Method for calculating maximum flexible temperature in takeoff stage of airplane

Abstract

According to the method for calculating the maximum flexible temperature in the takeoff stage of the airplane, thrust corresponding to the flexible temperature is obtained through a temperature-thrust curve, other takeoff performance calculation related to temperature parameters adopts the actual environment temperature, and decoupling of thrust reduction of the flexible temperature and other calculation of the takeoff performance is achieved. According to the calculation method, the maximum takeoff weight of the aircraft is obtained as a reference value, and whether the actual takeoff weight is smaller than the maximum takeoff weight and whether the environment temperature is lower than the maximum flexible temperature are compared. If the conditions are met, the corresponding thrust is calculated on the basis of the flexible temperature, the actual environment temperature is adopted for calculation of temperature parameters in the air density, and the corresponding take-off weight is recalculated; and adopting a golden section method to iteratively optimize the flexible temperature value until the calculated takeoff weight is consistent with the actual takeoff weight, and obtaining an optimal matching solution. According to the invention, the optimal matching of the takeoff weight and the thrust is realized, and the operation efficiency and the safety of the aircraft are improved.

Description

Technical Field

[0001] The invention provides a method for calculating the maximum flexible temperature of an aircraft during take-off phase, and belongs to the technical field of aircraft operation. Background Art

[0002] During the takeoff phase of civil aircraft, aircraft engines usually operate at maximum takeoff thrust (TOGA, Takeoff / Go-Around) to ensure sufficient climbing performance. However, long-term use of maximum thrust will increase engine wear and reduce fuel efficiency. The actual takeoff weight often does not reach the maximum takeoff weight, and the aircraft has sufficient performance to meet the safety margin even if the maximum takeoff thrust is not used. Therefore, the aviation industry widely adopts the Flex Temperature Method, which reduces thrust by setting a "hypothetical temperature" higher than the actual temperature, thereby reducing engine load and improving economy.

[0003] The thrust of a high bypass ratio turbofan engine decreases as the atmospheric temperature increases. Under standard sea level conditions, when the actual temperature is lower than the engine's thrust platform temperature (i.e., the highest temperature at which the engine can maintain maximum takeoff thrust), the engine increases the speed to maintain constant thrust; when the actual temperature exceeds the platform temperature, the thrust decreases as the temperature increases. The flexible temperature method reduces thrust output at lower actual temperatures by inputting an assumed temperature (higher than the actual temperature) and causing the engine to operate at the thrust corresponding to this temperature.

[0004] However, the traditional flexible temperature method has the following problems: Conservative performance: The traditional method directly regards the flexible temperature as the ambient temperature for calculation, which leads to conservative aircraft performance and affects takeoff performance (such as increased takeoff distance).

[0005] Low computational efficiency: Existing methods rely on temperature-weight models and cannot dynamically adjust the matching relationship between thrust and takeoff weight, resulting in a complex and time-consuming calculation process.

[0006] Insufficient economy: When runway length is limited, traditional methods may not fully utilize aircraft performance, resulting in low flexible temperature settings and failure to maximize engine load reduction and fuel saving potential. Summary of the invention

[0007] In view of the shortcomings of the prior art, the present invention aims to provide a method for calculating the maximum flexible temperature of an aircraft during takeoff, which realizes dynamic matching of thrust and takeoff weight through the temperature-thrust curve, thereby improving calculation accuracy and efficiency. By decoupling the calculation of flexible temperature and ambient temperature, the flight performance of the aircraft is fully utilized, a higher maximum flexible temperature is obtained, and thus economic efficiency is improved.

[0008] To achieve the above-mentioned invention objective, the present invention provides a method for calculating the maximum flexible temperature during the aircraft takeoff phase, which mainly includes the following steps: S1. Calculate the maximum takeoff weight of the aircraft as a reference value based on airport, meteorological, and aircraft configuration information; S2. Compare whether the actual takeoff weight is less than the maximum takeoff weight to ensure flight safety and efficiency; S3. Determine whether the ambient temperature is lower than the maximum flexible temperature. If the condition is met, continue to calculate the maximum flexible temperature; S4. If the ambient temperature meets the condition, the algorithm will calculate the corresponding thrust through the temperature-thrust curve based on the flexible temperature. The temperature parameter in the air density is calculated using the actual ambient temperature, and the corresponding takeoff weight is recalculated according to the thrust corresponding to the flexible temperature; S5. Verify whether the takeoff weight corresponding to the reduced thrust is equal to the actual takeoff weight. If the two are equal, directly output the current flexible temperature and end the process; S6. If the takeoff weight corresponding to the reduced thrust is not equal to the actual takeoff weight, further determine whether the takeoff weight corresponding to the reduced thrust is less than the actual takeoff weight. If the former is less than the latter, it is necessary to increase the flexible temperature and re-enter the loop calculation; otherwise, reduce the flexible temperature until the optimal solution, that is, the maximum flexible temperature, is found.

[0009] Step S1 includes the following sub-steps: S11. If the data read by the aircraft is the indicated airspeed, it needs to be converted to the true airspeed for calculating the ground speed in step S13: , where, is the true airspeed, is the indicated airspeed, is the air density under standard atmospheric conditions (when the altitude is at sea level and the ambient temperature is 15 °C, take 1.225 kg / m³), is the air density.

[0010] S12. The air density is obtained through the following formula: , where, is the static pressure, is the gas constant, is the ambient temperature.

[0011] S13. The aircraft takeoff distance is calculated through the following system of equations: , where, is the aircraft true airspeed, is the wind speed, is the aircraft thrust, is the aircraft drag, is the aircraft lift, is the friction coefficient, is the weight, is the aircraft angle of attack, is the engine mounting angle, is the acceleration due to gravity, is the aircraft climb angle, is the aircraft weight, is the fuel flow rate, is the horizontal distance, is the altitude, is the time, is the load factor, which is the ratio of the lift borne by the aircraft to the acceleration due to gravity. When the aircraft is not turning, this coefficient is 1.

[0012] When the aircraft is in the ground segment, it is 0. When the aircraft is in the air segment, it is 0.

[0013] S14. When using the flexible temperature method, the relationship between the aircraft engine thrust and the ambient temperature: , Since the thrust of a turbofan engine is proportional to the mass flow rate of air, and the mass flow rate ( is the cross-sectional area, is the flow velocity). At a fixed cross-sectional area and flow velocity, the thrust is proportional to the density, that is, inversely proportional to the ambient temperature.

[0014] Take the flexible temperature as the assumed temperature, and obtain the thrust value of the aircraft engine at this assumed temperature, that is, the reduced thrust value, through step S14. Specifically, determine the engine thrust at this assumed temperature by querying the engine performance curve or using a pre-established thrust model.

[0015] Substitute the reduced thrust value into the kinematic equation of step S13, where the ambient temperature in the air density of step S12 uses the actual ambient temperature, and calculate the corresponding takeoff speed, takeoff distance, and maximum takeoff weight. This can ensure that the calculation results more accurately reflect the actual flight conditions and avoid performance conservatism caused by the inconsistency between the assumed temperature and the actual temperature.

[0016] The present invention adopts a maximum flexible temperature calculation method based on the matching of temperature-thrust curves, delving into the underlying calculation logic. That is, the essence of flexible temperature is to reduce thrust, thereby improving calculation accuracy and efficiency. Through the decoupled calculation of flexible temperature and ambient temperature, the takeoff distance of the aircraft at the actual ambient temperature after thrust reduction is obtained on the premise of ensuring safety. When the maximum takeoff weight is limited by the runway length, this method makes full use of the flight performance of the aircraft to obtain a higher maximum flexible temperature, thus improving economy. Brief Description of the Drawings

[0017] Figure 1 is the flowchart of the present invention.

[0018] Figure 2 is the schematic diagram of the iterative process of the present invention. Detailed Description of the Invention

[0019] As Figure 1 shown, the optimization process of the flexible temperature algorithm first performs initialization settings, and then calculates the maximum takeoff weight of the aircraft as a reference value. Next, the system will compare whether the actual takeoff weight is less than the maximum takeoff weight. If the condition is met, the maximum flexible temperature will be calculated continuously. On this basis, it is further judged whether the ambient temperature is lower than the maximum flexible temperature to ensure flight safety and efficiency.

[0020] If the ambient temperature meets the condition, the algorithm will calculate the corresponding thrust based on the flexible temperature, and recalculate the corresponding takeoff weight according to this thrust. At this time, the system will verify again whether the takeoff weight corresponding to the reduced thrust is equal to the actual takeoff weight to ensure the accuracy of the calculation result. If the two are equal, the current flexible temperature will be directly output and the process will end; if not, it is necessary to further judge whether the takeoff weight corresponding to the reduced thrust is less than the actual takeoff weight. If the former is less than the latter, the flexible temperature needs to be increased and the loop calculation is re-entered; otherwise, the flexible temperature is decreased until the optimal solution is found.

[0021] The entire process fully considers the takeoff performance requirements of civil aviation aircraft under different environmental conditions. Through the dynamic adjustment of flexible temperature, the optimal matching of takeoff weight and thrust is achieved, thereby improving the operation efficiency and safety of the aircraft.

[0022] The above flowchart uses the golden section method for iterative calculation when finding the flexible temperature. The schematic diagram of the iterative process is as Figure 2 .

[0023] Beneficial Effects Brought by the Technical Solution of the Present Invention: (1) Improvement in calculation efficiency Taking Shuangliu Airport as an example, the improvement effect of calculation efficiency is shown in Table 1: Table 1 Improvement Effect of Flexible Temperature Calculation Efficiency

[0024] TOW35t Time (s) Number of iterations Time improvement rate (%) Traditional flexible temperature 17.63 124 22.8 Flexible temperature of this algorithm 13.6 56

[0025] As shown in Table 1, the flexible temperature of this algorithm is obtained through thrust iteration, which is deeper into the algorithm's underlying layer than the traditional flexible temperature obtained through maximum takeoff weight iteration. This reduces a large amount of unnecessary iterative calculations and ultimately improves the calculation efficiency. Under this operating condition at Shuangliu Airport, the number of iterations is reduced to 56 times (a decrease of 54.8%), corresponding to a 22.8% improvement in time efficiency. Among them, the number of iterations accumulates with each takeoff trajectory calculation.

[0026] (2)Improvement in calculation accuracy When the maximum takeoff weight is restricted by the runway length, since the takeoff distance and accelerate-stop distance obtained by this algorithm are shorter than those of the traditional flexible temperature algorithm, the corresponding field length limit weight is greater, so a higher flexible temperature can be obtained. Since the maximum takeoff weight at Shuangliu Airport is restricted by the obstacle limit weight and the influence of temperature on the obstacle limit weight is small, the flexible temperature obtained by this algorithm and the traditional flexible temperature algorithm at Shuangliu Airport is the same. The following is to exclude the influence of obstacles, set no obstacles, a runway of 2000 m, and the rest of the settings are the same as those at Shuangliu Airport. The improvement effect of the accuracy of this algorithm is tested under the condition of being restricted by the field length limit weight. At this time, the maximum takeoff weight obtained is 42 t, and the speed ratio V1 / V R is 0.95, V2 / V S is 1.136.

[0027] Table 2 Improvement effect of flexible temperature calculation accuracy TOW40t ℃ TOD(OEI) (m) TOD(AEO) (m) TOR(OEI) (m) TOR(AEO) (m) ASD(OEI) (m) ASD(AEO) (m) Traditional flexible temperature 31 1997.9 1809.9 1789.5 1651.6 1798.4 1840.6 Ambient temperature 31 1997.5 1809.4 1789.0 1651.2 1798.1 1840.2 Flexible temperature of this algorithm 35 1997.7 1814.7 1791.3 1652.9 1761.6 1799.4 Ambient temperature 35 2108.3 1918.3 1895.0 1751.2 1875.1 1914.8 Ambient temperature 15 1798.5 1600.3 1600.1 1459.3 1632.1 1677.7

[0028] As shown in Table 2, when the maximum takeoff weight is restricted by the runway length, when the ambient temperature is 35°C, the takeoff distance has exceeded the runway length. It is not until the ambient temperature drops to 31°C that the takeoff distance just reaches the runway length limit. Therefore, the temperature obtained by the traditional flexible temperature algorithm is 31°C. The flexible temperature of this algorithm calculates the takeoff distance using the actual ambient temperature. When the thrust drops to the ambient temperature of 35°C, the takeoff distance just reaches the runway length limit, which is 4°C higher than the traditional flexible temperature. Thus, on the premise of ensuring safety, the engine life is further extended and higher economic benefits are obtained.

[0029] (3)Comparison with international similar software Using Airbus PEP software, taking the A320-251 model as an example at Shuangliu Airport, calculate the flexible temperature when the maximum takeoff weight is 63 t and the takeoff weight is 58.7 t.

[0030] Table 3 Calculation results of A320 flexible temperature TOW58.7t ℃ TOD(OEI) (m) TOD(AEO) (m) TOR(OEI) (m) TOR(AEO) (m) ASD(AEO) (m) Flexible temperature 41 1506 1609 1362 1470 2035 Ambient temperature 41 1505.731 1609.323 1362.424 1469.654 2035.787 Ambient temperature 15 1388.603 1478.322 1250.388 1343.979 1856.084

[0031] As shown in Table 3, the takeoff distances corresponding to the flexible temperature algorithm of Airbus PEP software are the same as those when the environmental temperature is the flexible temperature. Therefore, instead of decoupling the thrust from the environmental temperature, the flexible temperature variable is directly mapped as the environmental temperature input value, which is consistent with the traditional flexible temperature algorithm described above.

[0032] In summary, through the temperature-thrust curve, the flexible temperature of this algorithm realizes the decoupling of the flexible temperature and the environmental temperature. Thus, on the premise of ensuring safety, the takeoff distance of the aircraft at the actual environmental temperature after reduced thrust is obtained. Since this algorithm delves deeper into the underlying algorithm logic, the calculation efficiency is improved. When the maximum takeoff weight is restricted by the runway length, this algorithm makes full use of the flight performance of the aircraft to obtain a higher maximum flexible temperature, thereby improving the economy.

Claims

1. A method for calculating the maximum flexible temperature during the takeoff phase of an aircraft, characterized in that, Including the following steps: S1. Calculate the maximum take-off weight of the aircraft as the reference value based on airport, meteorological, and aircraft configuration information; S2. Compare whether the actual take-off weight is less than the maximum take-off weight to ensure flight safety and efficiency; S3. Determine whether the ambient temperature is lower than the maximum flexible temperature. If the condition is met, continue to calculate the maximum flexible temperature; S4. If the ambient temperature meets the condition, the algorithm will calculate the thrust corresponding to the temperature-thrust curve based on the flexible temperature. The temperature parameter in the air density is calculated using the actual ambient temperature, and the corresponding take-off weight is recalculated according to the thrust corresponding to the flexible temperature; S5. Verify whether the take-off weight corresponding to the reduced thrust is equal to the actual take-off weight. If the two are equal, directly output the current flexible temperature and end the process; S6. If the take-off weight corresponding to the reduced thrust is not equal to the actual take-off weight, further determine whether the take-off weight corresponding to the reduced thrust is less than the actual take-off weight. If the former is less than the latter, the flexible temperature needs to be increased and the loop calculation is re-entered; otherwise, the flexible temperature is decreased until the optimal solution, i.e., the maximum flexible temperature, is found.

2. The maximum flexible temperature calculation method during the aircraft takeoff phase according to claim 1, characterized in that Step S1 includes the following sub-steps: S11. The data read by the aircraft is the indicated airspeed, which is converted to the true airspeed for calculating the ground speed in step S13; ， Among them, is the true airspeed, is the indicated airspeed, is the air density under standard atmospheric conditions, is the air density; S12. The air density is obtained through the following formula: ， Among them, is the static pressure, is the gas constant, is the ambient temperature; S13. The take-off distance of the aircraft is calculated through the following system of equations: ， Wherein, is the true airspeed of the aircraft, is the wind speed, is the thrust of the aircraft, is the drag of the aircraft, is the lift of the aircraft, is the friction coefficient, is the weight, is the angle of attack of the aircraft, is the engine mounting angle, is the acceleration due to gravity, is the climb angle of the aircraft, is the weight of the aircraft, is the fuel flow rate, is the horizontal distance, is the altitude, is the time, is the load factor, which is the ratio of the lift borne by the aircraft to the acceleration due to gravity. When the aircraft is not turning, this coefficient is 1; When the aircraft is in the ground segment, it is 0. When the aircraft is in the air segment, it is 0; S14. The relationship between the thrust of the aircraft engine and the ambient temperature when using the flexible temperature method: ， Since the thrust of a turbofan engine is proportional to the air mass flow rate, and the mass flow rate , is the cross-sectional area, is the flow velocity; at a fixed cross-sectional area and flow velocity, the thrust is proportional to the density, i.e., inversely proportional to the ambient temperature.

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