CN107291983A - A kind of computational methods of flying disc inclined throw movements - Google Patents
A kind of computational methods of flying disc inclined throw movements Download PDFInfo
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- CN107291983A CN107291983A CN201710355870.4A CN201710355870A CN107291983A CN 107291983 A CN107291983 A CN 107291983A CN 201710355870 A CN201710355870 A CN 201710355870A CN 107291983 A CN107291983 A CN 107291983A
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
Abstract
The present invention relates to a kind of computational methods of flying disc inclined throw movements, parameter of the soft flying disc of PU plastics used in parameter, ambient parameter and the match of upper 7 sizes of the Landing stage obtained according to identification the of the invention Landing stage different with area etc., optimal algorithm is generated, to assure success realizes that flying disc falls and is not dropped after landing on all Landing stages and on each Landing stage.
Description
Technical field
The invention belongs to inclined throw movements technical field, more particularly to a kind of computational methods of flying disc inclined throw movements.
Background technology
16th national college students' robot contest is the theme with " dance disk ceremonial music ", and inspiration is from the traditional gift of Ancient Times in China
Instrument and game " pitch-pot game ".The Spring and Autumn and the Warring States Periods, one of ceremony when nobility entertains the guests at a banquet is exactly people's archery of entertaining guests, and name, which is said, " penetrates
Gift ".At that time, man to be will not shoot an arrow as shame, and owner entertains guests people's archery, and guest can not decline.Later, in order that really
The guest for being not good at penetrating in fact participates in game, and wine pot is just thrown with arrow replaces drawing a bow, with happy welcome guest, to practise ceremony.In the course of time, pitch-pot game is just
A kind of gift received guests and graceful game during as feast and carouse.After Qin Han, it is prevailing in court official stratum not to wane, often
Feast and carouse is met, the program that there must be " refined song pitch-pot game " is added to the fun.Song Lv faces greatly《Book of Rites is passed》It is middle to say that " pitch-pot game, what is penetrated is thin.Yan Yinyou is penetrated
With happy guest, skill is said to practise appearance ".
Flying disc inclined throw movements are typically all people to complete, and a real machine for realizing flying disc inclined throw movements is there is no at present
People.Robot wants to realize flying disc inclined throw movements, and its key is to input a kind of flying disc inclined throw movements into robot system
Core algorithm.
The content of the invention
The present invention provides a kind of computational methods of flying disc inclined throw movements, and the algorithm of the present invention is input into robot program
In, the flying disc inclined throw movements of robot can be realized, upper 7 sizes of Landing stage and area that the present invention is obtained according to identification are not
Parameter of the soft flying disc of PU plastics used in parameter, ambient parameter and the match of same Landing stage etc., generates optimal algorithm,
To assure success realize that flying disc falls not drop after landing on all Landing stages and on each Landing stage.
The present invention is achieved through the following technical solutions there is provided a kind of computational methods of flying disc inclined throw movements, including with
Lower calculation procedure：
Horizontal direction speed：vx=v0cosθ
Vertical direction speed：vy=v0sinθ-gt
Horizontal displacement：X=v0cosθ·t (1)
Vertical direction displacement：
Eliminated t by (1), (2) and obtained：
According to trigonometric function relation：
By (4), formula is arranged：
In formula：X is horizontal displacement, and g is acceleration of gravity, and h is height, v0For initial velocity, θ is initial velocity and horizontal direction
Angle；
In inclined throw movements in addition to being affected by gravity, the influence of air drag, the formula of air drag are also received：
In formula：C is coefficient of air resistance；ρ is atmospheric density；S object front face areas；V is the relative fortune of object and air
Dynamic speed, the size of air drag is directly proportional to coefficient of air resistance and front face area, is directly proportional to velocity squared；
In uphill process, the acceleration of vertical direction is：
In uphill process, the acceleration of vertical direction is：
In fact, the motion of flying disc in the horizontal direction is not linear uniform motion, but level off to even acceleration straight line fortune
Dynamic, the horizontal direction acceleration suffered by it is：
Horizontal direction displacement correction is：
X=v0cosθ-axt (10)
The parameter of Landing stage upper 7 sizes of the invention obtained according to identification the Landing stage different with area, environment are joined
Parameter of the soft flying disc of PU plastics used in number and match etc., generates optimal algorithm, to assure success realizes that flying disc falls
Do not dropped after being landed on all Landing stages and on each Landing stage.
Preferably, the speed of object is less than 200 meter per seconds, resistance and object speed size square are directly proportional.
Preferably, because horizontal displacement x is nearer, the acceleration phase for the vertical direction for rising and falling can be approximately considered
Deng vertical direction displacement correction is：
Beneficial effects of the present invention are：
The parameter of Landing stage upper 7 sizes of the invention obtained according to identification the Landing stage different with area, environment are joined
Parameter of the soft flying disc of PU plastics used in number and match etc., generates optimal algorithm, to assure success realizes that flying disc falls
Do not dropped after being landed on all Landing stages and on each Landing stage.
Brief description of the drawings
In order to illustrate more clearly about the embodiment of the present invention or technical scheme of the prior art, below will be to embodiment or existing
There is the accompanying drawing used required in technology description to be briefly described, it should be apparent that, drawings in the following description are only this
Some embodiments of invention, for those of ordinary skill in the art, on the premise of not paying creative work, can be with
Other accompanying drawings are obtained according to these accompanying drawings.
Fig. 1 is competition structure place stereogram；
Fig. 2 is competition structure place plan；
Fig. 3 is competition structure place side view；
Fig. 4 is the parabola schematic diagram of inclined throw movements；
Embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, with reference to embodiments, to the present invention
It is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, it is not used to
Limit the present invention.
Below in conjunction with the accompanying drawings and specific embodiment to the present invention application principle be further described.
Embodiment 1, match is carried out on the place shown in Fig. 1.Every game is carried out between two teams, and there is a machine in every team
Device people.Competition area are divided into the rectangle place on both sides.Landed as shown in figure 1, place has promoter region, circle per side and set
The relief area of platform.There is the Landing stage of 7 different heights and area on column on field.In seven Landing stages, 5 are located at
On the center line for splitting both sides, platform in being referred to as；Another 2 each close to one side, and for a certain team participating in competition, what it is close to oneself one side is near
Platform, distant place is far from the table.The height of each Landing stage is different with size.There are 7 different heights and face on column on field
There is 7 sizes Landing stage different with area on long-pending Landing stage, Landing stage.In seven Landing stages, 5 are located at segmentation both sides
Center line on, be referred to as in platform；Another 2 each close to one side, and for a certain team participating in competition, what it is close to oneself one side is close-table, at a distance
Be far from the table.There is diameter 150mm hole in the center of Landing stage.When match starts, there is an inflation sandy beach ball on each hole.
Inflatable ball (diameter 30cm after inflation) on Landing stage, 7 kinds of colors.When match starts, inflation sandy beach ball is placed in each Landing stage
Centre.Available flying disc quantity is 50 in the match of branch team participating in competition, is placed on filling area, the position piled up and mode by team participating in competition from
It is fixed.After match starts, when robot is completely into filling area, team participating in competition can just be attached to flying disc in the robot of oneself.Two
The robot of team can be thrown a frisbee to any ball on any Landing stage, and ball and shot down from table.A certain team participating in competition
Flying disc falls on the Landing stage without ball, it is possible to score.If all balls shot down from Landing stage and a certain team participating in competition into
Its flying disc is fallen on all Landing stages and flying of not dropped after 3 seconds of at least one stop motion on each Landing stage work(
Disk, the team is achieved that triumph.If two teams do not win, as long as two teams are finished 50 flying discs or match has been carried out 3 minutes,
Match just terminates.The team participating in competition that score is high during end of match wins.The fortune that the soft flying disc of PU plastics is from circle to Landing stage
Row process is inclined throw movements, and its running orbit figure is as shown in Figure 4.
Horizontal direction speed：vx=v0cosθ
Vertical direction speed：cy=v0sinθ-gt
Horizontal displacement：X=v0cosθ·t (1)
Vertical direction displacement：
Eliminated t by (1), (2) and obtained：
According to trigonometric function relation：
By (4), formula is arranged：
Launch point is to the horizontal displacement x of Landing stage in formula, gravity acceleration g, and the height h of Landing stage is known ginseng
Number, initial velocity v0Angle theta with initial velocity and horizontal direction is known variables, in the inclined throw movements that this patent is related to, real
On border in addition to being affected by gravity, the influence of air drag, the formula of air drag are also received：
In formula：C is coefficient of air resistance；ρ is atmospheric density；S object front face areas；V is the relative fortune of object and air
Dynamic speed.From above formula, the size of air drag is directly proportional to coefficient of air resistance and front face area under normal circumstances, with speed
Degree square is directly proportional.
The route that its center of gravity is passed through during flying disc flight is called ballistic curve.Due to Action of Gravity Field and the shadow of air drag
Ring, trajectory is formed unequal arc.Liter arc is longer and directly stretches, and drop arc is then shorter and bends.The centre-of-gravity motion of flying disc, stably
Property etc. also can all have influence on ballistic curve.The range of flying disc that tiltedly casts out and penetrate it is high all do not calculated by projectile obtained value that
Big, certain route also will not be ideal curve.
Flying disc moves the resistance being subject in atmosphere, has substantial connection with the size of speed of moving body：The speed of object
During less than 200 meter per second, it is believed that resistance and object speed size square are directly proportional；When speed reaches 400~600 meter per second,
The cube of air drag and velocity magnitude is directly proportional；In the case where speed is very big, the high power of resistance and velocity magnitude into
Direct ratio.Therefore the speed that the Robot Design of patent of the present invention fires shells is below 200 meter per second.In a word, the speed of object of which movement
Degree is smaller, and the influence of air drag is just smaller, and the motion of projectile is closer to ideal situation.
In uphill process, the acceleration of vertical direction is：
In uphill process, the acceleration of vertical direction is：
In fact, the motion of flying disc in the horizontal direction is not linear uniform motion, but level off to even acceleration straight line fortune
Dynamic, the horizontal direction acceleration suffered by it is：
Horizontal direction displacement correction is：
X=v0ccsθ-axt (10)
Due to launch point to the closer to the distance of Landing stage, the acceleration for the vertical direction for rising and falling can be approximately considered
Equal, vertical direction displacement correction is：
Certainly, described above is also not limited to the example above, the technical characteristic of the invention without description can by or
Realized, will not be repeated here using prior art；Above example and accompanying drawing are merely to illustrate technical scheme not
It is limitation of the present invention, preferred embodiment the present invention is described in detail for reference, the ordinary skill people of this area
Member is it should be appreciated that change, remodeling, the addition that those skilled in the art are made in the essential scope of the present invention
Or replace without departure from spirit of the invention, it should also belong to the claims of the present invention.
Claims (3)
1. a kind of computational methods of flying disc inclined throw movements, including following calculation procedure：
Horizontal direction speed：vx=v0cosθ
Vertical direction speed：vy=v0sinθ-gt
Horizontal displacement：X=v0cosθ·t (1)
Vertical direction displacement：
Eliminated t by (1), (2) and obtained：
<mrow>
<mi>x</mi>
<mi>tan</mi>
<mi>&theta;</mi>
<mo>+</mo>
<mi>h</mi>
<mo>-</mo>
<mfrac>
<mrow>
<msup>
<mi>gx</mi>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<mn>2</mn>
<msubsup>
<mi>v</mi>
<mn>0</mn>
<mn>2</mn>
</msubsup>
<msup>
<mi>cos</mi>
<mn>2</mn>
</msup>
<mi>&theta;</mi>
</mrow>
</mfrac>
<mo>=</mo>
<mn>0</mn>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
</mrow>
According to trigonometric function relation：
<mrow>
<mi>x</mi>
<mi>tan</mi>
<mi>&theta;</mi>
<mo>+</mo>
<mi>h</mi>
<mo>-</mo>
<mfrac>
<mrow>
<msup>
<mi>gx</mi>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<mn>2</mn>
<msubsup>
<mi>v</mi>
<mn>0</mn>
<mn>2</mn>
</msubsup>
</mrow>
</mfrac>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<msup>
<mi>tan</mi>
<mn>2</mn>
</msup>
<mi>&theta;</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0</mn>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mo>)</mo>
</mrow>
</mrow>
By (4), formula is arranged：
<mrow>
<msup>
<mi>tan</mi>
<mn>2</mn>
</msup>
<mi>&theta;</mi>
<mo>-</mo>
<mfrac>
<mrow>
<mn>2</mn>
<msubsup>
<mi>v</mi>
<mn>0</mn>
<mn>2</mn>
</msubsup>
</mrow>
<mrow>
<mi>g</mi>
<mi>x</mi>
</mrow>
</mfrac>
<mi>tan</mi>
<mi>&theta;</mi>
<mo>+</mo>
<mn>1</mn>
<mo>-</mo>
<mfrac>
<mrow>
<mn>2</mn>
<msubsup>
<mi>hv</mi>
<mn>0</mn>
<mn>2</mn>
</msubsup>
</mrow>
<mrow>
<msup>
<mi>gx</mi>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>=</mo>
<mn>0</mn>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>5</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula：X is horizontal displacement, and g is acceleration of gravity, and h is height, v0For initial velocity, θ is initial velocity and the folder of horizontal direction
Angle；
In inclined throw movements in addition to being affected by gravity, the influence of air drag, the formula of air drag are also received：
<mrow>
<mi>F</mi>
<mo>=</mo>
<mfrac>
<mrow>
<msup>
<mi>C&rho;SV</mi>
<mn>2</mn>
</msup>
</mrow>
<mn>2</mn>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>6</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula：C is coefficient of air resistance；ρ is atmospheric density；S object front face areas；V is the relative motion speed of object and air
Degree, the size of air drag is directly proportional to coefficient of air resistance and front face area, is directly proportional to velocity squared；
In uphill process, the acceleration of vertical direction is：
<mrow>
<msub>
<mi>a</mi>
<mi>y</mi>
</msub>
<mo>=</mo>
<mi>g</mi>
<mo>+</mo>
<mfrac>
<mi>F</mi>
<mi>m</mi>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>7</mn>
<mo>)</mo>
</mrow>
</mrow>
In uphill process, the acceleration of vertical direction is：
<mrow>
<msub>
<mi>a</mi>
<mi>y</mi>
</msub>
<mo>=</mo>
<mi>g</mi>
<mo>-</mo>
<mfrac>
<mi>F</mi>
<mi>m</mi>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>8</mn>
<mo>)</mo>
</mrow>
</mrow>
In fact, the motion of flying disc in the horizontal direction is not linear uniform motion, but level off to uniformly accelrated rectilinear motion, its
Suffered horizontal direction acceleration is：
<mrow>
<msub>
<mi>a</mi>
<mi>x</mi>
</msub>
<mo>=</mo>
<mfrac>
<mi>F</mi>
<mi>m</mi>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>9</mn>
<mo>)</mo>
</mrow>
</mrow>
Horizontal direction displacement correction is：
X=v0cosθ-axt (10)。
2. a kind of computational methods of flying disc inclined throw movements according to claim 1, it is characterised in that：The speed of object is less than
200 meter per seconds, resistance and object speed size square are directly proportional.
3. a kind of computational methods of flying disc inclined throw movements according to claim 1, it is characterised in that：Due to horizontal displacement x
Relatively closely, rising can be approximately considered equal with the acceleration of the vertical direction fallen, vertical direction displacement correction is：
<mrow>
<mo>-</mo>
<mi>h</mi>
<mo>=</mo>
<msub>
<mi>v</mi>
<mn>0</mn>
</msub>
<mi>sin</mi>
<mi>&theta;</mi>
<mo>&CenterDot;</mo>
<mi>t</mi>
<mo>-</mo>
<mfrac>
<mrow>
<msub>
<mi>a</mi>
<mi>y</mi>
</msub>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
</mrow>
<mn>2</mn>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>11</mn>
<mo>)</mo>
</mrow>
<mo>.</mo>
</mrow>
1
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| CN201710355870.4A CN107291983A (en) | 2017-05-19 | 2017-05-19 | A kind of computational methods of flying disc inclined throw movements |
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| Application Number | Priority Date | Filing Date | Title |
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| CN201710355870.4A CN107291983A (en) | 2017-05-19 | 2017-05-19 | A kind of computational methods of flying disc inclined throw movements |
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| Publication Number | Publication Date |
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Family
ID=60094593
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107991053A (en) * | 2017-11-06 | 2018-05-04 | 中国航天空气动力技术研究院 | High-speed wind tunnel domestic model test vehicle separated track Forecasting Methodology and system |
| CN109001482A (en) * | 2018-08-06 | 2018-12-14 | 合肥移顺信息技术有限公司 | A kind of throwing object in high sky landing velocity correction method |
| CN109142778A (en) * | 2018-08-06 | 2019-01-04 | 合肥移顺信息技术有限公司 | A kind of throwing object in high sky landing speed detection system |
| CN109142777A (en) * | 2018-08-06 | 2019-01-04 | 合肥移顺信息技术有限公司 | A kind of throwing object in high sky landing speed detection method |
| CN109188011A (en) * | 2018-08-06 | 2019-01-11 | 合肥移顺信息技术有限公司 | A kind of throwing object in high sky landing velocity measuring correction system |
-
2017
- 2017-05-19 CN CN201710355870.4A patent/CN107291983A/en active Pending
Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107991053A (en) * | 2017-11-06 | 2018-05-04 | 中国航天空气动力技术研究院 | High-speed wind tunnel domestic model test vehicle separated track Forecasting Methodology and system |
| CN107991053B (en) * | 2017-11-06 | 2020-04-10 | 中国航天空气动力技术研究院 | Method and system for predicting separation trajectory of aircraft in high-speed wind tunnel launching model test |
| CN109001482A (en) * | 2018-08-06 | 2018-12-14 | 合肥移顺信息技术有限公司 | A kind of throwing object in high sky landing velocity correction method |
| CN109142778A (en) * | 2018-08-06 | 2019-01-04 | 合肥移顺信息技术有限公司 | A kind of throwing object in high sky landing speed detection system |
| CN109142777A (en) * | 2018-08-06 | 2019-01-04 | 合肥移顺信息技术有限公司 | A kind of throwing object in high sky landing speed detection method |
| CN109188011A (en) * | 2018-08-06 | 2019-01-11 | 合肥移顺信息技术有限公司 | A kind of throwing object in high sky landing velocity measuring correction system |
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Application publication date: 20171024 |