Longitudinal relaxation static stability margin design method of supersonic civil aircraft

Abstract

The invention discloses a longitudinal relaxation static stability margin design method suitable for a supersonic civil aircraft, which comprises the following steps: firstly, analyzing the longitudinal stability characteristic of the supersonic civil aircraft different from that of a conventional high subsonic transport aircraft; secondly, determining the design flight state of the relaxed static stability margin according to the change rule of the center of gravity and the focus position of the whole aircraft; thirdly, selecting a flight quality specification and a supersonic transport plane temporary airworthiness standard as a design basis for relaxing the static stability margin; then, based on the equivalence relation between the long-period dynamic stability and the fixed-load static stability, the relaxed constraint of the airworthiness standard on the static stability margin is determined; and finally, based on the corresponding relationship between the short-period mode and the operation expectation parameter, determining the relaxed constraint of the flight quality specification on the static stability margin. According to the design method, the technical problem that in the civil aircraft concept design stage, the supersonic civil aircraft lacks general stability margin relaxation constraint is solved, and the aircraft body operation stability characteristic meets the constraint conditions of the transient airworthiness standard and the flight quality specification of the supersonic transport aircraft at the same time.

Description

Technical Field

[0001] The present invention relates to the design of supersonic civil aircraft, and more particularly to a design method for relaxed static stability margin for optimizing the matching between center of gravity position and focal position in the conceptual design stage of civil aircraft based on special airworthiness requirements of supersonic civil aircraft. Background Art

[0002] The design of civil aircraft is usually divided into three main stages: conceptual design, preliminary design and detailed design. The conceptual design stage refers to the comprehensive conception of the designed aircraft according to the design requirements of the aircraft, forming one or several preliminary schemes that meet the design requirements. The main tasks of the conceptual design stage include preliminary design of aerodynamic layout, preliminary design of overall scheme, preliminary calculation and demonstration of performance, and preliminary estimation of aircraft weight, center of gravity position and moment of inertia. Many major decisions that have a global impact on civil aircraft design are made in the conceptual design stage, so the conceptual design stage is of great significance to civil aircraft.

[0003] Relaxation of static stability is a technical means to arrange and control the center of gravity of an aircraft during the conceptual design stage. It changes the relative position between the center of gravity and the focus of the entire aircraft by optimizing the design of aircraft components (such as wing position, horizontal tail or vertical tail area), thereby reducing the static stability margin of the aircraft and relaxing the static stability margin. The use of relaxed static stability design for large civil aircraft can effectively improve flight performance, reduce fuel consumption, and obtain significant economic benefits, thereby greatly enhancing the market competitiveness of the aircraft.

[0004] Supersonic civil aircraft need to relax the static stability design to keep the longitudinal static stability margin within a reasonable range of variation within the full flight envelope. Excessive longitudinal static stability margin will not only increase the trim angle of the longitudinal control surface, resulting in unacceptably high trim drag during supersonic flight, but will also reduce the flexibility of the aircraft's longitudinal movement, making the pitch acceleration process sluggish. In addition, although relaxing the longitudinal static stability design can bring economic benefits to supersonic civil aircraft, the design value of the longitudinal static stability margin is not allowed to be too low, otherwise it will cause the deterioration of short-period modes and the appearance of static instability under fixed loads.

[0005] The relaxation value of the longitudinal static stability margin is closely related to the configuration characteristics of the aircraft. For high-subsonic civil aircraft with conventional layout, when the relaxed static stability design is not adopted, the longitudinal static stability margin in the cruise state is generally 20%-30%. After the relaxed static stability design is adopted, the static stability margin can usually be relaxed to 5%-10%. Modern supersonic civil aircraft generally adopt a slender body layout with a small aspect ratio and a large sweep angle, and the wing plane shape is mainly a delta wing or an arrow wing. Multiple sets of elevator ailerons are usually arranged on the trailing edge of the wing, and a T tail or a V tail is used instead of a vertical tail to reduce the intensity of the rear body shock wave. In order to meet the design requirements of low sonic boom and low drag, the engine nacelles of small and medium-sized supersonic civil aircraft mainly adopt a tail-mounted layout, and the engines on both sides of the fuselage are close. The configuration characteristics of supersonic civil aircraft determine that the center of gravity of the whole aircraft is relatively far back, and the adjustable range of the longitudinal static stability margin is small. If the relaxed static stability margin range of conventional layout aircraft is directly referred to, it will be difficult to obtain ideal flight performance.

[0006] Civil aircraft must comply with the corresponding airworthiness regulations when designing for relaxed static stability. The current airworthiness standard adopted by my country for transport aircraft is the "Civil Aviation Regulations of China CCAR-25-R4", which still lacks clear quantitative clauses for relaxing static stability. In addition, the airworthiness regulations are aimed at conventional high-subsonic civil aircraft, and do not consider the particularity of supersonic civil aircraft in terms of airworthiness compliance requirements. At present, the only publicly published airworthiness regulation formulated for supersonic civil aircraft is the "Tentative Airworthiness Standards for Supersonic Transports" issued by the Federal Aviation Administration of the United States in January 1971, which is translated as "Tentative Airworthiness Standards for Supersonic Transports". This airworthiness standard takes into account the particularity of supersonic civil aircraft on the basis of the original high-subsonic transport aircraft airworthiness regulations, and proposes amendments to each clause in the high-subsonic transport aircraft airworthiness regulations, including amendments to the language description of the clauses, changes in the premise of airworthiness verification, changes and additions to qualitative or quantitative requirements, etc. The dynamic characteristics of supersonic civil aircraft after longitudinal relaxation of static stability design must meet the constraints of relevant regulations in the interim airworthiness standards for supersonic transport aircraft. In addition, since the requirements in the interim airworthiness standards for supersonic transport aircraft are still mainly qualitative descriptions, with only a few quantitative requirements, when designing the longitudinal relaxation of static stability margin for supersonic civil aircraft, it is also necessary to refer to the relevant evaluation criteria in the "Flying Qualities of Aircraft" compiled by Gao Jinyuan et al., the first edition in January 2003, so as to provide more comprehensive design constraints for the relaxation of longitudinal static stability margin. The flying quality of the aircraft is the most concerned issue for pilots and aircraft designers. To evaluate the quality of an aircraft, we must not only look at its flight performance (speed, altitude, range, flight time, etc.), aircraft structure, component strength and rigidity, and the quality of various airborne equipment, but also its flying quality. If the aircraft does not have good flying quality, even if it has good flight performance, it cannot be fully utilized.

[0007] In order to solve the longitudinal relaxed static stability design problem of supersonic civil aircraft in the conceptual design stage, a reasonable longitudinal relaxed static stability margin design method must be established for supersonic civil aircraft. This method should not only consider the special longitudinal stability design requirements of supersonic civil aircraft in the interim airworthiness standards for supersonic transport aircraft, but also refer to the aircraft flight quality specifications and use the quantitative evaluation indicators therein to give the main body flight quality level of supersonic civil aircraft under different stability margin design values, so as to establish a quantitative constraint boundary for the relaxation of the longitudinal static stability margin. Summary of the invention

[0008] In order to introduce airworthiness compliance requirements into the conceptual design stage of the aircraft and constrain the aircraft body handling stability characteristics after the stability margin changes through the flying quality specification, the present invention designs a supersonic civil aircraft longitudinal relaxed static stability margin design method based on the interim airworthiness standards and flying quality requirements of supersonic transport aircraft. The design method of the present invention includes the following steps:

[0009] In step 1, the longitudinal stability characteristics of supersonic civil aircraft, which are different from those of conventional high-subsonic transport aircraft, are analyzed;

[0010] Step 2: Determine the design flight state with relaxed static stability margin according to the change rules of the center of gravity and focus position of the whole aircraft;

[0011] Step 3: Select the flight quality specifications and interim airworthiness standards for supersonic transport aircraft as the design basis for relaxing the static stability margin;

[0012] Step 4: Based on the equivalent relationship between long-period dynamic stability and constant-load static stability, the relaxed constraints on static stability margin in airworthiness standards are determined;

[0013] Step 5 determines the relaxed constraints on static stability margin of flight quality specifications based on the correspondence between short-period modes and expected control parameters.

[0014] The design method of the present invention establishes a longitudinal static stability margin relaxation process that takes into account airworthiness compliance requirements and flight quality specification constraints. Based on the configuration and aerodynamic characteristics of supersonic civil aircraft, its longitudinal stability characteristics that are different from conventional layout aircraft are analyzed; and according to the change law of the center of gravity position and the focus position of the whole aircraft, the design flight state of the longitudinal relaxation of the static stability margin is determined; the relaxation of the longitudinal static stability margin is based on the equivalence relationship between the long-period mode and the static stability at fixed load, and the relaxation boundary of the longitudinal static stability margin in the transonic stage is established based on the correspondence between the characteristic roots of the short-period mode and the evaluation parameters of the CAP criterion, and the relaxation boundary of the longitudinal static stability margin in the take-off and supersonic cruise stages is established.

[0015] The technical effect of the method of the present invention is:

[0016] ① The method for designing the longitudinal relaxed static stability margin of a supersonic civil aircraft of the present invention can make the longitudinal stability characteristics of the supersonic civil aircraft body meet the airworthiness standards and flight quality specification requirements during the aircraft concept design stage, thereby saving the design cost of the aircraft.

[0017] ② The longitudinal relaxed static stability margin design method of a supersonic civil aircraft of the present invention can provide theoretical guidance for the center of gravity position design and fuel transmission scheme of a supersonic civil aircraft, thereby optimizing aircraft performance and improving design schemes, which is of great significance for promoting the smooth operation of supersonic civil aircraft.

[0018] ③ The method for designing the longitudinal relaxed static stability margin of a supersonic civil aircraft of the present invention can realize the design of the longitudinal static stability margin of different aircraft by changing the small disturbance linearization model of the supersonic civil aircraft, and has universality.

[0019] ④ The method for designing the longitudinal relaxed static stability margin of a supersonic civil aircraft of the present invention utilizes the "Interim Airworthiness Standards for Supersonic Transport Aircraft" and "Aircraft Flight Quality" to provide theoretical guidance for the design value of the longitudinal static stability margin, and the conclusion is reliable. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 It is a flow chart of the longitudinal relaxed static stability margin design of the supersonic civil aircraft of the present invention.

[0021] Figure 2 This is a three-dimensional diagram of the configuration and control surfaces of a supersonic civil aircraft.

[0022] Figure 2A This is a top view of the configuration and control surfaces of a supersonic civil aircraft.

[0023] Figure 3 This is a graph showing how the focal position of the entire aircraft changes with the flight Mach number.

[0024] Figure 4 It is the constraint boundary diagram of the CAP criterion on the short-period modal root locus during the takeoff phase.

[0025] Figure 5 It is the constraint boundary diagram of the CAP criterion on the short-period modal root trajectory in the supersonic cruise stage. DETAILED DESCRIPTION

[0026] The present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. The various parameter demonstrations listed are only preferred embodiments of the present invention. It should be noted that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention, and these improvements and modifications should also be considered as the protection scope of the present invention.

[0027] See also Figure 1 , Figure 2 , Figure 2A As shown, a method for designing a longitudinal relaxed static stability margin of a supersonic civil aircraft of the present invention comprises the following steps:

[0028] Step 1: Analysis of longitudinal stability characteristics of supersonic civil aircraft;

[0029] Before designing a supersonic civil aircraft with longitudinally relaxed static stability margin, it is necessary to analyze the difference between its longitudinal stability characteristics and those of conventionally arranged aircraft. Longitudinal stability characteristics include longitudinal static stability and longitudinal dynamic stability. Static stability refers to the initial tendency of the aircraft to automatically recover to its original equilibrium state after being subjected to some external transient disturbance, while dynamic stability refers to the whole process characteristics of whether the aircraft can recover to the reference state after being subjected to some external transient disturbance. An aircraft with dynamic stability must be statically stable. The longitudinal stability characteristics of an aircraft are mainly affected by configuration parameters such as wing position, wing shape, horizontal tail position, and horizontal tail area. The relevant aerodynamic parameters include zero-lift moment coefficient, longitudinal static stability derivative, lift line slope, and pitch damping derivative.

[0030] Due to the slender arrow-shaped wing layout, the lift line slope of the whole aircraft is significantly reduced, and the center of gravity is relatively far back, resulting in its longitudinal static stability margin being much smaller than that of conventional layout aircraft. In addition, supersonic civil aircraft use a smaller all-moving horizontal tail to replace the traditional horizontal tail, resulting in its weakened regulatory effect on the zero-lift moment coefficient and longitudinal static stability derivative. At the same time, due to the close distance between the aerodynamic focus of the all-moving horizontal tail and the center of gravity of the aircraft, the pitch damping of supersonic civil aircraft is seriously insufficient, and the short-period modal damping ratio will be lower than that of conventional layout aircraft.

[0031] like Figure 2 , Figure 2A As shown in the figure, a 20-seat small supersonic business jet is used as an example aircraft for explanation. The example aircraft adopts a slender arrow-shaped wing layout with a small aspect ratio and a large sweep angle, with a cruising speed of 1.8 Ma, a cruising altitude of 18 km, and a maximum take-off weight of 25 tons. The typical features of the example aircraft in configuration are: a slender nose, a long average aerodynamic chord length; large pitch and yaw axis moments of inertia, and a small roll axis moment of inertia; a T-tail layout, with redundant longitudinal and lateral control surfaces; the engine is tail-mounted, and the distance between the two engines is close.

[0032] For a longitudinally statically stable aircraft, two conditions must be met simultaneously to achieve balanced flight: one is that the aircraft can be in a balanced state before being disturbed, that is, it must be balanced at a positive angle of attack; the other is that the aircraft has a tendency to return to its original balanced state after being disturbed. The above two conditions are equivalent to the zero lift moment coefficient C of the entire aircraft. m0 is positive and the longitudinal static stability derivative C mα The aircraft's longitudinal static stability derivative C mα The expression is:

[0033]

[0034] C Lα is the slope of the lift line of the entire aircraft.

[0035] C m is the pitch moment coefficient of the whole aircraft.

[0036] C L is the lift coefficient.

[0037] is the pitch moment coefficient of the whole aircraft C m Lift coefficient C L The partial derivative of .

[0038] x ac is the dimensionless position of the global focus.

[0039] x cg It is the dimensionless position of the center of gravity of the entire machine.

[0040] K n is the longitudinal static stability margin of the aircraft, and K n =x ac -x cg , which can reflect the relative distance between the center of gravity and the focus of the aircraft.

[0041] In the present invention, C mα From the expression of C mα The value depends on C Lα and K n The product of, the lower the slope of the lift line of the whole aircraft, the closer the distance between the center of gravity and the focus, the smaller the value of the longitudinal static stability derivative will be.

[0042] In order to reduce the trim cost in the supersonic cruise phase, the longitudinal static stability margin K of supersonic civil aircraft is n The design value of is usually not too large. This is because when the flight speed increases to transonic and supersonic speeds, the focal position x of the entire aircraft ac There will be a significant backward shift. If the center of gravity position x cg If the distance from the focus is too far in front, the required trimming angle of the full-moving horizontal tail in the supersonic cruise phase will be large, which is likely to produce unacceptable high trim drag. The typical longitudinal aerodynamic parameter value of the example aircraft at a cruising altitude of 18 kilometers and a cruising speed of Mach 1.8 is C Lα =1.93, C mα = -0.15 and K n =7.8%; the longitudinal aerodynamic parameter value of the B747 aircraft at a cruising altitude of 10.6 kilometers and a cruising speed of 0.85 Mach is C Lα =4.9, C mα = -1.03 and K n =21%. It can be seen that the lift line slope, longitudinal static stability derivative and static stability margin of the example aircraft are all smaller than those of the B747 aircraft.

[0043] For conventional aircraft, the pitch damping moment of the whole aircraft is mainly provided by the horizontal tail, while the contribution of the wings, fuselage and other components is relatively small. Therefore, in the approximate estimation of the pitch damping derivative C mq Generally, only the pitch damping of the horizontal tail needs to be considered, and 10% to 25% is added based on the estimated results to consider the influence of the wing-body assembly. The approximate calculation expression of the aircraft's pitch damping derivative is:

[0044]

[0045] C mq is the pitch damping derivative.

[0046] C mq.t is the pitch damping derivative of the single horizontal tail.

[0047] V t is the air velocity at the horizontal tail.

[0048] V is the aircraft's flight speed. It reflects the blocking effect of the aircraft components in front of the horizontal tail on the airflow in the horizontal tail area.

[0049] C Lα.t is the slope of the horizontal tail lift line.

[0050] S t is the flat tail area.

[0051] l ht It is the horizontal tail force arm, that is, the longitudinal distance between the aerodynamic focus of the horizontal tail and the center of gravity of the aircraft.

[0052] S is the wing area.

[0053] c is the mean aerodynamic chord length.

[0054] In the present invention, the pitch damping derivative C of the whole aircraft is mq Proportional to the horizontal tail force arm l ht The square value and the flat tail area S t .

[0055] The example aircraft uses a smaller all-movable horizontal tail to replace the traditional horizontal tail, and the distance between the aerodynamic focus of the all-movable horizontal tail and the center of gravity of the aircraft is closer, that is, S t Value and l ht The values ​​are small, resulting in a small pitch damping of the aircraft. The pitch damping derivative value of the example aircraft in its supersonic cruise state is -1.3, which is only 6.3% of that of the B747 aircraft.

[0056] The short-period modal motion of an aircraft is dominated by the changes in the angle of attack and pitch rate, which is related to the aircraft's control response and flight safety, so it needs to be paid special attention to. sp and damping ratio ξ spThe expression is:

[0057]

[0058] ω sp is the short-period modal frequency.

[0059] ξ sp is the short period damping ratio.

[0060] M α is the derivative of the pitching moment with respect to the angle of attack.

[0061] Z α is the derivative of lift with respect to the angle of attack.

[0062] M q is the derivative of the pitch moment with respect to the pitch angular velocity.

[0063] Since the lift line slope and pitch damping of the example aircraft are small, Z α M q is a small quantity, so the short-period modal frequency ω in the above formula is sp The expression can be simplified to:

[0064]

[0065] ρ is the air density.

[0066] V is the aircraft flying speed.

[0067] C mα is the longitudinal static stability derivative of the aircraft.

[0068] σ is the ratio of the pitch axis moment of inertia to the product of the wing area and the mean aerodynamic chord length, and

[0069] I y is the pitch axis moment of inertia.

[0070] S is the wing area.

[0071] c is the aerodynamic chord length.

[0072] q is the flight pressure, and

[0073] The short-period modal frequency and damping ratio of the example aircraft at a cruising altitude of 18 kilometers and a cruising speed of 1.8 Mach are ω sp =1.0rad / s,ξ sp =0.23; the short-period modal frequency and damping ratio of the B747 aircraft at a cruising altitude of 10.6 km and a cruising speed of 0.85 Mach are ω sp =0.96rad / s,ξ sp= = 0.34. It can be seen that the short-period modal frequency of the example aircraft is close to that of the conventional layout aircraft, but the damping ratio is insufficient. Since the longitudinal static stability derivative value of the example aircraft in the cruise stage is small, only 14% of that of the B747 aircraft, even if the cruise dynamic pressure value of the example aircraft is high, its |qC mα |The value is still smaller than that of the B747 aircraft. In addition, the B747 aircraft is a 440-ton large wide-body passenger aircraft, while the example aircraft is only a 25-ton small business jet. Although the pitch axis moment of inertia of the example aircraft is larger than its roll axis and yaw axis, its value is still only 10% of that of the B747 aircraft, resulting in a smaller σ value. However, the reduction of σ value will make the two aircraft The values ​​are similar, thus offsetting the effect of the reduction of static stability derivatives on the short-period modal frequencies.

[0074] Step 2: determine the design flight state for longitudinal relaxation of static stability margin;

[0075] The size of the longitudinal static stability margin depends on the relative distance between the center of gravity and the focus. The longitudinal static stability margin value of supersonic civil aircraft will change in different flight states. Therefore, when relaxing the longitudinal static stability margin design based on airworthiness standards and flight quality specifications, it is necessary to select the closest distance, the farthest distance and a typical intermediate state between the two as the design point according to the change law of the center of gravity position and the focus position in the full flight envelope, so as to ensure that the design result of the longitudinal static stability margin can fully reflect the change range of the stability margin of the supersonic civil aircraft in the full flight envelope.

[0076] The size of the longitudinal static stability margin depends on the relative distance between the center of gravity and the focus. In order to determine the design flight state for longitudinal relaxation of the static stability margin, it is necessary to understand the change pattern of the focus position of the entire aircraft with the flight Mach number.

[0077] like Figure 3 As shown in the figure, the focus of the whole aircraft is the most forward at 56.5%c in the low-speed flight stage of 0.2Ma. In the transonic flight stage, the focus of the whole aircraft moves backward sharply under the action of the shock wave, and reaches the rear limit of 65.5%c at 1.14Ma. After that, as the example aircraft enters the supersonic flight stage, the weakening of the shock wave effect causes the focus of the whole aircraft to gradually move forward, and reaches 60.6%c in the cruise stage of 1.8Ma.

[0078] In terms of the change in the center of gravity position, since the example aircraft adopts an arrow-shaped wing layout, its load and fuel are mainly distributed at the rear of the fuselage. Without considering the use of a trim tank to adjust the center of gravity position, the rear limit of the center of gravity position of the example aircraft usually appears during the takeoff phase. As the load and fuel are continuously consumed, the center of gravity position of the entire aircraft will continue to move forward until it reaches the front limit during the landing phase.

[0079] Based on the above changes in the focus position and the center of gravity position of the aircraft, it can be seen that the longitudinal static stability margin of the example aircraft has three key design states, namely takeoff, transonic flight and supersonic cruise. In the takeoff stage, the center of gravity of the aircraft is the most rearward and the focus position of the aircraft is the most forward. ac -x cg |The value reaches the minimum, corresponding to K n In the transonic stage, due to the sharp backward movement of the focus position of the whole aircraft, |x ac -x cg | value reaches the maximum, corresponding to K n The supersonic cruise is the key flight state for the aircraft configuration scheme and aerodynamic layout design. Although the center of gravity and focus position of the aircraft in this state are not at x cg With x ac At the extreme point of the range of change, but its K n The design value is closely related to the economic performance of the aircraft, so it still needs to be paid attention to.

[0080] The Interim Airworthiness Standards for Supersonic Transport Aircraft are adopted as the basis for relaxing the longitudinal static stability margin. Based on the equivalent relationship between long-period modes and fixed-load static stability, it is proposed that in the transonic stage where the aircraft has speed static instability, the relaxation value of the longitudinal static stability margin shall not be lower than the degree of speed instability.

[0081] Aircraft Flying Qualities is adopted as the basis for relaxing the longitudinal static stability margin. Based on the correspondence between the short-period modal characteristic roots and the CAP criterion assessment parameters, it is proposed that during the takeoff and supersonic cruise phases when the aircraft has speed static stability, the relaxed value of the longitudinal static stability margin shall not cause the short-period modal root trajectory to exceed the restricted area enclosed by the secondary boundary of the CAP criterion.

[0082] Step 3: Select the basis for relaxing the longitudinal static stability margin;

[0083] The relaxation limit of the longitudinal static stability margin needs to be determined in accordance with the "Interim Airworthiness Standards for Supersonic Transport Aircraft" and the "Aircraft Flight Quality".

[0084] The Transport Aircraft Design Manual provides a relaxation requirement for the longitudinal static stability margin of high subsonic civil aircraft. The manual states that civil aircraft can appropriately relax the static stability degree under the premise of ensuring longitudinal static stability, but the doubling time of the long-period modal instability root should be no more than 6 seconds. This requirement indicates that the high subsonic civil aircraft must be longitudinally statically stable, that is, K n The value must be positive, but its long-period mode allows for a small amplitude divergence. The static stability margin K can be inferred by using the condition that the doubling time of the characteristic root of the long-period mode divergence is no more than 6 seconds. n design requirements.

[0085] Unlike high-subsonic civil aircraft, the Interim Airworthiness Standards for Supersonic Transport Aircraft states in Article 181, “Longitudinal and Lateral Dynamic Stability” that in order to prevent the crew from paying too much attention to the aircraft’s maintenance of the flight profile and altitude, the long-period modes of supersonic civil aircraft are not allowed to be dynamically unstable. Therefore, the relaxation of the longitudinal static stability margin of supersonic civil aircraft must be limited by the long-period modal dynamic stability.

[0086] Since the "Interim Airworthiness Standards for Supersonic Transport Aircraft" does not impose quantitative constraints on the short-period modes of the aircraft body, the design process of longitudinal relaxation of static stability margins also needs to refer to the "Aircraft Flight Quality". According to the CAP (Control Anticipation Parameter) criteria in the flight quality specifications, the body CAP criteria assessment level of supersonic civil aircraft within the full flight envelope shall not be lower than Level 2. Since the assessment parameters of this criterion can establish a corresponding functional relationship with the frequency and damping ratio of the short-period modes, the requirements for the CAP criterion assessment level are essentially requirements for the short-period modal characteristics of the aircraft.

[0087] Step 4: Determine the design constraints of the airworthiness standards on the longitudinal static stability margin;

[0088] The design constraints of the longitudinal static stability margin in the airworthiness standards need to be established through the static stability of the aircraft under load. Unlike high subsonic civil aircraft, the Interim Airworthiness Standards for Supersonic Transport Aircraft clearly stipulate that in order to prevent the crew from paying too much attention to the aircraft's maintenance of the flight profile and altitude, long-period modes within the full flight envelope of supersonic civil aircraft are not allowed to be dynamically unstable.

[0089] The dynamic stability of the long-period mode is equivalent to the static stability of the aircraft at constant load. The derivative of static stability at constant load can be expressed as the sum of the longitudinal static stability margin and the speed instability. Supersonic civil aircraft have speed instability in the transonic flight stage. If the design value of the longitudinal static stability margin is too low and less than the speed instability, the aircraft will show constant load instability and the long-period mode will diverge. Therefore, the relaxation boundary of the longitudinal static stability margin constrained by the airworthiness standard can be obtained by calculating the speed instability.

[0090] Determining the design constraints of the longitudinal static stability margin in airworthiness standards requires the use of the equivalent relationship between long-period modal dynamic stability and aircraft static stability at fixed loads.

[0091] The three-degree-of-freedom model is used to approximate the long-period mode, and the simplified expression of the coefficient matrix in the longitudinal small perturbation linearization model is obtained as follows:

[0092]

[0093] X Vis the derivative of the axial force with respect to the velocity.

[0094] X a is the derivative of the axial force with respect to the angle of attack.

[0095] g is the acceleration due to gravity.

[0096] Z V is the derivative of the normal force with respect to the velocity.

[0097] Z α is the derivative of lift with respect to the angle of attack.

[0098] M V is the derivative of the pitching moment with respect to velocity.

[0099] M α is the derivative of the pitching moment with respect to the angle of attack.

[0100] Let |λI-A lon |=0, the expression of the long-period mode approximate characteristic equation is obtained as follows:

[0101]

[0102] λ is the long-period modal characteristic root.

[0103] I is a 4×4 unit matrix substitution symbol.

[0104] A lon It is a simplified coefficient matrix substitute for the linearized model of small longitudinal disturbances.

[0105] The above long-period modal approximate characteristic equation takes into account the derivative of the pitch moment with respect to velocity: V When the Mach number is lower than 0.6, the compression effect of the air is not obvious. V is very small and can generally be ignored. However, during transonic cruise flight, the M V If it is large, it will obviously affect the long-period modal characteristics.

[0106] From formula (6), we can know that the condition for long-period modal stability of the aircraft is:

[0107]

[0108] After using dimensionless aerodynamic derivative processing, the long-period modal stability condition of the aircraft is equivalent to:

[0109]

[0110] C mα is the longitudinal static stability derivative of the aircraft.

[0111] C Lα is the slope of the lift line of the entire aircraft.

[0112] C m,M is the derivative of the pitching moment coefficient with respect to the Mach number.

[0113] M is the flight Mach number.

[0114] is the trim drag coefficient.

[0115] C L,M is the derivative of the lift coefficient with respect to the Mach number.

[0116] is the trim lift coefficient.

[0117] The lift line slope C of a general aircraft Lα The typical value is 3-6 ( / rad), and the drag coefficient The typical range is 0.01-0.05, so According to the Prandtl-Glauert transformation, at high subsonic speeds, neglect and C L,M After that, formula (8) can be further simplified as:

[0118]

[0119] On the other hand, the static stability derivative under load is defined as:

[0120]

[0121] C m is the pitching moment coefficient.

[0122] M is the flight Mach number.

[0123] C L is the lift coefficient.

[0124] n is the flight overload.

[0125] The necessary and sufficient condition for the aircraft to have constant load static stability is that the above constant load static stability derivative is always negative. When the aircraft is in trimmed flight, the overload satisfies n = 1, that is, the lift and gravity are balanced, then:

[0126]

[0127] L is the lift of the aircraft.

[0128] ρ is the air density.

[0129] a is the speed of sound.

[0130] M is the flight Mach number.

[0131] s is the reference area.

[0132] C L is the lift coefficient.

[0133] W is the weight of the aircraft.

[0134] In balanced flight, ρ, a, S, and W are all constants, so the balance equation of lift and gravity can be rewritten as:

[0135]

[0136] C L is the lift coefficient.

[0137] M is the flight Mach number.

[0138] Differentiating both sides of formula (12) yields:

[0139]

[0140] is the trim lift coefficient.

[0141] Substituting formula (13) into the definition of the static stability derivative under constant load, the judgment condition for static stability under constant load can be obtained as follows:

[0142]

[0143] C m is the pitching moment coefficient.

[0144] C m,M is the derivative of the pitch moment coefficient with respect to the flight Mach number.

[0145] M is the flight Mach number.

[0146] C L is the lift coefficient.

[0147] Comparing formula (9) with formula (14), it can be seen that the dynamic stability of the long-period mode and the static stability at constant load have the same judgment conditions. Therefore, the requirements for the dynamic stability of the long-period mode in the "Interim Airworthiness Standards for Supersonic Transport Aircraft" can also be equivalent to the requirements for the static stability at constant load.

[0148] During takeoff and supersonic cruise, supersonic civil aircraft has static speed stability, namely C m,M > 0. And because the aircraft itself is longitudinally statically stable, that is, K n >0, so In the transonic flight stage, affected by the air compression effect, the focus of the whole aircraft will move backward sharply, and the aircraft will have speed static instability, that is, C m,M <0. If the longitudinal static stability margin Kn The design value is too low, less than the speed instability The aircraft will show static instability at fixed load, and the long-period modes will also diverge. Therefore, the design constraint of the longitudinal static stability margin in the airworthiness standard is K in the transonic stage. n The design value shall not be less than

[0149] Step 5: Determine the constraints of the flying quality specifications on the longitudinal static stability margin;

[0150] The design constraints of the longitudinal static stability margin in the flight quality specification need to be established through the frequency and damping ratio of the short-period mode. When the longitudinal static stability margin of the aircraft is low, the short-period modal frequency is also low, and the aircraft's response speed to the longitudinal control input will be slower. If the longitudinal static stability is improved entirely by relying on the fly-by-wire flight control system, the stability margin of the closed-loop system may be reduced, and even cause safety problems such as control surface deflection saturation. Therefore, when relaxing the longitudinal static stability margin, it is necessary to comprehensively consider the changes in the short-period modal characteristics and determine the reasonable range of changes in the short-period modal frequency and damping ratio.

[0151] Since the airworthiness regulations do not impose quantitative constraints on the short-period modal characteristics of supersonic civil aircraft bodies, the CAP criteria in Chapter 3, Section 3.5 of Aircraft Flying Quality are referred to, requiring that in the process of relaxing the longitudinal static stability margin, the CAP criteria assessment level of the transport aircraft body shall not be lower than Level 2. Then, based on the corresponding relationship between the CAP criteria assessment parameters and the short-period modal frequency and damping ratio, the longitudinal static stability margin relaxation boundary constrained by the flying quality specifications can be obtained.

[0152] Determining the design constraints of the flight quality specifications on the longitudinal static stability margin requires the use of the correspondence between the CAP criterion assessment parameters and the short-period modal frequency and damping ratio.

[0153] The CAP criterion uses the pilot's control expectation parameters to evaluate the aircraft's longitudinal short-period characteristics. The evaluation results can reflect the aircraft's longitudinal stability and maneuverability. The control expectation parameters of the aircraft itself are defined as:

[0154]

[0155] ω sp is the short-period modal frequency.

[0156] g is the acceleration due to gravity.

[0157] V * To balance the flight speed.

[0158] Z α is the derivative of lift with respect to the angle of attack.

[0159] m is the mass of the aircraft.

[0160] When this assessment criterion is adopted, the flight quality level is defined by the relationship between the short-period damping ratio of the aircraft body and the control expectation parameter. In the parameter requirements of the CAP criterion, the upper limit of the control expectation value and the lower limit of the damping ratio value mainly reflect the stability requirements of the aircraft. A larger control expectation value and a smaller damping ratio indicate that the aircraft is not stable enough, and a small manipulation by the pilot can lead to a violent pitch response. The lower limit of the control expectation value and the upper limit of the damping ratio value mainly reflect the maneuverability requirements of the aircraft. A smaller control expectation value and a larger damping ratio indicate that the aircraft has an excessive stability margin, a relatively slow pitch response, and the pilot needs to control the pitch movement of the aircraft through large manipulations.

[0161] According to the Aircraft Flight Quality, the CAP rating of supersonic civil aircraft within the full flight envelope shall not be lower than Level 2. Specifically, for field flight phases such as takeoff, approach, and landing, the aircraft body should meet CAP>0.05, 0.25<ξ sp <2.0. Combined with the desired control parameter and the short-cycle frequency ω in equation (15), sp The corresponding relationship between , we can get the constraint condition of the second-level flight quality level on the short-period mode in the take-off stage as follows:

[0162]

[0163] ω sp is the short-period modal frequency.

[0164] ξ sp is the short period damping ratio.

[0165] Similarly, for non-field flight phases such as climb, supersonic cruise, and descent, the aircraft body should meet CAP>0.038, 0.3<ξ sp <2.0, so in the supersonic cruise state, the constraints of the second-level flight quality level on the short-period mode are:

[0166]

[0167] The real part Re, imaginary part Im and frequency ω of the short-period modal characteristic root sp and damping ratio ξ sp The corresponding relationship is:

[0168]

[0169] i is the imaginary unit.

[0170] When the frequency ω sp and damping ratio ξ spAfter the design requirements are determined, the short-period characteristic root value interval constrained by the flight quality specifications can be drawn in the complex plane, such as Figure 4 and Figure 5 shown.

[0171] exist Figure 4 and Figure 5 In the figure, the horizontal axis is the real axis, the vertical axis is the imaginary axis, and the boundary composed of the black solid line and the red dotted line divides the complex plane into two parts, left and right. Among them, the black solid line represents the secondary flight quality for the short period frequency ω sp The red dotted line represents the constraint boundary of the secondary flight quality for the short-period damping ratio ξ sp When the short-period characteristic root of a supersonic civil aircraft is located at Figure 4 and Figure 5 When the short-period modal characteristic root is located in the left area of ​​, the CAP criterion assessment level of the supersonic civil aircraft body is level 2 or level 1. Figure 4 and Figure 5 When it reaches the right area in the figure, the CAP rating of the supersonic civil aircraft has been reduced to level three.

[0172] In the takeoff and supersonic cruise states, the root loci of the short-period mode changing with the longitudinal static stability margin are plotted on Figure 4 and Figure 5 In the calculation, record the intersection of the root locus and the secondary flight quality boundary line, as well as the longitudinal static stability margin value corresponding to the intersection. Finally, the design constraint of the longitudinal static stability margin in the flying quality specification is K for takeoff and supersonic cruise. n The design value shall not be less than

Claims

1. A method for designing longitudinal relaxed static stability margin of supersonic civil aircraft, which is applied in the conceptual design stage of civil aircraft; it is characterized by The following steps are included: Step 1: Analysis of longitudinal stability characteristics of supersonic civil aircraft; For a longitudinally statically stable aircraft, two conditions must be met simultaneously to achieve trimmed flight; First, the aircraft must be in a balanced state before being disturbed, that is, it must be trimmed at a positive angle of attack; Second, the aircraft has a tendency to return to its original equilibrium state after being disturbed; The above two conditions are equivalent to the zero lift moment coefficient C of the whole machine. m0 is positive and the longitudinal static stability derivative C mα Negative; the aircraft's longitudinal static stability derivative C mα The expression is: C Lα is the lift line slope of the whole aircraft; C m is the pitch moment coefficient of the whole aircraft; C L is the lift coefficient; is the pitch moment coefficient of the whole aircraft C m Lift coefficient C L The partial derivative of x ac is the dimensionless position of the global focus; x cg is the dimensionless position of the center of gravity of the whole machine; K n is the longitudinal static stability margin of the aircraft, and K n =x ac -x cg , which can reflect the relative distance between the center of gravity and the focus of the aircraft; The approximate calculation expression of the pitch damping derivative of the aircraft is: C mq is the pitch damping derivative; C mq.t is the pitch damping derivative of the single horizontal tail; V t is the air velocity at the horizontal tail; V is the aircraft's flight speed; ratio It reflects the blocking effect of the aircraft components in front of the horizontal tail on the airflow in the horizontal tail area; C Lα.t is the slope of the horizontal tail lift line; S t is the horizontal tail area; l ht is the horizontal tail moment arm, i.e. the longitudinal distance between the aerodynamic focus of the horizontal tail and the center of gravity of the aircraft; S is the wing area; c is the average aerodynamic chord length; The short-period modal frequency ω of the aircraft sp and damping ratio ξ sp The expression is: ω sp is the short-period modal frequency; ξ sp is the short-period damping ratio; M α is the derivative of the pitching moment with respect to the angle of attack; Z α is the derivative of lift with respect to the angle of attack; M q is the derivative of the pitch moment with respect to the pitch angular velocity; Simplified short-period modal frequency ω sp The expression is: ρ is the air density; V is the aircraft flight speed; C mα is the longitudinal static stability derivative of the aircraft; σ is the ratio of the pitch axis moment of inertia to the product of the wing area and the mean aerodynamic chord length, and I y is the pitch axis moment of inertia; S is the wing area; c is the aerodynamic chord length; q is the flight pressure, and Step 2: determine the design flight state for longitudinal relaxation of static stability margin; There are three key design states for longitudinal static stability margin, namely take-off, transonic flight and supersonic cruise; During takeoff, the center of gravity of the aircraft is at the rear and the focus of the aircraft is at the front. ac -x cg |The value reaches the minimum, corresponding to K n The minimum design value of In the transonic stage, due to the sharp backward movement of the focus position of the whole aircraft, |x ac -x cg | value reaches the maximum, corresponding to K n The maximum design value of The center of gravity and focus position in supersonic cruise state are not at x cg With x ac At the extreme point of the variation range, K is also considered n The design value of Step 3: Select the basis for relaxing the longitudinal static stability margin; Set the relaxation boundary of longitudinal static stability margin; dynamic instability is not allowed in the long-period mode of supersonic civil aircraft; In the design process of longitudinally relaxing the static stability margin, the evaluation level of the expected parameter criteria for the body control of supersonic civil aircraft within the full flight envelope shall not be lower than Level 2; Step 4: Determine the design constraints of the airworthiness standards on the longitudinal static stability margin; The three-degree-of-freedom model is used to approximate the long-period mode, and the simplified expression of the coefficient matrix in the longitudinal small perturbation linearization model is obtained as follows: X V is the derivative of axial force with respect to velocity; X a is the derivative of the axial force with respect to the angle of attack; g is the acceleration due to gravity; Z V is the derivative of the normal force with respect to velocity; Z α is the derivative of lift with respect to the angle of attack; M V is the derivative of the pitching moment with respect to velocity; M α is the derivative of the pitching moment with respect to the angle of attack; Let |λI-A lon |=0, the expression of the long-period mode approximate characteristic equation is obtained as follows: λ is the long-period modal characteristic root; I is a 4×4-order identity matrix substitution symbol; A lon It is a simplified coefficient matrix substitute for the linear model of small longitudinal disturbances; From formula (6), we can know that the condition for long-period modal stability of the aircraft is: After using dimensionless aerodynamic derivative processing, the long-period modal stability condition of the aircraft is equivalent to: C mα is the longitudinal static stability derivative of the aircraft; C Lα is the lift line slope of the whole aircraft; C m,M is the derivative of the pitching moment coefficient with respect to the Mach number; M is the flight Mach number; is the trim drag coefficient; C L,M is the derivative of the lift coefficient with respect to the Mach number; is the trim lift coefficient; The lift line slope C of a general aircraft Lα The typical value is 3-6 ( / rad), and the drag coefficient The typical range is 0.01-0.05, so According to the Prandtl-Glauert transformation, at high subsonic speeds, neglect and C L,M After that, formula (8) is further simplified to: On the other hand, the static stability derivative under load is defined as: C m is the pitching moment coefficient; M is the flight Mach number; C L is the lift coefficient; n is the flight overload; The necessary and sufficient condition for the aircraft to have constant load static stability is that the above constant load static stability derivative is always negative; the overload of the aircraft during trimmed flight satisfies n = 1, that is, the lift and gravity are balanced, then: L is the lift of the aircraft; ρ is the air density; a is the speed of sound; M is the flight Mach number; S is the reference area; C L is the lift coefficient; W is the weight of the aircraft; In balanced flight, ρ, a, S, and W are all constants, so the balance equation of lift and gravity can be rewritten as: C L is the lift coefficient; M is the flight Mach number; Differentiating both sides of formula (12) yields: is the trim lift coefficient; Substituting formula (13) into the definition of the static stability derivative under constant load, the judgment condition for static stability under constant load can be obtained as follows: C m is the pitching moment coefficient; C m,M is the derivative of the pitch moment coefficient with respect to the flight Mach number; M is the flight Mach number; C L is the lift coefficient; Comparing formula (9) with formula (14), it can be seen that the dynamic stability of long-period modes and the static stability of fixed loads have the same judgment conditions. Therefore, the requirements for the dynamic stability of long-period modes can also be equivalent to the requirements for the static stability of fixed loads. During takeoff and supersonic cruise, supersonic civil aircraft has static speed stability, namely C m,M >0; and because the aircraft itself is longitudinally statically stable, that is, K n >0, so If the aircraft is stable at constant load, the aircraft will be unstable at transonic flight. However, due to the air compression effect, the focus of the whole aircraft will move backward sharply, and the aircraft will have speed static instability, that is, C m,M <0; if the longitudinal static stability margin K n The design value is too low, less than the speed instability The aircraft will show static instability at fixed load, and the long-period mode will also diverge; therefore, the design constraint of the longitudinal static stability margin in the airworthiness standard is K in the transonic stage. n The design value shall not be less than Step 5: Determine the constraints of the flying quality specifications on the longitudinal static stability margin; The control expectation parameter criterion uses the pilot's control expectation parameter to evaluate the aircraft's longitudinal short-period characteristics. The evaluation results reflect the aircraft's longitudinal stability and maneuverability. The desired control parameters of the aircraft are defined as: ω sp is the short-period modal frequency; g is the acceleration due to gravity; V * To balance the flight speed; Z α is the derivative of lift with respect to the angle of attack; m is the mass of the aircraft; The expected control parameter criteria assessment level of supersonic civil aircraft within the full flight envelope shall not be lower than Level 2; the expected control parameter is recorded as CAP, and the aircraft body should meet CAP>0.05, 0.25<ξ sp <2.0; combined with the expected manipulation parameter and the short-cycle frequency ω in formula (15) sp The corresponding relationship between , we can get the constraint condition of the second-level flight quality level on the short-period mode in the take-off stage as follows: ω sp is the short-period modal frequency; ξ sp is the short-period damping ratio; Similarly, for non-field flight phases such as climb, supersonic cruise, and descent, the aircraft body should meet CAP>0.038, 0.3<ξ sp <2.0, so in the supersonic cruise state, the constraints of the second-level flight quality level on the short-period mode are: The real part Re, imaginary part Im and frequency ω of the short-period modal characteristic root sp and damping ratio ξ sp The corresponding relationship is: i is the imaginary unit.

2. The method for designing longitudinal relaxed static stability margin of a supersonic civil aircraft according to claim 1, characterized in that: It is suitable for small supersonic business jets with 20 seats. The aircraft adopts a slender arrow-shaped wing layout with a small aspect ratio and a large sweep angle. The cruising speed is 1.8Ma, the cruising altitude is 18km, and the maximum take-off weight is 25 tons. The typical configuration features of this example aircraft are: a slender nose and a long average aerodynamic chord length; large pitch and yaw axis moments of inertia, and a small roll axis moment of inertia; a T-tail layout, and redundant longitudinal and lateral control surfaces; the engine is tail-mounted, and the distance between the two engines is close.

3. The method for designing longitudinal relaxed static stability margin of a supersonic civil aircraft according to claim 1 or 2, characterized in that: The typical longitudinal aerodynamic parameter value of the example aircraft at a cruising altitude of 18 kilometers and a cruising speed of 1.8 Mach is C Lα =1.93, C mα = -0.15 and K n =7.8%; the longitudinal aerodynamic parameter value of the B747 aircraft at a cruising altitude of 10.6 kilometers and a cruising speed of 0.85 Mach is C Lα =4.9, C mα = -1.03 and K n =21%. It can be seen that the lift line slope, longitudinal static stability derivative and static stability margin of the example aircraft are all smaller than those of the B747 aircraft.

4. The method for designing longitudinal relaxed static stability margin of a supersonic civil aircraft according to claim 1 or 2, characterized in that: The longitudinal stability characteristics of supersonic civil aircraft, which are different from those of conventional aircraft, are analyzed, and the physical reasons for this difference are given from the perspectives of configuration characteristics and aerodynamic data.

5. The method for designing longitudinal relaxed static stability margin of a supersonic civil aircraft according to claim 1 or 2, characterized in that: The relaxation of the longitudinal static stability margin is based on the equivalence between the long-period mode and the static stability under constant load. It is proposed that in the transonic stage where the aircraft has speed static instability, the relaxation value of the longitudinal static stability margin shall not be lower than the degree of speed instability.

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