CN112883495B - Directional broadband high-stealth satellite and top end shape design method thereof - Google Patents
Directional broadband high-stealth satellite and top end shape design method thereof Download PDFInfo
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Abstract
The invention discloses a directional broadband high-stealth satellite and a top end shape design method thereof
Forming gradient difference, and the projection areas of surface elements in the same phase in the incident wave direction are equal, the satellite body is shaped as a rotating body, and the generatrix control equation of the parabolic tip at the upper part of the rotating body is that z is-a rho 2 + c, z is a bus variable and represents the z-axis coordinate of the point on the bus, a is a bus control parameter, c is a bus control parameter, and ρ is a bus variable and represents the distance from the point on the bus to the z-axis. The invention aims to solve the problems that the stealth effect of the existing satellite stealth appearance in the key direction is insufficient, and the echo wave crest is too close to the tip direction, so that the high-strength echo exists in the key threat area and the satellite position is easily exposed, and the related satellite top appearance has the advantage of good stealth effect.
Description
Technical Field
The invention relates to a spacecraft structure design technology, in particular to a satellite top end shape design method with directional broadband and high stealth performance and a satellite.
Background
At present, the satellite technology is developed rapidly, and plays an important role in the aspects of communication, navigation, positioning, meteorological monitoring and the like. In modern war, the satellite is also responsible for key tasks such as information communication, battlefield monitoring, fire early warning, etc. However, the satellite system has the characteristics of fixed orbit and load signal release, is easy to be found and tracked by detection equipment, and further attacked by various anti-satellite weapons, and is difficult to normally function in wartime. Aiming at the threat faced by the satellite, in order to guarantee the survival capability of the satellite in the space, the satellite needs to be invisibly designed. At present, the design of the stealth of the satellite is mainly started from two aspects, namely the stealth of materials and the stealth of appearance. The stealth material refers to that special materials with wave absorption performance, such as ferrite materials and nano materials, are used on the outer surface of the satellite to absorb electromagnetic waves received by the surface of the satellite and reduce echoes. The appearance stealth means that the direction of a scattered electromagnetic wave crest is controlled through appearance design, so that the echo intensity is reduced, and the purpose of electromagnetic stealth is achieved. The material stealth and the appearance stealth are mutually matched, and the stealth performance of the satellite is improved together.
In the aspect of the appearance stealth technology, a key threat direction is firstly determined when a stealth satellite is designed. When a satellite is in a stealth state, the top (direction with better stealth performance) of the satellite is generally required to face a key threat direction. Therefore, when the stealth appearance of the satellite is designed, the appearance design of the top end of the satellite is important. The top of the stealth satellite is generally designed into a conical shape, a pyramid shape, an ellipsoid shape and the like. The top ends of the cone and the pyramid can obviously reduce the electromagnetic echo in the direction of the cone top, and the ellipsoidal shape can effectively reduce the size of the electromagnetic echo in a large range of directions.
However, if the objective of directional stealth is to provide stealth, the shapes of stealth satellites, such as conical, pyramidal and ellipsoidal shapes, have their own disadvantages. The conical shape and the pyramid shape have good hiding effect in the direction of the pointed top, but when the volume is larger, larger echo still exists in the direction of the pointed top. And echo wave crests exist in some directions close to the spires, so that the positions of the satellites are easily exposed, and the stealth of the satellites is not facilitated. Although the ellipsoid shape has no prominent echo maximum value in each direction, the stealth direction has no focus and pertinence, and the stealth capability is not correspondingly improved for the focus threat direction. In the application of stealth satellites, the top end appearance has room for improvement.
Disclosure of Invention
The technical problems to be solved by the invention are as follows: the invention aims to solve the problems that the stealth effect of the existing stealth appearance in the key direction is insufficient, and the echo wave crest is too close to the spire direction, so that a high-strength echo exists in a key threat area and the position of a satellite is easily exposed, and the related satellite top appearance has the advantage of good stealth effect.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
a directional broadband satellite with high stealth performance comprises a satellite body, wherein the phase term of the top outline surface element of the satellite body
Forming gradient difference, and the projection areas of the surface elements in the same phase in the incident wave direction are equal, wherein j is an imaginary number unit,
is a wave vector, and the wave vector is,
is the satellite surface point position vector.
Optionally, the upper part of the satellite body is a parabolic tip, and the lower part of the satellite body is an ellipsoidal base.
Optionally, the shape of the satellite body is a rotating body, and the function expression of the generatrix control equation of the parabolic tip at the upper part of the rotating body is as follows:
z＝-aρ 2 +c 0≤ρ≤R (1)
in the above formula, z is a bus variable and represents a z-axis coordinate of a point on the bus, a is a bus control parameter, c is a bus control parameter, ρ is a bus variable and represents a distance from the point on the bus to the z-axis, and R is a maximum radius of the rotating body.
In addition, the invention also provides a top end shape design method of the satellite with the directional broadband and the high stealth performance, which comprises the following steps:
1) obtaining a relational function expression of the current and the strength of the echo electric field excited by the current according to a Maxwell equation; obtaining the surface equivalent current by using the phase estimation condition of the surface equivalent current under the high-frequency condition and the approximate condition of the projection area such as the current 
The function approximation expression of (a);
2) equivalent current of surface
Substituting the function approximate expression into a relation function expression of the current and the strength of the echo electric field excited by the current, and simplifying to obtain the position vector of any scattering target point
Corresponding to the intensity of the echo electric field at the position of the target point
The function of (a) expresses:
in the above formula, j is an imaginary unit, ω is an angular frequency, μ is a dielectric permeability,
in order to be the wave vector of the incident wave,
is a vector of the position of the satellite surface points,
as a position vector of the scattering target point,
the current generated by the incident wave vertically irradiating on the plane is k, k is the wave vector of the incident wave, k is 2 pi/lambda, lambda is the wavelength of the incident wave,
for Nabla operator, d τ projection The projection area of the satellite surface area infinitesimal d tau 'in the incident wave direction is shown, and d tau' is the area infinitesimal of the satellite surface;
3) according to the surface equivalent current
Function approximation expression of (1) determining an arbitrary dispersionPosition vector of shooting target point
Corresponding to the intensity of the echo electric field at the position of the target point
Projected area d tau in incident wave direction from surface element d tau projection And the phase term of the surface element d tau
Determining, thereby determining, a phase term for a top surface element of the satellite body
Forming gradient difference, and when the projection areas of the surface elements in the same phase in the incident wave direction are equal, the intensity of the echo electric field at the position of the target point 
And the minimum is obtained, so that the condition that the top end appearance of the satellite body meets the requirement of directional broadband high stealth performance is as follows: phase term of top profile surface element of satellite body
Gradient difference is formed, and the projection areas of the surface elements in the same phase in the incident wave direction are equal.
Optionally, the relational function expression of the current obtained in step 1) and the strength of the echo electric field excited by the current is as follows:
in the above formula, the first and second carbon atoms are,
as a scattering target point position vector
The intensity of the echo electric field at the position corresponding to the target point, j is an imaginary unit, omega is an angular frequency, mu is medium permeability, k is an incident wave vector, k is 2 pi/lambda, lambda is an incident wave wavelength,
in order to be the Nabla operator, the operation,
is the equivalent current of the surface,
as a position vector of the scattering target point,
is the satellite surface point position vector, and d tau' is the area infinitesimal of the satellite surface.
Optionally, the surface equivalent current obtained in step 1)
The approximate function expression of (a) is:
in the above formula, the first and second carbon atoms are,
for the current generated by incident waves perpendicularly impinging on a plane, d τ projection Is the projection area of the satellite surface area infinitesimal d tau 'in the incident wave direction, d tau' is the area infinitesimal of the satellite surface, j is an imaginary unit,
in order to be the wave vector of the incident wave,
is the satellite surface point position vector.
Optionally, the echo electric field intensity obtained in step 2)
The functional expression of (a) is:
in the above formula, j is an imaginary unit, ω is an angular frequency, μ is a dielectric permeability,
in order to be the wave vector of the incident wave,
is a vector of the position of the satellite surface points,
as a position vector of the scattering target point,
the current generated by the incident wave vertically irradiating on the plane is k, k is the wave vector of the incident wave, k is 2 pi/lambda, lambda is the wavelength of the incident wave,
for Nabla operator, d τ projection The projection area of the satellite surface area infinitesimal d tau 'in the incident wave direction is shown, and d tau' is the area infinitesimal of the satellite surface.
Optionally, the simplification in step 2) refers to considering a distance term under far-field conditions
The distance term under far field condition is not greatly changed
Regarded as constant, thereby the echo electric field strength
Further reducing the function expression of (A) to obtain an arbitrary scattering target point position vector shown in the formula (2)
Corresponding to the intensity of the echo electric field at the position of the target point
Is used for the functional expression of (1).
Optionally, step 3) is followed by a step of determining a generatrix control equation of the parabolic tip at the upper part of the rotator if the satellite body is shaped as the rotator:
s1) establishing a rectangular coordinate system by taking the satellite top end direction as the z axis, taking the key direction of the satellite facing the greatest threat as the top end direction to emit the electromagnetic wave, and then taking the wave vector 
Wherein
The unit vector is oriented to the positive direction of the z axis, and the influence of the dark surface of the surface which cannot be directly irradiated by the electromagnetic wave on the intensity of the electric field echo is small, so that the equiphase area distribution of the top end of the satellite which is taken as the bright surface of the satellite at the moment is obtained only by considering the bright surface of the surface which can be directly irradiated by the electromagnetic wave at the moment; planes perpendicular to the z-axis are made on the z-axis at prescribed intervals dz, respectively, and the planes divide the satellite surface into a plurality of annular regions, and when the intervals dz are sufficiently small, the currents in the i-th annular region are considered to have a common phase value
S2) selecting two adjacent annular regions, and respectively calculating to obtain corresponding projection areas tau according to the geometric relationship 1 And τ 2 ；
S3) calculating the area difference of the two adjacent selected annular regions:
τ 1 -τ 2 ＝(2ρ 2 2 -ρ 1 2 -ρ 3 2 )π (6)
s4) describing the shape of the rotator bus of the satellite profile by a quadratic polynomial expressed by the following formula;
z＝-aρ 2 +bρ+c (7)
in the above formula, z is a bus variable and represents a z-axis coordinate of a point on the bus, a is a bus control parameter, c is a bus control parameter, and ρ is a bus variable and represents a distance from the point on the bus to the z-axis; determining (p) at the boundary of two adjacent annular regions 1 ,z 1 )、(ρ 2 ,z 2 )、(ρ 3 ,z 3 ) Equations at three points;
s5) since the annular region is cut at equal intervals, there are:
dz＝z 2 -z 1 ＝z 3 -z 2 (8)
the (rho) on the boundary of two adjacent annular regions 1 ,z 1 )、(ρ 2 ,z 2 )、(ρ 3 ,z 3 ) Substituting the equations at the three points to obtain:
when b is 0, i.e. z is-a ρ 2 + c, the difference of the projected areas of two adjacent annular regions is:
τ 1 -τ 2 ＝2ρ 2 2 -ρ 3 2 -ρ 1 2 ＝0 (10)
s6) the satellite adopts a quadratic polynomial z ═ a ρ since the two adjacent annular regions are arbitrarily obtained 2 When + c is the shape of the rotator of the bus, the projection areas of all the phase intervals are equal, so that the stealth performance of the satellite in the key direction can be greatly improved by the shape, and the functional expression of the bus control equation of the rotator of the satellite is determined as shown in the formula (1).
Optionally, calculating a corresponding cast in step S2)Shadow area tau 1 And τ 2 The functional expression of (a) is:
in the above formula, τ 1 Denotes the projected area, τ, of the 1 st of the two adjacent annular regions 2 Represents the projected area, rho, of the 2 nd annular region of two adjacent annular regions 1 Is the radius of the edge circle in the 1 st annular region, p 2 The outer edge radius of the 1 st annular region is equal to the inner edge radius, rho, of the 2 nd annular region 3 The radius of the outer edge circle of the 2 nd annular region.
Optionally, step S4) determines (ρ) at the boundary of two adjacent annular regions 1 ,z 1 )、(ρ 2 ,z 2 )、(ρ 3 ,z 3 ) The functional expression of the equation at three points is:
in the above formula, z 1 Is the z coordinate of the edge in the 1 st annular region, z 2 Is the z coordinate of the edge in the 2 nd annular region, z 3 Is the z coordinate of the outer edge of the 2 nd annular region.
Compared with the prior art, the invention has the following advantages: the invention provides a phase term of a surface element of the top end appearance of a satellite body aiming at the top end appearance of the satellite body
Form the gradient poor, and be in the characteristic that the surface element of same phase equals at the projection area of incident wave direction, through above-mentioned characteristic, can solve the stealthy not enough problem of effect of the key direction of current satellite stealth appearance to and the echo crest is too close to the pinnacle direction, lead to having the echo of heavy intensity in the key threat zone, expose the problem of satellite position easily, the satellite top appearance that relates to has stealthy effectual advantage.
Drawings
Fig. 1 is a schematic diagram of a satellite body side view equiphase area division in the embodiment of the present invention.
Fig. 2 is a schematic diagram of the partition of the satellite body into the top view equal phase regions according to the embodiment of the present invention.
Fig. 3 is a schematic view of a bus shape and a curve of a satellite body according to an embodiment of the invention.
Fig. 4 shows simulation results of RCS for directions of tops of parabolic satellites with different heights according to an embodiment of the present invention.
Fig. 5 shows the RCS simulation results of different directions for the same size cone and parabola satellites according to the embodiment of the invention.
Fig. 6 shows the RCS simulation results of different frequencies and tip directions of the same-sized cone and parabola satellites according to the embodiment of the invention.
Fig. 7 shows the results of RCS simulation in different directions for an example of a parabolic satellite tip profile according to an embodiment of the present invention.
Detailed Description
The embodiment provides a directional broadband satellite with high stealth performance, which comprises a satellite body, and a phase term of a surface element on the top outline of the satellite body
Forming gradient difference, and the projection areas of the surface elements in the same phase in the incident wave direction are equal, wherein j is an imaginary number unit,
the wave vector is the wave vector,
is the satellite surface point position vector. The present embodiment provides a phase term of a surface element of the top end profile of the satellite body for the top end profile of the satellite body
The characteristics that the gradient difference is formed and the projected areas of the surface elements in the same phase in the incident wave direction are equal are formed, and the resolution is possible by the characteristicsThe problem of the stealthy effect of the key direction of stealthy appearance of current satellite is not enough to and the echo crest is too close to the pinnacle direction, leads to having the echo of high strength in the key threat region, exposes the satellite position easily is solved, the top appearance of satellite that relates to has the effectual advantage of stealthy. With reference to figures 1 and 2 of the drawings, 
As vector of incident wave, p i Is an arbitrary ith point (x) i ,y i ) The distance to the z-axis is determined by making planes perpendicular to the z-axis at intervals dz, the planes dividing the satellite surface into a plurality of annular regions, and when dz is sufficiently small, the currents in any ith annular region have a common phase value
τ i Phase term representing projected area of i-th annular region and top surface element of satellite body
Gradient difference is formed, and the projection areas of the surface elements in the same phase in the incident wave direction are equal.
As an alternative embodiment, the satellite body in this embodiment has a parabolic tip at the upper portion and an ellipsoidal base at the lower portion, as shown in fig. 3.
In order to further improve the stealth effect of the satellite, in this embodiment, the shape of the satellite body is a rotator, and the function expression of the generatrix control equation of the parabolic tip at the upper part of the rotator is as follows:
z＝-aρ 2 +c 0≤ρ≤R (1)
in the above formula, z is a bus variable and represents a z-axis coordinate of a point on the bus, a is a bus control parameter, c is a bus control parameter, ρ is a bus variable and represents a distance from the point on the bus to the z-axis, and R is a maximum radius of a rotator. In an alternative embodiment, in this embodiment, the bus control parameter a is 1/0.16, the bus control parameter c is 0.4, and the maximum radius R of the rotating body is 0.4 m.
Referring to fig. 3, the function expression of the bus control equation of the ellipsoidal base at the lower part of the rotating body in this embodiment is:
in the above formula, z is a bus variable and represents a z-axis coordinate of a point on the bus, d and b are bus control parameters, ρ is a bus variable and represents a distance from the point on the bus to the z-axis, and R is a maximum radius of the rotating body.
Since the pyramid and cone have similar scattering properties, a cone apex profile of the same size, the same base and a parabolic apex are used as a comparison. The scattering characteristics of the satellite are analyzed, and the parabolic stealth satellite has the following advantages:
(1) the parabolic satellites with different parameters have good stealth characteristics, the appearance of the top parabola is kept, the height value of the satellite is changed between 0.3 meter and 1.1 meter, the RCS value of the top direction of the satellite under 4GHz incident wave frequency is analyzed in a simulation mode, and the RCS value is compared with a cylinder with the same cross section area and height, so that data shown in the figure 4 can be obtained.
(2) Analysis shows that as long as the satellite shape is designed into a parabolic shape, compared with a cylindrical shape without stealth design, the electromagnetic echo reduction effect of at least 25db can be achieved in the top end direction of the satellite, and the electromagnetic stealth effect is obvious.
(3) The position of the echo peak is more deviated from the apical direction than the conical shape.
At the incident wave frequency of 8GHz, the scattering characteristics of the conical and parabolic satellites with the same size are simulated and analyzed. As shown in fig. 5, the single station RCS peak of the parabolic stealth satellite profile is at a position 57 degrees off the vertex. The single station RCS peak of the cone-top satellite is at 45 degrees. The position of the parabola outline wave crest is farther away from the top end direction, so that the parabola outline wave crest is more difficult to be discovered by detection equipment in a key threat angle, and the parabola outline wave crest is more suitable for the design of the invisible satellite outline.
(4) The tip direction RCS values are lower at different frequencies relative to the conical shape.
The results of simulation tests on the RCS values in the tip direction of the parabolic satellite and the conical tip satellite having the same height and the cross-sectional area in the tip direction are shown in fig. 6, which are performed at different incident wave frequencies. The parabolic satellites have lower tip direction RCS values at most frequencies, and other frequencies are substantially equal to those of the cone-tipped satellites. The parabolic satellite vertices make better use of the destructive interference of surface currents, and have better stealth effects than the conical shape at most frequencies.
In this embodiment, the distribution of single station RCS at the top of a parabolic satellite is shown in fig. 7. As is clear from FIG. 7, when the radius of the cross-sectional circle is 0.4m, the RCS value in the distal direction is-3 dBsm or less under irradiation with an incident wave having a frequency of 4GHz, and the excellent stealth performance is obtained. The main peak of the RCS of a single station is at 74 degrees, the RCS values are all below-3 dBsm within an angle of 0-60 degrees, the top end of the parabolic satellite has a large stealth angle, and the method is suitable for satellite stealth design.
The embodiment further provides a method for designing a top end shape of the directional broadband high stealth satellite, which includes:
1) obtaining a relation function expression of the current and the strength of the electric field of the echo excited by the current according to a Maxwell equation; obtaining the surface equivalent current by using the phase estimation condition of the surface equivalent current under the high-frequency condition and the approximate condition of the projection area such as the current
A function approximation expression of (a);
2) equivalent current of plane
Substituting the function approximate expression into a relation function expression of the current and the strength of the echo electric field excited by the current, and simplifying to obtain the position vector of any scattering target point
Corresponding to the intensity of the echo electric field at the position of the target point
The function of (a) expresses:
in the above formula, j is an imaginary unit, ω is an angular frequency, μ is a dielectric permeability,
in order to be the wave vector of the incident wave,
is a vector of the position of the satellite surface points,
as a position vector of the scattering target point,
the current generated by the incident wave vertically irradiating on the plane, k is the wave vector of the incident wave, k is 2 pi/lambda, lambda is the wavelength of the incident wave,
for Nabla operator, d τ projection The projection area of the satellite surface area infinitesimal d tau 'in the incident wave direction is shown, and d tau' is the area infinitesimal of the satellite surface;
3) according to the surface equivalent current 
Determining the position vector of any scattering target point by using the function approximation expression
Corresponding to the intensity of the echo electric field at the position of the target point
Projected area d tau in incident wave direction from surface element d tau projection And the phase term of the surface element d tau
Determining, thereby determining, a phase term for a top surface element of the satellite body
Forming gradient difference, and when the projection areas of the surface elements in the same phase in the incident wave direction are equal, the intensity of the echo electric field at the position of the target point
And the minimum is obtained, so that the condition that the top end appearance of the satellite body meets the requirement of directional broadband high stealth performance is as follows: phase term of top profile surface element of satellite body
Gradient difference is formed, and the projection areas of the surface elements in the same phase in the incident wave direction are equal.
In this embodiment, the relational function expression of the current obtained in step 1) and the strength of the echo electric field excited by the current is as follows:
in the above formula, the first and second carbon atoms are,
as a scattering target point position vector
The intensity of the echo electric field at the position corresponding to the target point, j is an imaginary unit, omega is an angular frequency, mu is medium permeability, k is an incident wave vector, k is 2 pi/lambda, lambda is an incident wave wavelength,
in order to be the Nabla operator, the operation,
is the equivalent current of the surface,
as a position vector of the scattering target point, 
Is the position vector of the satellite surface point, and d tau' is the area infinitesimal of the satellite surface.
In this example, the surface equivalent current obtained in step 1) was obtained
The approximate function expression of (a) is:
in the above formula, the first and second carbon atoms are,
for the current generated by incident waves perpendicularly impinging on a plane, d τ projection Is the projection area of the satellite surface area infinitesimal d tau 'in the incident wave direction, d tau' is the area infinitesimal of the satellite surface, j is an imaginary unit,
in order to be the wave vector of the incident wave,
is the satellite surface point position vector.
In this embodiment, the strength of the echo electric field obtained in step 2)
The functional expression of (a) is:
in the above formula, j is an imaginary unit, ω is an angular frequency, μ is a dielectric permeability,
in order to be the wave vector of the incident wave,
is a vector of the position of the satellite surface points,
as a position vector of the scattering target point,
the current generated by the incident wave vertically irradiating on the plane is k, k is the wave vector of the incident wave, k is 2 pi/lambda, lambda is the wavelength of the incident wave,
for Nabla operator, d τ projection The projection area of the satellite surface area infinitesimal d tau 'in the incident wave direction is shown, and d tau' is the area infinitesimal of the satellite surface.
In this embodiment, the simplification in step 2) refers to considering the distance term under far-field condition
The distance term under far field condition is not greatly changed 
Regarded as constant, thereby measuring the echo electric field strength
Further reducing the function expression of (A) to obtain an arbitrary scattering target point position vector shown in the formula (2)
Corresponding to the intensity of the echo electric field at the position of the target point
Is used for the functional expression of (1). Therefore, the phase terms of the surface elements of the top end appearance of the satellite body are provided for the top end appearance of the satellite body in the embodiment are finally determined
The characteristic that the projection areas of surface elements in the same phase in the incident wave direction are equal and the design principle of the electromagnetic stealth appearance of the top of the satellite are formed.
According to the design principle, a satellite top end shape can be designed. If the phase of the satellite surface current has gradient difference, the profile of the satellite needs to have depth in the electromagnetic wave irradiation direction, so that a large number of planes vertical to incident electromagnetic waves are avoided. Surface element projection area d tau if different phase value is required projection If the two are equal, the satellite top profile is subjected to parameter analysis aiming at a specific incidence direction. Therefore, in this embodiment, step 3) is followed by the step of determining the generatrix control equation of the parabolic tip at the upper part of the rotator when the satellite body is in the shape of the rotator:
s1) establishing a rectangular coordinate system by taking the satellite top end direction as the z axis, taking the key direction of the satellite facing the greatest threat as the top end direction to emit the electromagnetic wave, and then taking the wave vector 
Wherein
The unit vector is oriented to the positive direction of the z axis, and the influence of the dark surface of the surface which cannot be directly irradiated by the electromagnetic wave on the intensity of the electric field echo is small, so that the equiphase area distribution of the top end of the satellite which is taken as the bright surface of the satellite at the moment is obtained only by considering the bright surface of the surface which can be directly irradiated by the electromagnetic wave at the moment; planes perpendicular to the z-axis are made at prescribed intervals dz on the z-axis, respectively, and the planes divide the satellite surface into a plurality of planesAnnular zones, the currents in the i-th annular zone being considered to have a common phase value when the separation dz is sufficiently small
In the present embodiment, the distribution of the equiphase region of the satellite top as the satellite bright face at this time is obtained as shown in fig. 1 and 2, where ρ i Is an arbitrary ith point (x) i ,y i ) Distance to z-axis and having:
planes perpendicular to the z-axis are made on the z-axis at intervals dz, respectively. The plane divides the satellite surface into a number of annular regions, and when dz is sufficiently small, the currents in the i-th annular region can be considered to have a common phase value
Available tau i The projected area of the i-th annular region is shown.
S2) selecting two adjacent annular regions, and respectively calculating to obtain corresponding projection areas tau according to the geometric relationship 1 And τ 2 ；
S3) calculating the area difference of the two adjacent selected annular regions:
τ 1 -τ 2 ＝(2ρ 2 2 -ρ 1 2 -ρ 3 2 )π (6)
S4) describing the shape of the rotator bus of the satellite profile by a quadratic polynomial expressed by the following formula;
z＝-aρ 2 +bρ+c (7)
in the above formula, z is a bus variable and represents a z-axis coordinate of a point on the bus, a is a bus control parameter, c is a bus control parameter, and ρ is a bus variable and represents a distance from the point on the bus to the z-axis; determining (p) at the boundary of two adjacent annular regions 1 ,z 1 )、(ρ 2 ,z 2 )、(ρ 3 ,z 3 ) Equations at three points;
s5) since the annular region is cut at equal intervals, there are:
dz＝z 2 -z 1 ＝z 3 -z 2 (8)
the (rho) on the boundary of two adjacent annular regions 1 ,z 1 )、(ρ 2 ,z 2 )、(ρ 3 ,z 3 ) Substituting the equations at the three points to obtain:
when b is 0, i.e. z is-a ρ 2 + c, the difference of the projected areas of two adjacent annular regions is:
τ 1 -τ 2 ＝2ρ 2 2 -ρ 3 2 -ρ 1 2 ＝0 (10)
s6) the satellite adopts a quadratic polynomial z ═ a ρ since the two adjacent annular regions are arbitrarily obtained 2 When + c is the shape of the rotator of the bus, the projection areas of all the phase intervals are equal, so that the stealth performance of the satellite in the key direction can be greatly improved by the shape, and the functional expression of the bus control equation of the rotator of the satellite is determined as shown in the formula (1).
Due to tau 1 、τ 2 The two equal-phase regions are arbitrarily selected, so when the satellite adopts a rotator shape with a quadratic polynomial shown in formula (1) as a bus, the projection areas of all phase regions are equal, and the appearance can greatly increase the stealth performance of the satellite in the key direction. The satellite with the shape has excellent stealth effect under different frequencies because the phase gradient difference exists even if the frequency of the incident wave changes.
In this embodiment, step S2) calculates the corresponding projection area τ 1 And τ 2 The functional expression of (a) is:
in the above formula, τ 1 Denotes the projected area, τ, of the 1 st of the two adjacent annular regions 2 Represents the projected area, rho, of the 2 nd annular region of two adjacent annular regions 1 Is the radius of the edge circle in the 1 st annular region, p 2 The outer edge radius of the 1 st annular region is equal to the inner edge radius, rho, of the 2 nd annular region 3 The radius of the outer edge circle of the 2 nd annular region.
In this embodiment, (ρ) at the boundary between two adjacent annular regions is determined in step S4) 1 ,z 1 )、(ρ 2 ,z 2 )、(ρ 3 ,z 3 ) The functional expression of the equation at three points is:
in the above formula, z 1 Is the z coordinate of the edge in the 1 st annular region, z 2 Is the z coordinate of the edge in the 2 nd annular region, z 3 Is the z coordinate of the outer edge of the 2 nd annular region.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-readable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein. The present application is directed to methods, apparatus (systems), and computer program products according to embodiments of the application wherein instructions, which execute via a flowchart and/or a processor of the computer program product, create means for implementing functions specified in the flowchart and/or block diagram block or blocks. These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks. These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above description is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above embodiments, and all technical solutions belonging to the idea of the present invention belong to the protection scope of the present invention. It should be noted that modifications and embellishments within the scope of the invention may occur to those skilled in the art without departing from the principle of the invention, and are considered to be within the scope of the invention.
Claims (8)
1. The directional broadband satellite with high stealth performance comprises a satellite body and is characterized in that the phase term of the surface element of the top outline of the satellite body
Forming gradient difference, and the projection areas of the surface elements in the same phase in the incident wave direction are equal, wherein j is an imaginary number unit,
is a wave vector, and the wave vector is,
the satellite body is a rotator, and the function expression of a bus control equation of the parabolic tip at the upper part of the rotator is as follows:
z＝-aρ 2 +c 0≤ρ≤R (1)
in the above formula, z is a bus variable and represents a z-axis coordinate of a point on the bus, a is a bus control parameter, c is a bus control parameter, ρ is a bus variable and represents a distance from the point on the bus to the z-axis, and R is a maximum radius of the rotating body.
2. The method for designing the top profile of a directional wideband high stealth satellite according to claim 1, comprising:
1) obtaining a relational function expression of the current and the strength of the echo electric field excited by the current according to a Maxwell equation; obtaining the surface equivalent current by using the phase estimation condition of the surface equivalent current under the high-frequency condition and the approximate condition of the projection area such as the current
A function approximation expression of (a);
2) equivalent current of plane
Substituting the function approximate expression into a relation function expression of the current and the strength of the echo electric field excited by the current, and simplifying to obtain the position vector of any scattering target point
Corresponding to the intensity of the echo electric field at the position of the target point
The function of (a) expresses:
in the above formula, j is an imaginary unit, ω is an angular frequency, μ is a dielectric permeability,
in order to be the wave vector of the incident wave,
is a vector of the position of the satellite surface points,
as a position vector of the scattering target point,
the current generated by the incident wave vertically irradiating on the plane is k, k is the wave vector of the incident wave, k is 2 pi/lambda, lambda is the wavelength of the incident wave,
for Nabla operator, d τ projection The projection area of the satellite surface area infinitesimal d tau 'in the incident wave direction is shown, and d tau' is the area infinitesimal of the satellite surface;
3) According to the surface equivalent current
Determining the position vector of any scattering target point by using the function approximation expression
Corresponding to the intensity of the echo electric field at the position of the target point
Projected area d tau in incident wave direction from surface element d tau projection And the phase term of the surface element d tau
Determining, thereby determining, a phase term for a top surface element of the satellite body
Bin in phase forming gradient differenceWhen the projection areas in the wave emitting directions are equal, the intensity of the echo electric field at the position of the target point
And the minimum is obtained, so that the condition that the top end appearance of the satellite body meets the requirement of directional broadband high stealth performance is as follows: phase term of top profile surface element of satellite body
Gradient difference is formed, and the projection areas of the surface elements in the same phase in the incident wave direction are equal.
3. The method as claimed in claim 2, wherein the relational function expression of the currents obtained in step 1) and the strength of the echo electric field excited by the currents is as follows:
in the above formula, the first and second carbon atoms are,
as a scattering target point position vector
The intensity of the echo electric field at the position corresponding to the target point, j is an imaginary unit, omega is an angular frequency, mu is medium permeability, k is an incident wave vector, k is 2 pi/lambda, lambda is an incident wave wavelength, 
In order to be the Nabla operator, the operation,
is the equivalent current of the surface,
as a position vector of the scattering target point,
is the satellite surface point position vector, and d tau' is the area infinitesimal of the satellite surface.
4. The method as claimed in claim 3, wherein the surface equivalent current obtained in step 1) is the same as the surface equivalent current obtained in step 1)
The approximate function expression of (a) is:
in the above formula, the first and second carbon atoms are,
for the current generated by incident waves perpendicularly impinging on a plane, d τ projection Is the projection area of the satellite surface area infinitesimal d tau 'in the incident wave direction, d tau' is the area infinitesimal of the satellite surface, j is an imaginary unit,
in order to be the wave vector of the incident wave,
is the satellite surface point position vector.
5. The method as claimed in claim 4, wherein the echo electric field strength obtained in step 2) is the same as that of the directional broadband high stealth satellite
The functional expression of (a) is:
in the above formula, j is an imaginary unit, ω is an angular frequency, μ is a dielectric permeability,
in order to be the wave vector of the incident wave,
is a vector of the position of the satellite surface points,
as a position vector of the scattering target point,
the current generated by the incident wave vertically irradiating on the plane is k, k is the wave vector of the incident wave, k is 2 pi/lambda, lambda is the wavelength of the incident wave, 
For Nabla operator, d τ projection The projection area of the satellite surface area infinitesimal d tau 'in the incident wave direction is shown, and d tau' is the area infinitesimal of the satellite surface.
6. The method as claimed in claim 1, further comprising, after the step 3), a step of determining a generatrix control equation of the parabolic tip at the upper part of the rotator when the satellite body is shaped as the rotator:
s1) establishing a rectangular coordinate system by taking the satellite top end direction as the z axis, taking the key direction of the satellite facing the greatest threat as the top end direction to emit the electromagnetic wave, and then taking the wave vector
Wherein
The unit vector is oriented to the positive direction of the z axis, and the influence of the dark surface of the surface which cannot be directly irradiated by the electromagnetic wave on the intensity of the electric field echo is small, so that the equiphase area distribution of the top end of the satellite which is taken as the bright surface of the satellite at the moment is obtained only by considering the bright surface of the surface which can be directly irradiated by the electromagnetic wave at the moment; planes perpendicular to the z-axis are made on the z-axis at prescribed intervals dz, respectively, and the planes divide the satellite surface into a plurality of annular regions, and when the intervals dz are sufficiently small, the currents in the i-th annular region are considered to have a common phase value
S2) selecting two adjacent annular regions, and respectively calculating to obtain corresponding projection areas tau according to the geometric relationship 1 And τ 2 ；
S3) calculating the area difference of the two adjacent selected annular regions:
τ 1 -τ 2 ＝(2ρ 2 2 -ρ 1 2 -ρ 3 2 )π (6)
s4) describing the shape of the rotator bus of the satellite profile by a quadratic polynomial expressed by the following formula;
z＝-aρ 2 +bρ+c (7)
in the above formula, z is a bus variable and represents a z-axis coordinate of a point on the bus, a is a bus control parameter, c is a bus control parameter, and ρ is a bus variable and represents a distance from the point on the bus to the z-axis; determining (p) at the boundary of two adjacent annular regions 1 ,z 1 )、(ρ 2 ,z 2 )、(ρ 3 ,z 3 ) Equations at three points;
s5) since the annular region is cut at equal intervals, there are:
dz＝z 2 -z 1 ＝z 3 -z 2 (8)
two adjacentAt the boundary of the annular region (p) 1 ,z 1 )、(ρ 2 ,z 2 )、(ρ 3 ,z 3 ) Substituting the equations at the three points to obtain:
when b is 0, i.e. z is-a ρ 2 + c, the difference of the projected areas of two adjacent annular regions is:
τ 1 -τ 2 ＝2ρ 2 2 -ρ 3 2 -ρ 1 2 ＝0 (10)
s6) the satellite adopts a quadratic polynomial z ═ a ρ since the two adjacent annular regions are arbitrarily obtained 2 When + c is the shape of the rotator of the bus, the projection areas of all the phase intervals are equal, so that the stealth performance of the satellite in the key direction can be greatly improved by the shape, and the functional expression of the bus control equation of the rotator of the satellite is determined as shown in the formula (1).
7. The method as claimed in claim 6, wherein the step S2) of calculating the corresponding projection area τ is performed by using the method 1 And τ 2 The functional expression of (a) is:
in the above formula, τ 1 Denotes the projected area, τ, of the 1 st of the two adjacent annular regions 2 Represents the projected area, rho, of the 2 nd annular region of two adjacent annular regions 1 Is the radius of the edge circle in the 1 st annular region, p 2 The outer edge radius of the 1 st annular region is equal to the inner edge radius, rho, of the 2 nd annular region 3 The radius of the outer edge circle of the 2 nd annular region.
8. The method as claimed in claim 6, wherein the step S4) is performed to determine the value of (p) at the boundary between two adjacent ring regions 1 ,z 1 )、(ρ 2 ,z 2 )、(ρ 3 ,z 3 ) The functional expression of the equation at three points is:
in the above formula, z 1 Is the z coordinate of the edge in the 1 st annular region, z 2 Is the z coordinate of the edge in the 2 nd annular region, z 3 Is the z coordinate of the outer edge of the 2 nd annular region.
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