Errors and Mistakes in Taking the Navigation Exam and Best Known Methods for Accuracy

 Abstract

After taking the Navigational Charting Exam as part of the USCG 100 Ton Master Requirement a set of notes was compiled which may help aid future mariners in passing the exam. Several tips and tricks are listed which I discovered after some frustration upon failing practice exams.  

1.0 Introduction

While taking the Navigation Charting Exam as part of the USCG 100 Ton Master exam I became frustrated after not passing several of the practice tests. The exam is made up of 10 questions, with most of the questions having a dependency which builds upon each other. As a result if a candidate gets an answer wrong in the first few questions, it’s likely the candidate will have incorrect answers on the exam going forward. More importantly the requirement for passing the exam is to have 90% of the answer correct; or no more than one incorrect answer.

In preparation for the exam the USCG issues practice tests. To illustrate the importance of errors, accuracy, precision and mistakes let’s look at one of the practice exam questions.

QUESTION: You are on course 056°psc, when you take the following bearings: 

New Point Comfort Spit Light "2" 260°psc

Horn Harbor Entrance Light "HH" 285°psc

Wolf Trap Light 336°psc

What is the position of the fix?

1. LAT 37°19.3'N, LONG 76°08.8'W 
2. LAT 37°19.2'N, LONG 76°08.7’W
3. LAT 37°19.2'N, LONG 76°08.2'W 
4. LAT 37°19.3'N, LONG 76°08.5’W

Examination of the answers shows there is only a variation of 1’ in the choices latitude and 6’ in the variation of longitude.  The examination are usual done on charts with a scale of 1:80,000, and one minute of latitude is a represents one nautical mile.  With this in mind let’s examine a simple 0.7mm lead mechanical pencil’s effects on judging out latitude from the sample question.  Considering 1 inch is equal to 25.4 millimeters and we are using three bearings which cause an overlap of three drawn lines to find our fix as asked in the sample question, it’s possible our 3 lines overlap in such a manner that the lines stack at the intersection as shown in the diagram below. 

Based on this diagram, roughly the overall stack of the three lines amounts to a thickness nearing (3*0.7mm=2.1mm) 2.1mm.  From this issue alone there is an error induced of nearly 1/10th of nautical mile.  The error is much worse if the lines don’t intersect exactly. 

Let’s also consider the errors introduced by starting the line just off the aid to navigation (ATON).  On a coastal chart of 1:80,000 line widths on the chart range from 0.1mm thick to nearly 1mm in thickness.  Using a caliber measurements of ATON features were done on chart 12221TR, the training chart used for some of the charting exams.  The following measurements were found:

Lighted Markers had terminations between 0.1mm-0.25mm diameter

Day Buoys had termination between 0.3-0.6mm diameter

Cape Henry Lighthouse 0.4mm diameter

Considering now the errors in alignment to these ATONs introduces a greater variance in selecting the correct answer to exam questions

.

 

Incorrect alignment to a non-lighted buoy

From the image above if the pencil used is a 0.7mm mechanical pencil, the error again is at worst 0.3mm (1/2 the largest diameter) + 0.7mm (width of the lead) = 1.0mm or 1/20th of a nautical mile. 

Consider the instance in which the candidate made the same errors on each of the three lights listed in the question, and added to it the three line stack, the summed errors amount to between 0.2 to 0.4 nautical miles in error.  Thus far our analysis hasn’t consider variations in the lead of pencil not in contact with the straight edge to draw the line, the variation in the straight edge to be truly straight, and a host of other errors.  In accounting for all the slight possible errors one could make in the mechanical tolerance associated with drafting lines for triangulation to achieve a fix I found the error could easily be between 2.67’ and 3’ of error.  

If I could eliminate all the errors in the mechanical tolerances I found I could achieve an error less than 0.04’.  To achieve this greater accuracy and precision I first needed to get into the minds of the examiners, and took from The American Practical Navigator (aka Bowditch).

2.0 Definitions from Bowditch

To understand the context of errors, accuracy, precision and mistakes, one should consider the definitions in context of how the USCG may define the terms.  From Pub. No. 9 The American Practical Navigator, 2002 Edition (aka Bowditch) the definitions are: 

“A standard is a value or quantity established by custom, agreement, or authority as a basis for comparison. Frequently, a standard is chosen as a model which approximates a mean or average condition.”

“A mistake is a blunder, such as an incorrect reading of an instrument, the taking of a wrong value from a table, a data entry error, or plotting a reciprocal bearing.”

“Accuracy is the degree of conformance with the correct value, while precision is a measure of refinement of a value.”

“Error is the difference between a specific value and the correct or standard value. As used here, it does not include mistakes, but is related to lack of perfection.”

In a later chapter in Bowditch the authors show a Pareto ranking of failures in navigation which resulted in ships going aground.  This Pareto ranking is shown below:

1. Failure to obtain or evaluate soundings 
2. Mis-identification of aids to navigation 
3. Failure to use available navigational aids effectively 
4. Failure to correct charts 
5. Failure to adjust a magnetic compass or keep a table of corrections 
6. Failure to apply deviation 
7. Failure to apply variation 
8. Failure to check gyro and magnetic compass readings regularly 
9. Failure to keep a dead reckoning plot 
10. Failure to plot new information 
11. Failure to properly evaluate information 
12. Poor judgment 
13. Failure to use information in charts and navigational publications 
14. Poor navigation team organization 
15. Failure to “keep ahead of the vessel” 
16. Failure to have backup navigational methods in place
17. Failure to recognize degradation of electronically obtained LOP’s or lat./long. positions 

The authors of Bowditch follow with, 

“Some of the errors listed above are mechanical and some are matters of judgment. Conscientiously applying the principles and procedures of this chapter will go a long way towards eliminating many of the mechanical errors. However, the navigator must guard against the feeling that in following a checklist he has eliminated all sources of error. A navigator’s judgment is just as important as his checklists. Systematic errors are treated differently. Generally, the navigator tries to discover the errors and eliminate them or compensate for them. In the case of a position determined by three or more lines of position resulting from readings with constant error, the error might be eliminated by finding and applying that correction which will bring all lines through a common point. 

Lines of position which are known to be of uncertain accuracy might better be considered as “bands of position”, with a width of twice the possible amount of error. Intersecting bands of position define areas of position. It is most probable that the vessel is near the center of the area, but the navigator must realize that he could be anywhere within the area, and must navigate accordingly. 

The recognition of a mistake, as contrasted with an error, is not always easy, since a mistake is random, may have any magnitude, and may be either positive or negative. A large mistake should be readily apparent if the navigator is alert and has an understanding of the size of error to be reasonably expected. A small mistake is usually not detected unless the work is checked. 

If results by two methods are compared, such as a dead reckoning position and a line of position, exact agreement is unlikely. But, if the discrepancy is unreasonably large, a mistake is a logical conclusion. If the 99.9 percent areas of the two results just touch, it is possible that no mistake has been made. However, the probability of either one having so great an error is remote if the errors are normal. The probability of both having 99.9 percent error of opposite sign at the same instant is extremely small. Perhaps a reasonable standard is that unless the most accurate result lies within the 95 percent area of the least accurate result, the possibility of a mistake should be investigated. “

3.0 Best Known Methods for Charting on the Exam

Using the above information from Bowditch, and my many years teach mechanical drafting in college I developed best known methods for charting.  Using these methods I achieve a perfect score on every practice exam and on the actual USCG exam.  First consider I will consider the tools needed, and then best practices.

3.1 Charting Tools

As a disclaimer I don’t have any financial interest in Weems and Plath, nor am I a big fan of theirs, although it may seems like as you read the next section.  The tools were recommended after I did extensive testing from many vendors.  Whenever a Weems and Plath tool would break I returned it to the retailer and they replaced immediately with no questions asked. I broken at least three Weems and Plath charting tools and everyone was replaced without a single question.

1. Purchase the absolute best compass with a mechanical screw wheel you can. Sharpen the lead and align it before and after every use.  The variation between the point of the compass and the arc the lead provides is the largest source of error you will have, nearly 0.4mm if not done correctly.
2. Purchase a bunch of wooden/lead art pencils with HB or softer leads.  Sharpen all of them the best you possibly can, to the finest point possible.  The softer leads draw darker lines, and with a very sharp pencil you can achieve a 0.1mm or less line thickness. After a line was drawn with a pencil set it aside and use another one for the next line.  This does require about 15 to 20 very sharp pencils for the charting exam, but its well worth not having to repeat the exam. Bring or buy a simple pencil sharpener too just in case. 
3. Purchase two of the Weems and Plath Professional Protractor Triangles.  Don’t use any others.  These triangles have two nice features.  First the protractors have a great spacing between the degrees so they are more precisely read.  Second they have small pencil holder on them which make perfect grips to hold them down to the paper chart or slide them along another tool.  The recommendation is to buy two because you may find it easier to slide them against each other on the chart to get to a meridian to take an angular measurement.
4. Purchase a Weems Parallel Plotter which is the roller plotter.  The device has several nice features.  First, the plotter can be used to roll over quickly to check a bearing from a near compass rose.  Secondly it has a build in scale of 1NM = 1 Inch for the 1:80,000 scale chart used in the exam.  Third there is nice line drawn about a 1/4 inch inward from the drawing edge of the tool.  This line allows you to align two close points accurately by using the line as a straight edge as opposed to making an error drawing a line.
5. Purchase the Weems and Plath 7" Compact ParaLock Plotter.  The ParaLock allows the user to align points on the chart using a line similar to the roller plotter, but additionally allow you to place your fingers through the paralock to hold it in place while the other straight edge is being stretched.  Once the second rule is in it’s desired place the user can tighten the screw locking the parallels in place.  Several usages for this tool include making a secondary meridian to take a bearing measurement, and using meridian crossing to draw an exact position transferred from the scales at the edge of the chart.
6. Purchase the Weems and Plath Chart Protractor. Make certain it’s the one with the pencil holder, which again can be used as a handle. The Chart Protractor has two significant features critical to the exam.  First it is the largest straight edge you’ll need.  On every exam, there was at least one question where I needed to draw a straight line so long the Chart Protractor was the only tool long enough to draw it in continuity.  The second great feature is the other long edge of the tool allows you to make markings on the tool which are erasable.
7. Purchase an Alvin Erasing Shield which is stainless steal.  This tool allows the user to cover or protect areas they don’t want to erase, while erasing others.
8. Purchase both the Staedtler Mars Erasers which are white and the Prismacolor Kneaded Rubber Erasers which are grey. The Mars white erasers are used for large line erasing and cleaning of the chart, while the grey gummy kneaded eraser is best used for fine work with the Alvin Erasing Shield.  The best way to use the kneading eraser is to roll it into a point, the expose the area to be cleaned using the stencil shielding the areas of the line you’d like to keep.
9. Purchase a simple cheap calculator that only does addition, subtraction, multiplication and division.  These type of calculators are the only ones the examiner will allowed in the room.
10. Purchase a Staedtler Mars Sandpaper Lead Pointer or bring fine grit sand paper.  The sandpaper is used to sharpen the lead of the compass keeping it at fine edge.
11. Purchase Neon Page Markers Colored Index Tabs Fluorescent Sticky Note for Page Marker.  These are transparent slips of paper, in various neon colors and have a temporary adhesive on one side.  During the exam the USCG will not allow permanent marks on the charts, so highlighters are out of the question.  The tabs are great for placing them on ATONs used in the questions so they are immediately visible as you go back to them. Because they are transparent you can see through them and you can write on them as well.
12. Purchase a simple cheap stencil with circles, squares, and triangles like the Westcott Technical All Purpose Drawing Template.  These type of templates will help you in drawing your fixes, GPS fixes, and DR Positions neatly.
13. By or make a roll-up bag for all your navigation tools. The bag will help you keep your tools in order while you're taking the exam and will help you transporting them without getting nicks or fractures in your straight edges.  

3.2 Do Some Simple Practicing

Using just simple plain white copy paper practice drawing lines, draw lines parallel to each other, draw circles using the compass and the stencil, practice erasing parts of these drawings. Use every straight and every tool at least 20 times.  

Although it’s going to seem basic let’s talk about how to draw a straight line. Drawing a straight line should be practiced several times, at various lengths and various widths.

Precise drawing style is important and critical in achieving a minimal error.  The best practice is to keep the pencil lead touching the to straight edge with the pencil as close to perpendicular to the chart as possible.  As the line is being drawn pull the pencil along the straight edge, keeping the two in contact, slightly rolling the pencil back and forth as the line is being drawn.  See style B in the drawing below. 

The rolling of the pencil as it is being pulled creates a line with an even thickness, and constant width as the graphite of the pencil is being laid down on the chart.

When the wood of the pencil is in contact with the straight edge the pencil will lean and tend to drift away from the straight edge and intended line as seen in Style A above.  Over the course of 6 to 8 inches using style A above could create an error of 1^o to 3^o off the intended course.

Another best practice can be used when one or both of your termination points is at an ATON.  The secret is to take the point of you compass to make a hole in the exact center of the ATON, push it down to create a small hole.  Place the point of the pencil into the newly created hole and use it to align your straight edge to the desired bearing.    Don’t move the pencil from the hole because once the straight edge is in place begin drawing the line from the hole.  If you practice this technique you’ll soon see your alignment is perfect to the ATON, meaning you’ve reduced the errors discussed earlier.

3.3 Best Known Methods for Plotting on charts.

1. THIS IS THE MOST IMPORT ONE - BE NEAT. Neatness counts not only in helping you achieve the correct answer but if you’re need, write legibly, and label everything correctly, if you do make a mistake you’ll find it easily and it will be apparent sooner than if your techniques are sloppy.
2. Find two methods to do everything and do everything twice.  If the two methods produce different answers, you’ve likely made a mistake.  

For example if you're asked to find the bearing between two points.  First use your Weems and Plath Professional Protractor Triangle and your  Weems Parallel Roller Plotter to determine the bearing off the closest meridian.  For argument sake let's say the bearing was found to be 223^o T (T stands for True North). Next on your scratch paper “Bearing = 223^o T using W&P Triangle”.  Remove the triangle from the chart.  Now use your Weems Parallel Roller Plotter to walk the angle to the nearest compass rose.  On the compass rose you see the bearing is 222^o T.  Again write on your scratch paper ““Bearing = 222^o T using Roller and Rose”. If the multiple choice answers include one of these two you're done, but if the includes both, try another method.  Use the Weems and Plath Paralock to walk the bearing to the compass rose.  If then you read the compass rose and it reads 223^o T you’ll like have the answer at 223^o T.  If there is a larger variation between the two or three methods you have have made a mistake somewhere, try taking the measurements once again.

3. Check your math, then check it again.  If you’re asked to perform calculations do it twice, then once more.  Remember one wrong answer of 10 is ok but 2 wrong answers on this exam means your coming back to take it again.
4. Label everything with it’s UNITS, TYPE, TIME and QUESTION NUMBER. 

For example if you’re doing a time of arrival calculation and you know the speed (say it’s 5.5 KN) and distance (8.0 NM).  (Note KN is Nautical Miles Per hour and NM is Nautical Miles.). You should write out on the scratch paper:

Time = Distance/Speed = 8.0 (NM) / 5.5 (NM/HR) = 1.454 HRS or 01:27 HH:MM

Another example if you are plotting on the chart.  

Notice in the figure above the each line is labeled with a course C=310^oT, where T stands for True North, and an arrow on the line indicating the direction.  Below the line the Speed, “S” is marked with proper units in nautical miles per hour.  The arrow reminds you that you’re going from one point to another.  If a mistake is made in the mathematics and your true bearing doesn’t fall within the compass quadrant the arrow on the path makes this mistake readily apparent.  As an example if once done with the math of the problem, and your heading is resolved to 220^oT, one should know that 220^oT is SSW and should point downward not NW. Ergo some mistake must have been made.  Also notice the marker is highlighted green with the Neon Page Markers Colored Index Tabs, making it easy to find on the chart.  

Each fix or DR in the example above is labeled with it’s question number on the exam, i.e. Q3, or Q6, for question 3 or 6 respectively.  The fixes were drawn using the stencil suggested, which adds a level of neatness and professionalism to your charting.  

5. During the exam you may run into an extremely confusing reference.  As an example see the extract from the Chart 12221TR of Cape Henry Light.  There are four possible features here, three of which could be mistaken for the Cape Henry Light.

First let’s actually look at the photograph of the area below.  In this photograph, the three crowded features near the shoreline become apparent.  The first is a tower marker TR on the chart.  The next structure is the actual Cape Henry Light, which is described in the Coastal Pilot Region 3 below. The next feature is an abandon lighthouse, and the further southward and slight to the west is the tank discussed in the Coastal Pilot below.

Extract from Coastal Pilot Region 3

“The Maryland pilots maintain a Pilot Tower with the Virginia pilots at Cape Henry, just north of Cape Henry Light. The pilots monitor VHF-FM channels 11, 13 and 16. The pilot boats are stationed in Lynnhaven Inlet. They are 52 feet long with a black hull and white house displaying the “PILOT” on each side.

Cape Henry Light (36°55'35"N., 76°00'26"W.), 164 feet above the water, is shown from an octagonal, pyramidal tower, upper and lower half of each face alternately black and white, on the beach near the turn of the cape. 

The gray octagonal, pyramidal tower 110 yards southwest of Cape Henry Light is the abandoned 1791 lighthouse. 

Local magnetic disturbance 

Differences of as much as 6° from the normal variation have been observed 3 to 17 miles offshore from Cape Henry to Currituck Beach Light. 

A naval restricted area extends northward and eastward from Cape Henry. (See 33 CFR 334.320, chapter 2, for limits and regulations.) 

The summer resort of Virginia Beach is about 5 miles southward of Cape Henry Light. Many high-rise buildings, two water tanks, and an aerobeacon 2.8 miles inland are prominent. A hotel cupola, 3.4 miles south of Cape Henry Light, is distinctive.“

The important take away is that one should read the Coastal Pilot about the landmarks and ATON when they are on the exam.  The Coastal Pilot gives you the exact LAT/LONG for the light, and explains which of the four possible features is the Cape Henry Light.  So before highlighting and using the ATON for bearings or triangulations to a fix be certain you are on the correct ATON. See below 

3.4 Being Methodical In Charting and in the Exam

During the charting exam you will be provided with two white sheets of paper for scratch paper, the exam book with the questions, an answer sheet, the chart needed for the exam, the light list, and the Coast Pilot for the region your chart is in, and your navigation tools. My recommendation is to treat every practice exam like it was the real exam, only use what is intended during the exam.

1. Do this before anything else:

At the top of one of the pages of the scrap paper write out the following:

• GO SLOW TAKE YOUR TIME
• READ ALL THE QUESTION, and ALL THE ANSWER BEFORE BEGINNING ANY CHARTING OR CALCULATIONS
• DOUBLE CHECK YOUR MARKS, and YOU ANSWERS.
• BE NEAT - GO SLOW

Although writing these down at first may seem like a waste of time, it actually sets you mind into a framework of doing the exam and eases stress about taking the exam.  Remember the USCG doesn’t grade of how fast you answer only that you answer correctly.

2. Set the answer sheet to the side don’t even mark on it until you’ve finished the exam.

3. Open the exam book and read the first question and all the answers twice. Below is an example from the sample test.

VARIATION IS 9° W

DEVIATION TABLE 

HDG.MAG. DEVIATION 

--------------------------------------- 

000° 2.0°E

030° 3.0°E

060° 4.0°E

090° 2.0°E

120° 1.0°E

150° 1.0°W

180° 2.0°W

210° 3.5°W

240 3.0°W

270° 1.5°W

300° 0.0°

330° 1.5°E

Q1. At 0939 your GPS position is LAT 36°57.0'N, LONG 75°41.0'W. You are on course 119° per standard magnetic compass at a speed of 12.8 knots. At 1017 your GPS indicates your position as LAT 36°54.2'N, LONG 75°33.1'W. What were the set and drift?

 (A) 103°T at 1.1 knots 

 (B) 091°T at 1.6 knots 

 (C) 275°T at 1.8 knots 

 (D) 280°T at 1.0 knot

On the scratch paper actual write out:

Q1 :   

GIVEN:   @ 0939 GPS  LAT 36°57.0'N, LONG 75°41.0’W 

    C=119°C S=12.8 KN

    @1017 GPS LAT 36°54.2'N, LONG 75°33.1’W.

           WANTED: SET and Drift

ANALYSIS:

T.   111^o.    Plot this course from our GPS fix at 0939

V.   9^oW

M  120°

D  1^oE

C 119°

1017-0939 = 0 hours 38 minutes

D=ST/60 = 12.8KN*38/60 HOURS= 8.106NM 

Immediately from plotting the results I get 275^oT and 1.8KN, therefore choose C.

4. Once you’ve finished the 10 questions on the scratch paper, bring out the bubble exam answer sheet.   Fill in each bubble correctly with the corset answers, then go from 1 to 10 and check you answers once more.

3.5 Take at least two practice exams every day leaving up to the actual exam.

1. Practice makes perfect, so running through the exams as much as possible on helps.  It helps you make mistakes, find answers and most of all get used to how the USCG examiners are asking questions. It should take you 30-45 minutes to actually do the practice exams correctly, but you should take the entire hour.  There is no reward for finishing first, only finishing with a passing grade of 90%.
2. On the Training Chart used for the examine familiarize yourself with every entry and corner.  Remember the Pareto ranking of failures in navigation from Bowditch, number 2 was the misidentification of ATON’s.  Let’s examine the area of the Chart 12221TR used in the exam.  Notice in the upper left the area generally called New Pt. Comfort.    When we examine this area closely as seen below several interesting ATONs and soundings pop out that would make it easy to choose the wrong one.

During the exam you may be asked use a given bearing from New Pt Comfort Light “2” which is in the green box.  But notice if you are not careful you may easily select the ATON in the red box, as it has a sounding of 2 next to it.  Or you may be not careful and select “2P” in the yellow. 

Similarly in the same region if ask to use the ATON “4” from New Point Comfort you could easily mistake the two ATON’s in the blue and purple box. One should double check that your assumptions before plotting bearings and positions to know the ATON’s are correct.  Familiarizing yourself with the chart and double checking the ATON’s is the best way to avoid such errors.

3. The Coastal Pilot for Region 3 is available online and sections of it or the entire hardcopy can be used for the exam. A great idea is to read through the sections several times that refer to chart 12221.  
4. The light list is also available in hard copy as well as Chart 1.  Questions of often arise where once a fix is obtained the what is the composition of the bottom.  Understanding how to navigate and look up the lights in the light list and Chart 1 will help you in the exam.

4.0 Conclusions

The best advice I got before the exams came from reading the side of the drink bottle, “As is in life, chill for best results.”  If you practice a couple times a day, go slow, double check your answers, draw straight lines, use the tips included in this paper, your likelihood to pass is better than not.

5.0 References

1. Pub. No. 9 American Practical Navigator: An Epitome of Navigation: Originally by Nathaniel Bowditch, LLD, 2017 ED. Prepared and published by the NATIONAL GEOSPATIAL-INTELLIGENCE AGENCYSpringfield, Virginia, 2017 (https://thenauticalalmanac.com/2017_Bowditch-_American_Practical_Navigator/Volume-_1/01-%20Vol.%201-%20Front%20Matter/Front%20Matter.pdf)
2. United States Coast Pilot 3 Atlantic Coast: Sandy Hook, New Jersey to Cape Henry, Virginia, NOAA, 2020 (53rd) Edition (https://nauticalcharts.noaa.gov/publications/coast-pilot/files/cp3/CPB3_WEB.pdf)
3. U.S.C.G. Merchant Marine Exam Master Less than 100 Gross Registered Tons Q350 Navigation Problems – Chart 12221TR (Sample Examination) (https://www.dco.uscg.mil/Portals/9/NMC/pdfs/examinations/q350_nav_problems_chart_12221TR.pdf)
4. Chart 12221TR Chesapeake Bay Entrance, NOAA, Jan 2014. (https://www.charts.noaa.gov/PDFs/12221.pdf)