Introduction
In a series of meetings (volunteer Saturdays 2/15 and 2/22 1600-1700) we'll discuss and try out some basic processes and tools for navigation - i.e. getting a vessel to a destination, safely and efficiently. The concepts will be available for preview on the Web, so that participants can come to class already acquainted with hands-on activities, and with questions (and suggestions about the Web presentation). The goals of the classes are:
- improving skill at navigation
- having fun doing the activities, and finding satisfaction in doing them well
- experiencing aesthetic appreciation of the concepts
- developing and improving versions of this curriculum that can be applied in future ed programs (both school and adult ed)
- developing a cadre of volunteer educators to implement any such ed programs
The topics covered will be excerpts from Topics 2-3 below, with some material from 1 and 4, of the more general syllabus given below; details are in each day's Web page (2/15 and 2/22). The actual amount of time and resources available will determine how much material is covered. Looking over the Web pages in advance would allow us to accelerate the pace, so prepare questions to bring to class. Suggestions for changes in content, order of presentation, etc. are welcome, either verbally in class, or email to dchesley@saltwedge.org.
General Navigation Syllabus
Topic 1: The Nautical Chart, Plotting, and Measuring Position
- Information contained on a chart: shoreline, depths, hazards, aids to navigation, landmarks, ranges
- Relation of flat chart to spherical Earth
- Geometric visualization meditations: intersections of lines and circles with other lines and circles, giving zero, one, or 2 points; angles
- Coordinates, points, lines of position (LOPs - including Lat & Lon), circles of position
- The bearing compass: getting the angle between a line of sight and Magnetic North
- Plotting your actual position on the chart: GPS coordinates; using any 2 LOPs from bearing compass and/or ranges
- Surveying as the reverse of navigation: 2 LOPs to plot a landmark
Topic 2: Measuring Angles between Landmarks, and plotting Circles of Position (COPs)
- Crude angle measurement with a protractor or pelorus
- COP from angle of elevation of top of object of known height
- Recipe to get a circle of position from the angle between 2 visible landmarks
- Plotting position from 2 COPs, or a COP and a LOP
- Geometry behind the "recipe" above; navigation as practical geometry - wealth of ed program material
- Better angle measurer than a protractor - a sextant!
Topic 3: The Sextant
- Anatomy and how it works (including avoiding damage)
- How to use it (horizontally and vertically); "pendulum-swinging"
- How to read results: index scale, micrometer drum, vernier; instrument errors
- Adjustments (e.g. mirrors) and calibrations (including parallax vs. index error)
Topic 4: Basic Tools, Concepts, and Measurements of Celestial Navigation
- Basic tools: sextant, watch, almanac, Pub. 229 or equivalent; organized work sheet, plotting paper, plotting tools (straightedge, dividers, protractor)
- Geographical Position of a celestial object: changes with Earth's rotation; tabulated in Almanac; interpolation
- Zenith and horizon (ideal)
- Zenith distance of object, as seen from non-GP, and object's height above horizon
- Sextant measurement (noting exact time!) of object's height (ideal case: spherical Earth, no atmosphere, eye at sea level, object VERY far away)
- Ideal circle of position - plot on globe, with radius in angular form
- For fix, need 2nd COP from 2nd measurement
Topic 5: Corrections to ideal COP
- Watch error (GP, center point of COP)
- Sextant index error
- Height of eye and dip correction; "artificial horizon"
- Refraction
- Parallax: correction for finite distance to celestial object
At this point, The COPs are known, and their points of intersection can be plotted or calculated. Calculation of the intersection points of 2 circles on a sphere is tremendously simplified by considering the line formed by the intersection of the planes of the 2 circles, then finding the 2 points on that line that are the correct distance from the center of the sphere. Topic 7 below will give details. Topic 6 will describe the classical graphical plotting solution.
Topic 6: Classical Plotting Method
- Publication 229
- Assumed Position (AP), as determined by meshlike data in 229
- Plotting paper - "zoom" in on expected location of fix, close enough to make Earth flat, and arcs on COPs become LOPs
- LOP through AP, corrected via actual measured celestial height, to parallel LOP
- Repeat with new AP for 2nd celestial observation
- Triangle of position from 3 or more celestial observations
Topic 7: Mathematical and Computer Algorithmic Calculation of Position