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{\plain {\fs28 \b Search Patterns}}
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{\plain {by }{Richard R. Shiffman, Design
 Engineer\par Digital Graphics Assoc.\par 
Los Angeles, Ca.      rrs@isi.edu}}
}
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{\plain {This is my third Mathcad document
 on navigation in general and specifically
 what's  needed  for search and rescue work.
 The first article covered the definition
 of latitude and longitude, and distance
 along different paths on a sphere. The 
second  covered the calculation of the search
 datum, the most probable position of the
 missing vessel. This document details a
 couple of different search patterns used
 to locate a missing vessel. One would start
 to run these patterns from the search datum
 calculated by the second article in this
 series.\par \par The main idea of a search
 pattern is to maximize the chances of finding
 the missing vessel or other\par object 
in the minimal search time. Therefore,  
you want to cover the search area as fast
 as possible, but not at the loss of visual
 coverage. First some important terms for
 describing details of a search pattern 
must be defined. The }{\i search area}{ 
is the usually rectangular area containing
 the search datum and is  where the search
 will be executed. One }{\i leg}{ of the
 search pattern is the path of the search
 vessel on a constant course in the search
 area.}{\i Track spacing}{ is the distance
 between legs of the search pattern. }{\i 
Track length}{ is the length of a leg of
 the search pattern; this can very as the
 pattern is run.  The length  of a  leg 
of the pattern is expressed as a multiple
 of initial leg's length.  No matter which
 search pattern is to be run, the maximum
 track spacing should be equal to the maximum
 visible distance between the legs. This
 allows you  to visually observe every point
 in the search area .}}
}
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{\plain {The simplest search pattern ( at
 least mathematically) would be an Archimedes
 spiral, r(}{\f1 q}{), defined above. Ts
 is the track spacing of the spiral. A good
 track spacing would  be equal to the maximum
 visible distance. This would give the searcher
  a 100%  visual overlap between two pieces
 of the track that are 2*}{\f1 p}{ radians
 apart. If you are looking for a small object,
 like a man in the water, your track spacing
 may be as small as 1/10 nautical mile. 
 The datum is at the center of the spiral.
 The pattern is run outward at constant 
speed from the datum until the missing vessel
 is found.}}
}
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{\plain {There  is one serious problem with
 using an Archimedes spiral as a practical
 real world search pattern. A vessel would
 have to continuously change course to follow
 a spiral. It would be very difficult for
 the vessel's human pilot to follow such
 a course. To solve this problem the expanding
 square was created. This pattern is a  
 manhattan geometry spiral. Manhattan geometry
 only allows turns of multiples of 90 degrees.
 To run the expanding square pattern shown
 below, the vessel operator only  needs 
to proceed at a constant speed and make 
90 degree turns to starboard (right) at 
the appropriate times.  Let x  equal the
 initial track length of the search pattern.
 The sequence of track lengths then  would
 be \{x, x, 2*x, 2*x, 3*x, 3*x, 4*x, 4*x,
 ...\}. The pilot's (or skipper's) responsibility
 is to  follow the search pattern, while
 the lookouts watch for the missing vessel.}}
}
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{\plain {To the left is an example of a 
expanding square search pattern. This demonstrates
 many of the features of a typical search
 pattern. The search datum is the predicted
 position of the missing vessel, therefore
 it's the start of the search. The track
 spacing is 1/4 nautical mile, so the minimum
 visibility is at least 1/4 of a mile. This
 is for a large object in the water, like
 a boat. In this example the course and 
track length of the initial leg are 000 
degrees and 1/4 nautical mile. The missing
 vessel would be found  near the end of 
the ninth leg of the pattern.}}
}
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!`Iy!!+t"#!#LG#e!PIs!!)0!A!#LG&K!`It!!)0!1!#LG&K!`Ir!!)0"#!#LG)1!PIr!!)0!A!#LG&K!PIs!!)0!Q!#LG#e!PIs!!+t!Q!$LG#e!PJk!%Iq5[Aa!PIz!!+t!q!$LG&K!pIs!!+t!Q!&LG.[!PIz!!+t!a!%LG)1""Is!!+t!Q!&LG4'!PIt!!)0!A!%LG)1"RIs!!+t!Q!&LG#e""Jl!#>{5[Aa!PIt!!)0#u!#LH+u!PIt
!!)0&;!#LG<7!PIt!!)0"S!#LG&K!PK#!"Iq5[DG""J%!!)0$W!&LI!!!PI{!!4&"c!#LG&K!PK#!!.[5hIq#u!&!(<6!"#e

.TXT 7 53 0 0
Cg a25.333333,25.333333,726
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {This  is an example of the sector
 search pattern. The vessel preforming this
 search starts at the datum,  then heads
 north on a 000 degree course. After traveling
 a single track length the vessel turns 
right 120 degrees. For the second leg the
 search vessel travels one more track length
 on a course of 120 degrees. At the finish
 of the second track, the vessel comes right
 120 degrees to a course of 240 degrees 
for the third leg. The third  leg is  two
 initial track lengths long. At the end 
of the fourth leg in this example the missing
 vessel would be located  (or maybe during
 the first leg if the lookouts have sharp
 eyes). In this pattern the track length
 is set to the maximum visible distance.}}
}
.TXT 54 -53 0 0
C x1,1,0,0
.TXT 4 0 0 0
Cg a73.166667,73.166667,280
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Before we describe the search pattern
 calculators for different patterns, some
 common functions used by all the patterns
 must be defined. These functions handle:
 1) time conversions, 2) the relationship
 between distance, time and speed, and 3)
 rotation of the chart displays.}}
}
.TXT 8 0 0 0
Cg a73.000000,73.000000,130
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {The function  }{\b hours}{ is used
 to convert\par time in hrs, min, sec to
 hrs and fractions of\par hrs for use in
 these calculation.}}
}
.TXT 0 39 0 0
Cg a37.000000,37.000000,147
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {The following functions take the
 time in hours and\par returns it in people
 readable form. They are used b}{y }{\b 
dtim(h)}{ and }{\b dtimr(h)}{ .}}
}
.EQN 7 0 0 0
{0:ghrs}NAME({0:h}NAME):{0:floor}NAME({0:h}NAME)
.EQN 1 -38 0 0
{0:hours}NAME({0:h}NAME,{0:m}NAME,{0:s}NAME):{0:h}NAME+({0:m}NAME)/(60)+({0:s}NAME)/(3600)
.EQN 2 38 0 0
{0:gmin}NAME({0:h}NAME):{0:floor}NAME({0:mod}NAME({0:h}NAME,1)*60)
.EQN 4 0 0 0
{0:gsec}NAME({0:h}NAME):{0:mod}NAME({0:h}NAME,(1)/(60))*3600
.TXT 4 0 0 0
Cg a30.666667,30.666667,42
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {gsr(h) rounds off to the nearest
 second}}
}
.EQN 5 0 0 0
{0:gsecr}NAME({0:h}NAME):{0:floor}NAME({0:mod}NAME({0:h}NAME+(1)/(2*3600),(1)/(60))*3600)
.TXT 6 -39 0 0
Cg a72.000000,72.000000,219
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {The function }{\b dtim(}{\b h)}{
 is used to convert time in hours to time
 in hours, minutes and seconds\par for display
 purposes.}{ }{\b dtimr(h)}{ converts hours
 to (hrs,min,sec), but rounds off fractions
 of  seconds.}}
}
.EQN 8 0 0 0
{0:dtim}NAME({0:h}NAME):({1,3}ö{0:gsec}NAME({0:h}NAME)ö{0:gmin}NAME({0:h}NAME)ö{0:ghrs}NAME({0:h}NAME))
.EQN 0 39 0 0
{0:dtimr}NAME({0:h}NAME):({1,3}ö{0:gsecr}NAME({0:h}NAME)ö{0:gmin}NAME({0:h}NAME)ö{0:ghrs}NAME({0:h}NAME))
.TXT 6 -39 0 0
Cg a73.000000,73.000000,147
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {The }{functions}{ below are used
 to define the relationship between  time
 and distance. They are used b}{y all the
 search pattern calculators. }}
}
.EQN 7 0 0 0
{0:D}NAME({0:t}NAME,{0:s}NAME):{0:s}NAME*{0:t}NAME
.EQN 0 13 0 0
{0:T}NAME({0:d}NAME,{0:s}NAME):({0:d}NAME)/({0:s}NAME)
.EQN 0 12 0 0
{0:S}NAME({0:d}NAME,{0:t}NAME):({0:d}NAME)/({0:t}NAME)
.TXT 5 -25 0 0
Cg a73.000000,73.000000,208
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {The function }{\b Mr(a)}{ is used
 to rotate the chart display counterclockwise
 when the initial leg's direction is other
 than 000 degrees or true north. It is used
 by all the search pattern calculators. 
 }}
}
.EQN 11 0 0 0
{0:Mr}NAME({0:a}NAME):({2,2}ö{0:cos}NAME(({0:\p}NAME)/(180)*{0:a}NAME)ö{0:sin}NAME(({0:\p}NAME)/(180)*{0:a}NAME)ö-{0:sin}NAME(({0:\p}NAME)/(180)*{0:a}NAME)ö{0:cos}NAME(({0:\p}NAME)/(180)*{0:a}NAME))
.TXT 16 0 0 0
C x1,1,0,0
.TXT 3 18 0 0
Cg a47.833333,47.833333,52
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {\fs24 \b Expanding Square Pattern
 Calculator (SS)}}
}
.TXT 3 -18 0 0
Cg a74.000000,74.000000,1140
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {The main purpose of the expanding
 square calculator is to generate a chart
 of the search pattern requested, and tables
 of courses and run times need to execute
 the pattern. Since the search vessel is
 running the selected pattern at constant
 speed, the only  thing its operator  must
 do to follow the desired pattern is come
 to the course given in these tables at 
the given time . \par \par Due to the vessel's
 inertia, the turn must be started before
 the vessel reaches the beginning of the
 new  leg or  it will overshoot the pattern.
 That lead  time is the value of 'delay_boat'.
 It is set to 15 seconds, which is the response
 time of a 40 foot powerboat used in our
 exercises.This time would need to be adjusted
 for different boats, but would not vary
 greatly. The other  lead time that must
 be added to the above time is the command
 time, given by  'delay_cmd'. This is the
 time need to inform the helmsman of the
 course you want to come to ( i.e. 'on my
 mark come to course 045 magnetic. ... 5,
 4, 3, 2, 1, mark!). This time is about 
10 seconds and is independent of vessel 
type. The total lead time is the value of
 'delay_tot'. }}
}
.TXT 25 0 0 0
Cg a73.000000,73.000000,392
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Following  the chart t}{he first
 table's entries contain:  the leg number,
 the direction of that leg,  the distance
 of that leg,  the run time for that leg
 and the total elapsed time. The second 
table's entries contain: the leg number,
 direction of the current leg, elapsed time
 to the verbal warning, the new course to
 come to, and the elapsed time till the 
command to turn the boat.\par }}
}
.TXT 10 4 0 0
Cg a73.000000,73.000000,74
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {\fs24 \b Enter  initial parameters
 for  expanding square search pattrem}}
}
.TXT 6 -4 0 0
Cg a72.000000,72.000000,20
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Enter track speed}}
}
.TXT 0 19 0 0
Cg a53.000000,53.000000,27
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Enter initial leg lenght}}
}
.TXT 0 20 0 0
Cg a33.000000,33.000000,24
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Enter  initial course}}
}
.TXT 0 25 0 0
Cg a66.000000,66.000000,25
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Number of legs to plot}}
}
.EQN 4 -64 0 0
{0:S.track}NAME:10
.EQN 0 10 0 0
{0:knots}NAME
.EQN 0 9 0 0
{0:L.track}NAME:(1)/(4)
.EQN 0 9 0 0
{0:miles}NAME
.EQN 0 11 0 0
{0:dirl1}NAME:000
.TXT 0 9 0 0
Cg a22.000000,22.000000,19
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {degress magnetic}}
}
.EQN 0 16 0 0
{0:N}NAME:9
.TXT 7 -64 0 0
Cg a73.000000,73.000000,41
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain { Basic  track length is stored 
in  L .}}
}
.EQN 0 27 0 0
{0:L}NAME:{0:L.track}NAME
.EQN 5 -27 0 0
{0:ia}NAME:1;{0:N}NAME
.EQN 4 0 0 0
({0:a}NAME)[({0:ia}NAME):{0:mod}NAME(({0:ia}NAME-1)*({0:\p}NAME)/(2),2*{0:\p}NAME)
.TXT 0 38 0 0
Cg a43.833333,43.833333,94
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Calculate the angle for each leg
 of the SS pattern; \par they  are 0, 90,
  180 and 270 degrees}}
}
.EQN 4 -38 0 0
({0:s}NAME)[({0:ia}NAME):{0:sin}NAME(({0:a}NAME)[({0:ia}NAME))
.EQN 0 14 0 0
({0:c}NAME)[({0:ia}NAME):{0:cos}NAME(({0:a}NAME)[({0:ia}NAME))
.TXT 1 24 0 0
Cg a35.000000,35.000000,38
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {The sines and cosines of the angles}}
}
.TXT 5 0 0 0
Cg a35.000000,35.000000,96
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {This function is used to c}{alculate
 the  scale factor for length of leg( i)
 of the pattern.}}
}
.EQN 1 -38 0 0
{0:Sf.ss}NAME({0:i}NAME):(({0:i}NAME-1)-{0:mod}NAME(({0:i}NAME-1),2))/(2)+1
.TXT 7 0 0 0
Cg a73.000000,73.000000,73
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Now  generate the (SS) search pattern
 for the chart; the origin is at:}}
}
.EQN 0 50 0 0
({0:Pss}NAME){52}(0):(({1,2}ö0ö0)){51}
.TXT 4 -50 0 0
Cg a73.000000,73.000000,21
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Leg 1 through  }{N}}
}
.EQN 3 0 0 0
{0:ip}NAME:1;{0:N}NAME
.EQN 0 19 0 0
({0:Pss}NAME){52}({0:ip}NAME):({0:Pss}NAME){52}({0:ip}NAME-1)+({2,2}ö({0:c}NAME)[(({0:ip}NAME))ö({0:s}NAME)[(({0:ip}NAME))ö-({0:s}NAME)[(({0:ip}NAME))ö({0:c}NAME)[(({0:ip}NAME)))*({2,1}ö{0:L}NAMEö0)*{0:Sf.ss}NAME({0:ip}NAME)
.TXT 8 -19 0 0
Cg a73.000000,73.000000,84
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Calculate vector of track lenghts
 for each leg of the}{ Expanding Square}{
 Search}}
}
.EQN 3 0 0 0
({0:l}NAME)[(0):0
.EQN 0 8 0 0
{0:ic}NAME:1;{0:cols}NAME({0:Pss}NAME)-1
.EQN 0 20 0 0
({0:l}NAME)[({0:ic}NAME):{0:L}NAME*{0:Sf.ss}NAME({0:ic}NAME)
.TXT 6 -28 0 0
Cg a73.000000,73.000000,55
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Calculate courses for each leg 
in the search pattern}}
}
.EQN 3 0 0 0
({0:Adeg}NAME)[(0):0
.EQN 3 0 0 0
{0:i}NAME:1;{0:cols}NAME({0:Pss}NAME)
.EQN 3 0 0 0
({0:Adeg}NAME)[({0:i}NAME):({0:i}NAME-1)*90
.EQN 4 0 0 0
{0:dirl}NAME:({0:mod}NAME({0:Adeg}NAME+{0:dirl1}NAME,360)){49}
.TXT 1 0 0 0
C x1,1,0,0
.TXT 4 0 0 0
Cg a73.000000,73.000000,97
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Calculate the run times for each
 leg and the total elapsed time form the
 vector of leg lengths}}
}
.EQN 4 0 0 0
{0:tvec}NAME:({0:T}NAME({0:l}NAME,{0:S.track}NAME)){49}
.EQN 0 16 0 0
{0:j}NAME:0;{0:last}NAME({0:l}NAME)
.EQN 3 -16 0 0
({0:sumt}NAME)[(0):({0:tvec}NAME)[(0)
.EQN 0 13 0 0
{0:jj}NAME:1;{0:last}NAME({0:l}NAME)
.EQN 0 17 0 0
({0:sumt}NAME)[({0:jj}NAME):({0:sumt}NAME)[({0:jj}NAME-1)+({0:tvec}NAME)[({0:jj}NAME)
.TXT 4 -30 0 0
Cg a73.000000,73.000000,50
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Converter times to  hours, minutes,
 and seconds}}
}
.EQN 3 0 0 0
{0:th}NAME:({0:ghrs}NAME({0:tvec}NAME)){49}
.EQN 0 17 0 0
{0:tm}NAME:({0:gmin}NAME({0:tvec}NAME)){49}
.EQN 0 18 0 0
{0:ts}NAME:({0:gsecr}NAME({0:tvec}NAME)){49}
.EQN 0 15 0 0
({0:leg}NAME)[({0:j}NAME):{0:j}NAME
.EQN 4 -50 0 0
{0:sth}NAME:({0:ghrs}NAME({0:sumt}NAME)){49}
.EQN 0 17 0 0
{0:stm}NAME:({0:gmin}NAME({0:sumt}NAME)){49}
.EQN 0 18 0 0
{0:sts}NAME:({0:gsecr}NAME({0:sumt}NAME)){49}
.TXT 5 -35 0 0
Cg a73.000000,73.000000,284
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Since the boat doesn't trun instantly,
  the command to turn must given before 
the end of the \par current leg is reached.
 Allow 15 seconds at 10 knotes for the boat
 to make the turn and 10\par seconds prior
 to that to warn the helm. The warning times
 and mark times are calculated below.}}
}
.EQN 7 0 0 0
{0:delay_boat}NAME:{0:hours}NAME(0,0,15)
.EQN 0 23 0 0
{0:delay_cmd}NAME:{0:hours}NAME(0,0,10)
.EQN 0 22 0 0
{0:delay_tot}NAME:{0:delay_boat}NAME+{0:delay_cmd}NAME
.EQN 4 -45 0 0
{0:wrnt}NAME:(({0:sumt}NAME-{0:delay_tot}NAME)){49}
.EQN 0 21 0 0
{0:mrkt}NAME:(({0:sumt}NAME-{0:delay_boat}NAME)){49}
.TXT 4 -21 0 0
Cg a73.000000,73.000000,50
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Converter times to  hours, minutes,
 and seconds}}
}
.EQN 4 0 0 0
{0:thw}NAME:({0:ghrs}NAME({0:wrnt}NAME)){49}
.EQN 0 16 0 0
{0:tmw}NAME:({0:gmin}NAME({0:wrnt}NAME)){49}
.EQN 0 17 0 0
{0:tsw}NAME:({0:gsecr}NAME({0:wrnt}NAME)){49}
.EQN 4 -33 0 0
{0:thm}NAME:({0:ghrs}NAME({0:mrkt}NAME)){49}
.EQN 0 16 0 0
{0:tmm}NAME:({0:gmin}NAME({0:mrkt}NAME)){49}
.EQN 0 17 0 0
{0:tsm}NAME:({0:gsecr}NAME({0:mrkt}NAME)){49}
.TXT 6 -33 0 0
Cg a73.000000,73.000000,89
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Calcuate chart display for search
 pattern. Rotate display to angle of the
 initial leg.}}
}
.EQN 3 0 0 0
{0:k}NAME:0;{0:cols}NAME({0:Pss}NAME)-1
.EQN 0 19 0 0
{0:PPss}NAME:{0:Mr}NAME({0:dirl1}NAME)*{0:Pss}NAME
.TXT 6 -19 0 0
Cg a54.500000,54.500000,145
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain { Mbb is the smallest bounding square
 that will inclose}{ the expanding square
 search pattern. it is used to control the
 scaling of the chart.}}
}
.EQN 5 0 0 0
{0:LP}NAME:({0:Pss}NAME){52}({0:cols}NAME({0:Pss}NAME)-1)
.EQN 3 0 0 0
({0:LP}NAME)[(0):{0:if}NAME(|(({0:LP}NAME)[(0))>|(({0:LP}NAME)[(1)),({0:LP}NAME)[(0),({0:LP}NAME)[(1))
.EQN 0 29 0 0
({0:LP}NAME)[(1):{0:if}NAME(|(({0:LP}NAME)[(1))>|(({0:LP}NAME)[(0)),({0:LP}NAME)[(1),({0:LP}NAME)[(0))
.EQN 8 -29 0 0
{0:mbbs}NAME:({2,4}ö({0:LP}NAME)[(1)ö-({0:LP}NAME)[(0)ö-({0:LP}NAME)[(1)ö-({0:LP}NAME)[(0)ö-({0:LP}NAME)[(1)ö({0:LP}NAME)[(0)ö({0:LP}NAME)[(1)ö({0:LP}NAME)[(0))
.EQN 0 31 0 0
{0:Mbb}NAME:{0:Mr}NAME({0:dirl1}NAME)*{0:mbbs}NAME
.TXT 0 22 0 0
Cg a42.000000,42.000000,31
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Generate &  }{Rotate the Mbb}}
}
.EQN 3 -22 0 0
{0:km}NAME:0;{0:cols}NAME({0:mbbs}NAME)-1
.TXT 0 22 0 0
Cg a23.000000,23.000000,19
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Indecies for Mbb}}
}
.TXT 3 -53 0 0
Cg a14.000000,14.000000,22
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Indecies for tables}}
}
.EQN 3 0 0 0
{0:n}NAME:1;{0:N}NAME
.EQN 0 10 0 0
{0:m}NAME:2;{0:N}NAME
.TXT 4 -10 0 0
C x1,1,0,0
.TXT 4 23 0 0
Cg a56.000000,56.000000,46
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {\fs24 \b Expanding Square Search
 Pattern}{ }}
}
.TXT 7 -23 0 0
Cg a72.000000,72.000000,14
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Track speed}}
}
.TXT 0 19 0 0
Cg a53.000000,53.000000,22
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Iinitial leg lenght}}
}
.TXT 0 20 0 0
Cg a33.000000,33.000000,17
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Initial course}}
}
.TXT 0 18 0 0
Cg a66.000000,66.000000,25
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Number of legs to plot}}
}
.EQN 4 -57 0 0
{0:S.track}NAME=?_n_u_l_l_
.EQN 0 10 0 0
{0:knots}NAME
.EQN 0 9 0 0
{0:L.track}NAME=?_n_u_l_l_
.EQN 0 11 0 0
{0:miles}NAME
.EQN 0 9 0 0
{0:dirl1}NAME=?_n_u_l_l_
.EQN 0 8 0 0
{0:degrees}NAME
.EQN 0 10 0 0
{0:N}NAME=?_n_u_l_l_
.EQN 4 -57 0 0
_n_u_l_l_&_n_u_l_l_&((({0:PPss}NAME){52}({0:k}NAME)))[(1),0,((({0:Mbb}NAME){52}({0:km}NAME)))[(1)@_n_u_l_l_&_n_u_l_l_&((({0:PPss}NAME){52}({0:k}NAME)))[(0),0,((({0:Mbb}NAME){52}({0:km}NAME)))[(0)
0 0 1 0 0
0 0 1 0 0
3 3 0 0 NO-TRACE-STRING
1 0 1 0 NO-TRACE-STRING
0 0 2 1 NO-TRACE-STRING
0 4 3 0 NO-TRACE-STRING
0 1 4 0 NO-TRACE-STRING
0 2 5 0 NO-TRACE-STRING
0 3 6 0 NO-TRACE-STRING
0 4 0 0 NO-TRACE-STRING
0 1 1 0 NO-TRACE-STRING
0 2 2 0 NO-TRACE-STRING
0 3 3 0 NO-TRACE-STRING
0 4 4 0 NO-TRACE-STRING
0 1 5 0 NO-TRACE-STRING
0 2 6 0 NO-TRACE-STRING
0 3 0 0 NO-TRACE-STRING
0 4 1 0 NO-TRACE-STRING
0 1 37 33
.TXT 4 57 0 0
Cg a23.000000,23.000000,190
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {On the left is}{ the chart of the
 expanding square search you have selected.
 The top of the chart is north ( course 
000) and the distances are in nautical miles.
 The datum is at 0,0.}}
}
.TXT 41 -57 0 0
Cg a73.000000,73.000000,6
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {leg}}
}
.TXT 0 6 0 0
Cg a72.000000,72.000000,12
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {direction}}
}
.TXT 0 9 0 0
Cg a72.000000,72.000000,11
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {distance}}
}
.TXT 0 12 0 0
Cg a10.333333,10.333333,16
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Time per  leg}}
}
.TXT 0 19 0 0
Cg a21.000000,21.000000,15
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Elapsed time}}
}
.TXT 0 16 0 0
Cg a11.000000,11.000000,14
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Track speed}}
}
.EQN 3 -62 0 0
({0:leg}NAME)[({0:n}NAME)=_n_u_l_l_
.EQN 0 6 0 0
({0:dirl}NAME)[({0:n}NAME)=_n_u_l_l_
.EQN 0 10 0 0
({0:l}NAME)[({0:n}NAME)=_n_u_l_l_
.EQN 0 11 0 0
({0:th}NAME)[({0:n}NAME)=_n_u_l_l_
.EQN 0 3 0 0
({0:tm}NAME)[({0:n}NAME)=_n_u_l_l_
.EQN 0 3 0 0
({0:ts}NAME)[({0:n}NAME)=_n_u_l_l_
.EQN 0 13 0 0
({0:sth}NAME)[({0:n}NAME)=_n_u_l_l_
.EQN 0 3 0 0
({0:stm}NAME)[({0:n}NAME)=_n_u_l_l_
.EQN 0 4 0 0
({0:sts}NAME)[({0:n}NAME)=_n_u_l_l_
.EQN 0 9 0 0
{0:S.track}NAME=?_n_u_l_l_
.TXT 0 10 0 0
Cg a74.000000,74.000000,9
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {knotes}}
}
.TXT 29 -72 0 0
Cg a72.000000,72.000000,6
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Leg}}
}
.TXT 0 4 0 0
Cg a68.000000,68.000000,12
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {on course}}
}
.TXT 0 10 0 0
Cg a69.000000,69.000000,20
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Spoken warning at}}
}
.TXT 0 16 0 0
Cg a71.000000,71.000000,17
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {come to course}}
}
.TXT 0 19 0 0
Cg a63.000000,63.000000,17
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Mark ( do it )}}
}
.EQN 3 -49 0 0
({0:leg}NAME)[({0:n}NAME)=_n_u_l_l_
.EQN 0 5 0 0
({0:dirl}NAME)[({0:n}NAME)=_n_u_l_l_
.EQN 0 9 0 0
({0:thw}NAME)[({0:n}NAME)=_n_u_l_l_
.EQN 0 4 0 0
({0:tmw}NAME)[({0:n}NAME)=_n_u_l_l_
.EQN 0 4 0 0
({0:tsw}NAME)[({0:n}NAME)=_n_u_l_l_
.EQN 0 12 0 0
({0:dirl}NAME)[({0:m}NAME)=_n_u_l_l_
.EQN 0 11 0 0
({0:thm}NAME)[({0:n}NAME)=_n_u_l_l_
.EQN 0 4 0 0
({0:tmm}NAME)[({0:n}NAME)=_n_u_l_l_
.EQN 0 4 0 0
({0:tsm}NAME)[({0:n}NAME)=_n_u_l_l_
.TXT 26 -53 0 0
C x1,1,0,0
.TXT 3 11 0 0
Cg a54.000000,54.000000,57
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {\fs24 \b Sector Search Pattern 
Calculator (VS) or (VM)}}
}
.TXT 3 -11 0 0
Cg a73.000000,73.000000,500
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {The sector seach pattern can be
 used by one or more vessels to search a
 circular area. If one boat is preforming
 the search (VS), he will run the pattern
 twice, but the second pattern is rotated
 to the right by 30 degrees.  If two boats
 are used (VM), the search time will be 
divided in half. When two boats are used
 the secound boat started his run from the
 datum when the first boat has finished 
his first leg. The second boats pattern 
is rotated by 90 degrees to the first boat's
 pattern.  }}
}
.TXT 10 0 0 0
Cg a73.000000,73.000000,768
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {The single search boat would start
 his search at the datum. He would then 
proceed on a 000 degree course at a fixed
 speed till he had covered one track length.
 The search vessel would then turn right
 120 degrees, bringing his course to 120.
 He would then run for a distance of one
 track length. After finishing the second
  leg of the pattern the vessel would turn
 right 120 degrees, coming to a course of
 240 degrees. For the third leg, the search
 vessel would proceed a distance of two 
track lengths.There are 7 legs in this search
 pattern, each time you finish a leg you
 come right 120 degrees. The first and seventh
 leg of the sector search pattern are one
 track length long. The second through sixth
 legs alternate between one and two track
 lengths long.}}
}
.TXT 24 6 0 0
Cg a73.000000,73.000000,100
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {\fs24 \b Enter initial parameters
 for }{\fs24 \b \fs24 \b Sector Search}{\fs24 
\b  search pattrem}}
}
.TXT 6 -6 0 0
Cg a72.000000,72.000000,20
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Enter track speed}}
}
.TXT 0 19 0 0
Cg a53.000000,53.000000,27
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Enter initial leg lenght}}
}
.TXT 0 20 0 0
Cg a33.000000,33.000000,23
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Enter initial course}}
}
.EQN 4 -39 0 0
{0:S.track}NAME:10
.EQN 0 10 0 0
{0:knots}NAME
.EQN 0 9 0 0
{0:L.track}NAME:(1)/(4)
.EQN 0 9 0 0
{0:miles}NAME
.EQN 0 11 0 0
{0:dirl1}NAME:000
.TXT 0 9 0 0
Cg a22.000000,22.000000,19
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {degress magnetic}}
}
.TXT 8 -48 0 0
Cg a73.000000,73.000000,52
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Define Basic sector search with
 track length  L .}}
}
.EQN 0 37 0 0
{0:L}NAME:{0:L.track}NAME
.EQN 4 -37 0 0
{0:ia}NAME:1;2
.EQN 0 9 0 0
({0:a}NAME)[(0):0
.EQN 0 7 0 0
({0:a}NAME)[({0:ia}NAME):({0:a}NAME)[({0:ia}NAME-1)+120*({0:\p}NAME)/(180)
.TXT 0 22 0 0
Cg a35.000000,35.000000,78
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Calculate the angles used in VS
 pattern, \par they are 0, 120, and 240 
degrees}}
}
.EQN 5 -38 0 0
{0:ia}NAME:0;2
.EQN 0 10 0 0
({0:s}NAME)[({0:ia}NAME):{0:sin}NAME(({0:a}NAME)[({0:ia}NAME))
.EQN 0 14 0 0
({0:c}NAME)[({0:ia}NAME):{0:cos}NAME(({0:a}NAME)[({0:ia}NAME))
.TXT 0 14 0 0
Cg a35.000000,35.000000,31
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {And needed sines and cosines}}
}
.EQN 5 -38 0 0
{0:SF.vs}NAME({0:i}NAME):{0:if}NAME(({0:i}NAME÷3)+({0:i}NAME÷5),2,1)
.TXT 0 38 0 0
Cg a35.000000,35.000000,103
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Calculate scale factor for length
 of leg( i). Leg 3 a}{nd 5 are 2*x long 
and the rest are 1*x long.}}
}
.TXT 8 -38 0 0
Cg a73.000000,73.000000,81
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Now  generate the vector search
 pattern }{for the chart}{;}{ the origin
 is at:}}
}
.EQN 0 51 0 0
({0:Pvs}NAME){52}(0):(({1,2}ö0ö0)){51}
.TXT 3 -51 0 0
Cg a73.000000,73.000000,22
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain { }{Legs 1 through 7}}
}
.EQN 3 0 0 0
{0:ip}NAME:1;7
.EQN 0 10 0 0
({0:im}NAME)[({0:ip}NAME):{0:mod}NAME({0:ip}NAME,3)
.EQN 0 16 0 0
({0:Pvs}NAME){52}({0:ip}NAME):({0:Pvs}NAME){52}({0:ip}NAME-1)+({2,2}ö({0:c}NAME)[((({0:im}NAME)[({0:ip}NAME)))ö({0:s}NAME)[((({0:im}NAME)[({0:ip}NAME)))ö-({0:s}NAME)[((({0:im}NAME)[({0:ip}NAME)))ö({0:c}NAME)[((({0:im}NAME)[({0:ip}NAME))))*({2,1}ö
{0:L}NAMEö0)*{0:SF.vs}NAME({0:ip}NAME)
.TXT 10 -26 0 0
Cg a73.000000,73.000000,72
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Calculate vector of track lenghts
 for each leg of the }{Sector Search}}
}
.EQN 4 0 0 0
{0:ic}NAME:1;{0:cols}NAME({0:Pvs}NAME)-1
.EQN 0 20 0 0
({0:l1}NAME)[({0:ic}NAME-1):{0:L}NAME*{0:SF.vs}NAME({0:ic}NAME)
.TXT 8 -20 0 0
Cg a73.000000,73.000000,55
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Calculate courses for each leg 
in the search pattern}}
}
.EQN 3 1 0 0
{0:i}NAME:0;{0:cols}NAME({0:Pvs}NAME)-2
.EQN 3 0 0 0
({0:A1deg}NAME)[({0:i}NAME):({0:im}NAME)[({0:i}NAME)*120
.EQN 5 0 0 0
{0:dirl}NAME:({0:mod}NAME({0:A1deg}NAME+{0:dirl1}NAME,360)){49}
.TXT 5 -1 0 0
C x1,1,0,0
.TXT 3 1 0 0
Cg a73.000000,73.000000,66
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Calculate the run times for each
 leg and the total elapsed time}}
}
.EQN 4 0 0 0
{0:tvec1}NAME:({0:T}NAME({0:l1}NAME,{0:S.track}NAME)){49}
.EQN 0 19 0 0
{0:j}NAME:0;{0:last}NAME({0:l1}NAME)
.EQN 3 -19 0 0
({0:sumt1}NAME)[(0):({0:tvec1}NAME)[(0)
.EQN 0 13 0 0
{0:jj}NAME:1;{0:last}NAME({0:l1}NAME)
.EQN 0 13 0 0
({0:sumt1}NAME)[({0:jj}NAME):({0:sumt1}NAME)[({0:jj}NAME-1)+({0:tvec1}NAME)[({0:jj}NAME)
.TXT 5 -26 0 0
Cg a73.000000,73.000000,50
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Converter times to  hours, minutes,
 and seconds}}
}
.EQN 4 0 0 0
{0:th}NAME:({0:ghrs}NAME({0:tvec1}NAME)){49}
.EQN 0 17 0 0
{0:tm}NAME:({0:gmin}NAME({0:tvec1}NAME)){49}
.EQN 0 18 0 0
{0:ts}NAME:({0:gsecr}NAME({0:tvec1}NAME)){49}
.EQN 0 15 0 0
({0:leg}NAME)[({0:j}NAME):{0:j}NAME+1
.EQN 4 -50 0 0
{0:sth}NAME:({0:ghrs}NAME({0:sumt1}NAME)){49}
.EQN 0 17 0 0
{0:stm}NAME:({0:gmin}NAME({0:sumt1}NAME)){49}
.EQN 0 18 0 0
{0:sts}NAME:({0:gsecr}NAME({0:sumt1}NAME)){49}
.TXT 7 -36 0 0
Cg a73.000000,73.000000,283
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Since the boat doesn't trun instantly
  the command to turn must given before 
the end of the \par current leg is reached.
 Allow 15 seconds at 10 knotes for the boat
 to make the turn and 10\par seconds prior
 to that to warn the helm. The warning times
 and mark times are calculated below.}}
}
.EQN 7 0 0 0
{0:delay_boat}NAME:{0:hours}NAME(0,0,15)
.EQN 0 23 0 0
{0:delay_cmd}NAME:{0:hours}NAME(0,0,10)
.EQN 0 22 0 0
{0:delay_tot}NAME:{0:delay_boat}NAME+{0:delay_cmd}NAME
.EQN 4 -45 0 0
{0:wrnt1}NAME:(({0:sumt1}NAME-{0:delay_tot}NAME)){49}
.EQN 0 23 0 0
{0:mrkt1}NAME:(({0:sumt1}NAME-{0:delay_boat}NAME)){49}
.TXT 6 -23 0 0
Cg a73.000000,73.000000,50
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Converter times to  hours, minutes,
 and seconds}}
}
.EQN 4 0 0 0
{0:thw1}NAME:({0:ghrs}NAME({0:wrnt1}NAME)){49}
.EQN 0 16 0 0
{0:tmw1}NAME:({0:gmin}NAME({0:wrnt1}NAME)){49}
.EQN 0 17 0 0
{0:tsw1}NAME:({0:gsecr}NAME({0:wrnt1}NAME)){49}
.EQN 4 -33 0 0
{0:thm1}NAME:({0:ghrs}NAME({0:mrkt1}NAME)){49}
.EQN 0 16 0 0
{0:tmm1}NAME:({0:gmin}NAME({0:mrkt1}NAME)){49}
.EQN 0 17 0 0
{0:tsm1}NAME:({0:gsecr}NAME({0:mrkt1}NAME)){49}
.TXT 7 -33 0 0
Cg a73.000000,73.000000,45
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Calcuate chart display for search
 pattern.}}
}
.EQN 3 0 0 0
{0:k}NAME:0;{0:cols}NAME({0:Pvs}NAME)-1
.EQN 0 19 0 0
{0:PPvs}NAME:{0:Mr}NAME({0:dirl1}NAME)*{0:Pvs}NAME
.TXT 7 -19 0 0
C x1,1,0,0
.TXT 3 21 0 0
Cg a56.000000,56.000000,36
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {\fs24 \b Sector Search Pattern}{
 }}
}
.TXT 7 -21 0 0
Cg a72.000000,72.000000,14
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Track speed}}
}
.TXT 0 19 0 0
Cg a53.000000,53.000000,21
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Initial leg lenght}}
}
.TXT 0 20 0 0
Cg a33.000000,33.000000,17
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Initial course}}
}
.EQN 4 -39 0 0
{0:S.track}NAME=?_n_u_l_l_
.EQN 0 10 0 0
{0:knots}NAME
.EQN 0 9 0 0
{0:L.track}NAME=?_n_u_l_l_
.EQN 0 11 0 0
{0:miles}NAME
.EQN 0 9 0 0
{0:dirl1}NAME=?_n_u_l_l_
.TXT 0 9 0 0
Cg a22.000000,22.000000,10
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {degress}}
}
.EQN 10 -48 0 0
_n_u_l_l_&_n_u_l_l_&((({0:PPvs}NAME){52}({0:k}NAME)))[(1),0@_n_u_l_l_&_n_u_l_l_&((({0:PPvs}NAME){52}({0:k}NAME)))[(0),0
0 0 1 0 0
0 0 1 0 0
3 3 0 0 NO-TRACE-STRING
1 0 1 0 NO-TRACE-STRING
0 3 2 0 NO-TRACE-STRING
0 4 3 0 NO-TRACE-STRING
0 1 4 0 NO-TRACE-STRING
0 2 5 0 NO-TRACE-STRING
0 3 6 0 NO-TRACE-STRING
0 4 0 0 NO-TRACE-STRING
0 1 1 0 NO-TRACE-STRING
0 2 2 0 NO-TRACE-STRING
0 3 3 0 NO-TRACE-STRING
0 4 4 0 NO-TRACE-STRING
0 1 5 0 NO-TRACE-STRING
0 2 6 0 NO-TRACE-STRING
0 3 0 0 NO-TRACE-STRING
0 4 1 0 NO-TRACE-STRING
0 1 32 30
.TXT 4 50 0 0
Cg a23.000000,23.000000,180
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {On the left is}{ the chart of the
 vector search you have selected. The top
 of the chart is north ( course 000) and
 the distances are in nautical miles. The
 datum is at 0,0.}}
}
.TXT 39 -49 0 0
Cg a73.000000,73.000000,6
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {leg}}
}
.TXT 0 6 0 0
Cg a72.000000,72.000000,12
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {direction}}
}
.TXT 0 9 0 0
Cg a72.000000,72.000000,11
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {distance}}
}
.TXT 0 12 0 0
Cg a10.333333,10.333333,16
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Time per  leg}}
}
.TXT 0 19 0 0
Cg a21.000000,21.000000,15
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Elapsed time}}
}
.TXT 0 16 0 0
Cg a11.000000,11.000000,14
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Track speed}}
}
.EQN 3 -62 0 0
({0:leg}NAME)[({0:j}NAME)=_n_u_l_l_
.EQN 0 6 0 0
({0:dirl}NAME)[({0:j}NAME)=_n_u_l_l_
.EQN 0 10 0 0
({0:l}NAME)[({0:j}NAME)=_n_u_l_l_
.EQN 0 11 0 0
({0:th}NAME)[({0:j}NAME)=_n_u_l_l_
.EQN 0 3 0 0
({0:tm}NAME)[({0:j}NAME)=_n_u_l_l_
.EQN 0 3 0 0
({0:ts}NAME)[({0:j}NAME)=_n_u_l_l_
.EQN 0 13 0 0
({0:sth}NAME)[({0:j}NAME)=_n_u_l_l_
.EQN 0 3 0 0
({0:stm}NAME)[({0:j}NAME)=_n_u_l_l_
.EQN 0 4 0 0
({0:sts}NAME)[({0:j}NAME)=_n_u_l_l_
.EQN 0 9 0 0
{0:S.track}NAME=?_n_u_l_l_
.TXT 0 10 0 0
Cg a74.000000,74.000000,9
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {knotes}}
}
.TXT 27 -72 0 0
Cg a72.000000,72.000000,6
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Leg}}
}
.TXT 0 4 0 0
Cg a68.000000,68.000000,12
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {on course}}
}
.TXT 0 10 0 0
Cg a69.000000,69.000000,20
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Spoken warning at}}
}
.TXT 0 16 0 0
Cg a71.000000,71.000000,17
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {come to course}}
}
.TXT 0 15 0 0
Cg a63.000000,63.000000,17
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Mark ( do it )}}
}
.EQN 3 -45 0 0
({0:leg}NAME)[({0:j}NAME)=_n_u_l_l_
.EQN 0 5 0 0
({0:dirl}NAME)[({0:j}NAME)=_n_u_l_l_
.EQN 0 9 0 0
({0:thw1}NAME)[({0:j}NAME)=_n_u_l_l_
.EQN 0 4 0 0
({0:tmw1}NAME)[({0:j}NAME)=_n_u_l_l_
.EQN 0 4 0 0
({0:tsw1}NAME)[({0:j}NAME)=_n_u_l_l_
.EQN 0 12 0 0
({0:dirl}NAME)[({0:jj}NAME)=_n_u_l_l_
.EQN 0 11 0 0
({0:thm1}NAME)[({0:j}NAME)=_n_u_l_l_
.EQN 0 4 0 0
({0:tmm1}NAME)[({0:j}NAME)=_n_u_l_l_
.EQN 0 4 0 0
({0:tsm1}NAME)[({0:j}NAME)=_n_u_l_l_
.TXT 24 -54 0 0
C x1,1,0,0
.TXT 3 18 0 0
Cg a47.833333,47.833333,50
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {\fs24 \b Parallel Track Pattern
 Calculator (PS)}}
}
.TXT 4 -18 0 0
Cg a74.000000,74.000000,611
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Parallel Track patterns are used
 when the search area is large and there
 is no preferred section to be searched 
first. These patterns can be used by one
 boat or a group of boats and is the easiest
 to follow.\par \par A parallel Track pattern
 single unit (PS) search pattern is described
 below. The operator simply steers a straight
 course for each leg. Each  long leg is 
at one track spacing from the next. The 
long legs are parallel with the long side
 of the search area. The short legs, which
 are one track spacing long, connect adjacent
 long legs of the pattern. Adjacent long
 legs are oppositely directed.}}
}
.TXT 17 8 0 0
Cg a73.000000,73.000000,62
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {\fs24 \b Enter parameters for Parallel
 Track Search Pattern}}
}
.TXT 4 -8 0 0
Cg a73.000000,73.000000,24
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Length of search area}}
}
.TXT 0 17 0 0
Cg a56.000000,56.000000,23
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Width of search area}}
}
.TXT 0 16 0 0
Cg a40.000000,40.000000,16
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Track spacing}}
}
.TXT 0 14 0 0
Cg a72.000000,72.000000,14
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Track speed}}
}
.TXT 0 16 0 0
Cg a33.000000,33.000000,24
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Direction of long leg}}
}
.EQN 4 -63 0 0
{0:PS.l}NAME:2
.TXT 0 9 0 0
Cg a64.000000,64.000000,8
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {miles}}
}
.EQN 0 8 0 0
{0:PS.w}NAME:1
.TXT 0 9 0 0
Cg a47.000000,47.000000,8
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {miles}}
}
.EQN 0 7 0 0
{0:T.sp}NAME:(1)/(4)
.TXT 0 9 0 0
Cg a31.000000,31.000000,8
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {miles}}
}
.EQN 0 5 0 0
{0:S.track}NAME:10
.EQN 0 10 0 0
{0:knots}NAME
.EQN 0 6 0 0
{0:lngd}NAME:090
.TXT 0 9 0 0
Cg a22.000000,22.000000,10
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {degress}}
}
.TXT 7 -72 0 0
Cg a73.000000,73.000000,53
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {\b0 Calculate Number of Long Legs
 inSearch Pattern}}
}
.EQN 5 0 0 0
{0:N}NAME:{0:floor}NAME(({0:PS.w}NAME)/({0:T.sp}NAME))
.EQN 0 20 0 0
{0:N}NAME=?_n_u_l_l_
.TXT 0 6 0 0
Cg a39.833333,39.833333,41
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {number of long legs in search pattern.}}
}
.EQN 7 -26 0 0
{0:C0}NAME:({0:T.sp}NAME)/(2)
.EQN 0 11 0 0
{0:C0}NAME=?_n_u_l_l_
.TXT 0 10 0 0
Cg a72.500000,72.500000,66
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Separation between search pattern
 legs and edge of search area.}}
}
.TXT 9 -21 0 0
Cg a73.000000,73.000000,110
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {\b0 Generate Search Are}{\b0 a 
Plot}{. This is the rectangle containing
 the parallel track search pattern. }}
}
.EQN 7 0 0 0
({0:PS}NAME){52}(0):({2,1}ö{0:C0}NAMEö-({0:C0}NAME))
.EQN 0 17 0 0
({0:PS}NAME){52}(1):({0:PS}NAME){52}(0)+({2,1}ö0ö{0:PS.l}NAME)
.EQN 0 22 0 0
({0:PS}NAME){52}(2):({0:PS}NAME){52}(1)+({2,1}ö-{0:PS.w}NAMEö0)
.EQN 0 24 0 0
({0:PS}NAME){52}(3):({0:PS}NAME){52}(2)+({2,1}ö0ö-{0:PS.l}NAME)
.EQN 7 -63 0 0
({0:PS}NAME){52}(4):({0:PS}NAME){52}(0)
.TXT 0 17 0 0
Cg a66.000000,66.000000,11
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Setting }}
}
.EQN 0 6 0 0
({0:PS}NAME){52}(4)
.TXT 0 5 0 0
Cg a52.000000,52.000000,12
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {equal to }}
}
.EQN 0 7 0 0
({0:PS}NAME){52}(0)
.TXT 0 5 0 0
Cg a56.000000,56.000000,58
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain { causes the search area to be drawn
 as a close figure. }}
}
.EQN 4 -40 0 0
{0:na}NAME:0;{0:cols}NAME({0:PS}NAME)-1
.TXT 0 19 0 0
Cg a54.000000,54.000000,54
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {This range spans all the points
 in the search area.}}
}
.TXT 9 -19 0 0
Cg a73.000000,73.000000,84
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {\b0 Generate }{\fs20 \b0 Parallel
 Track}{\b0  Search Pattern}{, the origin
 is at:}}
}
.EQN 0 50 0 0
({0:Pps}NAME){52}(0):(({1,2}ö0ö0)){51}
.EQN 4 -50 0 0
{0:LL}NAME:{0:PS.l}NAME-{0:T.sp}NAME
.EQN 0 15 0 0
{0:LL}NAME=?_n_u_l_l_
.TXT 0 10 0 0
Cg a58.000000,58.000000,22
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {length of long legs}}
}
.EQN 3 -10 0 0
{0:T.sp}NAME=?_n_u_l_l_
.TXT 0 10 0 0
Cg a60.000000,60.000000,23
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {length of short legs}}
}
.EQN 4 -25 0 0
{0:ip}NAME:1;2*{0:N}NAME-1
.EQN 0 15 0 0
{0:ix}NAME:(({1,4}ö-1ö0ö1ö0)){51}
.EQN 6 -15 0 0
({0:Pps}NAME){52}({0:ip}NAME):({0:Pps}NAME){52}({0:ip}NAME-1)+({2,1}ö-{0:T.sp}NAME*{0:mod}NAME({0:ip}NAME+1,2)ö{0:LL}NAME*(({0:ix}NAME)[({0:mod}NAME({0:ip}NAME,4))))
.TXT 0 44 0 0
Cg a29.000000,29.000000,80
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Calculate the rest of the points
 in the\par basic parallel track search 
pattern.}}
}
.TXT 18 -44 0 0
C x1,1,0,0
.TXT 8 38 0 0
Cg a35.000000,35.000000,100
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {the function }{\b Len(v1,v2)}{ 
is used to callculate distance between the
 two points: v1 and v2.}}
}
.EQN 1 -38 0 0
{0:Len}NAME({0:v1}NAME,{0:v2}NAME):\(((({0:v1}NAME)[(0)-({0:v2}NAME)[(0)))^(2)+((({0:v1}NAME)[(1)-({0:v2}NAME)[(1)))^(2))
.TXT 7 44 0 0
Cg a29.000000,29.000000,115
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {the function }{\b Angz(v1,v2)}{
 calculates the mathematical direction of
 the vector from point v1 to point v2.}}
}
.EQN 1 -44 0 0
{0:Angz}NAME({0:v1}NAME,{0:v2}NAME):{0:arg}NAME((({0:v2}NAME)[(0)-({0:v1}NAME)[(0))+(({0:v2}NAME)[(1)-({0:v1}NAME)[(1))*\(-1))
.EQN 6 0 0 0
{0:D.long}NAME({0:x}NAME):{0:mod}NAME({0:x}NAME+270,360)
.TXT 0 26 0 0
Cg a47.000000,47.000000,133
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Orientation of the search pattern
 equal the direction of the first long  
leg minus 90 degrees. This is using  modular
 arithmetic.}}
}
.TXT 15 -26 0 0
Cg a58.000000,58.000000,70
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {\b0 j  ranges all points in the
 seach pattern other than the origin}}
}
.EQN 4 0 0 0
{0:j}NAME:1;2*{0:N}NAME-1
.TXT 5 0 0 0
Cg a73.000000,73.000000,122
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {\b0 Calculate the Length of each
  Leg of the Search Pattern}{. \par Only
 legs 1 through 2*N-1 are valid. Leg 0 isn't
 used.}}
}
.EQN 5 0 0 0
({0:Vlen}NAME)[({0:j}NAME):{0:Len}NAME(({0:Pps}NAME){52}({0:j}NAME-1),({0:Pps}NAME){52}({0:j}NAME))
.TXT 10 0 0 0
Cg a73.000000,73.000000,73
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {\b0 Calculate direction for  legs
 of prototype search pattern.}{\b0   }}
}
.EQN 4 0 0 0
{0:ia}NAME:(({1,4}ö180ö270ö180ö090)){51}
.EQN 0 24 0 0
{0:Angv}NAME({0:j}NAME):({0:ia}NAME)[({0:mod}NAME({0:floor}NAME({0:j}NAME)-1,4))
.EQN 0 27 0 0
({0:Vangv}NAME)[({0:j}NAME):{0:Angv}NAME({0:j}NAME)
.TXT 5 -51 0 0
Cg a73.000000,73.000000,61
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {\b0 Compute the Courses for each
 Leg in the Search Pattern}}
}
.EQN 4 0 0 0
{0:dirl1}NAME:{0:D.long}NAME({0:lngd}NAME)
.EQN 0 17 0 0
{0:dirl}NAME:({0:mod}NAME({0:Vangv}NAME+{0:dirl1}NAME,360)){49}
.TXT 5 -17 0 0
C x1,1,0,0
.TXT 4 0 0 0
Cg a73.000000,73.000000,164
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {\b0 Calculate run time }{\b0 and
 the total elapsed time}{\b0  }{\b0 for 
each leg}{\b \par }{\b0 j is now redefined
 to range over all }{thelegs of the pattern.}{\b 
 }}
}
.EQN 6 0 0 0
{0:tvec}NAME:({0:T}NAME({0:Vlen}NAME,{0:S.track}NAME)){49}
.EQN 0 21 0 0
{0:j}NAME:0;{0:last}NAME({0:Vlen}NAME)
.EQN 3 -21 0 0
({0:sumt}NAME)[(0):({0:tvec}NAME)[(0)
.EQN 0 13 0 0
{0:jj}NAME:1;{0:last}NAME({0:Vlen}NAME)
.EQN 0 17 0 0
({0:sumt}NAME)[({0:jj}NAME):({0:sumt}NAME)[({0:jj}NAME-1)+({0:tvec}NAME)[({0:jj}NAME)
.TXT 4 -30 0 0
Cg a73.000000,73.000000,49
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Convert times to: hours, minutes,
 and seconds.}}
}
.EQN 4 0 0 0
{0:th}NAME:({0:ghrs}NAME({0:tvec}NAME)){49}
.EQN 0 17 0 0
{0:tm}NAME:({0:gmin}NAME({0:tvec}NAME)){49}
.EQN 0 18 0 0
{0:ts}NAME:({0:gsecr}NAME({0:tvec}NAME)){49}
.EQN 0 15 0 0
({0:leg}NAME)[({0:j}NAME):{0:j}NAME+1
.EQN 4 -50 0 0
{0:sth}NAME:({0:ghrs}NAME({0:sumt}NAME)){49}
.EQN 0 17 0 0
{0:stm}NAME:({0:gmin}NAME({0:sumt}NAME)){49}
.EQN 0 18 0 0
{0:sts}NAME:({0:gsecr}NAME({0:sumt}NAME)){49}
.TXT 6 -35 0 0
Cg a73.000000,73.000000,283
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Since the boat doesn't trun instantly
  the command to turn must given before 
the end of the \par current leg is reached.
 Allow 15 seconds at 10 knotes for the boat
 to make the turn and 10\par seconds prior
 to that to warn the helm. The warning times
 and mark times are calculated below.}}
}
.EQN 6 0 0 0
{0:Ltim_Cmd}NAME:10
.EQN 0 14 0 0
{0:Ltim_boat}NAME:15
.EQN 0 14 0 0
{0:Ltim_tot}NAME:{0:Ltim_Cmd}NAME+{0:Ltim_boat}NAME
.EQN 5 -28 0 0
{0:wrnt}NAME:(({0:sumt}NAME-{0:hours}NAME(0,0,25))){49}
.EQN 0 27 0 0
{0:mrkt}NAME:(({0:sumt}NAME-{0:hours}NAME(0,0,15))){49}
.TXT 4 -27 0 0
Cg a73.000000,73.000000,49
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Convert times to: hours, minutes,
 and seconds.}}
}
.EQN 4 0 0 0
{0:thw}NAME:({0:ghrs}NAME({0:wrnt}NAME)){49}
.EQN 0 16 0 0
{0:tmw}NAME:({0:gmin}NAME({0:wrnt}NAME)){49}
.EQN 0 17 0 0
{0:tsw}NAME:({0:gsecr}NAME({0:wrnt}NAME)){49}
.EQN 4 -33 0 0
{0:thm}NAME:({0:ghrs}NAME({0:mrkt}NAME)){49}
.EQN 0 16 0 0
{0:tmm}NAME:({0:gmin}NAME({0:mrkt}NAME)){49}
.EQN 0 17 0 0
{0:tsm}NAME:({0:gsecr}NAME({0:mrkt}NAME)){49}
.TXT 8 -33 0 0
Cg a73.000000,73.000000,55
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {\b0 Calcuate chart display for 
search pattern}{\b0 .}}
}
.EQN 4 0 0 0
{0:k}NAME:0;{0:cols}NAME({0:Pps}NAME)-1
.EQN 0 23 0 0
{0:na}NAME:0;{0:cols}NAME({0:PS}NAME)-1
.EQN 4 -23 0 0
{0:PPps}NAME:{0:Mr}NAME({0:dirl1}NAME)*{0:Pps}NAME
.EQN 0 23 0 0
{0:PPS}NAME:{0:Mr}NAME({0:dirl1}NAME)*{0:PS}NAME
.TXT 6 -23 0 0
Cg a73.000000,73.000000,111
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Calculate  bounding square for 
the search arrea to force the x and y scale
 factors of the plot to be equal.}}
}
.EQN 6 0 0 0
{0:Max}NAME({0:x}NAME,{0:y}NAME):({0:x}NAMEò{0:y}NAME)*{0:x}NAME+({0:y}NAME>{0:x}NAME)*{0:y}NAME
.EQN 0 28 0 0
{0:Min}NAME({0:x}NAME,{0:y}NAME):({0:x}NAMEó{0:y}NAME)*{0:x}NAME+({0:y}NAME<{0:x}NAME)*{0:y}NAME
.EQN 4 -28 0 0
{0:ij}NAME:1;{0:cols}NAME({0:PS}NAME)-1
.TXT 0 19 0 0
Cg a54.000000,54.000000,55
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Range over all the corner pointsof
 the search area. }}
}
.EQN 4 -19 0 0
({0:sxm}NAME)[(0):((({0:PS}NAME){52}(0)))[(0)
.EQN 0 16 0 0
({0:sxm}NAME)[(0*{0:ij}NAME):{0:Min}NAME(((({0:PS}NAME){52}({0:ij}NAME)))[(0),({0:sxm}NAME)[(0))
.EQN 0 27 0 0
({0:sxp}NAME)[(0):((({0:PS}NAME){52}(0)))[(0)
.EQN 0 17 0 0
({0:sxp}NAME)[(0*{0:ij}NAME):{0:Max}NAME(((({0:PS}NAME){52}({0:ij}NAME)))[(0),({0:sxp}NAME)[(0))
.EQN 5 -60 0 0
({0:sym}NAME)[(0):((({0:PS}NAME){52}(0)))[(1)
.EQN 0 16 0 0
({0:sym}NAME)[(0*{0:ij}NAME):{0:Min}NAME(((({0:PS}NAME){52}({0:ij}NAME)))[(1),({0:sym}NAME)[(0))
.EQN 0 27 0 0
({0:syp}NAME)[(0):((({0:PS}NAME){52}(0)))[(1)
.EQN 0 17 0 0
({0:syp}NAME)[(0*{0:ij}NAME):{0:Max}NAME(((({0:PS}NAME){52}({0:ij}NAME)))[(1),({0:syp}NAME)[(0))
.EQN 5 -60 0 0
{0:smax}NAME:{0:Max}NAME(({0:sxp}NAME)[(0),({0:syp}NAME)[(0))
.EQN 0 22 0 0
{0:smin}NAME:{0:Min}NAME(({0:sxm}NAME)[(0),({0:sym}NAME)[(0))
.EQN 0 21 0 0
{0:SPS}NAME:({2,5}ö{0:smin}NAMEö{0:smin}NAMEö{0:smax}NAMEö{0:smin}NAMEö{0:smax}NAMEö{0:smax}NAMEö{0:smin}NAMEö{0:smax}NAMEö{0:smin}NAMEö{0:smin}NAME)
.EQN 5 -43 0 0
{0:SSPS}NAME:{0:Mr}NAME({0:dirl1}NAME)*{0:SPS}NAME
.TXT 0 20 0 0
Cg a53.000000,53.000000,48
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Rotate square to match search area
 rectangle.}}
}
.TXT 9 -20 0 0
C x1,1,0,0
.TXT 5 20 0 0
Cg a56.000000,56.000000,44
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {\fs24 \b Parallel Track Search 
Pattern}{ }}
}
.TXT 8 -20 0 0
Cg a72.000000,72.000000,27
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Track speed  for pattern}}
}
.TXT 0 39 0 0
Cg a19.500000,19.500000,28
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Initial course first leg.}}
}
.EQN 3 -39 0 0
{0:S.track}NAME=?_n_u_l_l_
.EQN 0 10 0 0
{0:knots}NAME
.EQN 0 29 0 0
{0:lngd}NAME=?_n_u_l_l_
.TXT 0 9 0 0
Cg a22.000000,22.000000,10
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {degress}}
}
.TXT 5 -48 0 0
Cg a73.000000,73.000000,24
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Length of search area}}
}
.TXT 0 17 0 0
Cg a56.000000,56.000000,23
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Width of search area}}
}
.TXT 0 16 0 0
Cg a40.000000,40.000000,16
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Helvetica;}
{\f1\fnil Symbol;}
}
{\plain {Track spacing}}
}
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{\plain {miles}}
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.EQN 3 -43 0 0
_n_u_l_l_&_n_u_l_l_&((({0:PPps}NAME){52}({0:k}NAME)))[(1),0,((({0:PPS}NAME){52}({0:na}NAME)))[(1),((({0:SSPS}NAME){52}({0:na}NAME)))[(1)@_n_u_l_l_&_n_u_l_l_&((({0:PPps}NAME){52}({0:k}NAME)))[(0),0,((({0:PPS}NAME){52}({0:na}NAME)))[(0),((({0:SSPS}NAME
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0 0 1 0 0
0 0 1 0 0
3 3 0 0 NO-TRACE-STRING
1 0 1 0 NO-TRACE-STRING
0 1 4 0 NO-TRACE-STRING
2 0 6 0 NO-TRACE-STRING
0 1 4 0 NO-TRACE-STRING
0 2 5 0 NO-TRACE-STRING
0 3 6 0 NO-TRACE-STRING
0 4 0 0 NO-TRACE-STRING
0 1 1 0 NO-TRACE-STRING
0 2 2 0 NO-TRACE-STRING
0 3 3 0 NO-TRACE-STRING
0 4 4 0 NO-TRACE-STRING
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{\plain {This is}{ the chart of the parallel
 track search you have selected. The top
 of the chart is north ( course 000) and
 the distances are in nautical miles. The
 datum is at 0,0.}}
}
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{\plain {Time per  leg}}
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{\plain {Leg}}
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{\plain {on course}}
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{\plain {Mark ( do it )}}
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{\plain {------------------------------}{--------------------------}{--------------------------}{--------------------------}{--------------------------}}
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{\plain {\par Now that we have defined three
 search patterns,  which one should you 
use and what conditions affect the the choice.
 The Expanding Square and the Sector Search
 both start at the datum and work around
 it. The sector search passes through the
 datum several times, while the Expanding
 Square spirals out form the datum Both 
these patterns are used to search relatively
 small areas\par when you have a good  idea
 where the missing vessels or object is.
 The sector search is especially useful 
in a man overboard situation , if you lost
 sight of the victim. Since the datum is
 where you last saw the man, the sector 
search will cross the datum several time
 giving you a better chance to find him.
 (Note: If someone fall overboard don't 
lose sight of him!!!)\par \par The expanding
 square is use when you still have a good
 idea where to start looking but its a bigger
 object and may be farther away then you
 first expected. This pattern would be used
 when there's a equal probability of the
 object you are searching for could be anywhere
 in the search area. In another words there's
 no advantage to pass several times trough
 the datum.\par \par The Parallel Track 
search pattern is used to search a large
 area when there is no preferred point to
 start the search. There is both single 
boat and multiple boat versions of this 
pattern. Multiple boat version of the Parallel
 Track pattern, with N boats,  can cover
 the search  area in 1/N the time. This 
pattern is one of the simplest to preform.
 Now for a few closing comments.\par }}
}
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{\plain {Feel free to experiment with the
 search pattern calculators. In the beginning
 of each of the three pattern calculators
 there is parameter input section. Change
 the parameters to generate different search
 patterns.  If you want to extract one of
 the search pattern calculators from this
 document without all the rest, do the following.
  Just  copy the page  3, common functions,
 to a new  Mathcad.  Next append the search
 pattern calculator to your document that
 contains the common functions.}}
}
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{\plain {------------------------------}{--------------------------}{--------------------------}{--------------------------}{--------------------------}}
}
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{\plain {\b References}}
}
.TXT 3 0 0 0
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{\plain {1. United States Coast Guard, U.S.
 Coast Guard Auxiliary Boat Crew Manual,
 Comdtinst M16798.8,\par      Vol. 5, Pp}{.
 2-1 thru 2-10\par 2. Richard Shiffman, 
LatLong to Distance 11, Mathcad Document,
 1994,\par      (URL:= http://www.mathsoft.com/pub/apps/navigate.mcd
 )\par 3. Richard Shiffman, }{\fs20 \b0 
Search Datum}{ 9, Mathcad Document, 1995\par 
     (URL:=ftp://ftp.mathsoft.com/f}{tp/}{pub/c}{ontrib/sdatum9.mcd)}{\par 
}}
}