A static stability margin calculation method considering the influence of aircraft center of gravity height and drag

Abstract

The application provides a static stability margin calculation method considering the height of the center of gravity of an airplane and the influence of resistance, and the method comprises the following steps: obtaining aerodynamic force data of the airplane relative to a moment reference point; calculating aerodynamic force parameters under a current angle of attack according to the aerodynamic force data, wherein the aerodynamic force parameters comprise a lift coefficient, a resistance coefficient, a lift line slope, a resistance line slope and a moment line slope; obtaining a projection of a dimensionless distance between the moment reference point and an actual center of gravity on an axis of the airplane body; constructing a static stability margin calculation formula containing the aerodynamic force parameters and the dimensionless distance; judging a static stability state of the airplane according to a calculation value of the static stability margin calculation formula, wherein if the calculation value is negative, it indicates that the airplane is statically stable, if the calculation value is zero, it indicates that the airplane is neutrally stable, and if the calculation value is positive, it indicates that the airplane is statically unstable. The method can guarantee the accuracy of the calculation of the static stability margin of the airplane under the condition of approaching the left boundary of the speed envelope and other boundary conditions.

Description

Technical Field

[0001] This application belongs to the field of aircraft aerodynamic design technology, and specifically relates to a method for calculating static stability margin that takes into account the influence of aircraft center of gravity height and drag. Background Technology

[0002] In aircraft design, static stability margin is one of the key parameters for aerodynamic layout design and handling stability design. A suitable static stability margin can ensure good flight quality and flight safety of the aircraft.

[0003] The traditional definition of aircraft static stability margin is the dimensionless distance between the aircraft's aerodynamic focus and center of mass. This distance typically refers to the relative position of the aircraft's center of mass and focus on the x-axis of the fuselage. This definition stems from the fact that, when defining longitudinal static stability moment for aircraft, the traditional approach assumes that the longitudinal static stability moment caused by changes in angle of attack is the moment generated by the aircraft's lift on its center of mass, i.e.:

[0004] (1)

[0005] Where, x F The focal point is located on the aircraft's x-axis. G Refers to the position of the center of gravity. It is the head-down torque. According to general rules, the head-down torque is negative, so a "-" sign is added to the right side of the above equation.

[0006] Put the negative sign in the above formula into parentheses and introduce the intermediate parameter. and b A For the aircraft span, equation (1) becomes:

[0007] (2)

[0008] The lift of an aircraft, Y, is: Substituting into the above formula, we get:

[0009] (3)

[0010] The above formula is similar to the general formula for aerodynamic torque. By comparison, we can see that:

[0011] (4)

[0012] derivative This is called the longitudinal static stability coefficient, generally referred to as longitudinal static stability, and the longitudinal static stability coefficient... It can also be written as:

[0013] (5)

[0014] Then we get: (6)

[0015] Comparing equations (4) and (5), we can see that:

[0016] (7)

[0017] derivative This is called the longitudinal static stability margin of the aircraft. The above formula shows that the static stability margin of the aircraft is the dimensionless distance between the focal point and the center of gravity. Generally, a negative static stability margin means the focal point is behind the center of gravity, and the aircraft is considered statically stable; a static stability margin of 0 means the aircraft is considered neutrally stable; a positive static stability margin means the focal point is in front of the center of gravity, and the aircraft is considered statically unstable.

[0018] Generally, when obtaining aerodynamic data experimentally, the position at 25% of the mean aerodynamic chord length is often chosen as the reference point for the experimental moment in low-speed wind tunnel tests. After obtaining the experimental data, the lift coefficient and moment coefficient are differentiated with respect to the angle of attack to obtain... and At this point, equation (6) yields the dimensionless distance of the focus relative to the torque reference point. Let... Let be the dimensionless distance from the torque reference point to the actual center of gravity. Then, the static stability margin relative to the actual center of gravity is:

[0019] (8)

[0020] Equation (8) shows that the traditional method only considers the longitudinal static stability moment caused by lift when calculating the static stability margin, and does not consider the static stability moment caused by drag. For general flight conditions, since the drag is small, the method of determining the static stability margin by Equation (8) will not cause a large error when performing engineering calculations. However, when calculating the static stability margin at the left boundary of the velocity envelope, since the aircraft is close to stall at this time, the drag increases sharply, which leads to a large error in the calculation of Equation (8). In particular, for early warning aircraft, due to the superposition of adverse factors such as high center of gravity, the calculation result of Equation (8) may even be opposite to the actual static stability. Summary of the Invention

[0021] The purpose of this application is to provide a method for calculating static stability margin that takes into account the effects of aircraft center of gravity height and drag, in order to solve or mitigate at least one of the problems in the prior art.

[0022] The technical solution of this application is: a method for calculating static stability margin considering the influence of aircraft center of gravity altitude and drag, the method comprising:

[0023] Acquire aerodynamic data of the aircraft relative to a torque reference point;

[0024] The aerodynamic parameters at the current angle of attack are calculated based on the aerodynamic data. The aerodynamic parameters include the lift coefficient, drag coefficient, lift line slope, drag line slope, and moment line slope.

[0025] The dimensionless distance between the moment reference point and the actual center of gravity projected onto the body axis is obtained based on the moment reference point and the actual center of gravity position.

[0026] A static stability margin calculation formula is constructed, which includes aerodynamic parameters and dimensionless distance. The static stability state of the aircraft is determined based on the calculated value of the static stability margin calculation formula. A negative calculated value indicates that the aircraft is statically stable, a zero calculated value indicates that the aircraft is neutrally stable, and a positive calculated value indicates that the aircraft is statically unstable.

[0027] Furthermore, the aerodynamic data were obtained through wind tunnel testing.

[0028] Furthermore, the dimensionless distance of the projection of the torque reference point onto the body axis is... ;

[0029] The dimensionless distance of the projection of the actual center of gravity onto the body axis is: ;

[0030] In the formula, and , respectively, are the projected distances between the torque reference point and the actual center of gravity on the body axis, and C is the average aerodynamic chord length.

[0031] Furthermore, the static stability margin calculation formula is as follows:

[0032]

[0033] In the formula, C m This is the aerodynamic torque coefficient;

[0034] CL is the lift coefficient;

[0035] CD is the drag coefficient;

[0036] CLα is the slope of the lift line;

[0037] CDα is the slope of the resistance line;

[0038] C m0 α is the slope of the moment line at the moment reference point;

[0039] α is the angle of attack.

[0040] Furthermore, the method also includes the derivation process of the static stability margin calculation formula:

[0041] When using aerodynamic data in practice, the aerodynamic torque at the torque reference point is corrected to the actual center of gravity position. Let CP be the torque reference point position, CG be the actual center of gravity position, CF be the aerodynamic focus position, and the lift coefficient CL, drag coefficient CD, and torque coefficient C be... m0 As the aerodynamic coefficient relative to the test torque reference point, the lift coefficient and drag coefficient can be decomposed onto the fuselage axis to obtain the force coefficients C on the x-axis and z-axis of the fuselage axis. FX C FZ They are respectively:

[0042]

[0043] By correcting the moment coefficient at the moment reference point to the actual center of gravity, we obtain the aerodynamic moment coefficient C at the actual center of gravity. m for:

[0044]

[0045] In the formula, △x and △z are dimensionless distances of the projection distance between the torque reference point and the actual center of gravity on the body axis.

[0046] Taking into account the effects of lift and drag, and according to the definition of static stability, the aerodynamic moment coefficient C is used. m The equation for the angle of attack Taking the derivative, we obtain the expression for static stability as follows:

[0047]

[0048] make , , According to the formula for static stability margin The expression for static stability is transformed to obtain the formula for calculating the static stability margin.

[0049] Furthermore, the method also includes the calculation process of the static stability margin formula:

[0050] Construct intermediate parameters A~E, let: ;

[0051] The intermediate parameters A~E are calculated based on the dimensionless distance obtained from the aerodynamic parameters.

[0052] The intermediate parameters A to E are summed to obtain the calculated value of the static stability margin.

[0053] The static stability margin determination method of this application takes into account the effects of drag and center of gravity height, avoids the defects of traditional calculation methods, and ensures the accuracy of static stability margin calculation when the aircraft approaches the left boundary of the velocity envelope and other boundary conditions. This enables the aircraft to have flight quality that matches the design expectations during the aerodynamic and handling characteristics design process, and ensures flight safety. Attached Figure Description

[0054] To more clearly illustrate the technical solutions provided in this application, the accompanying drawings will be briefly described below. Obviously, the drawings described below are merely some embodiments of this application.

[0055] Figure 1 This is a schematic diagram of the static stability margin calculation method of this application.

[0056] Figure 2 This is a schematic diagram of aerodynamic decomposition in the method of this application. Detailed Implementation

[0057] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions in the embodiments of this application will be described in more detail below with reference to the accompanying drawings.

[0058] To more accurately calculate the static stability margin of an aircraft, this application proposes a method for calculating the static stability margin that considers the influence of the aircraft's center of gravity altitude and drag, based on the concept of static stability. This method takes into account the influence of aircraft drag and center of gravity altitude in the design of the aircraft's static stability margin, making the calculation of the aircraft's static stability margin more accurate and thus ensuring flight safety.

[0059] like Figure 1 As shown, the static stability margin calculation method considering the effects of aircraft center of gravity altitude and drag provided in this application is as follows:

[0060] Step S1: Obtain the aerodynamic data of the aircraft relative to the moment reference point through wind tunnel testing;

[0061] Step S2: Calculate the lift coefficient CL, drag coefficient CD, lift line slope CLα, drag line slope CDα, and moment line slope C at the current angle of attack α based on the aerodynamic data. m0 Aerodynamic parameters such as α;

[0062] For example, in one embodiment of this application, a velocity point near the left boundary of the velocity envelope is selected, and the trim angle of attack α at this point is found to be 14°. Based on aerodynamic data, the lift coefficient CL, drag coefficient CD, lift line slope CLα, drag line slope CDα, and moment line slope C at this angle of attack can be calculated. m0 The value of α;

[0063] Step S3: Project the distance between the torque reference point and the actual center of gravity onto the body axis to obtain the projected distance between the torque reference point and the actual center of gravity on the body axis. and Then, dimensionless transformation is performed to obtain the dimensionless distance. and C is the average aerodynamic chord length;

[0064] In this embodiment, the calculated torque reference point is the dimensionless distance between the actual center of gravity and the body axis. and They are 0.15 and 0.31 respectively;

[0065] Step S4: Construct the static stability margin calculation formula, and calculate the static stability margin of the aircraft under the current state according to the static stability margin calculation formula, wherein the static stability margin calculation formula is:

[0066]

[0067] If the calculated value of the above formula is negative, it indicates that the aircraft is statically stable; if the calculated value is 0, it indicates that the aircraft is neutrally stable; if the calculated value is positive, it indicates that the aircraft is statically unstable.

[0068] In addition, this application also provides the derivation process for the static stability margin calculation formula in the above process, as follows:

[0069] In practical applications, the aerodynamic torque at the torque reference point needs to be corrected to the actual center of gravity position. Let CP be the torque reference point position, CG be the actual center of gravity position, and CF be the aerodynamic focus position. The lift coefficient CL, drag coefficient CD, and torque coefficient C... m0 The aerodynamic coefficient relative to the test torque reference point, such as Figure 2 As shown, by decomposing the lift coefficient and drag coefficient onto the fuselage axis, the force coefficients C on the x-axis and z-axis of the fuselage axis can be obtained. FX C FZ They are respectively:

[0070] (9)

[0071] By correcting the moment coefficient at the moment reference point to the actual center of gravity, we obtain the aerodynamic moment coefficient C at the actual center of gravity. m for:

[0072] (10)

[0073] In the formula, Δx and Δz are dimensionless distances representing the projected distances between the torque reference point and the actual center of gravity on the body axis.

[0074] According to the definition of static stability of an aircraft, if the aerodynamic moment caused by the change in angle of attack causes the aircraft to nose-down, then the aircraft is statically stable. Therefore, in practice, the composition of the static stability moment includes not only lift but also the influence of drag. Traditional calculation methods ignore the drag factor. This application, taking into account the influence of lift and drag, uses the moment coefficient C from Equation 10 according to the definition of static stability. m The equation for the angle of attack Taking the derivative, we obtain the expression for static stability as follows:

[0075] (11)

[0076] make , , According to the formula for static stability margin Transforming equation 11, we get:

[0077] (12)

[0078] Equation 12 takes into account the height of the center of gravity. The formula for calculating the static stability margin influenced by the drag coefficient CD. Generally, after the wind tunnel test, the lift coefficient CL, drag coefficient CD, lift line slope CLα, drag line slope CDα, and moment line slope C can be obtained. m0 Parameters such as α.

[0079] For the calculation of Equation 12, intermediate parameters A~E can be constructed, let:

[0080] (13)

[0081] For example, in this embodiment of the application, substituting the data obtained in the above embodiment into Equation 13, the intermediate parameters can be calculated as follows: A=-0.27, B=0.2205, C=0.1236, D=-0.0478, E=0.0183. Then, substituting into Equation 12, the static stability margin is calculated as:

[0082] =A+B+C+D+E=0.0446>0, which means that the aircraft is statically unstable at the current calculation point.

[0083] The static stability margin determination method of this application takes into account the effects of drag and center of gravity height, avoids the defects of traditional calculation methods, and ensures the accuracy of static stability margin calculation when the aircraft approaches the left boundary of the velocity envelope and other boundary conditions. This enables the aircraft to have flight quality that matches the design expectations during the aerodynamic and handling characteristics design process, and ensures flight safety.

[0084] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for calculating static stability margin considering the effects of aircraft center of gravity altitude and drag, characterized in that, The method includes: Acquire aerodynamic data of the aircraft relative to a torque reference point; The aerodynamic parameters at the current angle of attack are calculated based on the aerodynamic data. The aerodynamic parameters include the lift coefficient, drag coefficient, lift line slope, drag line slope, and moment line slope. The dimensionless distance between the torque reference point and the actual center of gravity is projected onto the body axis as follows: The dimensionless distance of the projection of the actual center of gravity onto the body axis is: In the formula, and These are the projected distances between the torque reference point and the actual center of gravity on the body axis, respectively, and C is the average aerodynamic chord length. A static stability margin calculation formula incorporating aerodynamic parameters and dimensionless distance is constructed. The static stability state of the aircraft is determined based on the calculated value of this formula. A negative calculated value indicates static stability, a zero calculated value indicates neutral stability, and a positive calculated value indicates static instability. The static stability margin calculation formula is as follows: ； In the formula, C m This is the aerodynamic torque coefficient; CL is the lift coefficient; CD is the drag coefficient; CLα is the slope of the lift line; CDα is the slope of the resistance line; C m0 α is the slope of the moment line at the moment reference point; α is the angle of attack.

2. The static stability margin calculation method considering the effects of aircraft center of gravity altitude and drag as described in claim 1, characterized in that, The aerodynamic data were obtained through wind tunnel testing.

3. The static stability margin calculation method considering the effects of aircraft center of gravity altitude and drag as described in any one of claims 1 to 2, characterized in that, The method also includes the derivation of the static stability margin calculation formula: When using aerodynamic data in practice, the aerodynamic torque at the torque reference point is corrected to the actual center of gravity position. Let CP be the torque reference point position, CG be the actual center of gravity position, CF be the aerodynamic focus position, and the lift coefficient CL, drag coefficient CD, and torque coefficient C be... m0 As the aerodynamic coefficient relative to the test torque reference point, the lift coefficient and drag coefficient can be decomposed onto the fuselage axis to obtain the force coefficients C on the x-axis and z-axis of the fuselage axis. FX C FZ They are respectively: ； By correcting the moment coefficient at the moment reference point to the actual center of gravity, we obtain the aerodynamic moment coefficient C at the actual center of gravity. m for: ； In the formula, △x and △z are dimensionless distances between the moment reference point and the actual center of gravity projected onto the body axis. Taking into account the effects of lift and drag, and according to the definition of static stability, the aerodynamic moment coefficient C is used. m The equation for the angle of attack Taking the derivative, we obtain the expression for static stability as follows: ； make , , According to the formula for static stability margin The expression for static stability is transformed to obtain the formula for calculating the static stability margin.

4. The static stability margin calculation method considering the effects of aircraft center of gravity altitude and drag as described in claim 3, characterized in that, The method also includes the calculation process for the static stability margin formula: Construct intermediate parameters A~E, let: ; The intermediate parameters A~E are calculated based on the dimensionless distance obtained from the aerodynamic parameters. The intermediate parameters A to E are summed to obtain the calculated value of the static stability margin.

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