How To Calculate True Bearing

How To Calculate True Bearing

Welcome, in this article, we will discuss how to calculate true bearing. True bearing is the direction measured clockwise from the north in degrees. This is useful in navigation when you need to determine the direction of a particular destination or landmark. True bearing can be calculated using simple trigonometry.

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Table
  1. Steps to Calculate True Bearing
    1. Step 1: Determine the two points
    2. Step 2: Measure the distance
    3. Step 3: Determine the latitude and longitude of the two points
    4. Step 4: Calculate the difference in longitude
    5. Step 5: Calculate the true bearing
  2. Example Calculation of True Bearing
  3. Conclusion

Steps to Calculate True Bearing

Step 1: Determine the two points

The first step in calculating true bearing is to determine the two points of interest. For example, if you are navigating from point A to point B, point A would be your starting point and point B would be your destination. Remember to label your points for easy reference.

Step 2: Measure the distance

The next step is to measure the distance between the two points. You can use a map or a GPS device to get the distance. The distance should be recorded in the same unit used for the radius of the earth. Usually, miles or kilometers are used.

Step 3: Determine the latitude and longitude of the two points

The latitude and longitude of the two points can be obtained using a map or GPS device. The latitude is the angular distance of a location from the equator, while longitude is the angular distance of a location from the prime meridian. The latitude and longitude should be recorded in degrees, minutes, and seconds.

Step 4: Calculate the difference in longitude

The next step is to calculate the difference in longitude between the two points. This can be done by subtracting the longitude of point A from the longitude of point B. The difference in longitude should be in degrees.

Step 5: Calculate the true bearing

Finally, you can calculate the true bearing using the following formula:

True bearing = arctan(sin(Δlong) / (cos(latA) * tan(latB) - sin(latA) * cos(Δlong)))

Where:

  • Δlong is the difference in longitude in radians
  • latA is the latitude of point A in radians
  • latB is the latitude of point B in radians
  • arctan is the inverse tangent function
  • sin is the sine function
  • cos is the cosine function
  • tan is the tangent function

Example Calculation of True Bearing

Let's assume:

  • Distance = 100 km
  • LongitudeA = -0.1278°
  • LatitudeA = 51.5074°
  • LongitudeB = -0.0877°
  • LatitudeB = 51.5134°

Step 1: Determine the two points

Point A is your starting point, and Point B is your destination.

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Step 2: Measure the distance

The distance between Point A and Point B is 100 km.

Step 3: Determine the latitude and longitude of the two points

The latitude and longitude of Point A are 51.5074° and -0.1278°, respectively. The latitude and longitude of Point B are 51.5134° and -0.0877°, respectively.

Step 4: Calculate the difference in longitude

The difference in longitude between Point A and Point B is -0.0401°.

Step 5: Calculate the true bearing

Using the formula, we can calculate the true bearing as follows:

True bearing = arctan(sin(-0.0401°) / (cos(51.5074°) * tan(51.5134°) - sin(51.5074°) * cos(-0.0401°))) = 91.13°

Therefore, the true bearing from Point A to Point B is 91.13°.

Conclusion

Calculating true bearing may seem complicated, but it is an essential skill for navigation. Remember to label your points of interest and record the distance, latitude, and longitude in the correct units. Calculating true bearing using trigonometry may give you a different answer than the one obtained from a compass, but it is more accurate. Practice using the formula with different points to get a better understanding of how to calculate true bearing.

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