Provides information needed by Sea Scouts to explain and demonstrate US Power Squadron plotting & labeling standards, in coordination with the deck log, using more restrictive Ship 378 standards.

1. Navigation Position
FIXES, ESTIMATES, RANGES, IKWIA, & DANGER ANGLES

2. Where Are You?
 Know Exactly Where Your Are
 Electronic Fixes
 Visual Fixes
 Star Fixing
 Intelligent Guessing
 Dead Reckoning
 Estimated Position
 Somewhere Along Here
 Ranges
 I Know Where I Am (IKWIA)
2

3. Topics
 Motivation for Navigation
 Terms
 Fixes
 Position Estimation
 Danger Angle
 Plotting Standards
 Correlation w Deck Log
3

4. Piloting & Navigation
 A pilot is one who controls a boat
 Navigating is the process or activity of accurately determining position,
and planning & following a route.
 Piloting is navigating, using fixed points of reference on the sea or on land,
usually with reference to a nautical chart, to obtain a fix of the position of
the vessel with respect to a desired course or location.
 Horizontal fixes of position from known reference points may be obtained by
sight or by radar.
 Vertical fixes of position may be obtained by depth sounder
 Piloting is usually practiced close to shore or on inland waterways.
4

5. What is Piloting & Dead Reckoning?
 https://www.youtube.com/watch?v=u6AU5DfG8A0
5

6. Navigation Terms
 Course
 Planned route between two points
 Bearing
 Direction of travel between two points
 Heading
 Orientation of the boat in degrees
 Water Track
 Theoretical course of travel, plotted on a chart
 Ground Track
 Actual course of travel: Water Track moved by wind and current
6

7. Tracks 7

8. Navigation Position Terms (continued)
 Bearing
 Direction between two points in degrees
 Heading
 Orientation of the boat in degrees
 Fix
 A position determined with certainty
 Line of Position (LOP)
 Line from Boat to “Landmark” along a handheld compass bearing
 Range
 Position somewhere along a line of position (LOP)
8

9. Navigation Position Terms (continued)
 Dead Reckoning (DR)
 Estimated Position along a Water Track
 Estimated Position (EP)
 Estimated Position along a Water Track adjusted for current or wind
 Set
 Direction of tidal current in true degrees
 Drift
 Strength of tidal current in knots
 Danger Angle
 A magnetic bearing to a landmark to stay on either side of to avoid danger
9

10. I Know Where I Am! (IKWIA)
 Reasons for not formally navigating
 Familiarity with the area
 Help is easy to get
 Support system is close by
 Critical factors not a consideration: time of day, fuel, travel time, obstructions
 Why bother with formally navigating?
 You may know where you are, but can you precisely tell someone else?
 May be a legal requirement: When was the demarcation line crossed?
 Travel beyond familiar territory
 Skipper wants crew practice
 Critical factors may become a priority
10

11. Do I Have to Keep a Deck Log? (Moan)
 You’re Navigating all the Time!
 The difference is the level of formality
 While Traveling in Local Area
 Track time, time of day, fuel, position around obstructions, etc.
 Know where your are
 Normally, done in your head or with crew chatter
 Keep a chart handy
 Traveling in Confined Areas (e.g. narrow channel)
 Have navigator visually follow a chart, maintaining situation awareness
 Otherwise
 Keep a deck log
11

12. What is a Fix?
 Determination of exact vessel location by handheld compass bearings,
celestial calculations, radar, or satellite navigation instruments
 Bearings
 Visual Fix
 Celestial Calculations
 Star Fix
 RADAR
 Radar Fix
 Satellite
 Global Positioning System (GPS)
12

13. Electronic Fixes
 Represented by triangle around dot in the middle on precise location
 Global Positioning System (GPS) Fix (Gfix)
 RADAR Fix
 Others
 Doppler using Ground-Based Radio Signal Strength
13

14. Visual Fixes (Vfix)
 Represented by circle around dot in the middle on precise location
 Line of Position (LOP)
 2-LOP Fix
 3-LOP Fix
 Running Fix
 1-Object, 2-LOP Running Fix
 2-Object, 2-LOP Running Fix
 Double the Angle off the Bow
 Objects in the Water
14

15. Star Fixing
 Fixes on Stars with a Sextant, Day or Night with Watch and Star Chart
15

16. Dead Reckoning (DR)
 Represented by arc around a dot in the middle on estimated location
 Estimating position based on constant speed, time, & distance along a
Water Track
16

17. Estimated Position
 Represented by square around dot in the middle on estimated location
 Estimated Position from a Dead Reckoning position accounting for wind or current
 Water Track adjusted by Tidal Vector components: Set and Drift
 Adjustments based on other observations (e.g., landmark LOP)
17

18. Ranges
 Position somewhere along a line of position (LOP)
 Alignment with fixed objects in known locations
 Range Boards
 Lines Between 2 Points
 Corners (real or virtual)
 A pair of landmarks or markers a navigator may use to fix position
Note: These are the easiest LOPs to get!
18

19. Danger Angles
 Represented with LOP to a landmark with a Magnetic Bearing
 Range of bearings to a fixed object to avoid an obstruction
 Expressed as . . .
 No More Than (NMT)
 No Less Than (NLT)
 Warning:
 Danger Angles are wrt to magnetic bearing to a fixed object, not boat heading!
 Boat compass readings are irrelevant, though helpful to avoid navigating into an obstruction
19

20. Sailing Vessels use These Methods
Effectively
 Electronic Fixes: Radar and Satellite
 Celestial Fixes
 Bearing Fixes: 2-3 LOPs
 Objects in the Water Referenced on a Chart
 Ranges
 Danger Angles
 Monitoring objects along shoreline, improved w known water depth
Anything that does not depend on following a line at a constant speed
20

21. Power Vessels can also use These
Methods
 Dead Reckoning based on constant course & speed
 Including Estimated Position
 Running Fixes
21

22. Plotting & Labeling Standards
Summary
22

23. Ship 378 Plotting/Labeling Standards
 Same as US Power Squadron Standards
 Ship 378 Limitations
 Annotations are in the language of the chart plotted on
 Datum, Orientation, System of Measurements (Metric, Imperial, US Customary)
 Because 1’ Latitude = 1 nm, only knots (speed) and nm (distance) are used
 Exceptions
 Handheld Compass Bearings for Danger Angles are annotated on chart in Magnetic
 Fix Labeling
 GPS Fix (Gfix)
 Bearing Fix (Vfix, or assumed if blank)
 Running Fix (Rfix)
 See Deck Log Rules for More Information
23

24. Satellite Navigation System Fixes
 Use result from GPS Receiver (GPSr) to directly plot on chart
 Result: Latitude (Lat), Longitude (Long), and Altitude
 Altitude is irrelevant on the water. All answers are at sea level
 Vertical references that do matter are soundings, shown on a chart
 Compass Headings are available
 Ensure result is in language of the chart and decklog
 In USA, Datum is normally WGS84 or NAD27
 Report Lat/Long measurements in DDD˚ MM.mmm format
 Verify results by other means
24

25. Satellite Navigation Systems
 Global Positioning System (USA)
 GLONASS (Russian Federation)
 Compass (China)
 Galileo (European Union)
25

26. Satellite Nav System Operation
 Location determined by simultaneous radio signal strength received from 3 overhead
satellites
 Height determined using
 Location (determined from position)
 Overlap of 3 intersecting 3D spheres reflecting on to a 2D surface
 Time Offset
 Caused by time difference from top of 3D sphere intersection and 2D surface
 Recommendation: Use result (with care) and leave how it was determined to engineers.
Accurate when not jammed or degraded
 Verify results by other means
26

27. GPS Fix Notation
 Similar to Visual Fix Notation
 Label Time with “GPS Fix” suffix
 For Ship 378, Gfix is acceptable
27

28. Radar Fixes
 Sea Scouts unlikely to use It when it counts
 Routine navigation (expensive to procure & learn to operate)
 SEAL Piloting Test
 SEAL Navigation Test
 To complete Able requirement, Ship 378 uses
 Computer Simulation
 Opportunities at Sea Scout Academy to see radar use in operation
28

29. Radar Fix Notation
 Similar to Visual Fix Notation
 Label Time with “Radar Fix” suffix
 For Ship 378, Rfix for Radar Fix is unacceptable
 Used for Running Fix – something we do use on water
29

30. Radar Fix: Example
 https://www.youtube.com/watch?v=nrfu2z7wLXA
30

31. Celestial Fixes
 Sea Scouts unlikely to use it when it counts
 Routine Navigation
 SEAL Piloting Test
 SEAL Navigation Test
 For more information
 Learn to use a sextant with a wrist watch
 Have the right celestial data available
 Learn how to translate results into a fix for use on a chart
 Special Case
 Position easier to determine at high local noon and a wrist watch
31

32. Visual Fixes (Vfix)
 Represented by circle around dot in the middle on precise location
 Line of Position (LOP)
 2-LOP Fix
 3-LOP Fix
 Running Fix
 1-Object, 2-LOP Running Fix
 2-Object, 2-LOP Running Fix
 Double the Angle off the Bow
 Objects in the Water
32

33. Bearing Fix: 2 LOPs
 Handheld compass bearings taken from 2 fixed objects, ~90˚ apart
 Closer objects improve precision
 One leg can be a Range
 Object abeam of boat
 Line between two objects
 Perhaps take a bearing on an object being traveled to
 Provides useful information for other purposes
 Intersection of both LOPs approximates position
 Needs to be done rapidly for better position accuracy
 No need to slow or stop the boat
33

34. Bearing Fix: 3 LOP
 Handheld compass bearings taken from 3 fixed objects, ~60˚ apart*
 Closer objects improve precision
 One leg can be a range
 Range board alignment
 Line between two objects
 Perhaps take a bearing on an object being traveled to
 Provides useful information for other purposes
 Triangle formed by intersection bearings approximates position
 Choose the centroid (midpoint) of the triangle
 Needs to be done rapidly for better position accuracy
 No need to slow or stop the boat
34

35. *3-LOP Fix: Object ~60˚ Apart?!!
 Conventional wisdom is objects 120˚ apart
 Done correctly, 3 Objects 120˚ apart are also 60˚ apart
 Logic
 When an LOP is drawn, it is a line with 2 ends
 For a 3-LOP fix, theoretically the LOPs intersect at a single point
 Assume a circle with the intersection as the center
 There are 6 slices created by 3 LOPs
 Each slice is 60˚ (360/6 = 60) around the center
 When piloting along a shoreline, there may be no objects on the sea side of the boat!
Objects 60˚ apart are easier to find
35

36. Bearing Fix: 3-LOP Example
 https://www.youtube.com/watch?v=V8j00E89Bq4
36

37. Bearing Fix: Annotation
 Convert magnetic bearing to true for each object
 Draw LOP from each object
 Write true bearing below|left of LOP
 Add the prefix B to show it’s bearing LOP
 Standards show writing in the center
 Ship 378 prefers near the object (consistency w Course Line annotation)
 Don’t write on important chart data
 Write time above the line, over bearing
 Both true and magnetic direction shown in deck log
 In deck log, label LOPs as LOP1, LOP2, etc. on separate row for each
 Result shown as Vfix in deck log as start of a new course line
37

38. Visual Fix: Object in the Water
 Fixed Objects and Buoys are Drawn on Charts
 Fixed Objects are reliable for Fixes
 Day Marks, Oil Platforms
 Buoys are not supposed to be relied on but we do
 Plotting Fixes, done well, are within 1˚ of accuracy
 Boat compass resolution is usually 5˚
 Hand-Held Compass resolution we use is 1˚ (2˚ for an orienteering base compass)
 Helmsman are good, but not that good (reported to be within 2˚)
 Therefore, in real-time accuracy is with 4˚
 Unless a buoy is determined to be off (relative position to charts), the error is small
 Be suspicious after storms or floods (or earthquakes)
 Not used when landmarks or fixed objects are available
38

39. Visual Fix Annotation: General
 Visual Fixes are represented with circles around the fix location
 Used as starting points for new course lines
 Old course line terminated with a DR position.
 Course Bearing written above line, at starting end
 Course Speed written below line, at starting end
 Course Distance written below line, at the center
 Usually has no Suffix, because it’s understood by convention
 To reduce ambiguity, Ship 378 uses Vfix so the label and Decklog match
 Note: Don’t write on top critical information!
39

40. Bearing Fix: Running Fix
 Essentially, uses single object for current LOP, while advancing a previous
LOP to it--after traveling known heading at constant speed
 Method 1 uses a single object 2 handheld LOP bearings can be taken from
 Both bearings taken to the same object
 Method 2 uses two objects, one visible at a time, to take LOP bearings to
 Each bearing taken to separate objects
 Method 3 is Double the Angle of the Bow
 Method 2 is preferred because two LOPs, 90˚ apart can be made
 Much more difficult to complete → not discussed here
Note: Very difficult to do while sailing because constant bearing at constant speed is hard
to maintain. Best used by power vessels
40

41. Course Bearing vs Boat Heading:
Running Fix
 Course bearings are used to establish course lines
 When underway, unless all forces acting on the boat are accounted for, the boat doesn’t travel
course line bearing—even if boat compass say you are!
 If Compass Heading is set to Course Bearing, boat will not arrive at intended end point
 To compensate, it’s better to navigate toward an object on the horizon in the direction of the
course bearing
 Boat gets to intended location, but the Compass Heading is other than Course Bearing
 Actual Compass Heading is unknown and undeterminable using this approach
 Helmsman can zig-zag boat during travel to keep Boat Heading to match Course Bearing to
object on the horizon
 Boat gets to intended location, but the Compass Heading varies, even though on course
 What the actual Compass Heading is unknown and undeterminable using this approach
41

42. Use Boat Heading as Course for
Running Fix
 Confusing because literature keeps referring to a constant course when
constant heading is intended
 Running Fix travel time is short, relative to travel to a destination
 For procedures to work, the boat must maintain a constant heading
 Boat will drift while running, but the procedures are not affected by it
 The intersection of LOPs will yield correct result
 For Double the Angle off the Bow, travel time must be short (1-2 min)
42

43. Running Fix Procedure
 Establish a boat heading to follow while maintaining a constant speed
 Monitor boat compass, not horizon landmarks
 Wind and current are factors, but ignore it (procedure handles it)
 Use speedometer speed, if you have to
 Ideally, use ground speed from GPS
 When constant heading and speed conditions are established
 Take LOP bearing to object
 Record time of bearing
 Travel for some distance, then record another LOP bearing to object
43

44. Running Fix Procedure (continued)
 Draw both LOPs to the object
 LOP1 is the one made at the start of the procedure (previous one)
 LOP2 is the current one
 Determine distance traveled from 60D=ST
 Draw boat heading with distance traveled length starting anywhere on
LOP1, ideally from a DR position
 Advance LOP1 to the other end of the distance-traveled line
 Where LOP1 and LOP2 cross is approximate position for the fix
44

45. Running Fix
 https://www.youtube.com/watch?v=63O4drvKrI8
45

46. Running Fix Annotation
 Draw LOPs from fixed object
 Use same standards for bearing fixes
 Label bearing lines as LOP1 and LOP2 in decklog, as appropriate
 Draw advanced LOP1 as a dashed line
 Label same as LOP1
 Draw visual fix symbol (a circle) around the intersection
 Label fix as Running Fix
 Usually, “Running Fix”
 Ship 378, Rfix
46

47. Distance Off:
Double the Angle off the Bow
 Determines distance from a fixed object, based on following a given boat
heading at constant speed.
 Relies on special properties of an Isosceles triangle (2 identical angles)
 Distance traveled is distance to object
 Typically uses 30 & 60˚ or 22 & 44˚, but any double the smaller angle
between 45-90˚ works well
 A type of running fix
 Doesn’t work well in practice, except with short time intervals (1-2 min)
Note: Very difficult to do while sailing because constant course at speed is
hard to maintain. Best used by power vessels
47

48. Double the Angle of the Bow: Example
 https://www.youtube.com/watch?v=tmQRCHLSq0M
48

49. Limitations of Double Angle off Bow
 Procedure works perfectly if wind and current have little or no effect
following a constant course (not boat) heading
 Works well when course bearing = boat heading
 Distance Traveled = Distance to Object
 If boat drifts, an Isosceles triangle not created when 1st angle is double
 Distance Traveled ≠ Distance to Object
49

50. Double the Angle off the Bow
Procedure
 Establish a heading to follow while traveling constant speed
 Monitor boat compass, not horizon object
 Use speedometer speed, if you have to
 Ideally, use ground speed from GPS
 Take first LOP bearing to object
 Record time, speed, and course
 Double the smaller, first angle
 Take second LOP bearing at double the angle of the 1st bearing
 Record time
 Draw both LOPs
50

51. Double Angle off the Bow Procedure
(continued)
 Determine distance traveled along the course (heading) line (60D=ST)
 Distance traveled is distance to object
 The intersection course line with LOP2 is a running fix (maybe!)
51

52. Double the Angle off the Bow:
Annotation
 Draw and label course (heading) line like any other course line
 Draw LOPs from fixed object
 Use same standards for bearing fixes
 Label LOPs as LOP1 and LOP2, as appropriate
 Draw visual fix symbol (a circle) around the intersection of course line with
LOP2
 Label fix as Running Fix
 Usually, “Running Fix”
 Ship 378, Rfix
52

53. Dead Reckoning (DR)
 Represented by arc around a dot in the middle on estimated location
 Estimating position based on constant speed, time, & distance along a Water
Track
 Used in 2 cases
 Estimate along a Water Track
 Estimated location at a change of course without a fix
 Ship 378 calls the Holes in the Water (HIWs)
 Can be used to start a course line without a fix
 Note: Very difficult to do while sailing because constant bearing at constant
speed is hard to maintain. Best used by power vessels
53

54. Dead Reckoning: Example
 https://www.youtube.com/watch?v=8_uBYkIiLfs
54

55. Dead Reckoning: Case 1
 Dead Reckoning along a Water Track
 Course lines established with constant speed and direction
 At any time interval, an expected position along the line can be established
 From 60D=ST → D=ST/60
 Typically, crew establishes standards for take DR positions
 On the hour, every hour (SEAL standard)
 Consider hourly tide intervals listed in relevant Tide Tables
 Every hour or half hour from last fix (Preferred by Ship 378)
 DR position terminates established course line early
 Symbol is a half circle with dot in the middle
55

56. Dead Reckoning: Case 2
 Dead Reckoning position used as start of a course line
 Can be used in place of a non-existent GPS fix
 Happens with change in course after a pre-determined distance traveled
 Course line started with a DR handled like any other course line
 No disconnect with previous course line
 Symbol is arc around the angle greater than a half circle
56

57. Dead Reckoning Notation
 Along a Water Track
 Dot drawn on the course line at a distance from the start determined by time
since establish the course line
 Half-circle arc drawn above the line
 Time labeled at an angle to the bottom of the chart
 At change in direction
 Greater than half-circle arc drawn around change in angle
 Labeled only as DR (in place of Vfix or Gfix) in deck log and on chart
57

58. Guesstimating Position when Sailing
 For sailing, progress toward a destination is more important than progress
along a Water Track using constant speed and time variables
 Object followed on horizon can always be used to take bearings to
 Draw LOP bearing line
 Location will be along the bearing line
 If water depth is generally know, use it
 Compare chart detail to approximate location
 Works best with visible shoreline
 Draw a square on the bearing line where you think you are
 Do not make a deck log entry
 Normally, keep track of aids to navigation (ATONs) [orienteering collecting features]
58

59. Estimating Position
 Represented by square around dot in middle on estimated location
 Determined by Set and Drift from DR positions
 Learn how to determine Set and Drift from Tide Tables
 Somewhat determinable under certain circumstances when wind and current
vectors (speed and direction) are unknown/undetermined
 Tide Tables don’t factor in wind
 Inland waters don’t have tides
 Wind varies continuously
Note: Very difficult to do while sailing because constant bearing at constant speed
is hard to maintain. Best used by power vessels.
Heading (Water) Track is not constant and has variable speed due to wind
59

60. Estimated Position w Set & Drift:
Example
 https://www.youtube.com/watch?v=q8nitMyFGj0
60

61. Set & Drift
 Terms
 Set: Direction of tidal current in True at a specific hourly time interval
 Drift: Strength of tidal current in knots during the interval
 Result is a Tidal Vector
 If the boat wasn’t moving through the water, this is the new boat position
 Note: Wind component is not factored in
 Adding vectors to get Ground Track (actual course & speed)
 Water Track [vector] + Tidal Vector = Ground Track [vector]
Note: Set & Drift cannot be determined for inland waters (no tides)
61

62. Tracks 62

63. Estimating Position without Set & Drift
 Based on properties of an Isoceles triangle: sides the same
 Assumption is the boat is minimally pushed in direction of travel
 Motor is dominant
 Spread divider compass from beginning of course line to DR position
 Determine LOP bearing to a fixed object
 Draw LOP on chart
 Draw arc across LOP
 Where arc crosses LOP is an estimated position
63

64. Estimated Position: Annotation
 Draw a square around the estimated position
 Draw a line between DR position and estimated position
 Leave unlabeled as it is the same as the connected DR plot
64

65. Danger Angles
 Represented with an LOP to an object with a Magnetic Bearing
 Range of Bearings to a Fixed Object to Avoid an Obstruction
 Expressed as . . .
 No More Than (NMT)
 No Less Than (NLT)
 Warning:
 Danger Angles are wrt to magnetic bearing to a fixed object, not boat heading!
 Boat compass readings are irrelevant, though helpful to avoid navigating into an obstruction
65

66. Setting a Danger Angle
 Draw a line from where the boat is supposed to be to a distant object (landmark) to easy
take bearings on
 For planning purposes, a point to navigate to can be chosen
 On the water, use current (known) boat location
 Similar to LOP bearing annotation
 Instead of time above line, in the center, write either NMT or NLT
 Write magnetic bearing below the line, prefixed with “B”
 Determine NMT or NLT
 Virtually place boat to go over the obstruction, then determine this bearing
 If bearing is greater then the Danger Angle, it’s NMT, otherwise NLT
 Remember, 000M is also 360M
66

67. Using Boat Compass to Avoid Danger
 First, recognize Danger Angle has nothing to do with boat heading
 It is bearing from the center of the boat to a fixed object
 Once NMT or NLT is determined
 Use what is determined for the hand-held compass bearing to object
 Use the other one to avoid steering into an obstruction
 Avoid steering boat to a location such that bearing-to-object limit is exceeded!!!
67

68. Using Danger Angle
 Don’t be an idiot (sometimes called a Hero)
 If uncontrolled factors, such as wind, current, and visibility accounted for
 Consider using it without modification
 Otherwise, give your boat a wider berth around an obstruction
 Travel farther away to avoid the obstruction entirely
 Travel farther away to effectively negate uncontrollable factors
 Consider circumnavigation
 The Danger Angle bearing should not be the boat’s Water Track!
 To practice, establish a parallel shoreline as the obstruction
 The Danger Angle bearing course is parallel to the shoreline, set as course
68

69. Danger Angle Annotation
 Draw line of bearing from boat to landmark
 Write magnetic bearing below bearing line
 Write NMT or NLT above bearing on bearing line
 Draw parallel hash marks to indicate what to avoid
from the bearing line toward the obstruction
69

70. Conclusion
 Navigation Position terms explained
 Procedures explained, some cases demonstrated
 Processes need modification for inland waters
 Problems are similar
 Conditions are different
 Practice required
 Complete Ship 378 Bowditch Bay exercises
 Try each method on the water, where possible
 Recorded data in deck log needs to match plotted chart
70