CN115081361B - Method and device for rapidly solving parachute unfolding geometric characteristics and computer equipment - Google Patents
Method and device for rapidly solving parachute unfolding geometric characteristics and computer equipment Download PDFInfo
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Abstract
The application relates to a method and a device for rapidly solving the unfolding geometric characteristics of a parachute and computer equipment in the technical field of aerospace pneumatic deceleration. The method describes an axisymmetric canopy bus by using a parameter curve, and expresses a canopy bus equation as a univariate function described by a bottom radius by three geometric constraints of zero derivative at the top of the canopy, tangency between the bottom of the canopy and a canopy rope and unchanged canopy length, and obtains an analytical equation of the canopy bus under the given bottom radius; and solving the geometrical characteristic change of the parachute opening process by combining the power function parachute opening formula and the analytic equation of the canopy bus. The method combines the classical umbrella-opening empirical formula and the parameterized umbrella cover shape analysis description to solve the geometric characteristics of the umbrella cover in the whole umbrella-opening process, not only can meet the geometric constraint and the test data constraint in the umbrella-opening process, but also has quick solution and less memory consumption; in the field of computers, the data volume for describing the shape of the parachute can be greatly reduced, and the memory requirement and the calculation time requirement are reduced.
Description
Technical Field
The application relates to the technical field of aerospace pneumatic deceleration, in particular to a method and a device for quickly solving the unfolding geometric characteristics of a parachute and computer equipment.
Background
In the engineering field, a parachute is a key device in a spacecraft return or cargo air-drop task, and the geometrical characteristics of the parachute opening process are key data of dynamic calculation. The traditional method calculates the change rule of the shape of the canopy by a fluid-solid coupling method, a fluid-solid coupling calculation model starts from a basic mechanical object, the whole dynamic process is solved by large-scale finite element calculation, multi-step complex pre-and-post processing is needed, the calculation is time-consuming, and the rapid calculation requirements of engineering analysis and optimization cannot be met; in addition, flow field information around the parachute is not essential information for engineering practice, which necessarily consumes excessive computing time and computing resources because of the generation of excessive unnecessary redundant data. In the computer field, the parachute is also often used as a three-dimensional rendering object and widely applied to three-dimensional animation games and virtual reality applications, in these applications, feature extraction is lacked in the canopy appearance, continuous change of the canopy appearance of the parachute in the parachute opening process is often realized by adopting multi-frame data prepared in advance, and data is excessively relied on, so that the required memory is large, the program performance and rendering fidelity are influenced, the user experience is reduced, and the parachute is a technical short board which needs to be solved urgently at present.
Disclosure of Invention
Therefore, in order to solve the above technical problems, it is necessary to provide a method, a device and a computer device for quickly solving the unfolding geometric features of the parachute, which can quickly obtain the geometric shape data of the parachute during the unfolding process of the parachute, in combination with the key geometric features of the parachute canopy during the unfolding process. The method provides an analytic equation for describing the shape of the canopy in any state in the canopy opening process, and can provide three-dimensional graphic data of the canopy in the canopy opening process by combining a power function canopy opening formula widely applied in engineering.
A method for fast solution of parachute deployment geometry, the method comprising:
obtaining an umbrella canopy bus analytical expression according to an umbrella canopy bus parameter equation described by a preset parameter curve, the geometric constraint and the boundary constraint of the umbrella canopy; the canopy bus analytical expression comprises three parameters which are respectively: the tangent value of the included angle of the canopy height, the bottom radius and the parachute line and the bottom radius.
And solving a canopy length constraint equation obtained according to canopy length constraint under the given bottom radius by adopting a gradient method to obtain an expression of canopy height relative to the bottom radius.
And obtaining the canopy bus analytical expression taking the bottom radius as an independent variable according to the canopy bus analytical expression and the expression of the canopy height relative to the bottom radius.
And obtaining an expression of the bottom radius with respect to time in the umbrella opening process according to a calculation formula of the bottom area of the canopy and an evolution rule of the bottom area in the form of a power function along with time.
And obtaining the geometric characteristics of the canopy in each state in the parachute opening process according to a canopy bus analytical expression taking the bottom radius as an independent variable and the expression of the bottom radius in relation to time in the parachute opening process.
In one embodiment, obtaining an analytic expression of the canopy bus according to a canopy bus parameter equation described by a preset parameter curve, geometric constraints of the canopy and boundary constraints comprises:
establishing a coordinate system by taking a half of the central section of the canopy as a research object; the coordinate system takes the intersection point of the bottom radius of the umbrella coat section and the symmetry axis as the origin, and takes the straight line of the bottom radius as the originxAxis, about axis of symmetryyThe shaft is established.
Describing an axisymmetric canopy bus by adopting a preset parameter curve to obtain a canopy bus parameter equation, wherein the canopy bus parameter equation is as follows:
wherein s is a shape parameter,
and a, b, c, d, e and f are constant parameters.
Obtaining the geometric constraint of the canopy according to the physical characteristics in the umbrella opening process, wherein the geometric constraint of the canopy comprises the following steps: the top of the canopy is a pole, and the bottom of the canopy is tangent to the umbrella rope; the expression of the geometric constraint of the canopy is as follows:
wherein,
is an included angle between the umbrella rope and the radius of the bottom part,
is the tangent value of the included angle between the umbrella rope and the radius of the bottom.
Obtaining boundary conditions according to the height of the canopy and the radius of the bottom of the canopy; the boundary conditions are as follows:
wherein,
、
is composed of
The coordinate value of the bus of the umbrella coat,
、
is composed of
The coordinate value of the generatrix of the umbrella coat,
the radius of the bottom of the umbrella coat is,
is the height of the canopy.
Obtaining an umbrella canopy bus analytical expression according to the umbrella canopy bus parameter equation, the geometric constraint of the umbrella canopy and the boundary constraint, wherein the umbrella canopy bus analytical expression is as follows:
in one embodiment, solving a canopy length constraint equation obtained according to canopy length constraint under a given bottom radius by using a gradient method to obtain an expression of canopy height with respect to the bottom radius comprises:
obtaining an umbrella length constraint equation and an umbrella rope length constraint equation according to the geometric constraint among the height of the umbrella, the radius of the bottom of the umbrella and the tangent value of the included angle between the umbrella rope and the radius of the bottom; the canopy length constraint equation and the cord length constraint equation are as follows:
wherein,
is the total length of the semi-section curve of the canopy,lthe length of the umbrella rope is the length of the umbrella rope,
、
the derivative of the canopy bus parameter equation.
And solving the canopy length constraint equation under the given canopy bottom radius by adopting a gradient method to obtain an expression of the canopy height relative to the bottom radius.
In one embodiment, solving a canopy length constraint equation for a given canopy bottom radius using a gradient method to obtain an expression of canopy height with respect to bottom radius comprises:
the height of the canopy is used as an unknown number, and the umbrella height is set according to the length of the canopy and the current height of the canopyhThe difference between the calculated canopy length values is a function of canopy height; the function with respect to canopy height is:
an initial canopy height, step size, and threshold are set for a given canopy bottom radius.
Calculating a differential value of the function of the canopy height when the canopy height is the initial canopy height according to the function of the canopy height, the initial canopy height and the stepping amount;
calculating a new canopy height according to the differential value of the function related to the canopy height when the canopy height is the initial canopy height, the value of the function related to the canopy height when the canopy height is the initial canopy height, and the initial canopy height;
and when the absolute value of the function related to the height of the canopy corresponding to the new height of the canopy is greater than or equal to the threshold, taking the new height of the canopy as the initial height of the canopy, and continuing to calculate until the absolute value of the function related to the height of the canopy corresponding to the new height of the canopy is less than the threshold, so as to obtain the height of the canopy under the given radius of the bottom of the canopy.
And calculating the canopy height under the bottom radius of each given canopy by adopting the steps to obtain an expression of the canopy height relative to the bottom radius.
In one embodiment, an expression of the bottom radius with respect to time in the parachute opening process is obtained according to a calculation formula of the canopy bottom area and an evolution rule of the bottom area in the form of a power function with time, and the calculation formula of the canopy bottom area in the step is as follows:
wherein,
is composed of
The area of the bottom of the umbrella coat at any moment,
is composed of
The radius of the bottom of the canopy at any moment,
is the circumferential ratio.
The evolution rule of the bottom area of the power function form along with the time is expressed as
Wherein,
is composed oftThe area of the bottom at the moment of time,
and
representing the time of the initial state and the end state respectively,
，
and
the area of the bottom of the umbrella coat at the moment of the initial state and the end state respectively,nthe index is a constant index,
the expression of the bottom radius in relation to time in the process of opening the umbrella is as follows:
in one embodiment, obtaining the geometric characteristics of the canopy in each state in the umbrella opening process according to an analytical expression of a canopy bus taking a bottom radius as an independent variable and an expression of the bottom radius with respect to time in the umbrella opening process includes:
and obtaining the canopy bus analytical expression taking time as an independent variable according to the canopy bus analytical expression taking the bottom radius as the independent variable and the expression of the bottom radius with respect to time in the canopy opening process.
Analyzing and expressing the set time according to the umbrella coat busxIs equal to the constraint of 0And determining the maximum projection radius of the canopy at the set moment.
And determining the radius of the bottom of the canopy at a set moment according to the expression of the radius of the bottom with respect to time in the parachute opening process, and determining the volume corresponding to the rotating body of the bus of the canopy according to the radius of the bottom of the canopy at the set moment.
And determining the additional mass of the parachute under different expansion radiuses according to the corresponding volume and air density of the parachute canopy bus rotating body.
A device for rapidly solving for parachute deployment geometry, said device comprising:
the canopy bus analytical expression determining module is used for obtaining a canopy bus analytical expression according to a canopy bus parameter equation described by a preset parameter curve, geometric constraint and boundary constraint of the canopy; the canopy bus analytical expression comprises three parameters which are respectively: the height of the canopy, the radius of the bottom and the tangent value of the included angle between the umbrella rope and the radius of the bottom.
And the relation determination module of the canopy height relative to the bottom radius is used for solving a canopy length constraint equation obtained according to canopy length constraint under the given bottom radius by adopting a gradient method to obtain an expression of the canopy height relative to the bottom radius.
And the canopy bus analytical expression determining module is used for obtaining a canopy bus analytical expression with the bottom radius as the independent variable according to the canopy bus analytical expression and the expression of the canopy height relative to the bottom radius.
And the relation determination module of the bottom radius with respect to time is used for obtaining an expression of the bottom radius with respect to time in the parachute opening process according to a calculation formula of the bottom area of the canopy and an evolution rule of the bottom area in the form of a power function along with time.
And the geometric characteristic determining module of the canopy is used for obtaining the geometric characteristic of the canopy in each state in the canopy opening process according to a canopy bus analytical expression taking the bottom radius as an independent variable and the expression of the bottom radius in relation to time in the canopy opening process.
In one embodiment, the canopy generatrix is expressed analyticallyThe formula determining module is also used for establishing a coordinate system by taking a half of the central section of the canopy as a research object; the coordinate system takes the intersection point of the bottom radius of the umbrella coat section and the symmetry axis as the origin, and takes the straight line of the bottom radius as the originxAxis, about axis of symmetryyShaft building; describing an axisymmetric canopy bus by adopting a preset parameter curve to obtain a canopy bus parameter equation, wherein the canopy bus parameter equation is as follows:
wherein s is a shape parameter,
and a, b, c, d, e and f are constant parameters.
Obtaining the geometric constraint of the canopy according to the physical characteristics in the umbrella opening process, wherein the geometric constraint of the canopy comprises the following steps: the top of the umbrella coat is a pole, and the bottom of the umbrella coat is tangent to the umbrella rope; the expression of the geometric constraint of the canopy is as follows:
wherein,
is an included angle between the umbrella rope and the radius of the bottom part,
is the tangent value of the included angle between the umbrella rope and the radius of the bottom.
Obtaining boundary conditions according to the height of the canopy and the radius of the bottom of the canopy; the boundary conditions are as follows:
wherein,
、
is composed of
The coordinate value of the generatrix of the umbrella coat,
、
is composed of
The coordinate value of the bus of the umbrella coat,
the radius of the bottom of the umbrella coat is,
is the height of the canopy.
Obtaining an umbrella canopy bus analytical expression according to the umbrella canopy bus parameter equation, the geometric constraint of the umbrella canopy and the boundary constraint, wherein the umbrella canopy bus analytical expression is as follows:
in one embodiment, the relation determination module of the canopy height with respect to the bottom radius is further configured to obtain a canopy length constraint equation and a canopy cord length constraint equation according to geometric constraints among the canopy height, the canopy bottom radius and a tangent value of an included angle between a canopy cord and the bottom radius; the canopy length constraint equation and the cord length constraint equation are as follows:
wherein,
is the total length of the semi-section curve of the canopy,lthe length of the umbrella rope is the length of the umbrella rope,
、
is the derivative of the parameter equation of the canopy bus.
And solving a canopy length constraint equation under the given canopy bottom radius by adopting a gradient method to obtain an expression of canopy height relative to the bottom radius.
The method utilizes a parameter curve to describe an axisymmetric canopy bus, and expresses a canopy bus equation as a univariate function described by a bottom radius by three geometric constraints of zero derivative at the top of the canopy, tangency between the bottom of the canopy and a canopy rope and unchanged canopy length, so that an analytical equation of the canopy bus can be obtained as long as the bottom radius is given; and solving the change of the geometrical characteristics in the parachute opening process by combining a power function parachute opening formula widely applied in engineering and an analytical equation of a canopy bus. The method combines the classical umbrella-opening empirical formula and the parameterized umbrella cover shape analysis description to solve the geometric characteristics of the umbrella cover in the whole umbrella-opening process, not only can meet the geometric constraint and the test data constraint in the umbrella-opening process, but also has quick solution and less memory consumption; in the field of computers, the method can greatly reduce the data volume for describing the appearance of the parachute, and greatly reduce the memory requirement and the calculation time requirement.
Drawings
FIG. 1 is a schematic flow chart diagram of a method for rapidly solving parachute deployment geometry according to one embodiment;
FIG. 2 is a parachute system in one embodiment;
FIG. 3 is a geometric depiction of the configuration of the canopy in one embodiment;
FIG. 4 is a block diagram showing the structure of a device for rapidly solving the unfolding geometry of the parachute in one embodiment;
FIG. 5 is a diagram of the internal structure of a computer device in one embodiment;
FIG. 6 is a cross-sectional view of the canopy with different bottom diameter changes calculated according to another embodiment, wherein (a) the radius is 0.5m, (b) the radius is 1.0m, (c) the radius is 1.5m, (d) the radius is 2.0m, and (e) the radius is 2.5m;
FIG. 7 is the result of the parachute airdrop test in another embodiment;
fig. 8 is a three-dimensional view of the canopy profile during inflation of the canopy in another embodiment, wherein (a) is a three-dimensional view of the canopy profile at 0.01s, (b) is a three-dimensional view of the canopy profile at 0.03s, (c) is a three-dimensional view of the canopy profile at 0.06s, (d) is a three-dimensional view of the canopy profile at 0.1s, (e) is a three-dimensional view of the canopy profile at 0.16s, (f) is a three-dimensional view of the canopy profile at 0.20s, (g) is a three-dimensional view of the canopy profile at 0.22s, and (h) is a three-dimensional view of the canopy profile at 0.26 s.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of and not restrictive on the broad application.
In one embodiment, as shown in fig. 1, there is provided a method for rapidly solving for parachute deployment geometry, the method comprising the steps of:
step 100: obtaining an umbrella canopy bus analytical expression according to an umbrella canopy bus parameter equation described by a preset parameter curve, the geometric constraint and the boundary constraint of the umbrella canopy; the umbrella-coat bus analytical expression comprises three parameters which are respectively: the height of the canopy, the radius of the bottom and the tangent value of the included angle between the umbrella rope and the radius of the bottom.
Specifically, the parachute in the method is a circular parachute, that is, the canopy can be regarded as a rotation body of the canopy bus along the symmetry axis, as shown in fig. 2. Selecting the canopyHalf of the central section is the subject of study, and a coordinate system as shown in FIG. 3 is established, which uses the intersection point of the bottom radius of the canopy section and the symmetry axis as the origin, and uses the straight line of the bottom radius as the originxAxis, about axis of symmetryyEstablishing a shaft; the analytical expression of the umbrella coat bus is established under the coordinate system.
Canopy height is the distance from the top of the canopy to the bottom of the canopy, and in figure 3 canopy height is usedhAnd (4) showing.
The bottom radius is the distance from the lowermost end of the canopy bus to the axis of rotational symmetry, and is used as the bottom radius in FIG. 3rAnd (4) showing.
The tangent value of the included angle between the umbrella rope and the bottom radius is the included angle between the umbrella bottom radius and the umbrella rope in the umbrella opening process of the umbrella
The tangent value of (c). Common parameters for tangent value of included angle between umbrella rope at back side and bottom radiuskAnd (4) showing.
Step 102: and solving a canopy length constraint equation obtained according to canopy length constraint under the given bottom radius by adopting a gradient method to obtain an expression of the canopy height relative to the bottom radius.
Specifically, the canopy length constraint equation is derived from geometric constraints that the canopy length is constant during the parachute opening process.
Because of the expression of canopy height h with respect to bottom radius r, which is difficult to obtain from the canopy length constraint equation, there is an analytical solution to the canopy length constraint equation. Therefore, the solution is carried out by adopting a numerical analysis mode.
Step 104: and obtaining the canopy bus analytical expression taking the bottom radius as an independent variable according to the canopy bus analytical expression and the expression of the canopy height relative to the bottom radius.
Specifically, the analytical expression of the canopy bus comprises parameters of the height of the canopy, the radius of the bottom and the tangent value of an included angle between the canopy rope and the radius of the bottom.
As shown in fig. 3, the tangent of the bottom radius, the angle between the cord and the bottom radius
Can be obtained according to the tangent theorem of right-angled triangles,
。
replacing the canopy height in the canopy bus analytical expression with the canopy height expression relative to the bottom radius, and using the tangent value of the bottom radius and the included angle between the canopy rope and the bottom radius
And replacing to obtain the canopy bus analytical expression taking the bottom radius as an independent variable.
Step 106: and obtaining an expression of the bottom radius with respect to time in the umbrella opening process according to a calculation formula of the bottom area of the canopy and an evolution rule of the bottom area in the form of a power function along with time.
Specifically, the canopy is a body formed by rotating a canopy bus along a symmetry axis, so that the bottom of the canopy is a circle, the radius of the bottom of the canopy is the radius of the bottom, and the area of the bottom of the canopy is calculated by adopting a calculation formula of the area of the circle.
The evolution law of the bottom area over time in the form of a power function is a function of the change of the bottom area over time.
The calculation formula of the umbrella canopy bottom area is equal to the umbrella canopy bottom area expressed by the evolution rule of the power function form bottom area along with time, the time is used as an independent variable, the bottom radius is used as a dependent variable, and the equation is sorted to obtain the expression of the bottom radius in the umbrella opening process with respect to the time.
Step 108: and obtaining the geometric characteristics of the canopy in each state in the umbrella opening process according to an analytical expression of the canopy bus taking the bottom radius as an independent variable and an expression of the bottom radius with respect to time in the umbrella opening process.
Specifically, for any given moment, the bottom radius of the corresponding moment can be determined according to the expression of the bottom radius with respect to time in the parachute opening process, and the bottom radius is substituted into the canopy bus analytical expression with the bottom radius as an independent variable to obtain the canopy bus analytical expression at the corresponding moment. The canopy bus analytical expression can be used for calculating parameters such as the shape parameters, the volume of the canopy and the additional mass of the parachute at different unfolding radiuses.
By adopting the method, the canopy appearance data of the parachute at the given parachute opening radius can be quickly solved, the canopy envelope volume at the given parachute opening radius is solved, and a reference is provided for the calculation of the additional mass; and generating three-dimensional data of the circular umbrella for rapid three-dimensional rendering of the circular umbrella, thereby greatly reducing the memory requirement and the calculation time requirement.
In the method for quickly solving the unfolding geometric characteristics of the parachute, an axisymmetric canopy bus is described by using a parameter curve, and a canopy bus equation is expressed as a univariate function described by a bottom radius by three geometric constraints of zero derivative at the top of the canopy, tangency between the bottom of the canopy and a canopy rope and unchanged canopy length, so that an analytical equation of the canopy bus can be obtained as long as the bottom radius is given; and solving the geometrical characteristic change of the parachute in the parachute opening process by combining a power function parachute opening formula widely applied in engineering and an analytic equation of a canopy bus. The method combines a classical parachute opening empirical formula and parameterized parachute canopy appearance analytical description to solve the geometrical characteristics of the parachute canopy in the whole parachute opening process, not only can meet geometrical constraint and test data constraint in the parachute opening process, but also is rapid in solution and low in memory consumption; in the field of computers, the method can greatly reduce the data volume for describing the appearance of the parachute, and greatly reduce the memory requirement and the calculation time requirement.
In one embodiment, as shown in fig. 2-3, step 100 includes: establishing a coordinate system by taking a half of the central section of the canopy as a research object; the coordinate system takes the intersection point of the bottom radius of the umbrella coat section and the symmetry axis as the origin, and the straight line of the bottom radius as the originxAxis, about axis of symmetryyEstablishing a shaft; describing an axisymmetric canopy bus by adopting a preset parameter curve to obtain a canopy bus parameter squareThe parameter equation of the canopy bus is as follows:
wherein s is a shape parameter,
and a, b, c, d, e and f are constant parameters.
According to the physical characteristics in the umbrella opening process, obtaining the geometric constraints of the canopy, wherein the geometric constraints of the canopy comprise: the top of the canopy is a pole, and the bottom of the canopy is tangent to the umbrella rope; the expression of the geometric constraint of the canopy is:
wherein,
is an included angle between the umbrella rope and the radius of the bottom part,
is the tangent value of the included angle between the umbrella rope and the radius of the bottom.
Obtaining boundary conditions according to the height of the canopy and the radius of the bottom of the canopy; the boundary conditions are as follows:
wherein,
、
is composed of
The coordinate value of the generatrix of the umbrella coat,
、
is composed of
The coordinate value of the generatrix of the umbrella coat,
the radius of the bottom of the umbrella coat is,
is the height of the canopy.
Obtaining an umbrella canopy bus analytical expression according to an umbrella canopy bus parameter equation, the geometric constraint and the boundary constraint of the umbrella canopy, wherein the umbrella canopy bus analytical expression is as follows:
in one embodiment, step 102 comprises: obtaining an umbrella length constraint equation and an umbrella rope length constraint equation according to the geometric constraint among the height of the umbrella, the radius of the bottom of the umbrella and the tangent value of the included angle between the umbrella rope and the radius of the bottom; the canopy length constraint equation and the parachute cord length constraint equation are as follows:
wherein,
is the total length of the semi-section curve of the canopy,lthe length of the umbrella rope is the same as the length of the umbrella rope,
、
is the derivative of the umbrella canopy bus parameter equation; and solving a canopy length constraint equation under the given canopy bottom radius by adopting a gradient method to obtain an expression of canopy height relative to the bottom radius.
In one embodiment, the steps of: solving a canopy length constraint equation under the given canopy bottom radius by adopting a gradient method to obtain an expression of canopy height relative to the bottom radius, wherein the expression comprises the following steps: the height of the canopy is used as an unknown number, and the umbrella height is set according to the length of the canopy and the current height of the canopyhThe difference between the calculated canopy length values is a function of canopy height; the function for the canopy height is:
here, the parameters are
Also considered as a function variable is that,Lthe total length of the semi-section curve of the canopy is calculated under the condition that the canopy height meets the length constraint (set canopy height parameters);
is to make the umbrella clothes highhAs calculation of solution variableshValues in the case of different values.
Setting an initial canopy height, a stepping amount and a threshold value under a given canopy bottom radius; calculating a differential value of the function of the canopy height when the canopy height is the initial canopy height according to the function of the canopy height, the initial canopy height and the stepping amount; calculating a new canopy height according to a differential value of a function about the canopy height when the canopy height is the initial canopy height, a value of the function about the canopy height when the canopy height is the initial canopy height, and the initial canopy height; when the absolute value of the function value corresponding to the new canopy height and related to the canopy height is greater than or equal to the threshold value, taking the new canopy height as the initial canopy height, and continuing to calculate until the absolute value of the function value corresponding to the new canopy height and related to the canopy height is less than the threshold value, so as to obtain the canopy height under the given canopy bottom radius; and calculating the canopy height under the bottom radius of each given canopy by adopting the steps to obtain an expression of the canopy height relative to the bottom radius.
Specifically, the first equation in equation (5) is difficult to obtainhAboutrBut the integral equation is solved. The invention will be highhAs the unknown number, the given number is obtained by gradient methodrThe canopy length constraint equation below. Namely, the function:
。
the calculation algorithm is expressed as:
(1) Initialization, orderh 0 = L/2，dh = L/10000，
；
(2) Computing
；
(3) Computing
(4) Judgment of
If yes, outputting
(ii) a Otherwise, make it
And returning to the step (2).
The calculation result shows that the iteration step can be completed by two steps.
In one embodiment, the area of the canopy bottom in step 106 is calculated as:
wherein,
is composed of
The area of the bottom of the umbrella coat at any moment,
is composed of
The radius of the bottom of the umbrella coat is equal,
is the circumference ratio. The expression of the evolution law of the bottom area of the power function form with time is as follows:
wherein,
is composed oftThe area of the bottom at the moment of time,
and
respectively representing the time instants of the initial state and the final state,
，
and
the area of the bottom of the umbrella coat at the moment of the initial state and the end state respectively,nis a common index and is generally obtained through experiments.
The expression of the bottom radius in relation to time in the process of opening the umbrella is as follows:
in one embodiment, step 108 includes: obtaining an umbrella cover bus analytical expression taking time as an independent variable according to the umbrella cover bus analytical expression taking the bottom radius as the independent variable and an expression of the bottom radius with respect to time in the umbrella opening process; analyzing and expressing the set time according to the canopy busxThe derivative of which is equal to the constraint condition of 0, and determining the maximum projection radius of the canopy at the set moment; determining the radius of the bottom of the canopy at a set moment according to the expression of the radius of the bottom with respect to time in the process of opening the canopy, and determining the volume corresponding to the rotating body of the bus of the canopy according to the radius of the bottom of the canopy at the set moment; and determining the additional mass of the parachute under different expansion radiuses according to the corresponding volume and air density of the canopy bus rotating body.
Specifically, the maximum projection radius of the canopy can be determined by
Is determined by the maximum of
It can be determined when
When the utility model is used, the water is discharged,xthe maximum projection radius.
When the radius of the bottom of the canopy isrWhen the umbrella is used, the corresponding volume of the umbrella coat bus rotating body is as follows:
the volume calculation formula is discretely integrated, i.e. the volume is expressed as:
。
the additional mass of the parachute at different unfolding radii can be determined by the volume:
wherein
Is the density of air.
In the field of aerospace engineering, the conventional fluid-solid coupling method is time-consuming in calculation, complicated in front and back processing, usually the calculation time is dozens of hours, and the requirement of engineering optimization calculation cannot be met. The method adopted by the invention combines the classical umbrella-opening empirical formula and the parameterized umbrella cover shape analytic description to solve the geometric characteristics of the umbrella cover in the whole umbrella-opening process, not only can meet the geometric constraint and the test data constraint in the umbrella-opening process, but also has quick solution and less memory consumption. The geometrical characteristics of the parachute in the parachute opening process can be calculated within 1s by adopting a CPU (Central processing Unit) with the frequency of 2.5GHz, and the calculation time of the conventional fluid-solid coupling method is at least tens of hours. In the field of computers, the method provided by the invention can greatly reduce the data volume for describing the appearance of the parachute, and has high approximation degree with the real state.
It should be understood that, although the steps in the flowchart of fig. 1 are shown in order as indicated by the arrows, the steps are not necessarily performed in order as indicated by the arrows. The steps are not performed in the exact order shown and described, and may be performed in other orders, unless explicitly stated otherwise. Moreover, at least a portion of the steps in fig. 1 may include multiple sub-steps or multiple stages that are not necessarily performed at the same time, but may be performed at different times, and the order of performance of the sub-steps or stages is not necessarily sequential, but may be performed in turn or alternately with other steps or at least a portion of the sub-steps or stages of other steps.
In one embodiment, as shown in fig. 4, there is provided a device for rapidly solving the unfolding geometry of a parachute, comprising: the umbrella canopy bus analysis expression determination module, the umbrella canopy height relation determination module with respect to the bottom radius, the umbrella canopy bus analysis expression determination module with the bottom radius as an independent variable, the bottom radius relation determination module with respect to time and the umbrella canopy geometric feature determination module, wherein:
the canopy bus analytical expression determining module is used for obtaining a canopy bus analytical expression according to a canopy bus parameter equation described by a preset parameter curve, geometric constraint and boundary constraint of the canopy; the umbrella-coat bus analytical expression comprises three parameters which are respectively: the height of the canopy, the radius of the bottom and the tangent value of the included angle between the umbrella rope and the radius of the bottom.
And the relation determination module of the canopy height relative to the bottom radius is used for solving a canopy length constraint equation obtained according to canopy length constraint under the given bottom radius by adopting a gradient method to obtain an expression of the canopy height relative to the bottom radius.
And the canopy bus analytical expression determining module is used for obtaining a canopy bus analytical expression taking the bottom radius as the independent variable according to the canopy bus analytical expression and an expression of the canopy height relative to the bottom radius.
And the relation determination module of the bottom radius with respect to time is used for obtaining an expression of the bottom radius with respect to time in the parachute opening process according to a calculation formula of the bottom area of the canopy and an evolution rule of the bottom area in the form of a power function along with time.
And the geometric characteristic determining module of the canopy is used for obtaining the geometric characteristic of the canopy in each state in the umbrella opening process according to an analytical expression of the canopy bus taking the bottom radius as an independent variable and an expression of the bottom radius with respect to time in the umbrella opening process.
In one embodiment, the umbrella canopy bus resolution tableThe expression determining module is also used for establishing a coordinate system by taking a half of the central section of the canopy as a research object; the coordinate system takes the intersection point of the bottom radius of the umbrella coat section and the symmetry axis as the origin, and the straight line of the bottom radius as the originxAxis, about axis of symmetryyEstablishing a shaft; and describing the axisymmetric canopy bus by adopting a preset parameter curve to obtain a canopy bus parameter equation, wherein the canopy bus parameter equation is shown as the formula (1). According to the physical characteristics in the umbrella opening process, obtaining the geometric constraint of the canopy, wherein the geometric constraint of the canopy comprises the following steps: the top of the canopy is a pole, and the bottom of the canopy is tangent to the umbrella rope; the expression of the geometric constraint of the canopy is shown in formula (2).
Obtaining boundary conditions according to the height of the canopy and the radius of the bottom of the canopy; the boundary conditions are shown in formula (3).
And obtaining an umbrella canopy bus analytical expression according to the umbrella canopy bus parameter equation, the geometric constraint of the umbrella canopy and the boundary constraint, wherein the umbrella canopy bus analytical expression is shown as a formula (4).
In one embodiment, the relation determination module of the canopy height with respect to the bottom radius is further configured to obtain a canopy length constraint equation and a canopy cord length constraint equation according to geometric constraints among the canopy height, the canopy bottom radius and a tangent value of an included angle between a canopy cord and the bottom radius; the canopy length constraint equation and the parachute cord length constraint equation are shown in the formula (5).
And solving the canopy length constraint equation under the given canopy bottom radius by adopting a gradient method to obtain an expression of the canopy height relative to the bottom radius.
In one embodiment, the canopy bus analytic expression determining module is further configured to use the canopy height as an unknown, and set the canopy length according to the canopy height and the current canopy heighthThe difference between the calculated canopy length values is a function of canopy height; the function for canopy height is shown in equation (6). Setting an initial canopy height, a stepping amount and a threshold value under the radius of the bottom of a given canopy; calculating a differential value of the function of the canopy height when the canopy height is the initial canopy height according to the function of the canopy height, the initial canopy height and the stepping amount; root of herbaceous plantCalculating a new canopy height according to a differential value of a function about the canopy height when the canopy height is the initial canopy height, a value of the function about the canopy height when the canopy height is the initial canopy height, and the initial canopy height; when the absolute value of the function value corresponding to the new canopy height and related to the canopy height is larger than or equal to the threshold value, taking the new canopy height as the initial canopy height, and continuing to calculate until the absolute value of the function value corresponding to the new canopy height and related to the canopy height is smaller than the threshold value, so as to obtain the canopy height under the given canopy bottom radius; and calculating the canopy height under the bottom radius of each given canopy by adopting the steps to obtain an expression of the canopy height relative to the bottom radius.
In one embodiment, the relationship of the bottom radius with respect to time determines the formula for calculating the area of the bottom of the canopy in the module as shown in equation (7).
An expression of the evolution law of the bottom area of the power function form with time is shown in formula (8).
The expression of the bottom radius with respect to time in the process of opening the umbrella is shown as the formula (9).
In one embodiment, the geometric feature determination module of the canopy is further configured to obtain a canopy bus analytical expression with time as an independent variable according to a canopy bus analytical expression with the bottom radius as an independent variable and an expression of the bottom radius with respect to time in the canopy opening process; analyzing and expressing the set time according to the umbrella coat busxThe derivative of which is equal to the constraint condition of 0, and determining the maximum projection radius of the canopy at the set moment; determining the umbrella coat bottom radius at a set moment according to an expression of the bottom radius with respect to time in the umbrella opening process, and determining the volume corresponding to the umbrella coat bus rotating body according to the umbrella coat bottom radius at the set moment; and determining the additional mass of the parachute under different expansion radiuses according to the corresponding volume and air density of the canopy bus rotating body.
The specific definition of the rapid solution device for the parachute unfolding geometric features can be referred to the above definition of the rapid solution method for the parachute unfolding geometric features, and will not be described in detail herein. The modules in the device for rapidly solving the parachute unfolding geometrical characteristics can be wholly or partially realized by software, hardware and a combination thereof. The modules can be embedded in a hardware form or independent from a processor in the computer device, and can also be stored in a memory in the computer device in a software form, so that the processor can call and execute operations corresponding to the modules.
In one embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as shown in fig. 5. The computer device includes a processor, a memory, a network interface, a display screen, and an input device connected by a system bus. Wherein the processor of the computer device is configured to provide computing and control capabilities. The memory of the computer device comprises a nonvolatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of an operating system and computer programs in the non-volatile storage medium. The network interface of the computer device is used for communicating with an external terminal through a network connection. The computer program is executed by a processor to implement a method for fast solution of parachute deployment geometry. The display screen of the computer equipment can be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer equipment can be a touch layer covered on the display screen, a key, a track ball or a touch pad arranged on a shell of the computer equipment, an external keyboard, a touch pad or a mouse and the like.
It will be appreciated by those skilled in the art that the configuration shown in fig. 5 is a block diagram of only a portion of the configuration associated with the present application, and is not intended to limit the computing device to which the present application may be applied, and that a particular computing device may include more or less components than those shown, or may combine certain components, or have a different arrangement of components.
In an embodiment, a computer device is provided, comprising a memory storing a computer program and a processor implementing the steps of the above method embodiments when executing the computer program.
In a verification embodiment, a numerical simulation mode is adopted for verification, program operation is efficient, and a calculation result is stable. For a typical C9 parachute (nominal canopy diameter is 8.5m, canopy length is 9 m), the symmetric cross-sections of the canopy with different bottom diameter changes calculated by the above method are shown in fig. 6, where (a) radius is 0.5m, (b) radius is 1.0m, (C) radius is 1.5m, (d) radius is 2.0m, and (e) radius is 2.5m. The airdrop test results are shown in fig. 7. Comparing fig. 6 and fig. 7, it can be seen that the umbrella cover shape description method provided by the invention has a high approximation degree to the geometric characteristics of the umbrella cover, and can meet the engineering calculation requirements.
After obtaining the data of the symmetrical section, the canopy data in the three-dimensional space can be obtained by performing rotation transformation around the symmetrical axis, and the inflation process described by the formula (9) is used to provide a canopy profile three-dimensional diagram in the canopy inflation process, as shown in fig. 8, wherein (a) is a canopy profile three-dimensional diagram at 0.01s, (b) is a canopy profile three-dimensional diagram at 0.03s, (c) is a canopy profile three-dimensional diagram at 0.06s, (d) is a canopy profile three-dimensional diagram at 0.1s, (e) is a canopy profile three-dimensional diagram at 0.16s, (f) is a canopy profile three-dimensional diagram at 0.20s, (g) is a canopy profile three-dimensional diagram at 0.22s, and (h) is a canopy profile three-dimensional diagram at 0.26 s. The whole three-dimensional data is automatically generated by a program, extra data storage and data operation are not needed, and the three-dimensional model rendering of the parachute can be accelerated.
The technical features of the above embodiments can be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the above embodiments are not described, but should be considered as the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express several embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present patent application shall be subject to the appended claims.
Claims (7)
1. A method for rapidly solving for parachute deployment geometry, the method comprising:
obtaining an umbrella canopy bus analytical expression according to an umbrella canopy bus parameter equation described by a preset parameter curve, the geometric constraint and the boundary constraint of the umbrella canopy; the canopy bus analytical expression comprises three parameters which are respectively: the tangent values of the height of the canopy, the radius of the bottom and the included angle between the parachute cords and the radius of the bottom;
solving a canopy length constraint equation obtained according to canopy length constraint under a given bottom radius by adopting a gradient method to obtain an expression of canopy height relative to the bottom radius;
obtaining an umbrella coat bus analytical expression taking the bottom radius as an independent variable according to the umbrella coat bus analytical expression and the expression of the umbrella coat height relative to the bottom radius;
obtaining an expression of the bottom radius in the umbrella opening process with respect to time according to a calculation formula of the umbrella coat bottom area and an evolution rule of the bottom area in the form of a power function along with time;
obtaining the geometric characteristics of the canopy in each state in the umbrella opening process according to an analytical expression of the canopy bus taking the bottom radius as an independent variable and an expression of the bottom radius with respect to time in the umbrella opening process;
the method comprises the following steps of obtaining an umbrella canopy bus analytical expression according to an umbrella canopy bus parameter equation described by a preset parameter curve, geometric constraint and boundary constraint of an umbrella canopy, and comprises the following steps:
establishing a coordinate system by taking a half of the central section of the canopy as a research object; the coordinate system takes the intersection point of the bottom radius of the canopy section and the symmetry axis as the origin, and takes the straight line of the bottom radius asxAxis about the axis of symmetryyShaft building;
the method comprises the following steps of describing an axisymmetric canopy bus by adopting a preset parameter curve to obtain a canopy bus parameter equation, wherein the canopy bus parameter equation is as follows:
wherein,sas the parameters of the shape of the film,
，a，b，c，d，e，fis a constant parameter;
obtaining the geometric constraint of the canopy according to the physical characteristics in the umbrella opening process, wherein the geometric constraint of the canopy comprises the following steps: the top of the umbrella coat is a pole, and the bottom of the umbrella coat is tangent to the umbrella rope; the expression of the geometric constraint of the canopy is as follows:
wherein,
is an included angle between the umbrella rope and the radius of the bottom part,
the tangent value of the included angle between the umbrella rope and the radius of the bottom part;
obtaining boundary conditions according to the height of the canopy and the radius of the bottom of the canopy; the boundary conditions are as follows:
wherein,
、
is composed of
The coordinate value of the generatrix of the umbrella coat,
、
is composed of
The coordinate value of the generatrix of the umbrella coat,
the radius of the bottom of the umbrella coat is,
is the height of the canopy;
obtaining an umbrella canopy bus analytical expression according to the umbrella canopy bus parameter equation, the geometric constraint of the umbrella canopy and the boundary constraint, wherein the umbrella canopy bus analytical expression is as follows:
the method for obtaining the geometrical characteristics of the canopy in each state in the umbrella opening process according to the canopy bus analytical expression taking the bottom radius as an independent variable and the expression of the bottom radius with respect to time in the umbrella opening process comprises the following steps:
obtaining an umbrella cover bus analytical expression taking time as an independent variable according to the umbrella cover bus analytical expression taking the bottom radius as the independent variable and the expression of the bottom radius with respect to time in the umbrella opening process;
analyzing and expressing the set time according to the canopy busxThe derivative of which is equal to the constraint condition of 0, and determining the maximum projection radius of the canopy at the set moment;
determining the umbrella coat bottom radius at a set moment according to an expression of the bottom radius with respect to time in the umbrella opening process, and determining the volume corresponding to the umbrella coat bus rotating body according to the umbrella coat bottom radius at the set moment;
and determining the additional mass of the parachute under different expansion radiuses according to the corresponding volume and air density of the canopy bus rotating body.
2. The method of claim 1, wherein solving a canopy length constraint equation from a canopy length constraint at a given bottom radius using a gradient method to obtain an expression of canopy height with respect to bottom radius comprises:
obtaining an umbrella length constraint equation and an umbrella rope length constraint equation according to the geometric constraint among the height of the umbrella, the radius of the bottom of the umbrella and the tangent value of the included angle between the umbrella rope and the radius of the bottom; the canopy length constraint equation and the parachute cord length constraint equation are as follows:
wherein,
is the total length of the semi-section curve of the canopy,lthe length of the umbrella rope is the length of the umbrella rope,
、
is the derivative of the canopy bus parameter equation;
and solving the canopy length constraint equation under the given canopy bottom radius by adopting a gradient method to obtain an expression of the canopy height relative to the bottom radius.
3. The method of claim 2, wherein solving a canopy length constraint equation for a given canopy bottom radius using a gradient method to obtain an expression of canopy height with respect to bottom radius comprises:
the height of the canopy is used as an unknown number, and the umbrella height is set according to the length of the canopy and the current height of the canopyhThe difference between the calculated canopy length values is a function of canopy height; the function with respect to canopy height is:
setting an initial canopy height, a stepping amount and a threshold value under a given canopy bottom radius;
calculating a differential value of the function of the canopy height when the canopy height is the initial canopy height according to the function of the canopy height, the initial canopy height and the stepping amount;
calculating a new canopy height according to the differential value of the function related to the canopy height when the canopy height is the initial canopy height, the value of the function related to the canopy height when the canopy height is the initial canopy height, and the initial canopy height;
when the absolute value of the function value corresponding to the new canopy height and related to the canopy height is larger than or equal to the threshold value, taking the new canopy height as the initial canopy height, and continuing to calculate until the absolute value of the function value corresponding to the new canopy height and related to the canopy height is smaller than the threshold value, so as to obtain the canopy height under the given canopy bottom radius;
and calculating the canopy height under the bottom radius of each given canopy by adopting the steps to obtain an expression of the canopy height relative to the bottom radius.
4. The method according to claim 1, wherein the expression of the bottom radius with respect to time during the parachute opening process is obtained according to a calculation formula of the canopy bottom area and a time evolution law of the bottom area in the form of a power function, wherein the calculation formula of the canopy bottom area in the step is as follows:
wherein,
is composed of
The area of the bottom of the umbrella coat at any moment,
is composed of
The radius of the bottom of the canopy at any moment,
is the circumferential ratio;
the evolution rule of the bottom area of the power function form along with the time is expressed as
Wherein,
is composed oftThe area of the bottom at the moment of time,
and
representing the time of the initial state and the end state respectively,
，
and
the area of the bottom of the umbrella coat at the moment of the initial state and the end state respectively,nis a constant index;
the expression of the bottom radius in the umbrella opening process with respect to time is as follows:
5. a device for the rapid solution of parachute deployment geometry, said device comprising:
the canopy bus analytical expression determining module is used for obtaining a canopy bus analytical expression according to a canopy bus parameter equation described by a preset parameter curve, geometric constraint and boundary constraint of the canopy; the canopy bus analytical expression comprises three parameters which are respectively: the tangent values of the height of the canopy, the radius of the bottom and the included angle between the umbrella rope and the radius of the bottom;
the system comprises a relation determination module of the canopy height relative to the bottom radius, a data acquisition module and a data processing module, wherein the relation determination module is used for solving a canopy length constraint equation obtained according to canopy length constraint under a given bottom radius by adopting a gradient method to obtain an expression of the canopy height relative to the bottom radius;
the canopy bus analytical expression determining module is used for obtaining a canopy bus analytical expression with the bottom radius as the independent variable according to the canopy bus analytical expression and the expression of the canopy height relative to the bottom radius;
the relation determination module of the bottom radius with respect to time is used for obtaining an expression of the bottom radius with respect to time in the umbrella opening process according to a calculation formula of the bottom area of the canopy and an evolution rule of the bottom area in a power function form along with time;
the umbrella cover geometric characteristic determining module is used for obtaining the geometric characteristics of the umbrella cover in each state in the umbrella opening process according to an umbrella cover bus analytical expression taking the bottom radius as an independent variable and an expression of the bottom radius in relation to time in the umbrella opening process;
the canopy bus analytical expression determining module is also used for establishing a coordinate system by taking a half of the central section of the canopy as a research object; the coordinate system takes the intersection point of the bottom radius of the umbrella coat section and the symmetry axis as the origin, and takes the straight line of the bottom radius as the originxAxis about the axis of symmetryyEstablishing a shaft; describing an axisymmetric canopy bus by adopting a preset parameter curve to obtain a canopy bus parameter equation, wherein the canopy bus parameter equation is as follows:
wherein,sas the parameters of the shape of the film,
，a，b，c，d，e，fis a constant parameter;
obtaining the geometric constraint of the canopy according to the physical characteristics in the umbrella opening process, wherein the geometric constraint of the canopy comprises the following steps: the top of the umbrella coat is a pole, and the bottom of the umbrella coat is tangent to the umbrella rope; the expression of the geometric constraint of the canopy is as follows:
wherein,
is an included angle between the umbrella rope and the radius of the bottom part,
is the tangent value of the included angle between the umbrella rope and the radius of the bottom;
obtaining boundary conditions according to the height of the canopy and the radius of the bottom of the canopy; the boundary conditions are as follows:
wherein,
、
is composed of
The coordinate value of the generatrix of the umbrella coat,
、
is composed of
The coordinate value of the generatrix of the umbrella coat,
the radius of the bottom of the umbrella coat is,
is the height of the canopy;
obtaining an umbrella canopy bus analytical expression according to the umbrella canopy bus parameter equation, the geometric constraint of the umbrella canopy and the boundary constraint, wherein the umbrella canopy bus analytical expression is as follows:
the geometric characteristic determining module of the canopy is also used for analyzing an expression according to the canopy bus taking the bottom radius as an independent variable and in the canopy opening processObtaining an analytical expression of the umbrella coat bus by taking time as an independent variable through an expression of the bottom radius with respect to time; analyzing and expressing the set time according to the canopy busxThe derivative of the projection angle is equal to the constraint condition of 0, and the maximum projection radius of the canopy at the set moment is determined; determining the umbrella coat bottom radius at a set moment according to an expression of the bottom radius with respect to time in the umbrella opening process, and determining the volume corresponding to the umbrella coat bus rotating body according to the umbrella coat bottom radius at the set moment; and determining the additional mass of the parachute under different expansion radiuses according to the corresponding volume and air density of the canopy bus rotating body.
6. The device of claim 5, wherein the canopy height-to-bottom radius relationship determination module is further configured to obtain a canopy length constraint equation and a canopy cord length constraint equation based on geometric constraints among the canopy height, the canopy bottom radius, and a tangent of an angle between the canopy cord and the bottom radius; the canopy length constraint equation and the cord length constraint equation are as follows:
wherein,
is the total length of the semi-section curve of the canopy,lthe length of the umbrella rope is the same as the length of the umbrella rope,
、
is the derivative of the canopy bus parameter equation;
and solving the canopy length constraint equation under the given canopy bottom radius by adopting a gradient method to obtain an expression of the canopy height relative to the bottom radius.
7. A computer device comprising a memory and a processor, the memory storing a computer program, wherein the processor implements the steps of the method of any one of claims 1 to 4 when executing the computer program.
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