as follows:

[0146] 1) Under a given altitude H, temperature T, and flight weight W, let V1 = Va, V2 = Vmax according to the aircraft's speed range and its minimum operating speed Va and maximum operating speed Vmax;

[0147] 2) Solve for the speeds V1 and V2 calculate

[0148] 3) Judgment Then the speed corresponding to the maximum climb rate at height H is Vx=V1, calculate the climb rate ROCmax at speed V1, and output the calculation result;

[0149] 4) If The chord intercept method is used to iteratively calculate the speed point Vx corresponding to the maximum climb rate. The steps are as follows:

[0150] 5) Order Calculate the Vx like (where ε is an extremely small value), then the Vx at this time is the speed value corresponding to the maximum climb rate under the given conditions. Calculate the climb rate ROCmax at this time and output the calculation result; otherwise, continue the calculation according to the following steps:

[0151] 6) If Calculate If Then let V1 = Vx, otherwise let V2 = Vx, and return to perform the operations in steps 2) - 5) until The maximum climb rate ROCmax and the corresponding climb speed Vx under the given flight conditions can be obtained.

[0152] 3.3. The calculation method and specific steps for the ceiling of the aircraft under the given flight conditions are as follows: Based on the calculation of the fast climb speed and the maximum climb rate under the given flight altitude, temperature, and weight in 4, a calculation program is written using the chord cutting method to obtain the ceiling of the aircraft under the given temperature and flight weight. The implementation steps are as follows:

[0153] Step 1: Input the flight conditions: flight weight W, temperature t, and the maximum operating altitude Hmax of the aircraft;

[0154] Step 2, Let the ceiling be equal to the maximum flight altitude: Hcrmax = Hmax, call the calculation program for the maximum climb rate under the given altitude, temperature, and weight in 4, calculate the maximum climb rate ROCmax_Hmax at the Hmax altitude, and compare the relationship between ROCmax_Hmax and the required climb rate ROC0 for the aircraft ceiling. If ROCmax_Hmax ≥ ROC0, then take the ceiling of the aircraft as the maximum operating altitude, that is: Hcrmax = Hmax, and the calculation ends;

[0155] Step 3, If ROCmax_Hmax < ROC0, calculate the ceiling according to the following steps:

[0156] Step 4, Let H1 = 0, H2 = Hmax, call the calculation function for the maximum climb rate in 5 to obtain ROCmax_H1 and ROCmax_H2, and let Hcrmax = H1 + (ROC0 - ROCmax_H1) / (ROCmax_H2 - ROCmax_H1) × (H2 - H1), and calculate the maximum climb rate ROCmax_Hcrmax at the altitude Hcrmax;

[0157] Step 5: Compare the ROCmax_Hcrmax obtained in Step 4 with the climb rate ROC0 required for the ceiling. If |ROCmax_Hcrmax - ROC0| < ε, where ε is a very small threshold, then Hcrmax is the ceiling of the aircraft under the given conditions. Output the ceiling value Hcrmax and the speed Vmax corresponding to the maximum climb rate, and the calculation result. Otherwise, continue the calculation according to the following steps:

[0158] Step 6: If |ROCmax_Hcrmax - ROC0| ≥ ε in Step 5, then if ROCmax_H1 ≥ 0 and ROCmax_Hcrmax ≥ ROC0, let H1 = Hcrmax (obtained in Step 4); if ROCmax_H1 ≥ 0 and ROCmax_Hcrmax < ROC0, let H1 = Hcrmax (obtained in Step 4); return to execute the operations of Step 4 and Step 5 until |ROCmax_Hcrmax - ROC0| < ε;

[0159] Step 7: If |ROCmax_Hcrmax - ROC0| ≥ ε in Step 5 and ROCmax_H1 < 0, then let H2 = H1 + (ROC0 - ROC1) / ×(ROC2 - ROC1)×(H2 - H1), and return to repeat the operations of Step 4 and Step 5 until |ROCmax_Hcrmax - ROC0| < ε.

[0160] The method of this application can perform real-time calculation of relevant parameters of the climb performance in the flight management system or ground mission planning system of transport aircraft. It does not need to establish a climb performance database with a large amount of data, which reduces the workload of aircraft designers. Especially when the climb performance of the aircraft changes due to certain reasons and the climb performance data of the aircraft needs to be updated, it can greatly reduce the repetitive labor of aircraft designers and improve work efficiency. In this application, the characteristics of the flight speed range during the climb of transport aircraft are fully considered. The lift curve is processed into a linear function form, and the polar curve is processed into a binomial form. The engine thrust data is fitted into a polynomial to make the input original data smooth, ensuring the fluency of the calculation process and the convergence of the calculation result. This application fully considers the flight characteristics during the climb stage of transport aircraft, makes a reasonable approximation of the real-time calculation model of climb parameters to meet the calculation efficiency requirements of real-time calculation, and at the same time ensures that the calculation result meets the engineering accuracy requirements. The method of this application can be implemented in the programming of real-time calculation of the climb performance data of transport aircraft. When iteratively solving parameters, reasonable initial values are assigned to the parameters, effectively reducing the number of iterations and improving the convergence speed and calculation efficiency of real-time calculation.

[0161] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application shall be based on the protection scope of the claims.

Claims

1. A method for real-time calculation of climb performance data of transport aircraft, characterized in that: The method includes: Obtaining input data, where the input data includes aircraft basic layout parameters, aircraft longitudinal aerodynamic characteristic data, and engine power data; Determining the climb speed range of the transport aircraft and the corresponding aerodynamic characteristic data according to the input data, fitting the aircraft longitudinal aerodynamic characteristic data required for climb performance into a polynomial form, and fitting the engine thrust data into a polynomial form to form a fairing curve. Among them, the process of fitting the aircraft longitudinal aerodynamic characteristic data required for climb performance into a polynomial includes: Step 1: First, express the lift curve of the aircraft cruise configuration as a linear function of the angle of attack. The calculation model is: CL = f(Ma, ɑ) = K Ma ×ɑ+B Ma , where K Ma is the slope of the lift curve corresponding to the Mach number Ma, B Ma is the intercept of the lift curve corresponding to the Mach number Ma, ɑ is the angle of attack, and CL is the lift coefficient; Step 2: Express the drag coefficient CD as a quadratic function of the lift coefficient CL. The calculation model is: CD = f(Ma, CL) = + K1 Ma CL 2 +K2 Ma CL+CD0 Ma , where CD0 Ma K1 is the drag coefficient when the lift coefficient CL is zero at the corresponding Mach number Ma, Ma , K2 Ma , CD0 Ma is a constant value; Step three, interpolating the known lift coefficient curve to obtain the lift coefficient curve corresponding to any Mach number. Similarly, interpolating the known drag coefficient curve to obtain the drag coefficient curve corresponding to any Mach number. Specifically, it includes: At any climbing flight Mach number Ma x (Ma n-1 <Ma x ≤Ma n ) when the lift coefficient CL Ma_x The expression is: CL Ma_x =K Ma_x ×ɑ+B Ma_x , where K Ma_x = K Ma_n-1 + (Ma x - Ma n-1 ) / (Ma n - Ma n-1 ) × (K Ma_n - K Ma_n-1 ); B Ma_x =B Ma_n-1 +(Ma x -Ma n-1 ) / (Ma n -Ma n-1 )×(B Ma_n -B Ma_n-1 ); At a certain flight Mach number Ma x (Ma n-1 <Ma x ≤Ma n ) is expressed as: CD = f(Ma x , CL)=+K1 x CL 2 +K2 x CL+CD0 x , Wherein, K1 x = K1 Ma_n-1 + (Ma x - Ma n-1 ) / (Ma n - Ma n-1 ) × (K1 Ma_n - K1 Ma_n-1 ); K2 x =K2 Ma_n-1 +(Ma x -Ma n-1 ) / (Ma n -Ma n-1 )×(K2 Ma_n - K2 Ma_n-1 ); CD0 x =CD0 Ma_n-1 +(Ma x -Ma n-1 ) / (Ma n -Ma n-1 )×(CD0 Ma_n -CD0 Ma_n-1 ); Approximating the lift curve model and climb rate model of the aircraft in the climb state, and calculating the climb rate, fast climb speed, and the corresponding maximum climb rate and ceiling.

2. The method for real-time calculation of climb performance data of transport aircraft according to claim 1, characterized in that: The process of fitting the engine thrust data into a polynomial form includes: Step one: Fit the thrust of the aircraft in the climb state at different temperatures into a polynomial of speed. The calculation model is as follows: <h2 style=";text-align:left;direction:ltr">P<h2 style=";text-align:left;direction:ltr"> T1 <h2 style=";text-align:left;direction:ltr"> (f(h, Ma) = A3)<h2 style=";text-align:left;direction:ltr"> T1 <h2 style=";text-align:left;direction:ltr"> ×V<h2 style=";text-align:left;direction:ltr"> 3 <h2 style=";text-align:left;direction:ltr"> +A2<h2 style=";text-align:left;direction:ltr"> T1 <h2 style=";text-align:left;direction:ltr"> ×V<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +A1<h2 style=";text-align:left;direction:ltr"> T1 <h2 style=";text-align:left;direction:ltr"> ×V+A0<h2 style=";text-align:left;direction:ltr"> T1 …… <h2 style=";text-align:left;direction:ltr">P<h2 style=";text-align:left;direction:ltr"> Tn <h2 style=";text-align:left;direction:ltr"> (f(h, Ma) = A3)<h2 style=";text-align:left;direction:ltr"> Tn <h2 style=";text-align:left;direction:ltr"> ×V<h2 style=";text-align:left;direction:ltr"> 3 <h2 style=";text-align:left;direction:ltr"> +A2<h2 style=";text-align:left;direction:ltr"> Tn <h2 style=";text-align:left;direction:ltr"> ×V<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +A1<h2 style=";text-align:left;direction:ltr"> Tn <h2 style=";text-align:left;direction:ltr"> ×V+A0<h2 style=";text-align:left;direction:ltr"> Tn Among them, P represents thrust, T1~Tn represent different temperatures, h is height, A3, A2, A1, A0 are coefficients, A3 Tn 、A2 Tn 、A1 Tn is a linear function of height h: <h2 style=";text-align:left;direction:ltr">A3<h2 style=";text-align:left;direction:ltr"> Tn <h2 style=";text-align:left;direction:ltr"> =KA3<h2 style=";text-align:left;direction:ltr"> Tn <h2 style=";text-align:left;direction:ltr"> ×h+BA3<h2 style=";text-align:left;direction:ltr"> Tn <h2 style=";text-align:left;direction:ltr">A2<h2 style=";text-align:left;direction:ltr"> Tn <h2 style=";text-align:left;direction:ltr"> =KA2<h2 style=";text-align:left;direction:ltr"> Tn <h2 style=";text-align:left;direction:ltr"> ×h+BA2<h2 style=";text-align:left;direction:ltr"> Tn A1 Tn =KA1 Tn ×h+BA1 Tn A0 Tn =KA0 Tn ×h+BA0 Tn Among them, KA3 Tn KA2 Tn KA1 Tn KA0 Tn BA3 Tn BA2 Tn BA1 Tn BA0 Tn is a constant; Step two, interpolate the thrust curves of the climb state at different altitudes and temperatures to obtain the climb thrust curve at any altitude hx and temperature Tx. The interpolation process is as follows: When a certain flight speed V is required, at a height hx, temperature Tx (T i-1 ≤Tx≤T i ), the calculation model is as follows: P(Tx,hx,V)=P Ti-1 +(Tx-T i-1 ) / (T i -T i-1 )×(P Ti -P Ti-1 ) <h2 style=";text-align:left;direction:ltr">P(Tx, hx, V) = A3<h2 style=";text-align:left;direction:ltr"> Tx <h2 style=";text-align:left;direction:ltr"> ×Ma<h2 style=";text-align:left;direction:ltr"> 3 <h2 style=";text-align:left;direction:ltr"> +A2<h2 style=";text-align:left;direction:ltr"> Tx <h2 style=";text-align:left;direction:ltr"> ×Ma<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +A1<h2 style=";text-align:left;direction:ltr"> Tx <h2 style=";text-align:left;direction:ltr"> ×Ma+A0<h2 style=";text-align:left;direction:ltr"> Tx Where: A3 Tx = [KA3 Ti-1 + (Tx - T i-1 ) / (T i - T i-1 ) × (KA3 Ti - KA3 Ti-1 )] × h + BA3 Ti-1 + (Tx - T i-1 ) / (T i - T i-1 ) × (BA3 Ti - BA3 Ti-1 ) Similarly, we get A2 Tx 、A1 Tx 、A0 Tx expression.

3. The method for real-time calculation of climb performance data of transport aircraft according to claim 2, characterized in that: The process of calculating the climb rate includes: The longitudinal force balance equation of the aircraft during climb is: When the flight path angle of the aircraft during climb is very small, cosθ≈1, then the expression of the lift coefficient CL is as follows: Among them, L is lift, W is gravity, θ is the aircraft's flight path angle, P is the engine thrust, and ɑ is the fuselage angle of attack. is the engine installation angle, is a known quantity, and S is the wing reference area; The angle of attack ɑ can be obtained from the above formula; The expressions of the climb rate ROC and the climb gradient sinθ are as follows: sinθ = ROC / V Where V is the climbing speed and D is the resistance: D = 1 / 2ρV 2 S×CD.

4. The method for real-time calculation of climb performance data of transport aircraft according to claim 3, characterized in that: The process of calculating the fast climb speed includes: Step one, the climb rate of the aircraft at altitude H, weight m, gravity W, and climb speed V is expressed as: dH / dt = Vsinγ = (Pav - D)V / W Where H is the height, t is the time, is the available thrust. For transport aircraft, the aircraft’s angle of attack is small within the climbing speed range. When solving for the speed corresponding to the maximum climb rate, let Pav≈P, where P is the engine thrust and D is the drag. Step two, at the position corresponding to the maximum climb rate, the derivative of the climb rate with respect to speed is equal to zero, and there is the following expression: Step three, from step two, according to the calculation models of the engine thrust P and the drag D, there is: 1 / W×(4×A3 Tx ×V 3 +3×A2 Tx ×V 2 +2×A1 Tx ×V+A0 Tx +4×K2×W / (ρSV 3 )-2×K1×W-ρS×CD0×V)=0 Step 4: According to the chord intercept method, at altitude H, the climb speed calculation range is the aircraft's minimum operating speed V a ~Maximum operating speed V MO / Maximum operating Mach number M MO , solve the maximum climb rate ROCmax and the corresponding climb speed Vx within the climb speed calculation range, the process includes: 1) At a given altitude H, temperature T, and flight weight W, the minimum operating speed Va and the maximum operating speed V of the aircraft are within its speed range. MO , let V1 = Va, V2 = Vmax; 2) Solve for the speeds V1 and V2 calculate / dV) V2 ; 3) Judgment Then the speed corresponding to the maximum climb rate at the height H is Vx=V1, and the maximum climb rate ROCmax at the speed V1 is calculated and the calculation result is output; 4) If The chord intercept method is used to iteratively calculate the climbing speed Vx corresponding to the maximum climb rate. The steps are as follows: 5) Order Calculate the Vx like Among them, ε is a very small value, then Vx at this time is the speed value corresponding to the maximum climb rate under given conditions, calculate the maximum climb rate ROCmax at this time, and output the calculation result; otherwise, continue the calculation according to the following steps: 6) If calculate like Then let V1 = Vx, otherwise let V2 = Vx, and return to execute steps 2) to 5) until The maximum climb rate ROCmax and the corresponding climb speed Vx under given flight conditions can be obtained.

5. The method for real-time calculation of climb performance data of transport aircraft according to claim 1, characterized in that: The process of calculating the ceiling includes: Step one: Input flight conditions: flight weight W, temperature t, and the maximum service altitude Hmax of the aircraft; Step two, let the ceiling Hcrmax be equal to the maximum flight height: Hcrmax = Hmax. According to the maximum climb rate at the given altitude, temperature, and weight, calculate the maximum climb rate ROCmax_Hmax at the Hmax altitude, and compare the relationship between ROCmax_Hmax and the climb rate ROC0 required for the aircraft ceiling. If ROCmax_Hmax≥ROC0, then take the ceiling of the aircraft as the maximum service height, that is: Hcrmax = Hmax, and the calculation ends; Step three, if ROCmax_Hmax < ROC0, calculate the ceiling according to the following steps: Step 4: Let H1 = 0, H2 = Hmax. According to the calculation function of the maximum climb rate, obtain ROCmax_H1 and ROCmax_H2. Let Hcrmax = H1 + (ROC0 - ROCmax_H1) / (ROCmax_H2 - ROCmax_H1)×(H2 - H1), and calculate the maximum climb rate ROCmax_Hcrmax at height Hcrmax; Step 5: Compare the ROCmax_Hcrmax obtained in Step 4 with the climb rate ROC0 required for the ceiling. If |ROCmax_Hcrmax - ROC0| < ε, where ε is a threshold, then Hcrmax is the ceiling of the aircraft under the given conditions. Output the ceiling value Hcrmax and the speed Vmax corresponding to the maximum climb rate, and the calculation results; otherwise, continue the calculation according to the following steps: Step 6: If |ROCmax_Hcrmax - ROC0| ≥ ε in Step 5, then if ROCmax_H1 ≥ 0 and ROCmax_Hcrmax ≥ ROC0, let H1 = Hcrmax, where Hcrmax is obtained in Step 4; if ROCmax_H1 ≥ 0 and ROCmax_Hcrmax < ROC0, then let H2 = Hcrmax; Return to perform the operations of Step 4 and Step 5 until |ROCmax_Hcrmax - ROC0| < ε; Step 7: If |ROCmax_Hcrmax - ROC0| ≥ ε in Step 5 and ROCmax_H1 < 0, then let H2 = H1 + (ROC0 - ROC1) / ×(ROC2 - ROC1)×(H2 - H1), and return to repeat the operations of Step 4 and Step 5 until |ROCmax_Hcrmax - ROC0| < ε.

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