### Using Distance Off to Determine Your Position.

In many situations, you might not have precise latitude and longitude coordinates to locate yourself on a chart. In these cases, figuring out your distance from a known point or solving “distance-off” problems can be very helpful. This method uses different techniques, each suited for specific situations. As you’ll see, these problems are common in coastal navigation and throughout the rest of this course. Here’s a look at some of the most popular methods:

- Radar Ranges and Bearings

This method uses radar to determine the distance and bearing of a landmark or another ship. The process typically involves:

Measuring the Range: Using radar, measure the distance to a known object or landmark.

Taking Bearings: Use the radar to obtain bearings to the object at different times.

Plotting on the Chart: Plot these bearings and distances on a navigation chart to determine your position relative to the landmark.

- Horizontal Angle Between Two Objects

Using a sextant or other angular measuring device, you can measure the horizontal angle between two known objects visible from your position:

Measurement: Measure the angle between two known points (e.g., lighthouses, buoys).

Chart Work: Plot these points on a chart and draw lines from each point at the measured angle.

Intersection Point: The point where these lines intersect is your position, from which you can calculate the distance off from either point.

- Vertical Sextant Angle

This method uses the vertical angle measured between the sea horizon and the top of a known object (like a lighthouse) whose height is known:

Measure the Vertical Angle: Using a sextant, measure the angle from the horizon to the top of the object.

Distance Calculation: Apply the formula:

Distance = Height of Object / tan (angle)

- Three-Point Fix

This technique involves taking bearings to three known points that are visible and plotted on a chart:

Taking Bearings: Take the bearing to each of the three points using a compass or radar.

Plotting Bearings: Plot these bearings on a navigation chart.

Fix Position: The intersection of these three lines (or the center of the triangle formed if they do not intersect precisely) gives your position.

- Running Fix

A running fix is used when only one navigational aid is visible, and it involves taking two bearings of the same object at different times while the ship is moving:

First Bearing: Take an initial bearing and plot it on the chart.

Second Bearing: After a known period and having traveled a known distance, take a second bearing.

Advance the Line: Move the first bearing line forward along your course to match the distance traveled.

Intersection: The intersection of the advanced line and the second bearing line gives your position.

Each method has its advantages and situations where it is most effectively applied. The choice of method often depends on the available tools, visible landmarks or aids, and the specific circumstances of the voyage.

Each of these methods has its usefulness. Although you will not be tested on them specifically, we encourage you to take the time to try them out and see how they could apply to your chartwork and navigation.