959:(CBDR), the concept continues to prove very useful for conning officers (the person in control of navigating the vessel at any point in time) because CBDR will result in a collision or near miss if action is not taken by one of the two vessels involved. Simply altering course until a change in bearing (obtained by compass sighting) occurs, will provide some assurance of avoidance of collision, obviously not foolproof: the conning officer of the vessel having made the course change must continually monitor bearing lest the other vessel does the same. Significant course change, rather than a modest alteration, is prudent.
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is the range from missile to target. This acceleration depends explicitly on the velocity difference vector, which may be difficult to obtain in practice. By contrast, in the expressions that follow, dependence is only on the change of the line of sight and the magnitude of the closing velocity. If
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applied to the mirror while keeping it locked on the target is then also used (although amplified) to deflect the control surfaces that steer the missile, thereby making missile velocity vector rotation proportional to line of sight rotation. Although this does not result in a rotation rate that is
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Since the line of sight is not in general co-linear with the missile velocity vector, the applied acceleration does not necessarily preserve the missile kinetic energy. In practice, in the absence of engine throttling capability, this type of control may not be possible.
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does not change direction as the range closes. PN dictates that the missile velocity vector should rotate at a rate proportional to the rotation rate of the line of sight (Line-Of-Sight rate or LOS-rate), and in the same direction.
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If energy conserving control is required (as is the case when only using control surfaces), the following acceleration, which is orthogonal to the missile velocity, may be used:
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For example, if the line of sight rotates slowly from north to east, the missile should turn to the right by a certain factor faster than the LOS-rate. This factor is
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acceleration normal to the instantaneous line of sight is desired (as in the initial description), then the following expression is valid:
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it will keep pointing at the same direction if no external force or moment is applied, regardless of the movements of the missile. The
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always exactly proportional to the LOS-rate (which would require a constant airspeed), this implementation is equally effective.
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dictate which vessel must give way but they, of course, provide no guarantee that action will be taken by that vessel.
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source), and apply a moment to this gimballed mirror to keep it pointed at the target. Since the mirror is in fact a
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Proportional navigation can also be achieved using an acceleration normal to the instantaneous velocity difference:
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917:{\displaystyle {\vec {a}}=-N|{\vec {V}}_{r}|{\frac {{\vec {V}}_{m}}{|{\vec {V}}_{m}|}}\times {\vec {\Omega }}}
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The basis of proportional navigation was first discovered at sea, and was used by navigators on ships to
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495:{\displaystyle {\vec {\Omega }}={\frac {{\vec {R}}\times {\vec {V}}_{r}}{{\vec {R}}\cdot {\vec {R}}}}}
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775:{\displaystyle {\vec {a}}=-N|{\vec {V}}_{r}|{\frac {\vec {R}}{|{\vec {R}}|}}\times {\vec {\Omega }}}
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as a seeker. Simple electronics detect the directional error the seeker has with its target (an
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157:. It is based on the fact that two vehicles are on a collision course when their direct
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A missile (blue) intercepts a target (red) by maintaining constant bearing to it (green)
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is the proportionality constant generally having an integer value 3-5 (dimensionless),
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A rather simple hardware implementation of this guidance law can be found in early
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is the acceleration perpendicular to the missile's instantaneous velocity vector,
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364:{\displaystyle {\vec {a}}=N{\vec {V}}_{r}\times {\vec {\Omega }}}
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578:{\displaystyle {\vec {V}}_{r}={\vec {V}}_{t}-{\vec {V}}_{m}}
961:
International
Regulations for Preventing Collisions at Sea
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is the line of sight rate, and V is the closing velocity.
153:) used in some form or another by most homing air target
651:{\displaystyle {\vec {R}}={\vec {R}}_{t}-{\vec {R}}_{m}}
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585:is the target velocity relative to the missile and
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931:missiles. These missiles use a rapidly rotating
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51:introducing citations to additional sources
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206:{\displaystyle a_{n}=N{\dot {\lambda }}V}
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41:Relevant discussion may be found on the
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955:collisions. Commonly referred to as
16:Concept in missile guidance systems
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957:Constant Bearing Decreasing Range
285:{\displaystyle {\dot {\lambda }}}
34:relies largely or entirely on a
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62:"Proportional navigation"
986:Modern Missile Guidance
387:{\displaystyle \Omega }
135:Proportional navigation
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398:of the line of sight:
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984:Yanushevsky, Rafael.
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236:{\displaystyle a_{n}}
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1013:Yanushevsky, page 3.
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151:proportional control
47:improve this article
988:. CRC Press, 2007.
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256:{\displaystyle N}
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137:(also known as
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149:(analogous to
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45:. Please help
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64: –
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58:Find sources:
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36:single source
32:This article
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979:Bibliography
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147:guidance law
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1030:Navigation
1024:Categories
1001:References
73:newspapers
941:gyroscope
909:→
906:Ω
900:×
880:→
855:→
829:→
811:−
802:→
767:→
764:Ω
758:×
744:→
727:→
703:→
685:−
676:→
637:→
627:−
615:→
599:→
564:→
554:−
542:→
520:→
484:→
475:⋅
469:→
449:→
439:×
433:→
415:→
412:Ω
382:Ω
356:→
353:Ω
347:×
335:→
316:→
277:˙
274:λ
195:˙
192:λ
43:talk page
967:See also
155:missiles
103:May 2024
945:voltage
394:is the
145:) is a
143:Pro-Nav
87:scholar
992:
374:where
216:Where
89:
82:
75:
68:
60:
953:avoid
94:JSTOR
80:books
990:ISBN
505:and
66:news
141:or
49:by
1026::
937:IR
139:PN
996:.
893:|
887:m
877:V
869:|
862:m
852:V
842:|
836:r
826:V
818:|
814:N
808:=
799:a
751:|
741:R
734:|
724:R
716:|
710:r
700:V
692:|
688:N
682:=
673:a
644:m
634:R
622:t
612:R
605:=
596:R
571:m
561:V
549:t
539:V
532:=
527:r
517:V
481:R
466:R
456:r
446:V
430:R
421:=
342:r
332:V
325:N
322:=
313:a
251:N
229:n
225:a
201:V
186:N
183:=
178:n
174:a
122:.
120:N
105:)
101:(
91:·
84:·
77:·
70:·
53:.
39:.
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