CN108709556A - A kind of grid loxodrome and its design method suitable for polar navigation - Google Patents
A kind of grid loxodrome and its design method suitable for polar navigation Download PDFInfo
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- CN108709556A CN108709556A CN201810309028.1A CN201810309028A CN108709556A CN 108709556 A CN108709556 A CN 108709556A CN 201810309028 A CN201810309028 A CN 201810309028A CN 108709556 A CN108709556 A CN 108709556A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
- G01C21/20—Instruments for performing navigational calculations
- G01C21/203—Specially adapted for sailing ships
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Abstract
The present invention relates to naval technology, field of navigation technology, specifically propose a kind of grid loxodrome and its design method suitable for polar navigation.The grid loxodrome is defined as a curve that fixed angle is intersected with all grid heading reference lines on earth ellipsoid face.And give the calculation method of specific flight path equation and voyage, grid heading angle.The course line voyage is shorter, and grid heading angle is equal on course line and shows as straight line on polar stereographic projection figure, can with grid air navigation aid, the stringent fit applications of polar stereographic projection, more suitable for polar navigation.
Description
Technical field
The present invention relates to naval technology, field of navigation technology, and in particular to a kind of grid isogonism suitable for polar navigation
Course line and its design method.
Background technology
Generally use loxodrome in mid low latitude region navigation, but as latitude increases, loxodrome curvature is larger, navigates
Journey is longer, is no longer desirable for polar navigation, polar navigation generally use great-circle line.But geographical course angle is fast on great-circle line
The problems such as speed changes, polar region orientation error is larger is unfavorable for polar navigation control, thus nineteen forty-one Royal Air Force Maclure
Lieutenant colonel proposes polar region grid navigation technology in conjunction with polar region polar stereographic projection so that great-circle line, grid navigation technology and pole ball
Face projection solves the problems, such as the scheme of polar navigation with the use of a kind of early stage is become.As modern navigation is to precision and safety
Higher demand, early stage polar navigation scheme be also required to optimize it is matching, to the program carry out analysis be primarily present following four
Problem：
1, great-circle line is projected as non-rectilinear on polar stereographic projection figure, and intrinsic navigation can be caused to paint and calculate principle mistake
Difference；
2, polar region course uses grid heading angle, the grid heading angle on great-circle line and unequal, lattice on single course line
The irregular variation of net course angle is necessarily unfavorable for navigating by water control；
3, strict implement great-circle line, can only use track rudder execute, no image of Buddha mid low latitude region according to etc. course angles
Rule executed using course rudder；
4, great-circle line is based on earth sphere model, will necessarily exist using original reason error caused by earth model.
Therefore, the precise match that great-circle line, grid navigation technology and polar stereographic projection are unable to reach under stricti jurise is answered
With.And mid low latitude region, geographical course angle is equal in loxodrome and stringent straight line is projected as on Mercator projection figure, because
This can strictly coordinate realization to navigate by water with airmanship (navigation equipment), Mercator projection.For this purpose, using for reference mid low latitude region etc.
The design philosophy in angle course line, proposition devise a kind of " loxodrome " --- grid showing as straight line on polar stereographic projection figure
Loxodrome.
Invention content
For the deficiency of background technology, the object of the present invention is to provide a kind of stringent loxodromes in new polar region, are applied to
In polar navigation, navigation control and navigation is facilitated to paint calculation.The present invention proposes definition and the flight path equation of grid loxodrome, and
The voyage and course angle computational methods in the course line are given, it can be with grid air navigation aid, the stringent fit applications of polar stereographic projection.
In order to achieve the above object, the technical solution adopted in the present invention is：
A kind of grid loxodrome suitable for polar navigation, which is characterized in that the grid loxodrome is defined as ground
A curve that fixed angle is intersected with all grid heading reference lines on ball ellipsoid.
Further, the angle of grid loxodrome and grid heading reference line is set, i.e. grid heading angle is ψG, then lead to
Cross known pointGrid heading angle is ψGThe flight path equation of grid loxodrome be：
In formula,For the arbitrary transfer point on course line.
Further, the flight path equation derivation of the grid loxodrome includes：If AB is in grid loxodrome
Differential segmental arc,For departure point, AB and warp BC, weft AC constitute differential right angled triangle ABC, grid isogonism
Course line and angle, that is, grid heading angle of grid heading reference line are ψG, then utilizing the pass at grid heading angle and geographical course angle
System, it is ψ that can obtain geographical course angleG+ λ, then ∠ BAC are pi/2-(ψG+ λ), the differential arc length of warp isThe differential of weft
Arc length isTherefore meet
Being write formula (1) as integrated form can obtain
Ask definite integral that can obtain simultaneously on formula (2) both sides
Formula (3) is exactly to pass through known pointGrid heading angle is ψGGrid loxodrome equation,For boat
Arbitrary transfer point on line.
The present invention also proposes a kind of design method of the grid loxodrome suitable for polar navigation, which is characterized in that packet
It includes：
1st step：Grid loxodrome is defined to intersect admittedly for one on earth ellipsoid face and all grid heading reference lines
The curve at clamp angle；
2nd step：According to the definition that the 1st step determines, the flight path equation of grid loxodrome is obtained；
3rd step：According to the flight path equation that the 2nd step determines, the grid heading angle of grid loxodrome is obtained；
4th step：According to the flight path equation that the 2nd step determines, the voyage of grid loxodrome is obtained.
Further, in the 2nd step, the angle of grid loxodrome and grid heading reference line, i.e. grid heading angle are set
For ψG, then pass through known pointGrid heading angle is ψGThe flight path equation of grid loxodrome be：
In formula,For the arbitrary transfer point on course line.
Further, the flight path equation derivation of the grid loxodrome includes：If AB is in grid loxodrome
Differential segmental arc,For departure point, AB and warp BC, weft AC constitute differential right angled triangle ABC, grid isogonism
Course line and angle, that is, grid heading angle of grid heading reference line are ψG, then utilizing the pass at grid heading angle and geographical course angle
System, it is ψ that can obtain geographical course angleG+ λ, then ∠ BAC are pi/2-(ψG+ λ), the differential arc length of warp isThe differential of weft
Arc length isTherefore meet
Being write formula (1) as integrated form can obtain
Ask definite integral that can obtain simultaneously on formula (2) both sides
Formula (3) is exactly to pass through known pointGrid heading angle is ψGGrid loxodrome equation,For boat
Arbitrary transfer point on line.
Further, in the 3rd step, if the coordinate of known grid loxodrome starting point, terminalWithThen
According to formula (3) and point coordinates known to two solves grid heading angle, specific as follows：
Two coordinate points are substituted into formula (3) respectively, and carry out abbreviation to obtain
In formula,
Further, in the 4th step, with dSlIndicate the differential arc length of grid loxodrome, then
It can be obtained by formula (3), λ can be expressed as in grid loxodrome equationFunction, i.e.,
Therefore, the voyage of grid loxodrome is
Compared with prior art, the beneficial effects of the invention are as follows：The main feature of the present invention is as follows：
(1) grid loxodrome is close with great-circle line, big oval course line, and voyage is shorter；
(2) grid loxodrome is based on ellipsoid model of globe, and navigation homework precision is higher；
(3) grid heading angle is equal everywhere on course line, and straight line is shown as on polar region perspective view；
(4) can with grid air navigation aid, the stringent fit applications of polar stereographic projection, more suitable for polar navigation.
Description of the drawings
Fig. 1 is the grid loxodrome schematic diagram of the present invention.
Fig. 2 is emulation comparative graph compared with grid loxodrome is calculated with big oval course line course angle.
Fig. 3 is emulation comparative graph compared with grid loxodrome is calculated with great-circle line course angle.
Specific implementation mode
Below in conjunction with attached drawing, the present invention is described further.
The present invention be use for reference mid low latitude region loxodrome, Mercator projection and the stringent fit applications of airmanship think of
Think, it is proposed that the thought of grid loxodrome, the purpose that such course line proposes is to make polar region course line isogonism and in polar region perspective view
On show as stringent straight line so that polar region course line and polar region project, polar navigation method strictly matches, and navigation personnel is facilitated to navigate by water
Paint calculation and navigation monitoring.
Definition：Grid loxodrome intersects fixed angle for one on earth ellipsoid face with all grid heading reference lines
Curve.Specific research is as follows：
As shown in Fig. 1, if AB is the differential segmental arc in grid loxodrome,For departure point, AB and warp
Line BC, weft AC constitute differential right angled triangle ABC.Grid loxodrome and the angle of grid heading reference line are grid heading
Angle is ψG, then using the relationship at grid heading angle and geographical course angle, it is ψ that can obtain geographical course angleG+ λ, then ∠ BAC are pi/2-
(ψG+ λ), the differential arc length of warp isThe differential arc length of weft isTherefore meet
Being write formula (1) as integrated form can obtain
Ask definite integral that can obtain simultaneously on formula (2) both sides
Formula (3) is exactly to pass through known pointGrid heading angle is ψGGrid loxodrome equation,For boat
Arbitrary transfer point on line.
To verify projection of shape of the flight path equation on polar stereographic projection figure, by formula (3) by based on double projection
Polar stereographic projection converts, and can obtain equation of the course line on plane figure is
It is the known quantity determined by projecting reference position and known course line on the right side of equation it can be seen from formula (4), therefore
Party's formula is linear equation, that is, demonstrates arbitrary grid loxodrome and be projected as stringent straight line on polar stereographic projection figure.
The course angle and Modeling for Distance Calculation of Airline method of grid loxodrome is discussed below：
(1) grid loxodrome course angle computational methods
If the coordinate of known grid loxodrome starting point, terminalWithIt can be according to formula (3) and known to two
Point coordinates solves grid heading angle, specific as follows：
Two coordinate points are substituted into formula (3) respectively, and carry out abbreviation to obtain
In formula,
In special circumstances, λ1=λ2When=pi/2, ψG=pi/2.In addition, meeting this formula grid heading it can be seen from formula (5)
There are four angles, it is therefore desirable to which the quadrant that grid heading angle is carried out according to the relationship of two positions point coordinates judges.
(2) grid loxodrome course angle computational methods
The voyage of grid loxodrome can be acquired by calculating.As shown in Fig. 1, with dSlIndicate grid loxodrome
Differential arc length, then
It can be obtained by formula (3), λ can be expressed as in grid loxodrome equationFunction, i.e.,
Therefore, the voyage in course line is
Since formula (8) can not provide specific analytical expression, need to be solved using the method for numerical integration.
Embodiment
In order to verify grid loxodrome proposed by the present invention and great-circle line, the difference in big oval course line, carry out as follows
Flight-line design emulates：Known carrier sets out from starting point (70 ° of N, 10 ° of E), presses grid loxodrome, great-circle line and big respectively
It navigates by water to target point (75 ° of N, 170 ° of E) in oval course line.Grid loxodrome, big oval course line are calculated using WGS-84 with reference to ellipse
Spherical model, great-circle line calculate the sphere mould for being respectively adopted that navigation radius is mean radius of curvature at 6366707m and pole
Type.Calculate separately out grid heading angle and the voyage of grid loxodrome with the formula that derives of the present invention, and with great-circle line, big
The course in oval course line and voyage are compared, and the results are shown in Table 1, attached drawing 2 and attached drawing 3.
1 total Modeling for Distance Calculation of Airline results contrast of table
It can be seen that：As can be seen that comparing grid loxodrome and great-circle line, the two voyage difference is respectively 10.47n
Mile and 0.26n mile (use different radiuss of sphericity), and it is 0.464 ° that grid heading angle, which differs maximum value,；Compare grid isogonism
Course line and big oval course line, the two voyage differ 0.48n mile, and it is 0.471 ° that grid heading angle, which differs maximum value,.Therefore, lattice
Net loxodrome and great-circle line, big oval course line are more close, and voyage is equally shorter.Simultaneously, it is contemplated that great-circle line uses
The ellipsoid model that sphere model and navigation stage navigation equipment use is inconsistent, can there is an intrinsic original reason error, and grid
Loxodrome and big oval course line use ellipsoidal model, and navigation homework precision is higher, therefore grid loxodrome is a kind of high-precision
The polar region course line of degree.In addition, combining with theoretical analysis, grid heading angle is equal everywhere and in polar stereographic projection in grid loxodrome
Show as stringent straight line on figure, this course line feature it is equal everywhere with geographical course angle in mid low latitude region loxodrome and
It is the same that straight line is shown as on Mercator projection figure, therefore, can reach mid low latitude region using loxodrome, the geographical boat of output
The degree strictly coordinated to the airmanship at angle, Mercator projection, track rudder or course rudder so that grid loxodrome is in polar region
Also can strictly coordinate with grid navigation technology, polar stereographic projection, track rudder or the course rudder at output grid heading angle, convenient for boat
Calculation is painted in row control and navigation.
The above is presently preferred embodiments of the present invention, but the present invention should not be limited to the embodiment and attached drawing institute
Disclosure.So every do not depart from the lower equivalent or modification completed of spirit disclosed in this invention, guarantor of the present invention is both fallen within
The range of shield.
Claims (8)
1. a kind of grid loxodrome suitable for polar navigation, which is characterized in that the grid loxodrome is defined as the earth
A curve that fixed angle is intersected with all grid heading reference lines on ellipsoid.
2. the grid loxodrome according to claim 1 suitable for polar navigation, which is characterized in that setting grid isogonism
The angle in course line and grid heading reference line, i.e. grid heading angle are ψG, then pass through known pointGrid heading angle is ψG
The flight path equation of grid loxodrome be：
In formula,For the arbitrary transfer point on course line.
3. the grid loxodrome according to claim 2 suitable for polar navigation, which is characterized in that the grid isogonism
The flight path equation derivation in course line includes：If AB is the differential segmental arc in grid loxodrome,For departure point,
AB and warp BC, weft AC constitute differential right angled triangle ABC, angle, that is, lattice of grid loxodrome and grid heading reference line
Net course angle is ψG, then using the relationship at grid heading angle and geographical course angle, it is ψ that can obtain geographical course angleG+ λ, then ∠ BAC
For pi/2-(ψG+ λ), the differential arc length of warp isThe differential arc length of weft isTherefore meet
Being write formula (1) as integrated form can obtain
Ask definite integral that can obtain simultaneously on formula (2) both sides
Formula (3) is exactly to pass through known pointGrid heading angle is ψGGrid loxodrome equation,For on course line
Arbitrary transfer point.
4. a kind of design method of grid loxodrome suitable for polar navigation, which is characterized in that including：
1st step：It defines grid loxodrome and intersects geometrical clamp with all grid heading reference lines for one on earth ellipsoid face
The curve at angle；
2nd step：According to the definition that the 1st step determines, the flight path equation of grid loxodrome is obtained；
3rd step：According to the flight path equation that the 2nd step determines, the grid heading angle of grid loxodrome is obtained；
4th step：According to the flight path equation that the 2nd step determines, the voyage of grid loxodrome is obtained.
5. the design method of the grid loxodrome according to claim 4 suitable for polar navigation, which is characterized in that the
In 2 steps, the angle of grid loxodrome and grid heading reference line is set, i.e. grid heading angle is ψG, then pass through known pointGrid heading angle is ψGThe flight path equation of grid loxodrome be：
In formula,For the arbitrary transfer point on course line.
6. the design method of the grid loxodrome according to claim 5 suitable for polar navigation, which is characterized in that institute
The flight path equation derivation for stating grid loxodrome includes：If AB is the differential segmental arc in grid loxodrome,
For departure point, AB and warp BC, weft AC constitute differential right angled triangle ABC, grid loxodrome and grid heading reference
The angle of line, that is, grid heading angle is ψG, then using the relationship at grid heading angle and geographical course angle, geographical course angle can be obtained
For ψG+ λ, then ∠ BAC are pi/2-(ψG+ λ), the differential arc length of warp isThe differential arc length of weft is
Therefore meet
Being write formula (1) as integrated form can obtain
Ask definite integral that can obtain simultaneously on formula (2) both sides
Formula (3) is exactly to pass through known pointGrid heading angle is ψGGrid loxodrome equation,For on course line
Arbitrary transfer point.
7. the design method of the grid loxodrome according to claim 5 or 6 suitable for polar navigation, feature exist
In in the 3rd step, if the coordinate of known grid loxodrome starting point, terminalWithThen according to formula (3) and two
Known point coordinates solves grid heading angle, specific as follows：
Two coordinate points are substituted into formula (3) respectively, and carry out abbreviation to obtain
In formula,
8. the design method of the grid loxodrome according to claim 5 or 6 suitable for polar navigation, feature exist
In in the 4th step, with dSlIndicate the differential arc length of grid loxodrome, then
It can be obtained by formula (3), λ can be expressed as in grid loxodrome equationFunction, i.e.,
Therefore, the voyage of grid loxodrome is
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN112033407A (en) * | 2020-08-27 | 2020-12-04 | 中国人民解放军海军潜艇学院 | Great circle navigation method |
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| US20120110865A1 (en) * | 2010-11-08 | 2012-05-10 | Vaught Gregory V | Chart specific navigation plotter and method for inexpensive production thereof |
| CN103940420A (en) * | 2014-04-16 | 2014-07-23 | 中国人民解放军海军工程大学 | Method for designing equal-voyage great circle route |
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112033407A (en) * | 2020-08-27 | 2020-12-04 | 中国人民解放军海军潜艇学院 | Great circle navigation method |
| CN112033407B (en) * | 2020-08-27 | 2023-11-24 | 中国人民解放军海军潜艇学院 | Great circle navigation method |
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