Method for calculating final-initial-state weight ratio of climbing aircraft with linear temperature change and equal Mach number

Abstract

The invention belongs to the technical field of aircraft design, and particularly relates to a temperature linear change equal-Mach-number climbing aircraft final-initial-state weight ratio calculation method which comprises the steps that 1, the oil consumption rate SFC of an aircraft propulsion system in an equal-Mach-number climbing stage is determined, and the Mach number M and the lift-drag ratio # imgabs0 # climbing angle gamma of an aircraft are determined; step 2, determining a coefficient lambda of temperature change along with height in an equal Mach number climbing stage; 3, determining an initial state height h1 and a final state height h2 of the aircraft in an equal Mach number climbing stage, and calculating an initial climbing state position sound velocity a (h1) and a final climbing state position sound velocity a (h2) of the aircraft; step 4, according to the oil consumption rate SFC of the aircraft propulsion system in the equal Mach number climbing stage, the Mach number M of the aircraft, the climbing angle gamma of the lift-drag ratio # imgabs1 #, the coefficient lambda of the temperature changing along with the height, the sound velocity a (h1) of the climbing initial state position and the sound velocity a (h2) of the climbing final state position, calculating to obtain the final initial state weight ratio # imgabs2 #

Description

Technical Field

[0001] This application belongs to the technical field of aircraft design, and particularly relates to a method for calculating the ratio of the final state weight to the initial state weight of an aircraft with a linear temperature change and constant Mach number climb. Background Art

[0002] Hypersonic aircraft mostly use scramjet engines as the core power system. The ratio of the final state weight to the initial state weight during constant Mach number climb directly affects performance indicators such as the range and payload of the aircraft, and is an important reference for the design of hypersonic aircraft.

[0003] Currently, for the calculation of the ratio of the final state weight to the initial state weight of an aircraft with a constant Mach number climb and temperature change, the treatment of temperature is not concise and accurate enough. Usually, it requires complex numerical simulations and a large amount of experimental data support. The calculation process is cumbersome and inefficient, and there is a large deviation between the calculation result and the actual flight situation, with low accuracy, making it difficult to meet the requirements of rapid aircraft design and evaluation.

[0004] In view of the existence of the above technical defects, this application is proposed. Summary of the Invention

[0005] The purpose of this application is to provide a method for calculating the ratio of the final state weight to the initial state weight of an aircraft with a linear temperature change and constant Mach number climb, so as to overcome or mitigate at least one aspect of the known technical defects.

[0006] The technical solution of this application is as follows:

[0007] A method for calculating the ratio of the final state weight to the initial state weight of an aircraft with a linear temperature change and constant Mach number climb, comprising:

[0008] Step 1, determine the specific fuel consumption SFC of the aircraft propulsion system during the constant Mach number climb stage, and determine the Mach number M, lift-to-drag ratio climb angle γ of the aircraft;

[0009] Step 2, determine the coefficient λ of the temperature change with altitude during the constant Mach number climb stage;

[0010] Step 3, determine the initial altitude h1 and final altitude h2 of the aircraft during the constant Mach number climb stage, and calculate the speed of sound a(h1) at the initial climb position and the speed of sound a(h2) at the final climb position of the aircraft;

[0011] Step 4, use the specific fuel consumption SFC of the aircraft propulsion system during the constant Mach number climb stage, the Mach number M, lift-to-drag ratio climb angle γ of the aircraft, the coefficient λ of the temperature change with altitude, and the speed of sound a(h1) at the initial climb position and the speed of sound a(h2) at the final climb position to calculate to obtain the ratio of the final state weight to the initial state weight

[0012]

[0013] Among them,

[0014] W1 is the initial weight of the aircraft during climb; W2 is the final weight of the aircraft during climb; g is the acceleration due to gravity.

[0015] According to at least one embodiment of the present application, in the above method for calculating the ratio of the final weight to the initial weight of a temperature-linearly-varying constant-Mach-number climbing aircraft, in step two, calculating the speed of sound a(h1) at the initial position of the aircraft climb and the speed of sound a(h2) at the final position of the aircraft climb specifically includes:

[0016]

[0017]

[0018] Among them,

[0019] k is the specific heat ratio;

[0020] R is the air gas constant;

[0021] T0 is the reference point temperature;

[0022] h0 is the reference point altitude.

[0023] According to at least one embodiment of the present application, in the above method for calculating the ratio of the final weight to the initial weight of a temperature-linearly-varying constant-Mach-number climbing aircraft, in step two, the specific heat ratio k takes

[0024] According to at least one embodiment of the present application, in the above method for calculating the ratio of the final weight to the initial weight of a temperature-linearly-varying constant-Mach-number climbing aircraft, in step two, the air gas constant R takes 287 J / (kg·K).

[0025] According to at least one embodiment of the present application, in the above method for calculating the ratio of the final weight to the initial weight of a temperature-linearly-varying constant-Mach-number climbing aircraft, in step two, the reference point altitude h0 takes the ground altitude.

[0026] The present application has at least the following beneficial technical effects:

[0027] Provided is a method for calculating the ratio of the final weight to the initial weight of a temperature-linearly-varying constant-Mach-number climbing aircraft, which is applicable to the case where the atmospheric temperature varies with altitude. The atmospheric temperature is simply processed as linearly varying with altitude, and the calculation process is simple and efficient. An accurate calculation result of the ratio of the final weight to the initial weight of the aircraft can be obtained in a short time, which can provide effective support for the rapid design and evaluation of the aircraft. Description of the Drawings

[0028] Figure 1It is a schematic diagram of the forces acting on an aircraft during the climbing phase of flight provided by an embodiment of the present application;

[0029] Figure 2 is the ratio of the final weight to the initial weight of the aircraft flying at a constant Mach number of 7 provided by an embodiment of the present application schematic diagram showing the variation with flight time t;

[0030] Figure 3 is the ratio of the final weight to the initial weight of the aircraft with a flight duration of 15 minutes provided by an embodiment of the present application schematic diagram showing the variation with different Mach numbers M.

[0031] To better illustrate this embodiment, some contents in the drawings are omitted, enlarged or reduced, and are only used for exemplary illustration and should not be construed as a limitation to the present application. Detailed implementation manners

[0032] To make the technical solutions and their advantages of the present application clearer, the technical solutions of the present application will be further described clearly and completely below with reference to the drawings. It can be understood that the specific embodiments described herein are only partial embodiments of the present application, which are only used to explain the present application and not to limit the present application. It should be noted that for the convenience of description, only the parts related to the present application are shown in the drawings, and other related parts can refer to the general design.

[0033] In addition, unless otherwise defined, the technical terms or scientific terms used in the description of the present application should be the ordinary meanings understood by those of ordinary skill in the art to which the present application belongs. The "including" used in the description of the present application means that the concept appearing before this word covers the concepts listed after this word and their equivalents, without excluding other related concepts.

[0034] The forces acting on the aircraft during the climbing phase of flight are as Figure 1 shown.

[0035] The climbing state equation is:

[0036] W = mg …………(1)

[0037]

[0038]

[0039]

[0040]

[0041]

[0042] Wherein:

[0043] W is the weight of the aircraft, in N; m is the mass of the aircraft, in kg; g is the acceleration due to gravity, in m / s 2 ; V is the flight speed of the aircraft, in m / s; F is the thrust of the aircraft's propulsion system, in N; D is the drag of the aircraft, in N; γ is the climb angle of the aircraft, in rad; L is the lift of the aircraft, in N; h is the flight altitude of the aircraft, in m; x is the flight range of the aircraft, in m; SFC is the fuel consumption rate of the aircraft's propulsion system, in kg / (kg·s). L / D can be used as the lift-to-drag ratio of the aircraft.

[0044] Mach number formula:

[0045]

[0046] Where:

[0047] M is the Mach number; a is the speed of sound, k is the specific heat ratio, generally taking the value R is the air gas constant, generally taking the value 287 J / (kg·K); T is the atmospheric temperature, which varies with the altitude of the aircraft.

[0048] Due to climbing at a constant Mach number, that is Differentiating both sides of equation (7) with respect to the altitude h, we get:

[0049]

[0050] After rearrangement, we get:

[0051]

[0052] Because:

[0053]

[0054] So:

[0055]

[0056] Also because:

[0057]

[0058] So:

[0059]

[0060] After rearrangement, we get:

[0061]

[0062] Also because:

[0063]

[0064] Meanwhile, there is:

[0065]

[0066] Therefore:

[0067]

[0068] Dividing both sides of Equation (17) by \(W\cdot V\sin\gamma\) and arranging, we get:

[0069]

[0070] Substituting Equation (14) into Equation (18), we have:

[0071]

[0072] That is:

[0073]

[0074] Furthermore, there is:

[0075]

[0076] That is:

[0077]

[0078] When the climbing stage is in the case where the atmospheric temperature changes linearly with height, that is:

[0079] \(T = T_0+\lambda(h - h_0)\cdots\cdots(22)\)

[0080] Wherein,

[0081] \(T_0\) is the reference point temperature;

[0082] \(h_0\) is the reference point height, generally the ground height can be taken;

[0083] \(h\) is the flight height of the aircraft;

[0084] \(\lambda\) is the coefficient of temperature change with height, and further there is:

[0085]

[0086] Differentiating both sides of Equation (23) with respect to \(h\), we have:

[0087]

[0088] Equation (21) can be further simplified to:

[0089]

[0090] That is:

[0091]

[0092] By transforming Equation (24), we can obtain:

[0093]

[0094] Substituting Equation (26) into Equation (25), we can obtain:

[0095]

[0096] Integrating h on both sides of Equation (27), we can obtain:

[0097]

[0098] Where:

[0099] W2 is the weight of the aircraft at the end of the climbing state, with the unit of kg; W1 is the weight of the aircraft at the beginning of the climbing state, with the unit of kg; is the ratio of the weight of the aircraft at the end of the climbing state to the weight at the beginning of the climbing state; h2 is the height of the aircraft at the end of the climbing state, with the unit of m; a(h2) is the speed of sound at the position of the aircraft at the end of the climbing state, with the unit of m / s; h1 is the height of the aircraft at the beginning of the climbing state, with the unit of m; a(h1) is the speed of sound at the position of the aircraft at the beginning of the climbing state, with the unit of m / s.

[0100] Based on the above, the present application provides a method for calculating the ratio of the end-state weight to the initial-state weight of a temperature-linearly varying and constant-Mach-number climbing aircraft, which is applicable to the situation where the temperature changes with the position height, and can realize the rapid estimation of the ratio of the end-state weight to the initial-state weight in the constant-Mach-number climbing stage, providing effective support for the design and optimization of the aircraft.

[0101] Step 1: Determine the specific fuel consumption SFC of the aircraft propulsion system in the constant-Mach-number climbing stage, and determine the Mach number M, lift-to-drag ratio climb angle γ of the aircraft, which can be specifically obtained through experiments, technical manuals, or measurements.

[0102] Step 2: Determine the coefficient λ of the temperature change with height in the constant-Mach-number climbing stage, which can be specifically obtained through experiments, referring to technical materials, or measurements.

[0103] Step 3: Determine the initial height h1 and the end height h2 of the aircraft in the constant-Mach-number climbing stage, and calculate the speed of sound a(h1) at the initial position of the aircraft climb and the speed of sound a(h2) at the end position of the aircraft climb.

[0104]

[0105]

[0106] Among them,

[0107] k is the specific heat ratio, which can generally be taken as

[0108] R is the air gas constant, which can generally be taken as 287 J / (kg·K);

[0109] T0 is the reference point temperature;

[0110] h0 is the reference point height, which can generally be taken as the ground height.

[0111] Step 4: Using the specific fuel consumption SFC of the aircraft propulsion system during the constant Mach number climb phase, the Mach number M of the aircraft, the lift-to-drag ratio the climb angle γ, the coefficient λ of the temperature change with height, and the sound speeds a(h1) at the initial climb state position and a(h2) at the final climb state position of the aircraft, calculate to obtain the final-to-initial weight ratio

[0112]

[0113] Among them,

[0114] W1 is the initial weight of the aircraft during climb; W2 is the final weight of the aircraft during climb; g is the acceleration due to gravity.

[0115] In a specific example, the relevant parameters and their calculations are shown in the following table:

[0116] The atmospheric temperature T varying with the flight altitude can be calculated by Equation (22), and the final-to-initial weight ratio of the aircraft during the constant Mach number 7 flight is plotted versus the flight time t, as Figure 2 shown, and the final-to-initial weight ratio of the aircraft during the 15-minute flight duration is plotted versus different Mach numbers M, as Figure 3 shown.

[0117] The calculation method of the final-to-initial weight ratio of the constant Mach number climb aircraft with linearly varying temperature disclosed in the above embodiments is applicable to the case where the atmospheric temperature varies with height. The atmospheric temperature is simply processed as linearly varying with height, and factors such as the performance of the propulsion system, the aerodynamic characteristics of the aircraft, and the flight trajectory are comprehensively considered, which can more accurately reflect the weight change of the aircraft under actual flight conditions, can complete the calculation in a short time, obtain the final-to-initial weight ratio of the aircraft, and can provide effective support for the design of the aircraft.

[0118] So far, the technical solutions of the present application have been described in conjunction with the preferred embodiments shown in the accompanying drawings. Those skilled in the art should understand that the protection scope of the present application is obviously not limited to these specific embodiments. Without departing from the principle of the present application, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will fall within the protection scope of the present application.

Claims

1. A calculation method for the ratio of the final initial state weight of an aircraft with a linearly varying temperature and constant Mach number climb, characterized in that, Including: Step 1. Determine the specific fuel consumption (SFC) of the aircraft propulsion system during the constant Mach number climb phase, and determine the Mach number M and lift-to-drag ratio of the climbing angle γ; Step 2: Determine the coefficient λ of the temperature change with altitude during the constant Mach number climb phase; Step 3: Determine the initial altitude h1 and the final altitude h2 of the aircraft during the constant Mach number climb phase, and calculate the speed of sound a(h1) at the initial position of the aircraft climb and the speed of sound a(h2) at the final position of the aircraft climb; Step 4: Using the specific fuel consumption (SFC) of the aircraft propulsion system during the constant Mach number climb phase, the Mach number M of the aircraft, the lift-to-drag ratio the climb angle γ, the coefficient λ of temperature variation with altitude, and the speed of sound a(h1) at the initial climb state position and the speed of sound a(h2) at the final climb state position, calculate to obtain the final-to-initial weight ratio Wherein, W1 is the initial weight of the aircraft climb; W2 is the final weight of the aircraft climb; g is the acceleration due to gravity.

2. The method for calculating the final-to-initial weight ratio of a constant Mach number climb aircraft with linear temperature change according to claim 1, wherein In step 2, calculating the speed of sound a(h1) at the initial position of the aircraft climb and the speed of sound a(h2) at the final position of the aircraft climb, specifically: Wherein, k is the specific heat ratio; R is the air gas constant; T0 is the reference point temperature; h0 is the reference point altitude.

3. The method for calculating the final-to-initial weight ratio of a constant Mach number climb aircraft with linear temperature change according to claim 2, wherein In step two, the specific heat ratio k is taken as 4. The method for calculating the final-to-initial weight ratio of a constant Mach number climb aircraft with linear temperature change according to claim 3, wherein In step 2, the air gas constant R is taken as 287 J / (kg·K).

5. The method for calculating the final-to-initial weight ratio of a constant Mach number climb aircraft with linear temperature change according to claim 4, wherein In step 2, the reference point altitude h0 is taken as the ground altitude.

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