Hypersonic flight vehicle cruise flight range determination method considering variable lift-drag ratio

Abstract

The invention belongs to the technical field of hypersonic flight vehicle cruise flight range determination, and particularly relates to a hypersonic flight vehicle cruise flight range determination method considering a variable lift-drag ratio, and the method enables the integration process to be more scientific and accurate by substituting the corrected effective weight and the variable lift-drag ratio into a range integration formula. Accurate calculation of the cruise flight range of the hypersonic flight vehicle can be achieved, effective support can be provided for design and performance evaluation of the hypersonic flight vehicle, and improvement of the economical efficiency and efficiency of the flight vehicle is facilitated.

Description

Technical Field

[0001] This application belongs to the technical field of cruise flight range determination for hypersonic vehicles, specifically relating to a method for determining the cruise flight range of a hypersonic vehicle considering a variable lift-to-drag ratio. Background Technology

[0002] In the aviation field, cruise flight range calculation is a key issue in aircraft design and performance evaluation.

[0003] Currently, the Bregate range formula is mostly used to calculate the cruise range of low-speed aircraft. The Bregate range formula is derived under the assumption that the lift of the aircraft is equal to the drag and that the speed and specific energy are considered constant.

[0004] Applying the Bregate range formula to calculate the cruise range of hypersonic vehicles has significant limitations. Under hypersonic flight conditions, the vehicle's speed is sufficient to make the centrifugal effect significant, causing lift and drag to no longer maintain a constant ratio, rendering the assumptions of the Bregate range formula inapplicable. Furthermore, the lift-to-drag ratio of a hypersonic vehicle changes with flight conditions during cruise, further increasing the complexity of hypersonic range calculations.

[0005] Currently, most methods for calculating the cruise flight range of hypersonic vehicles are based on the assumption of a fixed lift-to-drag ratio, which cannot accurately reflect the actual performance of hypersonic vehicles, resulting in a large deviation between the calculation results and the actual situation.

[0006] Therefore, there is an urgent need for a method to calculate the range of hypersonic vehicles that can take into account variable lift-to-drag ratios, in order to support the design and performance evaluation of hypersonic vehicles. In view of this, this application is proposed. Summary of the Invention

[0007] The purpose of this application is to provide a method for determining the cruise flight range of a hypersonic vehicle that considers a variable lift-to-drag ratio. By correcting the effective weight of the vehicle and introducing a variation model of the lift-to-drag ratio, the method can accurately calculate the cruise flight range of the hypersonic vehicle, providing effective support for the design and performance evaluation of hypersonic vehicles.

[0008] The technical solution of this application is:

[0009] A method for determining the cruise flight range of a hypersonic vehicle considering a variable lift-to-drag ratio includes:

[0010] Step 1: Calculate the aircraft's effective weight correction factor: Where V is the flight speed, g is the gravitational acceleration, and r is the Earth's radius;

[0011] Step 2: Calculate the aircraft's maximum lift-to-drag ratio (L / D)max :

[0012]

[0013] Where k is the shape-related constant of the aircraft, C D0 This refers to the zero-lift drag coefficient of the aircraft.

[0014] Step 3: Calculate the initial integration parameters x initial :

[0015]

[0016] Among them, W initial Let q be the initial weight of the aircraft. ∞ For the dynamic pressure of the aircraft, S ref The reference area of ​​the aircraft;

[0017] Step 4: Calculate the final integration parameter x final :

[0018]

[0019] Among them, W final The final weight of the aircraft

[0020] Step 5: Calculate the aircraft's cruising range R:

[0021]

[0022] Where Isp is the specific impulse of the aircraft.

[0023] According to at least one embodiment of this application, in the above-described method for determining the cruise flight range of a hypersonic vehicle considering a variable lift-to-drag ratio, the gravitational acceleration g is taken as 9.81 m / s², and the Earth's radius is taken as 6,371,000 m.

[0024] According to at least one embodiment of this application, in the above-described method for determining the cruise flight range of a hypersonic vehicle considering a variable lift-to-drag ratio, the shape-related constant k of the vehicle is taken as 1.

[0025] According to at least one embodiment of this application, in the above-described method for determining the cruise flight range of a hypersonic vehicle considering a variable lift-to-drag ratio,

[0026] Where h is the flight altitude of the aircraft, H is the scale altitude, and ρ0 is the atmospheric density at sea level.

[0027] According to at least one embodiment of this application, in the above-described method for determining the cruise flight range of a hypersonic vehicle considering a variable lift-to-drag ratio, the dimensional altitude H is taken as 8500m.

[0028] This application has at least the following beneficial technical effects:

[0029] This paper presents a method for determining the cruise flight range of a hypersonic vehicle considering the variable lift-drag ratio. By substituting the modified effective weight and variable lift-drag ratio into the range integration formula, the integration process is made more scientific and accurate. This method enables accurate calculation of the cruise flight range of a hypersonic vehicle, providing effective support for the design and performance evaluation of hypersonic vehicles and helping to improve the vehicle's economy and efficiency. Attached Figure Description

[0030] Figure 1 This is a schematic diagram of the cruising flight trajectory of the aircraft provided in the embodiments of this application;

[0031] Figure 2 This is a schematic diagram of a method for determining the cruise flight range of a hypersonic vehicle considering a variable lift-to-drag ratio, provided in an embodiment of this application.

[0032] Figure 3 This is a schematic diagram illustrating the variation of the cruise flight range of an aircraft with the flight Mach number MA, as provided in the embodiments of this application.

[0033] To better illustrate this embodiment, some content in the accompanying drawings may be omitted, enlarged, or reduced. They are for illustrative purposes only and should not be construed as limiting the scope of this application. Detailed Implementation

[0034] To make the technical solution and advantages of this application clearer, the technical solution of this application will be described in a clearer and more complete manner below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are only some embodiments of this application, and are only used to explain this application, not to limit this application. It should be noted that, for ease of description, only the parts related to this application are shown in the accompanying drawings, and other related parts can be referred to the general design.

[0035] Furthermore, unless otherwise defined, the technical or scientific terms used in this application description shall have the ordinary meaning understood by one of ordinary skill in the art to which this application pertains. The word "comprising" as used in this application description indicates that the concept preceding the word encompasses the concepts listed following the word and their equivalents, without excluding other related concepts.

[0036] The initial weight W of the aircraft initial (kilograms);

[0037] The final weight W of the aircraft final (kilograms);

[0038] The flight speed of the aircraft, V (meters per second, m / s);

[0039] The specific impulse of the aircraft is Isp (seconds).

[0040] The zero-lift drag coefficient C of the aircraft D0 (dimensionless);

[0041] The shape-related constant k of the aircraft (dimensionless);

[0042] The dynamic pressure q of the aircraft ∞ (Pa);

[0043] Reference area S of the aircraft ref (square meters, m) 2 );

[0044] gravitational acceleration g (m / s²) 2 );

[0045] Earth's radius r (meters, meters);

[0046] The cruising range of the aircraft is R (meters, m).

[0047] The aircraft's cruise flight path, such as Figure 1 As shown, during the cruise of an aircraft, the conservation of energy is a fundamental physical law. Its total energy consists of potential energy and kinetic energy, and the rate of change of total energy equals the net thrust power. The rate of change of total energy can be expressed as:

[0048]

[0049] The left side of formula (1) It is the kinetic energy of the aircraft, which depends on the mass and speed of the aircraft. mgh on the left side of formula (1) is the gravitational potential energy of the aircraft, which is related to the mass, gravitational acceleration and altitude of the aircraft. (TD)·V on the right side of formula (1) represents the net thrust power, that is, the work done by the resultant force of thrust and drag per unit time.

[0050] Comparing the rate of change of total energy with the net thrust power, when lift equals gravity, the expression for total energy can be simplified to:

[0051]

[0052] For low-speed aircraft, assuming that lift and drag are equal and that speed and specific energy are constant, the famous Bregate range formula is derived:

[0053]

[0054] For hypersonic vehicles, their flight speeds are sufficient to make the centrifugal effect significant, necessitating a correction to the effective weight of hypersonic vehicles.

[0055]

[0056]

[0057]

[0058]

[0059] Right now:

[0060]

[0061] Scenario 1: With speed and lift-to-drag ratio remaining constant, the aircraft's range is:

[0062]

[0063] Case 2: When the speed remains constant but the lift-to-drag ratio changes, the expression for the lift-to-drag ratio is:

[0064]

[0065] Resistance C D It can be decomposed into zero-lift resistance C D0 and rising resistance The expression for the boost-to-drag ratio is:

[0066]

[0067] For formula (10) on C L Take the derivative and let:

[0068]

[0069] available:

[0070]

[0071]

[0072] The lift coefficient C at the maximum lift-to-drag ratio is obtained by sorting. L,maxL / D :

[0073]

[0074]

[0075] According to the hypersonic tangential wedge theory, n=2 is generally taken, which is applicable to the shape of slender hypersonic vehicles. Then the lift coefficient and the maximum lift-drag ratio at the maximum lift-drag ratio are respectively:

[0076]

[0077]

[0078] The conclusion is as follows:

[0079]

[0080]

[0081] get:

[0082]

[0083] Substituting formula (18) into formula (7), we get:

[0084]

[0085]

[0086]

[0087]

[0088] Right now:

[0089]

[0090] And because:

[0091]

[0092] have:

[0093]

[0094] We can obtain:

[0095]

[0096] Substituting formulas (23) and (25) into formula (22), we get:

[0097]

[0098]

[0099]

[0100]

[0101] Right now:

[0102]

[0103] Further refinement of formula (24):

[0104]

[0105] make have:

[0106]

[0107]

[0108]

[0109]

[0110] Substituting formulas (26) and (27) into formula (25), we get:

[0111]

[0112] And because:

[0113]

[0114] Substituting formula (31) into formula (30), we get:

[0115]

[0116]

[0117] Right now:

[0118]

[0119] Substituting formulas (28) and (29) into formula (33), we get:

[0120]

[0121] Substituting formula (16) into formula (34), we get:

[0122]

[0123] Formula (35) reflects the relationship between aircraft range and factors such as weight, lift-to-drag ratio, and dynamic pressure. h is the altitude, H is the scale altitude, which can be taken as 8500 meters, and ρ0 is the atmospheric density at sea level.

[0124] Based on the above, considering the variable lift-to-drag ratio, the cruise flight range of hypersonic vehicles can be calculated, and the calculation error of existing methods can be reduced, as follows.

[0125] Calculate the effective weight of the aircraft:

[0126] Considering the effect of centrifugal force on the aircraft's weight, the effective weight of the aircraft is calculated using the following formula:

[0127]

[0128] Where W is the weight of the aircraft, and the initial and final effective weights are calculated as follows:

[0129]

[0130]

[0131] Establish a mathematical model for the lift-to-drag ratio of the aircraft:

[0132] Based on the aerodynamic characteristics of the aircraft, the lift-to-drag ratio formula is determined as follows:

[0133]

[0134] Where n is a constant, which is generally taken as 2 for slender hypersonic vehicles.

[0135] To find the C value at the maximum lift-to-drag ratio L The value is obtained by differentiating the equation and setting the derivative to zero.

[0136]

[0137]

[0138] Integral calculation of cruise flight range:

[0139] Substituting the above calculation results into the cruise flight range integral formula, with the upper and lower limits of integration being correction parameters under the initial and final weights respectively, we obtain the cruise flight range of the aircraft:

[0140]

[0141] Based on the above, this application provides a method for determining the cruise flight range of a hypersonic vehicle considering a variable lift-to-drag ratio, such as... Figure 2 As shown.

[0142] Step 1: Calculate the aircraft's effective weight correction factor: Where V is the flight speed, g is the gravitational acceleration, and r is the Earth's radius.

[0143] The gravitational acceleration g is usually taken as 9.81 m / s^2, and the Earth's radius is usually taken as 6,371,000 m.

[0144] Step 2: Calculate the aircraft's maximum lift-to-drag ratio (L / D) max :

[0145]

[0146] Where k is the shape-related constant of the aircraft, C D0 This is the zero-lift drag coefficient of the aircraft.

[0147] The shape-related constant k of an aircraft can usually be taken as 1.

[0148] Step 3: Calculate the initial integration parameters x initial :

[0149]

[0150] Among them, W initial Let q be the initial weight of the aircraft. ∞ For the dynamic pressure of the aircraft, S ref This is the reference area of ​​the aircraft.

[0151]

[0152] Where h is the flight altitude of the aircraft, H is the scale altitude, and ρ0 is the atmospheric density at sea level.

[0153] The dimensional height H is typically taken as 8500m.

[0154] Step 4: Calculate the final integration parameter x final :

[0155]

[0156] Among them, W final This is the final weight of the aircraft.

[0157] Step 5: Calculate the aircraft's cruising range R:

[0158]

[0159] Where Isp is the specific impulse of the aircraft.

[0160] In a specific example, the initial weight W of the aircraft initial =10000kg, final weight W final =7000kg, flight speed V=1800m / s, specific impulse Isp=1200s, flight altitude h=30000m, zero-lift drag coefficient C D0 =0.02, shape-related constant k=1, dynamic pressure q ∞ =558489.8 Pa, reference area S ref =10m 2 And the acceleration due to gravity g = 9.81 m / s²2 The altitude is H = 8500m, and the atmospheric density at sea level is ρ0 = 1.225 kg / m³. 3 .

[0161] The method for determining the cruise flight range of a hypersonic vehicle considering a variable lift-to-drag ratio, disclosed in the above embodiments, is implemented as follows:

[0162] Calculate the effective weight correction factor for the aircraft:

[0163] The initial effective weight of the aircraft:

[0164] The final effective weight of the aircraft:

[0165] Establish a lift-to-drag ratio model:

[0166] When n = 2, the calculation yields:

[0167]

[0168]

[0169] Calculate the initial parameters for integration:

[0170] Calculate the final parameters of the integral:

[0171] Initial arctangent:

[0172] Final reversal:

[0173] Incorporate the cruise flight range of the aircraft into the calculation:

[0174]

[0175] The change in the aircraft's cruise range with Mach number MA was calculated as follows: Figure 3 As shown.

[0176] The method for determining the cruise flight range of a hypersonic vehicle considering a variable lift-to-drag ratio disclosed in the above embodiments has higher accuracy and stronger practical application value compared to existing methods. First, when calculating the effective weight, the influence of centrifugal effect on the vehicle's weight is introduced, correcting the deficiency in existing methods that do not consider centrifugal effect, making the calculation results closer to actual flight conditions, thereby improving the accuracy of cruise flight range calculation. Second, addressing the problem that existing methods typically treat the lift-to-drag ratio as a constant value, failing to accurately reflect the change in lift coefficient of a hypersonic vehicle under different weight states, a mathematical model of the lift-to-drag ratio is established, considering the influence of lift coefficient changes with weight, and introducing the concept of a variable lift-to-drag ratio. This allows for more accurate calculation of the lift-to-drag ratio under different weight states, further improving the reliability of the calculated cruise flight range results.

[0177] Furthermore, the method for determining the cruise flight range of a hypersonic vehicle considering the variable lift-to-drag ratio disclosed in the above embodiments makes the integration process more scientific and accurate by substituting the corrected effective weight and variable lift-to-drag ratio into the range integration formula. This enables accurate calculation of the cruise flight range of a hypersonic vehicle, providing effective support for the design and performance evaluation of hypersonic vehicles and helping to improve the economy and efficiency of the vehicle.

[0178] The technical solution of this application has been described in conjunction with the preferred embodiments shown in the accompanying drawings. Those skilled in the art should understand that the scope of protection of this application is obviously not limited to these specific embodiments. Without departing from the principles of this 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 all fall within the scope of protection of this application.

Claims

1. A method for determining the cruise flight range of a hypersonic vehicle considering a variable lift-to-drag ratio, characterized in that, include: Step 1: Calculate the aircraft's effective weight correction factor: Where V is the flight speed, g is the gravitational acceleration, and r is the Earth's radius; Step 2: Calculate the aircraft's maximum lift-to-drag ratio (L / D) max : Where k is the shape-related constant of the aircraft, C D0 This refers to the zero-lift drag coefficient of the aircraft. Step 3: Calculate the initial integration parameters x initial : Among them, W initial Let q be the initial weight of the aircraft. ∞ For the dynamic pressure of the aircraft, S ref The reference area of ​​the aircraft; Step 4: Calculate the final integration parameter x final : Among them, W final The final weight of the aircraft Step 5: Calculate the aircraft's cruising range R: Where Isp is the specific impulse of the aircraft.

2. The method for determining the cruise flight range of a hypersonic vehicle considering a variable lift-to-drag ratio according to claim 1, characterized in that, The gravitational acceleration g is taken as 9.81 m / s^2, and the Earth's radius is taken as 6,371,000 m.

3. The method for determining the cruise flight range of a hypersonic vehicle considering a variable lift-to-drag ratio according to claim 2, characterized in that, The shape-related constant k of the aircraft is set to 1.

4. The method for determining the cruise flight range of a hypersonic vehicle considering a variable lift-to-drag ratio according to claim 3, characterized in that, Where h is the flight altitude of the aircraft, H is the scale altitude, and ρ0 is the atmospheric density at sea level.

5. The method for determining the cruise flight range of a hypersonic vehicle considering a variable lift-to-drag ratio according to claim 4, characterized in that, The dimension height H is taken as 8500m.

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