Design method for longitudinal stability of wide-speed-range aircraft

Abstract

The invention discloses a method for designing the longitudinal stability of a wide-speed-domain aircraft, and provides key design parameters and design boundaries of the longitudinal stability based on the characteristics of wide flight speed domain, large flight height variation range and the like of the wide-speed-domain aircraft. According to the longitudinal stability design parameters and the boundary of the wide-speed-range aircraft, the stability requirement of the wide-speed-range aircraft under the whole flight mission profile can be well met, and therefore the difficulty of longitudinal stability, maneuverability and flight control design of the wide-speed-range aircraft is lowered.

Description

Technical Field

[0001] The present invention relates to the field of aircraft aerodynamic layout and handling and stability design, and particularly to a longitudinal stability design method for a wide-speed-range aircraft. Background Art

[0002] A wide-speed-range aircraft has a wide flight speed range and a large flight altitude change range. During the whole-range flight, the center of pressure and static stability change greatly, and the motion stability of the aircraft also changes significantly, resulting in difficult flight control. Therefore, there are high requirements for the aerodynamic layout and flight control coupling design of a wide-speed-range aircraft.

[0003] Since the longitudinal stability of a wide-speed-range aircraft shows significant non-linear changes with the changes of flight speed and flight altitude, the stability design under typical working conditions cannot meet the longitudinal stability requirements during the whole flight process. Therefore, the existing longitudinal stability design methods of aircraft cannot be effectively applied to the design of wide-speed-range aircraft. Summary of the Invention

[0004] The technical problem solved by the present invention is: overcoming the deficiencies of the prior art, providing a longitudinal stability design method for a wide-speed-range aircraft, and giving a longitudinal stability design method applicable to a wide-speed-range aircraft.

[0005] The technical solution of the present invention is: a longitudinal stability design method for a wide-speed-range aircraft, including the following steps:

[0006] (1) Establish a quantitative relationship between longitudinal static stability and dynamic stability. If the aircraft is longitudinally statically stable Cm α <0, Cm α is the pitch static stability derivative, then the longitudinal short-period motion of the aircraft is dynamically stable, and the short-period modal motion frequency is ω sp . If the aircraft is longitudinally statically unstable Cm α >0, then the longitudinal short-period motion of the aircraft diverges, and the aircraft is open-loop dynamically unstable. The double-amplitude time T 2 of the divergence of the angle of attack motion is used to measure the dynamic instability;

[0007] (2) Considering the longitudinal stability, maneuverability and flight control design difficulty of the aircraft comprehensively, give the boundary conditions that 1 / T 2 and ω sp should meet respectively, and establish a quantitative boundary of dynamic stability;

[0008] (3) Through the aerodynamic shape optimization of the aircraft and the reasonable design of the flight profile, make the aircraft meet the quantitative boundary of dynamic stability within the full speed range.

[0009] Further, in the step (2), 1 / T 2 and ω spThe boundary conditions to be satisfied are 1 / T 2 ≤2.5 s -1 , ω sp ≤5 rad / s.

[0010] Furthermore, in step (3), when the aircraft is statically unstable, 1 / T 2 is used as the evaluation parameter, and when the aircraft is statically stable, -ω sp is used as the evaluation parameter. Plot the above evaluation parameters along the flight profile to obtain the longitudinal dynamic stability region and dynamic instability region under the corresponding flight profile states, and then determine the maximum value of 1 / T 2 and the maximum value of ω sp to judge whether they are within the range of the dynamic stability quantification boundary requirements.

[0011] Furthermore, the short-period mode motion frequency is ω sp , and it is calculated by the following formula:

[0012]

[0013] where M α is the large derivative of pitch stability, and I zz is the pitch moment of inertia.

[0014] Furthermore, the doubling time T 2 , and it is calculated by the following formula:

[0015]

[0016] where M α is the large derivative of pitch stability, and I zz is the pitch moment of inertia.

[0017] The present invention also provides a longitudinal stability design system for a wide-speed-range aircraft, including:

[0018] The first module is used to establish the quantitative relationship between longitudinal static stability and dynamic stability. If the aircraft is longitudinally statically stable Cm α <0, Cm α is the pitch static stability derivative, then the longitudinal short-period motion of the aircraft is dynamically stable, and the short-period mode motion frequency is ω sp , if the aircraft is longitudinally statically unstable Cm α >0, then the longitudinal short-period motion of the aircraft diverges, and the aircraft is open-loop dynamically unstable. The doubling time T 2 of the angle-of-attack motion divergence is used to measure the dynamic instability;

[0019] The second module is used to respectively give 1 / T 2 and ωsp Establish the dynamic stability quantization boundary by satisfying the boundary conditions to be met.

[0020] The third module is used to make the aircraft satisfy the dynamic stability quantization boundary within the full speed range through the optimization of the aircraft aerodynamic configuration and the reasonable design of the flight profile.

[0021] Furthermore, in the second module, 1 / T 2 and ω sp The boundary conditions to be met are 1 / T 2 ≤2.5 s -1 , ω sp ≤5 rad / s.

[0022] Furthermore, in the third module, when the aircraft is statically unstable, 1 / T 2 is used as the evaluation parameter, and when the aircraft is statically stable, -ω sp is used as the evaluation parameter. Plot the above evaluation parameters along the flight profile to obtain the longitudinal dynamic stability region and dynamic instability region in the corresponding flight profile state, and then determine the maximum value of 1 / T 2 and the maximum value of ω sp , and judge whether they are within the range required by the dynamic stability quantization boundary.

[0023] Furthermore, the short-period mode motion frequency is ω sp , and it is calculated by the following formula:

[0024]

[0025] In the formula, M α is the large derivative of pitch stability, and I zz is the pitch moment of inertia.

[0026] Furthermore, the doubling time T 2 , and it is calculated by the following formula:

[0027]

[0028] In the formula, M α is the large derivative of pitch stability, and I zz is the pitch moment of inertia.

[0029] The advantages of the present invention compared with the prior art are as follows:

[0030] The present invention solves the technical problem that the existing longitudinal stability design method for aircraft cannot be effectively applied to the design of wide-speed-range aircraft. By taking the longitudinal short-period motion frequency of the aircraft and the double-amplitude time of the angle-of-attack motion divergence as key parameters, a quantitative relationship between the longitudinal static stability and dynamic stability of the wide-speed-range aircraft is established, and a longitudinal dynamic stability boundary constraint is established. The longitudinal dynamic stability is evaluated and designed along the typical flight profile. Furthermore, through the optimization of the aerodynamic shape and the reasonable design of the flight profile, the longitudinal stability of the aircraft is ensured to meet the established dynamic stability boundary requirements within the full speed range, effectively applied to the design of wide-speed-range aircraft, and the complexity of flight control design is reduced. Description of the Drawings

[0031] Figure 1 It is the nominal flight profile of a certain wide-speed-range aircraft in the embodiment of the present invention;

[0032] Figure 2 It is the change of dynamic stability of a certain wide-speed-range aircraft along the nominal flight profile in the embodiment of the present invention. Detailed Embodiment

[0033] To better understand the technical solution of the present invention, the following combines the drawings to specifically elaborate on the specific embodiments of the present invention.

[0034] The longitudinal stability design method of the wide-speed-range aircraft of the present invention has the following design steps:

[0035] (1) Establish a quantitative relationship between longitudinal static stability and dynamic stability

[0036] Longitudinal static stability characterizes the ability of the aircraft to return to the initial equilibrium position after being disturbed. From the perspective of attitude stability, it is desirable for the aircraft to be longitudinally statically stable. However, too large longitudinal static stability means that the aircraft is difficult to control and will also sacrifice certain flight performance, resulting in a decrease in the lift-to-drag ratio of the aircraft. Since the flight airspace and speed range of the wide-speed-range aircraft change greatly, the overall aircraft focus will move forward or backward significantly with the change of Mach number, making it difficult to achieve a full-course static stability design.

[0037] According to the definition, the focus is the point where the pitch moment increment is zero when the relative angle of attack changes along the X-axis of the aircraft body coordinate system, that is

[0038]

[0039]

[0040] In the above formula, l ref is the reference length of the aircraft, x MRC is the moment reference point, x ac is the focus position, Cm αis the pitch static stability derivative, is the pitch static stability derivative with respect to the relative moment reference point, Cz is the lift coefficient, Cz α is the derivative of the lift coefficient with respect to the angle of attack, Cm is the pitch moment coefficient, Cm MRC is the pitch moment coefficient about the moment reference point. The longitudinal static stability of the aircraft can be determined by the relative position between the focus and the center of mass of the aircraft. When the focus x ac is located in front of the center of mass, it means the aircraft is statically stable.

[0041] Static stability only reflects whether the aircraft has a tendency to return to the equilibrium state after being disturbed under static conditions. From a dynamic perspective, dynamic stability can better characterize the motion stability of the aircraft. In flight control design, more attention is paid to whether the dynamic stability of the closed-loop aircraft system meets the flight mission or control design requirements. For the longitudinal motion of the aircraft, in control augmentation design, the focus is mainly on the quality of the short-period mode characteristics, which is closely related to the stability of the aircraft attitude motion, while the long-period motion related to the trajectory motion is less concerned in aerodynamic layout design and flight control design.

[0042] After neglecting the long-period motion, the simplified second-order transfer function form describing the longitudinal short-period motion of the flight is:

[0043]

[0044]

[0045]

[0046] In the above formula, α is the angle of attack, δ e is the elevator, M δe is the large pitch control derivative, M α is the large pitch stability derivative, I zz is the pitch moment of inertia, ζ sp is the short-period damping, ω sp is the short-period mode motion frequency, is the dynamic pressure, S ref is the reference area, l ref is the reference length, Cm α is the pitch static stability derivative.

[0047] For a wide-speed-range aircraft, especially in the hypersonic flight phase, the pitch damping is very small. Therefore, in the above formula, ζ sp ≈0, and the stability of the short-period mode characteristic polynomial is determined by the sign of . If the aircraft is longitudinally statically stable (Cm α <0), then the short-period motion is dynamically stable, and the short-period mode motion frequency is ωsp If the aircraft is longitudinally statically unstable (Cm α > 0), the short-period motion will diverge, and the aircraft is open-loop dynamically unstable. The instability degree of the longitudinally dynamically unstable aircraft can be measured using the doubling time T 2 of the angle-of-attack motion divergence. The calculation method of the doubling time T 2 is as follows. First, simplify the pitch rotation motion equation of the aircraft, only consider the aerodynamic force caused by the angle of attack and the elevator deflection, ignore the damping moment, and assume There is:

[0048]

[0049] When the aircraft is longitudinally statically unstable, the transfer function from the elevator to the angle of attack is expressed as:

[0050]

[0051] In the above formula, Assume that the initial input of the system is zero. The time-domain solution of the angle-of-attack motion in the short-period mode has the following form:

[0052] α(t) = k(e bt + e -bt )

[0053] Ignore the exponentially stable term e -bt in the above formula, and assume that at time t 1 the angle-of-attack amplitude is α 1 , and at time t 2 the angle-of-attack amplitude is α 2 . There is:

[0054]

[0055] Divide the above two equations to obtain:

[0056]

[0057] The definition of the doubling time is T 2 = t 2 - t 1 . According to the above formula, the calculation formula of T 2 can be obtained as:

[0058]

[0059] Note that the calculation of the doubling time T 2 in the above formula requires M α > 0, that is, the aircraft is longitudinally statically unstable.

[0060] (2) Establish the dynamic stability quantification boundary

[0061] In modern aircraft design, the pursuit of longitudinal static stability design is not absolute, and static instability is also acceptable. If a longitudinal static stability design is fully adopted, when the static stability margin is too large, the required attitude trim and maneuvering control deflections will be relatively large, resulting in poor maneuverability and performance of the aircraft. If a static instability design is adopted, an excessive static instability degree also requires a relatively large trim deflection, and it is required that the response speed of the actuator is fast enough to suppress the divergence of the angle-of-attack motion, which leads to a high requirement for the closed-loop control bandwidth and may be difficult to meet in practice. In the ideal state, the longitudinal direction of the aircraft should be designed to be in a weakly statically unstable state. At this time, the aircraft has good maneuverability and can also achieve attitude trim and maneuvering control with relatively small deflections. For wide-speed-range aircraft, the flight speed changes in a large range. Therefore, there are both longitudinally statically stable and statically unstable operating points within the full speed range. Therefore, the coordinated design of the longitudinal stability margin within the full speed range is the key to the aerodynamic layout design of wide-speed-range aircraft.

[0062] The maximum double-amplitude divergence time T allowed for the aircraft 2 mainly depends on the ability constraints of the control surface drive mechanism (such as maximum deflection speed, acceleration, time delay, and bandwidth) and the maximum available deflection angle of the control surface. Obviously, T 2 must be greater than the time required for the control surface of the aircraft to deflect from zero to the maximum deflection angle, and an additional time margin is added to cope with the hysteresis and delay phenomena in the closed-loop flight control system, such as calculation delay. When analyzing the longitudinal static stability or instability degree of the aircraft along the nominal flight profile, the reciprocal of the double-amplitude divergence time T 2 and the short-period mode frequency ω sp can be used as these two parameters. When the aircraft is statically unstable, the reciprocal of T 2 is used as the evaluation parameter. When the aircraft is statically stable, the short-period mode frequency ω sp in the form of adding a negative sign (-ω sp , unit: rad / sec) is used as the evaluation parameter. In this way, by plotting the above evaluation parameters in a graph along the flight profile, the longitudinal dynamic stability region and dynamic instability region can be distinguished under different flight profile states.

[0063] When the double-amplitude divergence time T 2 is a small positive value, that is, the aircraft is in a weakly statically unstable state. At this time, the aircraft has the best maneuverability. However, according to the size scale, it is recommended that for aircraft with a total mass exceeding 1 ton, 1 / T 2 should not exceed 2.5 sec -1 , so as to more easily match a suitable control surface drive mechanism. When the evaluation parameter is negative, that is, the aircraft is longitudinally dynamically stable, the short-period frequency ω sp should not be too large either. For aircraft with a total mass exceeding 1 ton, it is recommended that it should satisfy ω sp≤5 rad / s, otherwise the maneuverability of the aircraft will decrease, it will be difficult to control, and a larger closed-loop control bandwidth and rudder surface size will be required.

[0064] (3) Through the optimization of the aircraft aerodynamic configuration and the reasonable design of the flight profile, the aircraft meets the dynamic stability quantification boundary within the full speed range.

[0065] Figure 1 The nominal flight profile of a certain wide speed range aircraft is given. Figure 2 For the variation of the dynamic stability of the wide speed range aircraft along the nominal flight profile, the following table shows the calculation results of the short period mode at typical state points of the wide speed range aircraft.

[0066]

[0067] It can be seen from the calculation results that the maximum amplitude doubling time of the short period mode of the wide speed range aircraft is in the hypersonic state (Ma = 8), T 2_max = 2.1 s, and the maximum frequency of the short period mode is in the transonic state (Ma = 1.1), ω sp_max = 3.46 rad / s, both of which meet the recommended dynamic stability boundary requirements. A smaller short period mode motion frequency means that a servo with a lower bandwidth can be selected, reducing the complexity of the flight control design.

[0068] The present invention also provides a longitudinal stability design system for a wide speed range aircraft, and the specific functions are realized by the foregoing method.

[0069] It can be understood that the present invention is described through embodiments. Those skilled in the art know that without departing from the spirit and scope of the present invention, various changes or equivalent replacements can be made to these features and embodiments. In addition, under the teaching of the present invention, these features and embodiments can be modified to adapt to specific situations without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed herein, and the embodiments that can fall within the scope of the claims of this application all belong to the scope protected by the present invention.

[0070] The content not detailedly described in the specification of the present invention belongs to the well-known technology of those skilled in the art.

Claims

1. A method for designing longitudinal stability of a wide-speed range aircraft, characterized in that: The steps include: (1) Establish the quantitative relationship between longitudinal static stability and dynamic stability. If the aircraft is longitudinally statically stable, Cm α <0, Cm α is the pitch static stability derivative, then the short-period longitudinal motion of the aircraft is dynamically stable, and the short-period modal motion frequency is ω sp , if the aircraft is longitudinally statically unstable Cm α >0, the short-period longitudinal motion of the aircraft diverges, and the aircraft is open-loop dynamically unstable. The dynamic instability is measured by the doubling time T2 of the divergence of the angle of attack motion; (2) Taking into account the longitudinal stability, maneuverability and flight control design difficulty of the aircraft, 1 / T2 and ω are given respectively. sp The boundary conditions that should be met should be used to establish the dynamic stability quantitative boundary; (3) Through the optimization of the aerodynamic shape of the aircraft and the rational design of the flight profile, the aircraft can meet the quantitative boundaries of dynamic stability over the entire speed range.

2. The method for designing longitudinal stability of a wide speed range aircraft according to claim 1, characterized in that: In step (2), 1 / T2 and ω sp The boundary condition to be met is 1 / T2≤2.5s -1 ,ω sp ≤5rad / s.

3. The method for designing longitudinal stability of a wide speed range aircraft according to claim 1, characterized in that: In step (3), when the aircraft is statically unstable, 1 / T2 is used as the evaluation parameter, and when the aircraft is statically stable, -ω sp As evaluation parameters, the above evaluation parameters are plotted along the flight profile to obtain the longitudinal dynamic stability area and dynamic instability area under the corresponding flight profile state, and then the maximum value of 1 / T2 and ω are determined. sp The maximum value of is determined to determine whether it is within the dynamic stability quantification boundary requirements.

4. The method for designing longitudinal stability of a wide speed range aircraft according to claim 1, characterized in that: The short-period modal motion frequency is ω sp , calculated by the following formula: Where M α is the large derivative of pitch stability, I zz is the pitch moment of inertia.

5. The method for designing longitudinal stability of a wide speed range aircraft according to claim 1, characterized in that: The doubling time T2 is calculated by the following formula: Where M α is the large derivative of pitch stability, I zz is the pitch moment of inertia.

6. A system for designing longitudinal stability of aircraft over a wide speed range, characterized in that: include: The first module is used to establish the quantitative relationship between longitudinal static stability and dynamic stability. If the aircraft is longitudinal statically stable Cm α <0, Cm α is the pitch static stability derivative, then the short-period longitudinal motion of the aircraft is dynamically stable, and the short-period modal motion frequency is ω sp , if the aircraft is longitudinally statically unstable Cm α >0, the short-period longitudinal motion of the aircraft diverges, and the aircraft is open-loop dynamically unstable. The dynamic instability is measured by the doubling time T2 of the divergence of the angle of attack motion; The second module is used to give 1 / T2 and ω according to the longitudinal stability, maneuverability and flight control design difficulty of the aircraft. sp The boundary conditions that should be met should be used to establish the dynamic stability quantitative boundary; The third module is used to ensure that the aircraft meets the quantitative boundary of dynamic stability in the entire speed range through the optimization of the aircraft's aerodynamic shape and the rational design of the flight profile.

7. The method for designing longitudinal stability of a wide speed range aircraft according to claim 6, characterized in that: In the second module, 1 / T2 and ω sp The boundary condition to be met is 1 / T2≤2.5s -1 ,ω sp ≤5rad / s.

8. The method for designing longitudinal stability of a wide speed range aircraft according to claim 6, characterized in that: In the third module, when the aircraft is statically unstable, 1 / T2 is used as the evaluation parameter, and when the aircraft is statically stable, -ω is used as the evaluation parameter. sp As evaluation parameters, the above evaluation parameters are plotted along the flight profile to obtain the longitudinal dynamic stability area and dynamic instability area under the corresponding flight profile state, and then the maximum value of 1 / T2 and ω are determined. sp The maximum value of is determined to determine whether it is within the dynamic stability quantification boundary requirements.

9. The method for designing longitudinal stability of a wide speed range aircraft according to claim 6, characterized in that: The short-period modal motion frequency is ω sp , calculated by the following formula: Where M α is the large derivative of pitch stability, I zz is the pitch moment of inertia.

10. The method for designing longitudinal stability of a wide speed range aircraft according to claim 6, characterized in that: The doubling time T2 is calculated by the following formula: Where M α is the large derivative of pitch stability, I zz is the pitch moment of inertia.

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