But if I’m cruising in unfamiliar waters, then “Where am I?” is a more difficult question to answer because there is no ‘memory map’, no street signs, no mile/km markers, no “Welcome to Manahawkin” signs that tell me where I am.
Of course, a GPS system, with integrated charts, is the perfect solution. But if we don’t have one, then we need to determine “Where am I?” in other ways… the answer will be our ‘position’.
What do we need to find our position?
- Charts (essential)…
- …preferably in a case with a clear cover so we can mark our position without writing on the chart itself…
- A grease pencil (China Marker) that writes on the clear cover and can be erased (essential)…
- A boat compass (essential)…
- A protractor and ruler/straight edge (essential)…
- A hand bearing compass would be helpful, but not essential…
- Binoculars (or monocular) would be helpful, but not essential…
When we find our position, we record it on the chart cover. That recorded position (called a “fix”) is identical to what the GPS system does on it’s digital chart.
Given that we at least have the ‘essential’ tools to find our position, how do we do it?
A “range” is the alignment of any two objects that are represented on the chart and can be seen from where we are in our boat. (Note, in British usage, a ‘range’ is called a ‘transit’.)
Examples of ranges:
- A Light house and the end of a peninsula
- The edge of two islands
- A water tower and a draw bridge
When we, sitting in the boat, are aligned with two objects that are represented on the chart, we can draw a line on the chart through the two objects… we will be someplace on that line… it’s call a “Line of Position”, an LOP.
If there is another range (preferably at 90°, plus or minus 30°, of the first range), then draw the second LOP… where they cross is our position, a very accurate fix.
In the real world, we may not be able to find TWO ranges at the same time. There is another way to determine an LOP…
Note: "Azimuth" and "Bearing" are often used interchangeably, but technically that is incorrect. An ‘azimuth’ is an angle between 0 and 360 degrees measured from North.
True azimuths (marked on your chart with a lower case “t”) are measured from ‘true’ north, the North Pole. Note that maps and charts are displayed with the top of the chart facing true north.
Magnetic azimuths (recorded with a lower case “m”) are measured from the Magnetic North Pole. The angle between the True North Pole and the Magnetic North Pole is called ‘declination’. See the planning post for definition and use of declination.
“Bearings”, technically, consist of an angle in degrees (0 to 90) and quadrant letters. For example “N 45° E” is Northeast, and “S 45° W” is Southwest. The first quadrant letter is always either "N" or "S" and the second is always either "E" or "W". I’ll use “azimuth” in these posts to be consistent and to match compass readings, which are 0 to 360.A “compass azimuth” is the compass reading from the object to our boat. We can use a compass azimuth in order to establish an LOP (which, when plotted with another LOP, determines our position).
How do we do that? Five steps…(easier than it sounds)
- A. If you are using a hand held compass, go to step 2.
B. Otherwise, you are using a compass fixed to the boat. You must align the boat with the object.
a. If a rowboat, with a reverse reading compass, align the object over the center of the transom so that you are rowing AWAY from the object.
b. If a kayak, canoe or sail boat (using a standard reading compass), align the object over the bow so that the boat is moving TOWARD the object.
- Note the compass reading to the object.
- Apply the declination to the reading so that we can plot an LOP that is a true azimuth and not a magnetic azimuth. To convert a magnetic azimuth to a true azimuth, we ADD the declination.
- If you are rowing, and using a reverse reading compass such as a Richie Rowing Compass, the result of step 3. is the true azimuth from the object to your boat. Go to step 5.
Otherwise, take the 180° reciprocal of step 3. result. For example, if step 3. result is 35°t, the reciprocal is 215°t… if step 3. result is 230°t, the reciprocal is 50°t. The result is the true azimuth from the object to your boat.
- Plot the true azimuth on the chart (cover) by placing your protractor centered on the object. Align a ruler from the center of the protractor through the azimuth (on protractor) and draw a line. This line is an LOP… our boat is someplace on that line.
Example: I use a Richie Reverse Reading compass on my boat. The declination in my area is 13° West (-13°) Let’s say I’m rowing north in Barnegat Bay (New Jersey) someplace west of Barnegat Lighthouse… I want to know exactly where I am so that I can set a compass course to my next anchorage at Tices Shoal.
Barnegat Bay West of Barnegat Lighthouse
Since I’m heading north, I turn the boat slightly to line up the center of the transom with the west end of Conklin Island…the compass reading is 54°m and I add -13 to it to get the true azimuth of 41°t. Using a protractor centered on the west end of Conklin Island and using a ruler, draw a line at 41°.
I turn the boat west to align the center of the transom with Barnegat Light, the compass reading is 286°m, add -13 to get true azimuth 273°t from the Light to my boat. Using the protractor centered on Barnegat light, draw a second LOP at 273°. Bingo! Where the lines cross is my approximate current position.
There is another way to estimate my position, answering “Where am I?”. It consists of a compass azimuth to a visible object on land, or a range, which tells me I am someplace on the resulting LOP, and an estimate of my distance from that object.
Note that I did not have to take the 180° reciprocal (Step 4. above) because I’m using a reverse reading compass.
What are the various ways to measure distance?
Because the earth is curved, a more distant object will appear lower than a closer object. The formula for determining “geographic distance” in miles is:
Square root of eye height (feet) above water plus square root of height (feet) of object above water
Distance (miles) = √Eye height (feet) + √Object height (feet)
Note: Due to atmospheric conditions such as haze, the practical limit of this technique is only about 15 miles...and that would be on a clear, calm day.
Example: In my boat, my eye height is about three feet. The square root of three is about 1.7. This means my ‘water’ horizon is 1.7 miles away (√3 + √0 = 1.7).
Example: I’m rowing north of Barnegat Light (172 feet above sea level). The break between the red top and white bottom is at about 85 feet. That color break point has just dipped below the horizon as I’m rowing. That means I’m about 10.9 miles north of the Light (√3 + √85 = 10.9). If I combine this ‘distance’ with a compass azimuth to the light, I’ve a reasonably accurate fix of my current position.
Example: I’m rowing in Round Valley Reservoir, returning to the ramp, and I see my friend in his kayak. The kayak is hidden but I can see his yellow life jacket… I assume the bottom of the jacket is about a foot above the water (binoculars would help.) This means he is about 2.7 miles away (√3 + √1 = 2.7).
In kayaks, sailboats and motor boats, there’s a technique called “Doubling the Bow Angle”. Let’s assume you know how fast you are going and that your course won’t change. You see a flag pole 30° off the port bow. You start timing. When the flag pole is 60° off the port bow (the angle has doubled… you can use any angle, e.g., the flag pole could be at 13° and second reading would therefore be at 26°), you stop timing and calculate how far you have traveled. The distance traveled is equal to the distance from your current position (when the flag pole is at 60° (or 26°)) to the flag pole.
If the initial sighting of the flag pole is at 45°, doubling the angle is 90° and now you know how far you are from the flag pole perpendicular to your course.
But if you are rowing, ‘doubling the bow angle’ isn’t very practical (unless you are using a FrontRower) because you are facing backwards and you’d have to turn around to get the bearings to the flag pole.
However, you can do this: while rowing a steady pace and course, you spot an especially tall tree on the shore 90° to your course (put the handle of the oar in the opposite oar lock and you’ll have 90° to your course.) Count the number of strokes it takes until the tree is 45° from your course. Multiply the number of strokes times your ‘standard’ distance covered per stroke. That distance times 1.4 is the distance you are then away from the tree (at 45°). (In a 45° right triangle, the hypotenuse is 1.4 times the length of a side.)
How do you determine 45°?
Consider the diagram below… if I spread my left hand, it forms the angles shown in the diagram. The little finger pointing over the center of the transom… chin on your hand about where the apex of the angles are and you now can measure 45° by sighting down your index finger… Palm down for bearings on one side and palm up for bearings on the other side.
|Your Hand as a Protractor|
Example: I’m rowing a steady 20 strokes a minute, at 16 feet per stroke, on a steady course of 40°m.
To my right, I see a small pier at 90° to my course. I start counting strokes and periodically check the bearing to the pier AND maintain a steady course of 40°m. When it’s 45° off my track, I stop counting at 113 strokes.
16 times 113 is 1600 feet (100 X 16) plus 208 feet (10 X 16, plus 3 X 16) for a total distance rowed of (call it) 1800 feet. 1800 times 1.4 (1800 plus 4 X 180) is 2520 feet from the pier. If I combine this with a compass azimuth to the pier, I have my current position.
This post has been about determining; “Where am I?” There are other techniques to help answer that question we’ll cover in Part 4 of this series on Piloting.
The fine print...
I’m not a professional pilot. I try to be accurate and I check my information, but I’m not perfect. This post is for information purposes and is intended to be only a starting point for learning the skills of piloting. As with any activity with a boat, there is always the opportunity for ugly surprises. Practice the skills under ideal circumstances and you’ll increase the probability of being able to use the skills during an ugly surprise to keep you and your boat safe.