CN116186861B - Snowmobile ski track design method, snowmobile ski track and readable storage medium - Google Patents
Snowmobile ski track design method, snowmobile ski track and readable storage medium Download PDFInfo
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Abstract
The invention discloses a design method of a snowmobile sled track, the snowmobile sled track and a readable storage medium, and the design method of the snowmobile sled track comprises the following steps: s1, preparing a snowmobile sled motion equation, a center line design formula and a three-dimensional curved surface design formula according to characteristics of a snowmobile sled body and a snowmobile sled track; obtaining a motion track, speed and acceleration of a snowmobile sled body through a snowmobile sled motion equation; s2, performing field evaluation: the site fitness is evaluated in an auxiliary mode according to a snowmobile sled motion equation and a central line design formula; s3, center line design is carried out: designing a track center line according to a snowmobile sled motion equation and a center line design formula; s4, performing three-dimensional curved surface design of the racetrack: and designing a three-dimensional curved surface of the snowmobile ski track according to the snowmobile ski motion equation and the three-dimensional curved surface design formula. The method can solve the problem that the design method of the snowmobile sled race track is lacking in the prior art, and the safety of the race track cannot be ensured.
Description
Technical Field
The invention relates to the technical field of design of snowmobile ski tracks, in particular to a design method of a snowmobile ski track, a snowmobile ski track and a readable storage medium.
Background
The key parameters of the length, the fall, the gradient, the number of curves, the curve combination mode and the like of each snowmobile sled track in the world are different, and the parameters need to be designed according to the actual situation of the field (such as mountain terrain trend and the requirement of a competition field) and the movement characteristics of the snowmobile sled body so as to ensure the safety of the snowmobile sled track.
And the key parameters such as the length, the drop, the gradient, the number of curves, the curve combination mode and the like of the snowmobile ski racing track can be effectively known by athletes through racing track design analysis, the key parameters are closely related to the technical key points of the racing track, and the capability of the athletes for obtaining the optimal sliding track can be improved by combining with the key parameters of the racing track for assisting training, so that the athletic performance of the athletes is improved.
Disclosure of Invention
In view of the above, the embodiments of the present invention provide a design method of a snowmobile ski track, a snowmobile ski track and a readable storage medium, so as to solve the problem that the prior art lacks the design method of the snowmobile ski track, and the security of the track cannot be guaranteed. The embodiment of the invention provides a design method of a snowmobile sled track, which comprises the following steps of:
s1, preparing a snowmobile sled motion equation, a center line design formula and a three-dimensional curved surface design formula according to characteristics of a snowmobile sled body and a snowmobile sled track;
obtaining the motion trail, speed and acceleration of the snowmobile sled body through the snowmobile sled motion equation;
s2, performing field evaluation: the site fitness is evaluated in an auxiliary mode according to the snowmobile sledge motion equation and the center line design formula;
s3, center line design is carried out: designing a track center line according to the snowmobile sled motion equation and the center line design formula;
s4, performing three-dimensional curved surface design of the racetrack: and designing a three-dimensional curved surface of the snowmobile ski track according to the snowmobile ski motion equation and the three-dimensional curved surface design formula.
Optionally, in step S1, the generating of the snowmobile ski equation of motion includes the following steps:
s111, constructing a racetrack mathematical model: establishing a mathematical model aiming at a three-dimensional track curved surface, and converting the mathematical model into a mathematical model which can be described by a mathematical formula;
s112, performing track curved surface division: dividing the racetrack into a curve part and a straight part; the curve is subdivided into an entrance curve area, a driving area and an exit curve area as a calculation unit of a motion equation
S113, coordinate system setting: converting the three-dimensional space curved rectangular coordinate system into a curved linear coordinate system which is more fit with the motion state of the racing car;
s114, obtaining the motion state of each point at each moment of the racing car.
Optionally, in step S113, the stress state of the snowmobile ski body is analyzed by the following formula:
traction force of racing car: fq=mgsin α, where the total mass of the racing car and the athlete is m, the gravitational acceleration is g, and the included angle between the gravitational force and the ice surface at a certain moment is α;
air resistance: fw=1/2 ρCdAv 2 The method comprises the steps that the racing car receives air resistance in the advancing direction, the air density is set to be rho, the windward area of the racing car and a sportsman is set to be A, the wind resistance coefficient is Cd, the wind suction coefficient is Cl, and the racing car speed is v;
wind suction force: fl=1/2 ρClAv 2 The method comprises the steps that the racing car receives air resistance in the advancing direction, the air density is set to be rho, the windward area of the racing car and a sportsman is set to be A, the wind resistance coefficient is Cd, the wind suction coefficient is Cl, and the racing car speed is v;
gravity n-axis component affecting racing car and ice force: g_n=mgcos αcos β; or, the gravity n-axis component affecting the racing car and ice forces is expressed as: g_n=mgcos α_n, wherein the interaction force of the racing car and the ice surface is from the sum of the gravity of the racing car and the athlete, the centrifugal force and the component of the wind suction force in the direction perpendicular to the ice surface, namely the sum of the components on the n axis; after the gravity is decomposed into traction force Fq, the residual component still needs to be decomposed again in the plane from the n axis to the t axis, and the component along the n axis is the gravity component affecting the acting force of the racing car and the ice surface;
the component of gravity in the direction of the t-axis that determines the lateral movement of the racing car: g_t=mgcos αsin β; or, the component of gravity in the direction of the t-axis that determines the lateral movement of the racing car is expressed as: g_t=mgcos α_t, wherein n in the formula refers to a component of the front side magnitude of the component on the n axis, and is the same as the cos β value, and is a simplified writing method for decomposing stress;
centrifugal force: fc= (mv ζ2)/(r+Δr), wherein the racing car is set to rise a certain height on the ice surface due to centrifugal action at a certain moment, the turning radius of the racing car is r, the distance between the racing car and the central line of the racing car is Δr, and the turning radius of the racing car is r+Δr;
centrifugal force is in the n-axis component of the vertical ice surface: fc_n= (mv ζ2)/(r+Δr) _n
Centrifugal force is in the transverse t-axis component of racing car: fc_t= (mv ζ2)/(r+Δr) _t
Friction force on ice: f=u (fc_n+g_n-Fl), where the coefficient of friction of the racing car and the ice surface is set to μ.
Optionally, in step S114, the method includes: obtaining the motion states of each moment and each point position of the racing car through an iterative algorithm;
after setting boundary conditions, the iterative algorithm extracts the motion trail of the racing car to conduct differentiation, and the motion equation after differentiation is calculated in a circulating way to obtain the motion states of each moment and each point position of the racing car;
the snowmobile sled equation of motion includes:
dividing the central line of a section of curve into a plurality of minimum quantities, wherein the length of each section is deltas, the initial point number is P0 point, and the initial point number is P1 and P2 … Pi points which continue backwards in sequence, wherein i represents the iteration number; carrying out stress analysis on the Pi point, and analyzing the spatial position and the motion state of the Pi+1 point by utilizing a motion equation, so as to reciprocate, and analyzing the motion trail of the racing car point by point;
for any point P i+1 And P i Establishing a motion formula between two points, P i The initial velocity of the point along the s-axis direction is V si V along the direction of t axis ti . The displacement between two points along the S axis is S i The height difference is h i The upward displacement along the t-axis direction is S ti The height difference is h ti 。
According to the basic formula, the acting force between the racing car and the ice surface under the action of gravity is as follows:
G_n＝mg cos α i cosβ i
the effort between racing car and the ice surface under the centrifugal force is:
substituting the wind suction formula can obtain the friction force between the racing car and the ice surface at the moment i as follows:
combined with gravity and wind resistance, pair P along s-axis i+1 And P i The dynamic equilibrium equation of the motion state of the point can be obtained by establishing:
pair P along t axis i+1 And P i The dynamic equilibrium equation of the motion state of the point can be obtained by establishing:
then P i The final speed of the dots is:
P i the spatial coordinates of the points are:
at the time of setting up P i+1 And P i After the motion equation between the points, an iterative algorithm can be adopted to set the starting point P 0 After the initial condition of (2), P can be obtained gradually by cyclic calculation 1 、P 2 ...P n The data of the speed, the acceleration, the space point position and the like of the points are integrated, and the given race can be obtainedAnd the key data such as complete racing car motion trail, maximum speed, average speed, maximum acceleration, average acceleration and the like in the three-dimensional curved surface section.
Optionally, in step S114, the method further includes: calculating the running state of the racing car through computer auxiliary calculation;
the computer-aided calculation analyzes the motion equation, and simultaneously adopts an iterative algorithm as basic operation logic of the motion equation.
In the invention, after a basic stress formula is determined, the motion state of the racing car can be calculated by combining the formula, and an iterative algorithm is adopted in the research. The iterative algorithm is a calculation method similar to integral operation, after boundary conditions are set, the motion trail of the racing car is extracted to conduct differentiation, and the motion states of each moment and each point position of the racing car are obtained step by step through circularly calculating the motion equation after differentiation.
The central line of a section of curve is divided into a plurality of minimum quantities, the length of each section is deltas, the initial point number is P0 point, and the initial point number is P1 and P2 … Pi points which continue backwards in sequence, wherein i represents the iteration number. Carrying out stress analysis on Pi points, resolving the spatial position and the motion state of Pi+1 points by utilizing a motion equation, and resolving the motion trail of the racing car point by point in a reciprocating way
The content of the iterative algorithm mainly includes speed, displacement and time. For the speed, let the P0 point initial speed be Vs0 along the s-axis component, vt0 along the t-axis component, and similarly, the following speed components be Vs1, vs2 … Vsi, and Vt1, vt2 … Vti in order, the final speed of the racing car is:
for displacement, the running track of the racing car is decomposed along an S-axis and a t-axis, and the component S in the S-axis direction satisfies the formula:the component St in the t-axis direction satisfies the formula: st= Σ (st1+st2. +sti). Setting the actual running distance of the racing car as D, and for each section deltas, the corresponding distance Di meets the formula: d (D)The driving track s-axis is decomposed and can be divided into vertical displacement h and horizontal displacement L, and for any Si, the corresponding vertical and horizontal displacements are hi and Li. The horizontal and vertical components Lti and hti of Sti are extracted in the same way. For any point Pi, its vertical displacement along the s-axis satisfies the formula: phi= Σ (h1+h2+ … +hi), whose vertical displacement in the track cross-sectional direction satisfies the formula: phti= Σ (ht1+ht2+ … + hti). For any point Pi, the corresponding track center line curve radius is set as ri, and the actual motion curve radius of the point P meets the formula: rpi=ri+ Σ (lt1+lt2+ … +lti).
For the time, setting the running time corresponding to each section deltas as t, and enabling the total running duration of the racing car to meet the formula: t= Σ (t1+t2+ … +ti).
Therefore, the track line of the racing car is differentiated into a plurality of segments of minimum quantity, then the motion equation is applied to each segment of minimum quantity for independent calculation, the initial condition of each segment bears the calculation result of the previous segment, the calculation is repeatedly circulated, and the integral operation is carried out on the whole segment of motion equation by adopting computer iteration and algorithm, so that the motion state of the racing car of the whole segment of track can be obtained. The calculation result of each section is assembled into a series of operation data, and the operation track, the maximum speed, the maximum acceleration, the total duration, the total distance, the stress condition of any point and the like of the racing car can be obtained by summarizing in a computer. The higher the subdivision level, the more accurate the result.
Optionally, in step S3, the centerline design includes the steps of:
s31, determining the basic distribution condition of the track plane: after the individual functional areas in each area of a departure area, an end vehicle receiving area and a destination area are determined according to mountain terrain walking, a preliminary track plane layout partition map is determined on a drawing, and on the premise that no line shape is specifically designed, the layout trend of the whole track can be basically determined, so that a judgment basis is provided for the next step of line shape walking;
s32, determining linear basic trend, and obtaining a central line preliminary arrangement diagram: the specific running route of the track is designed according to the mountain trend, and in the design process, the speed and acceleration indexes and the degree of fit between the central line and the mountain are monitored in real time by means of the snowmobile sled equation of motion and the degree of fit calculation formula between the track and the field, so that the reasonable and effective line shape is ensured;
s33, center line deepening design: and converting the initial layout of the central line into an accurate central line plane diagram controlled by parameters according to the central line design formula.
Optionally, in step S32, a calculation formula of the degree of fit between the track and the field is: i.e {0,1,2,3,..n } where i represents the number of segment points on the centerline, n represents the number of segments, the greater n is, the more accurate the fitness calculation result is, and for a 2 km-long track, n can take a value of 2000;
ΔZ i ＝Z ci -Z ti
wherein Z is ci Representing the elevation of a segment point with the sequence number i on a central line, Z ti Representing the surface elevation of a segmentation point with a corresponding central line number i on a field;
if DeltaZ i ≥0,ΔZ i ∈F；
If DeltaZ i ＜0,ΔZ i ∈E；
Then:
the total amount of filling is
The total amount of filling is
Filling square balance
Wherein, the three values of f, e and k respectively represent three key parameters of the field fitness, and the smaller the values, the better the fitness between the track and the field is.
Optionally, in step S4, the three-dimensional curved surface design of the track includes the following steps:
s41, generating a three-dimensional curved surface of the track: setting generation parameters on the track central line according to the generation logic and the generation formula of the three-dimensional curved surface, and automatically generating the three-dimensional curved surface of the track by a computer according to the generation parameters;
s42, three-dimensional curved surface adjustment and deepening of the track: and carrying out secondary deepening adjustment on the ice surface of the track according to the running track line and the speed acceleration parameter of the racing car of the snowmobile sled equation of motion.
Optionally, in step S42, the following steps are included:
the offset distance between the elliptic axis of the ice profile and the central line of the track is adjusted according to the track line of the racing car form, so that the ascending height and the bending position of the sliding track line of the racing car are improved;
adjusting the elliptical parameters of the cross section of the ice surface at the position where the track line of the racing car flies too high in the local racing car, so as to increase the safety height of the highest point of the ice surface;
the redundant curved surface of the racing track is trimmed according to the track line of the racing track, so that redundancy of ice surface design is avoided;
and in the initial curve of the track, the length of the horizontal section in the profile of the ice surface is increased, so that a safe buffer space is provided for racing riders.
A snowmobile ski track for use with a snowmobile ski track design method, the snowmobile ski track comprising: a curved portion and a straight portion.
A computer readable storage medium storing computer instructions for causing the computer to perform a snowmobile ski track design method.
According to the design method of the snowmobile sled track, the complex three-dimensional space curved rectangular coordinate system is converted into the curved linear coordinate system which is more fit with the movement state of the racing car through the snowmobile sled movement equation, so that the complex racing car driving state is simulated and calculated. And respectively carrying out field evaluation, center line design and three-dimensional curved surface design of the track by means of the snowmobile sled motion equation, the center line design formula and the three-dimensional curved surface design formula so as to realize the track design.
Drawings
The features and advantages of the present invention will be more clearly understood by reference to the accompanying drawings, which are illustrative and should not be construed as limiting the invention in any way, in which:
FIG. 1 is a schematic workflow diagram of a snowmobile ski track design provided by an embodiment of the present invention;
FIG. 2 is a schematic diagram of a snowmobile ski track design concept provided by an embodiment of the present invention;
FIG. 3 is a curved linear coordinate system for displaying the motion state of a racing car according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of a track division provided by an embodiment of the present invention;
FIG. 5 is a diagram of a longitudinal stress analysis of a racing car according to an embodiment of the present invention;
fig. 6 is a diagram of transverse stress analysis of a racing car according to an embodiment of the invention.
Reference numerals illustrate:
1-a curve portion; 2-straight track portion; 3-entering a bending zone; 4-driving area; 5-out-bending area.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to fall within the scope of the invention.
Example 1
The embodiment of the invention provides a design method of a snowmobile sled track, as shown in fig. 1 and 2, comprising the following steps:
s1, preparing a snowmobile sled motion equation, a center line design formula and a three-dimensional curved surface design formula according to characteristics of a snowmobile sled body and a snowmobile sled track;
obtaining the motion trail, speed and acceleration of the snowmobile sled body through the snowmobile sled motion equation;
in the step S1, the generation of the snowmobile sled equation of motion includes the following steps:
s111, constructing a racetrack mathematical model: establishing a mathematical model aiming at a three-dimensional track curved surface, and converting the mathematical model into a mathematical model which can be described by a mathematical formula;
s112, performing track curved surface division, as shown in FIG. 4: dividing the track into a curve part 1 and a straight part 2; and subdividing the curve into an entrance curve region 3, a travel region 4 and an exit curve region 5 as a calculation unit of the equation of motion
S113, coordinate system setting: converting the three-dimensional space curved rectangular coordinate system into a curved linear coordinate system which is more fit with the motion state of the racing car;
s114, obtaining the motion state of each point at each moment of the racing car.
In the present embodiment, in the above step S113, as shown in fig. 3, 5 and 6, the stress state of the snowmobile ski body is analyzed by the following formula:
traction force of racing car: fq=mgsin α, where the total mass of the racing car and the athlete is m, the gravitational acceleration is g, and the included angle between the gravitational force and the ice surface at a certain moment is α;
air resistance: fw=1/2 ρCdAv 2 The method comprises the steps that the racing car receives air resistance in the advancing direction, the air density is set to be rho, the windward area of the racing car and a sportsman is set to be A, the wind resistance coefficient is Cd, the wind suction coefficient is Cl, and the racing car speed is v;
wind suction force: fl=1/2 ρClAv 2 The method comprises the steps that the racing car receives air resistance in the advancing direction, the air density is set to be rho, the windward area of the racing car and a sportsman is set to be A, the wind resistance coefficient is Cd, the wind suction coefficient is Cl, and the racing car speed is v;
gravity n-axis component affecting racing car and ice force: g_n=mgcos αcos β; or, the gravity n-axis component affecting the racing car and ice forces is expressed as: g_n=mgcos α_n, wherein the interaction force of the racing car and the ice surface is from the sum of the gravity of the racing car and the athlete, the centrifugal force and the component of the wind suction force in the direction perpendicular to the ice surface, namely the sum of the components on the n axis; after the gravity is decomposed into traction force Fq, the residual component still needs to be decomposed again in the plane from the n axis to the t axis, and the component along the n axis is the gravity component affecting the acting force of the racing car and the ice surface;
the component of gravity in the direction of the t-axis that determines the lateral movement of the racing car: g_t=mgcos αsin β; or, the component of gravity in the direction of the t-axis that determines the lateral movement of the racing car is expressed as: g_t=mgcos α_t, wherein n in the formula refers to a component of the front side magnitude of the component on the n axis, and is the same as the cos β value, and is a simplified writing method for decomposing stress;
centrifugal force: fc= (mv ζ2)/(r+Δr), wherein the racing car is set to rise a certain height on the ice surface due to centrifugal action at a certain moment, the turning radius of the racing car is r, the distance between the racing car and the central line of the racing car is Δr, and the turning radius of the racing car is r+Δr;
centrifugal force is in the n-axis component of the vertical ice surface: fc_n= (mv ζ2)/(r+Δr) _n
Centrifugal force is in the transverse t-axis component of racing car: fc_t= (mv ζ2)/(r+Δr) _t
Friction force on ice: f=u (fc_n+g_n-Fl), where the coefficient of friction of the racing car and the ice surface is set to μ.
In step S114, the method further includes: obtaining the motion states of each moment and each point position of the racing car through an iterative algorithm; and, through the computer-aided calculation, in order to simulate and calculate the running state of the racing car;
and after setting boundary conditions, the iterative algorithm extracts the motion trail of the racing car to conduct differentiation, and the motion equation after differentiation is calculated through a circulation mode so as to obtain the motion states of each moment and each point of the racing car. The computer-aided calculation analyzes the motion equation, and simultaneously adopts an iterative algorithm as basic operation logic of the motion equation.
The specific snowmobile ski equations of motion include:
dividing the central line of a section of curve into a plurality of minimum quantities, wherein the length of each section is deltas, the initial point number is P0 point, and the initial point number is P1 and P2 … Pi points which continue backwards in sequence, wherein i represents the iteration number; carrying out stress analysis on the Pi point, and analyzing the spatial position and the motion state of the Pi+1 point by utilizing a motion equation, so as to reciprocate, and analyzing the motion trail of the racing car point by point;
for any point P i+1 And P i Establishing a motion formula between two points, P i The initial velocity of the point along the s-axis direction is V si V along the direction of t axis ti . The displacement between two points along the S axis is S i The height difference is h i The upward displacement along the t-axis direction is S ti The height difference is h ti 。
According to the basic formula, the acting force between the racing car and the ice surface under the action of gravity is as follows:
G_n＝mg cos α i cosβ i
the effort between racing car and the ice surface under the centrifugal force is:
substituting the wind suction formula can obtain the friction force between the racing car and the ice surface at the moment i as follows:
combined with gravity and wind resistance, pair P along s-axis i+1 And P i The dynamic equilibrium equation of the motion state of the point can be obtained by establishing:
pair P along t axis i+1 And P i The dynamic equilibrium equation of the motion state of the point can be obtained by establishing:
then P i The final speed of the dots is:
P i the spatial coordinates of the points are:
P i (s，t)＝(∑(S 0 +S 1 +…+S i )，∑(S t0 +S t1 +…+S ti ))
at the time of setting up P i+1 And P i After the motion equation between the points, an iterative algorithm can be adopted to set the starting point P 0 After the initial condition of (2), P can be obtained gradually by cyclic calculation 1 、P 2 ...P n And integrating the data to obtain the key data such as the complete racing track, maximum speed, average speed, maximum acceleration, average acceleration and the like in the given track three-dimensional curved surface section.
S2, performing field evaluation: the site fitness is evaluated in an auxiliary mode according to the snowmobile sledge motion equation and the center line design formula;
s3, center line design is carried out: designing a track center line according to the snowmobile sled motion equation and the center line design formula;
in addition, in step S3, the center line design includes the steps of:
s31, determining the basic distribution condition of the track plane: after the individual functional areas in each area of a departure area, an end vehicle receiving area and a destination area are determined according to mountain terrain walking, a preliminary track plane layout partition map is determined on a drawing, and on the premise that no line shape is specifically designed, the layout trend of the whole track can be basically determined, so that a judgment basis is provided for the next step of line shape walking;
s32, determining linear basic trend, and obtaining a central line preliminary arrangement diagram: the specific running route of the track is designed according to the mountain trend, and in the design process, the speed and acceleration indexes and the degree of fit between the central line and the mountain are monitored in real time by means of the snowmobile sled equation of motion and the degree of fit calculation formula between the track and the field, so that the reasonable and effective line shape is ensured;
s33, center line deepening design: and converting the initial layout of the central line into an accurate central line plane diagram controlled by parameters according to the central line design formula.
In the step S32 of the present embodiment, the calculation formula of the fitness between the track and the field is:
i∈{0，1，2，3，...n}
wherein i represents the serial number of the segmentation point on the central line, n represents the number of segments, the larger n is, the more accurate the matching degree calculation result is, and n can take a value of 2000 for a track with the length of 2 km;
ΔZ i ＝Z ci -Z ti
wherein Z is ci Representing the elevation of a segment point with the sequence number i on a central line, Z ti Representing the surface elevation of a segmentation point with a corresponding central line number i on a field;
if DeltaZ i ≥0,ΔZ i ∈F；
If DeltaZ i ＜0，ΔZ i ∈E；
Then:
the total amount of filling is
The total amount of filling is
Filling square balance
Wherein, the three values of f, e and k respectively represent three key parameters of the field fitness, and the smaller the values, the better the fitness between the track and the field is.
S4, performing three-dimensional curved surface design of the racetrack: and designing a three-dimensional curved surface of the snowmobile ski track according to the snowmobile ski motion equation and the three-dimensional curved surface design formula.
In the step S4 of the present embodiment, the three-dimensional curved surface design of the track includes the following steps:
s41, generating a three-dimensional curved surface of the track: setting generation parameters on the track central line according to the generation logic and the generation formula of the three-dimensional curved surface, and automatically generating the three-dimensional curved surface of the track by a computer according to the generation parameters;
s42, three-dimensional curved surface adjustment and deepening of the track: and carrying out secondary deepening adjustment on the ice surface of the track according to the running track line and the speed acceleration parameter of the racing car of the snowmobile sled equation of motion. In the step S42, the steps of:
the offset distance between the elliptic axis of the ice profile and the central line of the track is adjusted according to the track line of the racing car form, so that the ascending height and the bending position of the sliding track line of the racing car are improved;
adjusting the elliptical parameters of the cross section of the ice surface at the position where the track line of the racing car flies too high in the local racing car, so as to increase the safety height of the highest point of the ice surface;
the redundant curved surface of the racing track is trimmed according to the track line of the racing track, so that redundancy of ice surface design is avoided;
and in the initial curve of the track, the length of the horizontal section in the profile of the ice surface is increased, so that a safe buffer space is provided for racing riders.
Example 2
A snowmobile ski track for use with a snowmobile ski track design method, the snowmobile ski track comprising: a curve portion 1 and a straight portion 2.
Example 3
A computer readable storage medium storing computer instructions for causing the computer to perform a snowmobile ski track design method.
It will be appreciated by those skilled in the art that implementing all or part of the above-described embodiment method may be implemented by a computer program to instruct related hardware, where the program may be stored in a computer readable storage medium, and the program may include the above-described embodiment method when executed. The storage medium may be a magnetic Disk, an optical disc, a Read-Only Memory, a ROM, a random access Memory RandomAccessMemory, RAM, a Flash Memory, a Hard Disk Drive, abbreviated as: HDD or Solid-State Drive, SSD), etc.; the storage medium may also comprise a combination of memories of the kind described above.
Although embodiments of the present invention have been described in connection with the accompanying drawings, various modifications and variations may be made by those skilled in the art without departing from the spirit and scope of the invention, and such modifications and variations are within the scope of the invention as defined by the appended claims.
Claims (8)
1. A snowmobile ski track design method, comprising the steps of:
s1, preparing a snowmobile sled motion equation, a center line design formula and a three-dimensional curved surface design formula according to characteristics of a snowmobile sled body and a snowmobile sled track;
obtaining the motion trail, speed and acceleration of the snowmobile sled body through the snowmobile sled motion equation;
s2, performing field evaluation: the site fitness is evaluated in an auxiliary mode according to the snowmobile sledge motion equation and the center line design formula;
s3, center line design is carried out: designing a track center line according to the snowmobile sled motion equation and the center line design formula;
s4, performing three-dimensional curved surface design of the racetrack: designing a three-dimensional curved surface of the snowmobile ski track according to the snowmobile ski motion equation and the three-dimensional curved surface design formula;
in step S1, the generation of the snowmobile ski motion equation includes the following steps:
s111, constructing a racetrack mathematical model: establishing a mathematical model aiming at a three-dimensional track curved surface, and converting the mathematical model into a mathematical model described by a mathematical formula;
s112, performing track curved surface division: dividing the track into a curve part (1) and a straight part (2); the curve part (1) is subdivided into an entering curve area (3), a driving area (4) and an exiting curve area (5) as a calculation unit of a motion equation;
s113, coordinate system setting: converting the three-dimensional space curved rectangular coordinate system into a curved linear coordinate system which is more fit with the motion state of the racing car;
s114, obtaining the motion state of each moment and each point of the racing car;
in step S3, the centerline design includes the steps of:
s31, determining the basic distribution condition of the track plane: after determining the individual function areas in each area of a departure area, an end vehicle receiving area and a destination area according to mountain terrain walking, determining a preliminary track plane layout partition map on a drawing, and basically determining the layout trend of the whole track on the premise of not specifically designing the line shape so as to provide a judgment basis for the next step of designing the line shape walking;
s32, determining linear basic trend, and obtaining a central line preliminary arrangement diagram: the specific running route of the track is designed according to the mountain trend, and in the design process, the speed and acceleration indexes and the degree of fit between the central line and the mountain are monitored in real time by means of the snowmobile sled equation of motion and the degree of fit calculation formula between the track and the field, so that the reasonable and effective line shape is ensured;
s33, center line deepening design: converting the initial layout of the central line into an accurate central line plan controlled by parameters according to the central line design formula;
in step S32, the fitness calculation formula between the track and the field is: i.e {0,1,2,3,..n }
Wherein i represents the serial number of the segmentation point on the central line, n represents the number of segments, the larger n is, the more accurate the matching degree calculation result is, and n takes a value of 2000 for a track with the length of 2 km;
ΔZ i ＝Z ci -Z ti
wherein Z is ci Representing the elevation of a segment point with the sequence number i on a central line, Z ti Representing the surface elevation of a segmentation point with a corresponding central line number i on a field;
if DeltaZ i ≥0,ΔZ i ∈F；
If DeltaZ i ＜0,ΔZ i ∈E；
Then:
the total amount of filling is
Filling square balance
Wherein, the three values of f, e and k respectively represent three key parameters of the field fitness, and the smaller the values, the better the fitness between the track and the field is.
2. The snowmobile ski track design method according to claim 1, wherein in step S113, the stress state of the snowmobile ski body is analyzed by the following formula:
traction force of racing car: fq=mgsin α, where the total mass of the racing car and the athlete is m, the gravitational acceleration is g, and the included angle between the gravitational force and the ice surface at a certain moment is α;
air resistance: fw=1/2 ρCdAv 2 The method comprises the steps that the racing car receives air resistance in the advancing direction, the air density is set to be rho, the windward area of the racing car and a sportsman is set to be A, the wind resistance coefficient is Cd, the wind suction coefficient is Cl, and the racing car speed is v;
wind suction force: fl=1/2 ρClAv 2 The method comprises the steps that the racing car receives air resistance in the advancing direction, the air density is set to be rho, the windward area of the racing car and a sportsman is set to be A, the wind resistance coefficient is Cd, the wind suction coefficient is Cl, and the racing car speed is v;
gravity n-axis component affecting racing car and ice force: g_n=mgcos αcos β; or, the gravity n-axis component affecting the racing car and ice forces is expressed as: g_n=mgcos α_n, wherein the interaction force of the racing car and the ice surface is from the sum of the gravity of the racing car and the athlete, the centrifugal force and the component of the wind suction force in the direction perpendicular to the ice surface, namely the sum of the components on the n axis; after the gravity is decomposed into traction force Fq, the residual component still needs to be decomposed again in the plane from the n axis to the t axis, and the component along the n axis is the gravity component affecting the acting force of the racing car and the ice surface;
the component of gravity in the direction of the t-axis that determines the lateral movement of the racing car: g_t=mgcos αsin β; or, the component of gravity in the direction of the t-axis that determines the lateral movement of the racing car is expressed as: g_t=mgcos α_t, wherein n in the formula refers to a component of the front side magnitude of the component on the n axis, and is the same as the cos β value, and is a simplified writing method for decomposing stress;
centrifugal force: fc= (mv ζ2)/(r+Δr), wherein the racing car is set to rise a certain height on the ice surface due to centrifugal action at a certain moment, the turning radius of the racing car is r, the distance between the racing car and the central line of the racing car is Δr, and the turning radius of the racing car is r+Δr;
centrifugal force is in the n-axis component of the vertical ice surface: fc_n= (mv ζ2)/(r+Δr) _n
Centrifugal force is in the transverse t-axis component of racing car: fc_t= (mv ζ2)/(r+Δr) _t
Friction force on ice: f=μ (fc_n+g_n-Fl), where the coefficient of friction of the racing car with the ice surface is set to μ.
3. The snowmobile ski track design method according to claim 2, comprising, in step S114: according to a snowmobile sled motion equation, obtaining the motion states of each moment and each point position of the racing car through an iterative algorithm;
after setting boundary conditions, the iterative algorithm extracts the motion trail of the racing car to conduct differentiation, and the motion equation after differentiation is calculated in a circulating way to obtain the motion states of each moment and each point position of the racing car;
the snowmobile sled equation of motion includes:
dividing the central line of a section of curve into a plurality of very small quantities, wherein the length of each section is delta s, and the initial point number is P 0 The points are continued backwards and sequentially as P 1 、P 2 、…、P i Points, where i represents the iteration number; for P i The point is subjected to stress analysis, and P is resolved by utilizing a motion equation i+1 The space position and the motion state of the points are reciprocated in this way, and the motion trail of the racing car is analyzed point by point;
for any point P i+1 And P i Establishing a motion formula between two points, P i The initial velocity of the point along the s-axis direction is V si V along the direction of t axis ti The method comprises the steps of carrying out a first treatment on the surface of the The displacement between two points along the S axis is S i The height difference is h i The upward displacement along the t-axis direction is S ti The height difference is h ti ；
The acting force between the racing car and the ice surface under the action of gravity is as follows:
G_n＝mg cosα i cosβ i
the effort between racing car and the ice surface under the centrifugal force is:
substituting the wind suction formula to obtain the friction force between the racing car and the ice surface at the moment i is as follows:
combined with gravity and wind resistance, pair P along s-axis i+1 And P i The motion state of the point is established by a mechanical equilibrium equation to obtain:
pair P along t axis i+1 And P i The motion state of the point is established by a mechanical equilibrium equation to obtain:
then P i The final speed of the dots is:
P i the spatial coordinates of the points are:
P i (s，t)＝(∑(S 0 +S 1 +…+S i )，∑(S t0 +S t1 +…+S ti ))
at the time of setting up P i+1 And P i After the motion equation between the points, an iterative algorithm is adopted to set a starting point P 0 After the initial condition of (2), gradually obtaining P through cyclic calculation 1 、P 2 、…、P n And integrating the data to obtain the complete racing track movement track, maximum speed, average speed, maximum acceleration and average acceleration data in the given track three-dimensional curved surface section.
4. The snowmobile ski track design method according to claim 3, further comprising, in step S114: calculating the running state of the racing car through computer auxiliary calculation;
the computer-aided calculation analyzes the motion equation, and simultaneously adopts an iterative algorithm as basic operation logic of the motion equation.
5. The snowmobile ski track design method according to claim 1, wherein in step S4, the track three-dimensional curved surface design comprises the steps of:
s41, generating a three-dimensional curved surface of the track: setting generation parameters on the track central line according to the generation logic and the generation formula of the three-dimensional curved surface, and automatically generating the three-dimensional curved surface of the track by a computer according to the generation parameters;
s42, three-dimensional curved surface adjustment and deepening of the track: and carrying out secondary deepening adjustment on the ice surface of the track according to the running track line and the speed acceleration parameter of the racing car of the snowmobile sled equation of motion.
6. The snowmobile ski track design method according to claim 5, comprising the steps of:
the offset distance between the elliptic axis of the ice profile and the central line of the track is adjusted according to the track line of the racing car form, so that the ascending height and the bending position of the sliding track line of the racing car are improved;
adjusting the elliptical parameters of the cross section of the ice surface at the position where the track line of the racing car flies too high in the local racing car, so as to increase the safety height of the highest point of the ice surface;
the redundant curved surface of the racing track is trimmed according to the track line of the racing track, so that redundancy of ice surface design is avoided;
and in the initial curve of the track, the length of the horizontal section in the profile of the ice surface is increased, so that a safe buffer space is provided for racing riders.
7. A snowmobile ski track for use with the snowmobile ski track design method of any one of claims 1 to 6, comprising: a curved portion (1) and a straight portion (2).
8. A computer readable storage medium having stored thereon computer instructions for causing the computer to perform the snowmobile ski track design method of any one of claims 1-6.
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Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| KR20150052524A (en) * | 2013-11-06 | 2015-05-14 | 두산건설 주식회사 | Apparatus and method for two dimensional simulation of moving object running at high speed in a track of which planar curves and end-point slopes are varying |
| CN108827253A (en) * | 2018-03-29 | 2018-11-16 | 上海宝冶集团有限公司 | The installation of the support of pipelines of sled sled racing track and locating measurement method |
| CN115048715A (en) * | 2022-04-29 | 2022-09-13 | 哈尔滨工业大学（威海） | Path planning and control algorithm of unmanned formula car |
| CN115375733A (en) * | 2022-08-24 | 2022-11-22 | 东北大学 | Snow vehicle sled three-dimensional sliding track extraction method based on videos and point cloud data |
Family Cites Families (1)
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Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| KR20150052524A (en) * | 2013-11-06 | 2015-05-14 | 두산건설 주식회사 | Apparatus and method for two dimensional simulation of moving object running at high speed in a track of which planar curves and end-point slopes are varying |
| CN108827253A (en) * | 2018-03-29 | 2018-11-16 | 上海宝冶集团有限公司 | The installation of the support of pipelines of sled sled racing track and locating measurement method |
| CN115048715A (en) * | 2022-04-29 | 2022-09-13 | 哈尔滨工业大学（威海） | Path planning and control algorithm of unmanned formula car |
| CN115375733A (en) * | 2022-08-24 | 2022-11-22 | 东北大学 | Snow vehicle sled three-dimensional sliding track extraction method based on videos and point cloud data |
Non-Patent Citations (1)
| Title |
|---|
| 冰轮环境助力国家雪车雪橇飞驰2022年北京冬奥会;刘福来;;制冷技术(第02期);全文 * |
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